Properties

Label 6008.2.a.e.1.24
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 1.24
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.208469 q^{3} +0.579845 q^{5} +3.19554 q^{7} -2.95654 q^{9} +O(q^{10})\) \(q-0.208469 q^{3} +0.579845 q^{5} +3.19554 q^{7} -2.95654 q^{9} +3.04923 q^{11} +2.78895 q^{13} -0.120880 q^{15} +1.55837 q^{17} +4.47078 q^{19} -0.666172 q^{21} +8.96037 q^{23} -4.66378 q^{25} +1.24176 q^{27} +5.11237 q^{29} +4.73793 q^{31} -0.635670 q^{33} +1.85292 q^{35} +1.13154 q^{37} -0.581410 q^{39} -7.41008 q^{41} +6.89935 q^{43} -1.71433 q^{45} -8.88879 q^{47} +3.21147 q^{49} -0.324873 q^{51} -10.6957 q^{53} +1.76808 q^{55} -0.932020 q^{57} +2.39532 q^{59} -8.89043 q^{61} -9.44774 q^{63} +1.61716 q^{65} -13.7587 q^{67} -1.86796 q^{69} -4.02055 q^{71} +16.4034 q^{73} +0.972255 q^{75} +9.74392 q^{77} +4.37188 q^{79} +8.61075 q^{81} -10.2333 q^{83} +0.903615 q^{85} -1.06577 q^{87} +9.54961 q^{89} +8.91219 q^{91} -0.987713 q^{93} +2.59236 q^{95} +10.9152 q^{97} -9.01516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −0.208469 −0.120360 −0.0601799 0.998188i \(-0.519167\pi\)
−0.0601799 + 0.998188i \(0.519167\pi\)
\(4\) 0 0
\(5\) 0.579845 0.259315 0.129657 0.991559i \(-0.458612\pi\)
0.129657 + 0.991559i \(0.458612\pi\)
\(6\) 0 0
\(7\) 3.19554 1.20780 0.603900 0.797060i \(-0.293613\pi\)
0.603900 + 0.797060i \(0.293613\pi\)
\(8\) 0 0
\(9\) −2.95654 −0.985514
\(10\) 0 0
\(11\) 3.04923 0.919376 0.459688 0.888080i \(-0.347961\pi\)
0.459688 + 0.888080i \(0.347961\pi\)
\(12\) 0 0
\(13\) 2.78895 0.773515 0.386757 0.922181i \(-0.373595\pi\)
0.386757 + 0.922181i \(0.373595\pi\)
\(14\) 0 0
\(15\) −0.120880 −0.0312110
\(16\) 0 0
\(17\) 1.55837 0.377961 0.188981 0.981981i \(-0.439482\pi\)
0.188981 + 0.981981i \(0.439482\pi\)
\(18\) 0 0
\(19\) 4.47078 1.02567 0.512833 0.858488i \(-0.328596\pi\)
0.512833 + 0.858488i \(0.328596\pi\)
\(20\) 0 0
\(21\) −0.666172 −0.145371
\(22\) 0 0
\(23\) 8.96037 1.86837 0.934183 0.356793i \(-0.116130\pi\)
0.934183 + 0.356793i \(0.116130\pi\)
\(24\) 0 0
\(25\) −4.66378 −0.932756
\(26\) 0 0
\(27\) 1.24176 0.238976
\(28\) 0 0
\(29\) 5.11237 0.949343 0.474672 0.880163i \(-0.342567\pi\)
0.474672 + 0.880163i \(0.342567\pi\)
\(30\) 0 0
\(31\) 4.73793 0.850957 0.425479 0.904968i \(-0.360106\pi\)
0.425479 + 0.904968i \(0.360106\pi\)
\(32\) 0 0
\(33\) −0.635670 −0.110656
\(34\) 0 0
\(35\) 1.85292 0.313200
\(36\) 0 0
\(37\) 1.13154 0.186024 0.0930122 0.995665i \(-0.470350\pi\)
0.0930122 + 0.995665i \(0.470350\pi\)
\(38\) 0 0
\(39\) −0.581410 −0.0931001
\(40\) 0 0
\(41\) −7.41008 −1.15726 −0.578630 0.815590i \(-0.696413\pi\)
−0.578630 + 0.815590i \(0.696413\pi\)
\(42\) 0 0
\(43\) 6.89935 1.05214 0.526071 0.850441i \(-0.323665\pi\)
0.526071 + 0.850441i \(0.323665\pi\)
\(44\) 0 0
\(45\) −1.71433 −0.255558
\(46\) 0 0
\(47\) −8.88879 −1.29656 −0.648282 0.761400i \(-0.724512\pi\)
−0.648282 + 0.761400i \(0.724512\pi\)
\(48\) 0 0
\(49\) 3.21147 0.458782
\(50\) 0 0
\(51\) −0.324873 −0.0454913
\(52\) 0 0
\(53\) −10.6957 −1.46917 −0.734587 0.678515i \(-0.762624\pi\)
−0.734587 + 0.678515i \(0.762624\pi\)
\(54\) 0 0
\(55\) 1.76808 0.238408
\(56\) 0 0
\(57\) −0.932020 −0.123449
\(58\) 0 0
\(59\) 2.39532 0.311844 0.155922 0.987769i \(-0.450165\pi\)
0.155922 + 0.987769i \(0.450165\pi\)
\(60\) 0 0
\(61\) −8.89043 −1.13830 −0.569152 0.822233i \(-0.692728\pi\)
−0.569152 + 0.822233i \(0.692728\pi\)
\(62\) 0 0
\(63\) −9.44774 −1.19030
\(64\) 0 0
\(65\) 1.61716 0.200584
\(66\) 0 0
\(67\) −13.7587 −1.68089 −0.840445 0.541897i \(-0.817706\pi\)
−0.840445 + 0.541897i \(0.817706\pi\)
\(68\) 0 0
\(69\) −1.86796 −0.224876
\(70\) 0 0
\(71\) −4.02055 −0.477151 −0.238576 0.971124i \(-0.576680\pi\)
−0.238576 + 0.971124i \(0.576680\pi\)
\(72\) 0 0
\(73\) 16.4034 1.91987 0.959937 0.280217i \(-0.0904065\pi\)
0.959937 + 0.280217i \(0.0904065\pi\)
\(74\) 0 0
\(75\) 0.972255 0.112266
\(76\) 0 0
\(77\) 9.74392 1.11042
\(78\) 0 0
\(79\) 4.37188 0.491875 0.245937 0.969286i \(-0.420904\pi\)
0.245937 + 0.969286i \(0.420904\pi\)
\(80\) 0 0
\(81\) 8.61075 0.956750
\(82\) 0 0
\(83\) −10.2333 −1.12325 −0.561625 0.827392i \(-0.689824\pi\)
−0.561625 + 0.827392i \(0.689824\pi\)
\(84\) 0 0
\(85\) 0.903615 0.0980108
\(86\) 0 0
\(87\) −1.06577 −0.114263
\(88\) 0 0
\(89\) 9.54961 1.01226 0.506128 0.862458i \(-0.331076\pi\)
0.506128 + 0.862458i \(0.331076\pi\)
\(90\) 0 0
\(91\) 8.91219 0.934251
\(92\) 0 0
\(93\) −0.987713 −0.102421
\(94\) 0 0
\(95\) 2.59236 0.265970
\(96\) 0 0
\(97\) 10.9152 1.10827 0.554135 0.832427i \(-0.313049\pi\)
0.554135 + 0.832427i \(0.313049\pi\)
\(98\) 0 0
\(99\) −9.01516 −0.906058
\(100\) 0 0
\(101\) −8.34227 −0.830086 −0.415043 0.909802i \(-0.636234\pi\)
−0.415043 + 0.909802i \(0.636234\pi\)
\(102\) 0 0
\(103\) 12.8040 1.26161 0.630805 0.775941i \(-0.282725\pi\)
0.630805 + 0.775941i \(0.282725\pi\)
\(104\) 0 0
\(105\) −0.386276 −0.0376967
\(106\) 0 0
\(107\) 2.67523 0.258624 0.129312 0.991604i \(-0.458723\pi\)
0.129312 + 0.991604i \(0.458723\pi\)
\(108\) 0 0
\(109\) 2.53964 0.243253 0.121627 0.992576i \(-0.461189\pi\)
0.121627 + 0.992576i \(0.461189\pi\)
\(110\) 0 0
\(111\) −0.235892 −0.0223899
\(112\) 0 0
\(113\) 15.8522 1.49125 0.745625 0.666366i \(-0.232151\pi\)
0.745625 + 0.666366i \(0.232151\pi\)
\(114\) 0 0
\(115\) 5.19563 0.484495
\(116\) 0 0
\(117\) −8.24564 −0.762309
\(118\) 0 0
\(119\) 4.97985 0.456502
\(120\) 0 0
\(121\) −1.70222 −0.154747
\(122\) 0 0
\(123\) 1.54477 0.139288
\(124\) 0 0
\(125\) −5.60349 −0.501192
\(126\) 0 0
\(127\) −6.79382 −0.602854 −0.301427 0.953489i \(-0.597463\pi\)
−0.301427 + 0.953489i \(0.597463\pi\)
\(128\) 0 0
\(129\) −1.43830 −0.126636
\(130\) 0 0
\(131\) 15.5036 1.35455 0.677277 0.735728i \(-0.263160\pi\)
0.677277 + 0.735728i \(0.263160\pi\)
\(132\) 0 0
\(133\) 14.2865 1.23880
\(134\) 0 0
\(135\) 0.720026 0.0619699
\(136\) 0 0
\(137\) −8.60390 −0.735081 −0.367541 0.930008i \(-0.619800\pi\)
−0.367541 + 0.930008i \(0.619800\pi\)
\(138\) 0 0
\(139\) −22.2953 −1.89106 −0.945532 0.325530i \(-0.894457\pi\)
−0.945532 + 0.325530i \(0.894457\pi\)
\(140\) 0 0
\(141\) 1.85304 0.156054
\(142\) 0 0
\(143\) 8.50413 0.711151
\(144\) 0 0
\(145\) 2.96438 0.246178
\(146\) 0 0
\(147\) −0.669493 −0.0552189
\(148\) 0 0
\(149\) −0.584626 −0.0478944 −0.0239472 0.999713i \(-0.507623\pi\)
−0.0239472 + 0.999713i \(0.507623\pi\)
\(150\) 0 0
\(151\) −9.04696 −0.736231 −0.368116 0.929780i \(-0.619997\pi\)
−0.368116 + 0.929780i \(0.619997\pi\)
\(152\) 0 0
\(153\) −4.60740 −0.372486
\(154\) 0 0
\(155\) 2.74726 0.220666
\(156\) 0 0
\(157\) −13.2397 −1.05665 −0.528324 0.849043i \(-0.677179\pi\)
−0.528324 + 0.849043i \(0.677179\pi\)
\(158\) 0 0
\(159\) 2.22973 0.176829
\(160\) 0 0
\(161\) 28.6332 2.25661
\(162\) 0 0
\(163\) 8.10931 0.635170 0.317585 0.948230i \(-0.397128\pi\)
0.317585 + 0.948230i \(0.397128\pi\)
\(164\) 0 0
\(165\) −0.368590 −0.0286947
\(166\) 0 0
\(167\) 7.14341 0.552774 0.276387 0.961046i \(-0.410863\pi\)
0.276387 + 0.961046i \(0.410863\pi\)
\(168\) 0 0
\(169\) −5.22177 −0.401675
\(170\) 0 0
\(171\) −13.2180 −1.01081
\(172\) 0 0
\(173\) −17.5690 −1.33575 −0.667873 0.744275i \(-0.732795\pi\)
−0.667873 + 0.744275i \(0.732795\pi\)
\(174\) 0 0
\(175\) −14.9033 −1.12658
\(176\) 0 0
\(177\) −0.499351 −0.0375335
\(178\) 0 0
\(179\) 14.5631 1.08850 0.544249 0.838924i \(-0.316815\pi\)
0.544249 + 0.838924i \(0.316815\pi\)
\(180\) 0 0
\(181\) 11.9141 0.885569 0.442784 0.896628i \(-0.353991\pi\)
0.442784 + 0.896628i \(0.353991\pi\)
\(182\) 0 0
\(183\) 1.85338 0.137006
\(184\) 0 0
\(185\) 0.656119 0.0482388
\(186\) 0 0
\(187\) 4.75184 0.347489
\(188\) 0 0
\(189\) 3.96808 0.288635
\(190\) 0 0
\(191\) −2.73656 −0.198010 −0.0990051 0.995087i \(-0.531566\pi\)
−0.0990051 + 0.995087i \(0.531566\pi\)
\(192\) 0 0
\(193\) −19.0671 −1.37248 −0.686241 0.727374i \(-0.740741\pi\)
−0.686241 + 0.727374i \(0.740741\pi\)
\(194\) 0 0
\(195\) −0.337127 −0.0241422
\(196\) 0 0
\(197\) 19.7746 1.40888 0.704442 0.709762i \(-0.251197\pi\)
0.704442 + 0.709762i \(0.251197\pi\)
\(198\) 0 0
\(199\) 2.41087 0.170902 0.0854511 0.996342i \(-0.472767\pi\)
0.0854511 + 0.996342i \(0.472767\pi\)
\(200\) 0 0
\(201\) 2.86826 0.202312
\(202\) 0 0
\(203\) 16.3368 1.14662
\(204\) 0 0
\(205\) −4.29670 −0.300095
\(206\) 0 0
\(207\) −26.4917 −1.84130
\(208\) 0 0
\(209\) 13.6324 0.942974
\(210\) 0 0
\(211\) 18.9386 1.30379 0.651894 0.758310i \(-0.273975\pi\)
0.651894 + 0.758310i \(0.273975\pi\)
\(212\) 0 0
\(213\) 0.838160 0.0574298
\(214\) 0 0
\(215\) 4.00055 0.272836
\(216\) 0 0
\(217\) 15.1402 1.02779
\(218\) 0 0
\(219\) −3.41961 −0.231076
\(220\) 0 0
\(221\) 4.34622 0.292359
\(222\) 0 0
\(223\) −21.6160 −1.44751 −0.723756 0.690056i \(-0.757586\pi\)
−0.723756 + 0.690056i \(0.757586\pi\)
\(224\) 0 0
\(225\) 13.7887 0.919244
\(226\) 0 0
\(227\) −5.50262 −0.365222 −0.182611 0.983185i \(-0.558455\pi\)
−0.182611 + 0.983185i \(0.558455\pi\)
\(228\) 0 0
\(229\) −2.88740 −0.190805 −0.0954023 0.995439i \(-0.530414\pi\)
−0.0954023 + 0.995439i \(0.530414\pi\)
\(230\) 0 0
\(231\) −2.03131 −0.133650
\(232\) 0 0
\(233\) 1.57325 0.103067 0.0515336 0.998671i \(-0.483589\pi\)
0.0515336 + 0.998671i \(0.483589\pi\)
\(234\) 0 0
\(235\) −5.15412 −0.336218
\(236\) 0 0
\(237\) −0.911402 −0.0592019
\(238\) 0 0
\(239\) −8.27082 −0.534995 −0.267497 0.963559i \(-0.586197\pi\)
−0.267497 + 0.963559i \(0.586197\pi\)
\(240\) 0 0
\(241\) 23.2208 1.49578 0.747890 0.663822i \(-0.231067\pi\)
0.747890 + 0.663822i \(0.231067\pi\)
\(242\) 0 0
\(243\) −5.52034 −0.354130
\(244\) 0 0
\(245\) 1.86216 0.118969
\(246\) 0 0
\(247\) 12.4688 0.793368
\(248\) 0 0
\(249\) 2.13333 0.135194
\(250\) 0 0
\(251\) −10.0667 −0.635403 −0.317702 0.948191i \(-0.602911\pi\)
−0.317702 + 0.948191i \(0.602911\pi\)
\(252\) 0 0
\(253\) 27.3222 1.71773
\(254\) 0 0
\(255\) −0.188376 −0.0117966
\(256\) 0 0
\(257\) 7.15512 0.446324 0.223162 0.974781i \(-0.428362\pi\)
0.223162 + 0.974781i \(0.428362\pi\)
\(258\) 0 0
\(259\) 3.61589 0.224680
\(260\) 0 0
\(261\) −15.1149 −0.935591
\(262\) 0 0
\(263\) −1.30875 −0.0807007 −0.0403503 0.999186i \(-0.512847\pi\)
−0.0403503 + 0.999186i \(0.512847\pi\)
\(264\) 0 0
\(265\) −6.20187 −0.380978
\(266\) 0 0
\(267\) −1.99080 −0.121835
\(268\) 0 0
\(269\) 6.17056 0.376226 0.188113 0.982147i \(-0.439763\pi\)
0.188113 + 0.982147i \(0.439763\pi\)
\(270\) 0 0
\(271\) 17.7485 1.07815 0.539074 0.842259i \(-0.318774\pi\)
0.539074 + 0.842259i \(0.318774\pi\)
\(272\) 0 0
\(273\) −1.85792 −0.112446
\(274\) 0 0
\(275\) −14.2209 −0.857554
\(276\) 0 0
\(277\) 29.0542 1.74570 0.872849 0.487990i \(-0.162270\pi\)
0.872849 + 0.487990i \(0.162270\pi\)
\(278\) 0 0
\(279\) −14.0079 −0.838630
\(280\) 0 0
\(281\) −24.4700 −1.45976 −0.729880 0.683575i \(-0.760424\pi\)
−0.729880 + 0.683575i \(0.760424\pi\)
\(282\) 0 0
\(283\) −1.15813 −0.0688435 −0.0344217 0.999407i \(-0.510959\pi\)
−0.0344217 + 0.999407i \(0.510959\pi\)
\(284\) 0 0
\(285\) −0.540427 −0.0320121
\(286\) 0 0
\(287\) −23.6792 −1.39774
\(288\) 0 0
\(289\) −14.5715 −0.857145
\(290\) 0 0
\(291\) −2.27548 −0.133391
\(292\) 0 0
\(293\) −0.124693 −0.00728464 −0.00364232 0.999993i \(-0.501159\pi\)
−0.00364232 + 0.999993i \(0.501159\pi\)
\(294\) 0 0
\(295\) 1.38892 0.0808658
\(296\) 0 0
\(297\) 3.78639 0.219709
\(298\) 0 0
\(299\) 24.9900 1.44521
\(300\) 0 0
\(301\) 22.0472 1.27078
\(302\) 0 0
\(303\) 1.73911 0.0999090
\(304\) 0 0
\(305\) −5.15507 −0.295179
\(306\) 0 0
\(307\) 11.9553 0.682323 0.341162 0.940005i \(-0.389180\pi\)
0.341162 + 0.940005i \(0.389180\pi\)
\(308\) 0 0
\(309\) −2.66923 −0.151847
\(310\) 0 0
\(311\) −2.11162 −0.119739 −0.0598695 0.998206i \(-0.519068\pi\)
−0.0598695 + 0.998206i \(0.519068\pi\)
\(312\) 0 0
\(313\) −6.34549 −0.358669 −0.179334 0.983788i \(-0.557394\pi\)
−0.179334 + 0.983788i \(0.557394\pi\)
\(314\) 0 0
\(315\) −5.47822 −0.308663
\(316\) 0 0
\(317\) 14.9122 0.837551 0.418776 0.908090i \(-0.362459\pi\)
0.418776 + 0.908090i \(0.362459\pi\)
\(318\) 0 0
\(319\) 15.5888 0.872804
\(320\) 0 0
\(321\) −0.557703 −0.0311280
\(322\) 0 0
\(323\) 6.96714 0.387662
\(324\) 0 0
\(325\) −13.0070 −0.721501
\(326\) 0 0
\(327\) −0.529436 −0.0292779
\(328\) 0 0
\(329\) −28.4045 −1.56599
\(330\) 0 0
\(331\) 14.4476 0.794111 0.397056 0.917795i \(-0.370032\pi\)
0.397056 + 0.917795i \(0.370032\pi\)
\(332\) 0 0
\(333\) −3.34545 −0.183330
\(334\) 0 0
\(335\) −7.97790 −0.435879
\(336\) 0 0
\(337\) −1.79857 −0.0979746 −0.0489873 0.998799i \(-0.515599\pi\)
−0.0489873 + 0.998799i \(0.515599\pi\)
\(338\) 0 0
\(339\) −3.30470 −0.179486
\(340\) 0 0
\(341\) 14.4470 0.782350
\(342\) 0 0
\(343\) −12.1064 −0.653684
\(344\) 0 0
\(345\) −1.08313 −0.0583137
\(346\) 0 0
\(347\) −7.07176 −0.379632 −0.189816 0.981820i \(-0.560789\pi\)
−0.189816 + 0.981820i \(0.560789\pi\)
\(348\) 0 0
\(349\) 19.8847 1.06440 0.532202 0.846618i \(-0.321365\pi\)
0.532202 + 0.846618i \(0.321365\pi\)
\(350\) 0 0
\(351\) 3.46319 0.184851
\(352\) 0 0
\(353\) 19.0159 1.01211 0.506057 0.862500i \(-0.331103\pi\)
0.506057 + 0.862500i \(0.331103\pi\)
\(354\) 0 0
\(355\) −2.33129 −0.123732
\(356\) 0 0
\(357\) −1.03814 −0.0549444
\(358\) 0 0
\(359\) 23.2618 1.22771 0.613855 0.789419i \(-0.289618\pi\)
0.613855 + 0.789419i \(0.289618\pi\)
\(360\) 0 0
\(361\) 0.987853 0.0519922
\(362\) 0 0
\(363\) 0.354861 0.0186253
\(364\) 0 0
\(365\) 9.51143 0.497851
\(366\) 0 0
\(367\) 14.2686 0.744817 0.372408 0.928069i \(-0.378532\pi\)
0.372408 + 0.928069i \(0.378532\pi\)
\(368\) 0 0
\(369\) 21.9082 1.14050
\(370\) 0 0
\(371\) −34.1787 −1.77447
\(372\) 0 0
\(373\) −5.26356 −0.272537 −0.136268 0.990672i \(-0.543511\pi\)
−0.136268 + 0.990672i \(0.543511\pi\)
\(374\) 0 0
\(375\) 1.16816 0.0603233
\(376\) 0 0
\(377\) 14.2581 0.734331
\(378\) 0 0
\(379\) 9.94370 0.510774 0.255387 0.966839i \(-0.417797\pi\)
0.255387 + 0.966839i \(0.417797\pi\)
\(380\) 0 0
\(381\) 1.41630 0.0725594
\(382\) 0 0
\(383\) −25.1342 −1.28430 −0.642148 0.766580i \(-0.721957\pi\)
−0.642148 + 0.766580i \(0.721957\pi\)
\(384\) 0 0
\(385\) 5.64996 0.287949
\(386\) 0 0
\(387\) −20.3982 −1.03690
\(388\) 0 0
\(389\) 24.2426 1.22915 0.614575 0.788859i \(-0.289328\pi\)
0.614575 + 0.788859i \(0.289328\pi\)
\(390\) 0 0
\(391\) 13.9636 0.706170
\(392\) 0 0
\(393\) −3.23202 −0.163034
\(394\) 0 0
\(395\) 2.53501 0.127550
\(396\) 0 0
\(397\) 3.12269 0.156724 0.0783618 0.996925i \(-0.475031\pi\)
0.0783618 + 0.996925i \(0.475031\pi\)
\(398\) 0 0
\(399\) −2.97831 −0.149102
\(400\) 0 0
\(401\) −37.6466 −1.87998 −0.939990 0.341201i \(-0.889166\pi\)
−0.939990 + 0.341201i \(0.889166\pi\)
\(402\) 0 0
\(403\) 13.2138 0.658228
\(404\) 0 0
\(405\) 4.99290 0.248099
\(406\) 0 0
\(407\) 3.45033 0.171026
\(408\) 0 0
\(409\) 24.3796 1.20549 0.602746 0.797933i \(-0.294073\pi\)
0.602746 + 0.797933i \(0.294073\pi\)
\(410\) 0 0
\(411\) 1.79365 0.0884742
\(412\) 0 0
\(413\) 7.65435 0.376646
\(414\) 0 0
\(415\) −5.93372 −0.291275
\(416\) 0 0
\(417\) 4.64789 0.227608
\(418\) 0 0
\(419\) 13.4239 0.655803 0.327901 0.944712i \(-0.393659\pi\)
0.327901 + 0.944712i \(0.393659\pi\)
\(420\) 0 0
\(421\) 3.73356 0.181963 0.0909814 0.995853i \(-0.471000\pi\)
0.0909814 + 0.995853i \(0.471000\pi\)
\(422\) 0 0
\(423\) 26.2801 1.27778
\(424\) 0 0
\(425\) −7.26791 −0.352546
\(426\) 0 0
\(427\) −28.4097 −1.37484
\(428\) 0 0
\(429\) −1.77285 −0.0855940
\(430\) 0 0
\(431\) −8.62972 −0.415679 −0.207839 0.978163i \(-0.566643\pi\)
−0.207839 + 0.978163i \(0.566643\pi\)
\(432\) 0 0
\(433\) 1.84083 0.0884646 0.0442323 0.999021i \(-0.485916\pi\)
0.0442323 + 0.999021i \(0.485916\pi\)
\(434\) 0 0
\(435\) −0.617982 −0.0296300
\(436\) 0 0
\(437\) 40.0598 1.91632
\(438\) 0 0
\(439\) −14.6597 −0.699671 −0.349836 0.936811i \(-0.613763\pi\)
−0.349836 + 0.936811i \(0.613763\pi\)
\(440\) 0 0
\(441\) −9.49484 −0.452135
\(442\) 0 0
\(443\) −18.2695 −0.868010 −0.434005 0.900910i \(-0.642900\pi\)
−0.434005 + 0.900910i \(0.642900\pi\)
\(444\) 0 0
\(445\) 5.53729 0.262493
\(446\) 0 0
\(447\) 0.121877 0.00576457
\(448\) 0 0
\(449\) 4.89518 0.231018 0.115509 0.993306i \(-0.463150\pi\)
0.115509 + 0.993306i \(0.463150\pi\)
\(450\) 0 0
\(451\) −22.5950 −1.06396
\(452\) 0 0
\(453\) 1.88601 0.0886126
\(454\) 0 0
\(455\) 5.16769 0.242265
\(456\) 0 0
\(457\) 40.7988 1.90849 0.954243 0.299032i \(-0.0966637\pi\)
0.954243 + 0.299032i \(0.0966637\pi\)
\(458\) 0 0
\(459\) 1.93512 0.0903237
\(460\) 0 0
\(461\) −7.90001 −0.367940 −0.183970 0.982932i \(-0.558895\pi\)
−0.183970 + 0.982932i \(0.558895\pi\)
\(462\) 0 0
\(463\) −22.0966 −1.02692 −0.513458 0.858115i \(-0.671636\pi\)
−0.513458 + 0.858115i \(0.671636\pi\)
\(464\) 0 0
\(465\) −0.572720 −0.0265593
\(466\) 0 0
\(467\) −15.3767 −0.711550 −0.355775 0.934572i \(-0.615783\pi\)
−0.355775 + 0.934572i \(0.615783\pi\)
\(468\) 0 0
\(469\) −43.9664 −2.03018
\(470\) 0 0
\(471\) 2.76008 0.127178
\(472\) 0 0
\(473\) 21.0377 0.967314
\(474\) 0 0
\(475\) −20.8507 −0.956697
\(476\) 0 0
\(477\) 31.6224 1.44789
\(478\) 0 0
\(479\) −33.4740 −1.52947 −0.764733 0.644348i \(-0.777129\pi\)
−0.764733 + 0.644348i \(0.777129\pi\)
\(480\) 0 0
\(481\) 3.15581 0.143893
\(482\) 0 0
\(483\) −5.96915 −0.271606
\(484\) 0 0
\(485\) 6.32912 0.287390
\(486\) 0 0
\(487\) −2.16391 −0.0980561 −0.0490280 0.998797i \(-0.515612\pi\)
−0.0490280 + 0.998797i \(0.515612\pi\)
\(488\) 0 0
\(489\) −1.69054 −0.0764489
\(490\) 0 0
\(491\) 24.0871 1.08704 0.543519 0.839397i \(-0.317092\pi\)
0.543519 + 0.839397i \(0.317092\pi\)
\(492\) 0 0
\(493\) 7.96698 0.358815
\(494\) 0 0
\(495\) −5.22739 −0.234954
\(496\) 0 0
\(497\) −12.8478 −0.576303
\(498\) 0 0
\(499\) 20.6452 0.924205 0.462102 0.886827i \(-0.347095\pi\)
0.462102 + 0.886827i \(0.347095\pi\)
\(500\) 0 0
\(501\) −1.48918 −0.0665318
\(502\) 0 0
\(503\) −23.2605 −1.03714 −0.518568 0.855037i \(-0.673535\pi\)
−0.518568 + 0.855037i \(0.673535\pi\)
\(504\) 0 0
\(505\) −4.83722 −0.215253
\(506\) 0 0
\(507\) 1.08858 0.0483455
\(508\) 0 0
\(509\) 15.8219 0.701292 0.350646 0.936508i \(-0.385962\pi\)
0.350646 + 0.936508i \(0.385962\pi\)
\(510\) 0 0
\(511\) 52.4177 2.31882
\(512\) 0 0
\(513\) 5.55161 0.245110
\(514\) 0 0
\(515\) 7.42431 0.327154
\(516\) 0 0
\(517\) −27.1039 −1.19203
\(518\) 0 0
\(519\) 3.66259 0.160770
\(520\) 0 0
\(521\) −29.8509 −1.30779 −0.653895 0.756585i \(-0.726866\pi\)
−0.653895 + 0.756585i \(0.726866\pi\)
\(522\) 0 0
\(523\) 4.61148 0.201646 0.100823 0.994904i \(-0.467852\pi\)
0.100823 + 0.994904i \(0.467852\pi\)
\(524\) 0 0
\(525\) 3.10688 0.135595
\(526\) 0 0
\(527\) 7.38347 0.321629
\(528\) 0 0
\(529\) 57.2883 2.49079
\(530\) 0 0
\(531\) −7.08187 −0.307327
\(532\) 0 0
\(533\) −20.6663 −0.895158
\(534\) 0 0
\(535\) 1.55122 0.0670650
\(536\) 0 0
\(537\) −3.03596 −0.131011
\(538\) 0 0
\(539\) 9.79250 0.421793
\(540\) 0 0
\(541\) 34.3429 1.47652 0.738258 0.674518i \(-0.235648\pi\)
0.738258 + 0.674518i \(0.235648\pi\)
\(542\) 0 0
\(543\) −2.48373 −0.106587
\(544\) 0 0
\(545\) 1.47260 0.0630790
\(546\) 0 0
\(547\) −22.5261 −0.963145 −0.481572 0.876406i \(-0.659934\pi\)
−0.481572 + 0.876406i \(0.659934\pi\)
\(548\) 0 0
\(549\) 26.2849 1.12181
\(550\) 0 0
\(551\) 22.8563 0.973710
\(552\) 0 0
\(553\) 13.9705 0.594087
\(554\) 0 0
\(555\) −0.136781 −0.00580602
\(556\) 0 0
\(557\) 8.46758 0.358783 0.179391 0.983778i \(-0.442587\pi\)
0.179391 + 0.983778i \(0.442587\pi\)
\(558\) 0 0
\(559\) 19.2419 0.813847
\(560\) 0 0
\(561\) −0.990612 −0.0418237
\(562\) 0 0
\(563\) −1.77191 −0.0746772 −0.0373386 0.999303i \(-0.511888\pi\)
−0.0373386 + 0.999303i \(0.511888\pi\)
\(564\) 0 0
\(565\) 9.19181 0.386703
\(566\) 0 0
\(567\) 27.5160 1.15556
\(568\) 0 0
\(569\) 29.8311 1.25058 0.625292 0.780391i \(-0.284980\pi\)
0.625292 + 0.780391i \(0.284980\pi\)
\(570\) 0 0
\(571\) −4.65800 −0.194931 −0.0974656 0.995239i \(-0.531074\pi\)
−0.0974656 + 0.995239i \(0.531074\pi\)
\(572\) 0 0
\(573\) 0.570488 0.0238325
\(574\) 0 0
\(575\) −41.7892 −1.74273
\(576\) 0 0
\(577\) −24.9408 −1.03830 −0.519149 0.854683i \(-0.673751\pi\)
−0.519149 + 0.854683i \(0.673751\pi\)
\(578\) 0 0
\(579\) 3.97491 0.165192
\(580\) 0 0
\(581\) −32.7009 −1.35666
\(582\) 0 0
\(583\) −32.6138 −1.35072
\(584\) 0 0
\(585\) −4.78119 −0.197678
\(586\) 0 0
\(587\) 15.4967 0.639619 0.319809 0.947482i \(-0.396381\pi\)
0.319809 + 0.947482i \(0.396381\pi\)
\(588\) 0 0
\(589\) 21.1822 0.872799
\(590\) 0 0
\(591\) −4.12240 −0.169573
\(592\) 0 0
\(593\) −0.503990 −0.0206964 −0.0103482 0.999946i \(-0.503294\pi\)
−0.0103482 + 0.999946i \(0.503294\pi\)
\(594\) 0 0
\(595\) 2.88754 0.118378
\(596\) 0 0
\(597\) −0.502593 −0.0205698
\(598\) 0 0
\(599\) −43.5783 −1.78056 −0.890280 0.455414i \(-0.849491\pi\)
−0.890280 + 0.455414i \(0.849491\pi\)
\(600\) 0 0
\(601\) 5.34261 0.217930 0.108965 0.994046i \(-0.465246\pi\)
0.108965 + 0.994046i \(0.465246\pi\)
\(602\) 0 0
\(603\) 40.6781 1.65654
\(604\) 0 0
\(605\) −0.987024 −0.0401282
\(606\) 0 0
\(607\) 3.35319 0.136102 0.0680508 0.997682i \(-0.478322\pi\)
0.0680508 + 0.997682i \(0.478322\pi\)
\(608\) 0 0
\(609\) −3.40572 −0.138007
\(610\) 0 0
\(611\) −24.7904 −1.00291
\(612\) 0 0
\(613\) −33.3036 −1.34512 −0.672560 0.740042i \(-0.734805\pi\)
−0.672560 + 0.740042i \(0.734805\pi\)
\(614\) 0 0
\(615\) 0.895730 0.0361193
\(616\) 0 0
\(617\) −31.2608 −1.25851 −0.629255 0.777199i \(-0.716640\pi\)
−0.629255 + 0.777199i \(0.716640\pi\)
\(618\) 0 0
\(619\) 43.0606 1.73075 0.865375 0.501124i \(-0.167080\pi\)
0.865375 + 0.501124i \(0.167080\pi\)
\(620\) 0 0
\(621\) 11.1266 0.446495
\(622\) 0 0
\(623\) 30.5161 1.22260
\(624\) 0 0
\(625\) 20.0697 0.802790
\(626\) 0 0
\(627\) −2.84194 −0.113496
\(628\) 0 0
\(629\) 1.76337 0.0703100
\(630\) 0 0
\(631\) 10.4792 0.417171 0.208585 0.978004i \(-0.433114\pi\)
0.208585 + 0.978004i \(0.433114\pi\)
\(632\) 0 0
\(633\) −3.94812 −0.156924
\(634\) 0 0
\(635\) −3.93936 −0.156329
\(636\) 0 0
\(637\) 8.95662 0.354874
\(638\) 0 0
\(639\) 11.8869 0.470239
\(640\) 0 0
\(641\) −12.2340 −0.483215 −0.241607 0.970374i \(-0.577675\pi\)
−0.241607 + 0.970374i \(0.577675\pi\)
\(642\) 0 0
\(643\) −20.1966 −0.796478 −0.398239 0.917282i \(-0.630379\pi\)
−0.398239 + 0.917282i \(0.630379\pi\)
\(644\) 0 0
\(645\) −0.833993 −0.0328384
\(646\) 0 0
\(647\) 31.4718 1.23728 0.618641 0.785674i \(-0.287683\pi\)
0.618641 + 0.785674i \(0.287683\pi\)
\(648\) 0 0
\(649\) 7.30388 0.286702
\(650\) 0 0
\(651\) −3.15627 −0.123704
\(652\) 0 0
\(653\) 25.9978 1.01737 0.508686 0.860952i \(-0.330131\pi\)
0.508686 + 0.860952i \(0.330131\pi\)
\(654\) 0 0
\(655\) 8.98967 0.351255
\(656\) 0 0
\(657\) −48.4973 −1.89206
\(658\) 0 0
\(659\) 16.3870 0.638348 0.319174 0.947696i \(-0.396594\pi\)
0.319174 + 0.947696i \(0.396594\pi\)
\(660\) 0 0
\(661\) 1.75719 0.0683469 0.0341734 0.999416i \(-0.489120\pi\)
0.0341734 + 0.999416i \(0.489120\pi\)
\(662\) 0 0
\(663\) −0.906054 −0.0351882
\(664\) 0 0
\(665\) 8.28398 0.321239
\(666\) 0 0
\(667\) 45.8087 1.77372
\(668\) 0 0
\(669\) 4.50626 0.174222
\(670\) 0 0
\(671\) −27.1089 −1.04653
\(672\) 0 0
\(673\) −42.5123 −1.63873 −0.819365 0.573272i \(-0.805674\pi\)
−0.819365 + 0.573272i \(0.805674\pi\)
\(674\) 0 0
\(675\) −5.79127 −0.222906
\(676\) 0 0
\(677\) −27.6229 −1.06164 −0.530818 0.847486i \(-0.678115\pi\)
−0.530818 + 0.847486i \(0.678115\pi\)
\(678\) 0 0
\(679\) 34.8799 1.33857
\(680\) 0 0
\(681\) 1.14713 0.0439580
\(682\) 0 0
\(683\) −27.5194 −1.05300 −0.526501 0.850174i \(-0.676496\pi\)
−0.526501 + 0.850174i \(0.676496\pi\)
\(684\) 0 0
\(685\) −4.98893 −0.190617
\(686\) 0 0
\(687\) 0.601934 0.0229652
\(688\) 0 0
\(689\) −29.8299 −1.13643
\(690\) 0 0
\(691\) −35.7348 −1.35942 −0.679708 0.733483i \(-0.737893\pi\)
−0.679708 + 0.733483i \(0.737893\pi\)
\(692\) 0 0
\(693\) −28.8083 −1.09434
\(694\) 0 0
\(695\) −12.9278 −0.490380
\(696\) 0 0
\(697\) −11.5477 −0.437400
\(698\) 0 0
\(699\) −0.327975 −0.0124051
\(700\) 0 0
\(701\) −2.32970 −0.0879915 −0.0439958 0.999032i \(-0.514009\pi\)
−0.0439958 + 0.999032i \(0.514009\pi\)
\(702\) 0 0
\(703\) 5.05887 0.190799
\(704\) 0 0
\(705\) 1.07448 0.0404671
\(706\) 0 0
\(707\) −26.6580 −1.00258
\(708\) 0 0
\(709\) 14.6710 0.550981 0.275491 0.961304i \(-0.411160\pi\)
0.275491 + 0.961304i \(0.411160\pi\)
\(710\) 0 0
\(711\) −12.9256 −0.484749
\(712\) 0 0
\(713\) 42.4536 1.58990
\(714\) 0 0
\(715\) 4.93108 0.184412
\(716\) 0 0
\(717\) 1.72421 0.0643919
\(718\) 0 0
\(719\) −10.7057 −0.399256 −0.199628 0.979872i \(-0.563973\pi\)
−0.199628 + 0.979872i \(0.563973\pi\)
\(720\) 0 0
\(721\) 40.9155 1.52377
\(722\) 0 0
\(723\) −4.84081 −0.180032
\(724\) 0 0
\(725\) −23.8430 −0.885506
\(726\) 0 0
\(727\) −12.7963 −0.474590 −0.237295 0.971438i \(-0.576261\pi\)
−0.237295 + 0.971438i \(0.576261\pi\)
\(728\) 0 0
\(729\) −24.6814 −0.914127
\(730\) 0 0
\(731\) 10.7518 0.397669
\(732\) 0 0
\(733\) −11.4503 −0.422928 −0.211464 0.977386i \(-0.567823\pi\)
−0.211464 + 0.977386i \(0.567823\pi\)
\(734\) 0 0
\(735\) −0.388202 −0.0143190
\(736\) 0 0
\(737\) −41.9533 −1.54537
\(738\) 0 0
\(739\) 6.33103 0.232891 0.116445 0.993197i \(-0.462850\pi\)
0.116445 + 0.993197i \(0.462850\pi\)
\(740\) 0 0
\(741\) −2.59935 −0.0954896
\(742\) 0 0
\(743\) −5.13244 −0.188291 −0.0941455 0.995558i \(-0.530012\pi\)
−0.0941455 + 0.995558i \(0.530012\pi\)
\(744\) 0 0
\(745\) −0.338993 −0.0124197
\(746\) 0 0
\(747\) 30.2551 1.10698
\(748\) 0 0
\(749\) 8.54880 0.312366
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 2.09859 0.0764770
\(754\) 0 0
\(755\) −5.24583 −0.190915
\(756\) 0 0
\(757\) 20.6132 0.749199 0.374599 0.927187i \(-0.377780\pi\)
0.374599 + 0.927187i \(0.377780\pi\)
\(758\) 0 0
\(759\) −5.69584 −0.206746
\(760\) 0 0
\(761\) 12.9402 0.469082 0.234541 0.972106i \(-0.424641\pi\)
0.234541 + 0.972106i \(0.424641\pi\)
\(762\) 0 0
\(763\) 8.11551 0.293801
\(764\) 0 0
\(765\) −2.67158 −0.0965910
\(766\) 0 0
\(767\) 6.68043 0.241216
\(768\) 0 0
\(769\) 32.7924 1.18252 0.591262 0.806480i \(-0.298630\pi\)
0.591262 + 0.806480i \(0.298630\pi\)
\(770\) 0 0
\(771\) −1.49162 −0.0537194
\(772\) 0 0
\(773\) −17.3695 −0.624737 −0.312368 0.949961i \(-0.601122\pi\)
−0.312368 + 0.949961i \(0.601122\pi\)
\(774\) 0 0
\(775\) −22.0967 −0.793735
\(776\) 0 0
\(777\) −0.753802 −0.0270425
\(778\) 0 0
\(779\) −33.1288 −1.18696
\(780\) 0 0
\(781\) −12.2596 −0.438681
\(782\) 0 0
\(783\) 6.34831 0.226870
\(784\) 0 0
\(785\) −7.67700 −0.274004
\(786\) 0 0
\(787\) 51.0532 1.81985 0.909926 0.414772i \(-0.136139\pi\)
0.909926 + 0.414772i \(0.136139\pi\)
\(788\) 0 0
\(789\) 0.272833 0.00971312
\(790\) 0 0
\(791\) 50.6563 1.80113
\(792\) 0 0
\(793\) −24.7949 −0.880494
\(794\) 0 0
\(795\) 1.29290 0.0458544
\(796\) 0 0
\(797\) −28.7993 −1.02012 −0.510061 0.860138i \(-0.670377\pi\)
−0.510061 + 0.860138i \(0.670377\pi\)
\(798\) 0 0
\(799\) −13.8521 −0.490051
\(800\) 0 0
\(801\) −28.2338 −0.997592
\(802\) 0 0
\(803\) 50.0177 1.76509
\(804\) 0 0
\(805\) 16.6028 0.585173
\(806\) 0 0
\(807\) −1.28637 −0.0452825
\(808\) 0 0
\(809\) −3.69026 −0.129743 −0.0648713 0.997894i \(-0.520664\pi\)
−0.0648713 + 0.997894i \(0.520664\pi\)
\(810\) 0 0
\(811\) −13.6114 −0.477963 −0.238981 0.971024i \(-0.576813\pi\)
−0.238981 + 0.971024i \(0.576813\pi\)
\(812\) 0 0
\(813\) −3.70003 −0.129766
\(814\) 0 0
\(815\) 4.70214 0.164709
\(816\) 0 0
\(817\) 30.8455 1.07915
\(818\) 0 0
\(819\) −26.3493 −0.920717
\(820\) 0 0
\(821\) −15.2055 −0.530674 −0.265337 0.964156i \(-0.585483\pi\)
−0.265337 + 0.964156i \(0.585483\pi\)
\(822\) 0 0
\(823\) −33.2957 −1.16062 −0.580308 0.814397i \(-0.697068\pi\)
−0.580308 + 0.814397i \(0.697068\pi\)
\(824\) 0 0
\(825\) 2.96462 0.103215
\(826\) 0 0
\(827\) −5.40850 −0.188072 −0.0940360 0.995569i \(-0.529977\pi\)
−0.0940360 + 0.995569i \(0.529977\pi\)
\(828\) 0 0
\(829\) −21.9643 −0.762850 −0.381425 0.924400i \(-0.624567\pi\)
−0.381425 + 0.924400i \(0.624567\pi\)
\(830\) 0 0
\(831\) −6.05691 −0.210112
\(832\) 0 0
\(833\) 5.00467 0.173402
\(834\) 0 0
\(835\) 4.14207 0.143342
\(836\) 0 0
\(837\) 5.88335 0.203358
\(838\) 0 0
\(839\) 25.3586 0.875475 0.437738 0.899103i \(-0.355780\pi\)
0.437738 + 0.899103i \(0.355780\pi\)
\(840\) 0 0
\(841\) −2.86367 −0.0987474
\(842\) 0 0
\(843\) 5.10125 0.175696
\(844\) 0 0
\(845\) −3.02782 −0.104160
\(846\) 0 0
\(847\) −5.43951 −0.186904
\(848\) 0 0
\(849\) 0.241434 0.00828598
\(850\) 0 0
\(851\) 10.1390 0.347562
\(852\) 0 0
\(853\) 16.3661 0.560364 0.280182 0.959947i \(-0.409605\pi\)
0.280182 + 0.959947i \(0.409605\pi\)
\(854\) 0 0
\(855\) −7.66441 −0.262117
\(856\) 0 0
\(857\) 7.87516 0.269010 0.134505 0.990913i \(-0.457055\pi\)
0.134505 + 0.990913i \(0.457055\pi\)
\(858\) 0 0
\(859\) 16.9405 0.578004 0.289002 0.957329i \(-0.406677\pi\)
0.289002 + 0.957329i \(0.406677\pi\)
\(860\) 0 0
\(861\) 4.93639 0.168232
\(862\) 0 0
\(863\) −14.1957 −0.483227 −0.241613 0.970373i \(-0.577677\pi\)
−0.241613 + 0.970373i \(0.577677\pi\)
\(864\) 0 0
\(865\) −10.1873 −0.346378
\(866\) 0 0
\(867\) 3.03770 0.103166
\(868\) 0 0
\(869\) 13.3308 0.452218
\(870\) 0 0
\(871\) −38.3722 −1.30019
\(872\) 0 0
\(873\) −32.2712 −1.09221
\(874\) 0 0
\(875\) −17.9062 −0.605339
\(876\) 0 0
\(877\) 9.58125 0.323536 0.161768 0.986829i \(-0.448280\pi\)
0.161768 + 0.986829i \(0.448280\pi\)
\(878\) 0 0
\(879\) 0.0259947 0.000876778 0
\(880\) 0 0
\(881\) 24.6860 0.831693 0.415846 0.909435i \(-0.363485\pi\)
0.415846 + 0.909435i \(0.363485\pi\)
\(882\) 0 0
\(883\) −17.8432 −0.600472 −0.300236 0.953865i \(-0.597065\pi\)
−0.300236 + 0.953865i \(0.597065\pi\)
\(884\) 0 0
\(885\) −0.289546 −0.00973299
\(886\) 0 0
\(887\) 23.0149 0.772764 0.386382 0.922339i \(-0.373725\pi\)
0.386382 + 0.922339i \(0.373725\pi\)
\(888\) 0 0
\(889\) −21.7099 −0.728127
\(890\) 0 0
\(891\) 26.2561 0.879614
\(892\) 0 0
\(893\) −39.7398 −1.32984
\(894\) 0 0
\(895\) 8.44435 0.282263
\(896\) 0 0
\(897\) −5.20965 −0.173945
\(898\) 0 0
\(899\) 24.2220 0.807851
\(900\) 0 0
\(901\) −16.6680 −0.555291
\(902\) 0 0
\(903\) −4.59615 −0.152950
\(904\) 0 0
\(905\) 6.90834 0.229641
\(906\) 0 0
\(907\) 36.0339 1.19649 0.598244 0.801314i \(-0.295866\pi\)
0.598244 + 0.801314i \(0.295866\pi\)
\(908\) 0 0
\(909\) 24.6642 0.818061
\(910\) 0 0
\(911\) −55.2881 −1.83178 −0.915889 0.401432i \(-0.868513\pi\)
−0.915889 + 0.401432i \(0.868513\pi\)
\(912\) 0 0
\(913\) −31.2036 −1.03269
\(914\) 0 0
\(915\) 1.07467 0.0355276
\(916\) 0 0
\(917\) 49.5423 1.63603
\(918\) 0 0
\(919\) 3.15789 0.104169 0.0520846 0.998643i \(-0.483413\pi\)
0.0520846 + 0.998643i \(0.483413\pi\)
\(920\) 0 0
\(921\) −2.49231 −0.0821243
\(922\) 0 0
\(923\) −11.2131 −0.369083
\(924\) 0 0
\(925\) −5.27726 −0.173515
\(926\) 0 0
\(927\) −37.8554 −1.24333
\(928\) 0 0
\(929\) −10.8682 −0.356576 −0.178288 0.983978i \(-0.557056\pi\)
−0.178288 + 0.983978i \(0.557056\pi\)
\(930\) 0 0
\(931\) 14.3578 0.470557
\(932\) 0 0
\(933\) 0.440208 0.0144118
\(934\) 0 0
\(935\) 2.75533 0.0901088
\(936\) 0 0
\(937\) −40.9572 −1.33801 −0.669006 0.743257i \(-0.733280\pi\)
−0.669006 + 0.743257i \(0.733280\pi\)
\(938\) 0 0
\(939\) 1.32284 0.0431693
\(940\) 0 0
\(941\) −39.6996 −1.29417 −0.647085 0.762418i \(-0.724012\pi\)
−0.647085 + 0.762418i \(0.724012\pi\)
\(942\) 0 0
\(943\) −66.3971 −2.16219
\(944\) 0 0
\(945\) 2.30087 0.0748473
\(946\) 0 0
\(947\) 6.04548 0.196452 0.0982259 0.995164i \(-0.468683\pi\)
0.0982259 + 0.995164i \(0.468683\pi\)
\(948\) 0 0
\(949\) 45.7482 1.48505
\(950\) 0 0
\(951\) −3.10873 −0.100808
\(952\) 0 0
\(953\) −56.1196 −1.81789 −0.908946 0.416913i \(-0.863112\pi\)
−0.908946 + 0.416913i \(0.863112\pi\)
\(954\) 0 0
\(955\) −1.58678 −0.0513469
\(956\) 0 0
\(957\) −3.24978 −0.105050
\(958\) 0 0
\(959\) −27.4941 −0.887831
\(960\) 0 0
\(961\) −8.55202 −0.275872
\(962\) 0 0
\(963\) −7.90942 −0.254878
\(964\) 0 0
\(965\) −11.0560 −0.355905
\(966\) 0 0
\(967\) 8.71880 0.280378 0.140189 0.990125i \(-0.455229\pi\)
0.140189 + 0.990125i \(0.455229\pi\)
\(968\) 0 0
\(969\) −1.45244 −0.0466589
\(970\) 0 0
\(971\) 2.97156 0.0953620 0.0476810 0.998863i \(-0.484817\pi\)
0.0476810 + 0.998863i \(0.484817\pi\)
\(972\) 0 0
\(973\) −71.2455 −2.28403
\(974\) 0 0
\(975\) 2.71157 0.0868396
\(976\) 0 0
\(977\) 3.53151 0.112983 0.0564914 0.998403i \(-0.482009\pi\)
0.0564914 + 0.998403i \(0.482009\pi\)
\(978\) 0 0
\(979\) 29.1189 0.930645
\(980\) 0 0
\(981\) −7.50854 −0.239729
\(982\) 0 0
\(983\) −14.3768 −0.458548 −0.229274 0.973362i \(-0.573635\pi\)
−0.229274 + 0.973362i \(0.573635\pi\)
\(984\) 0 0
\(985\) 11.4662 0.365344
\(986\) 0 0
\(987\) 5.92146 0.188482
\(988\) 0 0
\(989\) 61.8208 1.96579
\(990\) 0 0
\(991\) −0.662619 −0.0210488 −0.0105244 0.999945i \(-0.503350\pi\)
−0.0105244 + 0.999945i \(0.503350\pi\)
\(992\) 0 0
\(993\) −3.01188 −0.0955790
\(994\) 0 0
\(995\) 1.39793 0.0443174
\(996\) 0 0
\(997\) 6.85229 0.217014 0.108507 0.994096i \(-0.465393\pi\)
0.108507 + 0.994096i \(0.465393\pi\)
\(998\) 0 0
\(999\) 1.40510 0.0444554
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 \(a_p\))