Properties

Label 8036.2.a.t.1.6
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.37724\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.37724 q^{3} +3.83294 q^{5} -1.10321 q^{9} +O(q^{10})\) \(q-1.37724 q^{3} +3.83294 q^{5} -1.10321 q^{9} +0.294657 q^{11} +2.83491 q^{13} -5.27887 q^{15} +3.23930 q^{17} -5.79243 q^{19} +5.90009 q^{23} +9.69141 q^{25} +5.65110 q^{27} +3.65123 q^{29} -1.59205 q^{31} -0.405813 q^{33} +5.20818 q^{37} -3.90435 q^{39} -1.00000 q^{41} +5.12051 q^{43} -4.22854 q^{45} -12.1496 q^{47} -4.46130 q^{51} -7.84750 q^{53} +1.12940 q^{55} +7.97757 q^{57} +2.50717 q^{59} +2.24588 q^{61} +10.8660 q^{65} -8.73987 q^{67} -8.12584 q^{69} -1.66646 q^{71} +12.8659 q^{73} -13.3474 q^{75} -0.253450 q^{79} -4.47329 q^{81} +12.7863 q^{83} +12.4160 q^{85} -5.02862 q^{87} -3.82433 q^{89} +2.19263 q^{93} -22.2020 q^{95} +18.4192 q^{97} -0.325068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 4q^{3} + 8q^{5} + 16q^{9} + O(q^{10}) \) \( 20q + 4q^{3} + 8q^{5} + 16q^{9} - 8q^{11} + 12q^{13} + 8q^{15} + 8q^{17} + 24q^{19} + 8q^{23} + 20q^{25} + 16q^{27} - 12q^{29} + 44q^{33} + 12q^{37} + 12q^{39} - 20q^{41} + 4q^{43} + 40q^{45} + 4q^{47} + 4q^{51} - 12q^{53} - 16q^{55} + 28q^{57} + 16q^{59} + 68q^{61} - 8q^{65} + 4q^{67} + 32q^{69} + 8q^{71} + 48q^{73} + 60q^{75} - 20q^{79} + 32q^{81} - 8q^{83} - 28q^{85} + 60q^{89} - 16q^{93} + 20q^{95} + 40q^{97} + O(q^{100}) \)

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
\(3\) −1.37724 −0.795150 −0.397575 0.917570i \(-0.630148\pi\)
−0.397575 + 0.917570i \(0.630148\pi\)
\(4\) 0 0
\(5\) 3.83294 1.71414 0.857071 0.515199i \(-0.172282\pi\)
0.857071 + 0.515199i \(0.172282\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.10321 −0.367737
\(10\) 0 0
\(11\) 0.294657 0.0888424 0.0444212 0.999013i \(-0.485856\pi\)
0.0444212 + 0.999013i \(0.485856\pi\)
\(12\) 0 0
\(13\) 2.83491 0.786262 0.393131 0.919482i \(-0.371392\pi\)
0.393131 + 0.919482i \(0.371392\pi\)
\(14\) 0 0
\(15\) −5.27887 −1.36300
\(16\) 0 0
\(17\) 3.23930 0.785646 0.392823 0.919614i \(-0.371498\pi\)
0.392823 + 0.919614i \(0.371498\pi\)
\(18\) 0 0
\(19\) −5.79243 −1.32888 −0.664438 0.747344i \(-0.731329\pi\)
−0.664438 + 0.747344i \(0.731329\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.90009 1.23025 0.615127 0.788428i \(-0.289105\pi\)
0.615127 + 0.788428i \(0.289105\pi\)
\(24\) 0 0
\(25\) 9.69141 1.93828
\(26\) 0 0
\(27\) 5.65110 1.08756
\(28\) 0 0
\(29\) 3.65123 0.678016 0.339008 0.940783i \(-0.389909\pi\)
0.339008 + 0.940783i \(0.389909\pi\)
\(30\) 0 0
\(31\) −1.59205 −0.285940 −0.142970 0.989727i \(-0.545665\pi\)
−0.142970 + 0.989727i \(0.545665\pi\)
\(32\) 0 0
\(33\) −0.405813 −0.0706430
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.20818 0.856219 0.428110 0.903727i \(-0.359180\pi\)
0.428110 + 0.903727i \(0.359180\pi\)
\(38\) 0 0
\(39\) −3.90435 −0.625196
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 5.12051 0.780871 0.390436 0.920630i \(-0.372324\pi\)
0.390436 + 0.920630i \(0.372324\pi\)
\(44\) 0 0
\(45\) −4.22854 −0.630353
\(46\) 0 0
\(47\) −12.1496 −1.77220 −0.886099 0.463496i \(-0.846595\pi\)
−0.886099 + 0.463496i \(0.846595\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −4.46130 −0.624706
\(52\) 0 0
\(53\) −7.84750 −1.07794 −0.538968 0.842326i \(-0.681186\pi\)
−0.538968 + 0.842326i \(0.681186\pi\)
\(54\) 0 0
\(55\) 1.12940 0.152288
\(56\) 0 0
\(57\) 7.97757 1.05666
\(58\) 0 0
\(59\) 2.50717 0.326406 0.163203 0.986593i \(-0.447817\pi\)
0.163203 + 0.986593i \(0.447817\pi\)
\(60\) 0 0
\(61\) 2.24588 0.287556 0.143778 0.989610i \(-0.454075\pi\)
0.143778 + 0.989610i \(0.454075\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.8660 1.34776
\(66\) 0 0
\(67\) −8.73987 −1.06774 −0.533872 0.845565i \(-0.679264\pi\)
−0.533872 + 0.845565i \(0.679264\pi\)
\(68\) 0 0
\(69\) −8.12584 −0.978236
\(70\) 0 0
\(71\) −1.66646 −0.197773 −0.0988865 0.995099i \(-0.531528\pi\)
−0.0988865 + 0.995099i \(0.531528\pi\)
\(72\) 0 0
\(73\) 12.8659 1.50584 0.752920 0.658112i \(-0.228645\pi\)
0.752920 + 0.658112i \(0.228645\pi\)
\(74\) 0 0
\(75\) −13.3474 −1.54122
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.253450 −0.0285154 −0.0142577 0.999898i \(-0.504539\pi\)
−0.0142577 + 0.999898i \(0.504539\pi\)
\(80\) 0 0
\(81\) −4.47329 −0.497033
\(82\) 0 0
\(83\) 12.7863 1.40348 0.701739 0.712435i \(-0.252407\pi\)
0.701739 + 0.712435i \(0.252407\pi\)
\(84\) 0 0
\(85\) 12.4160 1.34671
\(86\) 0 0
\(87\) −5.02862 −0.539125
\(88\) 0 0
\(89\) −3.82433 −0.405379 −0.202689 0.979243i \(-0.564968\pi\)
−0.202689 + 0.979243i \(0.564968\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 2.19263 0.227365
\(94\) 0 0
\(95\) −22.2020 −2.27788
\(96\) 0 0
\(97\) 18.4192 1.87018 0.935091 0.354406i \(-0.115317\pi\)
0.935091 + 0.354406i \(0.115317\pi\)
\(98\) 0 0
\(99\) −0.325068 −0.0326706
\(100\) 0 0
\(101\) −6.00514 −0.597533 −0.298767 0.954326i \(-0.596575\pi\)
−0.298767 + 0.954326i \(0.596575\pi\)
\(102\) 0 0
\(103\) 4.01323 0.395435 0.197717 0.980259i \(-0.436647\pi\)
0.197717 + 0.980259i \(0.436647\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.8319 1.14384 0.571918 0.820311i \(-0.306199\pi\)
0.571918 + 0.820311i \(0.306199\pi\)
\(108\) 0 0
\(109\) −17.7180 −1.69707 −0.848536 0.529137i \(-0.822516\pi\)
−0.848536 + 0.529137i \(0.822516\pi\)
\(110\) 0 0
\(111\) −7.17291 −0.680823
\(112\) 0 0
\(113\) 16.0057 1.50569 0.752845 0.658198i \(-0.228681\pi\)
0.752845 + 0.658198i \(0.228681\pi\)
\(114\) 0 0
\(115\) 22.6147 2.10883
\(116\) 0 0
\(117\) −3.12750 −0.289137
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.9132 −0.992107
\(122\) 0 0
\(123\) 1.37724 0.124182
\(124\) 0 0
\(125\) 17.9819 1.60835
\(126\) 0 0
\(127\) −19.0524 −1.69062 −0.845312 0.534273i \(-0.820585\pi\)
−0.845312 + 0.534273i \(0.820585\pi\)
\(128\) 0 0
\(129\) −7.05218 −0.620909
\(130\) 0 0
\(131\) 7.45949 0.651739 0.325870 0.945415i \(-0.394343\pi\)
0.325870 + 0.945415i \(0.394343\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 21.6603 1.86422
\(136\) 0 0
\(137\) 3.70701 0.316712 0.158356 0.987382i \(-0.449381\pi\)
0.158356 + 0.987382i \(0.449381\pi\)
\(138\) 0 0
\(139\) 12.7043 1.07756 0.538781 0.842446i \(-0.318885\pi\)
0.538781 + 0.842446i \(0.318885\pi\)
\(140\) 0 0
\(141\) 16.7329 1.40916
\(142\) 0 0
\(143\) 0.835325 0.0698534
\(144\) 0 0
\(145\) 13.9949 1.16222
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.09774 0.335700 0.167850 0.985813i \(-0.446318\pi\)
0.167850 + 0.985813i \(0.446318\pi\)
\(150\) 0 0
\(151\) −10.7756 −0.876908 −0.438454 0.898754i \(-0.644474\pi\)
−0.438454 + 0.898754i \(0.644474\pi\)
\(152\) 0 0
\(153\) −3.57363 −0.288911
\(154\) 0 0
\(155\) −6.10221 −0.490141
\(156\) 0 0
\(157\) 8.20658 0.654956 0.327478 0.944859i \(-0.393801\pi\)
0.327478 + 0.944859i \(0.393801\pi\)
\(158\) 0 0
\(159\) 10.8079 0.857121
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −16.2558 −1.27325 −0.636627 0.771172i \(-0.719671\pi\)
−0.636627 + 0.771172i \(0.719671\pi\)
\(164\) 0 0
\(165\) −1.55546 −0.121092
\(166\) 0 0
\(167\) 20.4805 1.58483 0.792416 0.609981i \(-0.208823\pi\)
0.792416 + 0.609981i \(0.208823\pi\)
\(168\) 0 0
\(169\) −4.96330 −0.381792
\(170\) 0 0
\(171\) 6.39028 0.488677
\(172\) 0 0
\(173\) −0.934381 −0.0710396 −0.0355198 0.999369i \(-0.511309\pi\)
−0.0355198 + 0.999369i \(0.511309\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.45298 −0.259542
\(178\) 0 0
\(179\) −3.62356 −0.270838 −0.135419 0.990788i \(-0.543238\pi\)
−0.135419 + 0.990788i \(0.543238\pi\)
\(180\) 0 0
\(181\) 3.44901 0.256363 0.128181 0.991751i \(-0.459086\pi\)
0.128181 + 0.991751i \(0.459086\pi\)
\(182\) 0 0
\(183\) −3.09312 −0.228650
\(184\) 0 0
\(185\) 19.9626 1.46768
\(186\) 0 0
\(187\) 0.954482 0.0697987
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.69472 0.412056 0.206028 0.978546i \(-0.433946\pi\)
0.206028 + 0.978546i \(0.433946\pi\)
\(192\) 0 0
\(193\) 23.3923 1.68382 0.841909 0.539620i \(-0.181432\pi\)
0.841909 + 0.539620i \(0.181432\pi\)
\(194\) 0 0
\(195\) −14.9651 −1.07167
\(196\) 0 0
\(197\) 3.84256 0.273771 0.136885 0.990587i \(-0.456291\pi\)
0.136885 + 0.990587i \(0.456291\pi\)
\(198\) 0 0
\(199\) 4.82239 0.341850 0.170925 0.985284i \(-0.445324\pi\)
0.170925 + 0.985284i \(0.445324\pi\)
\(200\) 0 0
\(201\) 12.0369 0.849017
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.83294 −0.267704
\(206\) 0 0
\(207\) −6.50904 −0.452410
\(208\) 0 0
\(209\) −1.70678 −0.118060
\(210\) 0 0
\(211\) −7.14339 −0.491771 −0.245886 0.969299i \(-0.579079\pi\)
−0.245886 + 0.969299i \(0.579079\pi\)
\(212\) 0 0
\(213\) 2.29512 0.157259
\(214\) 0 0
\(215\) 19.6266 1.33852
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −17.7194 −1.19737
\(220\) 0 0
\(221\) 9.18312 0.617724
\(222\) 0 0
\(223\) −22.2017 −1.48674 −0.743368 0.668882i \(-0.766773\pi\)
−0.743368 + 0.668882i \(0.766773\pi\)
\(224\) 0 0
\(225\) −10.6917 −0.712777
\(226\) 0 0
\(227\) −16.6344 −1.10407 −0.552033 0.833822i \(-0.686148\pi\)
−0.552033 + 0.833822i \(0.686148\pi\)
\(228\) 0 0
\(229\) 20.2931 1.34100 0.670502 0.741908i \(-0.266079\pi\)
0.670502 + 0.741908i \(0.266079\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 23.0911 1.51275 0.756374 0.654140i \(-0.226969\pi\)
0.756374 + 0.654140i \(0.226969\pi\)
\(234\) 0 0
\(235\) −46.5686 −3.03780
\(236\) 0 0
\(237\) 0.349062 0.0226740
\(238\) 0 0
\(239\) 3.75798 0.243083 0.121542 0.992586i \(-0.461216\pi\)
0.121542 + 0.992586i \(0.461216\pi\)
\(240\) 0 0
\(241\) −15.6661 −1.00914 −0.504572 0.863370i \(-0.668350\pi\)
−0.504572 + 0.863370i \(0.668350\pi\)
\(242\) 0 0
\(243\) −10.7925 −0.692340
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −16.4210 −1.04484
\(248\) 0 0
\(249\) −17.6098 −1.11597
\(250\) 0 0
\(251\) 9.71267 0.613058 0.306529 0.951861i \(-0.400832\pi\)
0.306529 + 0.951861i \(0.400832\pi\)
\(252\) 0 0
\(253\) 1.73850 0.109299
\(254\) 0 0
\(255\) −17.0999 −1.07084
\(256\) 0 0
\(257\) 9.93296 0.619601 0.309800 0.950802i \(-0.399738\pi\)
0.309800 + 0.950802i \(0.399738\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −4.02808 −0.249332
\(262\) 0 0
\(263\) 4.98671 0.307493 0.153747 0.988110i \(-0.450866\pi\)
0.153747 + 0.988110i \(0.450866\pi\)
\(264\) 0 0
\(265\) −30.0790 −1.84774
\(266\) 0 0
\(267\) 5.26703 0.322337
\(268\) 0 0
\(269\) −28.7677 −1.75400 −0.876999 0.480492i \(-0.840458\pi\)
−0.876999 + 0.480492i \(0.840458\pi\)
\(270\) 0 0
\(271\) −6.85014 −0.416116 −0.208058 0.978116i \(-0.566714\pi\)
−0.208058 + 0.978116i \(0.566714\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.85564 0.172201
\(276\) 0 0
\(277\) 20.6436 1.24035 0.620176 0.784463i \(-0.287061\pi\)
0.620176 + 0.784463i \(0.287061\pi\)
\(278\) 0 0
\(279\) 1.75636 0.105151
\(280\) 0 0
\(281\) −25.0914 −1.49683 −0.748414 0.663232i \(-0.769184\pi\)
−0.748414 + 0.663232i \(0.769184\pi\)
\(282\) 0 0
\(283\) 20.9648 1.24623 0.623115 0.782130i \(-0.285867\pi\)
0.623115 + 0.782130i \(0.285867\pi\)
\(284\) 0 0
\(285\) 30.5775 1.81126
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −6.50692 −0.382760
\(290\) 0 0
\(291\) −25.3676 −1.48708
\(292\) 0 0
\(293\) 7.12226 0.416087 0.208043 0.978120i \(-0.433290\pi\)
0.208043 + 0.978120i \(0.433290\pi\)
\(294\) 0 0
\(295\) 9.60983 0.559506
\(296\) 0 0
\(297\) 1.66514 0.0966210
\(298\) 0 0
\(299\) 16.7262 0.967302
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 8.27051 0.475128
\(304\) 0 0
\(305\) 8.60832 0.492911
\(306\) 0 0
\(307\) 2.75757 0.157383 0.0786915 0.996899i \(-0.474926\pi\)
0.0786915 + 0.996899i \(0.474926\pi\)
\(308\) 0 0
\(309\) −5.52717 −0.314430
\(310\) 0 0
\(311\) −2.57795 −0.146182 −0.0730911 0.997325i \(-0.523286\pi\)
−0.0730911 + 0.997325i \(0.523286\pi\)
\(312\) 0 0
\(313\) −9.32344 −0.526992 −0.263496 0.964660i \(-0.584876\pi\)
−0.263496 + 0.964660i \(0.584876\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.32284 0.0742984 0.0371492 0.999310i \(-0.488172\pi\)
0.0371492 + 0.999310i \(0.488172\pi\)
\(318\) 0 0
\(319\) 1.07586 0.0602366
\(320\) 0 0
\(321\) −16.2954 −0.909522
\(322\) 0 0
\(323\) −18.7634 −1.04403
\(324\) 0 0
\(325\) 27.4742 1.52400
\(326\) 0 0
\(327\) 24.4019 1.34943
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −3.42585 −0.188302 −0.0941508 0.995558i \(-0.530014\pi\)
−0.0941508 + 0.995558i \(0.530014\pi\)
\(332\) 0 0
\(333\) −5.74572 −0.314863
\(334\) 0 0
\(335\) −33.4994 −1.83027
\(336\) 0 0
\(337\) −11.2175 −0.611054 −0.305527 0.952183i \(-0.598833\pi\)
−0.305527 + 0.952183i \(0.598833\pi\)
\(338\) 0 0
\(339\) −22.0437 −1.19725
\(340\) 0 0
\(341\) −0.469107 −0.0254036
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −31.1458 −1.67684
\(346\) 0 0
\(347\) 0.348754 0.0187221 0.00936106 0.999956i \(-0.497020\pi\)
0.00936106 + 0.999956i \(0.497020\pi\)
\(348\) 0 0
\(349\) −22.5913 −1.20929 −0.604643 0.796496i \(-0.706684\pi\)
−0.604643 + 0.796496i \(0.706684\pi\)
\(350\) 0 0
\(351\) 16.0204 0.855104
\(352\) 0 0
\(353\) −5.99615 −0.319143 −0.159571 0.987186i \(-0.551011\pi\)
−0.159571 + 0.987186i \(0.551011\pi\)
\(354\) 0 0
\(355\) −6.38745 −0.339011
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.0664 1.05907 0.529533 0.848289i \(-0.322367\pi\)
0.529533 + 0.848289i \(0.322367\pi\)
\(360\) 0 0
\(361\) 14.5523 0.765911
\(362\) 0 0
\(363\) 15.0301 0.788874
\(364\) 0 0
\(365\) 49.3142 2.58122
\(366\) 0 0
\(367\) −0.869278 −0.0453759 −0.0226880 0.999743i \(-0.507222\pi\)
−0.0226880 + 0.999743i \(0.507222\pi\)
\(368\) 0 0
\(369\) 1.10321 0.0574309
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 20.9446 1.08447 0.542235 0.840227i \(-0.317578\pi\)
0.542235 + 0.840227i \(0.317578\pi\)
\(374\) 0 0
\(375\) −24.7653 −1.27888
\(376\) 0 0
\(377\) 10.3509 0.533098
\(378\) 0 0
\(379\) 22.3371 1.14738 0.573689 0.819073i \(-0.305512\pi\)
0.573689 + 0.819073i \(0.305512\pi\)
\(380\) 0 0
\(381\) 26.2397 1.34430
\(382\) 0 0
\(383\) 23.5563 1.20367 0.601835 0.798621i \(-0.294437\pi\)
0.601835 + 0.798621i \(0.294437\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.64901 −0.287155
\(388\) 0 0
\(389\) −10.8318 −0.549195 −0.274597 0.961559i \(-0.588545\pi\)
−0.274597 + 0.961559i \(0.588545\pi\)
\(390\) 0 0
\(391\) 19.1122 0.966544
\(392\) 0 0
\(393\) −10.2735 −0.518230
\(394\) 0 0
\(395\) −0.971458 −0.0488794
\(396\) 0 0
\(397\) −18.1223 −0.909533 −0.454766 0.890611i \(-0.650277\pi\)
−0.454766 + 0.890611i \(0.650277\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.39251 0.319227 0.159613 0.987180i \(-0.448975\pi\)
0.159613 + 0.987180i \(0.448975\pi\)
\(402\) 0 0
\(403\) −4.51330 −0.224824
\(404\) 0 0
\(405\) −17.1459 −0.851984
\(406\) 0 0
\(407\) 1.53463 0.0760686
\(408\) 0 0
\(409\) 20.3931 1.00837 0.504187 0.863595i \(-0.331792\pi\)
0.504187 + 0.863595i \(0.331792\pi\)
\(410\) 0 0
\(411\) −5.10545 −0.251833
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 49.0090 2.40576
\(416\) 0 0
\(417\) −17.4968 −0.856823
\(418\) 0 0
\(419\) 30.9267 1.51087 0.755435 0.655224i \(-0.227426\pi\)
0.755435 + 0.655224i \(0.227426\pi\)
\(420\) 0 0
\(421\) −17.5442 −0.855050 −0.427525 0.904004i \(-0.640614\pi\)
−0.427525 + 0.904004i \(0.640614\pi\)
\(422\) 0 0
\(423\) 13.4035 0.651703
\(424\) 0 0
\(425\) 31.3934 1.52280
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.15044 −0.0555439
\(430\) 0 0
\(431\) −4.18368 −0.201521 −0.100760 0.994911i \(-0.532128\pi\)
−0.100760 + 0.994911i \(0.532128\pi\)
\(432\) 0 0
\(433\) 34.6744 1.66635 0.833173 0.553013i \(-0.186522\pi\)
0.833173 + 0.553013i \(0.186522\pi\)
\(434\) 0 0
\(435\) −19.2744 −0.924136
\(436\) 0 0
\(437\) −34.1759 −1.63485
\(438\) 0 0
\(439\) 15.0297 0.717327 0.358663 0.933467i \(-0.383233\pi\)
0.358663 + 0.933467i \(0.383233\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.16103 −0.150185 −0.0750925 0.997177i \(-0.523925\pi\)
−0.0750925 + 0.997177i \(0.523925\pi\)
\(444\) 0 0
\(445\) −14.6584 −0.694876
\(446\) 0 0
\(447\) −5.64357 −0.266932
\(448\) 0 0
\(449\) 19.8314 0.935901 0.467951 0.883755i \(-0.344992\pi\)
0.467951 + 0.883755i \(0.344992\pi\)
\(450\) 0 0
\(451\) −0.294657 −0.0138748
\(452\) 0 0
\(453\) 14.8406 0.697273
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 21.4151 1.00176 0.500878 0.865518i \(-0.333011\pi\)
0.500878 + 0.865518i \(0.333011\pi\)
\(458\) 0 0
\(459\) 18.3056 0.854434
\(460\) 0 0
\(461\) 11.5514 0.538000 0.269000 0.963140i \(-0.413307\pi\)
0.269000 + 0.963140i \(0.413307\pi\)
\(462\) 0 0
\(463\) −23.9717 −1.11406 −0.557029 0.830493i \(-0.688059\pi\)
−0.557029 + 0.830493i \(0.688059\pi\)
\(464\) 0 0
\(465\) 8.40421 0.389736
\(466\) 0 0
\(467\) 41.1512 1.90425 0.952126 0.305706i \(-0.0988925\pi\)
0.952126 + 0.305706i \(0.0988925\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −11.3024 −0.520788
\(472\) 0 0
\(473\) 1.50879 0.0693744
\(474\) 0 0
\(475\) −56.1368 −2.57573
\(476\) 0 0
\(477\) 8.65744 0.396397
\(478\) 0 0
\(479\) −2.86717 −0.131004 −0.0655021 0.997852i \(-0.520865\pi\)
−0.0655021 + 0.997852i \(0.520865\pi\)
\(480\) 0 0
\(481\) 14.7647 0.673213
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 70.5995 3.20576
\(486\) 0 0
\(487\) −14.7224 −0.667134 −0.333567 0.942726i \(-0.608252\pi\)
−0.333567 + 0.942726i \(0.608252\pi\)
\(488\) 0 0
\(489\) 22.3881 1.01243
\(490\) 0 0
\(491\) −22.4449 −1.01293 −0.506463 0.862262i \(-0.669047\pi\)
−0.506463 + 0.862262i \(0.669047\pi\)
\(492\) 0 0
\(493\) 11.8274 0.532681
\(494\) 0 0
\(495\) −1.24597 −0.0560021
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 11.1361 0.498520 0.249260 0.968437i \(-0.419813\pi\)
0.249260 + 0.968437i \(0.419813\pi\)
\(500\) 0 0
\(501\) −28.2066 −1.26018
\(502\) 0 0
\(503\) −19.3862 −0.864389 −0.432194 0.901781i \(-0.642261\pi\)
−0.432194 + 0.901781i \(0.642261\pi\)
\(504\) 0 0
\(505\) −23.0173 −1.02426
\(506\) 0 0
\(507\) 6.83565 0.303582
\(508\) 0 0
\(509\) 9.36124 0.414930 0.207465 0.978242i \(-0.433479\pi\)
0.207465 + 0.978242i \(0.433479\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −32.7337 −1.44523
\(514\) 0 0
\(515\) 15.3824 0.677831
\(516\) 0 0
\(517\) −3.57996 −0.157446
\(518\) 0 0
\(519\) 1.28687 0.0564871
\(520\) 0 0
\(521\) 21.1882 0.928272 0.464136 0.885764i \(-0.346365\pi\)
0.464136 + 0.885764i \(0.346365\pi\)
\(522\) 0 0
\(523\) 2.91654 0.127531 0.0637657 0.997965i \(-0.479689\pi\)
0.0637657 + 0.997965i \(0.479689\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.15712 −0.224648
\(528\) 0 0
\(529\) 11.8111 0.513525
\(530\) 0 0
\(531\) −2.76594 −0.120032
\(532\) 0 0
\(533\) −2.83491 −0.122793
\(534\) 0 0
\(535\) 45.3511 1.96070
\(536\) 0 0
\(537\) 4.99051 0.215357
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −19.1177 −0.821935 −0.410968 0.911650i \(-0.634809\pi\)
−0.410968 + 0.911650i \(0.634809\pi\)
\(542\) 0 0
\(543\) −4.75011 −0.203847
\(544\) 0 0
\(545\) −67.9118 −2.90902
\(546\) 0 0
\(547\) 1.62679 0.0695566 0.0347783 0.999395i \(-0.488927\pi\)
0.0347783 + 0.999395i \(0.488927\pi\)
\(548\) 0 0
\(549\) −2.47768 −0.105745
\(550\) 0 0
\(551\) −21.1495 −0.900999
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −27.4933 −1.16703
\(556\) 0 0
\(557\) −9.02361 −0.382342 −0.191171 0.981557i \(-0.561229\pi\)
−0.191171 + 0.981557i \(0.561229\pi\)
\(558\) 0 0
\(559\) 14.5162 0.613969
\(560\) 0 0
\(561\) −1.31455 −0.0555004
\(562\) 0 0
\(563\) 39.7373 1.67473 0.837363 0.546647i \(-0.184096\pi\)
0.837363 + 0.546647i \(0.184096\pi\)
\(564\) 0 0
\(565\) 61.3488 2.58096
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −22.4800 −0.942410 −0.471205 0.882024i \(-0.656181\pi\)
−0.471205 + 0.882024i \(0.656181\pi\)
\(570\) 0 0
\(571\) −20.3494 −0.851594 −0.425797 0.904819i \(-0.640006\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(572\) 0 0
\(573\) −7.84300 −0.327646
\(574\) 0 0
\(575\) 57.1802 2.38458
\(576\) 0 0
\(577\) 27.0963 1.12803 0.564017 0.825763i \(-0.309255\pi\)
0.564017 + 0.825763i \(0.309255\pi\)
\(578\) 0 0
\(579\) −32.2169 −1.33889
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −2.31232 −0.0957664
\(584\) 0 0
\(585\) −11.9875 −0.495623
\(586\) 0 0
\(587\) 32.7604 1.35217 0.676083 0.736825i \(-0.263676\pi\)
0.676083 + 0.736825i \(0.263676\pi\)
\(588\) 0 0
\(589\) 9.22182 0.379979
\(590\) 0 0
\(591\) −5.29212 −0.217689
\(592\) 0 0
\(593\) 35.3446 1.45143 0.725714 0.687996i \(-0.241509\pi\)
0.725714 + 0.687996i \(0.241509\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.64159 −0.271822
\(598\) 0 0
\(599\) 20.9366 0.855446 0.427723 0.903910i \(-0.359316\pi\)
0.427723 + 0.903910i \(0.359316\pi\)
\(600\) 0 0
\(601\) 25.8264 1.05348 0.526741 0.850026i \(-0.323414\pi\)
0.526741 + 0.850026i \(0.323414\pi\)
\(602\) 0 0
\(603\) 9.64191 0.392649
\(604\) 0 0
\(605\) −41.8295 −1.70061
\(606\) 0 0
\(607\) −17.9433 −0.728297 −0.364149 0.931341i \(-0.618640\pi\)
−0.364149 + 0.931341i \(0.618640\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −34.4429 −1.39341
\(612\) 0 0
\(613\) 14.1662 0.572166 0.286083 0.958205i \(-0.407647\pi\)
0.286083 + 0.958205i \(0.407647\pi\)
\(614\) 0 0
\(615\) 5.27887 0.212865
\(616\) 0 0
\(617\) 39.7328 1.59958 0.799791 0.600279i \(-0.204944\pi\)
0.799791 + 0.600279i \(0.204944\pi\)
\(618\) 0 0
\(619\) −6.92778 −0.278451 −0.139226 0.990261i \(-0.544461\pi\)
−0.139226 + 0.990261i \(0.544461\pi\)
\(620\) 0 0
\(621\) 33.3420 1.33797
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 20.4663 0.818653
\(626\) 0 0
\(627\) 2.35065 0.0938757
\(628\) 0 0
\(629\) 16.8709 0.672686
\(630\) 0 0
\(631\) 39.4682 1.57121 0.785603 0.618731i \(-0.212353\pi\)
0.785603 + 0.618731i \(0.212353\pi\)
\(632\) 0 0
\(633\) 9.83816 0.391032
\(634\) 0 0
\(635\) −73.0265 −2.89797
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1.83846 0.0727284
\(640\) 0 0
\(641\) −9.71499 −0.383719 −0.191860 0.981422i \(-0.561452\pi\)
−0.191860 + 0.981422i \(0.561452\pi\)
\(642\) 0 0
\(643\) −39.6059 −1.56191 −0.780953 0.624590i \(-0.785266\pi\)
−0.780953 + 0.624590i \(0.785266\pi\)
\(644\) 0 0
\(645\) −27.0305 −1.06433
\(646\) 0 0
\(647\) −14.3703 −0.564955 −0.282478 0.959274i \(-0.591156\pi\)
−0.282478 + 0.959274i \(0.591156\pi\)
\(648\) 0 0
\(649\) 0.738755 0.0289987
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −35.7027 −1.39716 −0.698578 0.715534i \(-0.746184\pi\)
−0.698578 + 0.715534i \(0.746184\pi\)
\(654\) 0 0
\(655\) 28.5918 1.11717
\(656\) 0 0
\(657\) −14.1938 −0.553753
\(658\) 0 0
\(659\) −7.16822 −0.279234 −0.139617 0.990206i \(-0.544587\pi\)
−0.139617 + 0.990206i \(0.544587\pi\)
\(660\) 0 0
\(661\) 4.78101 0.185960 0.0929798 0.995668i \(-0.470361\pi\)
0.0929798 + 0.995668i \(0.470361\pi\)
\(662\) 0 0
\(663\) −12.6474 −0.491183
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 21.5426 0.834132
\(668\) 0 0
\(669\) 30.5771 1.18218
\(670\) 0 0
\(671\) 0.661764 0.0255471
\(672\) 0 0
\(673\) 16.1792 0.623664 0.311832 0.950137i \(-0.399057\pi\)
0.311832 + 0.950137i \(0.399057\pi\)
\(674\) 0 0
\(675\) 54.7672 2.10799
\(676\) 0 0
\(677\) −46.0847 −1.77118 −0.885590 0.464468i \(-0.846246\pi\)
−0.885590 + 0.464468i \(0.846246\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 22.9096 0.877897
\(682\) 0 0
\(683\) −45.3568 −1.73553 −0.867765 0.496975i \(-0.834444\pi\)
−0.867765 + 0.496975i \(0.834444\pi\)
\(684\) 0 0
\(685\) 14.2087 0.542888
\(686\) 0 0
\(687\) −27.9484 −1.06630
\(688\) 0 0
\(689\) −22.2469 −0.847541
\(690\) 0 0
\(691\) −46.4521 −1.76712 −0.883561 0.468315i \(-0.844861\pi\)
−0.883561 + 0.468315i \(0.844861\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 48.6946 1.84709
\(696\) 0 0
\(697\) −3.23930 −0.122697
\(698\) 0 0
\(699\) −31.8020 −1.20286
\(700\) 0 0
\(701\) 47.7384 1.80305 0.901527 0.432723i \(-0.142447\pi\)
0.901527 + 0.432723i \(0.142447\pi\)
\(702\) 0 0
\(703\) −30.1680 −1.13781
\(704\) 0 0
\(705\) 64.1361 2.41550
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 20.3344 0.763674 0.381837 0.924230i \(-0.375292\pi\)
0.381837 + 0.924230i \(0.375292\pi\)
\(710\) 0 0
\(711\) 0.279609 0.0104862
\(712\) 0 0
\(713\) −9.39321 −0.351779
\(714\) 0 0
\(715\) 3.20175 0.119739
\(716\) 0 0
\(717\) −5.17564 −0.193288
\(718\) 0 0
\(719\) 46.1440 1.72088 0.860441 0.509550i \(-0.170188\pi\)
0.860441 + 0.509550i \(0.170188\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 21.5760 0.802421
\(724\) 0 0
\(725\) 35.3855 1.31419
\(726\) 0 0
\(727\) −43.4046 −1.60979 −0.804894 0.593418i \(-0.797778\pi\)
−0.804894 + 0.593418i \(0.797778\pi\)
\(728\) 0 0
\(729\) 28.2838 1.04755
\(730\) 0 0
\(731\) 16.5869 0.613488
\(732\) 0 0
\(733\) −32.0809 −1.18493 −0.592467 0.805594i \(-0.701846\pi\)
−0.592467 + 0.805594i \(0.701846\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.57526 −0.0948610
\(738\) 0 0
\(739\) −27.2107 −1.00096 −0.500481 0.865748i \(-0.666843\pi\)
−0.500481 + 0.865748i \(0.666843\pi\)
\(740\) 0 0
\(741\) 22.6157 0.830808
\(742\) 0 0
\(743\) 21.4440 0.786704 0.393352 0.919388i \(-0.371315\pi\)
0.393352 + 0.919388i \(0.371315\pi\)
\(744\) 0 0
\(745\) 15.7064 0.575437
\(746\) 0 0
\(747\) −14.1060 −0.516110
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −31.8901 −1.16369 −0.581843 0.813301i \(-0.697668\pi\)
−0.581843 + 0.813301i \(0.697668\pi\)
\(752\) 0 0
\(753\) −13.3767 −0.487473
\(754\) 0 0
\(755\) −41.3023 −1.50314
\(756\) 0 0
\(757\) 13.2405 0.481234 0.240617 0.970620i \(-0.422650\pi\)
0.240617 + 0.970620i \(0.422650\pi\)
\(758\) 0 0
\(759\) −2.39433 −0.0869088
\(760\) 0 0
\(761\) −10.8471 −0.393208 −0.196604 0.980483i \(-0.562991\pi\)
−0.196604 + 0.980483i \(0.562991\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −13.6975 −0.495234
\(766\) 0 0
\(767\) 7.10760 0.256641
\(768\) 0 0
\(769\) 19.1030 0.688870 0.344435 0.938810i \(-0.388070\pi\)
0.344435 + 0.938810i \(0.388070\pi\)
\(770\) 0 0
\(771\) −13.6801 −0.492675
\(772\) 0 0
\(773\) 21.8868 0.787214 0.393607 0.919279i \(-0.371227\pi\)
0.393607 + 0.919279i \(0.371227\pi\)
\(774\) 0 0
\(775\) −15.4292 −0.554232
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.79243 0.207536
\(780\) 0 0
\(781\) −0.491035 −0.0175706
\(782\) 0 0
\(783\) 20.6335 0.737380
\(784\) 0 0
\(785\) 31.4553 1.12269
\(786\) 0 0
\(787\) 28.7321 1.02419 0.512094 0.858930i \(-0.328870\pi\)
0.512094 + 0.858930i \(0.328870\pi\)
\(788\) 0 0
\(789\) −6.86789 −0.244503
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 6.36686 0.226094
\(794\) 0 0
\(795\) 41.4259 1.46923
\(796\) 0 0
\(797\) −39.5018 −1.39922 −0.699612 0.714523i \(-0.746644\pi\)
−0.699612 + 0.714523i \(0.746644\pi\)
\(798\) 0 0
\(799\) −39.3562 −1.39232
\(800\) 0 0
\(801\) 4.21905 0.149073
\(802\) 0 0
\(803\) 3.79103 0.133782
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 39.6200 1.39469
\(808\) 0 0
\(809\) 15.9020 0.559086 0.279543 0.960133i \(-0.409817\pi\)
0.279543 + 0.960133i \(0.409817\pi\)
\(810\) 0 0
\(811\) 18.2762 0.641763 0.320882 0.947119i \(-0.396021\pi\)
0.320882 + 0.947119i \(0.396021\pi\)
\(812\) 0 0
\(813\) 9.43428 0.330875
\(814\) 0 0
\(815\) −62.3075 −2.18254
\(816\) 0 0
\(817\) −29.6602 −1.03768
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −47.6782 −1.66398 −0.831990 0.554790i \(-0.812799\pi\)
−0.831990 + 0.554790i \(0.812799\pi\)
\(822\) 0 0
\(823\) 21.5891 0.752549 0.376275 0.926508i \(-0.377205\pi\)
0.376275 + 0.926508i \(0.377205\pi\)
\(824\) 0 0
\(825\) −3.93290 −0.136926
\(826\) 0 0
\(827\) −27.9750 −0.972786 −0.486393 0.873740i \(-0.661688\pi\)
−0.486393 + 0.873740i \(0.661688\pi\)
\(828\) 0 0
\(829\) −42.6324 −1.48068 −0.740342 0.672231i \(-0.765336\pi\)
−0.740342 + 0.672231i \(0.765336\pi\)
\(830\) 0 0
\(831\) −28.4311 −0.986265
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 78.5006 2.71663
\(836\) 0 0
\(837\) −8.99682 −0.310975
\(838\) 0 0
\(839\) 44.3683 1.53176 0.765881 0.642982i \(-0.222303\pi\)
0.765881 + 0.642982i \(0.222303\pi\)
\(840\) 0 0
\(841\) −15.6685 −0.540294
\(842\) 0 0
\(843\) 34.5569 1.19020
\(844\) 0 0
\(845\) −19.0240 −0.654446
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −28.8736 −0.990940
\(850\) 0 0
\(851\) 30.7287 1.05337
\(852\) 0 0
\(853\) 41.9873 1.43762 0.718809 0.695207i \(-0.244687\pi\)
0.718809 + 0.695207i \(0.244687\pi\)
\(854\) 0 0
\(855\) 24.4935 0.837661
\(856\) 0 0
\(857\) −14.8736 −0.508073 −0.254037 0.967195i \(-0.581758\pi\)
−0.254037 + 0.967195i \(0.581758\pi\)
\(858\) 0 0
\(859\) 27.4283 0.935841 0.467920 0.883771i \(-0.345003\pi\)
0.467920 + 0.883771i \(0.345003\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18.1036 −0.616253 −0.308126 0.951345i \(-0.599702\pi\)
−0.308126 + 0.951345i \(0.599702\pi\)
\(864\) 0 0
\(865\) −3.58142 −0.121772
\(866\) 0 0
\(867\) 8.96159 0.304352
\(868\) 0 0
\(869\) −0.0746808 −0.00253337
\(870\) 0 0
\(871\) −24.7767 −0.839527
\(872\) 0 0
\(873\) −20.3202 −0.687735
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 48.2964 1.63085 0.815427 0.578860i \(-0.196502\pi\)
0.815427 + 0.578860i \(0.196502\pi\)
\(878\) 0 0
\(879\) −9.80906 −0.330851
\(880\) 0 0
\(881\) 24.5426 0.826861 0.413431 0.910536i \(-0.364330\pi\)
0.413431 + 0.910536i \(0.364330\pi\)
\(882\) 0 0
\(883\) 15.2037 0.511646 0.255823 0.966724i \(-0.417654\pi\)
0.255823 + 0.966724i \(0.417654\pi\)
\(884\) 0 0
\(885\) −13.2350 −0.444891
\(886\) 0 0
\(887\) −9.71937 −0.326344 −0.163172 0.986598i \(-0.552173\pi\)
−0.163172 + 0.986598i \(0.552173\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.31809 −0.0441576
\(892\) 0 0
\(893\) 70.3756 2.35503
\(894\) 0 0
\(895\) −13.8889 −0.464254
\(896\) 0 0
\(897\) −23.0360 −0.769150
\(898\) 0 0
\(899\) −5.81292 −0.193872
\(900\) 0 0
\(901\) −25.4204 −0.846877
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 13.2198 0.439442
\(906\) 0 0
\(907\) −26.8243 −0.890688 −0.445344 0.895360i \(-0.646919\pi\)
−0.445344 + 0.895360i \(0.646919\pi\)
\(908\) 0 0
\(909\) 6.62493 0.219735
\(910\) 0 0
\(911\) −44.8553 −1.48612 −0.743060 0.669224i \(-0.766627\pi\)
−0.743060 + 0.669224i \(0.766627\pi\)
\(912\) 0 0
\(913\) 3.76757 0.124688
\(914\) 0 0
\(915\) −11.8557 −0.391938
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −5.26072 −0.173535 −0.0867675 0.996229i \(-0.527654\pi\)
−0.0867675 + 0.996229i \(0.527654\pi\)
\(920\) 0 0
\(921\) −3.79784 −0.125143
\(922\) 0 0
\(923\) −4.72427 −0.155501
\(924\) 0 0
\(925\) 50.4746 1.65959
\(926\) 0 0
\(927\) −4.42743 −0.145416
\(928\) 0 0
\(929\) −28.4683 −0.934015 −0.467007 0.884253i \(-0.654668\pi\)
−0.467007 + 0.884253i \(0.654668\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 3.55046 0.116237
\(934\) 0 0
\(935\) 3.65847 0.119645
\(936\) 0 0
\(937\) 25.1023 0.820058 0.410029 0.912072i \(-0.365519\pi\)
0.410029 + 0.912072i \(0.365519\pi\)
\(938\) 0 0
\(939\) 12.8406 0.419038
\(940\) 0 0
\(941\) 54.2707 1.76917 0.884586 0.466376i \(-0.154441\pi\)
0.884586 + 0.466376i \(0.154441\pi\)
\(942\) 0 0
\(943\) −5.90009 −0.192133
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 40.9659 1.33121 0.665607 0.746302i \(-0.268173\pi\)
0.665607 + 0.746302i \(0.268173\pi\)
\(948\) 0 0
\(949\) 36.4737 1.18398
\(950\) 0 0
\(951\) −1.82187 −0.0590783
\(952\) 0 0
\(953\) −5.07815 −0.164497 −0.0822487 0.996612i \(-0.526210\pi\)
−0.0822487 + 0.996612i \(0.526210\pi\)
\(954\) 0 0
\(955\) 21.8275 0.706322
\(956\) 0 0
\(957\) −1.48172 −0.0478971
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −28.4654 −0.918238
\(962\) 0 0
\(963\) −13.0531 −0.420631
\(964\) 0 0
\(965\) 89.6614 2.88630
\(966\) 0 0
\(967\) 47.0412 1.51274 0.756372 0.654142i \(-0.226970\pi\)
0.756372 + 0.654142i \(0.226970\pi\)
\(968\) 0 0
\(969\) 25.8418 0.830157
\(970\) 0 0
\(971\) 1.37496 0.0441246 0.0220623 0.999757i \(-0.492977\pi\)
0.0220623 + 0.999757i \(0.492977\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −37.8386 −1.21181
\(976\) 0 0
\(977\) −17.6707 −0.565334 −0.282667 0.959218i \(-0.591219\pi\)
−0.282667 + 0.959218i \(0.591219\pi\)
\(978\) 0 0
\(979\) −1.12687 −0.0360148
\(980\) 0 0
\(981\) 19.5466 0.624076
\(982\) 0 0
\(983\) −5.49225 −0.175175 −0.0875877 0.996157i \(-0.527916\pi\)
−0.0875877 + 0.996157i \(0.527916\pi\)
\(984\) 0 0
\(985\) 14.7283 0.469282
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 30.2115 0.960670
\(990\) 0 0
\(991\) −13.1735 −0.418470 −0.209235 0.977865i \(-0.567097\pi\)
−0.209235 + 0.977865i \(0.567097\pi\)
\(992\) 0 0
\(993\) 4.71821 0.149728
\(994\) 0 0
\(995\) 18.4839 0.585980
\(996\) 0 0
\(997\) 41.1141 1.30210 0.651049 0.759036i \(-0.274329\pi\)
0.651049 + 0.759036i \(0.274329\pi\)
\(998\) 0 0
\(999\) 29.4320 0.931186
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 \(a_p\))