Properties

Label 8002.2.a.e.1.2
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.14716 q^{3} +1.00000 q^{4} -2.17339 q^{5} +3.14716 q^{6} +4.77090 q^{7} -1.00000 q^{8} +6.90459 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.14716 q^{3} +1.00000 q^{4} -2.17339 q^{5} +3.14716 q^{6} +4.77090 q^{7} -1.00000 q^{8} +6.90459 q^{9} +2.17339 q^{10} +0.464609 q^{11} -3.14716 q^{12} -3.54045 q^{13} -4.77090 q^{14} +6.84001 q^{15} +1.00000 q^{16} +2.17248 q^{17} -6.90459 q^{18} -7.81420 q^{19} -2.17339 q^{20} -15.0148 q^{21} -0.464609 q^{22} -2.67609 q^{23} +3.14716 q^{24} -0.276360 q^{25} +3.54045 q^{26} -12.2884 q^{27} +4.77090 q^{28} -4.66474 q^{29} -6.84001 q^{30} -2.75066 q^{31} -1.00000 q^{32} -1.46220 q^{33} -2.17248 q^{34} -10.3691 q^{35} +6.90459 q^{36} -3.49564 q^{37} +7.81420 q^{38} +11.1423 q^{39} +2.17339 q^{40} +0.752133 q^{41} +15.0148 q^{42} +0.446218 q^{43} +0.464609 q^{44} -15.0064 q^{45} +2.67609 q^{46} +6.33329 q^{47} -3.14716 q^{48} +15.7615 q^{49} +0.276360 q^{50} -6.83713 q^{51} -3.54045 q^{52} -5.24165 q^{53} +12.2884 q^{54} -1.00978 q^{55} -4.77090 q^{56} +24.5925 q^{57} +4.66474 q^{58} +12.6820 q^{59} +6.84001 q^{60} -6.29902 q^{61} +2.75066 q^{62} +32.9411 q^{63} +1.00000 q^{64} +7.69478 q^{65} +1.46220 q^{66} -7.37205 q^{67} +2.17248 q^{68} +8.42209 q^{69} +10.3691 q^{70} -10.7392 q^{71} -6.90459 q^{72} +14.9326 q^{73} +3.49564 q^{74} +0.869748 q^{75} -7.81420 q^{76} +2.21661 q^{77} -11.1423 q^{78} -2.14485 q^{79} -2.17339 q^{80} +17.9596 q^{81} -0.752133 q^{82} -1.26263 q^{83} -15.0148 q^{84} -4.72165 q^{85} -0.446218 q^{86} +14.6807 q^{87} -0.464609 q^{88} +10.3386 q^{89} +15.0064 q^{90} -16.8911 q^{91} -2.67609 q^{92} +8.65674 q^{93} -6.33329 q^{94} +16.9833 q^{95} +3.14716 q^{96} -5.61370 q^{97} -15.7615 q^{98} +3.20794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.14716 −1.81701 −0.908506 0.417873i \(-0.862776\pi\)
−0.908506 + 0.417873i \(0.862776\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.17339 −0.971971 −0.485986 0.873967i \(-0.661539\pi\)
−0.485986 + 0.873967i \(0.661539\pi\)
\(6\) 3.14716 1.28482
\(7\) 4.77090 1.80323 0.901616 0.432537i \(-0.142382\pi\)
0.901616 + 0.432537i \(0.142382\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.90459 2.30153
\(10\) 2.17339 0.687287
\(11\) 0.464609 0.140085 0.0700425 0.997544i \(-0.477687\pi\)
0.0700425 + 0.997544i \(0.477687\pi\)
\(12\) −3.14716 −0.908506
\(13\) −3.54045 −0.981943 −0.490972 0.871176i \(-0.663358\pi\)
−0.490972 + 0.871176i \(0.663358\pi\)
\(14\) −4.77090 −1.27508
\(15\) 6.84001 1.76608
\(16\) 1.00000 0.250000
\(17\) 2.17248 0.526903 0.263452 0.964673i \(-0.415139\pi\)
0.263452 + 0.964673i \(0.415139\pi\)
\(18\) −6.90459 −1.62743
\(19\) −7.81420 −1.79270 −0.896350 0.443347i \(-0.853791\pi\)
−0.896350 + 0.443347i \(0.853791\pi\)
\(20\) −2.17339 −0.485986
\(21\) −15.0148 −3.27649
\(22\) −0.464609 −0.0990551
\(23\) −2.67609 −0.558004 −0.279002 0.960290i \(-0.590004\pi\)
−0.279002 + 0.960290i \(0.590004\pi\)
\(24\) 3.14716 0.642410
\(25\) −0.276360 −0.0552720
\(26\) 3.54045 0.694339
\(27\) −12.2884 −2.36489
\(28\) 4.77090 0.901616
\(29\) −4.66474 −0.866220 −0.433110 0.901341i \(-0.642584\pi\)
−0.433110 + 0.901341i \(0.642584\pi\)
\(30\) −6.84001 −1.24881
\(31\) −2.75066 −0.494032 −0.247016 0.969011i \(-0.579450\pi\)
−0.247016 + 0.969011i \(0.579450\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.46220 −0.254536
\(34\) −2.17248 −0.372577
\(35\) −10.3691 −1.75269
\(36\) 6.90459 1.15076
\(37\) −3.49564 −0.574679 −0.287340 0.957829i \(-0.592771\pi\)
−0.287340 + 0.957829i \(0.592771\pi\)
\(38\) 7.81420 1.26763
\(39\) 11.1423 1.78420
\(40\) 2.17339 0.343644
\(41\) 0.752133 0.117463 0.0587317 0.998274i \(-0.481294\pi\)
0.0587317 + 0.998274i \(0.481294\pi\)
\(42\) 15.0148 2.31683
\(43\) 0.446218 0.0680476 0.0340238 0.999421i \(-0.489168\pi\)
0.0340238 + 0.999421i \(0.489168\pi\)
\(44\) 0.464609 0.0700425
\(45\) −15.0064 −2.23702
\(46\) 2.67609 0.394569
\(47\) 6.33329 0.923805 0.461903 0.886931i \(-0.347167\pi\)
0.461903 + 0.886931i \(0.347167\pi\)
\(48\) −3.14716 −0.454253
\(49\) 15.7615 2.25165
\(50\) 0.276360 0.0390832
\(51\) −6.83713 −0.957389
\(52\) −3.54045 −0.490972
\(53\) −5.24165 −0.719996 −0.359998 0.932953i \(-0.617223\pi\)
−0.359998 + 0.932953i \(0.617223\pi\)
\(54\) 12.2884 1.67223
\(55\) −1.00978 −0.136159
\(56\) −4.77090 −0.637539
\(57\) 24.5925 3.25736
\(58\) 4.66474 0.612510
\(59\) 12.6820 1.65105 0.825525 0.564365i \(-0.190879\pi\)
0.825525 + 0.564365i \(0.190879\pi\)
\(60\) 6.84001 0.883041
\(61\) −6.29902 −0.806507 −0.403254 0.915088i \(-0.632121\pi\)
−0.403254 + 0.915088i \(0.632121\pi\)
\(62\) 2.75066 0.349334
\(63\) 32.9411 4.15019
\(64\) 1.00000 0.125000
\(65\) 7.69478 0.954421
\(66\) 1.46220 0.179984
\(67\) −7.37205 −0.900639 −0.450320 0.892867i \(-0.648690\pi\)
−0.450320 + 0.892867i \(0.648690\pi\)
\(68\) 2.17248 0.263452
\(69\) 8.42209 1.01390
\(70\) 10.3691 1.23934
\(71\) −10.7392 −1.27451 −0.637257 0.770652i \(-0.719931\pi\)
−0.637257 + 0.770652i \(0.719931\pi\)
\(72\) −6.90459 −0.813714
\(73\) 14.9326 1.74773 0.873866 0.486167i \(-0.161605\pi\)
0.873866 + 0.486167i \(0.161605\pi\)
\(74\) 3.49564 0.406360
\(75\) 0.869748 0.100430
\(76\) −7.81420 −0.896350
\(77\) 2.21661 0.252606
\(78\) −11.1423 −1.26162
\(79\) −2.14485 −0.241314 −0.120657 0.992694i \(-0.538500\pi\)
−0.120657 + 0.992694i \(0.538500\pi\)
\(80\) −2.17339 −0.242993
\(81\) 17.9596 1.99551
\(82\) −0.752133 −0.0830592
\(83\) −1.26263 −0.138592 −0.0692960 0.997596i \(-0.522075\pi\)
−0.0692960 + 0.997596i \(0.522075\pi\)
\(84\) −15.0148 −1.63825
\(85\) −4.72165 −0.512135
\(86\) −0.446218 −0.0481169
\(87\) 14.6807 1.57393
\(88\) −0.464609 −0.0495275
\(89\) 10.3386 1.09589 0.547945 0.836514i \(-0.315410\pi\)
0.547945 + 0.836514i \(0.315410\pi\)
\(90\) 15.0064 1.58181
\(91\) −16.8911 −1.77067
\(92\) −2.67609 −0.279002
\(93\) 8.65674 0.897662
\(94\) −6.33329 −0.653229
\(95\) 16.9833 1.74245
\(96\) 3.14716 0.321205
\(97\) −5.61370 −0.569984 −0.284992 0.958530i \(-0.591991\pi\)
−0.284992 + 0.958530i \(0.591991\pi\)
\(98\) −15.7615 −1.59215
\(99\) 3.20794 0.322410
\(100\) −0.276360 −0.0276360
\(101\) 4.91550 0.489110 0.244555 0.969635i \(-0.421358\pi\)
0.244555 + 0.969635i \(0.421358\pi\)
\(102\) 6.83713 0.676976
\(103\) −13.7917 −1.35894 −0.679468 0.733705i \(-0.737789\pi\)
−0.679468 + 0.733705i \(0.737789\pi\)
\(104\) 3.54045 0.347169
\(105\) 32.6330 3.18466
\(106\) 5.24165 0.509114
\(107\) 14.6420 1.41550 0.707750 0.706463i \(-0.249710\pi\)
0.707750 + 0.706463i \(0.249710\pi\)
\(108\) −12.2884 −1.18245
\(109\) −11.7987 −1.13011 −0.565057 0.825052i \(-0.691146\pi\)
−0.565057 + 0.825052i \(0.691146\pi\)
\(110\) 1.00978 0.0962787
\(111\) 11.0013 1.04420
\(112\) 4.77090 0.450808
\(113\) −16.7188 −1.57277 −0.786387 0.617735i \(-0.788051\pi\)
−0.786387 + 0.617735i \(0.788051\pi\)
\(114\) −24.5925 −2.30330
\(115\) 5.81621 0.542364
\(116\) −4.66474 −0.433110
\(117\) −24.4453 −2.25997
\(118\) −12.6820 −1.16747
\(119\) 10.3647 0.950129
\(120\) −6.84001 −0.624404
\(121\) −10.7841 −0.980376
\(122\) 6.29902 0.570287
\(123\) −2.36708 −0.213432
\(124\) −2.75066 −0.247016
\(125\) 11.4676 1.02569
\(126\) −32.9411 −2.93463
\(127\) −6.91452 −0.613564 −0.306782 0.951780i \(-0.599252\pi\)
−0.306782 + 0.951780i \(0.599252\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.40432 −0.123643
\(130\) −7.69478 −0.674877
\(131\) 2.61568 0.228533 0.114267 0.993450i \(-0.463548\pi\)
0.114267 + 0.993450i \(0.463548\pi\)
\(132\) −1.46220 −0.127268
\(133\) −37.2808 −3.23265
\(134\) 7.37205 0.636848
\(135\) 26.7074 2.29861
\(136\) −2.17248 −0.186288
\(137\) −2.09352 −0.178861 −0.0894307 0.995993i \(-0.528505\pi\)
−0.0894307 + 0.995993i \(0.528505\pi\)
\(138\) −8.42209 −0.716936
\(139\) 0.169351 0.0143642 0.00718208 0.999974i \(-0.497714\pi\)
0.00718208 + 0.999974i \(0.497714\pi\)
\(140\) −10.3691 −0.876345
\(141\) −19.9318 −1.67856
\(142\) 10.7392 0.901217
\(143\) −1.64493 −0.137556
\(144\) 6.90459 0.575382
\(145\) 10.1383 0.841941
\(146\) −14.9326 −1.23583
\(147\) −49.6040 −4.09127
\(148\) −3.49564 −0.287340
\(149\) 16.4336 1.34629 0.673145 0.739511i \(-0.264943\pi\)
0.673145 + 0.739511i \(0.264943\pi\)
\(150\) −0.869748 −0.0710147
\(151\) 8.57860 0.698116 0.349058 0.937101i \(-0.386502\pi\)
0.349058 + 0.937101i \(0.386502\pi\)
\(152\) 7.81420 0.633815
\(153\) 15.0001 1.21268
\(154\) −2.21661 −0.178619
\(155\) 5.97826 0.480185
\(156\) 11.1423 0.892101
\(157\) −10.6449 −0.849558 −0.424779 0.905297i \(-0.639648\pi\)
−0.424779 + 0.905297i \(0.639648\pi\)
\(158\) 2.14485 0.170635
\(159\) 16.4963 1.30824
\(160\) 2.17339 0.171822
\(161\) −12.7674 −1.00621
\(162\) −17.9596 −1.41104
\(163\) 8.77566 0.687363 0.343681 0.939086i \(-0.388326\pi\)
0.343681 + 0.939086i \(0.388326\pi\)
\(164\) 0.752133 0.0587317
\(165\) 3.17793 0.247402
\(166\) 1.26263 0.0979994
\(167\) −14.8025 −1.14545 −0.572725 0.819748i \(-0.694114\pi\)
−0.572725 + 0.819748i \(0.694114\pi\)
\(168\) 15.0148 1.15842
\(169\) −0.465237 −0.0357874
\(170\) 4.72165 0.362134
\(171\) −53.9538 −4.12595
\(172\) 0.446218 0.0340238
\(173\) 11.2411 0.854648 0.427324 0.904099i \(-0.359456\pi\)
0.427324 + 0.904099i \(0.359456\pi\)
\(174\) −14.6807 −1.11294
\(175\) −1.31849 −0.0996683
\(176\) 0.464609 0.0350213
\(177\) −39.9121 −2.99998
\(178\) −10.3386 −0.774912
\(179\) −8.63646 −0.645519 −0.322760 0.946481i \(-0.604611\pi\)
−0.322760 + 0.946481i \(0.604611\pi\)
\(180\) −15.0064 −1.11851
\(181\) 9.03712 0.671724 0.335862 0.941911i \(-0.390972\pi\)
0.335862 + 0.941911i \(0.390972\pi\)
\(182\) 16.8911 1.25205
\(183\) 19.8240 1.46543
\(184\) 2.67609 0.197284
\(185\) 7.59740 0.558572
\(186\) −8.65674 −0.634743
\(187\) 1.00935 0.0738113
\(188\) 6.33329 0.461903
\(189\) −58.6265 −4.26445
\(190\) −16.9833 −1.23210
\(191\) −9.35417 −0.676844 −0.338422 0.940994i \(-0.609893\pi\)
−0.338422 + 0.940994i \(0.609893\pi\)
\(192\) −3.14716 −0.227126
\(193\) −4.91824 −0.354023 −0.177012 0.984209i \(-0.556643\pi\)
−0.177012 + 0.984209i \(0.556643\pi\)
\(194\) 5.61370 0.403040
\(195\) −24.2167 −1.73419
\(196\) 15.7615 1.12582
\(197\) 14.7015 1.04744 0.523718 0.851892i \(-0.324544\pi\)
0.523718 + 0.851892i \(0.324544\pi\)
\(198\) −3.20794 −0.227978
\(199\) 10.5778 0.749844 0.374922 0.927056i \(-0.377670\pi\)
0.374922 + 0.927056i \(0.377670\pi\)
\(200\) 0.276360 0.0195416
\(201\) 23.2010 1.63647
\(202\) −4.91550 −0.345853
\(203\) −22.2550 −1.56200
\(204\) −6.83713 −0.478695
\(205\) −1.63468 −0.114171
\(206\) 13.7917 0.960913
\(207\) −18.4773 −1.28426
\(208\) −3.54045 −0.245486
\(209\) −3.63055 −0.251130
\(210\) −32.6330 −2.25189
\(211\) −10.8499 −0.746937 −0.373469 0.927643i \(-0.621832\pi\)
−0.373469 + 0.927643i \(0.621832\pi\)
\(212\) −5.24165 −0.359998
\(213\) 33.7981 2.31581
\(214\) −14.6420 −1.00091
\(215\) −0.969807 −0.0661403
\(216\) 12.2884 0.836116
\(217\) −13.1231 −0.890855
\(218\) 11.7987 0.799111
\(219\) −46.9953 −3.17565
\(220\) −1.00978 −0.0680793
\(221\) −7.69154 −0.517389
\(222\) −11.0013 −0.738360
\(223\) 22.6580 1.51729 0.758646 0.651503i \(-0.225861\pi\)
0.758646 + 0.651503i \(0.225861\pi\)
\(224\) −4.77090 −0.318769
\(225\) −1.90815 −0.127210
\(226\) 16.7188 1.11212
\(227\) 7.21310 0.478750 0.239375 0.970927i \(-0.423057\pi\)
0.239375 + 0.970927i \(0.423057\pi\)
\(228\) 24.5925 1.62868
\(229\) 22.7121 1.50086 0.750430 0.660950i \(-0.229847\pi\)
0.750430 + 0.660950i \(0.229847\pi\)
\(230\) −5.81621 −0.383509
\(231\) −6.97601 −0.458988
\(232\) 4.66474 0.306255
\(233\) 3.14012 0.205716 0.102858 0.994696i \(-0.467201\pi\)
0.102858 + 0.994696i \(0.467201\pi\)
\(234\) 24.4453 1.59804
\(235\) −13.7647 −0.897912
\(236\) 12.6820 0.825525
\(237\) 6.75016 0.438470
\(238\) −10.3647 −0.671843
\(239\) 16.9961 1.09939 0.549694 0.835366i \(-0.314744\pi\)
0.549694 + 0.835366i \(0.314744\pi\)
\(240\) 6.84001 0.441521
\(241\) −23.5304 −1.51573 −0.757863 0.652414i \(-0.773756\pi\)
−0.757863 + 0.652414i \(0.773756\pi\)
\(242\) 10.7841 0.693231
\(243\) −19.6566 −1.26097
\(244\) −6.29902 −0.403254
\(245\) −34.2560 −2.18853
\(246\) 2.36708 0.150919
\(247\) 27.6658 1.76033
\(248\) 2.75066 0.174667
\(249\) 3.97370 0.251823
\(250\) −11.4676 −0.725275
\(251\) −1.14462 −0.0722479 −0.0361239 0.999347i \(-0.511501\pi\)
−0.0361239 + 0.999347i \(0.511501\pi\)
\(252\) 32.9411 2.07510
\(253\) −1.24334 −0.0781680
\(254\) 6.91452 0.433855
\(255\) 14.8598 0.930555
\(256\) 1.00000 0.0625000
\(257\) 15.7954 0.985288 0.492644 0.870231i \(-0.336031\pi\)
0.492644 + 0.870231i \(0.336031\pi\)
\(258\) 1.40432 0.0874290
\(259\) −16.6774 −1.03628
\(260\) 7.69478 0.477210
\(261\) −32.2081 −1.99363
\(262\) −2.61568 −0.161597
\(263\) −4.88652 −0.301316 −0.150658 0.988586i \(-0.548139\pi\)
−0.150658 + 0.988586i \(0.548139\pi\)
\(264\) 1.46220 0.0899921
\(265\) 11.3922 0.699816
\(266\) 37.2808 2.28583
\(267\) −32.5372 −1.99125
\(268\) −7.37205 −0.450320
\(269\) 5.45781 0.332769 0.166384 0.986061i \(-0.446791\pi\)
0.166384 + 0.986061i \(0.446791\pi\)
\(270\) −26.7074 −1.62536
\(271\) −2.93812 −0.178478 −0.0892391 0.996010i \(-0.528444\pi\)
−0.0892391 + 0.996010i \(0.528444\pi\)
\(272\) 2.17248 0.131726
\(273\) 53.1590 3.21733
\(274\) 2.09352 0.126474
\(275\) −0.128400 −0.00774278
\(276\) 8.42209 0.506950
\(277\) 9.57581 0.575354 0.287677 0.957727i \(-0.407117\pi\)
0.287677 + 0.957727i \(0.407117\pi\)
\(278\) −0.169351 −0.0101570
\(279\) −18.9921 −1.13703
\(280\) 10.3691 0.619669
\(281\) −29.9556 −1.78700 −0.893502 0.449059i \(-0.851759\pi\)
−0.893502 + 0.449059i \(0.851759\pi\)
\(282\) 19.9318 1.18692
\(283\) −11.7339 −0.697506 −0.348753 0.937215i \(-0.613395\pi\)
−0.348753 + 0.937215i \(0.613395\pi\)
\(284\) −10.7392 −0.637257
\(285\) −53.4492 −3.16606
\(286\) 1.64493 0.0972665
\(287\) 3.58835 0.211814
\(288\) −6.90459 −0.406857
\(289\) −12.2803 −0.722373
\(290\) −10.1383 −0.595342
\(291\) 17.6672 1.03567
\(292\) 14.9326 0.873866
\(293\) 2.11245 0.123411 0.0617053 0.998094i \(-0.480346\pi\)
0.0617053 + 0.998094i \(0.480346\pi\)
\(294\) 49.6040 2.89296
\(295\) −27.5629 −1.60477
\(296\) 3.49564 0.203180
\(297\) −5.70928 −0.331286
\(298\) −16.4336 −0.951970
\(299\) 9.47457 0.547928
\(300\) 0.869748 0.0502149
\(301\) 2.12886 0.122706
\(302\) −8.57860 −0.493643
\(303\) −15.4698 −0.888719
\(304\) −7.81420 −0.448175
\(305\) 13.6903 0.783902
\(306\) −15.0001 −0.857497
\(307\) −17.9660 −1.02538 −0.512688 0.858575i \(-0.671350\pi\)
−0.512688 + 0.858575i \(0.671350\pi\)
\(308\) 2.21661 0.126303
\(309\) 43.4046 2.46920
\(310\) −5.97826 −0.339542
\(311\) −11.6408 −0.660089 −0.330045 0.943965i \(-0.607064\pi\)
−0.330045 + 0.943965i \(0.607064\pi\)
\(312\) −11.1423 −0.630811
\(313\) −4.03950 −0.228326 −0.114163 0.993462i \(-0.536419\pi\)
−0.114163 + 0.993462i \(0.536419\pi\)
\(314\) 10.6449 0.600728
\(315\) −71.5940 −4.03387
\(316\) −2.14485 −0.120657
\(317\) 30.2160 1.69710 0.848549 0.529117i \(-0.177477\pi\)
0.848549 + 0.529117i \(0.177477\pi\)
\(318\) −16.4963 −0.925066
\(319\) −2.16728 −0.121345
\(320\) −2.17339 −0.121496
\(321\) −46.0808 −2.57198
\(322\) 12.7674 0.711499
\(323\) −16.9762 −0.944579
\(324\) 17.9596 0.997755
\(325\) 0.978438 0.0542740
\(326\) −8.77566 −0.486039
\(327\) 37.1324 2.05343
\(328\) −0.752133 −0.0415296
\(329\) 30.2155 1.66583
\(330\) −3.17793 −0.174939
\(331\) −9.39681 −0.516496 −0.258248 0.966079i \(-0.583145\pi\)
−0.258248 + 0.966079i \(0.583145\pi\)
\(332\) −1.26263 −0.0692960
\(333\) −24.1359 −1.32264
\(334\) 14.8025 0.809955
\(335\) 16.0224 0.875396
\(336\) −15.0148 −0.819123
\(337\) 36.6938 1.99884 0.999419 0.0340823i \(-0.0108508\pi\)
0.999419 + 0.0340823i \(0.0108508\pi\)
\(338\) 0.465237 0.0253055
\(339\) 52.6167 2.85775
\(340\) −4.72165 −0.256067
\(341\) −1.27798 −0.0692065
\(342\) 53.9538 2.91749
\(343\) 41.8004 2.25701
\(344\) −0.446218 −0.0240585
\(345\) −18.3045 −0.985482
\(346\) −11.2411 −0.604327
\(347\) 6.79205 0.364616 0.182308 0.983241i \(-0.441643\pi\)
0.182308 + 0.983241i \(0.441643\pi\)
\(348\) 14.6807 0.786966
\(349\) −23.8020 −1.27409 −0.637047 0.770825i \(-0.719844\pi\)
−0.637047 + 0.770825i \(0.719844\pi\)
\(350\) 1.31849 0.0704761
\(351\) 43.5063 2.32219
\(352\) −0.464609 −0.0247638
\(353\) −28.7773 −1.53166 −0.765830 0.643043i \(-0.777672\pi\)
−0.765830 + 0.643043i \(0.777672\pi\)
\(354\) 39.9121 2.12130
\(355\) 23.3406 1.23879
\(356\) 10.3386 0.547945
\(357\) −32.6193 −1.72639
\(358\) 8.63646 0.456451
\(359\) −10.3470 −0.546093 −0.273046 0.962001i \(-0.588031\pi\)
−0.273046 + 0.962001i \(0.588031\pi\)
\(360\) 15.0064 0.790906
\(361\) 42.0617 2.21377
\(362\) −9.03712 −0.474980
\(363\) 33.9394 1.78135
\(364\) −16.8911 −0.885336
\(365\) −32.4545 −1.69874
\(366\) −19.8240 −1.03622
\(367\) 16.8307 0.878557 0.439278 0.898351i \(-0.355234\pi\)
0.439278 + 0.898351i \(0.355234\pi\)
\(368\) −2.67609 −0.139501
\(369\) 5.19317 0.270345
\(370\) −7.59740 −0.394970
\(371\) −25.0074 −1.29832
\(372\) 8.65674 0.448831
\(373\) −21.1791 −1.09661 −0.548307 0.836277i \(-0.684727\pi\)
−0.548307 + 0.836277i \(0.684727\pi\)
\(374\) −1.00935 −0.0521924
\(375\) −36.0903 −1.86370
\(376\) −6.33329 −0.326614
\(377\) 16.5153 0.850579
\(378\) 58.6265 3.01542
\(379\) 14.5322 0.746469 0.373234 0.927737i \(-0.378249\pi\)
0.373234 + 0.927737i \(0.378249\pi\)
\(380\) 16.9833 0.871226
\(381\) 21.7611 1.11485
\(382\) 9.35417 0.478601
\(383\) 20.0820 1.02614 0.513070 0.858347i \(-0.328508\pi\)
0.513070 + 0.858347i \(0.328508\pi\)
\(384\) 3.14716 0.160603
\(385\) −4.81756 −0.245526
\(386\) 4.91824 0.250332
\(387\) 3.08095 0.156614
\(388\) −5.61370 −0.284992
\(389\) −17.2326 −0.873727 −0.436864 0.899528i \(-0.643911\pi\)
−0.436864 + 0.899528i \(0.643911\pi\)
\(390\) 24.2167 1.22626
\(391\) −5.81376 −0.294014
\(392\) −15.7615 −0.796077
\(393\) −8.23195 −0.415247
\(394\) −14.7015 −0.740649
\(395\) 4.66159 0.234550
\(396\) 3.20794 0.161205
\(397\) −4.12386 −0.206970 −0.103485 0.994631i \(-0.532999\pi\)
−0.103485 + 0.994631i \(0.532999\pi\)
\(398\) −10.5778 −0.530219
\(399\) 117.328 5.87377
\(400\) −0.276360 −0.0138180
\(401\) 9.40494 0.469660 0.234830 0.972036i \(-0.424547\pi\)
0.234830 + 0.972036i \(0.424547\pi\)
\(402\) −23.2010 −1.15716
\(403\) 9.73855 0.485112
\(404\) 4.91550 0.244555
\(405\) −39.0332 −1.93958
\(406\) 22.2550 1.10450
\(407\) −1.62411 −0.0805040
\(408\) 6.83713 0.338488
\(409\) 21.4215 1.05923 0.529613 0.848240i \(-0.322337\pi\)
0.529613 + 0.848240i \(0.322337\pi\)
\(410\) 1.63468 0.0807311
\(411\) 6.58863 0.324993
\(412\) −13.7917 −0.679468
\(413\) 60.5044 2.97723
\(414\) 18.4773 0.908111
\(415\) 2.74420 0.134707
\(416\) 3.54045 0.173585
\(417\) −0.532974 −0.0260999
\(418\) 3.63055 0.177576
\(419\) −5.82387 −0.284515 −0.142257 0.989830i \(-0.545436\pi\)
−0.142257 + 0.989830i \(0.545436\pi\)
\(420\) 32.6330 1.59233
\(421\) 28.3087 1.37968 0.689841 0.723961i \(-0.257680\pi\)
0.689841 + 0.723961i \(0.257680\pi\)
\(422\) 10.8499 0.528165
\(423\) 43.7288 2.12616
\(424\) 5.24165 0.254557
\(425\) −0.600386 −0.0291230
\(426\) −33.7981 −1.63752
\(427\) −30.0520 −1.45432
\(428\) 14.6420 0.707750
\(429\) 5.17684 0.249940
\(430\) 0.969807 0.0467683
\(431\) −36.3042 −1.74871 −0.874356 0.485285i \(-0.838716\pi\)
−0.874356 + 0.485285i \(0.838716\pi\)
\(432\) −12.2884 −0.591224
\(433\) 15.3140 0.735944 0.367972 0.929837i \(-0.380052\pi\)
0.367972 + 0.929837i \(0.380052\pi\)
\(434\) 13.1231 0.629929
\(435\) −31.9069 −1.52982
\(436\) −11.7987 −0.565057
\(437\) 20.9115 1.00033
\(438\) 46.9953 2.24552
\(439\) 19.2649 0.919465 0.459732 0.888057i \(-0.347945\pi\)
0.459732 + 0.888057i \(0.347945\pi\)
\(440\) 1.00978 0.0481393
\(441\) 108.827 5.18223
\(442\) 7.69154 0.365849
\(443\) 15.0494 0.715019 0.357509 0.933910i \(-0.383626\pi\)
0.357509 + 0.933910i \(0.383626\pi\)
\(444\) 11.0013 0.522099
\(445\) −22.4699 −1.06517
\(446\) −22.6580 −1.07289
\(447\) −51.7190 −2.44622
\(448\) 4.77090 0.225404
\(449\) −27.0747 −1.27773 −0.638867 0.769317i \(-0.720597\pi\)
−0.638867 + 0.769317i \(0.720597\pi\)
\(450\) 1.90815 0.0899512
\(451\) 0.349448 0.0164549
\(452\) −16.7188 −0.786387
\(453\) −26.9982 −1.26848
\(454\) −7.21310 −0.338528
\(455\) 36.7111 1.72104
\(456\) −24.5925 −1.15165
\(457\) −35.3447 −1.65336 −0.826678 0.562675i \(-0.809772\pi\)
−0.826678 + 0.562675i \(0.809772\pi\)
\(458\) −22.7121 −1.06127
\(459\) −26.6962 −1.24607
\(460\) 5.81621 0.271182
\(461\) −28.0998 −1.30874 −0.654370 0.756175i \(-0.727066\pi\)
−0.654370 + 0.756175i \(0.727066\pi\)
\(462\) 6.97601 0.324553
\(463\) −34.2886 −1.59353 −0.796764 0.604290i \(-0.793457\pi\)
−0.796764 + 0.604290i \(0.793457\pi\)
\(464\) −4.66474 −0.216555
\(465\) −18.8145 −0.872502
\(466\) −3.14012 −0.145463
\(467\) 35.1965 1.62870 0.814350 0.580375i \(-0.197094\pi\)
0.814350 + 0.580375i \(0.197094\pi\)
\(468\) −24.4453 −1.12999
\(469\) −35.1713 −1.62406
\(470\) 13.7647 0.634920
\(471\) 33.5013 1.54366
\(472\) −12.6820 −0.583734
\(473\) 0.207317 0.00953245
\(474\) −6.75016 −0.310045
\(475\) 2.15953 0.0990862
\(476\) 10.3647 0.475064
\(477\) −36.1915 −1.65709
\(478\) −16.9961 −0.777384
\(479\) 7.85768 0.359027 0.179513 0.983756i \(-0.442548\pi\)
0.179513 + 0.983756i \(0.442548\pi\)
\(480\) −6.84001 −0.312202
\(481\) 12.3761 0.564302
\(482\) 23.5304 1.07178
\(483\) 40.1810 1.82830
\(484\) −10.7841 −0.490188
\(485\) 12.2008 0.554008
\(486\) 19.6566 0.891640
\(487\) 13.9859 0.633761 0.316880 0.948465i \(-0.397365\pi\)
0.316880 + 0.948465i \(0.397365\pi\)
\(488\) 6.29902 0.285143
\(489\) −27.6184 −1.24895
\(490\) 34.2560 1.54753
\(491\) 18.0688 0.815433 0.407717 0.913108i \(-0.366325\pi\)
0.407717 + 0.913108i \(0.366325\pi\)
\(492\) −2.36708 −0.106716
\(493\) −10.1340 −0.456414
\(494\) −27.6658 −1.24474
\(495\) −6.97211 −0.313373
\(496\) −2.75066 −0.123508
\(497\) −51.2359 −2.29824
\(498\) −3.97370 −0.178066
\(499\) −32.1063 −1.43728 −0.718639 0.695384i \(-0.755234\pi\)
−0.718639 + 0.695384i \(0.755234\pi\)
\(500\) 11.4676 0.512847
\(501\) 46.5857 2.08129
\(502\) 1.14462 0.0510870
\(503\) 25.3731 1.13133 0.565664 0.824636i \(-0.308620\pi\)
0.565664 + 0.824636i \(0.308620\pi\)
\(504\) −32.9411 −1.46731
\(505\) −10.6833 −0.475401
\(506\) 1.24334 0.0552732
\(507\) 1.46417 0.0650262
\(508\) −6.91452 −0.306782
\(509\) −19.2114 −0.851530 −0.425765 0.904834i \(-0.639995\pi\)
−0.425765 + 0.904834i \(0.639995\pi\)
\(510\) −14.8598 −0.658001
\(511\) 71.2421 3.15157
\(512\) −1.00000 −0.0441942
\(513\) 96.0236 4.23955
\(514\) −15.7954 −0.696704
\(515\) 29.9748 1.32085
\(516\) −1.40432 −0.0618216
\(517\) 2.94251 0.129411
\(518\) 16.6774 0.732761
\(519\) −35.3776 −1.55290
\(520\) −7.69478 −0.337439
\(521\) 28.7275 1.25858 0.629288 0.777172i \(-0.283347\pi\)
0.629288 + 0.777172i \(0.283347\pi\)
\(522\) 32.2081 1.40971
\(523\) 0.223468 0.00977157 0.00488579 0.999988i \(-0.498445\pi\)
0.00488579 + 0.999988i \(0.498445\pi\)
\(524\) 2.61568 0.114267
\(525\) 4.14949 0.181098
\(526\) 4.88652 0.213062
\(527\) −5.97574 −0.260307
\(528\) −1.46220 −0.0636340
\(529\) −15.8385 −0.688631
\(530\) −11.3922 −0.494844
\(531\) 87.5637 3.79994
\(532\) −37.2808 −1.61633
\(533\) −2.66289 −0.115342
\(534\) 32.5372 1.40802
\(535\) −31.8229 −1.37582
\(536\) 7.37205 0.318424
\(537\) 27.1803 1.17292
\(538\) −5.45781 −0.235303
\(539\) 7.32295 0.315422
\(540\) 26.7074 1.14930
\(541\) −20.2502 −0.870626 −0.435313 0.900279i \(-0.643362\pi\)
−0.435313 + 0.900279i \(0.643362\pi\)
\(542\) 2.93812 0.126203
\(543\) −28.4412 −1.22053
\(544\) −2.17248 −0.0931442
\(545\) 25.6433 1.09844
\(546\) −53.1590 −2.27500
\(547\) 35.0313 1.49783 0.748914 0.662667i \(-0.230575\pi\)
0.748914 + 0.662667i \(0.230575\pi\)
\(548\) −2.09352 −0.0894307
\(549\) −43.4922 −1.85620
\(550\) 0.128400 0.00547497
\(551\) 36.4512 1.55287
\(552\) −8.42209 −0.358468
\(553\) −10.2329 −0.435145
\(554\) −9.57581 −0.406837
\(555\) −23.9102 −1.01493
\(556\) 0.169351 0.00718208
\(557\) 25.8517 1.09537 0.547686 0.836684i \(-0.315509\pi\)
0.547686 + 0.836684i \(0.315509\pi\)
\(558\) 18.9921 0.804002
\(559\) −1.57981 −0.0668189
\(560\) −10.3691 −0.438172
\(561\) −3.17659 −0.134116
\(562\) 29.9556 1.26360
\(563\) 7.04696 0.296994 0.148497 0.988913i \(-0.452556\pi\)
0.148497 + 0.988913i \(0.452556\pi\)
\(564\) −19.9318 −0.839282
\(565\) 36.3365 1.52869
\(566\) 11.7339 0.493212
\(567\) 85.6834 3.59837
\(568\) 10.7392 0.450609
\(569\) −21.0373 −0.881929 −0.440964 0.897525i \(-0.645363\pi\)
−0.440964 + 0.897525i \(0.645363\pi\)
\(570\) 53.4492 2.23874
\(571\) −19.3157 −0.808336 −0.404168 0.914685i \(-0.632439\pi\)
−0.404168 + 0.914685i \(0.632439\pi\)
\(572\) −1.64493 −0.0687778
\(573\) 29.4390 1.22983
\(574\) −3.58835 −0.149775
\(575\) 0.739566 0.0308420
\(576\) 6.90459 0.287691
\(577\) −24.4322 −1.01713 −0.508564 0.861024i \(-0.669823\pi\)
−0.508564 + 0.861024i \(0.669823\pi\)
\(578\) 12.2803 0.510795
\(579\) 15.4785 0.643264
\(580\) 10.1383 0.420971
\(581\) −6.02390 −0.249914
\(582\) −17.6672 −0.732328
\(583\) −2.43532 −0.100861
\(584\) −14.9326 −0.617916
\(585\) 53.1293 2.19663
\(586\) −2.11245 −0.0872644
\(587\) 7.87924 0.325211 0.162606 0.986691i \(-0.448010\pi\)
0.162606 + 0.986691i \(0.448010\pi\)
\(588\) −49.6040 −2.04563
\(589\) 21.4942 0.885652
\(590\) 27.5629 1.13475
\(591\) −46.2678 −1.90320
\(592\) −3.49564 −0.143670
\(593\) 25.6306 1.05252 0.526261 0.850323i \(-0.323594\pi\)
0.526261 + 0.850323i \(0.323594\pi\)
\(594\) 5.70928 0.234255
\(595\) −22.5265 −0.923498
\(596\) 16.4336 0.673145
\(597\) −33.2901 −1.36247
\(598\) −9.47457 −0.387444
\(599\) 41.5720 1.69859 0.849294 0.527921i \(-0.177028\pi\)
0.849294 + 0.527921i \(0.177028\pi\)
\(600\) −0.869748 −0.0355073
\(601\) −31.2181 −1.27341 −0.636707 0.771106i \(-0.719704\pi\)
−0.636707 + 0.771106i \(0.719704\pi\)
\(602\) −2.12886 −0.0867660
\(603\) −50.9010 −2.07285
\(604\) 8.57860 0.349058
\(605\) 23.4382 0.952897
\(606\) 15.4698 0.628419
\(607\) 46.4830 1.88669 0.943344 0.331816i \(-0.107661\pi\)
0.943344 + 0.331816i \(0.107661\pi\)
\(608\) 7.81420 0.316908
\(609\) 70.0400 2.83816
\(610\) −13.6903 −0.554302
\(611\) −22.4227 −0.907124
\(612\) 15.0001 0.606342
\(613\) 24.7412 0.999288 0.499644 0.866231i \(-0.333464\pi\)
0.499644 + 0.866231i \(0.333464\pi\)
\(614\) 17.9660 0.725051
\(615\) 5.14459 0.207450
\(616\) −2.21661 −0.0893096
\(617\) 17.0754 0.687428 0.343714 0.939074i \(-0.388315\pi\)
0.343714 + 0.939074i \(0.388315\pi\)
\(618\) −43.4046 −1.74599
\(619\) −18.3828 −0.738869 −0.369434 0.929257i \(-0.620449\pi\)
−0.369434 + 0.929257i \(0.620449\pi\)
\(620\) 5.97826 0.240093
\(621\) 32.8848 1.31962
\(622\) 11.6408 0.466753
\(623\) 49.3245 1.97615
\(624\) 11.1423 0.446050
\(625\) −23.5418 −0.941673
\(626\) 4.03950 0.161451
\(627\) 11.4259 0.456307
\(628\) −10.6449 −0.424779
\(629\) −7.59420 −0.302800
\(630\) 71.5940 2.85237
\(631\) 37.7998 1.50479 0.752393 0.658714i \(-0.228899\pi\)
0.752393 + 0.658714i \(0.228899\pi\)
\(632\) 2.14485 0.0853174
\(633\) 34.1463 1.35719
\(634\) −30.2160 −1.20003
\(635\) 15.0280 0.596367
\(636\) 16.4963 0.654121
\(637\) −55.8028 −2.21099
\(638\) 2.16728 0.0858035
\(639\) −74.1501 −2.93333
\(640\) 2.17339 0.0859109
\(641\) 16.1839 0.639226 0.319613 0.947548i \(-0.396447\pi\)
0.319613 + 0.947548i \(0.396447\pi\)
\(642\) 46.0808 1.81866
\(643\) 29.6242 1.16826 0.584132 0.811659i \(-0.301435\pi\)
0.584132 + 0.811659i \(0.301435\pi\)
\(644\) −12.7674 −0.503106
\(645\) 3.05213 0.120178
\(646\) 16.9762 0.667919
\(647\) −7.93801 −0.312075 −0.156038 0.987751i \(-0.549872\pi\)
−0.156038 + 0.987751i \(0.549872\pi\)
\(648\) −17.9596 −0.705519
\(649\) 5.89216 0.231287
\(650\) −0.978438 −0.0383775
\(651\) 41.3005 1.61869
\(652\) 8.77566 0.343681
\(653\) 4.28596 0.167723 0.0838613 0.996477i \(-0.473275\pi\)
0.0838613 + 0.996477i \(0.473275\pi\)
\(654\) −37.1324 −1.45199
\(655\) −5.68490 −0.222128
\(656\) 0.752133 0.0293658
\(657\) 103.104 4.02246
\(658\) −30.2155 −1.17792
\(659\) 15.6395 0.609227 0.304614 0.952476i \(-0.401473\pi\)
0.304614 + 0.952476i \(0.401473\pi\)
\(660\) 3.17793 0.123701
\(661\) −42.2031 −1.64151 −0.820755 0.571280i \(-0.806447\pi\)
−0.820755 + 0.571280i \(0.806447\pi\)
\(662\) 9.39681 0.365218
\(663\) 24.2065 0.940102
\(664\) 1.26263 0.0489997
\(665\) 81.0258 3.14205
\(666\) 24.1359 0.935249
\(667\) 12.4833 0.483355
\(668\) −14.8025 −0.572725
\(669\) −71.3083 −2.75694
\(670\) −16.0224 −0.618998
\(671\) −2.92659 −0.112980
\(672\) 15.0148 0.579208
\(673\) −9.29626 −0.358344 −0.179172 0.983818i \(-0.557342\pi\)
−0.179172 + 0.983818i \(0.557342\pi\)
\(674\) −36.6938 −1.41339
\(675\) 3.39601 0.130712
\(676\) −0.465237 −0.0178937
\(677\) 30.0770 1.15595 0.577976 0.816054i \(-0.303843\pi\)
0.577976 + 0.816054i \(0.303843\pi\)
\(678\) −52.6167 −2.02073
\(679\) −26.7824 −1.02781
\(680\) 4.72165 0.181067
\(681\) −22.7007 −0.869895
\(682\) 1.27798 0.0489364
\(683\) −11.6634 −0.446286 −0.223143 0.974786i \(-0.571632\pi\)
−0.223143 + 0.974786i \(0.571632\pi\)
\(684\) −53.9538 −2.06298
\(685\) 4.55004 0.173848
\(686\) −41.8004 −1.59595
\(687\) −71.4786 −2.72708
\(688\) 0.446218 0.0170119
\(689\) 18.5578 0.706995
\(690\) 18.3045 0.696841
\(691\) 5.73643 0.218224 0.109112 0.994029i \(-0.465199\pi\)
0.109112 + 0.994029i \(0.465199\pi\)
\(692\) 11.2411 0.427324
\(693\) 15.3048 0.581380
\(694\) −6.79205 −0.257823
\(695\) −0.368066 −0.0139616
\(696\) −14.6807 −0.556469
\(697\) 1.63399 0.0618918
\(698\) 23.8020 0.900921
\(699\) −9.88244 −0.373788
\(700\) −1.31849 −0.0498341
\(701\) 20.5718 0.776986 0.388493 0.921452i \(-0.372996\pi\)
0.388493 + 0.921452i \(0.372996\pi\)
\(702\) −43.5063 −1.64204
\(703\) 27.3156 1.03023
\(704\) 0.464609 0.0175106
\(705\) 43.3197 1.63152
\(706\) 28.7773 1.08305
\(707\) 23.4514 0.881979
\(708\) −39.9121 −1.49999
\(709\) −45.7623 −1.71864 −0.859320 0.511438i \(-0.829113\pi\)
−0.859320 + 0.511438i \(0.829113\pi\)
\(710\) −23.3406 −0.875957
\(711\) −14.8093 −0.555391
\(712\) −10.3386 −0.387456
\(713\) 7.36101 0.275672
\(714\) 32.6193 1.22075
\(715\) 3.57507 0.133700
\(716\) −8.63646 −0.322760
\(717\) −53.4894 −1.99760
\(718\) 10.3470 0.386146
\(719\) 21.0808 0.786180 0.393090 0.919500i \(-0.371406\pi\)
0.393090 + 0.919500i \(0.371406\pi\)
\(720\) −15.0064 −0.559255
\(721\) −65.7988 −2.45048
\(722\) −42.0617 −1.56537
\(723\) 74.0538 2.75409
\(724\) 9.03712 0.335862
\(725\) 1.28915 0.0478778
\(726\) −33.9394 −1.25961
\(727\) 25.3964 0.941902 0.470951 0.882159i \(-0.343911\pi\)
0.470951 + 0.882159i \(0.343911\pi\)
\(728\) 16.8911 0.626027
\(729\) 7.98350 0.295685
\(730\) 32.4545 1.20119
\(731\) 0.969399 0.0358545
\(732\) 19.8240 0.732716
\(733\) 40.0778 1.48031 0.740153 0.672438i \(-0.234753\pi\)
0.740153 + 0.672438i \(0.234753\pi\)
\(734\) −16.8307 −0.621233
\(735\) 107.809 3.97659
\(736\) 2.67609 0.0986421
\(737\) −3.42513 −0.126166
\(738\) −5.19317 −0.191163
\(739\) 26.6738 0.981211 0.490606 0.871382i \(-0.336776\pi\)
0.490606 + 0.871382i \(0.336776\pi\)
\(740\) 7.59740 0.279286
\(741\) −87.0684 −3.19854
\(742\) 25.0074 0.918051
\(743\) 29.5772 1.08508 0.542541 0.840029i \(-0.317462\pi\)
0.542541 + 0.840029i \(0.317462\pi\)
\(744\) −8.65674 −0.317371
\(745\) −35.7166 −1.30855
\(746\) 21.1791 0.775423
\(747\) −8.71796 −0.318974
\(748\) 1.00935 0.0369056
\(749\) 69.8558 2.55247
\(750\) 36.0903 1.31783
\(751\) −6.76616 −0.246901 −0.123450 0.992351i \(-0.539396\pi\)
−0.123450 + 0.992351i \(0.539396\pi\)
\(752\) 6.33329 0.230951
\(753\) 3.60230 0.131275
\(754\) −16.5153 −0.601450
\(755\) −18.6447 −0.678549
\(756\) −58.6265 −2.13223
\(757\) 54.1584 1.96842 0.984210 0.177006i \(-0.0566413\pi\)
0.984210 + 0.177006i \(0.0566413\pi\)
\(758\) −14.5322 −0.527833
\(759\) 3.91298 0.142032
\(760\) −16.9833 −0.616050
\(761\) −9.32399 −0.337995 −0.168997 0.985617i \(-0.554053\pi\)
−0.168997 + 0.985617i \(0.554053\pi\)
\(762\) −21.7611 −0.788320
\(763\) −56.2906 −2.03786
\(764\) −9.35417 −0.338422
\(765\) −32.6010 −1.17869
\(766\) −20.0820 −0.725591
\(767\) −44.8998 −1.62124
\(768\) −3.14716 −0.113563
\(769\) −32.8772 −1.18558 −0.592791 0.805356i \(-0.701974\pi\)
−0.592791 + 0.805356i \(0.701974\pi\)
\(770\) 4.81756 0.173613
\(771\) −49.7105 −1.79028
\(772\) −4.91824 −0.177012
\(773\) 16.3598 0.588423 0.294211 0.955740i \(-0.404943\pi\)
0.294211 + 0.955740i \(0.404943\pi\)
\(774\) −3.08095 −0.110743
\(775\) 0.760171 0.0273062
\(776\) 5.61370 0.201520
\(777\) 52.4862 1.88293
\(778\) 17.2326 0.617818
\(779\) −5.87731 −0.210577
\(780\) −24.2167 −0.867096
\(781\) −4.98955 −0.178540
\(782\) 5.81376 0.207899
\(783\) 57.3220 2.04852
\(784\) 15.7615 0.562911
\(785\) 23.1356 0.825746
\(786\) 8.23195 0.293624
\(787\) −3.75331 −0.133791 −0.0668956 0.997760i \(-0.521309\pi\)
−0.0668956 + 0.997760i \(0.521309\pi\)
\(788\) 14.7015 0.523718
\(789\) 15.3786 0.547494
\(790\) −4.66159 −0.165852
\(791\) −79.7638 −2.83607
\(792\) −3.20794 −0.113989
\(793\) 22.3014 0.791944
\(794\) 4.12386 0.146350
\(795\) −35.8529 −1.27157
\(796\) 10.5778 0.374922
\(797\) −22.0905 −0.782485 −0.391243 0.920288i \(-0.627955\pi\)
−0.391243 + 0.920288i \(0.627955\pi\)
\(798\) −117.328 −4.15338
\(799\) 13.7589 0.486756
\(800\) 0.276360 0.00977081
\(801\) 71.3839 2.52223
\(802\) −9.40494 −0.332100
\(803\) 6.93784 0.244831
\(804\) 23.2010 0.818236
\(805\) 27.7486 0.978008
\(806\) −9.73855 −0.343026
\(807\) −17.1766 −0.604644
\(808\) −4.91550 −0.172927
\(809\) −1.98014 −0.0696181 −0.0348090 0.999394i \(-0.511082\pi\)
−0.0348090 + 0.999394i \(0.511082\pi\)
\(810\) 39.0332 1.37149
\(811\) −7.90446 −0.277563 −0.138782 0.990323i \(-0.544319\pi\)
−0.138782 + 0.990323i \(0.544319\pi\)
\(812\) −22.2550 −0.780998
\(813\) 9.24672 0.324297
\(814\) 1.62411 0.0569249
\(815\) −19.0730 −0.668097
\(816\) −6.83713 −0.239347
\(817\) −3.48684 −0.121989
\(818\) −21.4215 −0.748986
\(819\) −116.626 −4.07525
\(820\) −1.63468 −0.0570855
\(821\) −6.71468 −0.234344 −0.117172 0.993112i \(-0.537383\pi\)
−0.117172 + 0.993112i \(0.537383\pi\)
\(822\) −6.58863 −0.229805
\(823\) −0.808931 −0.0281976 −0.0140988 0.999901i \(-0.504488\pi\)
−0.0140988 + 0.999901i \(0.504488\pi\)
\(824\) 13.7917 0.480456
\(825\) 0.404093 0.0140687
\(826\) −60.5044 −2.10522
\(827\) 17.7160 0.616045 0.308022 0.951379i \(-0.400333\pi\)
0.308022 + 0.951379i \(0.400333\pi\)
\(828\) −18.4773 −0.642132
\(829\) −23.6672 −0.821994 −0.410997 0.911637i \(-0.634819\pi\)
−0.410997 + 0.911637i \(0.634819\pi\)
\(830\) −2.74420 −0.0952525
\(831\) −30.1366 −1.04543
\(832\) −3.54045 −0.122743
\(833\) 34.2415 1.18640
\(834\) 0.532974 0.0184554
\(835\) 32.1716 1.11334
\(836\) −3.63055 −0.125565
\(837\) 33.8010 1.16833
\(838\) 5.82387 0.201182
\(839\) −19.5659 −0.675491 −0.337746 0.941237i \(-0.609664\pi\)
−0.337746 + 0.941237i \(0.609664\pi\)
\(840\) −32.6330 −1.12595
\(841\) −7.24020 −0.249662
\(842\) −28.3087 −0.975583
\(843\) 94.2751 3.24701
\(844\) −10.8499 −0.373469
\(845\) 1.01114 0.0347844
\(846\) −43.7288 −1.50343
\(847\) −51.4501 −1.76785
\(848\) −5.24165 −0.179999
\(849\) 36.9283 1.26738
\(850\) 0.600386 0.0205931
\(851\) 9.35466 0.320674
\(852\) 33.7981 1.15790
\(853\) 28.7187 0.983309 0.491655 0.870790i \(-0.336392\pi\)
0.491655 + 0.870790i \(0.336392\pi\)
\(854\) 30.0520 1.02836
\(855\) 117.263 4.01031
\(856\) −14.6420 −0.500455
\(857\) −32.5695 −1.11255 −0.556276 0.830997i \(-0.687770\pi\)
−0.556276 + 0.830997i \(0.687770\pi\)
\(858\) −5.17684 −0.176734
\(859\) 13.7296 0.468448 0.234224 0.972183i \(-0.424745\pi\)
0.234224 + 0.972183i \(0.424745\pi\)
\(860\) −0.969807 −0.0330702
\(861\) −11.2931 −0.384868
\(862\) 36.3042 1.23653
\(863\) −16.3660 −0.557104 −0.278552 0.960421i \(-0.589855\pi\)
−0.278552 + 0.960421i \(0.589855\pi\)
\(864\) 12.2884 0.418058
\(865\) −24.4314 −0.830693
\(866\) −15.3140 −0.520391
\(867\) 38.6481 1.31256
\(868\) −13.1231 −0.445427
\(869\) −0.996516 −0.0338045
\(870\) 31.9069 1.08174
\(871\) 26.1004 0.884377
\(872\) 11.7987 0.399555
\(873\) −38.7603 −1.31184
\(874\) −20.9115 −0.707343
\(875\) 54.7108 1.84956
\(876\) −46.9953 −1.58782
\(877\) −41.0199 −1.38514 −0.692572 0.721349i \(-0.743522\pi\)
−0.692572 + 0.721349i \(0.743522\pi\)
\(878\) −19.2649 −0.650160
\(879\) −6.64820 −0.224238
\(880\) −1.00978 −0.0340397
\(881\) −37.5027 −1.26350 −0.631749 0.775173i \(-0.717663\pi\)
−0.631749 + 0.775173i \(0.717663\pi\)
\(882\) −108.827 −3.66439
\(883\) 28.2312 0.950057 0.475028 0.879970i \(-0.342438\pi\)
0.475028 + 0.879970i \(0.342438\pi\)
\(884\) −7.69154 −0.258695
\(885\) 86.7447 2.91589
\(886\) −15.0494 −0.505595
\(887\) −35.0722 −1.17761 −0.588804 0.808276i \(-0.700401\pi\)
−0.588804 + 0.808276i \(0.700401\pi\)
\(888\) −11.0013 −0.369180
\(889\) −32.9885 −1.10640
\(890\) 22.4699 0.753192
\(891\) 8.34419 0.279541
\(892\) 22.6580 0.758646
\(893\) −49.4896 −1.65611
\(894\) 51.7190 1.72974
\(895\) 18.7704 0.627426
\(896\) −4.77090 −0.159385
\(897\) −29.8179 −0.995592
\(898\) 27.0747 0.903495
\(899\) 12.8311 0.427941
\(900\) −1.90815 −0.0636051
\(901\) −11.3874 −0.379368
\(902\) −0.349448 −0.0116353
\(903\) −6.69986 −0.222957
\(904\) 16.7188 0.556059
\(905\) −19.6412 −0.652896
\(906\) 26.9982 0.896954
\(907\) −5.26669 −0.174877 −0.0874387 0.996170i \(-0.527868\pi\)
−0.0874387 + 0.996170i \(0.527868\pi\)
\(908\) 7.21310 0.239375
\(909\) 33.9395 1.12570
\(910\) −36.7111 −1.21696
\(911\) 57.5271 1.90596 0.952980 0.303035i \(-0.0979998\pi\)
0.952980 + 0.303035i \(0.0979998\pi\)
\(912\) 24.5925 0.814339
\(913\) −0.586631 −0.0194147
\(914\) 35.3447 1.16910
\(915\) −43.0854 −1.42436
\(916\) 22.7121 0.750430
\(917\) 12.4792 0.412098
\(918\) 26.6962 0.881105
\(919\) 33.4468 1.10331 0.551655 0.834073i \(-0.313997\pi\)
0.551655 + 0.834073i \(0.313997\pi\)
\(920\) −5.81621 −0.191755
\(921\) 56.5419 1.86312
\(922\) 28.0998 0.925418
\(923\) 38.0217 1.25150
\(924\) −6.97601 −0.229494
\(925\) 0.966055 0.0317637
\(926\) 34.2886 1.12679
\(927\) −95.2260 −3.12763
\(928\) 4.66474 0.153128
\(929\) 11.5284 0.378233 0.189117 0.981955i \(-0.439438\pi\)
0.189117 + 0.981955i \(0.439438\pi\)
\(930\) 18.8145 0.616952
\(931\) −123.164 −4.03652
\(932\) 3.14012 0.102858
\(933\) 36.6354 1.19939
\(934\) −35.1965 −1.15166
\(935\) −2.19372 −0.0717424
\(936\) 24.4453 0.799021
\(937\) 3.19135 0.104257 0.0521284 0.998640i \(-0.483399\pi\)
0.0521284 + 0.998640i \(0.483399\pi\)
\(938\) 35.1713 1.14839
\(939\) 12.7129 0.414871
\(940\) −13.7647 −0.448956
\(941\) 12.9938 0.423586 0.211793 0.977315i \(-0.432070\pi\)
0.211793 + 0.977315i \(0.432070\pi\)
\(942\) −33.5013 −1.09153
\(943\) −2.01278 −0.0655451
\(944\) 12.6820 0.412763
\(945\) 127.419 4.14493
\(946\) −0.207317 −0.00674046
\(947\) 31.2482 1.01543 0.507715 0.861525i \(-0.330490\pi\)
0.507715 + 0.861525i \(0.330490\pi\)
\(948\) 6.75016 0.219235
\(949\) −52.8682 −1.71617
\(950\) −2.15953 −0.0700645
\(951\) −95.0943 −3.08364
\(952\) −10.3647 −0.335921
\(953\) −0.739162 −0.0239438 −0.0119719 0.999928i \(-0.503811\pi\)
−0.0119719 + 0.999928i \(0.503811\pi\)
\(954\) 36.1915 1.17174
\(955\) 20.3303 0.657873
\(956\) 16.9961 0.549694
\(957\) 6.82077 0.220484
\(958\) −7.85768 −0.253870
\(959\) −9.98798 −0.322529
\(960\) 6.84001 0.220760
\(961\) −23.4339 −0.755932
\(962\) −12.3761 −0.399022
\(963\) 101.097 3.25781
\(964\) −23.5304 −0.757863
\(965\) 10.6893 0.344100
\(966\) −40.1810 −1.29280
\(967\) 5.28271 0.169881 0.0849403 0.996386i \(-0.472930\pi\)
0.0849403 + 0.996386i \(0.472930\pi\)
\(968\) 10.7841 0.346615
\(969\) 53.4267 1.71631
\(970\) −12.2008 −0.391743
\(971\) 19.9107 0.638963 0.319482 0.947592i \(-0.396491\pi\)
0.319482 + 0.947592i \(0.396491\pi\)
\(972\) −19.6566 −0.630484
\(973\) 0.807957 0.0259019
\(974\) −13.9859 −0.448137
\(975\) −3.07930 −0.0986165
\(976\) −6.29902 −0.201627
\(977\) −33.3537 −1.06708 −0.533540 0.845775i \(-0.679139\pi\)
−0.533540 + 0.845775i \(0.679139\pi\)
\(978\) 27.6184 0.883138
\(979\) 4.80342 0.153518
\(980\) −34.2560 −1.09427
\(981\) −81.4654 −2.60099
\(982\) −18.0688 −0.576598
\(983\) −10.1301 −0.323099 −0.161550 0.986865i \(-0.551649\pi\)
−0.161550 + 0.986865i \(0.551649\pi\)
\(984\) 2.36708 0.0754597
\(985\) −31.9521 −1.01808
\(986\) 10.1340 0.322734
\(987\) −95.0929 −3.02684
\(988\) 27.6658 0.880165
\(989\) −1.19412 −0.0379709
\(990\) 6.97211 0.221588
\(991\) 11.6121 0.368870 0.184435 0.982845i \(-0.440954\pi\)
0.184435 + 0.982845i \(0.440954\pi\)
\(992\) 2.75066 0.0873334
\(993\) 29.5732 0.938478
\(994\) 51.2359 1.62510
\(995\) −22.9898 −0.728826
\(996\) 3.97370 0.125912
\(997\) 7.08944 0.224525 0.112262 0.993679i \(-0.464190\pi\)
0.112262 + 0.993679i \(0.464190\pi\)
\(998\) 32.1063 1.01631
\(999\) 42.9556 1.35906
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 \(a_p\))