Properties

Label 8048.2.a.v.1.8
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.66428 q^{3} -3.44274 q^{5} -4.43077 q^{7} -0.230172 q^{9} +O(q^{10})\) \(q-1.66428 q^{3} -3.44274 q^{5} -4.43077 q^{7} -0.230172 q^{9} -1.18904 q^{11} -3.49702 q^{13} +5.72968 q^{15} -2.17128 q^{17} -5.57445 q^{19} +7.37404 q^{21} +7.37514 q^{23} +6.85244 q^{25} +5.37591 q^{27} -4.21812 q^{29} +7.45326 q^{31} +1.97890 q^{33} +15.2540 q^{35} -5.18844 q^{37} +5.82003 q^{39} -1.01920 q^{41} +0.120646 q^{43} +0.792421 q^{45} -3.07754 q^{47} +12.6317 q^{49} +3.61361 q^{51} -2.80462 q^{53} +4.09355 q^{55} +9.27745 q^{57} -2.74850 q^{59} +10.9165 q^{61} +1.01984 q^{63} +12.0393 q^{65} +4.55806 q^{67} -12.2743 q^{69} +0.710487 q^{71} -3.34683 q^{73} -11.4044 q^{75} +5.26836 q^{77} +6.35019 q^{79} -8.25651 q^{81} +13.4018 q^{83} +7.47514 q^{85} +7.02013 q^{87} +9.71069 q^{89} +15.4945 q^{91} -12.4043 q^{93} +19.1914 q^{95} +7.58484 q^{97} +0.273683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + 14q^{11} - 31q^{13} + 2q^{15} - 9q^{17} + 8q^{19} - 28q^{21} + 4q^{23} + 22q^{25} + 4q^{27} - 47q^{29} + 5q^{31} - 26q^{33} + 13q^{35} - 67q^{37} + 9q^{39} - 28q^{41} - 15q^{43} - 57q^{45} + 10q^{47} + 20q^{49} + 11q^{51} - 58q^{53} - 15q^{55} - 31q^{57} + 32q^{59} - 55q^{61} + 16q^{63} - 44q^{65} - 22q^{67} - 44q^{69} + 47q^{71} - 5q^{73} + 25q^{75} - 50q^{77} + 14q^{79} - 28q^{81} + 16q^{83} - 78q^{85} + 11q^{87} - 20q^{89} + 15q^{91} - 83q^{93} + 27q^{95} - 8q^{97} + 70q^{99} + O(q^{100}) \)

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
\(3\) −1.66428 −0.960873 −0.480436 0.877030i \(-0.659522\pi\)
−0.480436 + 0.877030i \(0.659522\pi\)
\(4\) 0 0
\(5\) −3.44274 −1.53964 −0.769819 0.638262i \(-0.779654\pi\)
−0.769819 + 0.638262i \(0.779654\pi\)
\(6\) 0 0
\(7\) −4.43077 −1.67467 −0.837336 0.546689i \(-0.815888\pi\)
−0.837336 + 0.546689i \(0.815888\pi\)
\(8\) 0 0
\(9\) −0.230172 −0.0767239
\(10\) 0 0
\(11\) −1.18904 −0.358509 −0.179255 0.983803i \(-0.557369\pi\)
−0.179255 + 0.983803i \(0.557369\pi\)
\(12\) 0 0
\(13\) −3.49702 −0.969900 −0.484950 0.874542i \(-0.661162\pi\)
−0.484950 + 0.874542i \(0.661162\pi\)
\(14\) 0 0
\(15\) 5.72968 1.47940
\(16\) 0 0
\(17\) −2.17128 −0.526612 −0.263306 0.964712i \(-0.584813\pi\)
−0.263306 + 0.964712i \(0.584813\pi\)
\(18\) 0 0
\(19\) −5.57445 −1.27887 −0.639433 0.768847i \(-0.720831\pi\)
−0.639433 + 0.768847i \(0.720831\pi\)
\(20\) 0 0
\(21\) 7.37404 1.60915
\(22\) 0 0
\(23\) 7.37514 1.53782 0.768911 0.639356i \(-0.220799\pi\)
0.768911 + 0.639356i \(0.220799\pi\)
\(24\) 0 0
\(25\) 6.85244 1.37049
\(26\) 0 0
\(27\) 5.37591 1.03459
\(28\) 0 0
\(29\) −4.21812 −0.783284 −0.391642 0.920118i \(-0.628093\pi\)
−0.391642 + 0.920118i \(0.628093\pi\)
\(30\) 0 0
\(31\) 7.45326 1.33864 0.669322 0.742972i \(-0.266585\pi\)
0.669322 + 0.742972i \(0.266585\pi\)
\(32\) 0 0
\(33\) 1.97890 0.344482
\(34\) 0 0
\(35\) 15.2540 2.57839
\(36\) 0 0
\(37\) −5.18844 −0.852975 −0.426488 0.904493i \(-0.640249\pi\)
−0.426488 + 0.904493i \(0.640249\pi\)
\(38\) 0 0
\(39\) 5.82003 0.931950
\(40\) 0 0
\(41\) −1.01920 −0.159172 −0.0795861 0.996828i \(-0.525360\pi\)
−0.0795861 + 0.996828i \(0.525360\pi\)
\(42\) 0 0
\(43\) 0.120646 0.0183983 0.00919914 0.999958i \(-0.497072\pi\)
0.00919914 + 0.999958i \(0.497072\pi\)
\(44\) 0 0
\(45\) 0.792421 0.118127
\(46\) 0 0
\(47\) −3.07754 −0.448906 −0.224453 0.974485i \(-0.572059\pi\)
−0.224453 + 0.974485i \(0.572059\pi\)
\(48\) 0 0
\(49\) 12.6317 1.80453
\(50\) 0 0
\(51\) 3.61361 0.506007
\(52\) 0 0
\(53\) −2.80462 −0.385245 −0.192622 0.981273i \(-0.561699\pi\)
−0.192622 + 0.981273i \(0.561699\pi\)
\(54\) 0 0
\(55\) 4.09355 0.551975
\(56\) 0 0
\(57\) 9.27745 1.22883
\(58\) 0 0
\(59\) −2.74850 −0.357825 −0.178912 0.983865i \(-0.557258\pi\)
−0.178912 + 0.983865i \(0.557258\pi\)
\(60\) 0 0
\(61\) 10.9165 1.39771 0.698855 0.715263i \(-0.253693\pi\)
0.698855 + 0.715263i \(0.253693\pi\)
\(62\) 0 0
\(63\) 1.01984 0.128487
\(64\) 0 0
\(65\) 12.0393 1.49330
\(66\) 0 0
\(67\) 4.55806 0.556855 0.278428 0.960457i \(-0.410187\pi\)
0.278428 + 0.960457i \(0.410187\pi\)
\(68\) 0 0
\(69\) −12.2743 −1.47765
\(70\) 0 0
\(71\) 0.710487 0.0843193 0.0421597 0.999111i \(-0.486576\pi\)
0.0421597 + 0.999111i \(0.486576\pi\)
\(72\) 0 0
\(73\) −3.34683 −0.391717 −0.195859 0.980632i \(-0.562749\pi\)
−0.195859 + 0.980632i \(0.562749\pi\)
\(74\) 0 0
\(75\) −11.4044 −1.31686
\(76\) 0 0
\(77\) 5.26836 0.600385
\(78\) 0 0
\(79\) 6.35019 0.714452 0.357226 0.934018i \(-0.383723\pi\)
0.357226 + 0.934018i \(0.383723\pi\)
\(80\) 0 0
\(81\) −8.25651 −0.917390
\(82\) 0 0
\(83\) 13.4018 1.47104 0.735520 0.677503i \(-0.236938\pi\)
0.735520 + 0.677503i \(0.236938\pi\)
\(84\) 0 0
\(85\) 7.47514 0.810792
\(86\) 0 0
\(87\) 7.02013 0.752636
\(88\) 0 0
\(89\) 9.71069 1.02933 0.514665 0.857391i \(-0.327916\pi\)
0.514665 + 0.857391i \(0.327916\pi\)
\(90\) 0 0
\(91\) 15.4945 1.62426
\(92\) 0 0
\(93\) −12.4043 −1.28627
\(94\) 0 0
\(95\) 19.1914 1.96899
\(96\) 0 0
\(97\) 7.58484 0.770124 0.385062 0.922891i \(-0.374180\pi\)
0.385062 + 0.922891i \(0.374180\pi\)
\(98\) 0 0
\(99\) 0.273683 0.0275062
\(100\) 0 0
\(101\) −13.3257 −1.32595 −0.662977 0.748640i \(-0.730707\pi\)
−0.662977 + 0.748640i \(0.730707\pi\)
\(102\) 0 0
\(103\) −6.24375 −0.615215 −0.307607 0.951513i \(-0.599528\pi\)
−0.307607 + 0.951513i \(0.599528\pi\)
\(104\) 0 0
\(105\) −25.3869 −2.47750
\(106\) 0 0
\(107\) −3.29616 −0.318652 −0.159326 0.987226i \(-0.550932\pi\)
−0.159326 + 0.987226i \(0.550932\pi\)
\(108\) 0 0
\(109\) 0.636565 0.0609719 0.0304860 0.999535i \(-0.490295\pi\)
0.0304860 + 0.999535i \(0.490295\pi\)
\(110\) 0 0
\(111\) 8.63503 0.819600
\(112\) 0 0
\(113\) −8.76089 −0.824156 −0.412078 0.911149i \(-0.635197\pi\)
−0.412078 + 0.911149i \(0.635197\pi\)
\(114\) 0 0
\(115\) −25.3907 −2.36769
\(116\) 0 0
\(117\) 0.804916 0.0744145
\(118\) 0 0
\(119\) 9.62042 0.881902
\(120\) 0 0
\(121\) −9.58618 −0.871471
\(122\) 0 0
\(123\) 1.69623 0.152944
\(124\) 0 0
\(125\) −6.37746 −0.570418
\(126\) 0 0
\(127\) −10.2731 −0.911589 −0.455795 0.890085i \(-0.650645\pi\)
−0.455795 + 0.890085i \(0.650645\pi\)
\(128\) 0 0
\(129\) −0.200788 −0.0176784
\(130\) 0 0
\(131\) 18.7673 1.63970 0.819852 0.572576i \(-0.194056\pi\)
0.819852 + 0.572576i \(0.194056\pi\)
\(132\) 0 0
\(133\) 24.6991 2.14168
\(134\) 0 0
\(135\) −18.5078 −1.59290
\(136\) 0 0
\(137\) −7.56580 −0.646390 −0.323195 0.946332i \(-0.604757\pi\)
−0.323195 + 0.946332i \(0.604757\pi\)
\(138\) 0 0
\(139\) 10.6960 0.907222 0.453611 0.891200i \(-0.350136\pi\)
0.453611 + 0.891200i \(0.350136\pi\)
\(140\) 0 0
\(141\) 5.12189 0.431341
\(142\) 0 0
\(143\) 4.15810 0.347718
\(144\) 0 0
\(145\) 14.5219 1.20598
\(146\) 0 0
\(147\) −21.0227 −1.73392
\(148\) 0 0
\(149\) −0.548032 −0.0448966 −0.0224483 0.999748i \(-0.507146\pi\)
−0.0224483 + 0.999748i \(0.507146\pi\)
\(150\) 0 0
\(151\) 12.3768 1.00721 0.503605 0.863934i \(-0.332007\pi\)
0.503605 + 0.863934i \(0.332007\pi\)
\(152\) 0 0
\(153\) 0.499766 0.0404037
\(154\) 0 0
\(155\) −25.6596 −2.06103
\(156\) 0 0
\(157\) −17.4613 −1.39356 −0.696782 0.717283i \(-0.745386\pi\)
−0.696782 + 0.717283i \(0.745386\pi\)
\(158\) 0 0
\(159\) 4.66768 0.370171
\(160\) 0 0
\(161\) −32.6775 −2.57535
\(162\) 0 0
\(163\) −17.7025 −1.38657 −0.693285 0.720664i \(-0.743837\pi\)
−0.693285 + 0.720664i \(0.743837\pi\)
\(164\) 0 0
\(165\) −6.81282 −0.530377
\(166\) 0 0
\(167\) 8.39101 0.649316 0.324658 0.945832i \(-0.394751\pi\)
0.324658 + 0.945832i \(0.394751\pi\)
\(168\) 0 0
\(169\) −0.770825 −0.0592942
\(170\) 0 0
\(171\) 1.28308 0.0981196
\(172\) 0 0
\(173\) 4.47941 0.340563 0.170282 0.985395i \(-0.445532\pi\)
0.170282 + 0.985395i \(0.445532\pi\)
\(174\) 0 0
\(175\) −30.3616 −2.29512
\(176\) 0 0
\(177\) 4.57428 0.343824
\(178\) 0 0
\(179\) −10.6765 −0.797997 −0.398999 0.916951i \(-0.630642\pi\)
−0.398999 + 0.916951i \(0.630642\pi\)
\(180\) 0 0
\(181\) −8.00808 −0.595236 −0.297618 0.954685i \(-0.596192\pi\)
−0.297618 + 0.954685i \(0.596192\pi\)
\(182\) 0 0
\(183\) −18.1681 −1.34302
\(184\) 0 0
\(185\) 17.8625 1.31327
\(186\) 0 0
\(187\) 2.58174 0.188795
\(188\) 0 0
\(189\) −23.8194 −1.73261
\(190\) 0 0
\(191\) −0.844203 −0.0610844 −0.0305422 0.999533i \(-0.509723\pi\)
−0.0305422 + 0.999533i \(0.509723\pi\)
\(192\) 0 0
\(193\) 18.4651 1.32915 0.664573 0.747223i \(-0.268614\pi\)
0.664573 + 0.747223i \(0.268614\pi\)
\(194\) 0 0
\(195\) −20.0368 −1.43487
\(196\) 0 0
\(197\) −9.91364 −0.706318 −0.353159 0.935563i \(-0.614892\pi\)
−0.353159 + 0.935563i \(0.614892\pi\)
\(198\) 0 0
\(199\) 17.2198 1.22068 0.610341 0.792139i \(-0.291032\pi\)
0.610341 + 0.792139i \(0.291032\pi\)
\(200\) 0 0
\(201\) −7.58588 −0.535067
\(202\) 0 0
\(203\) 18.6895 1.31174
\(204\) 0 0
\(205\) 3.50883 0.245068
\(206\) 0 0
\(207\) −1.69755 −0.117988
\(208\) 0 0
\(209\) 6.62824 0.458485
\(210\) 0 0
\(211\) 10.4567 0.719867 0.359933 0.932978i \(-0.382799\pi\)
0.359933 + 0.932978i \(0.382799\pi\)
\(212\) 0 0
\(213\) −1.18245 −0.0810201
\(214\) 0 0
\(215\) −0.415351 −0.0283267
\(216\) 0 0
\(217\) −33.0236 −2.24179
\(218\) 0 0
\(219\) 5.57007 0.376390
\(220\) 0 0
\(221\) 7.59301 0.510761
\(222\) 0 0
\(223\) 2.52993 0.169417 0.0847083 0.996406i \(-0.473004\pi\)
0.0847083 + 0.996406i \(0.473004\pi\)
\(224\) 0 0
\(225\) −1.57724 −0.105149
\(226\) 0 0
\(227\) 26.9881 1.79126 0.895632 0.444795i \(-0.146723\pi\)
0.895632 + 0.444795i \(0.146723\pi\)
\(228\) 0 0
\(229\) −17.6989 −1.16958 −0.584789 0.811185i \(-0.698823\pi\)
−0.584789 + 0.811185i \(0.698823\pi\)
\(230\) 0 0
\(231\) −8.76802 −0.576894
\(232\) 0 0
\(233\) 1.68990 0.110709 0.0553544 0.998467i \(-0.482371\pi\)
0.0553544 + 0.998467i \(0.482371\pi\)
\(234\) 0 0
\(235\) 10.5952 0.691152
\(236\) 0 0
\(237\) −10.5685 −0.686498
\(238\) 0 0
\(239\) −25.8826 −1.67421 −0.837103 0.547045i \(-0.815753\pi\)
−0.837103 + 0.547045i \(0.815753\pi\)
\(240\) 0 0
\(241\) 24.9079 1.60446 0.802229 0.597016i \(-0.203647\pi\)
0.802229 + 0.597016i \(0.203647\pi\)
\(242\) 0 0
\(243\) −2.38659 −0.153100
\(244\) 0 0
\(245\) −43.4876 −2.77832
\(246\) 0 0
\(247\) 19.4940 1.24037
\(248\) 0 0
\(249\) −22.3044 −1.41348
\(250\) 0 0
\(251\) 24.5831 1.55167 0.775837 0.630933i \(-0.217328\pi\)
0.775837 + 0.630933i \(0.217328\pi\)
\(252\) 0 0
\(253\) −8.76933 −0.551323
\(254\) 0 0
\(255\) −12.4407 −0.779068
\(256\) 0 0
\(257\) 10.1488 0.633068 0.316534 0.948581i \(-0.397481\pi\)
0.316534 + 0.948581i \(0.397481\pi\)
\(258\) 0 0
\(259\) 22.9888 1.42845
\(260\) 0 0
\(261\) 0.970891 0.0600966
\(262\) 0 0
\(263\) −11.1732 −0.688972 −0.344486 0.938791i \(-0.611947\pi\)
−0.344486 + 0.938791i \(0.611947\pi\)
\(264\) 0 0
\(265\) 9.65558 0.593138
\(266\) 0 0
\(267\) −16.1613 −0.989056
\(268\) 0 0
\(269\) −19.4053 −1.18316 −0.591581 0.806245i \(-0.701496\pi\)
−0.591581 + 0.806245i \(0.701496\pi\)
\(270\) 0 0
\(271\) 12.6613 0.769117 0.384559 0.923101i \(-0.374354\pi\)
0.384559 + 0.923101i \(0.374354\pi\)
\(272\) 0 0
\(273\) −25.7872 −1.56071
\(274\) 0 0
\(275\) −8.14783 −0.491332
\(276\) 0 0
\(277\) −11.6562 −0.700351 −0.350175 0.936684i \(-0.613878\pi\)
−0.350175 + 0.936684i \(0.613878\pi\)
\(278\) 0 0
\(279\) −1.71553 −0.102706
\(280\) 0 0
\(281\) 18.2193 1.08687 0.543437 0.839450i \(-0.317123\pi\)
0.543437 + 0.839450i \(0.317123\pi\)
\(282\) 0 0
\(283\) −19.4899 −1.15855 −0.579276 0.815132i \(-0.696665\pi\)
−0.579276 + 0.815132i \(0.696665\pi\)
\(284\) 0 0
\(285\) −31.9398 −1.89195
\(286\) 0 0
\(287\) 4.51583 0.266561
\(288\) 0 0
\(289\) −12.2856 −0.722680
\(290\) 0 0
\(291\) −12.6233 −0.739991
\(292\) 0 0
\(293\) −3.98593 −0.232860 −0.116430 0.993199i \(-0.537145\pi\)
−0.116430 + 0.993199i \(0.537145\pi\)
\(294\) 0 0
\(295\) 9.46237 0.550921
\(296\) 0 0
\(297\) −6.39217 −0.370912
\(298\) 0 0
\(299\) −25.7910 −1.49153
\(300\) 0 0
\(301\) −0.534552 −0.0308111
\(302\) 0 0
\(303\) 22.1776 1.27407
\(304\) 0 0
\(305\) −37.5825 −2.15197
\(306\) 0 0
\(307\) 2.14719 0.122546 0.0612732 0.998121i \(-0.480484\pi\)
0.0612732 + 0.998121i \(0.480484\pi\)
\(308\) 0 0
\(309\) 10.3913 0.591143
\(310\) 0 0
\(311\) −1.36490 −0.0773963 −0.0386981 0.999251i \(-0.512321\pi\)
−0.0386981 + 0.999251i \(0.512321\pi\)
\(312\) 0 0
\(313\) 16.1919 0.915222 0.457611 0.889153i \(-0.348705\pi\)
0.457611 + 0.889153i \(0.348705\pi\)
\(314\) 0 0
\(315\) −3.51103 −0.197824
\(316\) 0 0
\(317\) 20.3104 1.14075 0.570374 0.821385i \(-0.306798\pi\)
0.570374 + 0.821385i \(0.306798\pi\)
\(318\) 0 0
\(319\) 5.01551 0.280815
\(320\) 0 0
\(321\) 5.48574 0.306184
\(322\) 0 0
\(323\) 12.1037 0.673466
\(324\) 0 0
\(325\) −23.9631 −1.32924
\(326\) 0 0
\(327\) −1.05942 −0.0585862
\(328\) 0 0
\(329\) 13.6359 0.751770
\(330\) 0 0
\(331\) 9.23075 0.507368 0.253684 0.967287i \(-0.418358\pi\)
0.253684 + 0.967287i \(0.418358\pi\)
\(332\) 0 0
\(333\) 1.19423 0.0654436
\(334\) 0 0
\(335\) −15.6922 −0.857356
\(336\) 0 0
\(337\) 17.1199 0.932580 0.466290 0.884632i \(-0.345590\pi\)
0.466290 + 0.884632i \(0.345590\pi\)
\(338\) 0 0
\(339\) 14.5806 0.791908
\(340\) 0 0
\(341\) −8.86222 −0.479916
\(342\) 0 0
\(343\) −24.9527 −1.34732
\(344\) 0 0
\(345\) 42.2572 2.27505
\(346\) 0 0
\(347\) −10.7339 −0.576226 −0.288113 0.957596i \(-0.593028\pi\)
−0.288113 + 0.957596i \(0.593028\pi\)
\(348\) 0 0
\(349\) 14.3070 0.765838 0.382919 0.923782i \(-0.374919\pi\)
0.382919 + 0.923782i \(0.374919\pi\)
\(350\) 0 0
\(351\) −18.7997 −1.00345
\(352\) 0 0
\(353\) 14.3791 0.765320 0.382660 0.923889i \(-0.375008\pi\)
0.382660 + 0.923889i \(0.375008\pi\)
\(354\) 0 0
\(355\) −2.44602 −0.129821
\(356\) 0 0
\(357\) −16.0111 −0.847396
\(358\) 0 0
\(359\) −22.5958 −1.19256 −0.596281 0.802776i \(-0.703355\pi\)
−0.596281 + 0.802776i \(0.703355\pi\)
\(360\) 0 0
\(361\) 12.0745 0.635499
\(362\) 0 0
\(363\) 15.9541 0.837373
\(364\) 0 0
\(365\) 11.5223 0.603103
\(366\) 0 0
\(367\) −33.8333 −1.76609 −0.883043 0.469292i \(-0.844509\pi\)
−0.883043 + 0.469292i \(0.844509\pi\)
\(368\) 0 0
\(369\) 0.234591 0.0122123
\(370\) 0 0
\(371\) 12.4266 0.645159
\(372\) 0 0
\(373\) −10.1865 −0.527438 −0.263719 0.964600i \(-0.584949\pi\)
−0.263719 + 0.964600i \(0.584949\pi\)
\(374\) 0 0
\(375\) 10.6139 0.548099
\(376\) 0 0
\(377\) 14.7508 0.759707
\(378\) 0 0
\(379\) 10.6614 0.547641 0.273821 0.961781i \(-0.411713\pi\)
0.273821 + 0.961781i \(0.411713\pi\)
\(380\) 0 0
\(381\) 17.0973 0.875921
\(382\) 0 0
\(383\) 29.1930 1.49169 0.745846 0.666119i \(-0.232046\pi\)
0.745846 + 0.666119i \(0.232046\pi\)
\(384\) 0 0
\(385\) −18.1376 −0.924376
\(386\) 0 0
\(387\) −0.0277692 −0.00141159
\(388\) 0 0
\(389\) −25.9539 −1.31591 −0.657957 0.753056i \(-0.728579\pi\)
−0.657957 + 0.753056i \(0.728579\pi\)
\(390\) 0 0
\(391\) −16.0135 −0.809836
\(392\) 0 0
\(393\) −31.2340 −1.57555
\(394\) 0 0
\(395\) −21.8620 −1.10000
\(396\) 0 0
\(397\) 2.93633 0.147370 0.0736852 0.997282i \(-0.476524\pi\)
0.0736852 + 0.997282i \(0.476524\pi\)
\(398\) 0 0
\(399\) −41.1062 −2.05788
\(400\) 0 0
\(401\) −16.7042 −0.834167 −0.417084 0.908868i \(-0.636948\pi\)
−0.417084 + 0.908868i \(0.636948\pi\)
\(402\) 0 0
\(403\) −26.0642 −1.29835
\(404\) 0 0
\(405\) 28.4250 1.41245
\(406\) 0 0
\(407\) 6.16927 0.305799
\(408\) 0 0
\(409\) 30.7034 1.51819 0.759093 0.650982i \(-0.225643\pi\)
0.759093 + 0.650982i \(0.225643\pi\)
\(410\) 0 0
\(411\) 12.5916 0.621099
\(412\) 0 0
\(413\) 12.1780 0.599239
\(414\) 0 0
\(415\) −46.1389 −2.26487
\(416\) 0 0
\(417\) −17.8011 −0.871725
\(418\) 0 0
\(419\) 1.56186 0.0763018 0.0381509 0.999272i \(-0.487853\pi\)
0.0381509 + 0.999272i \(0.487853\pi\)
\(420\) 0 0
\(421\) 8.04875 0.392272 0.196136 0.980577i \(-0.437161\pi\)
0.196136 + 0.980577i \(0.437161\pi\)
\(422\) 0 0
\(423\) 0.708363 0.0344418
\(424\) 0 0
\(425\) −14.8785 −0.721715
\(426\) 0 0
\(427\) −48.3683 −2.34071
\(428\) 0 0
\(429\) −6.92025 −0.334113
\(430\) 0 0
\(431\) −23.5999 −1.13677 −0.568383 0.822764i \(-0.692431\pi\)
−0.568383 + 0.822764i \(0.692431\pi\)
\(432\) 0 0
\(433\) 9.33138 0.448438 0.224219 0.974539i \(-0.428017\pi\)
0.224219 + 0.974539i \(0.428017\pi\)
\(434\) 0 0
\(435\) −24.1684 −1.15879
\(436\) 0 0
\(437\) −41.1123 −1.96667
\(438\) 0 0
\(439\) −24.0237 −1.14659 −0.573295 0.819349i \(-0.694335\pi\)
−0.573295 + 0.819349i \(0.694335\pi\)
\(440\) 0 0
\(441\) −2.90746 −0.138450
\(442\) 0 0
\(443\) −2.08695 −0.0991539 −0.0495769 0.998770i \(-0.515787\pi\)
−0.0495769 + 0.998770i \(0.515787\pi\)
\(444\) 0 0
\(445\) −33.4313 −1.58480
\(446\) 0 0
\(447\) 0.912079 0.0431399
\(448\) 0 0
\(449\) 5.51869 0.260443 0.130221 0.991485i \(-0.458431\pi\)
0.130221 + 0.991485i \(0.458431\pi\)
\(450\) 0 0
\(451\) 1.21187 0.0570647
\(452\) 0 0
\(453\) −20.5985 −0.967800
\(454\) 0 0
\(455\) −53.3435 −2.50078
\(456\) 0 0
\(457\) −18.9386 −0.885912 −0.442956 0.896543i \(-0.646070\pi\)
−0.442956 + 0.896543i \(0.646070\pi\)
\(458\) 0 0
\(459\) −11.6726 −0.544830
\(460\) 0 0
\(461\) 25.9924 1.21059 0.605293 0.796003i \(-0.293056\pi\)
0.605293 + 0.796003i \(0.293056\pi\)
\(462\) 0 0
\(463\) −35.9190 −1.66930 −0.834650 0.550781i \(-0.814330\pi\)
−0.834650 + 0.550781i \(0.814330\pi\)
\(464\) 0 0
\(465\) 42.7048 1.98039
\(466\) 0 0
\(467\) 9.83647 0.455177 0.227589 0.973757i \(-0.426916\pi\)
0.227589 + 0.973757i \(0.426916\pi\)
\(468\) 0 0
\(469\) −20.1957 −0.932550
\(470\) 0 0
\(471\) 29.0605 1.33904
\(472\) 0 0
\(473\) −0.143452 −0.00659595
\(474\) 0 0
\(475\) −38.1986 −1.75267
\(476\) 0 0
\(477\) 0.645545 0.0295575
\(478\) 0 0
\(479\) −12.2528 −0.559843 −0.279922 0.960023i \(-0.590308\pi\)
−0.279922 + 0.960023i \(0.590308\pi\)
\(480\) 0 0
\(481\) 18.1441 0.827300
\(482\) 0 0
\(483\) 54.3845 2.47458
\(484\) 0 0
\(485\) −26.1126 −1.18571
\(486\) 0 0
\(487\) 31.5386 1.42915 0.714576 0.699558i \(-0.246620\pi\)
0.714576 + 0.699558i \(0.246620\pi\)
\(488\) 0 0
\(489\) 29.4620 1.33232
\(490\) 0 0
\(491\) 30.4460 1.37401 0.687004 0.726654i \(-0.258926\pi\)
0.687004 + 0.726654i \(0.258926\pi\)
\(492\) 0 0
\(493\) 9.15870 0.412487
\(494\) 0 0
\(495\) −0.942220 −0.0423496
\(496\) 0 0
\(497\) −3.14800 −0.141207
\(498\) 0 0
\(499\) −20.7996 −0.931117 −0.465558 0.885017i \(-0.654146\pi\)
−0.465558 + 0.885017i \(0.654146\pi\)
\(500\) 0 0
\(501\) −13.9650 −0.623910
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 45.8768 2.04149
\(506\) 0 0
\(507\) 1.28287 0.0569742
\(508\) 0 0
\(509\) −23.3203 −1.03365 −0.516826 0.856090i \(-0.672887\pi\)
−0.516826 + 0.856090i \(0.672887\pi\)
\(510\) 0 0
\(511\) 14.8290 0.655998
\(512\) 0 0
\(513\) −29.9677 −1.32311
\(514\) 0 0
\(515\) 21.4956 0.947208
\(516\) 0 0
\(517\) 3.65932 0.160937
\(518\) 0 0
\(519\) −7.45499 −0.327238
\(520\) 0 0
\(521\) −25.4086 −1.11317 −0.556586 0.830790i \(-0.687889\pi\)
−0.556586 + 0.830790i \(0.687889\pi\)
\(522\) 0 0
\(523\) 30.6210 1.33896 0.669480 0.742830i \(-0.266517\pi\)
0.669480 + 0.742830i \(0.266517\pi\)
\(524\) 0 0
\(525\) 50.5301 2.20532
\(526\) 0 0
\(527\) −16.1831 −0.704946
\(528\) 0 0
\(529\) 31.3926 1.36490
\(530\) 0 0
\(531\) 0.632627 0.0274537
\(532\) 0 0
\(533\) 3.56416 0.154381
\(534\) 0 0
\(535\) 11.3478 0.490609
\(536\) 0 0
\(537\) 17.7686 0.766774
\(538\) 0 0
\(539\) −15.0196 −0.646939
\(540\) 0 0
\(541\) 12.1009 0.520257 0.260129 0.965574i \(-0.416235\pi\)
0.260129 + 0.965574i \(0.416235\pi\)
\(542\) 0 0
\(543\) 13.3277 0.571946
\(544\) 0 0
\(545\) −2.19153 −0.0938747
\(546\) 0 0
\(547\) −33.3069 −1.42410 −0.712050 0.702129i \(-0.752233\pi\)
−0.712050 + 0.702129i \(0.752233\pi\)
\(548\) 0 0
\(549\) −2.51266 −0.107238
\(550\) 0 0
\(551\) 23.5137 1.00172
\(552\) 0 0
\(553\) −28.1362 −1.19647
\(554\) 0 0
\(555\) −29.7281 −1.26189
\(556\) 0 0
\(557\) 31.7330 1.34457 0.672285 0.740292i \(-0.265313\pi\)
0.672285 + 0.740292i \(0.265313\pi\)
\(558\) 0 0
\(559\) −0.421900 −0.0178445
\(560\) 0 0
\(561\) −4.29673 −0.181408
\(562\) 0 0
\(563\) −36.9937 −1.55910 −0.779550 0.626341i \(-0.784552\pi\)
−0.779550 + 0.626341i \(0.784552\pi\)
\(564\) 0 0
\(565\) 30.1615 1.26890
\(566\) 0 0
\(567\) 36.5826 1.53633
\(568\) 0 0
\(569\) 9.61211 0.402961 0.201480 0.979493i \(-0.435425\pi\)
0.201480 + 0.979493i \(0.435425\pi\)
\(570\) 0 0
\(571\) 6.49307 0.271727 0.135863 0.990728i \(-0.456619\pi\)
0.135863 + 0.990728i \(0.456619\pi\)
\(572\) 0 0
\(573\) 1.40499 0.0586943
\(574\) 0 0
\(575\) 50.5377 2.10757
\(576\) 0 0
\(577\) 47.2064 1.96523 0.982614 0.185659i \(-0.0594419\pi\)
0.982614 + 0.185659i \(0.0594419\pi\)
\(578\) 0 0
\(579\) −30.7311 −1.27714
\(580\) 0 0
\(581\) −59.3803 −2.46351
\(582\) 0 0
\(583\) 3.33481 0.138114
\(584\) 0 0
\(585\) −2.77111 −0.114571
\(586\) 0 0
\(587\) −5.61084 −0.231584 −0.115792 0.993273i \(-0.536941\pi\)
−0.115792 + 0.993273i \(0.536941\pi\)
\(588\) 0 0
\(589\) −41.5478 −1.71195
\(590\) 0 0
\(591\) 16.4991 0.678681
\(592\) 0 0
\(593\) 25.0721 1.02959 0.514793 0.857314i \(-0.327869\pi\)
0.514793 + 0.857314i \(0.327869\pi\)
\(594\) 0 0
\(595\) −33.1206 −1.35781
\(596\) 0 0
\(597\) −28.6586 −1.17292
\(598\) 0 0
\(599\) 28.1633 1.15072 0.575361 0.817900i \(-0.304862\pi\)
0.575361 + 0.817900i \(0.304862\pi\)
\(600\) 0 0
\(601\) −26.8480 −1.09515 −0.547576 0.836756i \(-0.684449\pi\)
−0.547576 + 0.836756i \(0.684449\pi\)
\(602\) 0 0
\(603\) −1.04914 −0.0427241
\(604\) 0 0
\(605\) 33.0027 1.34175
\(606\) 0 0
\(607\) 42.2396 1.71445 0.857225 0.514942i \(-0.172186\pi\)
0.857225 + 0.514942i \(0.172186\pi\)
\(608\) 0 0
\(609\) −31.1045 −1.26042
\(610\) 0 0
\(611\) 10.7622 0.435393
\(612\) 0 0
\(613\) −32.3212 −1.30544 −0.652721 0.757598i \(-0.726373\pi\)
−0.652721 + 0.757598i \(0.726373\pi\)
\(614\) 0 0
\(615\) −5.83968 −0.235479
\(616\) 0 0
\(617\) 21.9580 0.883995 0.441997 0.897016i \(-0.354270\pi\)
0.441997 + 0.897016i \(0.354270\pi\)
\(618\) 0 0
\(619\) 11.7735 0.473216 0.236608 0.971605i \(-0.423964\pi\)
0.236608 + 0.971605i \(0.423964\pi\)
\(620\) 0 0
\(621\) 39.6481 1.59102
\(622\) 0 0
\(623\) −43.0258 −1.72379
\(624\) 0 0
\(625\) −12.3063 −0.492251
\(626\) 0 0
\(627\) −11.0313 −0.440546
\(628\) 0 0
\(629\) 11.2655 0.449187
\(630\) 0 0
\(631\) −18.3254 −0.729523 −0.364762 0.931101i \(-0.618850\pi\)
−0.364762 + 0.931101i \(0.618850\pi\)
\(632\) 0 0
\(633\) −17.4028 −0.691700
\(634\) 0 0
\(635\) 35.3675 1.40352
\(636\) 0 0
\(637\) −44.1733 −1.75021
\(638\) 0 0
\(639\) −0.163534 −0.00646930
\(640\) 0 0
\(641\) 19.9149 0.786592 0.393296 0.919412i \(-0.371335\pi\)
0.393296 + 0.919412i \(0.371335\pi\)
\(642\) 0 0
\(643\) −1.73358 −0.0683655 −0.0341828 0.999416i \(-0.510883\pi\)
−0.0341828 + 0.999416i \(0.510883\pi\)
\(644\) 0 0
\(645\) 0.691260 0.0272183
\(646\) 0 0
\(647\) 33.9039 1.33290 0.666449 0.745551i \(-0.267813\pi\)
0.666449 + 0.745551i \(0.267813\pi\)
\(648\) 0 0
\(649\) 3.26808 0.128283
\(650\) 0 0
\(651\) 54.9606 2.15407
\(652\) 0 0
\(653\) −15.6760 −0.613450 −0.306725 0.951798i \(-0.599233\pi\)
−0.306725 + 0.951798i \(0.599233\pi\)
\(654\) 0 0
\(655\) −64.6108 −2.52455
\(656\) 0 0
\(657\) 0.770346 0.0300541
\(658\) 0 0
\(659\) 39.2087 1.52736 0.763678 0.645598i \(-0.223392\pi\)
0.763678 + 0.645598i \(0.223392\pi\)
\(660\) 0 0
\(661\) 0.444082 0.0172728 0.00863640 0.999963i \(-0.497251\pi\)
0.00863640 + 0.999963i \(0.497251\pi\)
\(662\) 0 0
\(663\) −12.6369 −0.490776
\(664\) 0 0
\(665\) −85.0324 −3.29742
\(666\) 0 0
\(667\) −31.1092 −1.20455
\(668\) 0 0
\(669\) −4.21051 −0.162788
\(670\) 0 0
\(671\) −12.9801 −0.501092
\(672\) 0 0
\(673\) −7.69877 −0.296766 −0.148383 0.988930i \(-0.547407\pi\)
−0.148383 + 0.988930i \(0.547407\pi\)
\(674\) 0 0
\(675\) 36.8381 1.41790
\(676\) 0 0
\(677\) −23.7491 −0.912751 −0.456376 0.889787i \(-0.650853\pi\)
−0.456376 + 0.889787i \(0.650853\pi\)
\(678\) 0 0
\(679\) −33.6067 −1.28971
\(680\) 0 0
\(681\) −44.9158 −1.72118
\(682\) 0 0
\(683\) −50.6013 −1.93620 −0.968102 0.250556i \(-0.919387\pi\)
−0.968102 + 0.250556i \(0.919387\pi\)
\(684\) 0 0
\(685\) 26.0471 0.995207
\(686\) 0 0
\(687\) 29.4560 1.12382
\(688\) 0 0
\(689\) 9.80784 0.373649
\(690\) 0 0
\(691\) 23.7377 0.903025 0.451512 0.892265i \(-0.350885\pi\)
0.451512 + 0.892265i \(0.350885\pi\)
\(692\) 0 0
\(693\) −1.21263 −0.0460639
\(694\) 0 0
\(695\) −36.8235 −1.39679
\(696\) 0 0
\(697\) 2.21296 0.0838220
\(698\) 0 0
\(699\) −2.81246 −0.106377
\(700\) 0 0
\(701\) 38.6053 1.45810 0.729051 0.684460i \(-0.239962\pi\)
0.729051 + 0.684460i \(0.239962\pi\)
\(702\) 0 0
\(703\) 28.9227 1.09084
\(704\) 0 0
\(705\) −17.6333 −0.664109
\(706\) 0 0
\(707\) 59.0429 2.22054
\(708\) 0 0
\(709\) −25.7065 −0.965426 −0.482713 0.875779i \(-0.660349\pi\)
−0.482713 + 0.875779i \(0.660349\pi\)
\(710\) 0 0
\(711\) −1.46163 −0.0548156
\(712\) 0 0
\(713\) 54.9688 2.05860
\(714\) 0 0
\(715\) −14.3153 −0.535360
\(716\) 0 0
\(717\) 43.0759 1.60870
\(718\) 0 0
\(719\) 32.9169 1.22759 0.613796 0.789465i \(-0.289642\pi\)
0.613796 + 0.789465i \(0.289642\pi\)
\(720\) 0 0
\(721\) 27.6646 1.03028
\(722\) 0 0
\(723\) −41.4537 −1.54168
\(724\) 0 0
\(725\) −28.9044 −1.07348
\(726\) 0 0
\(727\) −31.5790 −1.17120 −0.585600 0.810600i \(-0.699141\pi\)
−0.585600 + 0.810600i \(0.699141\pi\)
\(728\) 0 0
\(729\) 28.7415 1.06450
\(730\) 0 0
\(731\) −0.261955 −0.00968875
\(732\) 0 0
\(733\) 3.80843 0.140668 0.0703338 0.997524i \(-0.477594\pi\)
0.0703338 + 0.997524i \(0.477594\pi\)
\(734\) 0 0
\(735\) 72.3755 2.66961
\(736\) 0 0
\(737\) −5.41971 −0.199638
\(738\) 0 0
\(739\) 1.43646 0.0528411 0.0264205 0.999651i \(-0.491589\pi\)
0.0264205 + 0.999651i \(0.491589\pi\)
\(740\) 0 0
\(741\) −32.4434 −1.19184
\(742\) 0 0
\(743\) 26.3477 0.966605 0.483302 0.875453i \(-0.339437\pi\)
0.483302 + 0.875453i \(0.339437\pi\)
\(744\) 0 0
\(745\) 1.88673 0.0691245
\(746\) 0 0
\(747\) −3.08472 −0.112864
\(748\) 0 0
\(749\) 14.6045 0.533638
\(750\) 0 0
\(751\) −4.72181 −0.172301 −0.0861506 0.996282i \(-0.527457\pi\)
−0.0861506 + 0.996282i \(0.527457\pi\)
\(752\) 0 0
\(753\) −40.9132 −1.49096
\(754\) 0 0
\(755\) −42.6101 −1.55074
\(756\) 0 0
\(757\) −39.9298 −1.45127 −0.725637 0.688078i \(-0.758455\pi\)
−0.725637 + 0.688078i \(0.758455\pi\)
\(758\) 0 0
\(759\) 14.5946 0.529751
\(760\) 0 0
\(761\) 39.2738 1.42367 0.711837 0.702344i \(-0.247863\pi\)
0.711837 + 0.702344i \(0.247863\pi\)
\(762\) 0 0
\(763\) −2.82047 −0.102108
\(764\) 0 0
\(765\) −1.72056 −0.0622071
\(766\) 0 0
\(767\) 9.61158 0.347054
\(768\) 0 0
\(769\) 42.4607 1.53117 0.765586 0.643334i \(-0.222449\pi\)
0.765586 + 0.643334i \(0.222449\pi\)
\(770\) 0 0
\(771\) −16.8905 −0.608297
\(772\) 0 0
\(773\) 44.8437 1.61292 0.806459 0.591291i \(-0.201381\pi\)
0.806459 + 0.591291i \(0.201381\pi\)
\(774\) 0 0
\(775\) 51.0730 1.83460
\(776\) 0 0
\(777\) −38.2598 −1.37256
\(778\) 0 0
\(779\) 5.68147 0.203560
\(780\) 0 0
\(781\) −0.844798 −0.0302292
\(782\) 0 0
\(783\) −22.6762 −0.810382
\(784\) 0 0
\(785\) 60.1147 2.14559
\(786\) 0 0
\(787\) −50.7168 −1.80786 −0.903929 0.427682i \(-0.859330\pi\)
−0.903929 + 0.427682i \(0.859330\pi\)
\(788\) 0 0
\(789\) 18.5954 0.662014
\(790\) 0 0
\(791\) 38.8175 1.38019
\(792\) 0 0
\(793\) −38.1752 −1.35564
\(794\) 0 0
\(795\) −16.0696 −0.569930
\(796\) 0 0
\(797\) 31.2596 1.10727 0.553635 0.832759i \(-0.313240\pi\)
0.553635 + 0.832759i \(0.313240\pi\)
\(798\) 0 0
\(799\) 6.68219 0.236399
\(800\) 0 0
\(801\) −2.23513 −0.0789743
\(802\) 0 0
\(803\) 3.97952 0.140434
\(804\) 0 0
\(805\) 112.500 3.96511
\(806\) 0 0
\(807\) 32.2959 1.13687
\(808\) 0 0
\(809\) −6.92457 −0.243455 −0.121727 0.992564i \(-0.538843\pi\)
−0.121727 + 0.992564i \(0.538843\pi\)
\(810\) 0 0
\(811\) −10.0880 −0.354236 −0.177118 0.984190i \(-0.556677\pi\)
−0.177118 + 0.984190i \(0.556677\pi\)
\(812\) 0 0
\(813\) −21.0719 −0.739024
\(814\) 0 0
\(815\) 60.9452 2.13482
\(816\) 0 0
\(817\) −0.672533 −0.0235289
\(818\) 0 0
\(819\) −3.56639 −0.124620
\(820\) 0 0
\(821\) 50.2386 1.75334 0.876669 0.481093i \(-0.159760\pi\)
0.876669 + 0.481093i \(0.159760\pi\)
\(822\) 0 0
\(823\) −50.8517 −1.77258 −0.886290 0.463131i \(-0.846726\pi\)
−0.886290 + 0.463131i \(0.846726\pi\)
\(824\) 0 0
\(825\) 13.5603 0.472108
\(826\) 0 0
\(827\) 7.04513 0.244983 0.122492 0.992470i \(-0.460912\pi\)
0.122492 + 0.992470i \(0.460912\pi\)
\(828\) 0 0
\(829\) −25.8119 −0.896483 −0.448241 0.893913i \(-0.647949\pi\)
−0.448241 + 0.893913i \(0.647949\pi\)
\(830\) 0 0
\(831\) 19.3991 0.672948
\(832\) 0 0
\(833\) −27.4269 −0.950285
\(834\) 0 0
\(835\) −28.8880 −0.999712
\(836\) 0 0
\(837\) 40.0680 1.38495
\(838\) 0 0
\(839\) −37.6885 −1.30115 −0.650576 0.759441i \(-0.725473\pi\)
−0.650576 + 0.759441i \(0.725473\pi\)
\(840\) 0 0
\(841\) −11.2075 −0.386466
\(842\) 0 0
\(843\) −30.3220 −1.04435
\(844\) 0 0
\(845\) 2.65375 0.0912917
\(846\) 0 0
\(847\) 42.4741 1.45943
\(848\) 0 0
\(849\) 32.4366 1.11322
\(850\) 0 0
\(851\) −38.2655 −1.31172
\(852\) 0 0
\(853\) −50.3708 −1.72466 −0.862332 0.506342i \(-0.830997\pi\)
−0.862332 + 0.506342i \(0.830997\pi\)
\(854\) 0 0
\(855\) −4.41731 −0.151069
\(856\) 0 0
\(857\) −49.3295 −1.68506 −0.842532 0.538647i \(-0.818936\pi\)
−0.842532 + 0.538647i \(0.818936\pi\)
\(858\) 0 0
\(859\) −47.9902 −1.63740 −0.818702 0.574219i \(-0.805306\pi\)
−0.818702 + 0.574219i \(0.805306\pi\)
\(860\) 0 0
\(861\) −7.51561 −0.256131
\(862\) 0 0
\(863\) 45.1553 1.53710 0.768552 0.639788i \(-0.220978\pi\)
0.768552 + 0.639788i \(0.220978\pi\)
\(864\) 0 0
\(865\) −15.4214 −0.524344
\(866\) 0 0
\(867\) 20.4466 0.694403
\(868\) 0 0
\(869\) −7.55063 −0.256138
\(870\) 0 0
\(871\) −15.9396 −0.540094
\(872\) 0 0
\(873\) −1.74582 −0.0590869
\(874\) 0 0
\(875\) 28.2571 0.955263
\(876\) 0 0
\(877\) −9.47313 −0.319885 −0.159942 0.987126i \(-0.551131\pi\)
−0.159942 + 0.987126i \(0.551131\pi\)
\(878\) 0 0
\(879\) 6.63370 0.223749
\(880\) 0 0
\(881\) −29.9715 −1.00976 −0.504882 0.863188i \(-0.668464\pi\)
−0.504882 + 0.863188i \(0.668464\pi\)
\(882\) 0 0
\(883\) 46.0660 1.55024 0.775122 0.631811i \(-0.217688\pi\)
0.775122 + 0.631811i \(0.217688\pi\)
\(884\) 0 0
\(885\) −15.7480 −0.529365
\(886\) 0 0
\(887\) −54.4170 −1.82715 −0.913573 0.406675i \(-0.866688\pi\)
−0.913573 + 0.406675i \(0.866688\pi\)
\(888\) 0 0
\(889\) 45.5176 1.52661
\(890\) 0 0
\(891\) 9.81732 0.328893
\(892\) 0 0
\(893\) 17.1556 0.574090
\(894\) 0 0
\(895\) 36.7563 1.22863
\(896\) 0 0
\(897\) 42.9235 1.43317
\(898\) 0 0
\(899\) −31.4387 −1.04854
\(900\) 0 0
\(901\) 6.08962 0.202875
\(902\) 0 0
\(903\) 0.889645 0.0296055
\(904\) 0 0
\(905\) 27.5697 0.916449
\(906\) 0 0
\(907\) 30.0368 0.997357 0.498678 0.866787i \(-0.333819\pi\)
0.498678 + 0.866787i \(0.333819\pi\)
\(908\) 0 0
\(909\) 3.06719 0.101732
\(910\) 0 0
\(911\) 42.0040 1.39166 0.695828 0.718209i \(-0.255038\pi\)
0.695828 + 0.718209i \(0.255038\pi\)
\(912\) 0 0
\(913\) −15.9353 −0.527381
\(914\) 0 0
\(915\) 62.5479 2.06777
\(916\) 0 0
\(917\) −83.1534 −2.74597
\(918\) 0 0
\(919\) 34.7108 1.14500 0.572502 0.819903i \(-0.305973\pi\)
0.572502 + 0.819903i \(0.305973\pi\)
\(920\) 0 0
\(921\) −3.57352 −0.117751
\(922\) 0 0
\(923\) −2.48459 −0.0817813
\(924\) 0 0
\(925\) −35.5535 −1.16899
\(926\) 0 0
\(927\) 1.43713 0.0472017
\(928\) 0 0
\(929\) −35.0708 −1.15064 −0.575318 0.817930i \(-0.695122\pi\)
−0.575318 + 0.817930i \(0.695122\pi\)
\(930\) 0 0
\(931\) −70.4147 −2.30775
\(932\) 0 0
\(933\) 2.27157 0.0743680
\(934\) 0 0
\(935\) −8.88824 −0.290676
\(936\) 0 0
\(937\) 28.9508 0.945781 0.472890 0.881121i \(-0.343211\pi\)
0.472890 + 0.881121i \(0.343211\pi\)
\(938\) 0 0
\(939\) −26.9479 −0.879412
\(940\) 0 0
\(941\) 4.91056 0.160080 0.0800398 0.996792i \(-0.474495\pi\)
0.0800398 + 0.996792i \(0.474495\pi\)
\(942\) 0 0
\(943\) −7.51673 −0.244778
\(944\) 0 0
\(945\) 82.0039 2.66759
\(946\) 0 0
\(947\) −16.2429 −0.527825 −0.263912 0.964547i \(-0.585013\pi\)
−0.263912 + 0.964547i \(0.585013\pi\)
\(948\) 0 0
\(949\) 11.7040 0.379926
\(950\) 0 0
\(951\) −33.8023 −1.09611
\(952\) 0 0
\(953\) 11.1190 0.360178 0.180089 0.983650i \(-0.442361\pi\)
0.180089 + 0.983650i \(0.442361\pi\)
\(954\) 0 0
\(955\) 2.90637 0.0940479
\(956\) 0 0
\(957\) −8.34721 −0.269827
\(958\) 0 0
\(959\) 33.5223 1.08249
\(960\) 0 0
\(961\) 24.5510 0.791969
\(962\) 0 0
\(963\) 0.758683 0.0244482
\(964\) 0 0
\(965\) −63.5704 −2.04640
\(966\) 0 0
\(967\) −24.8298 −0.798473 −0.399236 0.916848i \(-0.630725\pi\)
−0.399236 + 0.916848i \(0.630725\pi\)
\(968\) 0 0
\(969\) −20.1439 −0.647115
\(970\) 0 0
\(971\) −2.97994 −0.0956309 −0.0478154 0.998856i \(-0.515226\pi\)
−0.0478154 + 0.998856i \(0.515226\pi\)
\(972\) 0 0
\(973\) −47.3914 −1.51930
\(974\) 0 0
\(975\) 39.8814 1.27723
\(976\) 0 0
\(977\) −47.9009 −1.53249 −0.766243 0.642551i \(-0.777876\pi\)
−0.766243 + 0.642551i \(0.777876\pi\)
\(978\) 0 0
\(979\) −11.5464 −0.369025
\(980\) 0 0
\(981\) −0.146519 −0.00467800
\(982\) 0 0
\(983\) 42.3043 1.34930 0.674649 0.738139i \(-0.264295\pi\)
0.674649 + 0.738139i \(0.264295\pi\)
\(984\) 0 0
\(985\) 34.1301 1.08747
\(986\) 0 0
\(987\) −22.6939 −0.722355
\(988\) 0 0
\(989\) 0.889777 0.0282933
\(990\) 0 0
\(991\) −14.4541 −0.459151 −0.229575 0.973291i \(-0.573734\pi\)
−0.229575 + 0.973291i \(0.573734\pi\)
\(992\) 0 0
\(993\) −15.3626 −0.487516
\(994\) 0 0
\(995\) −59.2834 −1.87941
\(996\) 0 0
\(997\) −19.7728 −0.626211 −0.313105 0.949718i \(-0.601369\pi\)
−0.313105 + 0.949718i \(0.601369\pi\)
\(998\) 0 0
\(999\) −27.8926 −0.882483
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 \(a_p\))