Properties

Label 6023.2.a.b.1.18
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.95928 q^{2} +1.09252 q^{3} +1.83878 q^{4} +1.35010 q^{5} -2.14055 q^{6} +3.30535 q^{7} +0.315883 q^{8} -1.80641 q^{9} +O(q^{10})\) \(q-1.95928 q^{2} +1.09252 q^{3} +1.83878 q^{4} +1.35010 q^{5} -2.14055 q^{6} +3.30535 q^{7} +0.315883 q^{8} -1.80641 q^{9} -2.64522 q^{10} -1.41714 q^{11} +2.00889 q^{12} -1.08653 q^{13} -6.47611 q^{14} +1.47501 q^{15} -4.29645 q^{16} +0.206874 q^{17} +3.53925 q^{18} -1.00000 q^{19} +2.48253 q^{20} +3.61116 q^{21} +2.77657 q^{22} -2.29702 q^{23} +0.345108 q^{24} -3.17723 q^{25} +2.12882 q^{26} -5.25108 q^{27} +6.07781 q^{28} +3.93219 q^{29} -2.88995 q^{30} -1.07866 q^{31} +7.78619 q^{32} -1.54825 q^{33} -0.405325 q^{34} +4.46256 q^{35} -3.32157 q^{36} -2.28592 q^{37} +1.95928 q^{38} -1.18706 q^{39} +0.426474 q^{40} -10.0767 q^{41} -7.07527 q^{42} +8.76642 q^{43} -2.60580 q^{44} -2.43883 q^{45} +4.50051 q^{46} -0.177489 q^{47} -4.69395 q^{48} +3.92537 q^{49} +6.22508 q^{50} +0.226014 q^{51} -1.99789 q^{52} +7.11912 q^{53} +10.2883 q^{54} -1.91328 q^{55} +1.04411 q^{56} -1.09252 q^{57} -7.70426 q^{58} -8.86463 q^{59} +2.71221 q^{60} -1.63279 q^{61} +2.11339 q^{62} -5.97081 q^{63} -6.66241 q^{64} -1.46693 q^{65} +3.03345 q^{66} +3.90385 q^{67} +0.380396 q^{68} -2.50954 q^{69} -8.74339 q^{70} -5.36832 q^{71} -0.570613 q^{72} -10.3438 q^{73} +4.47876 q^{74} -3.47118 q^{75} -1.83878 q^{76} -4.68414 q^{77} +2.32577 q^{78} -7.59418 q^{79} -5.80064 q^{80} -0.317683 q^{81} +19.7430 q^{82} +5.04706 q^{83} +6.64011 q^{84} +0.279301 q^{85} -17.1759 q^{86} +4.29599 q^{87} -0.447650 q^{88} +15.1720 q^{89} +4.77834 q^{90} -3.59137 q^{91} -4.22371 q^{92} -1.17845 q^{93} +0.347751 q^{94} -1.35010 q^{95} +8.50655 q^{96} +0.326395 q^{97} -7.69089 q^{98} +2.55993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} + O(q^{10}) \) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} - 6q^{10} - 9q^{11} - 27q^{12} - 28q^{13} - 13q^{14} - 10q^{15} + 38q^{16} - 36q^{17} - 14q^{18} - 99q^{19} - 34q^{20} - 20q^{21} - 53q^{22} - 38q^{23} - 25q^{24} - 8q^{25} - 3q^{26} - 3q^{27} - 63q^{28} - 34q^{29} - 30q^{30} - 16q^{31} - 43q^{32} - 41q^{33} - 14q^{34} - 25q^{35} - 16q^{36} - 80q^{37} + 4q^{38} - 48q^{39} - 10q^{40} - 32q^{41} - 37q^{42} - 76q^{43} - 21q^{44} - 53q^{45} - 23q^{46} - 31q^{47} - 74q^{48} - 32q^{49} - 29q^{50} - 30q^{51} - 71q^{52} - 35q^{53} - 80q^{54} - 45q^{55} - 33q^{56} + 3q^{57} - 91q^{58} + 12q^{59} - 56q^{60} - 61q^{61} - 46q^{62} - 43q^{63} - 30q^{64} - 46q^{65} - 75q^{66} - 26q^{67} - 55q^{68} - 45q^{69} - 76q^{70} - 41q^{71} - 77q^{72} - 143q^{73} - 64q^{74} - 8q^{75} - 80q^{76} - 58q^{77} - 34q^{78} - 22q^{79} - 36q^{80} - 81q^{81} - 109q^{82} - 7q^{83} - 6q^{84} - 80q^{85} + 32q^{86} - 57q^{87} - 120q^{88} - 28q^{89} - 12q^{90} - 30q^{91} - 107q^{92} - 121q^{93} + 8q^{94} + 15q^{95} + 4q^{96} - 128q^{97} + 54q^{98} - 34q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95928 −1.38542 −0.692710 0.721216i \(-0.743583\pi\)
−0.692710 + 0.721216i \(0.743583\pi\)
\(3\) 1.09252 0.630765 0.315383 0.948965i \(-0.397867\pi\)
0.315383 + 0.948965i \(0.397867\pi\)
\(4\) 1.83878 0.919388
\(5\) 1.35010 0.603783 0.301891 0.953342i \(-0.402382\pi\)
0.301891 + 0.953342i \(0.402382\pi\)
\(6\) −2.14055 −0.873875
\(7\) 3.30535 1.24931 0.624653 0.780902i \(-0.285240\pi\)
0.624653 + 0.780902i \(0.285240\pi\)
\(8\) 0.315883 0.111682
\(9\) −1.80641 −0.602135
\(10\) −2.64522 −0.836493
\(11\) −1.41714 −0.427283 −0.213642 0.976912i \(-0.568532\pi\)
−0.213642 + 0.976912i \(0.568532\pi\)
\(12\) 2.00889 0.579918
\(13\) −1.08653 −0.301350 −0.150675 0.988583i \(-0.548145\pi\)
−0.150675 + 0.988583i \(0.548145\pi\)
\(14\) −6.47611 −1.73081
\(15\) 1.47501 0.380845
\(16\) −4.29645 −1.07411
\(17\) 0.206874 0.0501744 0.0250872 0.999685i \(-0.492014\pi\)
0.0250872 + 0.999685i \(0.492014\pi\)
\(18\) 3.53925 0.834210
\(19\) −1.00000 −0.229416
\(20\) 2.48253 0.555111
\(21\) 3.61116 0.788019
\(22\) 2.77657 0.591966
\(23\) −2.29702 −0.478962 −0.239481 0.970901i \(-0.576977\pi\)
−0.239481 + 0.970901i \(0.576977\pi\)
\(24\) 0.345108 0.0704448
\(25\) −3.17723 −0.635446
\(26\) 2.12882 0.417496
\(27\) −5.25108 −1.01057
\(28\) 6.07781 1.14860
\(29\) 3.93219 0.730189 0.365095 0.930970i \(-0.381037\pi\)
0.365095 + 0.930970i \(0.381037\pi\)
\(30\) −2.88995 −0.527630
\(31\) −1.07866 −0.193732 −0.0968662 0.995297i \(-0.530882\pi\)
−0.0968662 + 0.995297i \(0.530882\pi\)
\(32\) 7.78619 1.37642
\(33\) −1.54825 −0.269515
\(34\) −0.405325 −0.0695126
\(35\) 4.46256 0.754310
\(36\) −3.32157 −0.553596
\(37\) −2.28592 −0.375803 −0.187901 0.982188i \(-0.560169\pi\)
−0.187901 + 0.982188i \(0.560169\pi\)
\(38\) 1.95928 0.317837
\(39\) −1.18706 −0.190081
\(40\) 0.426474 0.0674314
\(41\) −10.0767 −1.57371 −0.786855 0.617138i \(-0.788292\pi\)
−0.786855 + 0.617138i \(0.788292\pi\)
\(42\) −7.07527 −1.09174
\(43\) 8.76642 1.33687 0.668433 0.743772i \(-0.266965\pi\)
0.668433 + 0.743772i \(0.266965\pi\)
\(44\) −2.60580 −0.392839
\(45\) −2.43883 −0.363559
\(46\) 4.50051 0.663563
\(47\) −0.177489 −0.0258895 −0.0129447 0.999916i \(-0.504121\pi\)
−0.0129447 + 0.999916i \(0.504121\pi\)
\(48\) −4.69395 −0.677514
\(49\) 3.92537 0.560767
\(50\) 6.22508 0.880360
\(51\) 0.226014 0.0316483
\(52\) −1.99789 −0.277057
\(53\) 7.11912 0.977887 0.488943 0.872315i \(-0.337382\pi\)
0.488943 + 0.872315i \(0.337382\pi\)
\(54\) 10.2883 1.40007
\(55\) −1.91328 −0.257986
\(56\) 1.04411 0.139524
\(57\) −1.09252 −0.144707
\(58\) −7.70426 −1.01162
\(59\) −8.86463 −1.15408 −0.577038 0.816717i \(-0.695792\pi\)
−0.577038 + 0.816717i \(0.695792\pi\)
\(60\) 2.71221 0.350144
\(61\) −1.63279 −0.209057 −0.104529 0.994522i \(-0.533333\pi\)
−0.104529 + 0.994522i \(0.533333\pi\)
\(62\) 2.11339 0.268401
\(63\) −5.97081 −0.752251
\(64\) −6.66241 −0.832801
\(65\) −1.46693 −0.181950
\(66\) 3.03345 0.373392
\(67\) 3.90385 0.476932 0.238466 0.971151i \(-0.423355\pi\)
0.238466 + 0.971151i \(0.423355\pi\)
\(68\) 0.380396 0.0461298
\(69\) −2.50954 −0.302113
\(70\) −8.74339 −1.04504
\(71\) −5.36832 −0.637102 −0.318551 0.947906i \(-0.603196\pi\)
−0.318551 + 0.947906i \(0.603196\pi\)
\(72\) −0.570613 −0.0672474
\(73\) −10.3438 −1.21065 −0.605325 0.795978i \(-0.706957\pi\)
−0.605325 + 0.795978i \(0.706957\pi\)
\(74\) 4.47876 0.520645
\(75\) −3.47118 −0.400818
\(76\) −1.83878 −0.210922
\(77\) −4.68414 −0.533807
\(78\) 2.32577 0.263342
\(79\) −7.59418 −0.854413 −0.427206 0.904154i \(-0.640502\pi\)
−0.427206 + 0.904154i \(0.640502\pi\)
\(80\) −5.80064 −0.648531
\(81\) −0.317683 −0.0352981
\(82\) 19.7430 2.18025
\(83\) 5.04706 0.553987 0.276994 0.960872i \(-0.410662\pi\)
0.276994 + 0.960872i \(0.410662\pi\)
\(84\) 6.64011 0.724495
\(85\) 0.279301 0.0302944
\(86\) −17.1759 −1.85212
\(87\) 4.29599 0.460578
\(88\) −0.447650 −0.0477196
\(89\) 15.1720 1.60823 0.804113 0.594477i \(-0.202641\pi\)
0.804113 + 0.594477i \(0.202641\pi\)
\(90\) 4.77834 0.503682
\(91\) −3.59137 −0.376478
\(92\) −4.22371 −0.440352
\(93\) −1.17845 −0.122200
\(94\) 0.347751 0.0358678
\(95\) −1.35010 −0.138517
\(96\) 8.50655 0.868196
\(97\) 0.326395 0.0331404 0.0165702 0.999863i \(-0.494725\pi\)
0.0165702 + 0.999863i \(0.494725\pi\)
\(98\) −7.69089 −0.776897
\(99\) 2.55993 0.257282
\(100\) −5.84222 −0.584222
\(101\) −8.43482 −0.839296 −0.419648 0.907687i \(-0.637847\pi\)
−0.419648 + 0.907687i \(0.637847\pi\)
\(102\) −0.442824 −0.0438462
\(103\) 1.22447 0.120651 0.0603254 0.998179i \(-0.480786\pi\)
0.0603254 + 0.998179i \(0.480786\pi\)
\(104\) −0.343217 −0.0336552
\(105\) 4.87542 0.475792
\(106\) −13.9484 −1.35478
\(107\) −6.20596 −0.599952 −0.299976 0.953947i \(-0.596979\pi\)
−0.299976 + 0.953947i \(0.596979\pi\)
\(108\) −9.65556 −0.929107
\(109\) −11.0781 −1.06109 −0.530544 0.847657i \(-0.678012\pi\)
−0.530544 + 0.847657i \(0.678012\pi\)
\(110\) 3.74864 0.357419
\(111\) −2.49741 −0.237043
\(112\) −14.2013 −1.34190
\(113\) −4.03396 −0.379483 −0.189741 0.981834i \(-0.560765\pi\)
−0.189741 + 0.981834i \(0.560765\pi\)
\(114\) 2.14055 0.200481
\(115\) −3.10121 −0.289189
\(116\) 7.23042 0.671327
\(117\) 1.96272 0.181453
\(118\) 17.3683 1.59888
\(119\) 0.683793 0.0626832
\(120\) 0.465930 0.0425334
\(121\) −8.99172 −0.817429
\(122\) 3.19909 0.289632
\(123\) −11.0089 −0.992642
\(124\) −1.98341 −0.178115
\(125\) −11.0401 −0.987454
\(126\) 11.6985 1.04218
\(127\) −13.2846 −1.17882 −0.589409 0.807835i \(-0.700639\pi\)
−0.589409 + 0.807835i \(0.700639\pi\)
\(128\) −2.51885 −0.222637
\(129\) 9.57747 0.843249
\(130\) 2.87412 0.252077
\(131\) −16.7920 −1.46713 −0.733563 0.679622i \(-0.762144\pi\)
−0.733563 + 0.679622i \(0.762144\pi\)
\(132\) −2.84688 −0.247789
\(133\) −3.30535 −0.286611
\(134\) −7.64874 −0.660751
\(135\) −7.08948 −0.610166
\(136\) 0.0653481 0.00560356
\(137\) −7.63686 −0.652461 −0.326231 0.945290i \(-0.605779\pi\)
−0.326231 + 0.945290i \(0.605779\pi\)
\(138\) 4.91688 0.418553
\(139\) −21.0840 −1.78832 −0.894162 0.447743i \(-0.852228\pi\)
−0.894162 + 0.447743i \(0.852228\pi\)
\(140\) 8.20564 0.693503
\(141\) −0.193910 −0.0163302
\(142\) 10.5180 0.882653
\(143\) 1.53977 0.128762
\(144\) 7.76114 0.646762
\(145\) 5.30885 0.440876
\(146\) 20.2664 1.67726
\(147\) 4.28853 0.353712
\(148\) −4.20329 −0.345509
\(149\) 14.9169 1.22204 0.611021 0.791615i \(-0.290759\pi\)
0.611021 + 0.791615i \(0.290759\pi\)
\(150\) 6.80101 0.555300
\(151\) 20.8606 1.69761 0.848806 0.528705i \(-0.177322\pi\)
0.848806 + 0.528705i \(0.177322\pi\)
\(152\) −0.315883 −0.0256215
\(153\) −0.373699 −0.0302118
\(154\) 9.17754 0.739547
\(155\) −1.45629 −0.116972
\(156\) −2.18273 −0.174758
\(157\) 0.966394 0.0771266 0.0385633 0.999256i \(-0.487722\pi\)
0.0385633 + 0.999256i \(0.487722\pi\)
\(158\) 14.8791 1.18372
\(159\) 7.77777 0.616817
\(160\) 10.5121 0.831057
\(161\) −7.59247 −0.598370
\(162\) 0.622429 0.0489027
\(163\) 8.34446 0.653589 0.326794 0.945095i \(-0.394032\pi\)
0.326794 + 0.945095i \(0.394032\pi\)
\(164\) −18.5287 −1.44685
\(165\) −2.09029 −0.162729
\(166\) −9.88861 −0.767505
\(167\) 8.37398 0.647998 0.323999 0.946057i \(-0.394973\pi\)
0.323999 + 0.946057i \(0.394973\pi\)
\(168\) 1.14070 0.0880072
\(169\) −11.8194 −0.909188
\(170\) −0.547229 −0.0419705
\(171\) 1.80641 0.138139
\(172\) 16.1195 1.22910
\(173\) −9.66201 −0.734589 −0.367295 0.930105i \(-0.619716\pi\)
−0.367295 + 0.930105i \(0.619716\pi\)
\(174\) −8.41704 −0.638094
\(175\) −10.5019 −0.793867
\(176\) 6.08867 0.458951
\(177\) −9.68477 −0.727952
\(178\) −29.7261 −2.22807
\(179\) −3.63403 −0.271620 −0.135810 0.990735i \(-0.543364\pi\)
−0.135810 + 0.990735i \(0.543364\pi\)
\(180\) −4.48446 −0.334252
\(181\) 0.636349 0.0472994 0.0236497 0.999720i \(-0.492471\pi\)
0.0236497 + 0.999720i \(0.492471\pi\)
\(182\) 7.03651 0.521581
\(183\) −1.78385 −0.131866
\(184\) −0.725590 −0.0534912
\(185\) −3.08622 −0.226903
\(186\) 2.30892 0.169298
\(187\) −0.293170 −0.0214387
\(188\) −0.326363 −0.0238025
\(189\) −17.3567 −1.26251
\(190\) 2.64522 0.191905
\(191\) −15.6053 −1.12916 −0.564581 0.825377i \(-0.690962\pi\)
−0.564581 + 0.825377i \(0.690962\pi\)
\(192\) −7.27880 −0.525302
\(193\) 13.9641 1.00516 0.502578 0.864532i \(-0.332385\pi\)
0.502578 + 0.864532i \(0.332385\pi\)
\(194\) −0.639500 −0.0459134
\(195\) −1.60264 −0.114768
\(196\) 7.21787 0.515562
\(197\) 15.8403 1.12858 0.564288 0.825578i \(-0.309151\pi\)
0.564288 + 0.825578i \(0.309151\pi\)
\(198\) −5.01561 −0.356444
\(199\) 0.692954 0.0491222 0.0245611 0.999698i \(-0.492181\pi\)
0.0245611 + 0.999698i \(0.492181\pi\)
\(200\) −1.00363 −0.0709676
\(201\) 4.26503 0.300832
\(202\) 16.5262 1.16278
\(203\) 12.9973 0.912230
\(204\) 0.415589 0.0290970
\(205\) −13.6045 −0.950179
\(206\) −2.39908 −0.167152
\(207\) 4.14935 0.288400
\(208\) 4.66824 0.323684
\(209\) 1.41714 0.0980255
\(210\) −9.55231 −0.659172
\(211\) −14.7828 −1.01769 −0.508844 0.860859i \(-0.669927\pi\)
−0.508844 + 0.860859i \(0.669927\pi\)
\(212\) 13.0905 0.899057
\(213\) −5.86498 −0.401862
\(214\) 12.1592 0.831186
\(215\) 11.8355 0.807177
\(216\) −1.65873 −0.112862
\(217\) −3.56534 −0.242031
\(218\) 21.7051 1.47005
\(219\) −11.3008 −0.763636
\(220\) −3.51809 −0.237189
\(221\) −0.224776 −0.0151201
\(222\) 4.89312 0.328405
\(223\) −10.2385 −0.685621 −0.342811 0.939405i \(-0.611379\pi\)
−0.342811 + 0.939405i \(0.611379\pi\)
\(224\) 25.7361 1.71957
\(225\) 5.73937 0.382625
\(226\) 7.90365 0.525743
\(227\) 2.60023 0.172583 0.0862917 0.996270i \(-0.472498\pi\)
0.0862917 + 0.996270i \(0.472498\pi\)
\(228\) −2.00889 −0.133042
\(229\) −4.16679 −0.275349 −0.137675 0.990478i \(-0.543963\pi\)
−0.137675 + 0.990478i \(0.543963\pi\)
\(230\) 6.07613 0.400648
\(231\) −5.11751 −0.336707
\(232\) 1.24211 0.0815487
\(233\) 17.2285 1.12867 0.564337 0.825544i \(-0.309132\pi\)
0.564337 + 0.825544i \(0.309132\pi\)
\(234\) −3.84551 −0.251389
\(235\) −0.239628 −0.0156316
\(236\) −16.3001 −1.06104
\(237\) −8.29678 −0.538934
\(238\) −1.33974 −0.0868426
\(239\) −13.7896 −0.891973 −0.445987 0.895040i \(-0.647147\pi\)
−0.445987 + 0.895040i \(0.647147\pi\)
\(240\) −6.33730 −0.409071
\(241\) −23.4523 −1.51070 −0.755348 0.655323i \(-0.772532\pi\)
−0.755348 + 0.655323i \(0.772532\pi\)
\(242\) 17.6173 1.13248
\(243\) 15.4062 0.988306
\(244\) −3.00233 −0.192205
\(245\) 5.29963 0.338581
\(246\) 21.5696 1.37523
\(247\) 1.08653 0.0691344
\(248\) −0.340729 −0.0216363
\(249\) 5.51400 0.349436
\(250\) 21.6306 1.36804
\(251\) 19.4600 1.22831 0.614153 0.789187i \(-0.289498\pi\)
0.614153 + 0.789187i \(0.289498\pi\)
\(252\) −10.9790 −0.691611
\(253\) 3.25519 0.204652
\(254\) 26.0283 1.63316
\(255\) 0.305141 0.0191087
\(256\) 18.2600 1.14125
\(257\) 9.70056 0.605104 0.302552 0.953133i \(-0.402161\pi\)
0.302552 + 0.953133i \(0.402161\pi\)
\(258\) −18.7649 −1.16825
\(259\) −7.55578 −0.469493
\(260\) −2.69735 −0.167283
\(261\) −7.10313 −0.439673
\(262\) 32.9002 2.03258
\(263\) 29.8241 1.83903 0.919516 0.393053i \(-0.128581\pi\)
0.919516 + 0.393053i \(0.128581\pi\)
\(264\) −0.489065 −0.0300999
\(265\) 9.61152 0.590431
\(266\) 6.47611 0.397076
\(267\) 16.5756 1.01441
\(268\) 7.17831 0.438485
\(269\) 2.46262 0.150149 0.0750744 0.997178i \(-0.476081\pi\)
0.0750744 + 0.997178i \(0.476081\pi\)
\(270\) 13.8903 0.845335
\(271\) −15.7138 −0.954544 −0.477272 0.878756i \(-0.658374\pi\)
−0.477272 + 0.878756i \(0.658374\pi\)
\(272\) −0.888827 −0.0538930
\(273\) −3.92364 −0.237469
\(274\) 14.9627 0.903933
\(275\) 4.50257 0.271515
\(276\) −4.61447 −0.277759
\(277\) 14.2146 0.854070 0.427035 0.904235i \(-0.359558\pi\)
0.427035 + 0.904235i \(0.359558\pi\)
\(278\) 41.3095 2.47758
\(279\) 1.94849 0.116653
\(280\) 1.40965 0.0842425
\(281\) 10.3988 0.620341 0.310170 0.950681i \(-0.399614\pi\)
0.310170 + 0.950681i \(0.399614\pi\)
\(282\) 0.379924 0.0226241
\(283\) −13.5063 −0.802867 −0.401434 0.915888i \(-0.631488\pi\)
−0.401434 + 0.915888i \(0.631488\pi\)
\(284\) −9.87113 −0.585744
\(285\) −1.47501 −0.0873719
\(286\) −3.01683 −0.178389
\(287\) −33.3069 −1.96605
\(288\) −14.0650 −0.828789
\(289\) −16.9572 −0.997483
\(290\) −10.4015 −0.610798
\(291\) 0.356593 0.0209038
\(292\) −19.0199 −1.11306
\(293\) 1.48763 0.0869083 0.0434541 0.999055i \(-0.486164\pi\)
0.0434541 + 0.999055i \(0.486164\pi\)
\(294\) −8.40243 −0.490040
\(295\) −11.9681 −0.696812
\(296\) −0.722083 −0.0419703
\(297\) 7.44151 0.431800
\(298\) −29.2264 −1.69304
\(299\) 2.49579 0.144335
\(300\) −6.38272 −0.368507
\(301\) 28.9761 1.67016
\(302\) −40.8717 −2.35190
\(303\) −9.21519 −0.529399
\(304\) 4.29645 0.246419
\(305\) −2.20443 −0.126225
\(306\) 0.732181 0.0418560
\(307\) 7.14367 0.407711 0.203855 0.979001i \(-0.434653\pi\)
0.203855 + 0.979001i \(0.434653\pi\)
\(308\) −8.61309 −0.490776
\(309\) 1.33776 0.0761024
\(310\) 2.85329 0.162056
\(311\) 11.1425 0.631831 0.315916 0.948787i \(-0.397688\pi\)
0.315916 + 0.948787i \(0.397688\pi\)
\(312\) −0.374971 −0.0212285
\(313\) 23.4691 1.32655 0.663276 0.748375i \(-0.269165\pi\)
0.663276 + 0.748375i \(0.269165\pi\)
\(314\) −1.89344 −0.106853
\(315\) −8.06119 −0.454196
\(316\) −13.9640 −0.785537
\(317\) −1.00000 −0.0561656
\(318\) −15.2388 −0.854551
\(319\) −5.57245 −0.311997
\(320\) −8.99492 −0.502831
\(321\) −6.78012 −0.378429
\(322\) 14.8758 0.828994
\(323\) −0.206874 −0.0115108
\(324\) −0.584148 −0.0324526
\(325\) 3.45217 0.191492
\(326\) −16.3491 −0.905495
\(327\) −12.1030 −0.669298
\(328\) −3.18305 −0.175754
\(329\) −0.586665 −0.0323439
\(330\) 4.09546 0.225448
\(331\) −14.2958 −0.785766 −0.392883 0.919589i \(-0.628522\pi\)
−0.392883 + 0.919589i \(0.628522\pi\)
\(332\) 9.28042 0.509329
\(333\) 4.12930 0.226284
\(334\) −16.4070 −0.897749
\(335\) 5.27059 0.287963
\(336\) −15.5152 −0.846422
\(337\) 15.9290 0.867708 0.433854 0.900983i \(-0.357153\pi\)
0.433854 + 0.900983i \(0.357153\pi\)
\(338\) 23.1576 1.25961
\(339\) −4.40717 −0.239364
\(340\) 0.513572 0.0278524
\(341\) 1.52861 0.0827786
\(342\) −3.53925 −0.191381
\(343\) −10.1628 −0.548737
\(344\) 2.76916 0.149303
\(345\) −3.38812 −0.182410
\(346\) 18.9306 1.01771
\(347\) −12.0200 −0.645266 −0.322633 0.946524i \(-0.604568\pi\)
−0.322633 + 0.946524i \(0.604568\pi\)
\(348\) 7.89936 0.423450
\(349\) −20.8762 −1.11748 −0.558739 0.829344i \(-0.688714\pi\)
−0.558739 + 0.829344i \(0.688714\pi\)
\(350\) 20.5761 1.09984
\(351\) 5.70547 0.304536
\(352\) −11.0341 −0.588120
\(353\) −20.8151 −1.10788 −0.553939 0.832557i \(-0.686876\pi\)
−0.553939 + 0.832557i \(0.686876\pi\)
\(354\) 18.9752 1.00852
\(355\) −7.24776 −0.384671
\(356\) 27.8978 1.47858
\(357\) 0.747056 0.0395384
\(358\) 7.12008 0.376308
\(359\) −14.0575 −0.741928 −0.370964 0.928647i \(-0.620973\pi\)
−0.370964 + 0.928647i \(0.620973\pi\)
\(360\) −0.770384 −0.0406028
\(361\) 1.00000 0.0526316
\(362\) −1.24679 −0.0655296
\(363\) −9.82361 −0.515606
\(364\) −6.60373 −0.346130
\(365\) −13.9652 −0.730970
\(366\) 3.49506 0.182690
\(367\) 6.86269 0.358229 0.179115 0.983828i \(-0.442677\pi\)
0.179115 + 0.983828i \(0.442677\pi\)
\(368\) 9.86905 0.514460
\(369\) 18.2025 0.947586
\(370\) 6.04677 0.314356
\(371\) 23.5312 1.22168
\(372\) −2.16691 −0.112349
\(373\) −5.93413 −0.307257 −0.153629 0.988129i \(-0.549096\pi\)
−0.153629 + 0.988129i \(0.549096\pi\)
\(374\) 0.574401 0.0297016
\(375\) −12.0615 −0.622852
\(376\) −0.0560658 −0.00289138
\(377\) −4.27245 −0.220042
\(378\) 34.0066 1.74911
\(379\) −9.97409 −0.512335 −0.256167 0.966632i \(-0.582460\pi\)
−0.256167 + 0.966632i \(0.582460\pi\)
\(380\) −2.48253 −0.127351
\(381\) −14.5137 −0.743558
\(382\) 30.5752 1.56436
\(383\) −9.02950 −0.461386 −0.230693 0.973027i \(-0.574099\pi\)
−0.230693 + 0.973027i \(0.574099\pi\)
\(384\) −2.75189 −0.140432
\(385\) −6.32406 −0.322304
\(386\) −27.3595 −1.39256
\(387\) −15.8357 −0.804975
\(388\) 0.600168 0.0304689
\(389\) −12.2856 −0.622906 −0.311453 0.950262i \(-0.600816\pi\)
−0.311453 + 0.950262i \(0.600816\pi\)
\(390\) 3.14003 0.159001
\(391\) −0.475195 −0.0240316
\(392\) 1.23996 0.0626273
\(393\) −18.3456 −0.925412
\(394\) −31.0356 −1.56355
\(395\) −10.2529 −0.515880
\(396\) 4.70713 0.236542
\(397\) −26.5271 −1.33136 −0.665679 0.746238i \(-0.731858\pi\)
−0.665679 + 0.746238i \(0.731858\pi\)
\(398\) −1.35769 −0.0680549
\(399\) −3.61116 −0.180784
\(400\) 13.6508 0.682542
\(401\) 16.6067 0.829299 0.414650 0.909981i \(-0.363904\pi\)
0.414650 + 0.909981i \(0.363904\pi\)
\(402\) −8.35638 −0.416779
\(403\) 1.17200 0.0583813
\(404\) −15.5098 −0.771639
\(405\) −0.428903 −0.0213124
\(406\) −25.4653 −1.26382
\(407\) 3.23946 0.160574
\(408\) 0.0713940 0.00353453
\(409\) 8.32216 0.411504 0.205752 0.978604i \(-0.434036\pi\)
0.205752 + 0.978604i \(0.434036\pi\)
\(410\) 26.6550 1.31640
\(411\) −8.34341 −0.411550
\(412\) 2.25153 0.110925
\(413\) −29.3007 −1.44180
\(414\) −8.12974 −0.399555
\(415\) 6.81404 0.334488
\(416\) −8.45995 −0.414783
\(417\) −23.0347 −1.12801
\(418\) −2.77657 −0.135806
\(419\) 3.26974 0.159737 0.0798687 0.996805i \(-0.474550\pi\)
0.0798687 + 0.996805i \(0.474550\pi\)
\(420\) 8.96481 0.437438
\(421\) −36.7913 −1.79310 −0.896548 0.442946i \(-0.853933\pi\)
−0.896548 + 0.442946i \(0.853933\pi\)
\(422\) 28.9636 1.40993
\(423\) 0.320618 0.0155890
\(424\) 2.24881 0.109212
\(425\) −0.657288 −0.0318832
\(426\) 11.4911 0.556747
\(427\) −5.39695 −0.261177
\(428\) −11.4114 −0.551589
\(429\) 1.68222 0.0812184
\(430\) −23.1891 −1.11828
\(431\) 38.2369 1.84181 0.920904 0.389790i \(-0.127452\pi\)
0.920904 + 0.389790i \(0.127452\pi\)
\(432\) 22.5610 1.08547
\(433\) 27.5835 1.32558 0.662788 0.748807i \(-0.269373\pi\)
0.662788 + 0.748807i \(0.269373\pi\)
\(434\) 6.98550 0.335315
\(435\) 5.80001 0.278089
\(436\) −20.3701 −0.975552
\(437\) 2.29702 0.109881
\(438\) 22.1414 1.05796
\(439\) −20.1410 −0.961277 −0.480639 0.876919i \(-0.659595\pi\)
−0.480639 + 0.876919i \(0.659595\pi\)
\(440\) −0.604372 −0.0288123
\(441\) −7.09080 −0.337657
\(442\) 0.440399 0.0209476
\(443\) 25.1639 1.19557 0.597787 0.801655i \(-0.296047\pi\)
0.597787 + 0.801655i \(0.296047\pi\)
\(444\) −4.59217 −0.217935
\(445\) 20.4837 0.971019
\(446\) 20.0601 0.949873
\(447\) 16.2970 0.770821
\(448\) −22.0216 −1.04042
\(449\) −17.7979 −0.839935 −0.419967 0.907539i \(-0.637958\pi\)
−0.419967 + 0.907539i \(0.637958\pi\)
\(450\) −11.2450 −0.530096
\(451\) 14.2800 0.672420
\(452\) −7.41754 −0.348892
\(453\) 22.7906 1.07079
\(454\) −5.09458 −0.239100
\(455\) −4.84871 −0.227311
\(456\) −0.345108 −0.0161612
\(457\) 5.26763 0.246409 0.123205 0.992381i \(-0.460683\pi\)
0.123205 + 0.992381i \(0.460683\pi\)
\(458\) 8.16390 0.381474
\(459\) −1.08631 −0.0507048
\(460\) −5.70242 −0.265877
\(461\) −25.6696 −1.19555 −0.597776 0.801663i \(-0.703949\pi\)
−0.597776 + 0.801663i \(0.703949\pi\)
\(462\) 10.0266 0.466481
\(463\) 20.6569 0.960007 0.480004 0.877266i \(-0.340635\pi\)
0.480004 + 0.877266i \(0.340635\pi\)
\(464\) −16.8945 −0.784306
\(465\) −1.59103 −0.0737821
\(466\) −33.7554 −1.56369
\(467\) 34.5045 1.59668 0.798340 0.602208i \(-0.205712\pi\)
0.798340 + 0.602208i \(0.205712\pi\)
\(468\) 3.60900 0.166826
\(469\) 12.9036 0.595834
\(470\) 0.469498 0.0216563
\(471\) 1.05580 0.0486488
\(472\) −2.80019 −0.128889
\(473\) −12.4232 −0.571221
\(474\) 16.2557 0.746650
\(475\) 3.17723 0.145781
\(476\) 1.25734 0.0576302
\(477\) −12.8600 −0.588820
\(478\) 27.0176 1.23576
\(479\) 32.6560 1.49209 0.746045 0.665896i \(-0.231951\pi\)
0.746045 + 0.665896i \(0.231951\pi\)
\(480\) 11.4847 0.524202
\(481\) 2.48373 0.113248
\(482\) 45.9497 2.09295
\(483\) −8.29490 −0.377431
\(484\) −16.5338 −0.751535
\(485\) 0.440666 0.0200096
\(486\) −30.1850 −1.36922
\(487\) 26.9587 1.22161 0.610807 0.791780i \(-0.290845\pi\)
0.610807 + 0.791780i \(0.290845\pi\)
\(488\) −0.515771 −0.0233478
\(489\) 9.11647 0.412261
\(490\) −10.3835 −0.469077
\(491\) −28.1663 −1.27113 −0.635564 0.772048i \(-0.719232\pi\)
−0.635564 + 0.772048i \(0.719232\pi\)
\(492\) −20.2430 −0.912623
\(493\) 0.813469 0.0366368
\(494\) −2.12882 −0.0957802
\(495\) 3.45615 0.155343
\(496\) 4.63440 0.208091
\(497\) −17.7442 −0.795935
\(498\) −10.8035 −0.484115
\(499\) −22.8390 −1.02241 −0.511207 0.859458i \(-0.670801\pi\)
−0.511207 + 0.859458i \(0.670801\pi\)
\(500\) −20.3002 −0.907854
\(501\) 9.14872 0.408735
\(502\) −38.1277 −1.70172
\(503\) 6.32814 0.282158 0.141079 0.989998i \(-0.454943\pi\)
0.141079 + 0.989998i \(0.454943\pi\)
\(504\) −1.88608 −0.0840126
\(505\) −11.3879 −0.506753
\(506\) −6.37784 −0.283529
\(507\) −12.9130 −0.573484
\(508\) −24.4274 −1.08379
\(509\) 8.44673 0.374395 0.187197 0.982322i \(-0.440060\pi\)
0.187197 + 0.982322i \(0.440060\pi\)
\(510\) −0.597857 −0.0264736
\(511\) −34.1899 −1.51247
\(512\) −30.7387 −1.35847
\(513\) 5.25108 0.231841
\(514\) −19.0061 −0.838323
\(515\) 1.65316 0.0728469
\(516\) 17.6108 0.775273
\(517\) 0.251527 0.0110621
\(518\) 14.8039 0.650445
\(519\) −10.5559 −0.463353
\(520\) −0.463377 −0.0203204
\(521\) 32.4555 1.42190 0.710951 0.703241i \(-0.248265\pi\)
0.710951 + 0.703241i \(0.248265\pi\)
\(522\) 13.9170 0.609131
\(523\) 4.73071 0.206860 0.103430 0.994637i \(-0.467018\pi\)
0.103430 + 0.994637i \(0.467018\pi\)
\(524\) −30.8767 −1.34886
\(525\) −11.4735 −0.500744
\(526\) −58.4337 −2.54783
\(527\) −0.223147 −0.00972041
\(528\) 6.65198 0.289490
\(529\) −17.7237 −0.770595
\(530\) −18.8317 −0.817995
\(531\) 16.0131 0.694910
\(532\) −6.07781 −0.263506
\(533\) 10.9486 0.474237
\(534\) −32.4763 −1.40539
\(535\) −8.37866 −0.362241
\(536\) 1.23316 0.0532645
\(537\) −3.97024 −0.171329
\(538\) −4.82496 −0.208019
\(539\) −5.56278 −0.239606
\(540\) −13.0360 −0.560979
\(541\) −0.870463 −0.0374241 −0.0187121 0.999825i \(-0.505957\pi\)
−0.0187121 + 0.999825i \(0.505957\pi\)
\(542\) 30.7877 1.32244
\(543\) 0.695222 0.0298348
\(544\) 1.61076 0.0690609
\(545\) −14.9565 −0.640667
\(546\) 7.68751 0.328995
\(547\) −2.52665 −0.108032 −0.0540159 0.998540i \(-0.517202\pi\)
−0.0540159 + 0.998540i \(0.517202\pi\)
\(548\) −14.0425 −0.599865
\(549\) 2.94948 0.125881
\(550\) −8.82180 −0.376163
\(551\) −3.93219 −0.167517
\(552\) −0.792720 −0.0337404
\(553\) −25.1015 −1.06742
\(554\) −27.8503 −1.18325
\(555\) −3.37175 −0.143123
\(556\) −38.7688 −1.64416
\(557\) −28.2554 −1.19722 −0.598609 0.801041i \(-0.704280\pi\)
−0.598609 + 0.801041i \(0.704280\pi\)
\(558\) −3.81764 −0.161614
\(559\) −9.52500 −0.402865
\(560\) −19.1732 −0.810214
\(561\) −0.320293 −0.0135228
\(562\) −20.3742 −0.859433
\(563\) −28.9467 −1.21996 −0.609979 0.792417i \(-0.708822\pi\)
−0.609979 + 0.792417i \(0.708822\pi\)
\(564\) −0.356557 −0.0150138
\(565\) −5.44624 −0.229125
\(566\) 26.4627 1.11231
\(567\) −1.05005 −0.0440981
\(568\) −1.69576 −0.0711525
\(569\) 24.2234 1.01550 0.507749 0.861505i \(-0.330478\pi\)
0.507749 + 0.861505i \(0.330478\pi\)
\(570\) 2.88995 0.121047
\(571\) −9.16192 −0.383414 −0.191707 0.981452i \(-0.561402\pi\)
−0.191707 + 0.981452i \(0.561402\pi\)
\(572\) 2.83128 0.118382
\(573\) −17.0491 −0.712237
\(574\) 65.2576 2.72380
\(575\) 7.29817 0.304355
\(576\) 12.0350 0.501459
\(577\) 35.5549 1.48017 0.740086 0.672513i \(-0.234785\pi\)
0.740086 + 0.672513i \(0.234785\pi\)
\(578\) 33.2239 1.38193
\(579\) 15.2560 0.634017
\(580\) 9.76178 0.405336
\(581\) 16.6823 0.692100
\(582\) −0.698665 −0.0289606
\(583\) −10.0888 −0.417834
\(584\) −3.26743 −0.135207
\(585\) 2.64986 0.109558
\(586\) −2.91468 −0.120404
\(587\) 14.0418 0.579568 0.289784 0.957092i \(-0.406416\pi\)
0.289784 + 0.957092i \(0.406416\pi\)
\(588\) 7.88565 0.325199
\(589\) 1.07866 0.0444453
\(590\) 23.4489 0.965377
\(591\) 17.3058 0.711867
\(592\) 9.82135 0.403655
\(593\) 4.86700 0.199864 0.0999318 0.994994i \(-0.468138\pi\)
0.0999318 + 0.994994i \(0.468138\pi\)
\(594\) −14.5800 −0.598224
\(595\) 0.923189 0.0378471
\(596\) 27.4289 1.12353
\(597\) 0.757064 0.0309846
\(598\) −4.88995 −0.199965
\(599\) −24.7783 −1.01241 −0.506207 0.862412i \(-0.668953\pi\)
−0.506207 + 0.862412i \(0.668953\pi\)
\(600\) −1.09649 −0.0447639
\(601\) 9.44860 0.385417 0.192708 0.981256i \(-0.438273\pi\)
0.192708 + 0.981256i \(0.438273\pi\)
\(602\) −56.7723 −2.31387
\(603\) −7.05194 −0.287177
\(604\) 38.3580 1.56076
\(605\) −12.1397 −0.493550
\(606\) 18.0551 0.733440
\(607\) −21.7500 −0.882804 −0.441402 0.897309i \(-0.645519\pi\)
−0.441402 + 0.897309i \(0.645519\pi\)
\(608\) −7.78619 −0.315772
\(609\) 14.1998 0.575403
\(610\) 4.31909 0.174875
\(611\) 0.192848 0.00780179
\(612\) −0.687149 −0.0277763
\(613\) −40.6741 −1.64281 −0.821406 0.570344i \(-0.806810\pi\)
−0.821406 + 0.570344i \(0.806810\pi\)
\(614\) −13.9964 −0.564850
\(615\) −14.8631 −0.599340
\(616\) −1.47964 −0.0596164
\(617\) −15.8428 −0.637808 −0.318904 0.947787i \(-0.603315\pi\)
−0.318904 + 0.947787i \(0.603315\pi\)
\(618\) −2.62104 −0.105434
\(619\) −20.8158 −0.836658 −0.418329 0.908296i \(-0.637384\pi\)
−0.418329 + 0.908296i \(0.637384\pi\)
\(620\) −2.67780 −0.107543
\(621\) 12.0618 0.484025
\(622\) −21.8312 −0.875351
\(623\) 50.1487 2.00917
\(624\) 5.10013 0.204169
\(625\) 0.980961 0.0392384
\(626\) −45.9825 −1.83783
\(627\) 1.54825 0.0618311
\(628\) 1.77698 0.0709093
\(629\) −0.472898 −0.0188557
\(630\) 15.7941 0.629253
\(631\) 4.70719 0.187390 0.0936950 0.995601i \(-0.470132\pi\)
0.0936950 + 0.995601i \(0.470132\pi\)
\(632\) −2.39887 −0.0954221
\(633\) −16.1504 −0.641922
\(634\) 1.95928 0.0778129
\(635\) −17.9355 −0.711750
\(636\) 14.3016 0.567094
\(637\) −4.26504 −0.168987
\(638\) 10.9180 0.432247
\(639\) 9.69735 0.383621
\(640\) −3.40070 −0.134425
\(641\) 36.0110 1.42235 0.711175 0.703015i \(-0.248163\pi\)
0.711175 + 0.703015i \(0.248163\pi\)
\(642\) 13.2841 0.524283
\(643\) 7.47568 0.294812 0.147406 0.989076i \(-0.452908\pi\)
0.147406 + 0.989076i \(0.452908\pi\)
\(644\) −13.9608 −0.550134
\(645\) 12.9305 0.509139
\(646\) 0.405325 0.0159473
\(647\) 5.01812 0.197283 0.0986413 0.995123i \(-0.468550\pi\)
0.0986413 + 0.995123i \(0.468550\pi\)
\(648\) −0.100351 −0.00394215
\(649\) 12.5624 0.493117
\(650\) −6.76376 −0.265296
\(651\) −3.89520 −0.152665
\(652\) 15.3436 0.600901
\(653\) 2.78281 0.108900 0.0544498 0.998517i \(-0.482660\pi\)
0.0544498 + 0.998517i \(0.482660\pi\)
\(654\) 23.7132 0.927258
\(655\) −22.6709 −0.885825
\(656\) 43.2939 1.69034
\(657\) 18.6851 0.728975
\(658\) 1.14944 0.0448098
\(659\) −19.2027 −0.748030 −0.374015 0.927423i \(-0.622019\pi\)
−0.374015 + 0.927423i \(0.622019\pi\)
\(660\) −3.84357 −0.149611
\(661\) −0.771891 −0.0300231 −0.0150115 0.999887i \(-0.504779\pi\)
−0.0150115 + 0.999887i \(0.504779\pi\)
\(662\) 28.0094 1.08862
\(663\) −0.245571 −0.00953721
\(664\) 1.59428 0.0618701
\(665\) −4.46256 −0.173051
\(666\) −8.09045 −0.313499
\(667\) −9.03232 −0.349733
\(668\) 15.3979 0.595761
\(669\) −11.1857 −0.432466
\(670\) −10.3266 −0.398950
\(671\) 2.31389 0.0893267
\(672\) 28.1172 1.08464
\(673\) −28.2625 −1.08944 −0.544720 0.838618i \(-0.683364\pi\)
−0.544720 + 0.838618i \(0.683364\pi\)
\(674\) −31.2094 −1.20214
\(675\) 16.6839 0.642164
\(676\) −21.7333 −0.835897
\(677\) 27.6614 1.06311 0.531556 0.847023i \(-0.321607\pi\)
0.531556 + 0.847023i \(0.321607\pi\)
\(678\) 8.63487 0.331620
\(679\) 1.07885 0.0414026
\(680\) 0.0882265 0.00338333
\(681\) 2.84080 0.108860
\(682\) −2.99496 −0.114683
\(683\) −14.6514 −0.560621 −0.280311 0.959909i \(-0.590437\pi\)
−0.280311 + 0.959909i \(0.590437\pi\)
\(684\) 3.32157 0.127004
\(685\) −10.3105 −0.393945
\(686\) 19.9117 0.760231
\(687\) −4.55229 −0.173681
\(688\) −37.6645 −1.43595
\(689\) −7.73516 −0.294686
\(690\) 6.63828 0.252715
\(691\) −19.3766 −0.737121 −0.368560 0.929604i \(-0.620149\pi\)
−0.368560 + 0.929604i \(0.620149\pi\)
\(692\) −17.7663 −0.675373
\(693\) 8.46146 0.321424
\(694\) 23.5505 0.893964
\(695\) −28.4655 −1.07976
\(696\) 1.35703 0.0514381
\(697\) −2.08460 −0.0789600
\(698\) 40.9023 1.54817
\(699\) 18.8224 0.711929
\(700\) −19.3106 −0.729872
\(701\) −51.8637 −1.95887 −0.979433 0.201772i \(-0.935330\pi\)
−0.979433 + 0.201772i \(0.935330\pi\)
\(702\) −11.1786 −0.421910
\(703\) 2.28592 0.0862151
\(704\) 9.44155 0.355842
\(705\) −0.261798 −0.00985988
\(706\) 40.7827 1.53488
\(707\) −27.8801 −1.04854
\(708\) −17.8081 −0.669270
\(709\) 24.6515 0.925805 0.462903 0.886409i \(-0.346808\pi\)
0.462903 + 0.886409i \(0.346808\pi\)
\(710\) 14.2004 0.532931
\(711\) 13.7182 0.514472
\(712\) 4.79257 0.179609
\(713\) 2.47770 0.0927905
\(714\) −1.46369 −0.0547773
\(715\) 2.07884 0.0777441
\(716\) −6.68217 −0.249724
\(717\) −15.0653 −0.562626
\(718\) 27.5426 1.02788
\(719\) −16.3896 −0.611229 −0.305615 0.952155i \(-0.598862\pi\)
−0.305615 + 0.952155i \(0.598862\pi\)
\(720\) 10.4783 0.390504
\(721\) 4.04732 0.150730
\(722\) −1.95928 −0.0729168
\(723\) −25.6221 −0.952895
\(724\) 1.17010 0.0434865
\(725\) −12.4935 −0.463996
\(726\) 19.2472 0.714331
\(727\) −17.7282 −0.657502 −0.328751 0.944417i \(-0.606628\pi\)
−0.328751 + 0.944417i \(0.606628\pi\)
\(728\) −1.13445 −0.0420457
\(729\) 17.7846 0.658687
\(730\) 27.3616 1.01270
\(731\) 1.81355 0.0670765
\(732\) −3.28010 −0.121236
\(733\) 4.28168 0.158148 0.0790738 0.996869i \(-0.474804\pi\)
0.0790738 + 0.996869i \(0.474804\pi\)
\(734\) −13.4459 −0.496298
\(735\) 5.78994 0.213565
\(736\) −17.8850 −0.659251
\(737\) −5.53230 −0.203785
\(738\) −35.6639 −1.31280
\(739\) −22.8692 −0.841258 −0.420629 0.907233i \(-0.638191\pi\)
−0.420629 + 0.907233i \(0.638191\pi\)
\(740\) −5.67487 −0.208612
\(741\) 1.18706 0.0436076
\(742\) −46.1042 −1.69254
\(743\) −26.0113 −0.954264 −0.477132 0.878832i \(-0.658324\pi\)
−0.477132 + 0.878832i \(0.658324\pi\)
\(744\) −0.372253 −0.0136475
\(745\) 20.1393 0.737848
\(746\) 11.6266 0.425680
\(747\) −9.11704 −0.333575
\(748\) −0.539073 −0.0197105
\(749\) −20.5129 −0.749524
\(750\) 23.6318 0.862911
\(751\) −27.6445 −1.00876 −0.504380 0.863482i \(-0.668279\pi\)
−0.504380 + 0.863482i \(0.668279\pi\)
\(752\) 0.762575 0.0278082
\(753\) 21.2604 0.774773
\(754\) 8.37093 0.304851
\(755\) 28.1639 1.02499
\(756\) −31.9151 −1.16074
\(757\) −17.3556 −0.630802 −0.315401 0.948959i \(-0.602139\pi\)
−0.315401 + 0.948959i \(0.602139\pi\)
\(758\) 19.5420 0.709799
\(759\) 3.55636 0.129088
\(760\) −0.426474 −0.0154698
\(761\) 12.3745 0.448577 0.224288 0.974523i \(-0.427994\pi\)
0.224288 + 0.974523i \(0.427994\pi\)
\(762\) 28.4363 1.03014
\(763\) −36.6170 −1.32562
\(764\) −28.6947 −1.03814
\(765\) −0.504531 −0.0182414
\(766\) 17.6913 0.639213
\(767\) 9.63171 0.347781
\(768\) 19.9493 0.719859
\(769\) −14.9409 −0.538784 −0.269392 0.963031i \(-0.586823\pi\)
−0.269392 + 0.963031i \(0.586823\pi\)
\(770\) 12.3906 0.446526
\(771\) 10.5980 0.381679
\(772\) 25.6768 0.924128
\(773\) −16.1533 −0.580992 −0.290496 0.956876i \(-0.593820\pi\)
−0.290496 + 0.956876i \(0.593820\pi\)
\(774\) 31.0266 1.11523
\(775\) 3.42714 0.123107
\(776\) 0.103103 0.00370117
\(777\) −8.25482 −0.296140
\(778\) 24.0710 0.862987
\(779\) 10.0767 0.361034
\(780\) −2.94690 −0.105516
\(781\) 7.60764 0.272223
\(782\) 0.931040 0.0332939
\(783\) −20.6482 −0.737908
\(784\) −16.8652 −0.602327
\(785\) 1.30473 0.0465677
\(786\) 35.9441 1.28208
\(787\) 8.65422 0.308490 0.154245 0.988033i \(-0.450706\pi\)
0.154245 + 0.988033i \(0.450706\pi\)
\(788\) 29.1268 1.03760
\(789\) 32.5833 1.16000
\(790\) 20.0883 0.714710
\(791\) −13.3337 −0.474090
\(792\) 0.808637 0.0287337
\(793\) 1.77408 0.0629994
\(794\) 51.9740 1.84449
\(795\) 10.5008 0.372424
\(796\) 1.27419 0.0451624
\(797\) 25.9918 0.920677 0.460339 0.887743i \(-0.347728\pi\)
0.460339 + 0.887743i \(0.347728\pi\)
\(798\) 7.07527 0.250462
\(799\) −0.0367180 −0.00129899
\(800\) −24.7385 −0.874639
\(801\) −27.4067 −0.968369
\(802\) −32.5372 −1.14893
\(803\) 14.6586 0.517290
\(804\) 7.84243 0.276581
\(805\) −10.2506 −0.361286
\(806\) −2.29627 −0.0808826
\(807\) 2.69046 0.0947086
\(808\) −2.66442 −0.0937339
\(809\) −11.2645 −0.396037 −0.198019 0.980198i \(-0.563451\pi\)
−0.198019 + 0.980198i \(0.563451\pi\)
\(810\) 0.840342 0.0295266
\(811\) −32.6225 −1.14553 −0.572766 0.819719i \(-0.694130\pi\)
−0.572766 + 0.819719i \(0.694130\pi\)
\(812\) 23.8991 0.838693
\(813\) −17.1676 −0.602093
\(814\) −6.34701 −0.222463
\(815\) 11.2659 0.394626
\(816\) −0.971059 −0.0339939
\(817\) −8.76642 −0.306698
\(818\) −16.3054 −0.570106
\(819\) 6.48748 0.226691
\(820\) −25.0156 −0.873583
\(821\) −35.7329 −1.24709 −0.623544 0.781788i \(-0.714308\pi\)
−0.623544 + 0.781788i \(0.714308\pi\)
\(822\) 16.3471 0.570169
\(823\) −44.1765 −1.53990 −0.769948 0.638107i \(-0.779718\pi\)
−0.769948 + 0.638107i \(0.779718\pi\)
\(824\) 0.386790 0.0134745
\(825\) 4.91914 0.171263
\(826\) 57.4084 1.99749
\(827\) −3.54828 −0.123386 −0.0616928 0.998095i \(-0.519650\pi\)
−0.0616928 + 0.998095i \(0.519650\pi\)
\(828\) 7.62973 0.265151
\(829\) 45.0046 1.56308 0.781538 0.623858i \(-0.214436\pi\)
0.781538 + 0.623858i \(0.214436\pi\)
\(830\) −13.3506 −0.463406
\(831\) 15.5297 0.538718
\(832\) 7.23893 0.250965
\(833\) 0.812058 0.0281361
\(834\) 45.1314 1.56277
\(835\) 11.3057 0.391250
\(836\) 2.60580 0.0901234
\(837\) 5.66412 0.195780
\(838\) −6.40634 −0.221303
\(839\) 9.67733 0.334099 0.167049 0.985949i \(-0.446576\pi\)
0.167049 + 0.985949i \(0.446576\pi\)
\(840\) 1.54006 0.0531372
\(841\) −13.5379 −0.466824
\(842\) 72.0844 2.48419
\(843\) 11.3609 0.391290
\(844\) −27.1822 −0.935650
\(845\) −15.9574 −0.548952
\(846\) −0.628179 −0.0215972
\(847\) −29.7208 −1.02122
\(848\) −30.5870 −1.05036
\(849\) −14.7559 −0.506421
\(850\) 1.28781 0.0441715
\(851\) 5.25081 0.179995
\(852\) −10.7844 −0.369467
\(853\) 3.44644 0.118004 0.0590019 0.998258i \(-0.481208\pi\)
0.0590019 + 0.998258i \(0.481208\pi\)
\(854\) 10.5741 0.361839
\(855\) 2.43883 0.0834061
\(856\) −1.96036 −0.0670036
\(857\) 53.9772 1.84383 0.921913 0.387398i \(-0.126626\pi\)
0.921913 + 0.387398i \(0.126626\pi\)
\(858\) −3.29594 −0.112522
\(859\) −21.2518 −0.725103 −0.362551 0.931964i \(-0.618094\pi\)
−0.362551 + 0.931964i \(0.618094\pi\)
\(860\) 21.7629 0.742109
\(861\) −36.3884 −1.24011
\(862\) −74.9168 −2.55168
\(863\) −26.4634 −0.900823 −0.450412 0.892821i \(-0.648723\pi\)
−0.450412 + 0.892821i \(0.648723\pi\)
\(864\) −40.8859 −1.39097
\(865\) −13.0447 −0.443532
\(866\) −54.0437 −1.83648
\(867\) −18.5260 −0.629177
\(868\) −6.55587 −0.222521
\(869\) 10.7620 0.365076
\(870\) −11.3638 −0.385270
\(871\) −4.24167 −0.143723
\(872\) −3.49938 −0.118504
\(873\) −0.589602 −0.0199550
\(874\) −4.50051 −0.152232
\(875\) −36.4914 −1.23363
\(876\) −20.7796 −0.702078
\(877\) −52.9999 −1.78968 −0.894840 0.446387i \(-0.852710\pi\)
−0.894840 + 0.446387i \(0.852710\pi\)
\(878\) 39.4618 1.33177
\(879\) 1.62526 0.0548187
\(880\) 8.22031 0.277106
\(881\) −42.6380 −1.43651 −0.718255 0.695780i \(-0.755059\pi\)
−0.718255 + 0.695780i \(0.755059\pi\)
\(882\) 13.8929 0.467797
\(883\) −7.80742 −0.262740 −0.131370 0.991333i \(-0.541938\pi\)
−0.131370 + 0.991333i \(0.541938\pi\)
\(884\) −0.413312 −0.0139012
\(885\) −13.0754 −0.439525
\(886\) −49.3031 −1.65637
\(887\) 16.7371 0.561978 0.280989 0.959711i \(-0.409338\pi\)
0.280989 + 0.959711i \(0.409338\pi\)
\(888\) −0.788889 −0.0264734
\(889\) −43.9103 −1.47271
\(890\) −40.1332 −1.34527
\(891\) 0.450200 0.0150823
\(892\) −18.8263 −0.630352
\(893\) 0.177489 0.00593945
\(894\) −31.9304 −1.06791
\(895\) −4.90630 −0.164000
\(896\) −8.32570 −0.278142
\(897\) 2.72669 0.0910416
\(898\) 34.8711 1.16366
\(899\) −4.24148 −0.141461
\(900\) 10.5534 0.351780
\(901\) 1.47276 0.0490649
\(902\) −27.9785 −0.931584
\(903\) 31.6569 1.05348
\(904\) −1.27426 −0.0423812
\(905\) 0.859134 0.0285586
\(906\) −44.6531 −1.48350
\(907\) 21.6370 0.718443 0.359222 0.933252i \(-0.383042\pi\)
0.359222 + 0.933252i \(0.383042\pi\)
\(908\) 4.78124 0.158671
\(909\) 15.2367 0.505370
\(910\) 9.49998 0.314921
\(911\) 38.4160 1.27278 0.636389 0.771368i \(-0.280427\pi\)
0.636389 + 0.771368i \(0.280427\pi\)
\(912\) 4.69395 0.155432
\(913\) −7.15238 −0.236709
\(914\) −10.3208 −0.341380
\(915\) −2.40838 −0.0796185
\(916\) −7.66179 −0.253153
\(917\) −55.5036 −1.83289
\(918\) 2.12839 0.0702475
\(919\) 19.4972 0.643152 0.321576 0.946884i \(-0.395787\pi\)
0.321576 + 0.946884i \(0.395787\pi\)
\(920\) −0.979619 −0.0322971
\(921\) 7.80458 0.257170
\(922\) 50.2939 1.65634
\(923\) 5.83285 0.191991
\(924\) −9.40995 −0.309565
\(925\) 7.26290 0.238803
\(926\) −40.4726 −1.33001
\(927\) −2.21189 −0.0726481
\(928\) 30.6168 1.00504
\(929\) 58.8023 1.92924 0.964620 0.263645i \(-0.0849247\pi\)
0.964620 + 0.263645i \(0.0849247\pi\)
\(930\) 3.11727 0.102219
\(931\) −3.92537 −0.128649
\(932\) 31.6793 1.03769
\(933\) 12.1733 0.398537
\(934\) −67.6040 −2.21207
\(935\) −0.395808 −0.0129443
\(936\) 0.619989 0.0202650
\(937\) 10.8334 0.353911 0.176955 0.984219i \(-0.443375\pi\)
0.176955 + 0.984219i \(0.443375\pi\)
\(938\) −25.2818 −0.825480
\(939\) 25.6404 0.836743
\(940\) −0.440622 −0.0143715
\(941\) 28.4602 0.927775 0.463888 0.885894i \(-0.346454\pi\)
0.463888 + 0.885894i \(0.346454\pi\)
\(942\) −2.06861 −0.0673990
\(943\) 23.1463 0.753747
\(944\) 38.0865 1.23961
\(945\) −23.4333 −0.762284
\(946\) 24.3406 0.791380
\(947\) −10.1038 −0.328330 −0.164165 0.986433i \(-0.552493\pi\)
−0.164165 + 0.986433i \(0.552493\pi\)
\(948\) −15.2559 −0.495489
\(949\) 11.2389 0.364829
\(950\) −6.22508 −0.201968
\(951\) −1.09252 −0.0354273
\(952\) 0.215999 0.00700056
\(953\) 33.0190 1.06959 0.534795 0.844982i \(-0.320389\pi\)
0.534795 + 0.844982i \(0.320389\pi\)
\(954\) 25.1964 0.815763
\(955\) −21.0688 −0.681769
\(956\) −25.3559 −0.820069
\(957\) −6.08800 −0.196797
\(958\) −63.9822 −2.06717
\(959\) −25.2425 −0.815124
\(960\) −9.82710 −0.317168
\(961\) −29.8365 −0.962468
\(962\) −4.86631 −0.156896
\(963\) 11.2105 0.361252
\(964\) −43.1236 −1.38892
\(965\) 18.8529 0.606896
\(966\) 16.2520 0.522901
\(967\) 9.35160 0.300727 0.150364 0.988631i \(-0.451956\pi\)
0.150364 + 0.988631i \(0.451956\pi\)
\(968\) −2.84033 −0.0912917
\(969\) −0.226014 −0.00726061
\(970\) −0.863388 −0.0277217
\(971\) −32.0250 −1.02773 −0.513866 0.857871i \(-0.671787\pi\)
−0.513866 + 0.857871i \(0.671787\pi\)
\(972\) 28.3285 0.908637
\(973\) −69.6902 −2.23417
\(974\) −52.8195 −1.69245
\(975\) 3.77155 0.120786
\(976\) 7.01521 0.224551
\(977\) −3.79725 −0.121485 −0.0607423 0.998153i \(-0.519347\pi\)
−0.0607423 + 0.998153i \(0.519347\pi\)
\(978\) −17.8617 −0.571155
\(979\) −21.5008 −0.687167
\(980\) 9.74484 0.311287
\(981\) 20.0115 0.638919
\(982\) 55.1857 1.76105
\(983\) 12.8516 0.409904 0.204952 0.978772i \(-0.434296\pi\)
0.204952 + 0.978772i \(0.434296\pi\)
\(984\) −3.47753 −0.110860
\(985\) 21.3860 0.681415
\(986\) −1.59381 −0.0507574
\(987\) −0.640942 −0.0204014
\(988\) 1.99789 0.0635613
\(989\) −20.1367 −0.640308
\(990\) −6.77157 −0.215215
\(991\) −3.54322 −0.112554 −0.0562770 0.998415i \(-0.517923\pi\)
−0.0562770 + 0.998415i \(0.517923\pi\)
\(992\) −8.39863 −0.266657
\(993\) −15.6184 −0.495634
\(994\) 34.7658 1.10270
\(995\) 0.935557 0.0296591
\(996\) 10.1390 0.321267
\(997\) −13.6204 −0.431363 −0.215681 0.976464i \(-0.569197\pi\)
−0.215681 + 0.976464i \(0.569197\pi\)
\(998\) 44.7480 1.41647
\(999\) 12.0036 0.379776
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 \(a_p\))