Properties

Label 6008.2.a.e.1.41
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.41
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.21288 q^{3} +0.631281 q^{5} +4.31774 q^{7} +1.89684 q^{9} +O(q^{10})\) \(q+2.21288 q^{3} +0.631281 q^{5} +4.31774 q^{7} +1.89684 q^{9} -2.74984 q^{11} -3.87462 q^{13} +1.39695 q^{15} +3.58469 q^{17} +4.36126 q^{19} +9.55464 q^{21} -4.21696 q^{23} -4.60148 q^{25} -2.44116 q^{27} +4.85071 q^{29} +7.80799 q^{31} -6.08508 q^{33} +2.72570 q^{35} -2.92265 q^{37} -8.57408 q^{39} +2.10427 q^{41} +6.74428 q^{43} +1.19744 q^{45} +3.69909 q^{47} +11.6429 q^{49} +7.93249 q^{51} -3.10581 q^{53} -1.73592 q^{55} +9.65095 q^{57} +3.55015 q^{59} +14.8343 q^{61} +8.19005 q^{63} -2.44598 q^{65} +13.5276 q^{67} -9.33162 q^{69} +5.91516 q^{71} +10.0555 q^{73} -10.1825 q^{75} -11.8731 q^{77} +3.57721 q^{79} -11.0925 q^{81} -1.16410 q^{83} +2.26295 q^{85} +10.7340 q^{87} +1.16450 q^{89} -16.7296 q^{91} +17.2782 q^{93} +2.75318 q^{95} -12.5312 q^{97} -5.21601 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.21288 1.27761 0.638803 0.769370i \(-0.279430\pi\)
0.638803 + 0.769370i \(0.279430\pi\)
\(4\) 0 0
\(5\) 0.631281 0.282317 0.141159 0.989987i \(-0.454917\pi\)
0.141159 + 0.989987i \(0.454917\pi\)
\(6\) 0 0
\(7\) 4.31774 1.63195 0.815976 0.578086i \(-0.196200\pi\)
0.815976 + 0.578086i \(0.196200\pi\)
\(8\) 0 0
\(9\) 1.89684 0.632280
\(10\) 0 0
\(11\) −2.74984 −0.829109 −0.414555 0.910024i \(-0.636063\pi\)
−0.414555 + 0.910024i \(0.636063\pi\)
\(12\) 0 0
\(13\) −3.87462 −1.07463 −0.537314 0.843382i \(-0.680561\pi\)
−0.537314 + 0.843382i \(0.680561\pi\)
\(14\) 0 0
\(15\) 1.39695 0.360691
\(16\) 0 0
\(17\) 3.58469 0.869415 0.434707 0.900572i \(-0.356852\pi\)
0.434707 + 0.900572i \(0.356852\pi\)
\(18\) 0 0
\(19\) 4.36126 1.00054 0.500271 0.865869i \(-0.333234\pi\)
0.500271 + 0.865869i \(0.333234\pi\)
\(20\) 0 0
\(21\) 9.55464 2.08499
\(22\) 0 0
\(23\) −4.21696 −0.879296 −0.439648 0.898170i \(-0.644897\pi\)
−0.439648 + 0.898170i \(0.644897\pi\)
\(24\) 0 0
\(25\) −4.60148 −0.920297
\(26\) 0 0
\(27\) −2.44116 −0.469802
\(28\) 0 0
\(29\) 4.85071 0.900753 0.450377 0.892839i \(-0.351290\pi\)
0.450377 + 0.892839i \(0.351290\pi\)
\(30\) 0 0
\(31\) 7.80799 1.40236 0.701179 0.712986i \(-0.252658\pi\)
0.701179 + 0.712986i \(0.252658\pi\)
\(32\) 0 0
\(33\) −6.08508 −1.05928
\(34\) 0 0
\(35\) 2.72570 0.460728
\(36\) 0 0
\(37\) −2.92265 −0.480481 −0.240240 0.970713i \(-0.577226\pi\)
−0.240240 + 0.970713i \(0.577226\pi\)
\(38\) 0 0
\(39\) −8.57408 −1.37295
\(40\) 0 0
\(41\) 2.10427 0.328631 0.164316 0.986408i \(-0.447458\pi\)
0.164316 + 0.986408i \(0.447458\pi\)
\(42\) 0 0
\(43\) 6.74428 1.02849 0.514247 0.857642i \(-0.328072\pi\)
0.514247 + 0.857642i \(0.328072\pi\)
\(44\) 0 0
\(45\) 1.19744 0.178503
\(46\) 0 0
\(47\) 3.69909 0.539567 0.269784 0.962921i \(-0.413048\pi\)
0.269784 + 0.962921i \(0.413048\pi\)
\(48\) 0 0
\(49\) 11.6429 1.66327
\(50\) 0 0
\(51\) 7.93249 1.11077
\(52\) 0 0
\(53\) −3.10581 −0.426616 −0.213308 0.976985i \(-0.568424\pi\)
−0.213308 + 0.976985i \(0.568424\pi\)
\(54\) 0 0
\(55\) −1.73592 −0.234072
\(56\) 0 0
\(57\) 9.65095 1.27830
\(58\) 0 0
\(59\) 3.55015 0.462191 0.231095 0.972931i \(-0.425769\pi\)
0.231095 + 0.972931i \(0.425769\pi\)
\(60\) 0 0
\(61\) 14.8343 1.89934 0.949671 0.313249i \(-0.101417\pi\)
0.949671 + 0.313249i \(0.101417\pi\)
\(62\) 0 0
\(63\) 8.19005 1.03185
\(64\) 0 0
\(65\) −2.44598 −0.303386
\(66\) 0 0
\(67\) 13.5276 1.65266 0.826328 0.563189i \(-0.190426\pi\)
0.826328 + 0.563189i \(0.190426\pi\)
\(68\) 0 0
\(69\) −9.33162 −1.12339
\(70\) 0 0
\(71\) 5.91516 0.702001 0.351000 0.936375i \(-0.385842\pi\)
0.351000 + 0.936375i \(0.385842\pi\)
\(72\) 0 0
\(73\) 10.0555 1.17690 0.588451 0.808533i \(-0.299738\pi\)
0.588451 + 0.808533i \(0.299738\pi\)
\(74\) 0 0
\(75\) −10.1825 −1.17578
\(76\) 0 0
\(77\) −11.8731 −1.35307
\(78\) 0 0
\(79\) 3.57721 0.402467 0.201234 0.979543i \(-0.435505\pi\)
0.201234 + 0.979543i \(0.435505\pi\)
\(80\) 0 0
\(81\) −11.0925 −1.23250
\(82\) 0 0
\(83\) −1.16410 −0.127776 −0.0638882 0.997957i \(-0.520350\pi\)
−0.0638882 + 0.997957i \(0.520350\pi\)
\(84\) 0 0
\(85\) 2.26295 0.245451
\(86\) 0 0
\(87\) 10.7340 1.15081
\(88\) 0 0
\(89\) 1.16450 0.123437 0.0617183 0.998094i \(-0.480342\pi\)
0.0617183 + 0.998094i \(0.480342\pi\)
\(90\) 0 0
\(91\) −16.7296 −1.75374
\(92\) 0 0
\(93\) 17.2782 1.79166
\(94\) 0 0
\(95\) 2.75318 0.282470
\(96\) 0 0
\(97\) −12.5312 −1.27235 −0.636173 0.771546i \(-0.719484\pi\)
−0.636173 + 0.771546i \(0.719484\pi\)
\(98\) 0 0
\(99\) −5.21601 −0.524229
\(100\) 0 0
\(101\) −9.26514 −0.921916 −0.460958 0.887422i \(-0.652494\pi\)
−0.460958 + 0.887422i \(0.652494\pi\)
\(102\) 0 0
\(103\) −1.27125 −0.125260 −0.0626300 0.998037i \(-0.519949\pi\)
−0.0626300 + 0.998037i \(0.519949\pi\)
\(104\) 0 0
\(105\) 6.03166 0.588629
\(106\) 0 0
\(107\) 6.95788 0.672644 0.336322 0.941747i \(-0.390817\pi\)
0.336322 + 0.941747i \(0.390817\pi\)
\(108\) 0 0
\(109\) 0.584876 0.0560209 0.0280105 0.999608i \(-0.491083\pi\)
0.0280105 + 0.999608i \(0.491083\pi\)
\(110\) 0 0
\(111\) −6.46748 −0.613866
\(112\) 0 0
\(113\) −7.48539 −0.704167 −0.352083 0.935969i \(-0.614527\pi\)
−0.352083 + 0.935969i \(0.614527\pi\)
\(114\) 0 0
\(115\) −2.66208 −0.248240
\(116\) 0 0
\(117\) −7.34954 −0.679465
\(118\) 0 0
\(119\) 15.4778 1.41884
\(120\) 0 0
\(121\) −3.43836 −0.312578
\(122\) 0 0
\(123\) 4.65649 0.419862
\(124\) 0 0
\(125\) −6.06123 −0.542133
\(126\) 0 0
\(127\) 8.11738 0.720301 0.360151 0.932894i \(-0.382725\pi\)
0.360151 + 0.932894i \(0.382725\pi\)
\(128\) 0 0
\(129\) 14.9243 1.31401
\(130\) 0 0
\(131\) 9.04443 0.790216 0.395108 0.918635i \(-0.370707\pi\)
0.395108 + 0.918635i \(0.370707\pi\)
\(132\) 0 0
\(133\) 18.8308 1.63284
\(134\) 0 0
\(135\) −1.54106 −0.132633
\(136\) 0 0
\(137\) 9.13433 0.780398 0.390199 0.920730i \(-0.372406\pi\)
0.390199 + 0.920730i \(0.372406\pi\)
\(138\) 0 0
\(139\) 9.67848 0.820918 0.410459 0.911879i \(-0.365369\pi\)
0.410459 + 0.911879i \(0.365369\pi\)
\(140\) 0 0
\(141\) 8.18564 0.689355
\(142\) 0 0
\(143\) 10.6546 0.890984
\(144\) 0 0
\(145\) 3.06216 0.254298
\(146\) 0 0
\(147\) 25.7643 2.12500
\(148\) 0 0
\(149\) 3.89320 0.318944 0.159472 0.987202i \(-0.449021\pi\)
0.159472 + 0.987202i \(0.449021\pi\)
\(150\) 0 0
\(151\) −8.83702 −0.719146 −0.359573 0.933117i \(-0.617078\pi\)
−0.359573 + 0.933117i \(0.617078\pi\)
\(152\) 0 0
\(153\) 6.79958 0.549713
\(154\) 0 0
\(155\) 4.92904 0.395910
\(156\) 0 0
\(157\) 11.4867 0.916736 0.458368 0.888762i \(-0.348434\pi\)
0.458368 + 0.888762i \(0.348434\pi\)
\(158\) 0 0
\(159\) −6.87278 −0.545047
\(160\) 0 0
\(161\) −18.2077 −1.43497
\(162\) 0 0
\(163\) −18.0117 −1.41078 −0.705392 0.708818i \(-0.749229\pi\)
−0.705392 + 0.708818i \(0.749229\pi\)
\(164\) 0 0
\(165\) −3.84139 −0.299052
\(166\) 0 0
\(167\) 8.30351 0.642545 0.321273 0.946987i \(-0.395889\pi\)
0.321273 + 0.946987i \(0.395889\pi\)
\(168\) 0 0
\(169\) 2.01272 0.154824
\(170\) 0 0
\(171\) 8.27261 0.632622
\(172\) 0 0
\(173\) −16.4024 −1.24705 −0.623527 0.781802i \(-0.714301\pi\)
−0.623527 + 0.781802i \(0.714301\pi\)
\(174\) 0 0
\(175\) −19.8680 −1.50188
\(176\) 0 0
\(177\) 7.85607 0.590498
\(178\) 0 0
\(179\) −6.43860 −0.481243 −0.240622 0.970619i \(-0.577351\pi\)
−0.240622 + 0.970619i \(0.577351\pi\)
\(180\) 0 0
\(181\) 9.27665 0.689528 0.344764 0.938689i \(-0.387959\pi\)
0.344764 + 0.938689i \(0.387959\pi\)
\(182\) 0 0
\(183\) 32.8266 2.42661
\(184\) 0 0
\(185\) −1.84501 −0.135648
\(186\) 0 0
\(187\) −9.85734 −0.720840
\(188\) 0 0
\(189\) −10.5403 −0.766694
\(190\) 0 0
\(191\) 2.88178 0.208518 0.104259 0.994550i \(-0.466753\pi\)
0.104259 + 0.994550i \(0.466753\pi\)
\(192\) 0 0
\(193\) −23.9742 −1.72570 −0.862849 0.505462i \(-0.831322\pi\)
−0.862849 + 0.505462i \(0.831322\pi\)
\(194\) 0 0
\(195\) −5.41265 −0.387608
\(196\) 0 0
\(197\) 0.980826 0.0698810 0.0349405 0.999389i \(-0.488876\pi\)
0.0349405 + 0.999389i \(0.488876\pi\)
\(198\) 0 0
\(199\) −18.3854 −1.30331 −0.651653 0.758517i \(-0.725924\pi\)
−0.651653 + 0.758517i \(0.725924\pi\)
\(200\) 0 0
\(201\) 29.9349 2.11145
\(202\) 0 0
\(203\) 20.9441 1.46999
\(204\) 0 0
\(205\) 1.32838 0.0927783
\(206\) 0 0
\(207\) −7.99888 −0.555961
\(208\) 0 0
\(209\) −11.9928 −0.829559
\(210\) 0 0
\(211\) 7.91434 0.544846 0.272423 0.962178i \(-0.412175\pi\)
0.272423 + 0.962178i \(0.412175\pi\)
\(212\) 0 0
\(213\) 13.0896 0.896881
\(214\) 0 0
\(215\) 4.25754 0.290362
\(216\) 0 0
\(217\) 33.7129 2.28858
\(218\) 0 0
\(219\) 22.2515 1.50362
\(220\) 0 0
\(221\) −13.8893 −0.934297
\(222\) 0 0
\(223\) −11.0381 −0.739164 −0.369582 0.929198i \(-0.620499\pi\)
−0.369582 + 0.929198i \(0.620499\pi\)
\(224\) 0 0
\(225\) −8.72827 −0.581885
\(226\) 0 0
\(227\) 12.4984 0.829548 0.414774 0.909924i \(-0.363861\pi\)
0.414774 + 0.909924i \(0.363861\pi\)
\(228\) 0 0
\(229\) −28.8715 −1.90788 −0.953941 0.299993i \(-0.903016\pi\)
−0.953941 + 0.299993i \(0.903016\pi\)
\(230\) 0 0
\(231\) −26.2738 −1.72869
\(232\) 0 0
\(233\) −23.1048 −1.51364 −0.756821 0.653622i \(-0.773249\pi\)
−0.756821 + 0.653622i \(0.773249\pi\)
\(234\) 0 0
\(235\) 2.33516 0.152329
\(236\) 0 0
\(237\) 7.91593 0.514195
\(238\) 0 0
\(239\) −16.0749 −1.03980 −0.519899 0.854228i \(-0.674031\pi\)
−0.519899 + 0.854228i \(0.674031\pi\)
\(240\) 0 0
\(241\) 3.20222 0.206273 0.103137 0.994667i \(-0.467112\pi\)
0.103137 + 0.994667i \(0.467112\pi\)
\(242\) 0 0
\(243\) −17.2229 −1.10485
\(244\) 0 0
\(245\) 7.34991 0.469569
\(246\) 0 0
\(247\) −16.8983 −1.07521
\(248\) 0 0
\(249\) −2.57601 −0.163248
\(250\) 0 0
\(251\) −23.1396 −1.46056 −0.730278 0.683150i \(-0.760610\pi\)
−0.730278 + 0.683150i \(0.760610\pi\)
\(252\) 0 0
\(253\) 11.5960 0.729032
\(254\) 0 0
\(255\) 5.00763 0.313590
\(256\) 0 0
\(257\) −3.47729 −0.216907 −0.108454 0.994102i \(-0.534590\pi\)
−0.108454 + 0.994102i \(0.534590\pi\)
\(258\) 0 0
\(259\) −12.6192 −0.784121
\(260\) 0 0
\(261\) 9.20101 0.569528
\(262\) 0 0
\(263\) −16.2698 −1.00324 −0.501619 0.865089i \(-0.667262\pi\)
−0.501619 + 0.865089i \(0.667262\pi\)
\(264\) 0 0
\(265\) −1.96064 −0.120441
\(266\) 0 0
\(267\) 2.57690 0.157703
\(268\) 0 0
\(269\) −4.20248 −0.256230 −0.128115 0.991759i \(-0.540893\pi\)
−0.128115 + 0.991759i \(0.540893\pi\)
\(270\) 0 0
\(271\) −10.1689 −0.617714 −0.308857 0.951109i \(-0.599946\pi\)
−0.308857 + 0.951109i \(0.599946\pi\)
\(272\) 0 0
\(273\) −37.0206 −2.24059
\(274\) 0 0
\(275\) 12.6534 0.763027
\(276\) 0 0
\(277\) −0.162834 −0.00978374 −0.00489187 0.999988i \(-0.501557\pi\)
−0.00489187 + 0.999988i \(0.501557\pi\)
\(278\) 0 0
\(279\) 14.8105 0.886682
\(280\) 0 0
\(281\) −9.64772 −0.575534 −0.287767 0.957700i \(-0.592913\pi\)
−0.287767 + 0.957700i \(0.592913\pi\)
\(282\) 0 0
\(283\) 13.9268 0.827865 0.413932 0.910308i \(-0.364155\pi\)
0.413932 + 0.910308i \(0.364155\pi\)
\(284\) 0 0
\(285\) 6.09246 0.360886
\(286\) 0 0
\(287\) 9.08567 0.536310
\(288\) 0 0
\(289\) −4.15000 −0.244118
\(290\) 0 0
\(291\) −27.7300 −1.62556
\(292\) 0 0
\(293\) −6.12245 −0.357677 −0.178839 0.983878i \(-0.557234\pi\)
−0.178839 + 0.983878i \(0.557234\pi\)
\(294\) 0 0
\(295\) 2.24114 0.130484
\(296\) 0 0
\(297\) 6.71282 0.389517
\(298\) 0 0
\(299\) 16.3391 0.944916
\(300\) 0 0
\(301\) 29.1201 1.67845
\(302\) 0 0
\(303\) −20.5026 −1.17785
\(304\) 0 0
\(305\) 9.36463 0.536217
\(306\) 0 0
\(307\) 18.8744 1.07722 0.538611 0.842555i \(-0.318949\pi\)
0.538611 + 0.842555i \(0.318949\pi\)
\(308\) 0 0
\(309\) −2.81313 −0.160033
\(310\) 0 0
\(311\) −13.3670 −0.757976 −0.378988 0.925402i \(-0.623728\pi\)
−0.378988 + 0.925402i \(0.623728\pi\)
\(312\) 0 0
\(313\) 7.22783 0.408541 0.204270 0.978914i \(-0.434518\pi\)
0.204270 + 0.978914i \(0.434518\pi\)
\(314\) 0 0
\(315\) 5.17022 0.291309
\(316\) 0 0
\(317\) 12.4311 0.698199 0.349099 0.937086i \(-0.386488\pi\)
0.349099 + 0.937086i \(0.386488\pi\)
\(318\) 0 0
\(319\) −13.3387 −0.746823
\(320\) 0 0
\(321\) 15.3970 0.859374
\(322\) 0 0
\(323\) 15.6338 0.869886
\(324\) 0 0
\(325\) 17.8290 0.988976
\(326\) 0 0
\(327\) 1.29426 0.0715727
\(328\) 0 0
\(329\) 15.9717 0.880548
\(330\) 0 0
\(331\) −20.0366 −1.10131 −0.550657 0.834732i \(-0.685623\pi\)
−0.550657 + 0.834732i \(0.685623\pi\)
\(332\) 0 0
\(333\) −5.54380 −0.303798
\(334\) 0 0
\(335\) 8.53970 0.466573
\(336\) 0 0
\(337\) 1.82672 0.0995077 0.0497539 0.998762i \(-0.484156\pi\)
0.0497539 + 0.998762i \(0.484156\pi\)
\(338\) 0 0
\(339\) −16.5643 −0.899648
\(340\) 0 0
\(341\) −21.4708 −1.16271
\(342\) 0 0
\(343\) 20.0467 1.08242
\(344\) 0 0
\(345\) −5.89087 −0.317154
\(346\) 0 0
\(347\) −8.77305 −0.470962 −0.235481 0.971879i \(-0.575667\pi\)
−0.235481 + 0.971879i \(0.575667\pi\)
\(348\) 0 0
\(349\) 15.7589 0.843552 0.421776 0.906700i \(-0.361407\pi\)
0.421776 + 0.906700i \(0.361407\pi\)
\(350\) 0 0
\(351\) 9.45859 0.504862
\(352\) 0 0
\(353\) −25.6824 −1.36693 −0.683467 0.729982i \(-0.739529\pi\)
−0.683467 + 0.729982i \(0.739529\pi\)
\(354\) 0 0
\(355\) 3.73413 0.198187
\(356\) 0 0
\(357\) 34.2504 1.81272
\(358\) 0 0
\(359\) −28.4542 −1.50176 −0.750878 0.660441i \(-0.770369\pi\)
−0.750878 + 0.660441i \(0.770369\pi\)
\(360\) 0 0
\(361\) 0.0206039 0.00108442
\(362\) 0 0
\(363\) −7.60867 −0.399352
\(364\) 0 0
\(365\) 6.34782 0.332260
\(366\) 0 0
\(367\) −10.0337 −0.523753 −0.261876 0.965101i \(-0.584341\pi\)
−0.261876 + 0.965101i \(0.584341\pi\)
\(368\) 0 0
\(369\) 3.99145 0.207787
\(370\) 0 0
\(371\) −13.4101 −0.696216
\(372\) 0 0
\(373\) 33.1622 1.71708 0.858538 0.512750i \(-0.171373\pi\)
0.858538 + 0.512750i \(0.171373\pi\)
\(374\) 0 0
\(375\) −13.4128 −0.692633
\(376\) 0 0
\(377\) −18.7947 −0.967975
\(378\) 0 0
\(379\) −24.1456 −1.24028 −0.620138 0.784493i \(-0.712923\pi\)
−0.620138 + 0.784493i \(0.712923\pi\)
\(380\) 0 0
\(381\) 17.9628 0.920262
\(382\) 0 0
\(383\) −14.7826 −0.755356 −0.377678 0.925937i \(-0.623277\pi\)
−0.377678 + 0.925937i \(0.623277\pi\)
\(384\) 0 0
\(385\) −7.49526 −0.381994
\(386\) 0 0
\(387\) 12.7928 0.650296
\(388\) 0 0
\(389\) 31.7155 1.60804 0.804021 0.594601i \(-0.202690\pi\)
0.804021 + 0.594601i \(0.202690\pi\)
\(390\) 0 0
\(391\) −15.1165 −0.764473
\(392\) 0 0
\(393\) 20.0142 1.00958
\(394\) 0 0
\(395\) 2.25822 0.113623
\(396\) 0 0
\(397\) −7.28802 −0.365775 −0.182888 0.983134i \(-0.558544\pi\)
−0.182888 + 0.983134i \(0.558544\pi\)
\(398\) 0 0
\(399\) 41.6703 2.08612
\(400\) 0 0
\(401\) −29.4462 −1.47047 −0.735237 0.677810i \(-0.762929\pi\)
−0.735237 + 0.677810i \(0.762929\pi\)
\(402\) 0 0
\(403\) −30.2530 −1.50701
\(404\) 0 0
\(405\) −7.00249 −0.347957
\(406\) 0 0
\(407\) 8.03683 0.398371
\(408\) 0 0
\(409\) −2.97949 −0.147326 −0.0736631 0.997283i \(-0.523469\pi\)
−0.0736631 + 0.997283i \(0.523469\pi\)
\(410\) 0 0
\(411\) 20.2132 0.997042
\(412\) 0 0
\(413\) 15.3286 0.754273
\(414\) 0 0
\(415\) −0.734873 −0.0360735
\(416\) 0 0
\(417\) 21.4173 1.04881
\(418\) 0 0
\(419\) −31.9364 −1.56020 −0.780098 0.625657i \(-0.784831\pi\)
−0.780098 + 0.625657i \(0.784831\pi\)
\(420\) 0 0
\(421\) 1.36468 0.0665104 0.0332552 0.999447i \(-0.489413\pi\)
0.0332552 + 0.999447i \(0.489413\pi\)
\(422\) 0 0
\(423\) 7.01657 0.341157
\(424\) 0 0
\(425\) −16.4949 −0.800120
\(426\) 0 0
\(427\) 64.0508 3.09963
\(428\) 0 0
\(429\) 23.5774 1.13833
\(430\) 0 0
\(431\) −19.0647 −0.918312 −0.459156 0.888356i \(-0.651848\pi\)
−0.459156 + 0.888356i \(0.651848\pi\)
\(432\) 0 0
\(433\) −12.1700 −0.584851 −0.292425 0.956288i \(-0.594462\pi\)
−0.292425 + 0.956288i \(0.594462\pi\)
\(434\) 0 0
\(435\) 6.77619 0.324893
\(436\) 0 0
\(437\) −18.3912 −0.879773
\(438\) 0 0
\(439\) 6.34306 0.302738 0.151369 0.988477i \(-0.451632\pi\)
0.151369 + 0.988477i \(0.451632\pi\)
\(440\) 0 0
\(441\) 22.0846 1.05165
\(442\) 0 0
\(443\) 35.7721 1.69958 0.849792 0.527119i \(-0.176728\pi\)
0.849792 + 0.527119i \(0.176728\pi\)
\(444\) 0 0
\(445\) 0.735126 0.0348483
\(446\) 0 0
\(447\) 8.61519 0.407484
\(448\) 0 0
\(449\) −6.74464 −0.318299 −0.159150 0.987254i \(-0.550875\pi\)
−0.159150 + 0.987254i \(0.550875\pi\)
\(450\) 0 0
\(451\) −5.78641 −0.272471
\(452\) 0 0
\(453\) −19.5553 −0.918786
\(454\) 0 0
\(455\) −10.5611 −0.495111
\(456\) 0 0
\(457\) 32.0403 1.49878 0.749390 0.662129i \(-0.230347\pi\)
0.749390 + 0.662129i \(0.230347\pi\)
\(458\) 0 0
\(459\) −8.75081 −0.408453
\(460\) 0 0
\(461\) 5.61403 0.261471 0.130736 0.991417i \(-0.458266\pi\)
0.130736 + 0.991417i \(0.458266\pi\)
\(462\) 0 0
\(463\) 1.00691 0.0467953 0.0233976 0.999726i \(-0.492552\pi\)
0.0233976 + 0.999726i \(0.492552\pi\)
\(464\) 0 0
\(465\) 10.9074 0.505817
\(466\) 0 0
\(467\) −6.76760 −0.313167 −0.156584 0.987665i \(-0.550048\pi\)
−0.156584 + 0.987665i \(0.550048\pi\)
\(468\) 0 0
\(469\) 58.4085 2.69705
\(470\) 0 0
\(471\) 25.4186 1.17123
\(472\) 0 0
\(473\) −18.5457 −0.852734
\(474\) 0 0
\(475\) −20.0683 −0.920796
\(476\) 0 0
\(477\) −5.89122 −0.269740
\(478\) 0 0
\(479\) 24.6305 1.12539 0.562697 0.826663i \(-0.309764\pi\)
0.562697 + 0.826663i \(0.309764\pi\)
\(480\) 0 0
\(481\) 11.3242 0.516338
\(482\) 0 0
\(483\) −40.2915 −1.83333
\(484\) 0 0
\(485\) −7.91068 −0.359206
\(486\) 0 0
\(487\) 28.6500 1.29826 0.649128 0.760680i \(-0.275134\pi\)
0.649128 + 0.760680i \(0.275134\pi\)
\(488\) 0 0
\(489\) −39.8577 −1.80243
\(490\) 0 0
\(491\) 31.6220 1.42708 0.713541 0.700614i \(-0.247090\pi\)
0.713541 + 0.700614i \(0.247090\pi\)
\(492\) 0 0
\(493\) 17.3883 0.783129
\(494\) 0 0
\(495\) −3.29277 −0.147999
\(496\) 0 0
\(497\) 25.5401 1.14563
\(498\) 0 0
\(499\) 17.0030 0.761160 0.380580 0.924748i \(-0.375724\pi\)
0.380580 + 0.924748i \(0.375724\pi\)
\(500\) 0 0
\(501\) 18.3747 0.820920
\(502\) 0 0
\(503\) 22.4988 1.00317 0.501587 0.865107i \(-0.332750\pi\)
0.501587 + 0.865107i \(0.332750\pi\)
\(504\) 0 0
\(505\) −5.84890 −0.260273
\(506\) 0 0
\(507\) 4.45390 0.197805
\(508\) 0 0
\(509\) 3.67071 0.162701 0.0813507 0.996686i \(-0.474077\pi\)
0.0813507 + 0.996686i \(0.474077\pi\)
\(510\) 0 0
\(511\) 43.4168 1.92065
\(512\) 0 0
\(513\) −10.6466 −0.470057
\(514\) 0 0
\(515\) −0.802516 −0.0353631
\(516\) 0 0
\(517\) −10.1719 −0.447360
\(518\) 0 0
\(519\) −36.2966 −1.59325
\(520\) 0 0
\(521\) −2.12912 −0.0932783 −0.0466391 0.998912i \(-0.514851\pi\)
−0.0466391 + 0.998912i \(0.514851\pi\)
\(522\) 0 0
\(523\) −17.2832 −0.755741 −0.377870 0.925859i \(-0.623343\pi\)
−0.377870 + 0.925859i \(0.623343\pi\)
\(524\) 0 0
\(525\) −43.9655 −1.91881
\(526\) 0 0
\(527\) 27.9892 1.21923
\(528\) 0 0
\(529\) −5.21729 −0.226839
\(530\) 0 0
\(531\) 6.73407 0.292234
\(532\) 0 0
\(533\) −8.15324 −0.353156
\(534\) 0 0
\(535\) 4.39238 0.189899
\(536\) 0 0
\(537\) −14.2478 −0.614840
\(538\) 0 0
\(539\) −32.0161 −1.37903
\(540\) 0 0
\(541\) 26.6126 1.14416 0.572082 0.820196i \(-0.306136\pi\)
0.572082 + 0.820196i \(0.306136\pi\)
\(542\) 0 0
\(543\) 20.5281 0.880946
\(544\) 0 0
\(545\) 0.369221 0.0158157
\(546\) 0 0
\(547\) −6.20409 −0.265268 −0.132634 0.991165i \(-0.542343\pi\)
−0.132634 + 0.991165i \(0.542343\pi\)
\(548\) 0 0
\(549\) 28.1383 1.20092
\(550\) 0 0
\(551\) 21.1552 0.901242
\(552\) 0 0
\(553\) 15.4454 0.656807
\(554\) 0 0
\(555\) −4.08279 −0.173305
\(556\) 0 0
\(557\) 19.4296 0.823260 0.411630 0.911351i \(-0.364960\pi\)
0.411630 + 0.911351i \(0.364960\pi\)
\(558\) 0 0
\(559\) −26.1316 −1.10525
\(560\) 0 0
\(561\) −21.8131 −0.920950
\(562\) 0 0
\(563\) −3.14872 −0.132703 −0.0663513 0.997796i \(-0.521136\pi\)
−0.0663513 + 0.997796i \(0.521136\pi\)
\(564\) 0 0
\(565\) −4.72538 −0.198798
\(566\) 0 0
\(567\) −47.8946 −2.01138
\(568\) 0 0
\(569\) −6.93003 −0.290522 −0.145261 0.989393i \(-0.546402\pi\)
−0.145261 + 0.989393i \(0.546402\pi\)
\(570\) 0 0
\(571\) 14.8975 0.623441 0.311721 0.950174i \(-0.399095\pi\)
0.311721 + 0.950174i \(0.399095\pi\)
\(572\) 0 0
\(573\) 6.37703 0.266404
\(574\) 0 0
\(575\) 19.4043 0.809213
\(576\) 0 0
\(577\) 3.63261 0.151228 0.0756138 0.997137i \(-0.475908\pi\)
0.0756138 + 0.997137i \(0.475908\pi\)
\(578\) 0 0
\(579\) −53.0519 −2.20476
\(580\) 0 0
\(581\) −5.02627 −0.208525
\(582\) 0 0
\(583\) 8.54049 0.353711
\(584\) 0 0
\(585\) −4.63962 −0.191825
\(586\) 0 0
\(587\) −28.5083 −1.17666 −0.588331 0.808620i \(-0.700215\pi\)
−0.588331 + 0.808620i \(0.700215\pi\)
\(588\) 0 0
\(589\) 34.0527 1.40312
\(590\) 0 0
\(591\) 2.17045 0.0892804
\(592\) 0 0
\(593\) 3.85582 0.158340 0.0791698 0.996861i \(-0.474773\pi\)
0.0791698 + 0.996861i \(0.474773\pi\)
\(594\) 0 0
\(595\) 9.77080 0.400564
\(596\) 0 0
\(597\) −40.6847 −1.66511
\(598\) 0 0
\(599\) −31.1346 −1.27213 −0.636063 0.771637i \(-0.719438\pi\)
−0.636063 + 0.771637i \(0.719438\pi\)
\(600\) 0 0
\(601\) −5.67089 −0.231320 −0.115660 0.993289i \(-0.536898\pi\)
−0.115660 + 0.993289i \(0.536898\pi\)
\(602\) 0 0
\(603\) 25.6596 1.04494
\(604\) 0 0
\(605\) −2.17057 −0.0882462
\(606\) 0 0
\(607\) 37.6120 1.52662 0.763312 0.646030i \(-0.223572\pi\)
0.763312 + 0.646030i \(0.223572\pi\)
\(608\) 0 0
\(609\) 46.3467 1.87806
\(610\) 0 0
\(611\) −14.3326 −0.579834
\(612\) 0 0
\(613\) 9.68281 0.391085 0.195542 0.980695i \(-0.437353\pi\)
0.195542 + 0.980695i \(0.437353\pi\)
\(614\) 0 0
\(615\) 2.93955 0.118534
\(616\) 0 0
\(617\) −8.61903 −0.346989 −0.173495 0.984835i \(-0.555506\pi\)
−0.173495 + 0.984835i \(0.555506\pi\)
\(618\) 0 0
\(619\) −32.4573 −1.30457 −0.652285 0.757973i \(-0.726190\pi\)
−0.652285 + 0.757973i \(0.726190\pi\)
\(620\) 0 0
\(621\) 10.2943 0.413095
\(622\) 0 0
\(623\) 5.02800 0.201443
\(624\) 0 0
\(625\) 19.1811 0.767243
\(626\) 0 0
\(627\) −26.5386 −1.05985
\(628\) 0 0
\(629\) −10.4768 −0.417737
\(630\) 0 0
\(631\) 48.5078 1.93107 0.965533 0.260282i \(-0.0838154\pi\)
0.965533 + 0.260282i \(0.0838154\pi\)
\(632\) 0 0
\(633\) 17.5135 0.696099
\(634\) 0 0
\(635\) 5.12435 0.203353
\(636\) 0 0
\(637\) −45.1117 −1.78739
\(638\) 0 0
\(639\) 11.2201 0.443861
\(640\) 0 0
\(641\) −26.4815 −1.04596 −0.522979 0.852346i \(-0.675179\pi\)
−0.522979 + 0.852346i \(0.675179\pi\)
\(642\) 0 0
\(643\) −42.4550 −1.67426 −0.837130 0.547003i \(-0.815768\pi\)
−0.837130 + 0.547003i \(0.815768\pi\)
\(644\) 0 0
\(645\) 9.42142 0.370968
\(646\) 0 0
\(647\) −32.1869 −1.26540 −0.632698 0.774399i \(-0.718053\pi\)
−0.632698 + 0.774399i \(0.718053\pi\)
\(648\) 0 0
\(649\) −9.76237 −0.383207
\(650\) 0 0
\(651\) 74.6025 2.92390
\(652\) 0 0
\(653\) 27.2003 1.06443 0.532214 0.846610i \(-0.321360\pi\)
0.532214 + 0.846610i \(0.321360\pi\)
\(654\) 0 0
\(655\) 5.70957 0.223092
\(656\) 0 0
\(657\) 19.0736 0.744131
\(658\) 0 0
\(659\) −40.7249 −1.58642 −0.793208 0.608951i \(-0.791591\pi\)
−0.793208 + 0.608951i \(0.791591\pi\)
\(660\) 0 0
\(661\) −22.1828 −0.862811 −0.431406 0.902158i \(-0.641982\pi\)
−0.431406 + 0.902158i \(0.641982\pi\)
\(662\) 0 0
\(663\) −30.7354 −1.19366
\(664\) 0 0
\(665\) 11.8875 0.460978
\(666\) 0 0
\(667\) −20.4552 −0.792029
\(668\) 0 0
\(669\) −24.4259 −0.944361
\(670\) 0 0
\(671\) −40.7921 −1.57476
\(672\) 0 0
\(673\) 14.3194 0.551973 0.275986 0.961162i \(-0.410996\pi\)
0.275986 + 0.961162i \(0.410996\pi\)
\(674\) 0 0
\(675\) 11.2330 0.432357
\(676\) 0 0
\(677\) 18.9297 0.727528 0.363764 0.931491i \(-0.381491\pi\)
0.363764 + 0.931491i \(0.381491\pi\)
\(678\) 0 0
\(679\) −54.1063 −2.07641
\(680\) 0 0
\(681\) 27.6575 1.05984
\(682\) 0 0
\(683\) 12.9336 0.494891 0.247445 0.968902i \(-0.420409\pi\)
0.247445 + 0.968902i \(0.420409\pi\)
\(684\) 0 0
\(685\) 5.76632 0.220320
\(686\) 0 0
\(687\) −63.8892 −2.43752
\(688\) 0 0
\(689\) 12.0338 0.458453
\(690\) 0 0
\(691\) −44.8246 −1.70521 −0.852605 0.522556i \(-0.824978\pi\)
−0.852605 + 0.522556i \(0.824978\pi\)
\(692\) 0 0
\(693\) −22.5214 −0.855516
\(694\) 0 0
\(695\) 6.10983 0.231759
\(696\) 0 0
\(697\) 7.54314 0.285717
\(698\) 0 0
\(699\) −51.1281 −1.93384
\(700\) 0 0
\(701\) 49.4281 1.86687 0.933436 0.358744i \(-0.116795\pi\)
0.933436 + 0.358744i \(0.116795\pi\)
\(702\) 0 0
\(703\) −12.7464 −0.480741
\(704\) 0 0
\(705\) 5.16744 0.194617
\(706\) 0 0
\(707\) −40.0044 −1.50452
\(708\) 0 0
\(709\) 13.0612 0.490523 0.245261 0.969457i \(-0.421126\pi\)
0.245261 + 0.969457i \(0.421126\pi\)
\(710\) 0 0
\(711\) 6.78538 0.254472
\(712\) 0 0
\(713\) −32.9260 −1.23309
\(714\) 0 0
\(715\) 6.72605 0.251540
\(716\) 0 0
\(717\) −35.5718 −1.32845
\(718\) 0 0
\(719\) 2.99554 0.111715 0.0558574 0.998439i \(-0.482211\pi\)
0.0558574 + 0.998439i \(0.482211\pi\)
\(720\) 0 0
\(721\) −5.48893 −0.204418
\(722\) 0 0
\(723\) 7.08613 0.263536
\(724\) 0 0
\(725\) −22.3204 −0.828961
\(726\) 0 0
\(727\) 1.96927 0.0730360 0.0365180 0.999333i \(-0.488373\pi\)
0.0365180 + 0.999333i \(0.488373\pi\)
\(728\) 0 0
\(729\) −4.83471 −0.179063
\(730\) 0 0
\(731\) 24.1762 0.894188
\(732\) 0 0
\(733\) 12.4034 0.458131 0.229065 0.973411i \(-0.426433\pi\)
0.229065 + 0.973411i \(0.426433\pi\)
\(734\) 0 0
\(735\) 16.2645 0.599924
\(736\) 0 0
\(737\) −37.1987 −1.37023
\(738\) 0 0
\(739\) 17.1146 0.629570 0.314785 0.949163i \(-0.398068\pi\)
0.314785 + 0.949163i \(0.398068\pi\)
\(740\) 0 0
\(741\) −37.3938 −1.37370
\(742\) 0 0
\(743\) 4.63712 0.170119 0.0850597 0.996376i \(-0.472892\pi\)
0.0850597 + 0.996376i \(0.472892\pi\)
\(744\) 0 0
\(745\) 2.45770 0.0900433
\(746\) 0 0
\(747\) −2.20811 −0.0807904
\(748\) 0 0
\(749\) 30.0423 1.09772
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −51.2051 −1.86602
\(754\) 0 0
\(755\) −5.57864 −0.203027
\(756\) 0 0
\(757\) −36.3014 −1.31940 −0.659698 0.751531i \(-0.729316\pi\)
−0.659698 + 0.751531i \(0.729316\pi\)
\(758\) 0 0
\(759\) 25.6605 0.931417
\(760\) 0 0
\(761\) 31.0581 1.12586 0.562928 0.826506i \(-0.309675\pi\)
0.562928 + 0.826506i \(0.309675\pi\)
\(762\) 0 0
\(763\) 2.52534 0.0914235
\(764\) 0 0
\(765\) 4.29244 0.155194
\(766\) 0 0
\(767\) −13.7555 −0.496683
\(768\) 0 0
\(769\) 25.1935 0.908501 0.454251 0.890874i \(-0.349907\pi\)
0.454251 + 0.890874i \(0.349907\pi\)
\(770\) 0 0
\(771\) −7.69482 −0.277122
\(772\) 0 0
\(773\) 38.5118 1.38517 0.692586 0.721335i \(-0.256471\pi\)
0.692586 + 0.721335i \(0.256471\pi\)
\(774\) 0 0
\(775\) −35.9284 −1.29058
\(776\) 0 0
\(777\) −27.9249 −1.00180
\(778\) 0 0
\(779\) 9.17726 0.328809
\(780\) 0 0
\(781\) −16.2658 −0.582035
\(782\) 0 0
\(783\) −11.8414 −0.423176
\(784\) 0 0
\(785\) 7.25132 0.258811
\(786\) 0 0
\(787\) −9.50028 −0.338649 −0.169324 0.985560i \(-0.554159\pi\)
−0.169324 + 0.985560i \(0.554159\pi\)
\(788\) 0 0
\(789\) −36.0031 −1.28174
\(790\) 0 0
\(791\) −32.3200 −1.14917
\(792\) 0 0
\(793\) −57.4775 −2.04109
\(794\) 0 0
\(795\) −4.33866 −0.153876
\(796\) 0 0
\(797\) 23.4926 0.832152 0.416076 0.909330i \(-0.363405\pi\)
0.416076 + 0.909330i \(0.363405\pi\)
\(798\) 0 0
\(799\) 13.2601 0.469108
\(800\) 0 0
\(801\) 2.20887 0.0780465
\(802\) 0 0
\(803\) −27.6509 −0.975781
\(804\) 0 0
\(805\) −11.4942 −0.405116
\(806\) 0 0
\(807\) −9.29958 −0.327361
\(808\) 0 0
\(809\) −0.398415 −0.0140075 −0.00700376 0.999975i \(-0.502229\pi\)
−0.00700376 + 0.999975i \(0.502229\pi\)
\(810\) 0 0
\(811\) 2.79876 0.0982778 0.0491389 0.998792i \(-0.484352\pi\)
0.0491389 + 0.998792i \(0.484352\pi\)
\(812\) 0 0
\(813\) −22.5024 −0.789195
\(814\) 0 0
\(815\) −11.3704 −0.398288
\(816\) 0 0
\(817\) 29.4136 1.02905
\(818\) 0 0
\(819\) −31.7334 −1.10885
\(820\) 0 0
\(821\) −38.0781 −1.32894 −0.664468 0.747317i \(-0.731342\pi\)
−0.664468 + 0.747317i \(0.731342\pi\)
\(822\) 0 0
\(823\) 4.59598 0.160206 0.0801029 0.996787i \(-0.474475\pi\)
0.0801029 + 0.996787i \(0.474475\pi\)
\(824\) 0 0
\(825\) 28.0004 0.974848
\(826\) 0 0
\(827\) −3.42383 −0.119058 −0.0595291 0.998227i \(-0.518960\pi\)
−0.0595291 + 0.998227i \(0.518960\pi\)
\(828\) 0 0
\(829\) −5.34995 −0.185811 −0.0929057 0.995675i \(-0.529616\pi\)
−0.0929057 + 0.995675i \(0.529616\pi\)
\(830\) 0 0
\(831\) −0.360332 −0.0124998
\(832\) 0 0
\(833\) 41.7360 1.44607
\(834\) 0 0
\(835\) 5.24185 0.181402
\(836\) 0 0
\(837\) −19.0606 −0.658830
\(838\) 0 0
\(839\) −36.7103 −1.26738 −0.633690 0.773587i \(-0.718461\pi\)
−0.633690 + 0.773587i \(0.718461\pi\)
\(840\) 0 0
\(841\) −5.47065 −0.188643
\(842\) 0 0
\(843\) −21.3492 −0.735307
\(844\) 0 0
\(845\) 1.27059 0.0437096
\(846\) 0 0
\(847\) −14.8459 −0.510112
\(848\) 0 0
\(849\) 30.8184 1.05769
\(850\) 0 0
\(851\) 12.3247 0.422485
\(852\) 0 0
\(853\) −7.10322 −0.243210 −0.121605 0.992579i \(-0.538804\pi\)
−0.121605 + 0.992579i \(0.538804\pi\)
\(854\) 0 0
\(855\) 5.22234 0.178600
\(856\) 0 0
\(857\) 27.0754 0.924879 0.462439 0.886651i \(-0.346974\pi\)
0.462439 + 0.886651i \(0.346974\pi\)
\(858\) 0 0
\(859\) −26.9035 −0.917935 −0.458967 0.888453i \(-0.651780\pi\)
−0.458967 + 0.888453i \(0.651780\pi\)
\(860\) 0 0
\(861\) 20.1055 0.685194
\(862\) 0 0
\(863\) −13.7747 −0.468895 −0.234447 0.972129i \(-0.575328\pi\)
−0.234447 + 0.972129i \(0.575328\pi\)
\(864\) 0 0
\(865\) −10.3545 −0.352065
\(866\) 0 0
\(867\) −9.18345 −0.311886
\(868\) 0 0
\(869\) −9.83676 −0.333689
\(870\) 0 0
\(871\) −52.4143 −1.77599
\(872\) 0 0
\(873\) −23.7696 −0.804479
\(874\) 0 0
\(875\) −26.1708 −0.884735
\(876\) 0 0
\(877\) −16.4117 −0.554182 −0.277091 0.960844i \(-0.589370\pi\)
−0.277091 + 0.960844i \(0.589370\pi\)
\(878\) 0 0
\(879\) −13.5483 −0.456971
\(880\) 0 0
\(881\) 39.4153 1.32794 0.663968 0.747761i \(-0.268871\pi\)
0.663968 + 0.747761i \(0.268871\pi\)
\(882\) 0 0
\(883\) 7.22326 0.243082 0.121541 0.992586i \(-0.461216\pi\)
0.121541 + 0.992586i \(0.461216\pi\)
\(884\) 0 0
\(885\) 4.95938 0.166708
\(886\) 0 0
\(887\) −2.90973 −0.0976993 −0.0488497 0.998806i \(-0.515556\pi\)
−0.0488497 + 0.998806i \(0.515556\pi\)
\(888\) 0 0
\(889\) 35.0487 1.17550
\(890\) 0 0
\(891\) 30.5027 1.02188
\(892\) 0 0
\(893\) 16.1327 0.539860
\(894\) 0 0
\(895\) −4.06456 −0.135863
\(896\) 0 0
\(897\) 36.1565 1.20723
\(898\) 0 0
\(899\) 37.8743 1.26318
\(900\) 0 0
\(901\) −11.1334 −0.370906
\(902\) 0 0
\(903\) 64.4392 2.14440
\(904\) 0 0
\(905\) 5.85617 0.194666
\(906\) 0 0
\(907\) 17.8466 0.592588 0.296294 0.955097i \(-0.404249\pi\)
0.296294 + 0.955097i \(0.404249\pi\)
\(908\) 0 0
\(909\) −17.5745 −0.582909
\(910\) 0 0
\(911\) 33.7075 1.11678 0.558390 0.829578i \(-0.311419\pi\)
0.558390 + 0.829578i \(0.311419\pi\)
\(912\) 0 0
\(913\) 3.20109 0.105941
\(914\) 0 0
\(915\) 20.7228 0.685075
\(916\) 0 0
\(917\) 39.0515 1.28959
\(918\) 0 0
\(919\) 29.6883 0.979328 0.489664 0.871911i \(-0.337119\pi\)
0.489664 + 0.871911i \(0.337119\pi\)
\(920\) 0 0
\(921\) 41.7669 1.37627
\(922\) 0 0
\(923\) −22.9190 −0.754389
\(924\) 0 0
\(925\) 13.4485 0.442185
\(926\) 0 0
\(927\) −2.41136 −0.0791994
\(928\) 0 0
\(929\) 43.0337 1.41189 0.705945 0.708266i \(-0.250522\pi\)
0.705945 + 0.708266i \(0.250522\pi\)
\(930\) 0 0
\(931\) 50.7776 1.66417
\(932\) 0 0
\(933\) −29.5797 −0.968395
\(934\) 0 0
\(935\) −6.22275 −0.203506
\(936\) 0 0
\(937\) 52.8530 1.72663 0.863317 0.504663i \(-0.168383\pi\)
0.863317 + 0.504663i \(0.168383\pi\)
\(938\) 0 0
\(939\) 15.9943 0.521955
\(940\) 0 0
\(941\) 44.6043 1.45406 0.727029 0.686607i \(-0.240901\pi\)
0.727029 + 0.686607i \(0.240901\pi\)
\(942\) 0 0
\(943\) −8.87360 −0.288964
\(944\) 0 0
\(945\) −6.65389 −0.216451
\(946\) 0 0
\(947\) −34.6742 −1.12676 −0.563380 0.826198i \(-0.690499\pi\)
−0.563380 + 0.826198i \(0.690499\pi\)
\(948\) 0 0
\(949\) −38.9611 −1.26473
\(950\) 0 0
\(951\) 27.5085 0.892024
\(952\) 0 0
\(953\) −22.9288 −0.742735 −0.371368 0.928486i \(-0.621111\pi\)
−0.371368 + 0.928486i \(0.621111\pi\)
\(954\) 0 0
\(955\) 1.81921 0.0588683
\(956\) 0 0
\(957\) −29.5169 −0.954146
\(958\) 0 0
\(959\) 39.4396 1.27357
\(960\) 0 0
\(961\) 29.9648 0.966605
\(962\) 0 0
\(963\) 13.1980 0.425299
\(964\) 0 0
\(965\) −15.1344 −0.487194
\(966\) 0 0
\(967\) 29.9139 0.961965 0.480982 0.876730i \(-0.340280\pi\)
0.480982 + 0.876730i \(0.340280\pi\)
\(968\) 0 0
\(969\) 34.5957 1.11137
\(970\) 0 0
\(971\) −14.3020 −0.458973 −0.229487 0.973312i \(-0.573705\pi\)
−0.229487 + 0.973312i \(0.573705\pi\)
\(972\) 0 0
\(973\) 41.7891 1.33970
\(974\) 0 0
\(975\) 39.4535 1.26352
\(976\) 0 0
\(977\) −29.3000 −0.937391 −0.468696 0.883360i \(-0.655276\pi\)
−0.468696 + 0.883360i \(0.655276\pi\)
\(978\) 0 0
\(979\) −3.20219 −0.102342
\(980\) 0 0
\(981\) 1.10941 0.0354209
\(982\) 0 0
\(983\) −12.9742 −0.413813 −0.206907 0.978361i \(-0.566340\pi\)
−0.206907 + 0.978361i \(0.566340\pi\)
\(984\) 0 0
\(985\) 0.619177 0.0197286
\(986\) 0 0
\(987\) 35.3434 1.12499
\(988\) 0 0
\(989\) −28.4403 −0.904350
\(990\) 0 0
\(991\) 43.0365 1.36710 0.683549 0.729905i \(-0.260436\pi\)
0.683549 + 0.729905i \(0.260436\pi\)
\(992\) 0 0
\(993\) −44.3387 −1.40705
\(994\) 0 0
\(995\) −11.6063 −0.367946
\(996\) 0 0
\(997\) −51.1614 −1.62030 −0.810149 0.586224i \(-0.800614\pi\)
−0.810149 + 0.586224i \(0.800614\pi\)
\(998\) 0 0
\(999\) 7.13467 0.225731
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 \(a_p\))