Properties

Label 4003.2.a.b.1.8
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.64207 q^{2} +1.02501 q^{3} +4.98054 q^{4} +2.32673 q^{5} -2.70814 q^{6} -0.493904 q^{7} -7.87479 q^{8} -1.94936 q^{9} +O(q^{10})\) \(q-2.64207 q^{2} +1.02501 q^{3} +4.98054 q^{4} +2.32673 q^{5} -2.70814 q^{6} -0.493904 q^{7} -7.87479 q^{8} -1.94936 q^{9} -6.14739 q^{10} +2.96142 q^{11} +5.10508 q^{12} +0.776601 q^{13} +1.30493 q^{14} +2.38491 q^{15} +10.8447 q^{16} +6.61446 q^{17} +5.15036 q^{18} -7.31111 q^{19} +11.5884 q^{20} -0.506254 q^{21} -7.82428 q^{22} -8.89506 q^{23} -8.07170 q^{24} +0.413674 q^{25} -2.05183 q^{26} -5.07312 q^{27} -2.45991 q^{28} -2.08930 q^{29} -6.30110 q^{30} +0.878413 q^{31} -12.9028 q^{32} +3.03547 q^{33} -17.4759 q^{34} -1.14918 q^{35} -9.70888 q^{36} +4.25838 q^{37} +19.3165 q^{38} +0.796020 q^{39} -18.3225 q^{40} -11.1405 q^{41} +1.33756 q^{42} -7.88750 q^{43} +14.7495 q^{44} -4.53564 q^{45} +23.5014 q^{46} +10.9205 q^{47} +11.1158 q^{48} -6.75606 q^{49} -1.09296 q^{50} +6.77986 q^{51} +3.86789 q^{52} -10.8022 q^{53} +13.4036 q^{54} +6.89043 q^{55} +3.88939 q^{56} -7.49393 q^{57} +5.52008 q^{58} +2.76488 q^{59} +11.8781 q^{60} +8.06297 q^{61} -2.32083 q^{62} +0.962798 q^{63} +12.4008 q^{64} +1.80694 q^{65} -8.01993 q^{66} -0.138871 q^{67} +32.9436 q^{68} -9.11748 q^{69} +3.03622 q^{70} -10.2433 q^{71} +15.3508 q^{72} -11.2894 q^{73} -11.2509 q^{74} +0.424018 q^{75} -36.4132 q^{76} -1.46266 q^{77} -2.10314 q^{78} +12.0755 q^{79} +25.2326 q^{80} +0.648113 q^{81} +29.4339 q^{82} -5.70804 q^{83} -2.52142 q^{84} +15.3901 q^{85} +20.8393 q^{86} -2.14155 q^{87} -23.3206 q^{88} -11.7510 q^{89} +11.9835 q^{90} -0.383566 q^{91} -44.3022 q^{92} +0.900378 q^{93} -28.8528 q^{94} -17.0110 q^{95} -13.2254 q^{96} -6.74086 q^{97} +17.8500 q^{98} -5.77289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64207 −1.86823 −0.934113 0.356978i \(-0.883807\pi\)
−0.934113 + 0.356978i \(0.883807\pi\)
\(3\) 1.02501 0.591787 0.295894 0.955221i \(-0.404383\pi\)
0.295894 + 0.955221i \(0.404383\pi\)
\(4\) 4.98054 2.49027
\(5\) 2.32673 1.04055 0.520273 0.854000i \(-0.325830\pi\)
0.520273 + 0.854000i \(0.325830\pi\)
\(6\) −2.70814 −1.10559
\(7\) −0.493904 −0.186678 −0.0933391 0.995634i \(-0.529754\pi\)
−0.0933391 + 0.995634i \(0.529754\pi\)
\(8\) −7.87479 −2.78416
\(9\) −1.94936 −0.649788
\(10\) −6.14739 −1.94397
\(11\) 2.96142 0.892902 0.446451 0.894808i \(-0.352688\pi\)
0.446451 + 0.894808i \(0.352688\pi\)
\(12\) 5.10508 1.47371
\(13\) 0.776601 0.215390 0.107695 0.994184i \(-0.465653\pi\)
0.107695 + 0.994184i \(0.465653\pi\)
\(14\) 1.30493 0.348757
\(15\) 2.38491 0.615781
\(16\) 10.8447 2.71117
\(17\) 6.61446 1.60424 0.802122 0.597161i \(-0.203705\pi\)
0.802122 + 0.597161i \(0.203705\pi\)
\(18\) 5.15036 1.21395
\(19\) −7.31111 −1.67728 −0.838642 0.544683i \(-0.816650\pi\)
−0.838642 + 0.544683i \(0.816650\pi\)
\(20\) 11.5884 2.59124
\(21\) −0.506254 −0.110474
\(22\) −7.82428 −1.66814
\(23\) −8.89506 −1.85475 −0.927374 0.374135i \(-0.877940\pi\)
−0.927374 + 0.374135i \(0.877940\pi\)
\(24\) −8.07170 −1.64763
\(25\) 0.413674 0.0827348
\(26\) −2.05183 −0.402398
\(27\) −5.07312 −0.976323
\(28\) −2.45991 −0.464879
\(29\) −2.08930 −0.387974 −0.193987 0.981004i \(-0.562142\pi\)
−0.193987 + 0.981004i \(0.562142\pi\)
\(30\) −6.30110 −1.15042
\(31\) 0.878413 0.157768 0.0788838 0.996884i \(-0.474864\pi\)
0.0788838 + 0.996884i \(0.474864\pi\)
\(32\) −12.9028 −2.28091
\(33\) 3.03547 0.528408
\(34\) −17.4759 −2.99709
\(35\) −1.14918 −0.194247
\(36\) −9.70888 −1.61815
\(37\) 4.25838 0.700074 0.350037 0.936736i \(-0.386169\pi\)
0.350037 + 0.936736i \(0.386169\pi\)
\(38\) 19.3165 3.13354
\(39\) 0.796020 0.127465
\(40\) −18.3225 −2.89704
\(41\) −11.1405 −1.73985 −0.869926 0.493183i \(-0.835833\pi\)
−0.869926 + 0.493183i \(0.835833\pi\)
\(42\) 1.33756 0.206390
\(43\) −7.88750 −1.20283 −0.601416 0.798936i \(-0.705397\pi\)
−0.601416 + 0.798936i \(0.705397\pi\)
\(44\) 14.7495 2.22357
\(45\) −4.53564 −0.676134
\(46\) 23.5014 3.46509
\(47\) 10.9205 1.59292 0.796460 0.604691i \(-0.206704\pi\)
0.796460 + 0.604691i \(0.206704\pi\)
\(48\) 11.1158 1.60443
\(49\) −6.75606 −0.965151
\(50\) −1.09296 −0.154567
\(51\) 6.77986 0.949370
\(52\) 3.86789 0.536380
\(53\) −10.8022 −1.48380 −0.741898 0.670513i \(-0.766074\pi\)
−0.741898 + 0.670513i \(0.766074\pi\)
\(54\) 13.4036 1.82399
\(55\) 6.89043 0.929105
\(56\) 3.88939 0.519741
\(57\) −7.49393 −0.992595
\(58\) 5.52008 0.724823
\(59\) 2.76488 0.359957 0.179979 0.983671i \(-0.442397\pi\)
0.179979 + 0.983671i \(0.442397\pi\)
\(60\) 11.8781 1.53346
\(61\) 8.06297 1.03236 0.516179 0.856481i \(-0.327354\pi\)
0.516179 + 0.856481i \(0.327354\pi\)
\(62\) −2.32083 −0.294746
\(63\) 0.962798 0.121301
\(64\) 12.4008 1.55010
\(65\) 1.80694 0.224123
\(66\) −8.01993 −0.987185
\(67\) −0.138871 −0.0169657 −0.00848287 0.999964i \(-0.502700\pi\)
−0.00848287 + 0.999964i \(0.502700\pi\)
\(68\) 32.9436 3.99500
\(69\) −9.11748 −1.09762
\(70\) 3.03622 0.362897
\(71\) −10.2433 −1.21566 −0.607829 0.794068i \(-0.707960\pi\)
−0.607829 + 0.794068i \(0.707960\pi\)
\(72\) 15.3508 1.80911
\(73\) −11.2894 −1.32132 −0.660662 0.750684i \(-0.729724\pi\)
−0.660662 + 0.750684i \(0.729724\pi\)
\(74\) −11.2509 −1.30790
\(75\) 0.424018 0.0489614
\(76\) −36.4132 −4.17689
\(77\) −1.46266 −0.166685
\(78\) −2.10314 −0.238134
\(79\) 12.0755 1.35860 0.679299 0.733862i \(-0.262284\pi\)
0.679299 + 0.733862i \(0.262284\pi\)
\(80\) 25.2326 2.82109
\(81\) 0.648113 0.0720126
\(82\) 29.4339 3.25044
\(83\) −5.70804 −0.626539 −0.313269 0.949664i \(-0.601424\pi\)
−0.313269 + 0.949664i \(0.601424\pi\)
\(84\) −2.52142 −0.275109
\(85\) 15.3901 1.66929
\(86\) 20.8393 2.24716
\(87\) −2.14155 −0.229598
\(88\) −23.3206 −2.48598
\(89\) −11.7510 −1.24560 −0.622801 0.782381i \(-0.714005\pi\)
−0.622801 + 0.782381i \(0.714005\pi\)
\(90\) 11.9835 1.26317
\(91\) −0.383566 −0.0402087
\(92\) −44.3022 −4.61882
\(93\) 0.900378 0.0933649
\(94\) −28.8528 −2.97593
\(95\) −17.0110 −1.74529
\(96\) −13.2254 −1.34982
\(97\) −6.74086 −0.684431 −0.342215 0.939622i \(-0.611177\pi\)
−0.342215 + 0.939622i \(0.611177\pi\)
\(98\) 17.8500 1.80312
\(99\) −5.77289 −0.580197
\(100\) 2.06032 0.206032
\(101\) −1.13676 −0.113112 −0.0565561 0.998399i \(-0.518012\pi\)
−0.0565561 + 0.998399i \(0.518012\pi\)
\(102\) −17.9129 −1.77364
\(103\) −6.15488 −0.606458 −0.303229 0.952918i \(-0.598065\pi\)
−0.303229 + 0.952918i \(0.598065\pi\)
\(104\) −6.11556 −0.599680
\(105\) −1.17792 −0.114953
\(106\) 28.5402 2.77207
\(107\) 11.1794 1.08075 0.540374 0.841425i \(-0.318283\pi\)
0.540374 + 0.841425i \(0.318283\pi\)
\(108\) −25.2669 −2.43131
\(109\) 13.4404 1.28736 0.643679 0.765295i \(-0.277407\pi\)
0.643679 + 0.765295i \(0.277407\pi\)
\(110\) −18.2050 −1.73578
\(111\) 4.36486 0.414294
\(112\) −5.35622 −0.506115
\(113\) −13.2241 −1.24402 −0.622011 0.783009i \(-0.713684\pi\)
−0.622011 + 0.783009i \(0.713684\pi\)
\(114\) 19.7995 1.85439
\(115\) −20.6964 −1.92995
\(116\) −10.4058 −0.966158
\(117\) −1.51388 −0.139958
\(118\) −7.30501 −0.672481
\(119\) −3.26691 −0.299477
\(120\) −18.7807 −1.71443
\(121\) −2.22999 −0.202726
\(122\) −21.3029 −1.92868
\(123\) −11.4191 −1.02962
\(124\) 4.37497 0.392884
\(125\) −10.6711 −0.954456
\(126\) −2.54378 −0.226618
\(127\) 0.798224 0.0708310 0.0354155 0.999373i \(-0.488725\pi\)
0.0354155 + 0.999373i \(0.488725\pi\)
\(128\) −6.95811 −0.615016
\(129\) −8.08473 −0.711820
\(130\) −4.77406 −0.418713
\(131\) −15.7436 −1.37552 −0.687760 0.725938i \(-0.741406\pi\)
−0.687760 + 0.725938i \(0.741406\pi\)
\(132\) 15.1183 1.31588
\(133\) 3.61099 0.313112
\(134\) 0.366906 0.0316958
\(135\) −11.8038 −1.01591
\(136\) −52.0875 −4.46646
\(137\) −18.6132 −1.59023 −0.795115 0.606459i \(-0.792590\pi\)
−0.795115 + 0.606459i \(0.792590\pi\)
\(138\) 24.0890 2.05059
\(139\) 10.9726 0.930680 0.465340 0.885132i \(-0.345932\pi\)
0.465340 + 0.885132i \(0.345932\pi\)
\(140\) −5.72354 −0.483727
\(141\) 11.1936 0.942669
\(142\) 27.0636 2.27113
\(143\) 2.29984 0.192322
\(144\) −21.1402 −1.76168
\(145\) −4.86124 −0.403704
\(146\) 29.8274 2.46853
\(147\) −6.92500 −0.571164
\(148\) 21.2090 1.74337
\(149\) 1.99896 0.163761 0.0818807 0.996642i \(-0.473907\pi\)
0.0818807 + 0.996642i \(0.473907\pi\)
\(150\) −1.12029 −0.0914710
\(151\) −4.34393 −0.353504 −0.176752 0.984255i \(-0.556559\pi\)
−0.176752 + 0.984255i \(0.556559\pi\)
\(152\) 57.5734 4.66982
\(153\) −12.8940 −1.04242
\(154\) 3.86444 0.311406
\(155\) 2.04383 0.164164
\(156\) 3.96461 0.317422
\(157\) 8.39098 0.669673 0.334837 0.942276i \(-0.391319\pi\)
0.334837 + 0.942276i \(0.391319\pi\)
\(158\) −31.9043 −2.53817
\(159\) −11.0723 −0.878091
\(160\) −30.0213 −2.37339
\(161\) 4.39330 0.346241
\(162\) −1.71236 −0.134536
\(163\) −4.93579 −0.386601 −0.193300 0.981140i \(-0.561919\pi\)
−0.193300 + 0.981140i \(0.561919\pi\)
\(164\) −55.4856 −4.33270
\(165\) 7.06272 0.549832
\(166\) 15.0810 1.17052
\(167\) 7.80826 0.604221 0.302110 0.953273i \(-0.402309\pi\)
0.302110 + 0.953273i \(0.402309\pi\)
\(168\) 3.98664 0.307576
\(169\) −12.3969 −0.953607
\(170\) −40.6617 −3.11861
\(171\) 14.2520 1.08988
\(172\) −39.2840 −2.99537
\(173\) 15.1926 1.15507 0.577535 0.816366i \(-0.304015\pi\)
0.577535 + 0.816366i \(0.304015\pi\)
\(174\) 5.65811 0.428941
\(175\) −0.204315 −0.0154448
\(176\) 32.1156 2.42081
\(177\) 2.83402 0.213018
\(178\) 31.0469 2.32706
\(179\) 11.6776 0.872828 0.436414 0.899746i \(-0.356248\pi\)
0.436414 + 0.899746i \(0.356248\pi\)
\(180\) −22.5899 −1.68375
\(181\) 22.1145 1.64376 0.821878 0.569663i \(-0.192926\pi\)
0.821878 + 0.569663i \(0.192926\pi\)
\(182\) 1.01341 0.0751188
\(183\) 8.26459 0.610936
\(184\) 70.0467 5.16391
\(185\) 9.90811 0.728458
\(186\) −2.37886 −0.174427
\(187\) 19.5882 1.43243
\(188\) 54.3900 3.96680
\(189\) 2.50564 0.182258
\(190\) 44.9442 3.26060
\(191\) 3.56942 0.258274 0.129137 0.991627i \(-0.458779\pi\)
0.129137 + 0.991627i \(0.458779\pi\)
\(192\) 12.7109 0.917327
\(193\) 14.1884 1.02131 0.510653 0.859787i \(-0.329404\pi\)
0.510653 + 0.859787i \(0.329404\pi\)
\(194\) 17.8098 1.27867
\(195\) 1.85212 0.132633
\(196\) −33.6488 −2.40349
\(197\) −18.4248 −1.31271 −0.656356 0.754452i \(-0.727903\pi\)
−0.656356 + 0.754452i \(0.727903\pi\)
\(198\) 15.2524 1.08394
\(199\) 15.9680 1.13194 0.565971 0.824425i \(-0.308502\pi\)
0.565971 + 0.824425i \(0.308502\pi\)
\(200\) −3.25760 −0.230347
\(201\) −0.142343 −0.0100401
\(202\) 3.00341 0.211319
\(203\) 1.03191 0.0724262
\(204\) 33.7673 2.36419
\(205\) −25.9209 −1.81039
\(206\) 16.2616 1.13300
\(207\) 17.3397 1.20519
\(208\) 8.42198 0.583959
\(209\) −21.6513 −1.49765
\(210\) 3.11214 0.214758
\(211\) 8.51245 0.586021 0.293010 0.956109i \(-0.405343\pi\)
0.293010 + 0.956109i \(0.405343\pi\)
\(212\) −53.8007 −3.69505
\(213\) −10.4995 −0.719411
\(214\) −29.5366 −2.01908
\(215\) −18.3521 −1.25160
\(216\) 39.9498 2.71824
\(217\) −0.433852 −0.0294518
\(218\) −35.5105 −2.40508
\(219\) −11.5717 −0.781942
\(220\) 34.3180 2.31372
\(221\) 5.13680 0.345538
\(222\) −11.5323 −0.773996
\(223\) 13.2510 0.887353 0.443676 0.896187i \(-0.353674\pi\)
0.443676 + 0.896187i \(0.353674\pi\)
\(224\) 6.37274 0.425797
\(225\) −0.806402 −0.0537601
\(226\) 34.9391 2.32411
\(227\) −6.83741 −0.453815 −0.226908 0.973916i \(-0.572862\pi\)
−0.226908 + 0.973916i \(0.572862\pi\)
\(228\) −37.3238 −2.47183
\(229\) −19.9059 −1.31542 −0.657709 0.753273i \(-0.728474\pi\)
−0.657709 + 0.753273i \(0.728474\pi\)
\(230\) 54.6814 3.60558
\(231\) −1.49923 −0.0986422
\(232\) 16.4528 1.08018
\(233\) −13.6658 −0.895276 −0.447638 0.894215i \(-0.647735\pi\)
−0.447638 + 0.894215i \(0.647735\pi\)
\(234\) 3.99977 0.261473
\(235\) 25.4091 1.65751
\(236\) 13.7706 0.896389
\(237\) 12.3774 0.804001
\(238\) 8.63140 0.559491
\(239\) 15.2687 0.987648 0.493824 0.869562i \(-0.335599\pi\)
0.493824 + 0.869562i \(0.335599\pi\)
\(240\) 25.8636 1.66949
\(241\) 4.11200 0.264877 0.132439 0.991191i \(-0.457719\pi\)
0.132439 + 0.991191i \(0.457719\pi\)
\(242\) 5.89178 0.378738
\(243\) 15.8837 1.01894
\(244\) 40.1579 2.57085
\(245\) −15.7195 −1.00428
\(246\) 30.1700 1.92357
\(247\) −5.67781 −0.361271
\(248\) −6.91732 −0.439250
\(249\) −5.85077 −0.370777
\(250\) 28.1939 1.78314
\(251\) 19.8514 1.25301 0.626504 0.779418i \(-0.284485\pi\)
0.626504 + 0.779418i \(0.284485\pi\)
\(252\) 4.79525 0.302073
\(253\) −26.3420 −1.65611
\(254\) −2.10896 −0.132328
\(255\) 15.7749 0.987863
\(256\) −6.41772 −0.401107
\(257\) −23.0628 −1.43862 −0.719309 0.694690i \(-0.755542\pi\)
−0.719309 + 0.694690i \(0.755542\pi\)
\(258\) 21.3604 1.32984
\(259\) −2.10323 −0.130688
\(260\) 8.99953 0.558127
\(261\) 4.07281 0.252101
\(262\) 41.5956 2.56978
\(263\) −5.93944 −0.366242 −0.183121 0.983090i \(-0.558620\pi\)
−0.183121 + 0.983090i \(0.558620\pi\)
\(264\) −23.9037 −1.47117
\(265\) −25.1338 −1.54396
\(266\) −9.54048 −0.584964
\(267\) −12.0448 −0.737131
\(268\) −0.691650 −0.0422493
\(269\) −18.0932 −1.10316 −0.551582 0.834120i \(-0.685976\pi\)
−0.551582 + 0.834120i \(0.685976\pi\)
\(270\) 31.1865 1.89795
\(271\) 18.0167 1.09444 0.547220 0.836989i \(-0.315686\pi\)
0.547220 + 0.836989i \(0.315686\pi\)
\(272\) 71.7316 4.34937
\(273\) −0.393157 −0.0237950
\(274\) 49.1773 2.97091
\(275\) 1.22506 0.0738741
\(276\) −45.4100 −2.73336
\(277\) −29.7144 −1.78537 −0.892683 0.450686i \(-0.851179\pi\)
−0.892683 + 0.450686i \(0.851179\pi\)
\(278\) −28.9903 −1.73872
\(279\) −1.71235 −0.102516
\(280\) 9.04955 0.540814
\(281\) 1.14465 0.0682843 0.0341421 0.999417i \(-0.489130\pi\)
0.0341421 + 0.999417i \(0.489130\pi\)
\(282\) −29.5742 −1.76112
\(283\) 19.4627 1.15694 0.578470 0.815704i \(-0.303650\pi\)
0.578470 + 0.815704i \(0.303650\pi\)
\(284\) −51.0172 −3.02732
\(285\) −17.4363 −1.03284
\(286\) −6.07634 −0.359302
\(287\) 5.50233 0.324792
\(288\) 25.1523 1.48211
\(289\) 26.7511 1.57360
\(290\) 12.8437 0.754211
\(291\) −6.90942 −0.405037
\(292\) −56.2272 −3.29045
\(293\) −2.31783 −0.135409 −0.0677046 0.997705i \(-0.521568\pi\)
−0.0677046 + 0.997705i \(0.521568\pi\)
\(294\) 18.2963 1.06706
\(295\) 6.43314 0.374552
\(296\) −33.5338 −1.94911
\(297\) −15.0237 −0.871761
\(298\) −5.28140 −0.305943
\(299\) −6.90791 −0.399495
\(300\) 2.11184 0.121927
\(301\) 3.89566 0.224542
\(302\) 11.4770 0.660425
\(303\) −1.16519 −0.0669384
\(304\) −79.2865 −4.54740
\(305\) 18.7604 1.07422
\(306\) 34.0669 1.94747
\(307\) −13.0843 −0.746759 −0.373380 0.927679i \(-0.621801\pi\)
−0.373380 + 0.927679i \(0.621801\pi\)
\(308\) −7.28482 −0.415091
\(309\) −6.30878 −0.358894
\(310\) −5.39994 −0.306696
\(311\) 15.8629 0.899504 0.449752 0.893153i \(-0.351512\pi\)
0.449752 + 0.893153i \(0.351512\pi\)
\(312\) −6.26849 −0.354883
\(313\) −6.77606 −0.383006 −0.191503 0.981492i \(-0.561336\pi\)
−0.191503 + 0.981492i \(0.561336\pi\)
\(314\) −22.1696 −1.25110
\(315\) 2.24017 0.126219
\(316\) 60.1424 3.38327
\(317\) 17.5246 0.984278 0.492139 0.870517i \(-0.336215\pi\)
0.492139 + 0.870517i \(0.336215\pi\)
\(318\) 29.2538 1.64047
\(319\) −6.18730 −0.346422
\(320\) 28.8533 1.61295
\(321\) 11.4589 0.639573
\(322\) −11.6074 −0.646856
\(323\) −48.3591 −2.69077
\(324\) 3.22795 0.179331
\(325\) 0.321260 0.0178203
\(326\) 13.0407 0.722257
\(327\) 13.7765 0.761842
\(328\) 87.7289 4.84402
\(329\) −5.39368 −0.297363
\(330\) −18.6602 −1.02721
\(331\) −12.0475 −0.662188 −0.331094 0.943598i \(-0.607418\pi\)
−0.331094 + 0.943598i \(0.607418\pi\)
\(332\) −28.4291 −1.56025
\(333\) −8.30114 −0.454899
\(334\) −20.6300 −1.12882
\(335\) −0.323114 −0.0176536
\(336\) −5.49016 −0.299513
\(337\) 18.8516 1.02691 0.513457 0.858115i \(-0.328365\pi\)
0.513457 + 0.858115i \(0.328365\pi\)
\(338\) 32.7535 1.78155
\(339\) −13.5548 −0.736196
\(340\) 76.6508 4.15697
\(341\) 2.60135 0.140871
\(342\) −37.6548 −2.03614
\(343\) 6.79417 0.366851
\(344\) 62.1123 3.34887
\(345\) −21.2139 −1.14212
\(346\) −40.1399 −2.15793
\(347\) −26.1619 −1.40445 −0.702223 0.711957i \(-0.747809\pi\)
−0.702223 + 0.711957i \(0.747809\pi\)
\(348\) −10.6660 −0.571760
\(349\) 12.5396 0.671230 0.335615 0.941999i \(-0.391056\pi\)
0.335615 + 0.941999i \(0.391056\pi\)
\(350\) 0.539815 0.0288543
\(351\) −3.93979 −0.210291
\(352\) −38.2106 −2.03663
\(353\) 11.1603 0.594001 0.297001 0.954877i \(-0.404014\pi\)
0.297001 + 0.954877i \(0.404014\pi\)
\(354\) −7.48768 −0.397966
\(355\) −23.8335 −1.26495
\(356\) −58.5262 −3.10188
\(357\) −3.34860 −0.177227
\(358\) −30.8531 −1.63064
\(359\) 32.8588 1.73422 0.867110 0.498117i \(-0.165975\pi\)
0.867110 + 0.498117i \(0.165975\pi\)
\(360\) 35.7172 1.88246
\(361\) 34.4523 1.81328
\(362\) −58.4280 −3.07091
\(363\) −2.28575 −0.119971
\(364\) −1.91036 −0.100130
\(365\) −26.2674 −1.37490
\(366\) −21.8356 −1.14137
\(367\) −13.3290 −0.695768 −0.347884 0.937538i \(-0.613100\pi\)
−0.347884 + 0.937538i \(0.613100\pi\)
\(368\) −96.4640 −5.02853
\(369\) 21.7169 1.13053
\(370\) −26.1779 −1.36092
\(371\) 5.33525 0.276992
\(372\) 4.48437 0.232504
\(373\) 8.88503 0.460050 0.230025 0.973185i \(-0.426119\pi\)
0.230025 + 0.973185i \(0.426119\pi\)
\(374\) −51.7534 −2.67611
\(375\) −10.9380 −0.564835
\(376\) −85.9967 −4.43494
\(377\) −1.62255 −0.0835658
\(378\) −6.62007 −0.340499
\(379\) 22.6120 1.16150 0.580750 0.814082i \(-0.302759\pi\)
0.580750 + 0.814082i \(0.302759\pi\)
\(380\) −84.7238 −4.34624
\(381\) 0.818184 0.0419168
\(382\) −9.43065 −0.482514
\(383\) −0.491019 −0.0250899 −0.0125450 0.999921i \(-0.503993\pi\)
−0.0125450 + 0.999921i \(0.503993\pi\)
\(384\) −7.13210 −0.363959
\(385\) −3.40321 −0.173444
\(386\) −37.4868 −1.90803
\(387\) 15.3756 0.781586
\(388\) −33.5731 −1.70442
\(389\) −33.0524 −1.67583 −0.837913 0.545804i \(-0.816224\pi\)
−0.837913 + 0.545804i \(0.816224\pi\)
\(390\) −4.89344 −0.247789
\(391\) −58.8361 −2.97547
\(392\) 53.2025 2.68713
\(393\) −16.1372 −0.814016
\(394\) 48.6796 2.45244
\(395\) 28.0964 1.41368
\(396\) −28.7521 −1.44485
\(397\) −24.9472 −1.25206 −0.626031 0.779798i \(-0.715322\pi\)
−0.626031 + 0.779798i \(0.715322\pi\)
\(398\) −42.1886 −2.11472
\(399\) 3.70128 0.185296
\(400\) 4.48616 0.224308
\(401\) 4.24375 0.211923 0.105961 0.994370i \(-0.466208\pi\)
0.105961 + 0.994370i \(0.466208\pi\)
\(402\) 0.376081 0.0187572
\(403\) 0.682176 0.0339816
\(404\) −5.66169 −0.281680
\(405\) 1.50798 0.0749324
\(406\) −2.72639 −0.135308
\(407\) 12.6109 0.625097
\(408\) −53.3899 −2.64320
\(409\) −9.07084 −0.448524 −0.224262 0.974529i \(-0.571997\pi\)
−0.224262 + 0.974529i \(0.571997\pi\)
\(410\) 68.4849 3.38223
\(411\) −19.0786 −0.941078
\(412\) −30.6546 −1.51024
\(413\) −1.36559 −0.0671961
\(414\) −45.8127 −2.25157
\(415\) −13.2811 −0.651942
\(416\) −10.0203 −0.491287
\(417\) 11.2469 0.550765
\(418\) 57.2042 2.79795
\(419\) 22.3057 1.08970 0.544852 0.838532i \(-0.316586\pi\)
0.544852 + 0.838532i \(0.316586\pi\)
\(420\) −5.86666 −0.286264
\(421\) −19.7844 −0.964234 −0.482117 0.876107i \(-0.660132\pi\)
−0.482117 + 0.876107i \(0.660132\pi\)
\(422\) −22.4905 −1.09482
\(423\) −21.2880 −1.03506
\(424\) 85.0650 4.13112
\(425\) 2.73623 0.132727
\(426\) 27.7403 1.34402
\(427\) −3.98233 −0.192719
\(428\) 55.6792 2.69135
\(429\) 2.35735 0.113814
\(430\) 48.4875 2.33827
\(431\) −13.1267 −0.632289 −0.316145 0.948711i \(-0.602388\pi\)
−0.316145 + 0.948711i \(0.602388\pi\)
\(432\) −55.0163 −2.64697
\(433\) 23.5459 1.13154 0.565772 0.824562i \(-0.308578\pi\)
0.565772 + 0.824562i \(0.308578\pi\)
\(434\) 1.14627 0.0550226
\(435\) −4.98280 −0.238907
\(436\) 66.9405 3.20587
\(437\) 65.0328 3.11094
\(438\) 30.5732 1.46084
\(439\) −5.08283 −0.242590 −0.121295 0.992616i \(-0.538705\pi\)
−0.121295 + 0.992616i \(0.538705\pi\)
\(440\) −54.2606 −2.58677
\(441\) 13.1700 0.627144
\(442\) −13.5718 −0.645544
\(443\) −27.4957 −1.30636 −0.653180 0.757202i \(-0.726566\pi\)
−0.653180 + 0.757202i \(0.726566\pi\)
\(444\) 21.7394 1.03170
\(445\) −27.3414 −1.29610
\(446\) −35.0101 −1.65778
\(447\) 2.04895 0.0969119
\(448\) −6.12479 −0.289369
\(449\) −20.1737 −0.952054 −0.476027 0.879431i \(-0.657924\pi\)
−0.476027 + 0.879431i \(0.657924\pi\)
\(450\) 2.13057 0.100436
\(451\) −32.9917 −1.55352
\(452\) −65.8632 −3.09795
\(453\) −4.45255 −0.209199
\(454\) 18.0649 0.847829
\(455\) −0.892455 −0.0418389
\(456\) 59.0131 2.76354
\(457\) 36.5943 1.71181 0.855905 0.517133i \(-0.173001\pi\)
0.855905 + 0.517133i \(0.173001\pi\)
\(458\) 52.5927 2.45750
\(459\) −33.5560 −1.56626
\(460\) −103.079 −4.80609
\(461\) −19.9762 −0.930385 −0.465193 0.885209i \(-0.654015\pi\)
−0.465193 + 0.885209i \(0.654015\pi\)
\(462\) 3.96107 0.184286
\(463\) −26.6366 −1.23791 −0.618955 0.785427i \(-0.712444\pi\)
−0.618955 + 0.785427i \(0.712444\pi\)
\(464\) −22.6578 −1.05186
\(465\) 2.09494 0.0971504
\(466\) 36.1060 1.67258
\(467\) −21.8308 −1.01021 −0.505103 0.863059i \(-0.668546\pi\)
−0.505103 + 0.863059i \(0.668546\pi\)
\(468\) −7.53992 −0.348533
\(469\) 0.0685887 0.00316713
\(470\) −67.1326 −3.09659
\(471\) 8.60080 0.396304
\(472\) −21.7729 −1.00218
\(473\) −23.3582 −1.07401
\(474\) −32.7021 −1.50205
\(475\) −3.02442 −0.138770
\(476\) −16.2710 −0.745778
\(477\) 21.0574 0.964153
\(478\) −40.3409 −1.84515
\(479\) 9.28019 0.424023 0.212011 0.977267i \(-0.431999\pi\)
0.212011 + 0.977267i \(0.431999\pi\)
\(480\) −30.7720 −1.40454
\(481\) 3.30706 0.150789
\(482\) −10.8642 −0.494851
\(483\) 4.50316 0.204901
\(484\) −11.1065 −0.504842
\(485\) −15.6842 −0.712181
\(486\) −41.9658 −1.90361
\(487\) 28.8945 1.30934 0.654668 0.755917i \(-0.272809\pi\)
0.654668 + 0.755917i \(0.272809\pi\)
\(488\) −63.4942 −2.87425
\(489\) −5.05921 −0.228785
\(490\) 41.5321 1.87623
\(491\) 22.0320 0.994290 0.497145 0.867667i \(-0.334382\pi\)
0.497145 + 0.867667i \(0.334382\pi\)
\(492\) −56.8730 −2.56403
\(493\) −13.8196 −0.622404
\(494\) 15.0012 0.674935
\(495\) −13.4320 −0.603721
\(496\) 9.52610 0.427734
\(497\) 5.05922 0.226937
\(498\) 15.4581 0.692696
\(499\) −13.3085 −0.595769 −0.297884 0.954602i \(-0.596281\pi\)
−0.297884 + 0.954602i \(0.596281\pi\)
\(500\) −53.1480 −2.37685
\(501\) 8.00350 0.357570
\(502\) −52.4487 −2.34090
\(503\) −38.8551 −1.73246 −0.866231 0.499643i \(-0.833464\pi\)
−0.866231 + 0.499643i \(0.833464\pi\)
\(504\) −7.58183 −0.337722
\(505\) −2.64494 −0.117698
\(506\) 69.5975 3.09398
\(507\) −12.7069 −0.564332
\(508\) 3.97559 0.176388
\(509\) 11.9069 0.527765 0.263883 0.964555i \(-0.414997\pi\)
0.263883 + 0.964555i \(0.414997\pi\)
\(510\) −41.6784 −1.84555
\(511\) 5.57587 0.246662
\(512\) 30.8723 1.36438
\(513\) 37.0902 1.63757
\(514\) 60.9336 2.68766
\(515\) −14.3207 −0.631047
\(516\) −40.2663 −1.77262
\(517\) 32.3402 1.42232
\(518\) 5.55688 0.244155
\(519\) 15.5725 0.683556
\(520\) −14.2293 −0.623995
\(521\) 13.1056 0.574167 0.287083 0.957906i \(-0.407314\pi\)
0.287083 + 0.957906i \(0.407314\pi\)
\(522\) −10.7607 −0.470981
\(523\) 9.88203 0.432111 0.216056 0.976381i \(-0.430681\pi\)
0.216056 + 0.976381i \(0.430681\pi\)
\(524\) −78.4113 −3.42542
\(525\) −0.209424 −0.00914002
\(526\) 15.6924 0.684222
\(527\) 5.81023 0.253098
\(528\) 32.9187 1.43260
\(529\) 56.1221 2.44009
\(530\) 66.4053 2.88446
\(531\) −5.38976 −0.233896
\(532\) 17.9846 0.779733
\(533\) −8.65171 −0.374747
\(534\) 31.8232 1.37713
\(535\) 26.0113 1.12457
\(536\) 1.09358 0.0472353
\(537\) 11.9696 0.516528
\(538\) 47.8036 2.06096
\(539\) −20.0075 −0.861785
\(540\) −58.7892 −2.52988
\(541\) 15.8552 0.681669 0.340835 0.940123i \(-0.389290\pi\)
0.340835 + 0.940123i \(0.389290\pi\)
\(542\) −47.6015 −2.04466
\(543\) 22.6675 0.972754
\(544\) −85.3451 −3.65914
\(545\) 31.2722 1.33955
\(546\) 1.03875 0.0444544
\(547\) 5.31702 0.227339 0.113670 0.993519i \(-0.463739\pi\)
0.113670 + 0.993519i \(0.463739\pi\)
\(548\) −92.7035 −3.96010
\(549\) −15.7177 −0.670814
\(550\) −3.23670 −0.138014
\(551\) 15.2751 0.650742
\(552\) 71.7982 3.05594
\(553\) −5.96413 −0.253621
\(554\) 78.5075 3.33547
\(555\) 10.1559 0.431092
\(556\) 54.6492 2.31764
\(557\) −36.5698 −1.54951 −0.774755 0.632261i \(-0.782127\pi\)
−0.774755 + 0.632261i \(0.782127\pi\)
\(558\) 4.52414 0.191522
\(559\) −6.12544 −0.259078
\(560\) −12.4625 −0.526636
\(561\) 20.0780 0.847695
\(562\) −3.02425 −0.127570
\(563\) 27.3771 1.15381 0.576904 0.816812i \(-0.304261\pi\)
0.576904 + 0.816812i \(0.304261\pi\)
\(564\) 55.7500 2.34750
\(565\) −30.7690 −1.29446
\(566\) −51.4219 −2.16142
\(567\) −0.320106 −0.0134432
\(568\) 80.6640 3.38459
\(569\) −12.6810 −0.531617 −0.265808 0.964026i \(-0.585639\pi\)
−0.265808 + 0.964026i \(0.585639\pi\)
\(570\) 46.0681 1.92958
\(571\) 13.2561 0.554751 0.277376 0.960762i \(-0.410535\pi\)
0.277376 + 0.960762i \(0.410535\pi\)
\(572\) 11.4544 0.478934
\(573\) 3.65867 0.152843
\(574\) −14.5375 −0.606785
\(575\) −3.67966 −0.153452
\(576\) −24.1736 −1.00723
\(577\) −41.1712 −1.71398 −0.856990 0.515333i \(-0.827668\pi\)
−0.856990 + 0.515333i \(0.827668\pi\)
\(578\) −70.6784 −2.93983
\(579\) 14.5432 0.604396
\(580\) −24.2116 −1.00533
\(581\) 2.81922 0.116961
\(582\) 18.2552 0.756701
\(583\) −31.9898 −1.32488
\(584\) 88.9015 3.67877
\(585\) −3.52239 −0.145633
\(586\) 6.12387 0.252975
\(587\) 5.17284 0.213506 0.106753 0.994286i \(-0.465955\pi\)
0.106753 + 0.994286i \(0.465955\pi\)
\(588\) −34.4902 −1.42235
\(589\) −6.42218 −0.264621
\(590\) −16.9968 −0.699747
\(591\) −18.8855 −0.776846
\(592\) 46.1807 1.89802
\(593\) −34.4971 −1.41663 −0.708313 0.705899i \(-0.750543\pi\)
−0.708313 + 0.705899i \(0.750543\pi\)
\(594\) 39.6936 1.62865
\(595\) −7.60122 −0.311619
\(596\) 9.95590 0.407810
\(597\) 16.3673 0.669868
\(598\) 18.2512 0.746346
\(599\) 22.3063 0.911410 0.455705 0.890131i \(-0.349387\pi\)
0.455705 + 0.890131i \(0.349387\pi\)
\(600\) −3.33905 −0.136316
\(601\) −6.22133 −0.253773 −0.126887 0.991917i \(-0.540498\pi\)
−0.126887 + 0.991917i \(0.540498\pi\)
\(602\) −10.2926 −0.419496
\(603\) 0.270709 0.0110241
\(604\) −21.6351 −0.880319
\(605\) −5.18858 −0.210946
\(606\) 3.07851 0.125056
\(607\) −41.2831 −1.67563 −0.837814 0.545955i \(-0.816167\pi\)
−0.837814 + 0.545955i \(0.816167\pi\)
\(608\) 94.3338 3.82574
\(609\) 1.05772 0.0428609
\(610\) −49.5662 −2.00688
\(611\) 8.48087 0.343099
\(612\) −64.2190 −2.59590
\(613\) 25.8987 1.04604 0.523018 0.852321i \(-0.324806\pi\)
0.523018 + 0.852321i \(0.324806\pi\)
\(614\) 34.5696 1.39511
\(615\) −26.5691 −1.07137
\(616\) 11.5181 0.464078
\(617\) 38.4627 1.54845 0.774225 0.632910i \(-0.218140\pi\)
0.774225 + 0.632910i \(0.218140\pi\)
\(618\) 16.6682 0.670495
\(619\) −25.8680 −1.03972 −0.519860 0.854251i \(-0.674016\pi\)
−0.519860 + 0.854251i \(0.674016\pi\)
\(620\) 10.1794 0.408813
\(621\) 45.1257 1.81083
\(622\) −41.9110 −1.68048
\(623\) 5.80385 0.232526
\(624\) 8.63257 0.345579
\(625\) −26.8972 −1.07589
\(626\) 17.9028 0.715541
\(627\) −22.1927 −0.886290
\(628\) 41.7916 1.66767
\(629\) 28.1669 1.12309
\(630\) −5.91869 −0.235806
\(631\) −25.1744 −1.00218 −0.501088 0.865396i \(-0.667067\pi\)
−0.501088 + 0.865396i \(0.667067\pi\)
\(632\) −95.0918 −3.78255
\(633\) 8.72530 0.346800
\(634\) −46.3011 −1.83885
\(635\) 1.85725 0.0737028
\(636\) −55.1460 −2.18668
\(637\) −5.24676 −0.207884
\(638\) 16.3473 0.647195
\(639\) 19.9680 0.789921
\(640\) −16.1897 −0.639952
\(641\) 0.360829 0.0142519 0.00712594 0.999975i \(-0.497732\pi\)
0.00712594 + 0.999975i \(0.497732\pi\)
\(642\) −30.2752 −1.19487
\(643\) 3.78669 0.149332 0.0746662 0.997209i \(-0.476211\pi\)
0.0746662 + 0.997209i \(0.476211\pi\)
\(644\) 21.8810 0.862233
\(645\) −18.8110 −0.740681
\(646\) 127.768 5.02697
\(647\) −11.5272 −0.453179 −0.226590 0.973990i \(-0.572758\pi\)
−0.226590 + 0.973990i \(0.572758\pi\)
\(648\) −5.10375 −0.200494
\(649\) 8.18798 0.321406
\(650\) −0.848791 −0.0332923
\(651\) −0.444700 −0.0174292
\(652\) −24.5829 −0.962739
\(653\) −35.2744 −1.38039 −0.690197 0.723622i \(-0.742476\pi\)
−0.690197 + 0.723622i \(0.742476\pi\)
\(654\) −36.3985 −1.42329
\(655\) −36.6310 −1.43129
\(656\) −120.815 −4.71703
\(657\) 22.0071 0.858580
\(658\) 14.2505 0.555542
\(659\) −6.14081 −0.239212 −0.119606 0.992821i \(-0.538163\pi\)
−0.119606 + 0.992821i \(0.538163\pi\)
\(660\) 35.1762 1.36923
\(661\) 0.711705 0.0276821 0.0138411 0.999904i \(-0.495594\pi\)
0.0138411 + 0.999904i \(0.495594\pi\)
\(662\) 31.8302 1.23712
\(663\) 5.26524 0.204485
\(664\) 44.9496 1.74438
\(665\) 8.40179 0.325807
\(666\) 21.9322 0.849855
\(667\) 18.5845 0.719594
\(668\) 38.8893 1.50467
\(669\) 13.5823 0.525124
\(670\) 0.853691 0.0329810
\(671\) 23.8779 0.921794
\(672\) 6.53209 0.251981
\(673\) −44.1131 −1.70043 −0.850217 0.526432i \(-0.823529\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(674\) −49.8074 −1.91851
\(675\) −2.09862 −0.0807760
\(676\) −61.7432 −2.37474
\(677\) −9.04562 −0.347652 −0.173826 0.984776i \(-0.555613\pi\)
−0.173826 + 0.984776i \(0.555613\pi\)
\(678\) 35.8127 1.37538
\(679\) 3.32934 0.127768
\(680\) −121.194 −4.64756
\(681\) −7.00839 −0.268562
\(682\) −6.87295 −0.263179
\(683\) −9.59421 −0.367112 −0.183556 0.983009i \(-0.558761\pi\)
−0.183556 + 0.983009i \(0.558761\pi\)
\(684\) 70.9827 2.71409
\(685\) −43.3078 −1.65471
\(686\) −17.9507 −0.685360
\(687\) −20.4036 −0.778447
\(688\) −85.5373 −3.26108
\(689\) −8.38899 −0.319595
\(690\) 56.0487 2.13374
\(691\) 8.70008 0.330967 0.165483 0.986213i \(-0.447082\pi\)
0.165483 + 0.986213i \(0.447082\pi\)
\(692\) 75.6672 2.87644
\(693\) 2.85125 0.108310
\(694\) 69.1217 2.62382
\(695\) 25.5302 0.968415
\(696\) 16.8642 0.639236
\(697\) −73.6883 −2.79114
\(698\) −33.1305 −1.25401
\(699\) −14.0075 −0.529813
\(700\) −1.01760 −0.0384617
\(701\) −30.4119 −1.14864 −0.574321 0.818630i \(-0.694734\pi\)
−0.574321 + 0.818630i \(0.694734\pi\)
\(702\) 10.4092 0.392870
\(703\) −31.1335 −1.17422
\(704\) 36.7239 1.38408
\(705\) 26.0444 0.980890
\(706\) −29.4862 −1.10973
\(707\) 0.561452 0.0211156
\(708\) 14.1149 0.530472
\(709\) 44.2104 1.66036 0.830179 0.557497i \(-0.188238\pi\)
0.830179 + 0.557497i \(0.188238\pi\)
\(710\) 62.9697 2.36321
\(711\) −23.5395 −0.882801
\(712\) 92.5364 3.46795
\(713\) −7.81354 −0.292619
\(714\) 8.84723 0.331099
\(715\) 5.35111 0.200120
\(716\) 58.1609 2.17357
\(717\) 15.6505 0.584477
\(718\) −86.8152 −3.23991
\(719\) −37.5002 −1.39852 −0.699261 0.714866i \(-0.746488\pi\)
−0.699261 + 0.714866i \(0.746488\pi\)
\(720\) −49.1876 −1.83311
\(721\) 3.03992 0.113212
\(722\) −91.0255 −3.38762
\(723\) 4.21482 0.156751
\(724\) 110.142 4.09339
\(725\) −0.864291 −0.0320989
\(726\) 6.03911 0.224132
\(727\) −50.2627 −1.86414 −0.932071 0.362276i \(-0.882000\pi\)
−0.932071 + 0.362276i \(0.882000\pi\)
\(728\) 3.02050 0.111947
\(729\) 14.3365 0.530983
\(730\) 69.4002 2.56862
\(731\) −52.1716 −1.92963
\(732\) 41.1621 1.52139
\(733\) 42.4330 1.56730 0.783648 0.621205i \(-0.213356\pi\)
0.783648 + 0.621205i \(0.213356\pi\)
\(734\) 35.2162 1.29985
\(735\) −16.1126 −0.594322
\(736\) 114.771 4.23052
\(737\) −0.411254 −0.0151487
\(738\) −57.3775 −2.11209
\(739\) 4.92702 0.181243 0.0906217 0.995885i \(-0.471115\pi\)
0.0906217 + 0.995885i \(0.471115\pi\)
\(740\) 49.3477 1.81406
\(741\) −5.81979 −0.213795
\(742\) −14.0961 −0.517484
\(743\) −44.3385 −1.62662 −0.813310 0.581830i \(-0.802337\pi\)
−0.813310 + 0.581830i \(0.802337\pi\)
\(744\) −7.09029 −0.259942
\(745\) 4.65105 0.170401
\(746\) −23.4749 −0.859476
\(747\) 11.1270 0.407117
\(748\) 97.5598 3.56714
\(749\) −5.52153 −0.201752
\(750\) 28.8989 1.05524
\(751\) −7.54396 −0.275283 −0.137642 0.990482i \(-0.543952\pi\)
−0.137642 + 0.990482i \(0.543952\pi\)
\(752\) 118.429 4.31867
\(753\) 20.3478 0.741514
\(754\) 4.28690 0.156120
\(755\) −10.1071 −0.367837
\(756\) 12.4794 0.453872
\(757\) −3.41994 −0.124300 −0.0621499 0.998067i \(-0.519796\pi\)
−0.0621499 + 0.998067i \(0.519796\pi\)
\(758\) −59.7425 −2.16995
\(759\) −27.0007 −0.980064
\(760\) 133.958 4.85916
\(761\) 0.188752 0.00684227 0.00342113 0.999994i \(-0.498911\pi\)
0.00342113 + 0.999994i \(0.498911\pi\)
\(762\) −2.16170 −0.0783101
\(763\) −6.63827 −0.240322
\(764\) 17.7776 0.643171
\(765\) −30.0009 −1.08468
\(766\) 1.29731 0.0468736
\(767\) 2.14721 0.0775312
\(768\) −6.57819 −0.237370
\(769\) −3.54424 −0.127809 −0.0639043 0.997956i \(-0.520355\pi\)
−0.0639043 + 0.997956i \(0.520355\pi\)
\(770\) 8.99152 0.324032
\(771\) −23.6395 −0.851356
\(772\) 70.6660 2.54333
\(773\) 46.2757 1.66442 0.832211 0.554459i \(-0.187075\pi\)
0.832211 + 0.554459i \(0.187075\pi\)
\(774\) −40.6234 −1.46018
\(775\) 0.363377 0.0130529
\(776\) 53.0828 1.90556
\(777\) −2.15582 −0.0773397
\(778\) 87.3269 3.13082
\(779\) 81.4493 2.91822
\(780\) 9.22457 0.330293
\(781\) −30.3348 −1.08546
\(782\) 155.449 5.55884
\(783\) 10.5993 0.378788
\(784\) −73.2672 −2.61669
\(785\) 19.5236 0.696826
\(786\) 42.6357 1.52076
\(787\) −32.9728 −1.17535 −0.587677 0.809095i \(-0.699958\pi\)
−0.587677 + 0.809095i \(0.699958\pi\)
\(788\) −91.7653 −3.26900
\(789\) −6.08796 −0.216737
\(790\) −74.2326 −2.64108
\(791\) 6.53145 0.232232
\(792\) 45.4603 1.61536
\(793\) 6.26171 0.222360
\(794\) 65.9122 2.33914
\(795\) −25.7623 −0.913694
\(796\) 79.5292 2.81884
\(797\) −22.2197 −0.787062 −0.393531 0.919311i \(-0.628747\pi\)
−0.393531 + 0.919311i \(0.628747\pi\)
\(798\) −9.77904 −0.346174
\(799\) 72.2333 2.55543
\(800\) −5.33756 −0.188711
\(801\) 22.9069 0.809377
\(802\) −11.2123 −0.395919
\(803\) −33.4326 −1.17981
\(804\) −0.708945 −0.0250026
\(805\) 10.2220 0.360279
\(806\) −1.80236 −0.0634854
\(807\) −18.5457 −0.652839
\(808\) 8.95177 0.314922
\(809\) −2.63715 −0.0927172 −0.0463586 0.998925i \(-0.514762\pi\)
−0.0463586 + 0.998925i \(0.514762\pi\)
\(810\) −3.98420 −0.139991
\(811\) −0.783721 −0.0275201 −0.0137601 0.999905i \(-0.504380\pi\)
−0.0137601 + 0.999905i \(0.504380\pi\)
\(812\) 5.13949 0.180361
\(813\) 18.4673 0.647675
\(814\) −33.3188 −1.16782
\(815\) −11.4842 −0.402275
\(816\) 73.5253 2.57390
\(817\) 57.6664 2.01749
\(818\) 23.9658 0.837945
\(819\) 0.747710 0.0261271
\(820\) −129.100 −4.50837
\(821\) −2.12851 −0.0742856 −0.0371428 0.999310i \(-0.511826\pi\)
−0.0371428 + 0.999310i \(0.511826\pi\)
\(822\) 50.4070 1.75815
\(823\) −31.8659 −1.11077 −0.555387 0.831592i \(-0.687430\pi\)
−0.555387 + 0.831592i \(0.687430\pi\)
\(824\) 48.4683 1.68847
\(825\) 1.25570 0.0437177
\(826\) 3.60797 0.125537
\(827\) 32.4426 1.12814 0.564070 0.825727i \(-0.309235\pi\)
0.564070 + 0.825727i \(0.309235\pi\)
\(828\) 86.3611 3.00125
\(829\) 38.8086 1.34788 0.673939 0.738787i \(-0.264601\pi\)
0.673939 + 0.738787i \(0.264601\pi\)
\(830\) 35.0895 1.21797
\(831\) −30.4574 −1.05656
\(832\) 9.63045 0.333876
\(833\) −44.6877 −1.54834
\(834\) −29.7152 −1.02895
\(835\) 18.1677 0.628719
\(836\) −107.835 −3.72955
\(837\) −4.45630 −0.154032
\(838\) −58.9332 −2.03581
\(839\) 24.5690 0.848217 0.424108 0.905611i \(-0.360588\pi\)
0.424108 + 0.905611i \(0.360588\pi\)
\(840\) 9.27584 0.320047
\(841\) −24.6348 −0.849476
\(842\) 52.2719 1.80141
\(843\) 1.17328 0.0404098
\(844\) 42.3965 1.45935
\(845\) −28.8442 −0.992271
\(846\) 56.2445 1.93373
\(847\) 1.10140 0.0378445
\(848\) −117.146 −4.02282
\(849\) 19.9494 0.684662
\(850\) −7.22932 −0.247964
\(851\) −37.8786 −1.29846
\(852\) −52.2929 −1.79153
\(853\) 3.84572 0.131675 0.0658374 0.997830i \(-0.479028\pi\)
0.0658374 + 0.997830i \(0.479028\pi\)
\(854\) 10.5216 0.360042
\(855\) 33.1606 1.13407
\(856\) −88.0350 −3.00897
\(857\) −3.82526 −0.130668 −0.0653342 0.997863i \(-0.520811\pi\)
−0.0653342 + 0.997863i \(0.520811\pi\)
\(858\) −6.22828 −0.212630
\(859\) −8.00146 −0.273006 −0.136503 0.990640i \(-0.543586\pi\)
−0.136503 + 0.990640i \(0.543586\pi\)
\(860\) −91.4032 −3.11682
\(861\) 5.63992 0.192208
\(862\) 34.6816 1.18126
\(863\) 25.1596 0.856443 0.428221 0.903674i \(-0.359140\pi\)
0.428221 + 0.903674i \(0.359140\pi\)
\(864\) 65.4575 2.22691
\(865\) 35.3491 1.20190
\(866\) −62.2100 −2.11398
\(867\) 27.4200 0.931234
\(868\) −2.16081 −0.0733428
\(869\) 35.7606 1.21309
\(870\) 13.1649 0.446332
\(871\) −0.107847 −0.00365426
\(872\) −105.840 −3.58421
\(873\) 13.1404 0.444735
\(874\) −171.821 −5.81194
\(875\) 5.27052 0.178176
\(876\) −57.6332 −1.94725
\(877\) 47.0932 1.59023 0.795113 0.606462i \(-0.207412\pi\)
0.795113 + 0.606462i \(0.207412\pi\)
\(878\) 13.4292 0.453213
\(879\) −2.37579 −0.0801334
\(880\) 74.7244 2.51896
\(881\) −32.7410 −1.10307 −0.551537 0.834150i \(-0.685958\pi\)
−0.551537 + 0.834150i \(0.685958\pi\)
\(882\) −34.7961 −1.17165
\(883\) 9.65046 0.324764 0.162382 0.986728i \(-0.448082\pi\)
0.162382 + 0.986728i \(0.448082\pi\)
\(884\) 25.5840 0.860483
\(885\) 6.59400 0.221655
\(886\) 72.6456 2.44058
\(887\) −26.5622 −0.891871 −0.445935 0.895065i \(-0.647129\pi\)
−0.445935 + 0.895065i \(0.647129\pi\)
\(888\) −34.3724 −1.15346
\(889\) −0.394246 −0.0132226
\(890\) 72.2378 2.42142
\(891\) 1.91934 0.0643002
\(892\) 65.9971 2.20975
\(893\) −79.8410 −2.67178
\(894\) −5.41346 −0.181053
\(895\) 27.1707 0.908217
\(896\) 3.43664 0.114810
\(897\) −7.08064 −0.236416
\(898\) 53.3002 1.77865
\(899\) −1.83527 −0.0612097
\(900\) −4.01631 −0.133877
\(901\) −71.4507 −2.38037
\(902\) 87.1663 2.90232
\(903\) 3.99308 0.132881
\(904\) 104.137 3.46355
\(905\) 51.4544 1.71040
\(906\) 11.7639 0.390831
\(907\) 25.7393 0.854660 0.427330 0.904096i \(-0.359454\pi\)
0.427330 + 0.904096i \(0.359454\pi\)
\(908\) −34.0540 −1.13012
\(909\) 2.21597 0.0734990
\(910\) 2.35793 0.0781646
\(911\) −25.9725 −0.860507 −0.430253 0.902708i \(-0.641576\pi\)
−0.430253 + 0.902708i \(0.641576\pi\)
\(912\) −81.2691 −2.69109
\(913\) −16.9039 −0.559438
\(914\) −96.6848 −3.19805
\(915\) 19.2295 0.635707
\(916\) −99.1419 −3.27574
\(917\) 7.77580 0.256780
\(918\) 88.6573 2.92613
\(919\) 14.8970 0.491408 0.245704 0.969345i \(-0.420981\pi\)
0.245704 + 0.969345i \(0.420981\pi\)
\(920\) 162.980 5.37328
\(921\) −13.4115 −0.441922
\(922\) 52.7786 1.73817
\(923\) −7.95497 −0.261841
\(924\) −7.46698 −0.245645
\(925\) 1.76158 0.0579205
\(926\) 70.3759 2.31269
\(927\) 11.9981 0.394069
\(928\) 26.9578 0.884935
\(929\) −23.8673 −0.783062 −0.391531 0.920165i \(-0.628054\pi\)
−0.391531 + 0.920165i \(0.628054\pi\)
\(930\) −5.53497 −0.181499
\(931\) 49.3943 1.61883
\(932\) −68.0630 −2.22948
\(933\) 16.2596 0.532315
\(934\) 57.6784 1.88729
\(935\) 45.5765 1.49051
\(936\) 11.9215 0.389665
\(937\) 27.8986 0.911407 0.455704 0.890132i \(-0.349388\pi\)
0.455704 + 0.890132i \(0.349388\pi\)
\(938\) −0.181216 −0.00591692
\(939\) −6.94550 −0.226658
\(940\) 126.551 4.12763
\(941\) 56.3426 1.83672 0.918359 0.395749i \(-0.129515\pi\)
0.918359 + 0.395749i \(0.129515\pi\)
\(942\) −22.7239 −0.740386
\(943\) 99.0953 3.22699
\(944\) 29.9842 0.975903
\(945\) 5.82994 0.189648
\(946\) 61.7140 2.00650
\(947\) 30.6416 0.995717 0.497859 0.867258i \(-0.334120\pi\)
0.497859 + 0.867258i \(0.334120\pi\)
\(948\) 61.6463 2.00218
\(949\) −8.76735 −0.284600
\(950\) 7.99072 0.259253
\(951\) 17.9628 0.582483
\(952\) 25.7262 0.833791
\(953\) −16.6997 −0.540958 −0.270479 0.962726i \(-0.587182\pi\)
−0.270479 + 0.962726i \(0.587182\pi\)
\(954\) −55.6352 −1.80125
\(955\) 8.30507 0.268746
\(956\) 76.0461 2.45951
\(957\) −6.34202 −0.205008
\(958\) −24.5189 −0.792170
\(959\) 9.19311 0.296861
\(960\) 29.5747 0.954520
\(961\) −30.2284 −0.975109
\(962\) −8.73749 −0.281708
\(963\) −21.7926 −0.702258
\(964\) 20.4800 0.659616
\(965\) 33.0127 1.06272
\(966\) −11.8977 −0.382801
\(967\) −50.3165 −1.61807 −0.809034 0.587762i \(-0.800009\pi\)
−0.809034 + 0.587762i \(0.800009\pi\)
\(968\) 17.5607 0.564421
\(969\) −49.5683 −1.59236
\(970\) 41.4387 1.33052
\(971\) −53.8266 −1.72738 −0.863689 0.504026i \(-0.831852\pi\)
−0.863689 + 0.504026i \(0.831852\pi\)
\(972\) 79.1093 2.53743
\(973\) −5.41939 −0.173738
\(974\) −76.3414 −2.44613
\(975\) 0.329293 0.0105458
\(976\) 87.4402 2.79889
\(977\) −51.7565 −1.65584 −0.827918 0.560849i \(-0.810475\pi\)
−0.827918 + 0.560849i \(0.810475\pi\)
\(978\) 13.3668 0.427422
\(979\) −34.7996 −1.11220
\(980\) −78.2917 −2.50094
\(981\) −26.2003 −0.836510
\(982\) −58.2101 −1.85756
\(983\) −15.5608 −0.496312 −0.248156 0.968720i \(-0.579825\pi\)
−0.248156 + 0.968720i \(0.579825\pi\)
\(984\) 89.9226 2.86663
\(985\) −42.8695 −1.36594
\(986\) 36.5124 1.16279
\(987\) −5.52855 −0.175976
\(988\) −28.2786 −0.899661
\(989\) 70.1598 2.23095
\(990\) 35.4882 1.12789
\(991\) −9.59922 −0.304929 −0.152465 0.988309i \(-0.548721\pi\)
−0.152465 + 0.988309i \(0.548721\pi\)
\(992\) −11.3340 −0.359855
\(993\) −12.3487 −0.391874
\(994\) −13.3668 −0.423969
\(995\) 37.1532 1.17784
\(996\) −29.1400 −0.923335
\(997\) −41.8528 −1.32549 −0.662745 0.748845i \(-0.730609\pi\)
−0.662745 + 0.748845i \(0.730609\pi\)
\(998\) 35.1619 1.11303
\(999\) −21.6033 −0.683498
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 \(a_p\))