Properties

Label 8042.2.a.a.1.5
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.01737 q^{3} +1.00000 q^{4} -1.22094 q^{5} -3.01737 q^{6} +2.53637 q^{7} +1.00000 q^{8} +6.10451 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.01737 q^{3} +1.00000 q^{4} -1.22094 q^{5} -3.01737 q^{6} +2.53637 q^{7} +1.00000 q^{8} +6.10451 q^{9} -1.22094 q^{10} +0.137455 q^{11} -3.01737 q^{12} -0.806951 q^{13} +2.53637 q^{14} +3.68404 q^{15} +1.00000 q^{16} +2.15852 q^{17} +6.10451 q^{18} +1.07604 q^{19} -1.22094 q^{20} -7.65317 q^{21} +0.137455 q^{22} -5.61126 q^{23} -3.01737 q^{24} -3.50930 q^{25} -0.806951 q^{26} -9.36747 q^{27} +2.53637 q^{28} +3.70442 q^{29} +3.68404 q^{30} -1.71836 q^{31} +1.00000 q^{32} -0.414753 q^{33} +2.15852 q^{34} -3.09677 q^{35} +6.10451 q^{36} -3.29300 q^{37} +1.07604 q^{38} +2.43487 q^{39} -1.22094 q^{40} -7.64932 q^{41} -7.65317 q^{42} +5.20520 q^{43} +0.137455 q^{44} -7.45327 q^{45} -5.61126 q^{46} +4.92416 q^{47} -3.01737 q^{48} -0.566819 q^{49} -3.50930 q^{50} -6.51306 q^{51} -0.806951 q^{52} -1.93351 q^{53} -9.36747 q^{54} -0.167825 q^{55} +2.53637 q^{56} -3.24682 q^{57} +3.70442 q^{58} -11.7080 q^{59} +3.68404 q^{60} -0.669111 q^{61} -1.71836 q^{62} +15.4833 q^{63} +1.00000 q^{64} +0.985242 q^{65} -0.414753 q^{66} +5.09018 q^{67} +2.15852 q^{68} +16.9312 q^{69} -3.09677 q^{70} -7.94119 q^{71} +6.10451 q^{72} +2.48803 q^{73} -3.29300 q^{74} +10.5888 q^{75} +1.07604 q^{76} +0.348637 q^{77} +2.43487 q^{78} -13.0996 q^{79} -1.22094 q^{80} +9.95156 q^{81} -7.64932 q^{82} +4.45477 q^{83} -7.65317 q^{84} -2.63543 q^{85} +5.20520 q^{86} -11.1776 q^{87} +0.137455 q^{88} +12.1306 q^{89} -7.45327 q^{90} -2.04673 q^{91} -5.61126 q^{92} +5.18491 q^{93} +4.92416 q^{94} -1.31379 q^{95} -3.01737 q^{96} +9.54246 q^{97} -0.566819 q^{98} +0.839097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 67q + 67q^{2} - 11q^{3} + 67q^{4} - 20q^{5} - 11q^{6} - 40q^{7} + 67q^{8} + 24q^{9} + O(q^{10}) \) \( 67q + 67q^{2} - 11q^{3} + 67q^{4} - 20q^{5} - 11q^{6} - 40q^{7} + 67q^{8} + 24q^{9} - 20q^{10} - 13q^{11} - 11q^{12} - 51q^{13} - 40q^{14} - 31q^{15} + 67q^{16} - 34q^{17} + 24q^{18} - 33q^{19} - 20q^{20} - 39q^{21} - 13q^{22} - 43q^{23} - 11q^{24} - 9q^{25} - 51q^{26} - 29q^{27} - 40q^{28} - 63q^{29} - 31q^{30} - 43q^{31} + 67q^{32} - 49q^{33} - 34q^{34} - 20q^{35} + 24q^{36} - 77q^{37} - 33q^{38} - 40q^{39} - 20q^{40} - 50q^{41} - 39q^{42} - 56q^{43} - 13q^{44} - 48q^{45} - 43q^{46} - 48q^{47} - 11q^{48} + q^{49} - 9q^{50} - 18q^{51} - 51q^{52} - 91q^{53} - 29q^{54} - 58q^{55} - 40q^{56} - 65q^{57} - 63q^{58} - 17q^{59} - 31q^{60} - 45q^{61} - 43q^{62} - 67q^{63} + 67q^{64} - 65q^{65} - 49q^{66} - 112q^{67} - 34q^{68} - 57q^{69} - 20q^{70} - 75q^{71} + 24q^{72} - 79q^{73} - 77q^{74} - 5q^{75} - 33q^{76} - 85q^{77} - 40q^{78} - 80q^{79} - 20q^{80} - 77q^{81} - 50q^{82} - 22q^{83} - 39q^{84} - 134q^{85} - 56q^{86} - 49q^{87} - 13q^{88} - 77q^{89} - 48q^{90} - 17q^{91} - 43q^{92} - 97q^{93} - 48q^{94} - 73q^{95} - 11q^{96} - 87q^{97} + q^{98} - 44q^{99} + O(q^{100}) \)

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
\(3\) −3.01737 −1.74208 −0.871039 0.491213i \(-0.836554\pi\)
−0.871039 + 0.491213i \(0.836554\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.22094 −0.546023 −0.273011 0.962011i \(-0.588020\pi\)
−0.273011 + 0.962011i \(0.588020\pi\)
\(6\) −3.01737 −1.23184
\(7\) 2.53637 0.958658 0.479329 0.877635i \(-0.340880\pi\)
0.479329 + 0.877635i \(0.340880\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.10451 2.03484
\(10\) −1.22094 −0.386096
\(11\) 0.137455 0.0414443 0.0207221 0.999785i \(-0.493403\pi\)
0.0207221 + 0.999785i \(0.493403\pi\)
\(12\) −3.01737 −0.871039
\(13\) −0.806951 −0.223808 −0.111904 0.993719i \(-0.535695\pi\)
−0.111904 + 0.993719i \(0.535695\pi\)
\(14\) 2.53637 0.677874
\(15\) 3.68404 0.951214
\(16\) 1.00000 0.250000
\(17\) 2.15852 0.523519 0.261759 0.965133i \(-0.415697\pi\)
0.261759 + 0.965133i \(0.415697\pi\)
\(18\) 6.10451 1.43885
\(19\) 1.07604 0.246861 0.123431 0.992353i \(-0.460610\pi\)
0.123431 + 0.992353i \(0.460610\pi\)
\(20\) −1.22094 −0.273011
\(21\) −7.65317 −1.67006
\(22\) 0.137455 0.0293055
\(23\) −5.61126 −1.17003 −0.585014 0.811023i \(-0.698911\pi\)
−0.585014 + 0.811023i \(0.698911\pi\)
\(24\) −3.01737 −0.615918
\(25\) −3.50930 −0.701859
\(26\) −0.806951 −0.158256
\(27\) −9.36747 −1.80277
\(28\) 2.53637 0.479329
\(29\) 3.70442 0.687894 0.343947 0.938989i \(-0.388236\pi\)
0.343947 + 0.938989i \(0.388236\pi\)
\(30\) 3.68404 0.672610
\(31\) −1.71836 −0.308626 −0.154313 0.988022i \(-0.549316\pi\)
−0.154313 + 0.988022i \(0.549316\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.414753 −0.0721992
\(34\) 2.15852 0.370184
\(35\) −3.09677 −0.523449
\(36\) 6.10451 1.01742
\(37\) −3.29300 −0.541366 −0.270683 0.962669i \(-0.587250\pi\)
−0.270683 + 0.962669i \(0.587250\pi\)
\(38\) 1.07604 0.174557
\(39\) 2.43487 0.389891
\(40\) −1.22094 −0.193048
\(41\) −7.64932 −1.19462 −0.597312 0.802009i \(-0.703764\pi\)
−0.597312 + 0.802009i \(0.703764\pi\)
\(42\) −7.65317 −1.18091
\(43\) 5.20520 0.793785 0.396893 0.917865i \(-0.370089\pi\)
0.396893 + 0.917865i \(0.370089\pi\)
\(44\) 0.137455 0.0207221
\(45\) −7.45327 −1.11107
\(46\) −5.61126 −0.827335
\(47\) 4.92416 0.718263 0.359132 0.933287i \(-0.383073\pi\)
0.359132 + 0.933287i \(0.383073\pi\)
\(48\) −3.01737 −0.435520
\(49\) −0.566819 −0.0809741
\(50\) −3.50930 −0.496290
\(51\) −6.51306 −0.912011
\(52\) −0.806951 −0.111904
\(53\) −1.93351 −0.265588 −0.132794 0.991144i \(-0.542395\pi\)
−0.132794 + 0.991144i \(0.542395\pi\)
\(54\) −9.36747 −1.27475
\(55\) −0.167825 −0.0226295
\(56\) 2.53637 0.338937
\(57\) −3.24682 −0.430051
\(58\) 3.70442 0.486414
\(59\) −11.7080 −1.52425 −0.762124 0.647431i \(-0.775843\pi\)
−0.762124 + 0.647431i \(0.775843\pi\)
\(60\) 3.68404 0.475607
\(61\) −0.669111 −0.0856708 −0.0428354 0.999082i \(-0.513639\pi\)
−0.0428354 + 0.999082i \(0.513639\pi\)
\(62\) −1.71836 −0.218231
\(63\) 15.4833 1.95071
\(64\) 1.00000 0.125000
\(65\) 0.985242 0.122204
\(66\) −0.414753 −0.0510525
\(67\) 5.09018 0.621864 0.310932 0.950432i \(-0.399359\pi\)
0.310932 + 0.950432i \(0.399359\pi\)
\(68\) 2.15852 0.261759
\(69\) 16.9312 2.03828
\(70\) −3.09677 −0.370134
\(71\) −7.94119 −0.942446 −0.471223 0.882014i \(-0.656187\pi\)
−0.471223 + 0.882014i \(0.656187\pi\)
\(72\) 6.10451 0.719424
\(73\) 2.48803 0.291202 0.145601 0.989343i \(-0.453488\pi\)
0.145601 + 0.989343i \(0.453488\pi\)
\(74\) −3.29300 −0.382804
\(75\) 10.5888 1.22269
\(76\) 1.07604 0.123431
\(77\) 0.348637 0.0397309
\(78\) 2.43487 0.275695
\(79\) −13.0996 −1.47382 −0.736912 0.675988i \(-0.763717\pi\)
−0.736912 + 0.675988i \(0.763717\pi\)
\(80\) −1.22094 −0.136506
\(81\) 9.95156 1.10573
\(82\) −7.64932 −0.844726
\(83\) 4.45477 0.488975 0.244487 0.969652i \(-0.421380\pi\)
0.244487 + 0.969652i \(0.421380\pi\)
\(84\) −7.65317 −0.835029
\(85\) −2.63543 −0.285853
\(86\) 5.20520 0.561291
\(87\) −11.1776 −1.19837
\(88\) 0.137455 0.0146528
\(89\) 12.1306 1.28584 0.642921 0.765933i \(-0.277722\pi\)
0.642921 + 0.765933i \(0.277722\pi\)
\(90\) −7.45327 −0.785643
\(91\) −2.04673 −0.214555
\(92\) −5.61126 −0.585014
\(93\) 5.18491 0.537650
\(94\) 4.92416 0.507889
\(95\) −1.31379 −0.134792
\(96\) −3.01737 −0.307959
\(97\) 9.54246 0.968890 0.484445 0.874822i \(-0.339022\pi\)
0.484445 + 0.874822i \(0.339022\pi\)
\(98\) −0.566819 −0.0572573
\(99\) 0.839097 0.0843324
\(100\) −3.50930 −0.350930
\(101\) 4.64189 0.461886 0.230943 0.972967i \(-0.425819\pi\)
0.230943 + 0.972967i \(0.425819\pi\)
\(102\) −6.51306 −0.644889
\(103\) 14.4225 1.42109 0.710546 0.703651i \(-0.248448\pi\)
0.710546 + 0.703651i \(0.248448\pi\)
\(104\) −0.806951 −0.0791281
\(105\) 9.34409 0.911890
\(106\) −1.93351 −0.187799
\(107\) 12.9553 1.25243 0.626216 0.779650i \(-0.284603\pi\)
0.626216 + 0.779650i \(0.284603\pi\)
\(108\) −9.36747 −0.901385
\(109\) −16.0244 −1.53486 −0.767431 0.641132i \(-0.778465\pi\)
−0.767431 + 0.641132i \(0.778465\pi\)
\(110\) −0.167825 −0.0160015
\(111\) 9.93620 0.943103
\(112\) 2.53637 0.239665
\(113\) 2.36333 0.222323 0.111161 0.993802i \(-0.464543\pi\)
0.111161 + 0.993802i \(0.464543\pi\)
\(114\) −3.24682 −0.304092
\(115\) 6.85103 0.638862
\(116\) 3.70442 0.343947
\(117\) −4.92605 −0.455413
\(118\) −11.7080 −1.07781
\(119\) 5.47482 0.501876
\(120\) 3.68404 0.336305
\(121\) −10.9811 −0.998282
\(122\) −0.669111 −0.0605784
\(123\) 23.0808 2.08113
\(124\) −1.71836 −0.154313
\(125\) 10.3894 0.929254
\(126\) 15.4833 1.37936
\(127\) −11.3836 −1.01013 −0.505065 0.863081i \(-0.668532\pi\)
−0.505065 + 0.863081i \(0.668532\pi\)
\(128\) 1.00000 0.0883883
\(129\) −15.7060 −1.38284
\(130\) 0.985242 0.0864115
\(131\) 16.1468 1.41075 0.705376 0.708833i \(-0.250778\pi\)
0.705376 + 0.708833i \(0.250778\pi\)
\(132\) −0.414753 −0.0360996
\(133\) 2.72924 0.236655
\(134\) 5.09018 0.439724
\(135\) 11.4371 0.984353
\(136\) 2.15852 0.185092
\(137\) −21.5338 −1.83976 −0.919880 0.392200i \(-0.871714\pi\)
−0.919880 + 0.392200i \(0.871714\pi\)
\(138\) 16.9312 1.44128
\(139\) 0.441567 0.0374532 0.0187266 0.999825i \(-0.494039\pi\)
0.0187266 + 0.999825i \(0.494039\pi\)
\(140\) −3.09677 −0.261725
\(141\) −14.8580 −1.25127
\(142\) −7.94119 −0.666410
\(143\) −0.110920 −0.00927556
\(144\) 6.10451 0.508710
\(145\) −4.52289 −0.375606
\(146\) 2.48803 0.205911
\(147\) 1.71030 0.141063
\(148\) −3.29300 −0.270683
\(149\) 14.4044 1.18005 0.590027 0.807383i \(-0.299117\pi\)
0.590027 + 0.807383i \(0.299117\pi\)
\(150\) 10.5888 0.864575
\(151\) −13.4602 −1.09538 −0.547688 0.836683i \(-0.684492\pi\)
−0.547688 + 0.836683i \(0.684492\pi\)
\(152\) 1.07604 0.0872786
\(153\) 13.1767 1.06528
\(154\) 0.348637 0.0280940
\(155\) 2.09801 0.168517
\(156\) 2.43487 0.194946
\(157\) −17.3613 −1.38558 −0.692791 0.721138i \(-0.743619\pi\)
−0.692791 + 0.721138i \(0.743619\pi\)
\(158\) −13.0996 −1.04215
\(159\) 5.83411 0.462675
\(160\) −1.22094 −0.0965241
\(161\) −14.2322 −1.12166
\(162\) 9.95156 0.781868
\(163\) 2.59472 0.203234 0.101617 0.994824i \(-0.467598\pi\)
0.101617 + 0.994824i \(0.467598\pi\)
\(164\) −7.64932 −0.597312
\(165\) 0.506390 0.0394224
\(166\) 4.45477 0.345757
\(167\) −20.0621 −1.55245 −0.776226 0.630454i \(-0.782869\pi\)
−0.776226 + 0.630454i \(0.782869\pi\)
\(168\) −7.65317 −0.590455
\(169\) −12.3488 −0.949910
\(170\) −2.63543 −0.202129
\(171\) 6.56872 0.502322
\(172\) 5.20520 0.396893
\(173\) 13.8284 1.05135 0.525676 0.850685i \(-0.323813\pi\)
0.525676 + 0.850685i \(0.323813\pi\)
\(174\) −11.1776 −0.847372
\(175\) −8.90088 −0.672843
\(176\) 0.137455 0.0103611
\(177\) 35.3273 2.65536
\(178\) 12.1306 0.909227
\(179\) 10.1664 0.759870 0.379935 0.925013i \(-0.375946\pi\)
0.379935 + 0.925013i \(0.375946\pi\)
\(180\) −7.45327 −0.555534
\(181\) −0.529361 −0.0393471 −0.0196736 0.999806i \(-0.506263\pi\)
−0.0196736 + 0.999806i \(0.506263\pi\)
\(182\) −2.04673 −0.151714
\(183\) 2.01895 0.149245
\(184\) −5.61126 −0.413668
\(185\) 4.02057 0.295598
\(186\) 5.18491 0.380176
\(187\) 0.296700 0.0216969
\(188\) 4.92416 0.359132
\(189\) −23.7594 −1.72824
\(190\) −1.31379 −0.0953121
\(191\) −17.2259 −1.24642 −0.623211 0.782054i \(-0.714172\pi\)
−0.623211 + 0.782054i \(0.714172\pi\)
\(192\) −3.01737 −0.217760
\(193\) −5.40764 −0.389250 −0.194625 0.980878i \(-0.562349\pi\)
−0.194625 + 0.980878i \(0.562349\pi\)
\(194\) 9.54246 0.685109
\(195\) −2.97284 −0.212889
\(196\) −0.566819 −0.0404870
\(197\) 0.799118 0.0569348 0.0284674 0.999595i \(-0.490937\pi\)
0.0284674 + 0.999595i \(0.490937\pi\)
\(198\) 0.839097 0.0596320
\(199\) 23.0955 1.63720 0.818600 0.574365i \(-0.194751\pi\)
0.818600 + 0.574365i \(0.194751\pi\)
\(200\) −3.50930 −0.248145
\(201\) −15.3589 −1.08334
\(202\) 4.64189 0.326602
\(203\) 9.39579 0.659455
\(204\) −6.51306 −0.456005
\(205\) 9.33939 0.652291
\(206\) 14.4225 1.00486
\(207\) −34.2540 −2.38082
\(208\) −0.806951 −0.0559520
\(209\) 0.147907 0.0102310
\(210\) 9.34409 0.644803
\(211\) 13.5050 0.929724 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(212\) −1.93351 −0.132794
\(213\) 23.9615 1.64181
\(214\) 12.9553 0.885603
\(215\) −6.35525 −0.433425
\(216\) −9.36747 −0.637375
\(217\) −4.35839 −0.295867
\(218\) −16.0244 −1.08531
\(219\) −7.50731 −0.507297
\(220\) −0.167825 −0.0113148
\(221\) −1.74182 −0.117168
\(222\) 9.93620 0.666874
\(223\) −23.0827 −1.54573 −0.772866 0.634570i \(-0.781177\pi\)
−0.772866 + 0.634570i \(0.781177\pi\)
\(224\) 2.53637 0.169468
\(225\) −21.4226 −1.42817
\(226\) 2.36333 0.157206
\(227\) −2.95811 −0.196337 −0.0981684 0.995170i \(-0.531298\pi\)
−0.0981684 + 0.995170i \(0.531298\pi\)
\(228\) −3.24682 −0.215026
\(229\) −28.5272 −1.88513 −0.942566 0.334020i \(-0.891595\pi\)
−0.942566 + 0.334020i \(0.891595\pi\)
\(230\) 6.85103 0.451744
\(231\) −1.05197 −0.0692143
\(232\) 3.70442 0.243207
\(233\) −3.91475 −0.256464 −0.128232 0.991744i \(-0.540930\pi\)
−0.128232 + 0.991744i \(0.540930\pi\)
\(234\) −4.92605 −0.322026
\(235\) −6.01213 −0.392188
\(236\) −11.7080 −0.762124
\(237\) 39.5264 2.56752
\(238\) 5.47482 0.354880
\(239\) 27.0971 1.75277 0.876384 0.481612i \(-0.159949\pi\)
0.876384 + 0.481612i \(0.159949\pi\)
\(240\) 3.68404 0.237804
\(241\) 26.8742 1.73112 0.865561 0.500803i \(-0.166962\pi\)
0.865561 + 0.500803i \(0.166962\pi\)
\(242\) −10.9811 −0.705892
\(243\) −1.92512 −0.123497
\(244\) −0.669111 −0.0428354
\(245\) 0.692053 0.0442137
\(246\) 23.0808 1.47158
\(247\) −0.868314 −0.0552495
\(248\) −1.71836 −0.109116
\(249\) −13.4417 −0.851832
\(250\) 10.3894 0.657082
\(251\) −19.1225 −1.20700 −0.603501 0.797363i \(-0.706228\pi\)
−0.603501 + 0.797363i \(0.706228\pi\)
\(252\) 15.4833 0.975357
\(253\) −0.771296 −0.0484910
\(254\) −11.3836 −0.714270
\(255\) 7.95208 0.497978
\(256\) 1.00000 0.0625000
\(257\) −14.1320 −0.881533 −0.440766 0.897622i \(-0.645293\pi\)
−0.440766 + 0.897622i \(0.645293\pi\)
\(258\) −15.7060 −0.977813
\(259\) −8.35228 −0.518985
\(260\) 0.985242 0.0611021
\(261\) 22.6137 1.39975
\(262\) 16.1468 0.997553
\(263\) −20.0912 −1.23888 −0.619438 0.785045i \(-0.712640\pi\)
−0.619438 + 0.785045i \(0.712640\pi\)
\(264\) −0.414753 −0.0255263
\(265\) 2.36071 0.145017
\(266\) 2.72924 0.167341
\(267\) −36.6025 −2.24004
\(268\) 5.09018 0.310932
\(269\) 29.9173 1.82409 0.912046 0.410089i \(-0.134502\pi\)
0.912046 + 0.410089i \(0.134502\pi\)
\(270\) 11.4371 0.696043
\(271\) 18.7229 1.13734 0.568668 0.822567i \(-0.307459\pi\)
0.568668 + 0.822567i \(0.307459\pi\)
\(272\) 2.15852 0.130880
\(273\) 6.17574 0.373773
\(274\) −21.5338 −1.30091
\(275\) −0.482371 −0.0290880
\(276\) 16.9312 1.01914
\(277\) −6.84176 −0.411081 −0.205541 0.978649i \(-0.565895\pi\)
−0.205541 + 0.978649i \(0.565895\pi\)
\(278\) 0.441567 0.0264834
\(279\) −10.4897 −0.628003
\(280\) −3.09677 −0.185067
\(281\) −1.59746 −0.0952965 −0.0476482 0.998864i \(-0.515173\pi\)
−0.0476482 + 0.998864i \(0.515173\pi\)
\(282\) −14.8580 −0.884782
\(283\) −11.6118 −0.690253 −0.345126 0.938556i \(-0.612164\pi\)
−0.345126 + 0.938556i \(0.612164\pi\)
\(284\) −7.94119 −0.471223
\(285\) 3.96418 0.234818
\(286\) −0.110920 −0.00655881
\(287\) −19.4015 −1.14524
\(288\) 6.10451 0.359712
\(289\) −12.3408 −0.725928
\(290\) −4.52289 −0.265593
\(291\) −28.7931 −1.68788
\(292\) 2.48803 0.145601
\(293\) −4.40276 −0.257212 −0.128606 0.991696i \(-0.541050\pi\)
−0.128606 + 0.991696i \(0.541050\pi\)
\(294\) 1.71030 0.0997468
\(295\) 14.2948 0.832273
\(296\) −3.29300 −0.191402
\(297\) −1.28761 −0.0747145
\(298\) 14.4044 0.834425
\(299\) 4.52802 0.261862
\(300\) 10.5888 0.611347
\(301\) 13.2023 0.760969
\(302\) −13.4602 −0.774548
\(303\) −14.0063 −0.804641
\(304\) 1.07604 0.0617153
\(305\) 0.816946 0.0467782
\(306\) 13.1767 0.753264
\(307\) −14.2102 −0.811018 −0.405509 0.914091i \(-0.632906\pi\)
−0.405509 + 0.914091i \(0.632906\pi\)
\(308\) 0.348637 0.0198654
\(309\) −43.5180 −2.47565
\(310\) 2.09801 0.119159
\(311\) −21.5820 −1.22380 −0.611900 0.790935i \(-0.709595\pi\)
−0.611900 + 0.790935i \(0.709595\pi\)
\(312\) 2.43487 0.137847
\(313\) −5.62071 −0.317701 −0.158851 0.987303i \(-0.550779\pi\)
−0.158851 + 0.987303i \(0.550779\pi\)
\(314\) −17.3613 −0.979755
\(315\) −18.9043 −1.06513
\(316\) −13.0996 −0.736912
\(317\) −29.4976 −1.65675 −0.828375 0.560174i \(-0.810734\pi\)
−0.828375 + 0.560174i \(0.810734\pi\)
\(318\) 5.83411 0.327161
\(319\) 0.509192 0.0285093
\(320\) −1.22094 −0.0682528
\(321\) −39.0908 −2.18184
\(322\) −14.2322 −0.793132
\(323\) 2.32266 0.129236
\(324\) 9.95156 0.552864
\(325\) 2.83183 0.157082
\(326\) 2.59472 0.143708
\(327\) 48.3516 2.67385
\(328\) −7.64932 −0.422363
\(329\) 12.4895 0.688569
\(330\) 0.506390 0.0278758
\(331\) −11.8249 −0.649958 −0.324979 0.945721i \(-0.605357\pi\)
−0.324979 + 0.945721i \(0.605357\pi\)
\(332\) 4.45477 0.244487
\(333\) −20.1022 −1.10159
\(334\) −20.0621 −1.09775
\(335\) −6.21482 −0.339552
\(336\) −7.65317 −0.417515
\(337\) −31.5618 −1.71928 −0.859642 0.510898i \(-0.829313\pi\)
−0.859642 + 0.510898i \(0.829313\pi\)
\(338\) −12.3488 −0.671688
\(339\) −7.13103 −0.387304
\(340\) −2.63543 −0.142927
\(341\) −0.236197 −0.0127908
\(342\) 6.56872 0.355195
\(343\) −19.1923 −1.03628
\(344\) 5.20520 0.280645
\(345\) −20.6721 −1.11295
\(346\) 13.8284 0.743418
\(347\) 8.09057 0.434325 0.217162 0.976136i \(-0.430320\pi\)
0.217162 + 0.976136i \(0.430320\pi\)
\(348\) −11.1776 −0.599183
\(349\) −36.9391 −1.97730 −0.988652 0.150224i \(-0.952000\pi\)
−0.988652 + 0.150224i \(0.952000\pi\)
\(350\) −8.90088 −0.475772
\(351\) 7.55909 0.403474
\(352\) 0.137455 0.00732638
\(353\) −22.5658 −1.20106 −0.600528 0.799604i \(-0.705043\pi\)
−0.600528 + 0.799604i \(0.705043\pi\)
\(354\) 35.3273 1.87762
\(355\) 9.69574 0.514597
\(356\) 12.1306 0.642921
\(357\) −16.5195 −0.874307
\(358\) 10.1664 0.537309
\(359\) −20.2189 −1.06711 −0.533556 0.845765i \(-0.679145\pi\)
−0.533556 + 0.845765i \(0.679145\pi\)
\(360\) −7.45327 −0.392822
\(361\) −17.8421 −0.939060
\(362\) −0.529361 −0.0278226
\(363\) 33.1340 1.73909
\(364\) −2.04673 −0.107278
\(365\) −3.03775 −0.159003
\(366\) 2.01895 0.105532
\(367\) 33.4484 1.74599 0.872996 0.487727i \(-0.162174\pi\)
0.872996 + 0.487727i \(0.162174\pi\)
\(368\) −5.61126 −0.292507
\(369\) −46.6954 −2.43087
\(370\) 4.02057 0.209019
\(371\) −4.90410 −0.254608
\(372\) 5.18491 0.268825
\(373\) −19.7495 −1.02259 −0.511295 0.859405i \(-0.670834\pi\)
−0.511295 + 0.859405i \(0.670834\pi\)
\(374\) 0.296700 0.0153420
\(375\) −31.3486 −1.61883
\(376\) 4.92416 0.253944
\(377\) −2.98929 −0.153956
\(378\) −23.7594 −1.22205
\(379\) 18.5701 0.953881 0.476941 0.878936i \(-0.341746\pi\)
0.476941 + 0.878936i \(0.341746\pi\)
\(380\) −1.31379 −0.0673958
\(381\) 34.3485 1.75973
\(382\) −17.2259 −0.881353
\(383\) −23.9812 −1.22538 −0.612690 0.790323i \(-0.709913\pi\)
−0.612690 + 0.790323i \(0.709913\pi\)
\(384\) −3.01737 −0.153979
\(385\) −0.425666 −0.0216940
\(386\) −5.40764 −0.275241
\(387\) 31.7752 1.61522
\(388\) 9.54246 0.484445
\(389\) −12.6126 −0.639483 −0.319742 0.947505i \(-0.603596\pi\)
−0.319742 + 0.947505i \(0.603596\pi\)
\(390\) −2.97284 −0.150536
\(391\) −12.1120 −0.612532
\(392\) −0.566819 −0.0286287
\(393\) −48.7209 −2.45764
\(394\) 0.799118 0.0402590
\(395\) 15.9939 0.804741
\(396\) 0.839097 0.0421662
\(397\) −5.43803 −0.272927 −0.136464 0.990645i \(-0.543574\pi\)
−0.136464 + 0.990645i \(0.543574\pi\)
\(398\) 23.0955 1.15767
\(399\) −8.23513 −0.412272
\(400\) −3.50930 −0.175465
\(401\) −12.0188 −0.600191 −0.300096 0.953909i \(-0.597019\pi\)
−0.300096 + 0.953909i \(0.597019\pi\)
\(402\) −15.3589 −0.766035
\(403\) 1.38663 0.0690729
\(404\) 4.64189 0.230943
\(405\) −12.1503 −0.603753
\(406\) 9.39579 0.466305
\(407\) −0.452640 −0.0224365
\(408\) −6.51306 −0.322445
\(409\) −12.3241 −0.609386 −0.304693 0.952451i \(-0.598554\pi\)
−0.304693 + 0.952451i \(0.598554\pi\)
\(410\) 9.33939 0.461240
\(411\) 64.9755 3.20501
\(412\) 14.4225 0.710546
\(413\) −29.6958 −1.46123
\(414\) −34.2540 −1.68349
\(415\) −5.43902 −0.266991
\(416\) −0.806951 −0.0395641
\(417\) −1.33237 −0.0652464
\(418\) 0.147907 0.00723439
\(419\) 13.0762 0.638814 0.319407 0.947618i \(-0.396516\pi\)
0.319407 + 0.947618i \(0.396516\pi\)
\(420\) 9.34409 0.455945
\(421\) 20.1913 0.984061 0.492031 0.870578i \(-0.336255\pi\)
0.492031 + 0.870578i \(0.336255\pi\)
\(422\) 13.5050 0.657414
\(423\) 30.0596 1.46155
\(424\) −1.93351 −0.0938995
\(425\) −7.57490 −0.367437
\(426\) 23.9615 1.16094
\(427\) −1.69711 −0.0821291
\(428\) 12.9553 0.626216
\(429\) 0.334685 0.0161588
\(430\) −6.35525 −0.306478
\(431\) 4.48938 0.216246 0.108123 0.994138i \(-0.465516\pi\)
0.108123 + 0.994138i \(0.465516\pi\)
\(432\) −9.36747 −0.450692
\(433\) 0.826963 0.0397413 0.0198707 0.999803i \(-0.493675\pi\)
0.0198707 + 0.999803i \(0.493675\pi\)
\(434\) −4.35839 −0.209209
\(435\) 13.6472 0.654335
\(436\) −16.0244 −0.767431
\(437\) −6.03795 −0.288835
\(438\) −7.50731 −0.358713
\(439\) −3.58838 −0.171264 −0.0856321 0.996327i \(-0.527291\pi\)
−0.0856321 + 0.996327i \(0.527291\pi\)
\(440\) −0.167825 −0.00800074
\(441\) −3.46015 −0.164769
\(442\) −1.74182 −0.0828501
\(443\) −16.1827 −0.768864 −0.384432 0.923153i \(-0.625603\pi\)
−0.384432 + 0.923153i \(0.625603\pi\)
\(444\) 9.93620 0.471551
\(445\) −14.8108 −0.702099
\(446\) −23.0827 −1.09300
\(447\) −43.4634 −2.05575
\(448\) 2.53637 0.119832
\(449\) 27.3050 1.28860 0.644300 0.764773i \(-0.277149\pi\)
0.644300 + 0.764773i \(0.277149\pi\)
\(450\) −21.4226 −1.00987
\(451\) −1.05144 −0.0495103
\(452\) 2.36333 0.111161
\(453\) 40.6144 1.90823
\(454\) −2.95811 −0.138831
\(455\) 2.49894 0.117152
\(456\) −3.24682 −0.152046
\(457\) −10.5724 −0.494554 −0.247277 0.968945i \(-0.579536\pi\)
−0.247277 + 0.968945i \(0.579536\pi\)
\(458\) −28.5272 −1.33299
\(459\) −20.2199 −0.943784
\(460\) 6.85103 0.319431
\(461\) 34.4944 1.60657 0.803283 0.595598i \(-0.203085\pi\)
0.803283 + 0.595598i \(0.203085\pi\)
\(462\) −1.05197 −0.0489419
\(463\) −7.64417 −0.355255 −0.177627 0.984098i \(-0.556842\pi\)
−0.177627 + 0.984098i \(0.556842\pi\)
\(464\) 3.70442 0.171973
\(465\) −6.33048 −0.293569
\(466\) −3.91475 −0.181348
\(467\) −2.34336 −0.108438 −0.0542189 0.998529i \(-0.517267\pi\)
−0.0542189 + 0.998529i \(0.517267\pi\)
\(468\) −4.92605 −0.227707
\(469\) 12.9106 0.596155
\(470\) −6.01213 −0.277319
\(471\) 52.3854 2.41379
\(472\) −11.7080 −0.538903
\(473\) 0.715481 0.0328979
\(474\) 39.5264 1.81551
\(475\) −3.77615 −0.173262
\(476\) 5.47482 0.250938
\(477\) −11.8031 −0.540429
\(478\) 27.0971 1.23939
\(479\) −0.134962 −0.00616657 −0.00308329 0.999995i \(-0.500981\pi\)
−0.00308329 + 0.999995i \(0.500981\pi\)
\(480\) 3.68404 0.168153
\(481\) 2.65729 0.121162
\(482\) 26.8742 1.22409
\(483\) 42.9439 1.95402
\(484\) −10.9811 −0.499141
\(485\) −11.6508 −0.529036
\(486\) −1.92512 −0.0873253
\(487\) −27.9801 −1.26790 −0.633950 0.773374i \(-0.718567\pi\)
−0.633950 + 0.773374i \(0.718567\pi\)
\(488\) −0.669111 −0.0302892
\(489\) −7.82923 −0.354050
\(490\) 0.692053 0.0312638
\(491\) 35.1814 1.58771 0.793857 0.608104i \(-0.208070\pi\)
0.793857 + 0.608104i \(0.208070\pi\)
\(492\) 23.0808 1.04056
\(493\) 7.99608 0.360125
\(494\) −0.868314 −0.0390673
\(495\) −1.02449 −0.0460474
\(496\) −1.71836 −0.0771564
\(497\) −20.1418 −0.903484
\(498\) −13.4417 −0.602336
\(499\) 12.4147 0.555759 0.277880 0.960616i \(-0.410368\pi\)
0.277880 + 0.960616i \(0.410368\pi\)
\(500\) 10.3894 0.464627
\(501\) 60.5348 2.70450
\(502\) −19.1225 −0.853479
\(503\) 23.2076 1.03478 0.517388 0.855751i \(-0.326904\pi\)
0.517388 + 0.855751i \(0.326904\pi\)
\(504\) 15.4833 0.689682
\(505\) −5.66749 −0.252200
\(506\) −0.771296 −0.0342883
\(507\) 37.2610 1.65482
\(508\) −11.3836 −0.505065
\(509\) −12.7492 −0.565100 −0.282550 0.959253i \(-0.591180\pi\)
−0.282550 + 0.959253i \(0.591180\pi\)
\(510\) 7.95208 0.352124
\(511\) 6.31058 0.279163
\(512\) 1.00000 0.0441942
\(513\) −10.0798 −0.445034
\(514\) −14.1320 −0.623338
\(515\) −17.6091 −0.775948
\(516\) −15.7060 −0.691418
\(517\) 0.676851 0.0297679
\(518\) −8.35228 −0.366978
\(519\) −41.7253 −1.83154
\(520\) 0.985242 0.0432057
\(521\) 3.93655 0.172463 0.0862317 0.996275i \(-0.472517\pi\)
0.0862317 + 0.996275i \(0.472517\pi\)
\(522\) 22.6137 0.989775
\(523\) 20.9972 0.918143 0.459072 0.888399i \(-0.348182\pi\)
0.459072 + 0.888399i \(0.348182\pi\)
\(524\) 16.1468 0.705376
\(525\) 26.8572 1.17215
\(526\) −20.0912 −0.876018
\(527\) −3.70911 −0.161571
\(528\) −0.414753 −0.0180498
\(529\) 8.48625 0.368967
\(530\) 2.36071 0.102543
\(531\) −71.4715 −3.10160
\(532\) 2.72924 0.118328
\(533\) 6.17263 0.267366
\(534\) −36.6025 −1.58395
\(535\) −15.8176 −0.683856
\(536\) 5.09018 0.219862
\(537\) −30.6757 −1.32375
\(538\) 29.9173 1.28983
\(539\) −0.0779121 −0.00335591
\(540\) 11.4371 0.492176
\(541\) 2.69617 0.115917 0.0579587 0.998319i \(-0.481541\pi\)
0.0579587 + 0.998319i \(0.481541\pi\)
\(542\) 18.7229 0.804218
\(543\) 1.59728 0.0685457
\(544\) 2.15852 0.0925459
\(545\) 19.5649 0.838069
\(546\) 6.17574 0.264297
\(547\) −14.7569 −0.630959 −0.315480 0.948932i \(-0.602165\pi\)
−0.315480 + 0.948932i \(0.602165\pi\)
\(548\) −21.5338 −0.919880
\(549\) −4.08460 −0.174326
\(550\) −0.482371 −0.0205684
\(551\) 3.98612 0.169814
\(552\) 16.9312 0.720642
\(553\) −33.2256 −1.41289
\(554\) −6.84176 −0.290678
\(555\) −12.1315 −0.514955
\(556\) 0.441567 0.0187266
\(557\) −5.78948 −0.245308 −0.122654 0.992449i \(-0.539141\pi\)
−0.122654 + 0.992449i \(0.539141\pi\)
\(558\) −10.4897 −0.444065
\(559\) −4.20034 −0.177656
\(560\) −3.09677 −0.130862
\(561\) −0.895253 −0.0377976
\(562\) −1.59746 −0.0673848
\(563\) 17.2791 0.728225 0.364113 0.931355i \(-0.381372\pi\)
0.364113 + 0.931355i \(0.381372\pi\)
\(564\) −14.8580 −0.625635
\(565\) −2.88549 −0.121393
\(566\) −11.6118 −0.488082
\(567\) 25.2409 1.06002
\(568\) −7.94119 −0.333205
\(569\) 11.3445 0.475587 0.237793 0.971316i \(-0.423576\pi\)
0.237793 + 0.971316i \(0.423576\pi\)
\(570\) 3.96418 0.166041
\(571\) −24.6047 −1.02968 −0.514838 0.857287i \(-0.672148\pi\)
−0.514838 + 0.857287i \(0.672148\pi\)
\(572\) −0.110920 −0.00463778
\(573\) 51.9769 2.17136
\(574\) −19.4015 −0.809804
\(575\) 19.6916 0.821196
\(576\) 6.10451 0.254355
\(577\) −5.98598 −0.249199 −0.124600 0.992207i \(-0.539765\pi\)
−0.124600 + 0.992207i \(0.539765\pi\)
\(578\) −12.3408 −0.513309
\(579\) 16.3168 0.678105
\(580\) −4.52289 −0.187803
\(581\) 11.2990 0.468760
\(582\) −28.7931 −1.19351
\(583\) −0.265771 −0.0110071
\(584\) 2.48803 0.102956
\(585\) 6.01443 0.248666
\(586\) −4.40276 −0.181877
\(587\) −24.4051 −1.00731 −0.503654 0.863906i \(-0.668011\pi\)
−0.503654 + 0.863906i \(0.668011\pi\)
\(588\) 1.71030 0.0705316
\(589\) −1.84902 −0.0761877
\(590\) 14.2948 0.588506
\(591\) −2.41123 −0.0991849
\(592\) −3.29300 −0.135342
\(593\) −25.8698 −1.06235 −0.531173 0.847263i \(-0.678249\pi\)
−0.531173 + 0.847263i \(0.678249\pi\)
\(594\) −1.28761 −0.0528311
\(595\) −6.68444 −0.274035
\(596\) 14.4044 0.590027
\(597\) −69.6878 −2.85213
\(598\) 4.52802 0.185164
\(599\) −9.41724 −0.384778 −0.192389 0.981319i \(-0.561624\pi\)
−0.192389 + 0.981319i \(0.561624\pi\)
\(600\) 10.5888 0.432288
\(601\) −15.6127 −0.636853 −0.318427 0.947947i \(-0.603154\pi\)
−0.318427 + 0.947947i \(0.603154\pi\)
\(602\) 13.2023 0.538086
\(603\) 31.0731 1.26539
\(604\) −13.4602 −0.547688
\(605\) 13.4073 0.545085
\(606\) −14.0063 −0.568967
\(607\) 9.72071 0.394552 0.197276 0.980348i \(-0.436791\pi\)
0.197276 + 0.980348i \(0.436791\pi\)
\(608\) 1.07604 0.0436393
\(609\) −28.3506 −1.14882
\(610\) 0.816946 0.0330772
\(611\) −3.97356 −0.160753
\(612\) 13.1767 0.532638
\(613\) 8.20603 0.331438 0.165719 0.986173i \(-0.447005\pi\)
0.165719 + 0.986173i \(0.447005\pi\)
\(614\) −14.2102 −0.573477
\(615\) −28.1804 −1.13634
\(616\) 0.348637 0.0140470
\(617\) −20.1399 −0.810801 −0.405400 0.914139i \(-0.632868\pi\)
−0.405400 + 0.914139i \(0.632868\pi\)
\(618\) −43.5180 −1.75055
\(619\) −34.1228 −1.37151 −0.685755 0.727833i \(-0.740528\pi\)
−0.685755 + 0.727833i \(0.740528\pi\)
\(620\) 2.09801 0.0842583
\(621\) 52.5633 2.10929
\(622\) −21.5820 −0.865358
\(623\) 30.7677 1.23268
\(624\) 2.43487 0.0974728
\(625\) 4.86165 0.194466
\(626\) −5.62071 −0.224649
\(627\) −0.446291 −0.0178232
\(628\) −17.3613 −0.692791
\(629\) −7.10802 −0.283415
\(630\) −18.9043 −0.753164
\(631\) 25.6941 1.02286 0.511432 0.859323i \(-0.329115\pi\)
0.511432 + 0.859323i \(0.329115\pi\)
\(632\) −13.0996 −0.521076
\(633\) −40.7496 −1.61965
\(634\) −29.4976 −1.17150
\(635\) 13.8987 0.551554
\(636\) 5.83411 0.231338
\(637\) 0.457395 0.0181227
\(638\) 0.509192 0.0201591
\(639\) −48.4771 −1.91772
\(640\) −1.22094 −0.0482620
\(641\) −23.5666 −0.930824 −0.465412 0.885094i \(-0.654094\pi\)
−0.465412 + 0.885094i \(0.654094\pi\)
\(642\) −39.0908 −1.54279
\(643\) −12.3993 −0.488979 −0.244489 0.969652i \(-0.578620\pi\)
−0.244489 + 0.969652i \(0.578620\pi\)
\(644\) −14.2322 −0.560829
\(645\) 19.1761 0.755060
\(646\) 2.32266 0.0913839
\(647\) 7.93563 0.311982 0.155991 0.987758i \(-0.450143\pi\)
0.155991 + 0.987758i \(0.450143\pi\)
\(648\) 9.95156 0.390934
\(649\) −1.60932 −0.0631713
\(650\) 2.83183 0.111074
\(651\) 13.1509 0.515423
\(652\) 2.59472 0.101617
\(653\) 2.23194 0.0873424 0.0436712 0.999046i \(-0.486095\pi\)
0.0436712 + 0.999046i \(0.486095\pi\)
\(654\) 48.3516 1.89070
\(655\) −19.7143 −0.770303
\(656\) −7.64932 −0.298656
\(657\) 15.1882 0.592549
\(658\) 12.4895 0.486892
\(659\) −32.6108 −1.27033 −0.635167 0.772374i \(-0.719069\pi\)
−0.635167 + 0.772374i \(0.719069\pi\)
\(660\) 0.506390 0.0197112
\(661\) 2.99151 0.116356 0.0581781 0.998306i \(-0.481471\pi\)
0.0581781 + 0.998306i \(0.481471\pi\)
\(662\) −11.8249 −0.459589
\(663\) 5.25572 0.204115
\(664\) 4.45477 0.172879
\(665\) −3.33225 −0.129219
\(666\) −20.1022 −0.778944
\(667\) −20.7865 −0.804856
\(668\) −20.0621 −0.776226
\(669\) 69.6490 2.69279
\(670\) −6.21482 −0.240099
\(671\) −0.0919727 −0.00355056
\(672\) −7.65317 −0.295227
\(673\) 12.8025 0.493500 0.246750 0.969079i \(-0.420637\pi\)
0.246750 + 0.969079i \(0.420637\pi\)
\(674\) −31.5618 −1.21572
\(675\) 32.8732 1.26529
\(676\) −12.3488 −0.474955
\(677\) −37.2355 −1.43108 −0.715539 0.698573i \(-0.753819\pi\)
−0.715539 + 0.698573i \(0.753819\pi\)
\(678\) −7.13103 −0.273865
\(679\) 24.2032 0.928835
\(680\) −2.63543 −0.101064
\(681\) 8.92572 0.342034
\(682\) −0.236197 −0.00904444
\(683\) 34.9802 1.33848 0.669241 0.743046i \(-0.266620\pi\)
0.669241 + 0.743046i \(0.266620\pi\)
\(684\) 6.56872 0.251161
\(685\) 26.2916 1.00455
\(686\) −19.1923 −0.732764
\(687\) 86.0771 3.28405
\(688\) 5.20520 0.198446
\(689\) 1.56025 0.0594407
\(690\) −20.6721 −0.786973
\(691\) 45.2095 1.71985 0.859926 0.510419i \(-0.170510\pi\)
0.859926 + 0.510419i \(0.170510\pi\)
\(692\) 13.8284 0.525676
\(693\) 2.12826 0.0808460
\(694\) 8.09057 0.307114
\(695\) −0.539128 −0.0204503
\(696\) −11.1776 −0.423686
\(697\) −16.5112 −0.625408
\(698\) −36.9391 −1.39816
\(699\) 11.8123 0.446781
\(700\) −8.90088 −0.336422
\(701\) −0.514658 −0.0194384 −0.00971919 0.999953i \(-0.503094\pi\)
−0.00971919 + 0.999953i \(0.503094\pi\)
\(702\) 7.55909 0.285300
\(703\) −3.54341 −0.133642
\(704\) 0.137455 0.00518053
\(705\) 18.1408 0.683222
\(706\) −22.5658 −0.849274
\(707\) 11.7736 0.442791
\(708\) 35.3273 1.32768
\(709\) −7.66312 −0.287795 −0.143897 0.989593i \(-0.545964\pi\)
−0.143897 + 0.989593i \(0.545964\pi\)
\(710\) 9.69574 0.363875
\(711\) −79.9669 −2.99899
\(712\) 12.1306 0.454614
\(713\) 9.64214 0.361101
\(714\) −16.5195 −0.618228
\(715\) 0.135427 0.00506467
\(716\) 10.1664 0.379935
\(717\) −81.7621 −3.05346
\(718\) −20.2189 −0.754563
\(719\) 39.9815 1.49106 0.745529 0.666473i \(-0.232197\pi\)
0.745529 + 0.666473i \(0.232197\pi\)
\(720\) −7.45327 −0.277767
\(721\) 36.5809 1.36234
\(722\) −17.8421 −0.664015
\(723\) −81.0895 −3.01575
\(724\) −0.529361 −0.0196736
\(725\) −12.9999 −0.482805
\(726\) 33.1340 1.22972
\(727\) 8.90783 0.330373 0.165187 0.986262i \(-0.447177\pi\)
0.165187 + 0.986262i \(0.447177\pi\)
\(728\) −2.04673 −0.0758568
\(729\) −24.0459 −0.890588
\(730\) −3.03775 −0.112432
\(731\) 11.2355 0.415561
\(732\) 2.01895 0.0746227
\(733\) −41.0364 −1.51571 −0.757857 0.652420i \(-0.773754\pi\)
−0.757857 + 0.652420i \(0.773754\pi\)
\(734\) 33.4484 1.23460
\(735\) −2.08818 −0.0770237
\(736\) −5.61126 −0.206834
\(737\) 0.699671 0.0257727
\(738\) −46.6954 −1.71888
\(739\) −27.4996 −1.01159 −0.505794 0.862654i \(-0.668800\pi\)
−0.505794 + 0.862654i \(0.668800\pi\)
\(740\) 4.02057 0.147799
\(741\) 2.62002 0.0962490
\(742\) −4.90410 −0.180035
\(743\) −41.4321 −1.52000 −0.759998 0.649925i \(-0.774800\pi\)
−0.759998 + 0.649925i \(0.774800\pi\)
\(744\) 5.18491 0.190088
\(745\) −17.5870 −0.644336
\(746\) −19.7495 −0.723080
\(747\) 27.1942 0.994984
\(748\) 0.296700 0.0108484
\(749\) 32.8593 1.20065
\(750\) −31.3486 −1.14469
\(751\) 32.2074 1.17526 0.587632 0.809128i \(-0.300060\pi\)
0.587632 + 0.809128i \(0.300060\pi\)
\(752\) 4.92416 0.179566
\(753\) 57.6996 2.10269
\(754\) −2.98929 −0.108863
\(755\) 16.4342 0.598100
\(756\) −23.7594 −0.864120
\(757\) 51.0877 1.85682 0.928408 0.371563i \(-0.121178\pi\)
0.928408 + 0.371563i \(0.121178\pi\)
\(758\) 18.5701 0.674496
\(759\) 2.32729 0.0844751
\(760\) −1.31379 −0.0476561
\(761\) 36.2040 1.31239 0.656197 0.754590i \(-0.272164\pi\)
0.656197 + 0.754590i \(0.272164\pi\)
\(762\) 34.3485 1.24431
\(763\) −40.6439 −1.47141
\(764\) −17.2259 −0.623211
\(765\) −16.0880 −0.581665
\(766\) −23.9812 −0.866475
\(767\) 9.44776 0.341139
\(768\) −3.01737 −0.108880
\(769\) −28.7434 −1.03651 −0.518257 0.855225i \(-0.673419\pi\)
−0.518257 + 0.855225i \(0.673419\pi\)
\(770\) −0.425666 −0.0153399
\(771\) 42.6416 1.53570
\(772\) −5.40764 −0.194625
\(773\) 42.0247 1.51152 0.755761 0.654847i \(-0.227267\pi\)
0.755761 + 0.654847i \(0.227267\pi\)
\(774\) 31.7752 1.14214
\(775\) 6.03022 0.216612
\(776\) 9.54246 0.342554
\(777\) 25.2019 0.904113
\(778\) −12.6126 −0.452183
\(779\) −8.23100 −0.294906
\(780\) −2.97284 −0.106445
\(781\) −1.09156 −0.0390590
\(782\) −12.1120 −0.433125
\(783\) −34.7011 −1.24011
\(784\) −0.566819 −0.0202435
\(785\) 21.1972 0.756559
\(786\) −48.7209 −1.73782
\(787\) −35.7797 −1.27541 −0.637705 0.770281i \(-0.720116\pi\)
−0.637705 + 0.770281i \(0.720116\pi\)
\(788\) 0.799118 0.0284674
\(789\) 60.6226 2.15822
\(790\) 15.9939 0.569038
\(791\) 5.99427 0.213132
\(792\) 0.839097 0.0298160
\(793\) 0.539940 0.0191738
\(794\) −5.43803 −0.192989
\(795\) −7.12312 −0.252631
\(796\) 23.0955 0.818600
\(797\) −37.1514 −1.31597 −0.657985 0.753031i \(-0.728591\pi\)
−0.657985 + 0.753031i \(0.728591\pi\)
\(798\) −8.23513 −0.291521
\(799\) 10.6289 0.376024
\(800\) −3.50930 −0.124072
\(801\) 74.0515 2.61648
\(802\) −12.0188 −0.424399
\(803\) 0.341993 0.0120687
\(804\) −15.3589 −0.541668
\(805\) 17.3768 0.612450
\(806\) 1.38663 0.0488419
\(807\) −90.2716 −3.17771
\(808\) 4.64189 0.163301
\(809\) −2.55407 −0.0897963 −0.0448981 0.998992i \(-0.514296\pi\)
−0.0448981 + 0.998992i \(0.514296\pi\)
\(810\) −12.1503 −0.426918
\(811\) 45.3194 1.59138 0.795690 0.605704i \(-0.207108\pi\)
0.795690 + 0.605704i \(0.207108\pi\)
\(812\) 9.39579 0.329728
\(813\) −56.4940 −1.98133
\(814\) −0.452640 −0.0158650
\(815\) −3.16801 −0.110970
\(816\) −6.51306 −0.228003
\(817\) 5.60101 0.195955
\(818\) −12.3241 −0.430901
\(819\) −12.4943 −0.436586
\(820\) 9.33939 0.326146
\(821\) 5.30166 0.185029 0.0925146 0.995711i \(-0.470510\pi\)
0.0925146 + 0.995711i \(0.470510\pi\)
\(822\) 64.9755 2.26628
\(823\) 23.6127 0.823085 0.411543 0.911390i \(-0.364990\pi\)
0.411543 + 0.911390i \(0.364990\pi\)
\(824\) 14.4225 0.502432
\(825\) 1.45549 0.0506737
\(826\) −29.6958 −1.03325
\(827\) 21.4154 0.744688 0.372344 0.928095i \(-0.378554\pi\)
0.372344 + 0.928095i \(0.378554\pi\)
\(828\) −34.2540 −1.19041
\(829\) −47.1120 −1.63627 −0.818134 0.575028i \(-0.804991\pi\)
−0.818134 + 0.575028i \(0.804991\pi\)
\(830\) −5.43902 −0.188791
\(831\) 20.6441 0.716136
\(832\) −0.806951 −0.0279760
\(833\) −1.22349 −0.0423914
\(834\) −1.33237 −0.0461362
\(835\) 24.4947 0.847674
\(836\) 0.147907 0.00511549
\(837\) 16.0966 0.556381
\(838\) 13.0762 0.451710
\(839\) −23.6781 −0.817459 −0.408729 0.912656i \(-0.634028\pi\)
−0.408729 + 0.912656i \(0.634028\pi\)
\(840\) 9.34409 0.322402
\(841\) −15.2773 −0.526802
\(842\) 20.1913 0.695836
\(843\) 4.82012 0.166014
\(844\) 13.5050 0.464862
\(845\) 15.0772 0.518672
\(846\) 30.0596 1.03347
\(847\) −27.8522 −0.957012
\(848\) −1.93351 −0.0663970
\(849\) 35.0372 1.20247
\(850\) −7.57490 −0.259817
\(851\) 18.4779 0.633414
\(852\) 23.9615 0.820907
\(853\) −55.6344 −1.90489 −0.952443 0.304718i \(-0.901438\pi\)
−0.952443 + 0.304718i \(0.901438\pi\)
\(854\) −1.69711 −0.0580740
\(855\) −8.02003 −0.274279
\(856\) 12.9553 0.442802
\(857\) −16.6179 −0.567658 −0.283829 0.958875i \(-0.591605\pi\)
−0.283829 + 0.958875i \(0.591605\pi\)
\(858\) 0.334685 0.0114260
\(859\) 25.9876 0.886684 0.443342 0.896353i \(-0.353793\pi\)
0.443342 + 0.896353i \(0.353793\pi\)
\(860\) −6.35525 −0.216712
\(861\) 58.5416 1.99509
\(862\) 4.48938 0.152909
\(863\) −38.7168 −1.31793 −0.658967 0.752172i \(-0.729006\pi\)
−0.658967 + 0.752172i \(0.729006\pi\)
\(864\) −9.36747 −0.318688
\(865\) −16.8837 −0.574061
\(866\) 0.826963 0.0281014
\(867\) 37.2367 1.26462
\(868\) −4.35839 −0.147933
\(869\) −1.80061 −0.0610816
\(870\) 13.6472 0.462684
\(871\) −4.10753 −0.139178
\(872\) −16.0244 −0.542655
\(873\) 58.2521 1.97153
\(874\) −6.03795 −0.204237
\(875\) 26.3513 0.890837
\(876\) −7.50731 −0.253649
\(877\) −47.0422 −1.58850 −0.794251 0.607590i \(-0.792137\pi\)
−0.794251 + 0.607590i \(0.792137\pi\)
\(878\) −3.58838 −0.121102
\(879\) 13.2848 0.448084
\(880\) −0.167825 −0.00565738
\(881\) 42.9098 1.44567 0.722833 0.691023i \(-0.242840\pi\)
0.722833 + 0.691023i \(0.242840\pi\)
\(882\) −3.46015 −0.116509
\(883\) 22.7450 0.765429 0.382715 0.923867i \(-0.374989\pi\)
0.382715 + 0.923867i \(0.374989\pi\)
\(884\) −1.74182 −0.0585839
\(885\) −43.1326 −1.44989
\(886\) −16.1827 −0.543669
\(887\) −45.3202 −1.52170 −0.760852 0.648926i \(-0.775219\pi\)
−0.760852 + 0.648926i \(0.775219\pi\)
\(888\) 9.93620 0.333437
\(889\) −28.8730 −0.968370
\(890\) −14.8108 −0.496459
\(891\) 1.36789 0.0458261
\(892\) −23.0827 −0.772866
\(893\) 5.29861 0.177311
\(894\) −43.4634 −1.45363
\(895\) −12.4126 −0.414906
\(896\) 2.53637 0.0847342
\(897\) −13.6627 −0.456184
\(898\) 27.3050 0.911178
\(899\) −6.36551 −0.212302
\(900\) −21.4226 −0.714085
\(901\) −4.17353 −0.139040
\(902\) −1.05144 −0.0350091
\(903\) −39.8363 −1.32567
\(904\) 2.36333 0.0786030
\(905\) 0.646320 0.0214844
\(906\) 40.6144 1.34932
\(907\) 16.7116 0.554900 0.277450 0.960740i \(-0.410511\pi\)
0.277450 + 0.960740i \(0.410511\pi\)
\(908\) −2.95811 −0.0981684
\(909\) 28.3365 0.939863
\(910\) 2.49894 0.0828391
\(911\) −9.91377 −0.328458 −0.164229 0.986422i \(-0.552514\pi\)
−0.164229 + 0.986422i \(0.552514\pi\)
\(912\) −3.24682 −0.107513
\(913\) 0.612331 0.0202652
\(914\) −10.5724 −0.349703
\(915\) −2.46503 −0.0814913
\(916\) −28.5272 −0.942566
\(917\) 40.9543 1.35243
\(918\) −20.2199 −0.667356
\(919\) 41.8962 1.38203 0.691014 0.722842i \(-0.257164\pi\)
0.691014 + 0.722842i \(0.257164\pi\)
\(920\) 6.85103 0.225872
\(921\) 42.8774 1.41286
\(922\) 34.4944 1.13601
\(923\) 6.40815 0.210927
\(924\) −1.05197 −0.0346072
\(925\) 11.5561 0.379963
\(926\) −7.64417 −0.251203
\(927\) 88.0424 2.89169
\(928\) 3.70442 0.121604
\(929\) 6.89624 0.226258 0.113129 0.993580i \(-0.463913\pi\)
0.113129 + 0.993580i \(0.463913\pi\)
\(930\) −6.33048 −0.207585
\(931\) −0.609921 −0.0199893
\(932\) −3.91475 −0.128232
\(933\) 65.1207 2.13196
\(934\) −2.34336 −0.0766770
\(935\) −0.362254 −0.0118470
\(936\) −4.92605 −0.161013
\(937\) 53.5823 1.75046 0.875229 0.483709i \(-0.160711\pi\)
0.875229 + 0.483709i \(0.160711\pi\)
\(938\) 12.9106 0.421545
\(939\) 16.9597 0.553460
\(940\) −6.01213 −0.196094
\(941\) −26.8872 −0.876497 −0.438248 0.898854i \(-0.644401\pi\)
−0.438248 + 0.898854i \(0.644401\pi\)
\(942\) 52.3854 1.70681
\(943\) 42.9223 1.39774
\(944\) −11.7080 −0.381062
\(945\) 29.0089 0.943658
\(946\) 0.715481 0.0232623
\(947\) −5.49723 −0.178636 −0.0893181 0.996003i \(-0.528469\pi\)
−0.0893181 + 0.996003i \(0.528469\pi\)
\(948\) 39.5264 1.28376
\(949\) −2.00772 −0.0651734
\(950\) −3.77615 −0.122515
\(951\) 89.0051 2.88619
\(952\) 5.47482 0.177440
\(953\) 53.2061 1.72351 0.861757 0.507322i \(-0.169365\pi\)
0.861757 + 0.507322i \(0.169365\pi\)
\(954\) −11.8031 −0.382141
\(955\) 21.0318 0.680574
\(956\) 27.0971 0.876384
\(957\) −1.53642 −0.0496654
\(958\) −0.134962 −0.00436043
\(959\) −54.6178 −1.76370
\(960\) 3.68404 0.118902
\(961\) −28.0473 −0.904750
\(962\) 2.65729 0.0856746
\(963\) 79.0856 2.54850
\(964\) 26.8742 0.865561
\(965\) 6.60242 0.212539
\(966\) 42.9439 1.38170
\(967\) −28.0150 −0.900903 −0.450451 0.892801i \(-0.648737\pi\)
−0.450451 + 0.892801i \(0.648737\pi\)
\(968\) −10.9811 −0.352946
\(969\) −7.00833 −0.225140
\(970\) −11.6508 −0.374085
\(971\) 15.9083 0.510521 0.255261 0.966872i \(-0.417839\pi\)
0.255261 + 0.966872i \(0.417839\pi\)
\(972\) −1.92512 −0.0617483
\(973\) 1.11998 0.0359048
\(974\) −27.9801 −0.896540
\(975\) −8.54468 −0.273649
\(976\) −0.669111 −0.0214177
\(977\) 3.73835 0.119600 0.0598001 0.998210i \(-0.480954\pi\)
0.0598001 + 0.998210i \(0.480954\pi\)
\(978\) −7.82923 −0.250351
\(979\) 1.66741 0.0532908
\(980\) 0.692053 0.0221068
\(981\) −97.8213 −3.12320
\(982\) 35.1814 1.12268
\(983\) −22.5899 −0.720507 −0.360253 0.932855i \(-0.617310\pi\)
−0.360253 + 0.932855i \(0.617310\pi\)
\(984\) 23.0808 0.735790
\(985\) −0.975678 −0.0310877
\(986\) 7.99608 0.254647
\(987\) −37.6855 −1.19954
\(988\) −0.868314 −0.0276247
\(989\) −29.2077 −0.928752
\(990\) −1.02449 −0.0325604
\(991\) −9.21541 −0.292737 −0.146369 0.989230i \(-0.546759\pi\)
−0.146369 + 0.989230i \(0.546759\pi\)
\(992\) −1.71836 −0.0545578
\(993\) 35.6802 1.13228
\(994\) −20.1418 −0.638859
\(995\) −28.1983 −0.893948
\(996\) −13.4417 −0.425916
\(997\) −37.0961 −1.17484 −0.587422 0.809281i \(-0.699857\pi\)
−0.587422 + 0.809281i \(0.699857\pi\)
\(998\) 12.4147 0.392981
\(999\) 30.8471 0.975959
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 \(a_p\))