Properties

Label 4028.2.a.d.1.17
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Root \(-2.53438\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.53438 q^{3} -2.27936 q^{5} +1.27718 q^{7} +3.42306 q^{9} +O(q^{10})\) \(q+2.53438 q^{3} -2.27936 q^{5} +1.27718 q^{7} +3.42306 q^{9} +0.683995 q^{11} -4.05395 q^{13} -5.77675 q^{15} +0.471295 q^{17} -1.00000 q^{19} +3.23685 q^{21} -4.28297 q^{23} +0.195468 q^{25} +1.07220 q^{27} -9.77368 q^{29} -9.37733 q^{31} +1.73350 q^{33} -2.91114 q^{35} +2.27596 q^{37} -10.2742 q^{39} +1.23060 q^{41} -0.166983 q^{43} -7.80238 q^{45} +5.60808 q^{47} -5.36882 q^{49} +1.19444 q^{51} +1.00000 q^{53} -1.55907 q^{55} -2.53438 q^{57} -7.90151 q^{59} +0.280568 q^{61} +4.37185 q^{63} +9.24039 q^{65} +2.83519 q^{67} -10.8547 q^{69} +9.88384 q^{71} +12.2089 q^{73} +0.495391 q^{75} +0.873582 q^{77} -9.28523 q^{79} -7.55184 q^{81} +12.4165 q^{83} -1.07425 q^{85} -24.7702 q^{87} -13.1886 q^{89} -5.17761 q^{91} -23.7657 q^{93} +2.27936 q^{95} -0.0580025 q^{97} +2.34136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) 2.53438 1.46322 0.731611 0.681722i \(-0.238769\pi\)
0.731611 + 0.681722i \(0.238769\pi\)
\(4\) 0 0
\(5\) −2.27936 −1.01936 −0.509680 0.860364i \(-0.670236\pi\)
−0.509680 + 0.860364i \(0.670236\pi\)
\(6\) 0 0
\(7\) 1.27718 0.482728 0.241364 0.970435i \(-0.422405\pi\)
0.241364 + 0.970435i \(0.422405\pi\)
\(8\) 0 0
\(9\) 3.42306 1.14102
\(10\) 0 0
\(11\) 0.683995 0.206232 0.103116 0.994669i \(-0.467119\pi\)
0.103116 + 0.994669i \(0.467119\pi\)
\(12\) 0 0
\(13\) −4.05395 −1.12436 −0.562181 0.827014i \(-0.690038\pi\)
−0.562181 + 0.827014i \(0.690038\pi\)
\(14\) 0 0
\(15\) −5.77675 −1.49155
\(16\) 0 0
\(17\) 0.471295 0.114306 0.0571529 0.998365i \(-0.481798\pi\)
0.0571529 + 0.998365i \(0.481798\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 3.23685 0.706338
\(22\) 0 0
\(23\) −4.28297 −0.893061 −0.446531 0.894768i \(-0.647341\pi\)
−0.446531 + 0.894768i \(0.647341\pi\)
\(24\) 0 0
\(25\) 0.195468 0.0390937
\(26\) 0 0
\(27\) 1.07220 0.206344
\(28\) 0 0
\(29\) −9.77368 −1.81493 −0.907464 0.420131i \(-0.861984\pi\)
−0.907464 + 0.420131i \(0.861984\pi\)
\(30\) 0 0
\(31\) −9.37733 −1.68422 −0.842109 0.539308i \(-0.818686\pi\)
−0.842109 + 0.539308i \(0.818686\pi\)
\(32\) 0 0
\(33\) 1.73350 0.301764
\(34\) 0 0
\(35\) −2.91114 −0.492073
\(36\) 0 0
\(37\) 2.27596 0.374166 0.187083 0.982344i \(-0.440097\pi\)
0.187083 + 0.982344i \(0.440097\pi\)
\(38\) 0 0
\(39\) −10.2742 −1.64519
\(40\) 0 0
\(41\) 1.23060 0.192187 0.0960937 0.995372i \(-0.469365\pi\)
0.0960937 + 0.995372i \(0.469365\pi\)
\(42\) 0 0
\(43\) −0.166983 −0.0254646 −0.0127323 0.999919i \(-0.504053\pi\)
−0.0127323 + 0.999919i \(0.504053\pi\)
\(44\) 0 0
\(45\) −7.80238 −1.16311
\(46\) 0 0
\(47\) 5.60808 0.818023 0.409011 0.912529i \(-0.365874\pi\)
0.409011 + 0.912529i \(0.365874\pi\)
\(48\) 0 0
\(49\) −5.36882 −0.766974
\(50\) 0 0
\(51\) 1.19444 0.167255
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −1.55907 −0.210225
\(56\) 0 0
\(57\) −2.53438 −0.335686
\(58\) 0 0
\(59\) −7.90151 −1.02869 −0.514345 0.857584i \(-0.671965\pi\)
−0.514345 + 0.857584i \(0.671965\pi\)
\(60\) 0 0
\(61\) 0.280568 0.0359230 0.0179615 0.999839i \(-0.494282\pi\)
0.0179615 + 0.999839i \(0.494282\pi\)
\(62\) 0 0
\(63\) 4.37185 0.550802
\(64\) 0 0
\(65\) 9.24039 1.14613
\(66\) 0 0
\(67\) 2.83519 0.346374 0.173187 0.984889i \(-0.444594\pi\)
0.173187 + 0.984889i \(0.444594\pi\)
\(68\) 0 0
\(69\) −10.8547 −1.30675
\(70\) 0 0
\(71\) 9.88384 1.17300 0.586498 0.809951i \(-0.300506\pi\)
0.586498 + 0.809951i \(0.300506\pi\)
\(72\) 0 0
\(73\) 12.2089 1.42894 0.714471 0.699665i \(-0.246667\pi\)
0.714471 + 0.699665i \(0.246667\pi\)
\(74\) 0 0
\(75\) 0.495391 0.0572028
\(76\) 0 0
\(77\) 0.873582 0.0995539
\(78\) 0 0
\(79\) −9.28523 −1.04467 −0.522335 0.852740i \(-0.674939\pi\)
−0.522335 + 0.852740i \(0.674939\pi\)
\(80\) 0 0
\(81\) −7.55184 −0.839093
\(82\) 0 0
\(83\) 12.4165 1.36289 0.681444 0.731870i \(-0.261352\pi\)
0.681444 + 0.731870i \(0.261352\pi\)
\(84\) 0 0
\(85\) −1.07425 −0.116519
\(86\) 0 0
\(87\) −24.7702 −2.65564
\(88\) 0 0
\(89\) −13.1886 −1.39799 −0.698995 0.715126i \(-0.746369\pi\)
−0.698995 + 0.715126i \(0.746369\pi\)
\(90\) 0 0
\(91\) −5.17761 −0.542761
\(92\) 0 0
\(93\) −23.7657 −2.46438
\(94\) 0 0
\(95\) 2.27936 0.233857
\(96\) 0 0
\(97\) −0.0580025 −0.00588926 −0.00294463 0.999996i \(-0.500937\pi\)
−0.00294463 + 0.999996i \(0.500937\pi\)
\(98\) 0 0
\(99\) 2.34136 0.235315
\(100\) 0 0
\(101\) −14.6990 −1.46260 −0.731302 0.682054i \(-0.761087\pi\)
−0.731302 + 0.682054i \(0.761087\pi\)
\(102\) 0 0
\(103\) 14.8976 1.46790 0.733952 0.679201i \(-0.237674\pi\)
0.733952 + 0.679201i \(0.237674\pi\)
\(104\) 0 0
\(105\) −7.37793 −0.720012
\(106\) 0 0
\(107\) 18.2259 1.76196 0.880981 0.473152i \(-0.156884\pi\)
0.880981 + 0.473152i \(0.156884\pi\)
\(108\) 0 0
\(109\) −8.25332 −0.790524 −0.395262 0.918568i \(-0.629346\pi\)
−0.395262 + 0.918568i \(0.629346\pi\)
\(110\) 0 0
\(111\) 5.76815 0.547488
\(112\) 0 0
\(113\) 11.7052 1.10113 0.550564 0.834793i \(-0.314413\pi\)
0.550564 + 0.834793i \(0.314413\pi\)
\(114\) 0 0
\(115\) 9.76242 0.910350
\(116\) 0 0
\(117\) −13.8769 −1.28292
\(118\) 0 0
\(119\) 0.601927 0.0551786
\(120\) 0 0
\(121\) −10.5322 −0.957468
\(122\) 0 0
\(123\) 3.11880 0.281213
\(124\) 0 0
\(125\) 10.9512 0.979509
\(126\) 0 0
\(127\) −7.48112 −0.663842 −0.331921 0.943307i \(-0.607697\pi\)
−0.331921 + 0.943307i \(0.607697\pi\)
\(128\) 0 0
\(129\) −0.423197 −0.0372604
\(130\) 0 0
\(131\) −2.12916 −0.186026 −0.0930130 0.995665i \(-0.529650\pi\)
−0.0930130 + 0.995665i \(0.529650\pi\)
\(132\) 0 0
\(133\) −1.27718 −0.110745
\(134\) 0 0
\(135\) −2.44392 −0.210339
\(136\) 0 0
\(137\) −1.92478 −0.164445 −0.0822224 0.996614i \(-0.526202\pi\)
−0.0822224 + 0.996614i \(0.526202\pi\)
\(138\) 0 0
\(139\) −13.2021 −1.11979 −0.559894 0.828564i \(-0.689158\pi\)
−0.559894 + 0.828564i \(0.689158\pi\)
\(140\) 0 0
\(141\) 14.2130 1.19695
\(142\) 0 0
\(143\) −2.77288 −0.231880
\(144\) 0 0
\(145\) 22.2777 1.85006
\(146\) 0 0
\(147\) −13.6066 −1.12225
\(148\) 0 0
\(149\) 2.44056 0.199938 0.0999692 0.994991i \(-0.468126\pi\)
0.0999692 + 0.994991i \(0.468126\pi\)
\(150\) 0 0
\(151\) −7.96295 −0.648016 −0.324008 0.946054i \(-0.605030\pi\)
−0.324008 + 0.946054i \(0.605030\pi\)
\(152\) 0 0
\(153\) 1.61327 0.130425
\(154\) 0 0
\(155\) 21.3743 1.71682
\(156\) 0 0
\(157\) 3.20936 0.256134 0.128067 0.991765i \(-0.459123\pi\)
0.128067 + 0.991765i \(0.459123\pi\)
\(158\) 0 0
\(159\) 2.53438 0.200989
\(160\) 0 0
\(161\) −5.47011 −0.431105
\(162\) 0 0
\(163\) −7.18403 −0.562697 −0.281348 0.959606i \(-0.590782\pi\)
−0.281348 + 0.959606i \(0.590782\pi\)
\(164\) 0 0
\(165\) −3.95126 −0.307606
\(166\) 0 0
\(167\) −6.29950 −0.487470 −0.243735 0.969842i \(-0.578373\pi\)
−0.243735 + 0.969842i \(0.578373\pi\)
\(168\) 0 0
\(169\) 3.43448 0.264191
\(170\) 0 0
\(171\) −3.42306 −0.261768
\(172\) 0 0
\(173\) −5.62900 −0.427965 −0.213983 0.976837i \(-0.568644\pi\)
−0.213983 + 0.976837i \(0.568644\pi\)
\(174\) 0 0
\(175\) 0.249648 0.0188716
\(176\) 0 0
\(177\) −20.0254 −1.50520
\(178\) 0 0
\(179\) −5.95898 −0.445395 −0.222698 0.974888i \(-0.571486\pi\)
−0.222698 + 0.974888i \(0.571486\pi\)
\(180\) 0 0
\(181\) −12.4109 −0.922497 −0.461248 0.887271i \(-0.652598\pi\)
−0.461248 + 0.887271i \(0.652598\pi\)
\(182\) 0 0
\(183\) 0.711065 0.0525634
\(184\) 0 0
\(185\) −5.18773 −0.381410
\(186\) 0 0
\(187\) 0.322363 0.0235735
\(188\) 0 0
\(189\) 1.36938 0.0996079
\(190\) 0 0
\(191\) −14.3275 −1.03670 −0.518351 0.855168i \(-0.673454\pi\)
−0.518351 + 0.855168i \(0.673454\pi\)
\(192\) 0 0
\(193\) −6.27032 −0.451347 −0.225674 0.974203i \(-0.572458\pi\)
−0.225674 + 0.974203i \(0.572458\pi\)
\(194\) 0 0
\(195\) 23.4186 1.67704
\(196\) 0 0
\(197\) −17.3079 −1.23314 −0.616570 0.787300i \(-0.711478\pi\)
−0.616570 + 0.787300i \(0.711478\pi\)
\(198\) 0 0
\(199\) 13.6715 0.969146 0.484573 0.874751i \(-0.338975\pi\)
0.484573 + 0.874751i \(0.338975\pi\)
\(200\) 0 0
\(201\) 7.18544 0.506822
\(202\) 0 0
\(203\) −12.4827 −0.876115
\(204\) 0 0
\(205\) −2.80498 −0.195908
\(206\) 0 0
\(207\) −14.6609 −1.01900
\(208\) 0 0
\(209\) −0.683995 −0.0473129
\(210\) 0 0
\(211\) 18.0437 1.24218 0.621091 0.783739i \(-0.286690\pi\)
0.621091 + 0.783739i \(0.286690\pi\)
\(212\) 0 0
\(213\) 25.0494 1.71635
\(214\) 0 0
\(215\) 0.380614 0.0259576
\(216\) 0 0
\(217\) −11.9765 −0.813018
\(218\) 0 0
\(219\) 30.9419 2.09086
\(220\) 0 0
\(221\) −1.91061 −0.128521
\(222\) 0 0
\(223\) 5.67427 0.379977 0.189989 0.981786i \(-0.439155\pi\)
0.189989 + 0.981786i \(0.439155\pi\)
\(224\) 0 0
\(225\) 0.669101 0.0446067
\(226\) 0 0
\(227\) 28.4395 1.88760 0.943799 0.330521i \(-0.107224\pi\)
0.943799 + 0.330521i \(0.107224\pi\)
\(228\) 0 0
\(229\) −23.0630 −1.52405 −0.762024 0.647548i \(-0.775794\pi\)
−0.762024 + 0.647548i \(0.775794\pi\)
\(230\) 0 0
\(231\) 2.21399 0.145670
\(232\) 0 0
\(233\) −4.42250 −0.289727 −0.144864 0.989452i \(-0.546274\pi\)
−0.144864 + 0.989452i \(0.546274\pi\)
\(234\) 0 0
\(235\) −12.7828 −0.833859
\(236\) 0 0
\(237\) −23.5323 −1.52858
\(238\) 0 0
\(239\) 1.23936 0.0801675 0.0400837 0.999196i \(-0.487238\pi\)
0.0400837 + 0.999196i \(0.487238\pi\)
\(240\) 0 0
\(241\) −10.3316 −0.665518 −0.332759 0.943012i \(-0.607980\pi\)
−0.332759 + 0.943012i \(0.607980\pi\)
\(242\) 0 0
\(243\) −22.3558 −1.43412
\(244\) 0 0
\(245\) 12.2375 0.781822
\(246\) 0 0
\(247\) 4.05395 0.257946
\(248\) 0 0
\(249\) 31.4681 1.99421
\(250\) 0 0
\(251\) −3.88927 −0.245489 −0.122744 0.992438i \(-0.539170\pi\)
−0.122744 + 0.992438i \(0.539170\pi\)
\(252\) 0 0
\(253\) −2.92953 −0.184178
\(254\) 0 0
\(255\) −2.72255 −0.170493
\(256\) 0 0
\(257\) 7.70877 0.480860 0.240430 0.970667i \(-0.422712\pi\)
0.240430 + 0.970667i \(0.422712\pi\)
\(258\) 0 0
\(259\) 2.90681 0.180620
\(260\) 0 0
\(261\) −33.4559 −2.07087
\(262\) 0 0
\(263\) 11.7299 0.723298 0.361649 0.932314i \(-0.382214\pi\)
0.361649 + 0.932314i \(0.382214\pi\)
\(264\) 0 0
\(265\) −2.27936 −0.140020
\(266\) 0 0
\(267\) −33.4249 −2.04557
\(268\) 0 0
\(269\) −21.2401 −1.29503 −0.647516 0.762052i \(-0.724192\pi\)
−0.647516 + 0.762052i \(0.724192\pi\)
\(270\) 0 0
\(271\) −10.4709 −0.636065 −0.318032 0.948080i \(-0.603022\pi\)
−0.318032 + 0.948080i \(0.603022\pi\)
\(272\) 0 0
\(273\) −13.1220 −0.794180
\(274\) 0 0
\(275\) 0.133699 0.00806238
\(276\) 0 0
\(277\) −18.1470 −1.09035 −0.545173 0.838323i \(-0.683536\pi\)
−0.545173 + 0.838323i \(0.683536\pi\)
\(278\) 0 0
\(279\) −32.0992 −1.92173
\(280\) 0 0
\(281\) −5.75924 −0.343568 −0.171784 0.985135i \(-0.554953\pi\)
−0.171784 + 0.985135i \(0.554953\pi\)
\(282\) 0 0
\(283\) −13.4253 −0.798053 −0.399027 0.916939i \(-0.630652\pi\)
−0.399027 + 0.916939i \(0.630652\pi\)
\(284\) 0 0
\(285\) 5.77675 0.342185
\(286\) 0 0
\(287\) 1.57169 0.0927742
\(288\) 0 0
\(289\) −16.7779 −0.986934
\(290\) 0 0
\(291\) −0.147000 −0.00861730
\(292\) 0 0
\(293\) 2.18029 0.127374 0.0636868 0.997970i \(-0.479714\pi\)
0.0636868 + 0.997970i \(0.479714\pi\)
\(294\) 0 0
\(295\) 18.0104 1.04860
\(296\) 0 0
\(297\) 0.733376 0.0425548
\(298\) 0 0
\(299\) 17.3629 1.00412
\(300\) 0 0
\(301\) −0.213267 −0.0122925
\(302\) 0 0
\(303\) −37.2527 −2.14011
\(304\) 0 0
\(305\) −0.639514 −0.0366185
\(306\) 0 0
\(307\) 15.4042 0.879165 0.439583 0.898202i \(-0.355126\pi\)
0.439583 + 0.898202i \(0.355126\pi\)
\(308\) 0 0
\(309\) 37.7561 2.14787
\(310\) 0 0
\(311\) 11.9536 0.677826 0.338913 0.940818i \(-0.389941\pi\)
0.338913 + 0.940818i \(0.389941\pi\)
\(312\) 0 0
\(313\) 0.866842 0.0489968 0.0244984 0.999700i \(-0.492201\pi\)
0.0244984 + 0.999700i \(0.492201\pi\)
\(314\) 0 0
\(315\) −9.96502 −0.561465
\(316\) 0 0
\(317\) 20.9663 1.17758 0.588792 0.808284i \(-0.299604\pi\)
0.588792 + 0.808284i \(0.299604\pi\)
\(318\) 0 0
\(319\) −6.68515 −0.374296
\(320\) 0 0
\(321\) 46.1912 2.57814
\(322\) 0 0
\(323\) −0.471295 −0.0262236
\(324\) 0 0
\(325\) −0.792419 −0.0439555
\(326\) 0 0
\(327\) −20.9170 −1.15671
\(328\) 0 0
\(329\) 7.16251 0.394882
\(330\) 0 0
\(331\) 27.0956 1.48931 0.744654 0.667451i \(-0.232615\pi\)
0.744654 + 0.667451i \(0.232615\pi\)
\(332\) 0 0
\(333\) 7.79076 0.426931
\(334\) 0 0
\(335\) −6.46242 −0.353080
\(336\) 0 0
\(337\) 33.9085 1.84711 0.923556 0.383464i \(-0.125269\pi\)
0.923556 + 0.383464i \(0.125269\pi\)
\(338\) 0 0
\(339\) 29.6653 1.61120
\(340\) 0 0
\(341\) −6.41404 −0.347340
\(342\) 0 0
\(343\) −15.7972 −0.852967
\(344\) 0 0
\(345\) 24.7416 1.33205
\(346\) 0 0
\(347\) −29.1422 −1.56444 −0.782219 0.623004i \(-0.785912\pi\)
−0.782219 + 0.623004i \(0.785912\pi\)
\(348\) 0 0
\(349\) −11.2954 −0.604629 −0.302315 0.953208i \(-0.597759\pi\)
−0.302315 + 0.953208i \(0.597759\pi\)
\(350\) 0 0
\(351\) −4.34662 −0.232005
\(352\) 0 0
\(353\) 22.3141 1.18766 0.593830 0.804591i \(-0.297615\pi\)
0.593830 + 0.804591i \(0.297615\pi\)
\(354\) 0 0
\(355\) −22.5288 −1.19570
\(356\) 0 0
\(357\) 1.52551 0.0807385
\(358\) 0 0
\(359\) 32.3908 1.70952 0.854761 0.519021i \(-0.173704\pi\)
0.854761 + 0.519021i \(0.173704\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −26.6924 −1.40099
\(364\) 0 0
\(365\) −27.8284 −1.45661
\(366\) 0 0
\(367\) 21.8121 1.13858 0.569292 0.822135i \(-0.307217\pi\)
0.569292 + 0.822135i \(0.307217\pi\)
\(368\) 0 0
\(369\) 4.21242 0.219290
\(370\) 0 0
\(371\) 1.27718 0.0663077
\(372\) 0 0
\(373\) 9.02171 0.467127 0.233563 0.972342i \(-0.424961\pi\)
0.233563 + 0.972342i \(0.424961\pi\)
\(374\) 0 0
\(375\) 27.7546 1.43324
\(376\) 0 0
\(377\) 39.6220 2.04064
\(378\) 0 0
\(379\) 12.0094 0.616881 0.308440 0.951244i \(-0.400193\pi\)
0.308440 + 0.951244i \(0.400193\pi\)
\(380\) 0 0
\(381\) −18.9600 −0.971349
\(382\) 0 0
\(383\) −1.44318 −0.0737430 −0.0368715 0.999320i \(-0.511739\pi\)
−0.0368715 + 0.999320i \(0.511739\pi\)
\(384\) 0 0
\(385\) −1.99121 −0.101481
\(386\) 0 0
\(387\) −0.571592 −0.0290557
\(388\) 0 0
\(389\) 32.6304 1.65443 0.827213 0.561889i \(-0.189925\pi\)
0.827213 + 0.561889i \(0.189925\pi\)
\(390\) 0 0
\(391\) −2.01854 −0.102082
\(392\) 0 0
\(393\) −5.39610 −0.272197
\(394\) 0 0
\(395\) 21.1644 1.06489
\(396\) 0 0
\(397\) −19.5675 −0.982065 −0.491032 0.871141i \(-0.663380\pi\)
−0.491032 + 0.871141i \(0.663380\pi\)
\(398\) 0 0
\(399\) −3.23685 −0.162045
\(400\) 0 0
\(401\) −2.11783 −0.105759 −0.0528797 0.998601i \(-0.516840\pi\)
−0.0528797 + 0.998601i \(0.516840\pi\)
\(402\) 0 0
\(403\) 38.0152 1.89367
\(404\) 0 0
\(405\) 17.2133 0.855337
\(406\) 0 0
\(407\) 1.55675 0.0771651
\(408\) 0 0
\(409\) 11.6225 0.574694 0.287347 0.957827i \(-0.407227\pi\)
0.287347 + 0.957827i \(0.407227\pi\)
\(410\) 0 0
\(411\) −4.87811 −0.240619
\(412\) 0 0
\(413\) −10.0916 −0.496577
\(414\) 0 0
\(415\) −28.3017 −1.38927
\(416\) 0 0
\(417\) −33.4591 −1.63850
\(418\) 0 0
\(419\) −10.4119 −0.508657 −0.254328 0.967118i \(-0.581854\pi\)
−0.254328 + 0.967118i \(0.581854\pi\)
\(420\) 0 0
\(421\) 8.67091 0.422594 0.211297 0.977422i \(-0.432231\pi\)
0.211297 + 0.977422i \(0.432231\pi\)
\(422\) 0 0
\(423\) 19.1968 0.933380
\(424\) 0 0
\(425\) 0.0921233 0.00446864
\(426\) 0 0
\(427\) 0.358335 0.0173410
\(428\) 0 0
\(429\) −7.02752 −0.339292
\(430\) 0 0
\(431\) −0.404087 −0.0194642 −0.00973210 0.999953i \(-0.503098\pi\)
−0.00973210 + 0.999953i \(0.503098\pi\)
\(432\) 0 0
\(433\) 28.3610 1.36294 0.681472 0.731844i \(-0.261340\pi\)
0.681472 + 0.731844i \(0.261340\pi\)
\(434\) 0 0
\(435\) 56.4601 2.70705
\(436\) 0 0
\(437\) 4.28297 0.204882
\(438\) 0 0
\(439\) 36.2499 1.73011 0.865056 0.501676i \(-0.167283\pi\)
0.865056 + 0.501676i \(0.167283\pi\)
\(440\) 0 0
\(441\) −18.3778 −0.875133
\(442\) 0 0
\(443\) −6.10105 −0.289870 −0.144935 0.989441i \(-0.546297\pi\)
−0.144935 + 0.989441i \(0.546297\pi\)
\(444\) 0 0
\(445\) 30.0616 1.42505
\(446\) 0 0
\(447\) 6.18530 0.292554
\(448\) 0 0
\(449\) 8.12113 0.383260 0.191630 0.981467i \(-0.438623\pi\)
0.191630 + 0.981467i \(0.438623\pi\)
\(450\) 0 0
\(451\) 0.841724 0.0396352
\(452\) 0 0
\(453\) −20.1811 −0.948191
\(454\) 0 0
\(455\) 11.8016 0.553268
\(456\) 0 0
\(457\) −20.5365 −0.960657 −0.480329 0.877089i \(-0.659483\pi\)
−0.480329 + 0.877089i \(0.659483\pi\)
\(458\) 0 0
\(459\) 0.505320 0.0235863
\(460\) 0 0
\(461\) 2.96682 0.138178 0.0690892 0.997610i \(-0.477991\pi\)
0.0690892 + 0.997610i \(0.477991\pi\)
\(462\) 0 0
\(463\) −23.4093 −1.08792 −0.543962 0.839110i \(-0.683076\pi\)
−0.543962 + 0.839110i \(0.683076\pi\)
\(464\) 0 0
\(465\) 54.1704 2.51209
\(466\) 0 0
\(467\) 27.8918 1.29068 0.645339 0.763896i \(-0.276716\pi\)
0.645339 + 0.763896i \(0.276716\pi\)
\(468\) 0 0
\(469\) 3.62104 0.167204
\(470\) 0 0
\(471\) 8.13371 0.374782
\(472\) 0 0
\(473\) −0.114215 −0.00525163
\(474\) 0 0
\(475\) −0.195468 −0.00896871
\(476\) 0 0
\(477\) 3.42306 0.156731
\(478\) 0 0
\(479\) 10.2425 0.467993 0.233996 0.972237i \(-0.424820\pi\)
0.233996 + 0.972237i \(0.424820\pi\)
\(480\) 0 0
\(481\) −9.22663 −0.420698
\(482\) 0 0
\(483\) −13.8633 −0.630803
\(484\) 0 0
\(485\) 0.132208 0.00600328
\(486\) 0 0
\(487\) 6.09948 0.276394 0.138197 0.990405i \(-0.455869\pi\)
0.138197 + 0.990405i \(0.455869\pi\)
\(488\) 0 0
\(489\) −18.2070 −0.823350
\(490\) 0 0
\(491\) 23.8845 1.07789 0.538946 0.842340i \(-0.318823\pi\)
0.538946 + 0.842340i \(0.318823\pi\)
\(492\) 0 0
\(493\) −4.60629 −0.207457
\(494\) 0 0
\(495\) −5.33679 −0.239871
\(496\) 0 0
\(497\) 12.6234 0.566237
\(498\) 0 0
\(499\) −35.4851 −1.58853 −0.794265 0.607572i \(-0.792144\pi\)
−0.794265 + 0.607572i \(0.792144\pi\)
\(500\) 0 0
\(501\) −15.9653 −0.713277
\(502\) 0 0
\(503\) 21.8640 0.974867 0.487433 0.873160i \(-0.337933\pi\)
0.487433 + 0.873160i \(0.337933\pi\)
\(504\) 0 0
\(505\) 33.5042 1.49092
\(506\) 0 0
\(507\) 8.70427 0.386570
\(508\) 0 0
\(509\) −28.8469 −1.27862 −0.639309 0.768950i \(-0.720779\pi\)
−0.639309 + 0.768950i \(0.720779\pi\)
\(510\) 0 0
\(511\) 15.5929 0.689790
\(512\) 0 0
\(513\) −1.07220 −0.0473386
\(514\) 0 0
\(515\) −33.9569 −1.49632
\(516\) 0 0
\(517\) 3.83590 0.168703
\(518\) 0 0
\(519\) −14.2660 −0.626208
\(520\) 0 0
\(521\) 39.8171 1.74442 0.872209 0.489134i \(-0.162687\pi\)
0.872209 + 0.489134i \(0.162687\pi\)
\(522\) 0 0
\(523\) −19.3763 −0.847265 −0.423633 0.905834i \(-0.639245\pi\)
−0.423633 + 0.905834i \(0.639245\pi\)
\(524\) 0 0
\(525\) 0.632701 0.0276134
\(526\) 0 0
\(527\) −4.41949 −0.192516
\(528\) 0 0
\(529\) −4.65616 −0.202442
\(530\) 0 0
\(531\) −27.0474 −1.17376
\(532\) 0 0
\(533\) −4.98879 −0.216088
\(534\) 0 0
\(535\) −41.5433 −1.79607
\(536\) 0 0
\(537\) −15.1023 −0.651712
\(538\) 0 0
\(539\) −3.67224 −0.158175
\(540\) 0 0
\(541\) 17.7548 0.763341 0.381670 0.924299i \(-0.375349\pi\)
0.381670 + 0.924299i \(0.375349\pi\)
\(542\) 0 0
\(543\) −31.4539 −1.34982
\(544\) 0 0
\(545\) 18.8123 0.805828
\(546\) 0 0
\(547\) −25.5212 −1.09121 −0.545604 0.838043i \(-0.683700\pi\)
−0.545604 + 0.838043i \(0.683700\pi\)
\(548\) 0 0
\(549\) 0.960401 0.0409889
\(550\) 0 0
\(551\) 9.77368 0.416373
\(552\) 0 0
\(553\) −11.8589 −0.504291
\(554\) 0 0
\(555\) −13.1477 −0.558087
\(556\) 0 0
\(557\) 27.2435 1.15435 0.577173 0.816622i \(-0.304156\pi\)
0.577173 + 0.816622i \(0.304156\pi\)
\(558\) 0 0
\(559\) 0.676940 0.0286315
\(560\) 0 0
\(561\) 0.816990 0.0344933
\(562\) 0 0
\(563\) 17.7988 0.750130 0.375065 0.926999i \(-0.377620\pi\)
0.375065 + 0.926999i \(0.377620\pi\)
\(564\) 0 0
\(565\) −26.6802 −1.12245
\(566\) 0 0
\(567\) −9.64503 −0.405053
\(568\) 0 0
\(569\) 38.8181 1.62734 0.813671 0.581326i \(-0.197466\pi\)
0.813671 + 0.581326i \(0.197466\pi\)
\(570\) 0 0
\(571\) 14.7885 0.618880 0.309440 0.950919i \(-0.399858\pi\)
0.309440 + 0.950919i \(0.399858\pi\)
\(572\) 0 0
\(573\) −36.3113 −1.51693
\(574\) 0 0
\(575\) −0.837186 −0.0349131
\(576\) 0 0
\(577\) −30.1701 −1.25600 −0.627999 0.778214i \(-0.716126\pi\)
−0.627999 + 0.778214i \(0.716126\pi\)
\(578\) 0 0
\(579\) −15.8913 −0.660422
\(580\) 0 0
\(581\) 15.8581 0.657904
\(582\) 0 0
\(583\) 0.683995 0.0283282
\(584\) 0 0
\(585\) 31.6304 1.30776
\(586\) 0 0
\(587\) −18.2448 −0.753044 −0.376522 0.926408i \(-0.622880\pi\)
−0.376522 + 0.926408i \(0.622880\pi\)
\(588\) 0 0
\(589\) 9.37733 0.386386
\(590\) 0 0
\(591\) −43.8648 −1.80436
\(592\) 0 0
\(593\) −26.0618 −1.07023 −0.535115 0.844779i \(-0.679732\pi\)
−0.535115 + 0.844779i \(0.679732\pi\)
\(594\) 0 0
\(595\) −1.37201 −0.0562468
\(596\) 0 0
\(597\) 34.6487 1.41808
\(598\) 0 0
\(599\) 28.7331 1.17400 0.587002 0.809585i \(-0.300308\pi\)
0.587002 + 0.809585i \(0.300308\pi\)
\(600\) 0 0
\(601\) −28.4158 −1.15910 −0.579552 0.814935i \(-0.696772\pi\)
−0.579552 + 0.814935i \(0.696772\pi\)
\(602\) 0 0
\(603\) 9.70504 0.395220
\(604\) 0 0
\(605\) 24.0065 0.976004
\(606\) 0 0
\(607\) −30.7862 −1.24957 −0.624786 0.780796i \(-0.714814\pi\)
−0.624786 + 0.780796i \(0.714814\pi\)
\(608\) 0 0
\(609\) −31.6359 −1.28195
\(610\) 0 0
\(611\) −22.7349 −0.919754
\(612\) 0 0
\(613\) 25.5989 1.03393 0.516964 0.856007i \(-0.327062\pi\)
0.516964 + 0.856007i \(0.327062\pi\)
\(614\) 0 0
\(615\) −7.10887 −0.286657
\(616\) 0 0
\(617\) −39.7094 −1.59864 −0.799319 0.600907i \(-0.794806\pi\)
−0.799319 + 0.600907i \(0.794806\pi\)
\(618\) 0 0
\(619\) −43.0046 −1.72850 −0.864251 0.503060i \(-0.832207\pi\)
−0.864251 + 0.503060i \(0.832207\pi\)
\(620\) 0 0
\(621\) −4.59218 −0.184278
\(622\) 0 0
\(623\) −16.8442 −0.674848
\(624\) 0 0
\(625\) −25.9391 −1.03757
\(626\) 0 0
\(627\) −1.73350 −0.0692293
\(628\) 0 0
\(629\) 1.07265 0.0427694
\(630\) 0 0
\(631\) −39.0678 −1.55526 −0.777631 0.628720i \(-0.783579\pi\)
−0.777631 + 0.628720i \(0.783579\pi\)
\(632\) 0 0
\(633\) 45.7296 1.81759
\(634\) 0 0
\(635\) 17.0522 0.676694
\(636\) 0 0
\(637\) 21.7649 0.862357
\(638\) 0 0
\(639\) 33.8330 1.33841
\(640\) 0 0
\(641\) 36.3811 1.43697 0.718484 0.695543i \(-0.244836\pi\)
0.718484 + 0.695543i \(0.244836\pi\)
\(642\) 0 0
\(643\) −31.4795 −1.24143 −0.620715 0.784037i \(-0.713157\pi\)
−0.620715 + 0.784037i \(0.713157\pi\)
\(644\) 0 0
\(645\) 0.964618 0.0379818
\(646\) 0 0
\(647\) 41.2170 1.62041 0.810203 0.586149i \(-0.199357\pi\)
0.810203 + 0.586149i \(0.199357\pi\)
\(648\) 0 0
\(649\) −5.40459 −0.212149
\(650\) 0 0
\(651\) −30.3530 −1.18963
\(652\) 0 0
\(653\) −21.0470 −0.823631 −0.411816 0.911267i \(-0.635105\pi\)
−0.411816 + 0.911267i \(0.635105\pi\)
\(654\) 0 0
\(655\) 4.85312 0.189627
\(656\) 0 0
\(657\) 41.7918 1.63045
\(658\) 0 0
\(659\) −47.7553 −1.86028 −0.930141 0.367203i \(-0.880315\pi\)
−0.930141 + 0.367203i \(0.880315\pi\)
\(660\) 0 0
\(661\) −24.5466 −0.954752 −0.477376 0.878699i \(-0.658412\pi\)
−0.477376 + 0.878699i \(0.658412\pi\)
\(662\) 0 0
\(663\) −4.84219 −0.188055
\(664\) 0 0
\(665\) 2.91114 0.112889
\(666\) 0 0
\(667\) 41.8604 1.62084
\(668\) 0 0
\(669\) 14.3807 0.555991
\(670\) 0 0
\(671\) 0.191907 0.00740849
\(672\) 0 0
\(673\) −19.1448 −0.737979 −0.368989 0.929434i \(-0.620296\pi\)
−0.368989 + 0.929434i \(0.620296\pi\)
\(674\) 0 0
\(675\) 0.209580 0.00806675
\(676\) 0 0
\(677\) −13.2507 −0.509264 −0.254632 0.967038i \(-0.581954\pi\)
−0.254632 + 0.967038i \(0.581954\pi\)
\(678\) 0 0
\(679\) −0.0740795 −0.00284291
\(680\) 0 0
\(681\) 72.0764 2.76198
\(682\) 0 0
\(683\) −43.8509 −1.67791 −0.838954 0.544203i \(-0.816832\pi\)
−0.838954 + 0.544203i \(0.816832\pi\)
\(684\) 0 0
\(685\) 4.38725 0.167628
\(686\) 0 0
\(687\) −58.4504 −2.23002
\(688\) 0 0
\(689\) −4.05395 −0.154443
\(690\) 0 0
\(691\) 39.5843 1.50586 0.752929 0.658102i \(-0.228641\pi\)
0.752929 + 0.658102i \(0.228641\pi\)
\(692\) 0 0
\(693\) 2.99033 0.113593
\(694\) 0 0
\(695\) 30.0923 1.14147
\(696\) 0 0
\(697\) 0.579976 0.0219682
\(698\) 0 0
\(699\) −11.2083 −0.423936
\(700\) 0 0
\(701\) −43.8680 −1.65687 −0.828435 0.560085i \(-0.810769\pi\)
−0.828435 + 0.560085i \(0.810769\pi\)
\(702\) 0 0
\(703\) −2.27596 −0.0858396
\(704\) 0 0
\(705\) −32.3965 −1.22012
\(706\) 0 0
\(707\) −18.7732 −0.706039
\(708\) 0 0
\(709\) −43.1969 −1.62229 −0.811147 0.584843i \(-0.801156\pi\)
−0.811147 + 0.584843i \(0.801156\pi\)
\(710\) 0 0
\(711\) −31.7839 −1.19199
\(712\) 0 0
\(713\) 40.1628 1.50411
\(714\) 0 0
\(715\) 6.32038 0.236369
\(716\) 0 0
\(717\) 3.14100 0.117303
\(718\) 0 0
\(719\) 5.62546 0.209794 0.104897 0.994483i \(-0.466549\pi\)
0.104897 + 0.994483i \(0.466549\pi\)
\(720\) 0 0
\(721\) 19.0269 0.708598
\(722\) 0 0
\(723\) −26.1842 −0.973800
\(724\) 0 0
\(725\) −1.91045 −0.0709522
\(726\) 0 0
\(727\) −4.63839 −0.172028 −0.0860141 0.996294i \(-0.527413\pi\)
−0.0860141 + 0.996294i \(0.527413\pi\)
\(728\) 0 0
\(729\) −34.0024 −1.25935
\(730\) 0 0
\(731\) −0.0786982 −0.00291076
\(732\) 0 0
\(733\) −23.6696 −0.874257 −0.437128 0.899399i \(-0.644004\pi\)
−0.437128 + 0.899399i \(0.644004\pi\)
\(734\) 0 0
\(735\) 31.0143 1.14398
\(736\) 0 0
\(737\) 1.93926 0.0714334
\(738\) 0 0
\(739\) −23.8493 −0.877311 −0.438656 0.898655i \(-0.644545\pi\)
−0.438656 + 0.898655i \(0.644545\pi\)
\(740\) 0 0
\(741\) 10.2742 0.377433
\(742\) 0 0
\(743\) −4.10688 −0.150667 −0.0753334 0.997158i \(-0.524002\pi\)
−0.0753334 + 0.997158i \(0.524002\pi\)
\(744\) 0 0
\(745\) −5.56291 −0.203809
\(746\) 0 0
\(747\) 42.5025 1.55508
\(748\) 0 0
\(749\) 23.2777 0.850548
\(750\) 0 0
\(751\) 39.5478 1.44312 0.721560 0.692352i \(-0.243425\pi\)
0.721560 + 0.692352i \(0.243425\pi\)
\(752\) 0 0
\(753\) −9.85688 −0.359205
\(754\) 0 0
\(755\) 18.1504 0.660561
\(756\) 0 0
\(757\) 28.7611 1.04534 0.522670 0.852535i \(-0.324936\pi\)
0.522670 + 0.852535i \(0.324936\pi\)
\(758\) 0 0
\(759\) −7.42453 −0.269493
\(760\) 0 0
\(761\) −18.3747 −0.666083 −0.333042 0.942912i \(-0.608075\pi\)
−0.333042 + 0.942912i \(0.608075\pi\)
\(762\) 0 0
\(763\) −10.5409 −0.381608
\(764\) 0 0
\(765\) −3.67722 −0.132950
\(766\) 0 0
\(767\) 32.0323 1.15662
\(768\) 0 0
\(769\) 23.6592 0.853174 0.426587 0.904447i \(-0.359716\pi\)
0.426587 + 0.904447i \(0.359716\pi\)
\(770\) 0 0
\(771\) 19.5369 0.703605
\(772\) 0 0
\(773\) −7.11589 −0.255941 −0.127970 0.991778i \(-0.540846\pi\)
−0.127970 + 0.991778i \(0.540846\pi\)
\(774\) 0 0
\(775\) −1.83297 −0.0658423
\(776\) 0 0
\(777\) 7.36694 0.264288
\(778\) 0 0
\(779\) −1.23060 −0.0440908
\(780\) 0 0
\(781\) 6.76049 0.241909
\(782\) 0 0
\(783\) −10.4793 −0.374499
\(784\) 0 0
\(785\) −7.31527 −0.261093
\(786\) 0 0
\(787\) −18.0116 −0.642045 −0.321023 0.947072i \(-0.604027\pi\)
−0.321023 + 0.947072i \(0.604027\pi\)
\(788\) 0 0
\(789\) 29.7280 1.05835
\(790\) 0 0
\(791\) 14.9496 0.531545
\(792\) 0 0
\(793\) −1.13741 −0.0403905
\(794\) 0 0
\(795\) −5.77675 −0.204880
\(796\) 0 0
\(797\) 25.2309 0.893725 0.446863 0.894603i \(-0.352541\pi\)
0.446863 + 0.894603i \(0.352541\pi\)
\(798\) 0 0
\(799\) 2.64306 0.0935048
\(800\) 0 0
\(801\) −45.1454 −1.59514
\(802\) 0 0
\(803\) 8.35082 0.294694
\(804\) 0 0
\(805\) 12.4683 0.439451
\(806\) 0 0
\(807\) −53.8304 −1.89492
\(808\) 0 0
\(809\) 3.88600 0.136624 0.0683122 0.997664i \(-0.478239\pi\)
0.0683122 + 0.997664i \(0.478239\pi\)
\(810\) 0 0
\(811\) −39.8142 −1.39807 −0.699033 0.715090i \(-0.746386\pi\)
−0.699033 + 0.715090i \(0.746386\pi\)
\(812\) 0 0
\(813\) −26.5373 −0.930704
\(814\) 0 0
\(815\) 16.3750 0.573590
\(816\) 0 0
\(817\) 0.166983 0.00584199
\(818\) 0 0
\(819\) −17.7233 −0.619301
\(820\) 0 0
\(821\) 16.6695 0.581769 0.290885 0.956758i \(-0.406050\pi\)
0.290885 + 0.956758i \(0.406050\pi\)
\(822\) 0 0
\(823\) −17.4097 −0.606863 −0.303432 0.952853i \(-0.598132\pi\)
−0.303432 + 0.952853i \(0.598132\pi\)
\(824\) 0 0
\(825\) 0.338845 0.0117971
\(826\) 0 0
\(827\) 41.1975 1.43258 0.716288 0.697805i \(-0.245840\pi\)
0.716288 + 0.697805i \(0.245840\pi\)
\(828\) 0 0
\(829\) 20.2073 0.701830 0.350915 0.936407i \(-0.385871\pi\)
0.350915 + 0.936407i \(0.385871\pi\)
\(830\) 0 0
\(831\) −45.9913 −1.59542
\(832\) 0 0
\(833\) −2.53030 −0.0876696
\(834\) 0 0
\(835\) 14.3588 0.496907
\(836\) 0 0
\(837\) −10.0543 −0.347528
\(838\) 0 0
\(839\) −26.8630 −0.927412 −0.463706 0.885989i \(-0.653481\pi\)
−0.463706 + 0.885989i \(0.653481\pi\)
\(840\) 0 0
\(841\) 66.5249 2.29396
\(842\) 0 0
\(843\) −14.5961 −0.502716
\(844\) 0 0
\(845\) −7.82841 −0.269306
\(846\) 0 0
\(847\) −13.4514 −0.462196
\(848\) 0 0
\(849\) −34.0248 −1.16773
\(850\) 0 0
\(851\) −9.74788 −0.334153
\(852\) 0 0
\(853\) −11.3972 −0.390234 −0.195117 0.980780i \(-0.562509\pi\)
−0.195117 + 0.980780i \(0.562509\pi\)
\(854\) 0 0
\(855\) 7.80238 0.266836
\(856\) 0 0
\(857\) 36.1562 1.23507 0.617537 0.786542i \(-0.288131\pi\)
0.617537 + 0.786542i \(0.288131\pi\)
\(858\) 0 0
\(859\) 37.5140 1.27996 0.639981 0.768391i \(-0.278942\pi\)
0.639981 + 0.768391i \(0.278942\pi\)
\(860\) 0 0
\(861\) 3.98326 0.135749
\(862\) 0 0
\(863\) −32.4883 −1.10591 −0.552957 0.833209i \(-0.686501\pi\)
−0.552957 + 0.833209i \(0.686501\pi\)
\(864\) 0 0
\(865\) 12.8305 0.436250
\(866\) 0 0
\(867\) −42.5215 −1.44410
\(868\) 0 0
\(869\) −6.35105 −0.215445
\(870\) 0 0
\(871\) −11.4937 −0.389450
\(872\) 0 0
\(873\) −0.198546 −0.00671977
\(874\) 0 0
\(875\) 13.9867 0.472836
\(876\) 0 0
\(877\) 18.9563 0.640109 0.320055 0.947399i \(-0.396299\pi\)
0.320055 + 0.947399i \(0.396299\pi\)
\(878\) 0 0
\(879\) 5.52567 0.186376
\(880\) 0 0
\(881\) 14.9684 0.504299 0.252149 0.967688i \(-0.418863\pi\)
0.252149 + 0.967688i \(0.418863\pi\)
\(882\) 0 0
\(883\) 42.9519 1.44545 0.722724 0.691137i \(-0.242890\pi\)
0.722724 + 0.691137i \(0.242890\pi\)
\(884\) 0 0
\(885\) 45.6450 1.53434
\(886\) 0 0
\(887\) −33.7975 −1.13481 −0.567404 0.823440i \(-0.692052\pi\)
−0.567404 + 0.823440i \(0.692052\pi\)
\(888\) 0 0
\(889\) −9.55472 −0.320455
\(890\) 0 0
\(891\) −5.16542 −0.173048
\(892\) 0 0
\(893\) −5.60808 −0.187667
\(894\) 0 0
\(895\) 13.5826 0.454018
\(896\) 0 0
\(897\) 44.0042 1.46926
\(898\) 0 0
\(899\) 91.6510 3.05673
\(900\) 0 0
\(901\) 0.471295 0.0157011
\(902\) 0 0
\(903\) −0.540498 −0.0179866
\(904\) 0 0
\(905\) 28.2889 0.940356
\(906\) 0 0
\(907\) −52.9182 −1.75712 −0.878560 0.477632i \(-0.841495\pi\)
−0.878560 + 0.477632i \(0.841495\pi\)
\(908\) 0 0
\(909\) −50.3155 −1.66886
\(910\) 0 0
\(911\) 9.46241 0.313503 0.156752 0.987638i \(-0.449898\pi\)
0.156752 + 0.987638i \(0.449898\pi\)
\(912\) 0 0
\(913\) 8.49283 0.281071
\(914\) 0 0
\(915\) −1.62077 −0.0535810
\(916\) 0 0
\(917\) −2.71932 −0.0897998
\(918\) 0 0
\(919\) −44.5335 −1.46902 −0.734512 0.678596i \(-0.762589\pi\)
−0.734512 + 0.678596i \(0.762589\pi\)
\(920\) 0 0
\(921\) 39.0401 1.28641
\(922\) 0 0
\(923\) −40.0685 −1.31887
\(924\) 0 0
\(925\) 0.444879 0.0146275
\(926\) 0 0
\(927\) 50.9954 1.67491
\(928\) 0 0
\(929\) 58.7018 1.92594 0.962971 0.269604i \(-0.0868927\pi\)
0.962971 + 0.269604i \(0.0868927\pi\)
\(930\) 0 0
\(931\) 5.36882 0.175956
\(932\) 0 0
\(933\) 30.2949 0.991811
\(934\) 0 0
\(935\) −0.734781 −0.0240299
\(936\) 0 0
\(937\) −49.1190 −1.60465 −0.802323 0.596890i \(-0.796403\pi\)
−0.802323 + 0.596890i \(0.796403\pi\)
\(938\) 0 0
\(939\) 2.19690 0.0716932
\(940\) 0 0
\(941\) 0.186194 0.00606975 0.00303487 0.999995i \(-0.499034\pi\)
0.00303487 + 0.999995i \(0.499034\pi\)
\(942\) 0 0
\(943\) −5.27062 −0.171635
\(944\) 0 0
\(945\) −3.12131 −0.101536
\(946\) 0 0
\(947\) −26.5194 −0.861764 −0.430882 0.902408i \(-0.641797\pi\)
−0.430882 + 0.902408i \(0.641797\pi\)
\(948\) 0 0
\(949\) −49.4942 −1.60665
\(950\) 0 0
\(951\) 53.1365 1.72307
\(952\) 0 0
\(953\) −0.310683 −0.0100640 −0.00503200 0.999987i \(-0.501602\pi\)
−0.00503200 + 0.999987i \(0.501602\pi\)
\(954\) 0 0
\(955\) 32.6575 1.05677
\(956\) 0 0
\(957\) −16.9427 −0.547679
\(958\) 0 0
\(959\) −2.45828 −0.0793820
\(960\) 0 0
\(961\) 56.9342 1.83659
\(962\) 0 0
\(963\) 62.3883 2.01043
\(964\) 0 0
\(965\) 14.2923 0.460085
\(966\) 0 0
\(967\) −22.4435 −0.721734 −0.360867 0.932617i \(-0.617519\pi\)
−0.360867 + 0.932617i \(0.617519\pi\)
\(968\) 0 0
\(969\) −1.19444 −0.0383709
\(970\) 0 0
\(971\) 3.77769 0.121232 0.0606159 0.998161i \(-0.480694\pi\)
0.0606159 + 0.998161i \(0.480694\pi\)
\(972\) 0 0
\(973\) −16.8614 −0.540553
\(974\) 0 0
\(975\) −2.00829 −0.0643167
\(976\) 0 0
\(977\) −18.0410 −0.577184 −0.288592 0.957452i \(-0.593187\pi\)
−0.288592 + 0.957452i \(0.593187\pi\)
\(978\) 0 0
\(979\) −9.02094 −0.288311
\(980\) 0 0
\(981\) −28.2516 −0.902004
\(982\) 0 0
\(983\) 48.3170 1.54107 0.770537 0.637395i \(-0.219988\pi\)
0.770537 + 0.637395i \(0.219988\pi\)
\(984\) 0 0
\(985\) 39.4510 1.25701
\(986\) 0 0
\(987\) 18.1525 0.577800
\(988\) 0 0
\(989\) 0.715183 0.0227415
\(990\) 0 0
\(991\) −23.2630 −0.738974 −0.369487 0.929236i \(-0.620467\pi\)
−0.369487 + 0.929236i \(0.620467\pi\)
\(992\) 0 0
\(993\) 68.6704 2.17919
\(994\) 0 0
\(995\) −31.1622 −0.987908
\(996\) 0 0
\(997\) 15.2301 0.482343 0.241172 0.970482i \(-0.422468\pi\)
0.241172 + 0.970482i \(0.422468\pi\)
\(998\) 0 0
\(999\) 2.44028 0.0772069
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 \(a_p\))