Properties

Label 8036.2.a.q.1.5
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.72996\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.72996 q^{3} -0.138351 q^{5} -0.00725198 q^{9} +O(q^{10})\) \(q-1.72996 q^{3} -0.138351 q^{5} -0.00725198 q^{9} +2.69315 q^{11} -5.05004 q^{13} +0.239341 q^{15} -4.38217 q^{17} +5.73074 q^{19} +8.09997 q^{23} -4.98086 q^{25} +5.20241 q^{27} +3.49382 q^{29} -2.84591 q^{31} -4.65904 q^{33} -4.04732 q^{37} +8.73635 q^{39} -1.00000 q^{41} -10.8473 q^{43} +0.00100332 q^{45} +0.549726 q^{47} +7.58096 q^{51} +11.8734 q^{53} -0.372600 q^{55} -9.91392 q^{57} -9.85476 q^{59} -7.09909 q^{61} +0.698677 q^{65} -2.80347 q^{67} -14.0126 q^{69} +14.5599 q^{71} -7.81173 q^{73} +8.61667 q^{75} -10.5320 q^{79} -8.97819 q^{81} -2.44863 q^{83} +0.606276 q^{85} -6.04415 q^{87} +1.78532 q^{89} +4.92331 q^{93} -0.792851 q^{95} -5.82664 q^{97} -0.0195307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) −1.72996 −0.998791 −0.499395 0.866374i \(-0.666444\pi\)
−0.499395 + 0.866374i \(0.666444\pi\)
\(4\) 0 0
\(5\) −0.138351 −0.0618723 −0.0309362 0.999521i \(-0.509849\pi\)
−0.0309362 + 0.999521i \(0.509849\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.00725198 −0.00241733
\(10\) 0 0
\(11\) 2.69315 0.812016 0.406008 0.913869i \(-0.366920\pi\)
0.406008 + 0.913869i \(0.366920\pi\)
\(12\) 0 0
\(13\) −5.05004 −1.40063 −0.700315 0.713834i \(-0.746957\pi\)
−0.700315 + 0.713834i \(0.746957\pi\)
\(14\) 0 0
\(15\) 0.239341 0.0617975
\(16\) 0 0
\(17\) −4.38217 −1.06283 −0.531416 0.847111i \(-0.678340\pi\)
−0.531416 + 0.847111i \(0.678340\pi\)
\(18\) 0 0
\(19\) 5.73074 1.31472 0.657361 0.753576i \(-0.271673\pi\)
0.657361 + 0.753576i \(0.271673\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.09997 1.68896 0.844480 0.535587i \(-0.179910\pi\)
0.844480 + 0.535587i \(0.179910\pi\)
\(24\) 0 0
\(25\) −4.98086 −0.996172
\(26\) 0 0
\(27\) 5.20241 1.00121
\(28\) 0 0
\(29\) 3.49382 0.648785 0.324393 0.945923i \(-0.394840\pi\)
0.324393 + 0.945923i \(0.394840\pi\)
\(30\) 0 0
\(31\) −2.84591 −0.511141 −0.255571 0.966790i \(-0.582263\pi\)
−0.255571 + 0.966790i \(0.582263\pi\)
\(32\) 0 0
\(33\) −4.65904 −0.811034
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.04732 −0.665376 −0.332688 0.943037i \(-0.607956\pi\)
−0.332688 + 0.943037i \(0.607956\pi\)
\(38\) 0 0
\(39\) 8.73635 1.39894
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −10.8473 −1.65420 −0.827102 0.562051i \(-0.810012\pi\)
−0.827102 + 0.562051i \(0.810012\pi\)
\(44\) 0 0
\(45\) 0.00100332 0.000149566 0
\(46\) 0 0
\(47\) 0.549726 0.0801858 0.0400929 0.999196i \(-0.487235\pi\)
0.0400929 + 0.999196i \(0.487235\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 7.58096 1.06155
\(52\) 0 0
\(53\) 11.8734 1.63094 0.815471 0.578797i \(-0.196478\pi\)
0.815471 + 0.578797i \(0.196478\pi\)
\(54\) 0 0
\(55\) −0.372600 −0.0502413
\(56\) 0 0
\(57\) −9.91392 −1.31313
\(58\) 0 0
\(59\) −9.85476 −1.28298 −0.641490 0.767131i \(-0.721684\pi\)
−0.641490 + 0.767131i \(0.721684\pi\)
\(60\) 0 0
\(61\) −7.09909 −0.908945 −0.454473 0.890761i \(-0.650172\pi\)
−0.454473 + 0.890761i \(0.650172\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.698677 0.0866602
\(66\) 0 0
\(67\) −2.80347 −0.342498 −0.171249 0.985228i \(-0.554780\pi\)
−0.171249 + 0.985228i \(0.554780\pi\)
\(68\) 0 0
\(69\) −14.0126 −1.68692
\(70\) 0 0
\(71\) 14.5599 1.72794 0.863969 0.503545i \(-0.167971\pi\)
0.863969 + 0.503545i \(0.167971\pi\)
\(72\) 0 0
\(73\) −7.81173 −0.914294 −0.457147 0.889391i \(-0.651129\pi\)
−0.457147 + 0.889391i \(0.651129\pi\)
\(74\) 0 0
\(75\) 8.61667 0.994967
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −10.5320 −1.18494 −0.592471 0.805592i \(-0.701847\pi\)
−0.592471 + 0.805592i \(0.701847\pi\)
\(80\) 0 0
\(81\) −8.97819 −0.997577
\(82\) 0 0
\(83\) −2.44863 −0.268772 −0.134386 0.990929i \(-0.542906\pi\)
−0.134386 + 0.990929i \(0.542906\pi\)
\(84\) 0 0
\(85\) 0.606276 0.0657598
\(86\) 0 0
\(87\) −6.04415 −0.648001
\(88\) 0 0
\(89\) 1.78532 0.189243 0.0946216 0.995513i \(-0.469836\pi\)
0.0946216 + 0.995513i \(0.469836\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 4.92331 0.510523
\(94\) 0 0
\(95\) −0.792851 −0.0813448
\(96\) 0 0
\(97\) −5.82664 −0.591605 −0.295803 0.955249i \(-0.595587\pi\)
−0.295803 + 0.955249i \(0.595587\pi\)
\(98\) 0 0
\(99\) −0.0195307 −0.00196291
\(100\) 0 0
\(101\) 10.2817 1.02307 0.511533 0.859264i \(-0.329078\pi\)
0.511533 + 0.859264i \(0.329078\pi\)
\(102\) 0 0
\(103\) 14.5850 1.43710 0.718552 0.695473i \(-0.244805\pi\)
0.718552 + 0.695473i \(0.244805\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.0163 1.25834 0.629168 0.777269i \(-0.283396\pi\)
0.629168 + 0.777269i \(0.283396\pi\)
\(108\) 0 0
\(109\) 4.37091 0.418658 0.209329 0.977845i \(-0.432872\pi\)
0.209329 + 0.977845i \(0.432872\pi\)
\(110\) 0 0
\(111\) 7.00169 0.664571
\(112\) 0 0
\(113\) 12.0509 1.13366 0.566828 0.823836i \(-0.308170\pi\)
0.566828 + 0.823836i \(0.308170\pi\)
\(114\) 0 0
\(115\) −1.12064 −0.104500
\(116\) 0 0
\(117\) 0.0366228 0.00338578
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −3.74692 −0.340629
\(122\) 0 0
\(123\) 1.72996 0.155985
\(124\) 0 0
\(125\) 1.38086 0.123508
\(126\) 0 0
\(127\) −5.44928 −0.483545 −0.241773 0.970333i \(-0.577729\pi\)
−0.241773 + 0.970333i \(0.577729\pi\)
\(128\) 0 0
\(129\) 18.7654 1.65220
\(130\) 0 0
\(131\) −21.1505 −1.84793 −0.923966 0.382475i \(-0.875072\pi\)
−0.923966 + 0.382475i \(0.875072\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.719757 −0.0619469
\(136\) 0 0
\(137\) −11.3964 −0.973657 −0.486829 0.873498i \(-0.661846\pi\)
−0.486829 + 0.873498i \(0.661846\pi\)
\(138\) 0 0
\(139\) 20.9983 1.78106 0.890528 0.454929i \(-0.150335\pi\)
0.890528 + 0.454929i \(0.150335\pi\)
\(140\) 0 0
\(141\) −0.951003 −0.0800889
\(142\) 0 0
\(143\) −13.6005 −1.13733
\(144\) 0 0
\(145\) −0.483372 −0.0401418
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.743622 −0.0609199 −0.0304599 0.999536i \(-0.509697\pi\)
−0.0304599 + 0.999536i \(0.509697\pi\)
\(150\) 0 0
\(151\) 21.2384 1.72836 0.864178 0.503186i \(-0.167839\pi\)
0.864178 + 0.503186i \(0.167839\pi\)
\(152\) 0 0
\(153\) 0.0317794 0.00256921
\(154\) 0 0
\(155\) 0.393734 0.0316255
\(156\) 0 0
\(157\) −16.9815 −1.35527 −0.677637 0.735396i \(-0.736996\pi\)
−0.677637 + 0.735396i \(0.736996\pi\)
\(158\) 0 0
\(159\) −20.5405 −1.62897
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −24.9441 −1.95377 −0.976887 0.213755i \(-0.931430\pi\)
−0.976887 + 0.213755i \(0.931430\pi\)
\(164\) 0 0
\(165\) 0.644581 0.0501806
\(166\) 0 0
\(167\) 16.4889 1.27595 0.637973 0.770058i \(-0.279773\pi\)
0.637973 + 0.770058i \(0.279773\pi\)
\(168\) 0 0
\(169\) 12.5029 0.961763
\(170\) 0 0
\(171\) −0.0415592 −0.00317811
\(172\) 0 0
\(173\) 4.58584 0.348655 0.174327 0.984688i \(-0.444225\pi\)
0.174327 + 0.984688i \(0.444225\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.0483 1.28143
\(178\) 0 0
\(179\) −22.6645 −1.69402 −0.847011 0.531576i \(-0.821600\pi\)
−0.847011 + 0.531576i \(0.821600\pi\)
\(180\) 0 0
\(181\) −2.18126 −0.162132 −0.0810660 0.996709i \(-0.525832\pi\)
−0.0810660 + 0.996709i \(0.525832\pi\)
\(182\) 0 0
\(183\) 12.2811 0.907846
\(184\) 0 0
\(185\) 0.559950 0.0411683
\(186\) 0 0
\(187\) −11.8018 −0.863037
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 20.1964 1.46136 0.730680 0.682720i \(-0.239203\pi\)
0.730680 + 0.682720i \(0.239203\pi\)
\(192\) 0 0
\(193\) 10.0768 0.725346 0.362673 0.931916i \(-0.381864\pi\)
0.362673 + 0.931916i \(0.381864\pi\)
\(194\) 0 0
\(195\) −1.20868 −0.0865554
\(196\) 0 0
\(197\) −2.87850 −0.205085 −0.102542 0.994729i \(-0.532698\pi\)
−0.102542 + 0.994729i \(0.532698\pi\)
\(198\) 0 0
\(199\) 19.9273 1.41261 0.706304 0.707909i \(-0.250361\pi\)
0.706304 + 0.707909i \(0.250361\pi\)
\(200\) 0 0
\(201\) 4.84988 0.342084
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.138351 0.00966283
\(206\) 0 0
\(207\) −0.0587408 −0.00408277
\(208\) 0 0
\(209\) 15.4338 1.06758
\(210\) 0 0
\(211\) 17.2509 1.18760 0.593802 0.804611i \(-0.297626\pi\)
0.593802 + 0.804611i \(0.297626\pi\)
\(212\) 0 0
\(213\) −25.1879 −1.72585
\(214\) 0 0
\(215\) 1.50074 0.102349
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 13.5139 0.913188
\(220\) 0 0
\(221\) 22.1301 1.48863
\(222\) 0 0
\(223\) −6.73906 −0.451281 −0.225640 0.974211i \(-0.572447\pi\)
−0.225640 + 0.974211i \(0.572447\pi\)
\(224\) 0 0
\(225\) 0.0361211 0.00240807
\(226\) 0 0
\(227\) −1.93020 −0.128112 −0.0640560 0.997946i \(-0.520404\pi\)
−0.0640560 + 0.997946i \(0.520404\pi\)
\(228\) 0 0
\(229\) −6.41374 −0.423832 −0.211916 0.977288i \(-0.567970\pi\)
−0.211916 + 0.977288i \(0.567970\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.12913 −0.336021 −0.168010 0.985785i \(-0.553734\pi\)
−0.168010 + 0.985785i \(0.553734\pi\)
\(234\) 0 0
\(235\) −0.0760550 −0.00496128
\(236\) 0 0
\(237\) 18.2199 1.18351
\(238\) 0 0
\(239\) 3.36794 0.217854 0.108927 0.994050i \(-0.465259\pi\)
0.108927 + 0.994050i \(0.465259\pi\)
\(240\) 0 0
\(241\) 2.39150 0.154050 0.0770250 0.997029i \(-0.475458\pi\)
0.0770250 + 0.997029i \(0.475458\pi\)
\(242\) 0 0
\(243\) −0.0753646 −0.00483464
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −28.9405 −1.84144
\(248\) 0 0
\(249\) 4.23602 0.268447
\(250\) 0 0
\(251\) 8.70091 0.549197 0.274598 0.961559i \(-0.411455\pi\)
0.274598 + 0.961559i \(0.411455\pi\)
\(252\) 0 0
\(253\) 21.8145 1.37146
\(254\) 0 0
\(255\) −1.04883 −0.0656803
\(256\) 0 0
\(257\) 2.25116 0.140424 0.0702118 0.997532i \(-0.477632\pi\)
0.0702118 + 0.997532i \(0.477632\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.0253371 −0.00156833
\(262\) 0 0
\(263\) 4.82702 0.297647 0.148823 0.988864i \(-0.452451\pi\)
0.148823 + 0.988864i \(0.452451\pi\)
\(264\) 0 0
\(265\) −1.64270 −0.100910
\(266\) 0 0
\(267\) −3.08852 −0.189014
\(268\) 0 0
\(269\) −9.07027 −0.553024 −0.276512 0.961010i \(-0.589179\pi\)
−0.276512 + 0.961010i \(0.589179\pi\)
\(270\) 0 0
\(271\) −8.67279 −0.526834 −0.263417 0.964682i \(-0.584850\pi\)
−0.263417 + 0.964682i \(0.584850\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −13.4142 −0.808908
\(276\) 0 0
\(277\) 26.9015 1.61635 0.808177 0.588940i \(-0.200454\pi\)
0.808177 + 0.588940i \(0.200454\pi\)
\(278\) 0 0
\(279\) 0.0206385 0.00123560
\(280\) 0 0
\(281\) −15.2508 −0.909788 −0.454894 0.890546i \(-0.650323\pi\)
−0.454894 + 0.890546i \(0.650323\pi\)
\(282\) 0 0
\(283\) −23.1544 −1.37639 −0.688194 0.725526i \(-0.741596\pi\)
−0.688194 + 0.725526i \(0.741596\pi\)
\(284\) 0 0
\(285\) 1.37160 0.0812465
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2.20338 0.129611
\(290\) 0 0
\(291\) 10.0798 0.590890
\(292\) 0 0
\(293\) 1.68125 0.0982198 0.0491099 0.998793i \(-0.484362\pi\)
0.0491099 + 0.998793i \(0.484362\pi\)
\(294\) 0 0
\(295\) 1.36341 0.0793810
\(296\) 0 0
\(297\) 14.0109 0.812995
\(298\) 0 0
\(299\) −40.9052 −2.36561
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −17.7869 −1.02183
\(304\) 0 0
\(305\) 0.982164 0.0562385
\(306\) 0 0
\(307\) 21.2887 1.21501 0.607506 0.794315i \(-0.292170\pi\)
0.607506 + 0.794315i \(0.292170\pi\)
\(308\) 0 0
\(309\) −25.2314 −1.43537
\(310\) 0 0
\(311\) −24.0159 −1.36181 −0.680907 0.732369i \(-0.738414\pi\)
−0.680907 + 0.732369i \(0.738414\pi\)
\(312\) 0 0
\(313\) 18.9342 1.07022 0.535111 0.844782i \(-0.320270\pi\)
0.535111 + 0.844782i \(0.320270\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 31.5827 1.77386 0.886930 0.461904i \(-0.152833\pi\)
0.886930 + 0.461904i \(0.152833\pi\)
\(318\) 0 0
\(319\) 9.40938 0.526824
\(320\) 0 0
\(321\) −22.5177 −1.25681
\(322\) 0 0
\(323\) −25.1130 −1.39733
\(324\) 0 0
\(325\) 25.1535 1.39527
\(326\) 0 0
\(327\) −7.56149 −0.418151
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 35.9104 1.97382 0.986908 0.161286i \(-0.0515641\pi\)
0.986908 + 0.161286i \(0.0515641\pi\)
\(332\) 0 0
\(333\) 0.0293511 0.00160843
\(334\) 0 0
\(335\) 0.387862 0.0211912
\(336\) 0 0
\(337\) 6.58274 0.358585 0.179292 0.983796i \(-0.442619\pi\)
0.179292 + 0.983796i \(0.442619\pi\)
\(338\) 0 0
\(339\) −20.8476 −1.13229
\(340\) 0 0
\(341\) −7.66448 −0.415055
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1.93865 0.104373
\(346\) 0 0
\(347\) 12.0202 0.645280 0.322640 0.946522i \(-0.395430\pi\)
0.322640 + 0.946522i \(0.395430\pi\)
\(348\) 0 0
\(349\) 36.7866 1.96914 0.984570 0.174993i \(-0.0559903\pi\)
0.984570 + 0.174993i \(0.0559903\pi\)
\(350\) 0 0
\(351\) −26.2724 −1.40232
\(352\) 0 0
\(353\) −2.41501 −0.128538 −0.0642691 0.997933i \(-0.520472\pi\)
−0.0642691 + 0.997933i \(0.520472\pi\)
\(354\) 0 0
\(355\) −2.01437 −0.106911
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.93153 0.207498 0.103749 0.994604i \(-0.466916\pi\)
0.103749 + 0.994604i \(0.466916\pi\)
\(360\) 0 0
\(361\) 13.8413 0.728492
\(362\) 0 0
\(363\) 6.48201 0.340217
\(364\) 0 0
\(365\) 1.08076 0.0565695
\(366\) 0 0
\(367\) −32.4268 −1.69266 −0.846332 0.532656i \(-0.821194\pi\)
−0.846332 + 0.532656i \(0.821194\pi\)
\(368\) 0 0
\(369\) 0.00725198 0.000377523 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.7318 0.555673 0.277836 0.960628i \(-0.410383\pi\)
0.277836 + 0.960628i \(0.410383\pi\)
\(374\) 0 0
\(375\) −2.38882 −0.123358
\(376\) 0 0
\(377\) −17.6439 −0.908708
\(378\) 0 0
\(379\) 17.6723 0.907764 0.453882 0.891062i \(-0.350039\pi\)
0.453882 + 0.891062i \(0.350039\pi\)
\(380\) 0 0
\(381\) 9.42701 0.482960
\(382\) 0 0
\(383\) −20.9037 −1.06813 −0.534066 0.845443i \(-0.679337\pi\)
−0.534066 + 0.845443i \(0.679337\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.0786648 0.00399875
\(388\) 0 0
\(389\) 34.3177 1.73998 0.869989 0.493072i \(-0.164126\pi\)
0.869989 + 0.493072i \(0.164126\pi\)
\(390\) 0 0
\(391\) −35.4954 −1.79508
\(392\) 0 0
\(393\) 36.5895 1.84570
\(394\) 0 0
\(395\) 1.45711 0.0733150
\(396\) 0 0
\(397\) −13.8093 −0.693067 −0.346534 0.938038i \(-0.612641\pi\)
−0.346534 + 0.938038i \(0.612641\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4.27497 0.213482 0.106741 0.994287i \(-0.465958\pi\)
0.106741 + 0.994287i \(0.465958\pi\)
\(402\) 0 0
\(403\) 14.3720 0.715920
\(404\) 0 0
\(405\) 1.24214 0.0617224
\(406\) 0 0
\(407\) −10.9001 −0.540296
\(408\) 0 0
\(409\) 29.5945 1.46336 0.731678 0.681650i \(-0.238738\pi\)
0.731678 + 0.681650i \(0.238738\pi\)
\(410\) 0 0
\(411\) 19.7152 0.972480
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.338769 0.0166295
\(416\) 0 0
\(417\) −36.3262 −1.77890
\(418\) 0 0
\(419\) 24.8741 1.21518 0.607589 0.794251i \(-0.292137\pi\)
0.607589 + 0.794251i \(0.292137\pi\)
\(420\) 0 0
\(421\) 7.30826 0.356183 0.178091 0.984014i \(-0.443008\pi\)
0.178091 + 0.984014i \(0.443008\pi\)
\(422\) 0 0
\(423\) −0.00398661 −0.000193835 0
\(424\) 0 0
\(425\) 21.8270 1.05876
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 23.5283 1.13596
\(430\) 0 0
\(431\) −21.9690 −1.05821 −0.529105 0.848556i \(-0.677472\pi\)
−0.529105 + 0.848556i \(0.677472\pi\)
\(432\) 0 0
\(433\) 9.89063 0.475313 0.237657 0.971349i \(-0.423621\pi\)
0.237657 + 0.971349i \(0.423621\pi\)
\(434\) 0 0
\(435\) 0.836212 0.0400933
\(436\) 0 0
\(437\) 46.4188 2.22051
\(438\) 0 0
\(439\) −6.10305 −0.291283 −0.145641 0.989337i \(-0.546525\pi\)
−0.145641 + 0.989337i \(0.546525\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 28.3435 1.34664 0.673321 0.739350i \(-0.264867\pi\)
0.673321 + 0.739350i \(0.264867\pi\)
\(444\) 0 0
\(445\) −0.247000 −0.0117089
\(446\) 0 0
\(447\) 1.28643 0.0608462
\(448\) 0 0
\(449\) 22.3983 1.05704 0.528521 0.848920i \(-0.322747\pi\)
0.528521 + 0.848920i \(0.322747\pi\)
\(450\) 0 0
\(451\) −2.69315 −0.126816
\(452\) 0 0
\(453\) −36.7415 −1.72627
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.90893 0.323186 0.161593 0.986857i \(-0.448337\pi\)
0.161593 + 0.986857i \(0.448337\pi\)
\(458\) 0 0
\(459\) −22.7978 −1.06411
\(460\) 0 0
\(461\) 16.8884 0.786573 0.393286 0.919416i \(-0.371338\pi\)
0.393286 + 0.919416i \(0.371338\pi\)
\(462\) 0 0
\(463\) −28.3956 −1.31966 −0.659828 0.751417i \(-0.729371\pi\)
−0.659828 + 0.751417i \(0.729371\pi\)
\(464\) 0 0
\(465\) −0.681143 −0.0315872
\(466\) 0 0
\(467\) 19.9414 0.922780 0.461390 0.887197i \(-0.347351\pi\)
0.461390 + 0.887197i \(0.347351\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 29.3773 1.35364
\(472\) 0 0
\(473\) −29.2136 −1.34324
\(474\) 0 0
\(475\) −28.5440 −1.30969
\(476\) 0 0
\(477\) −0.0861060 −0.00394252
\(478\) 0 0
\(479\) 34.5557 1.57889 0.789445 0.613822i \(-0.210369\pi\)
0.789445 + 0.613822i \(0.210369\pi\)
\(480\) 0 0
\(481\) 20.4392 0.931945
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.806119 0.0366040
\(486\) 0 0
\(487\) 13.9840 0.633674 0.316837 0.948480i \(-0.397379\pi\)
0.316837 + 0.948480i \(0.397379\pi\)
\(488\) 0 0
\(489\) 43.1522 1.95141
\(490\) 0 0
\(491\) 25.3725 1.14504 0.572522 0.819890i \(-0.305965\pi\)
0.572522 + 0.819890i \(0.305965\pi\)
\(492\) 0 0
\(493\) −15.3105 −0.689549
\(494\) 0 0
\(495\) 0.00270209 0.000121450 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −12.7146 −0.569185 −0.284593 0.958649i \(-0.591858\pi\)
−0.284593 + 0.958649i \(0.591858\pi\)
\(500\) 0 0
\(501\) −28.5250 −1.27440
\(502\) 0 0
\(503\) 21.7738 0.970844 0.485422 0.874280i \(-0.338666\pi\)
0.485422 + 0.874280i \(0.338666\pi\)
\(504\) 0 0
\(505\) −1.42248 −0.0632994
\(506\) 0 0
\(507\) −21.6295 −0.960600
\(508\) 0 0
\(509\) 38.5413 1.70831 0.854156 0.520017i \(-0.174074\pi\)
0.854156 + 0.520017i \(0.174074\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 29.8137 1.31631
\(514\) 0 0
\(515\) −2.01785 −0.0889169
\(516\) 0 0
\(517\) 1.48050 0.0651122
\(518\) 0 0
\(519\) −7.93330 −0.348233
\(520\) 0 0
\(521\) 9.28852 0.406938 0.203469 0.979081i \(-0.434778\pi\)
0.203469 + 0.979081i \(0.434778\pi\)
\(522\) 0 0
\(523\) −7.16308 −0.313220 −0.156610 0.987661i \(-0.550057\pi\)
−0.156610 + 0.987661i \(0.550057\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.4713 0.543257
\(528\) 0 0
\(529\) 42.6095 1.85259
\(530\) 0 0
\(531\) 0.0714666 0.00310138
\(532\) 0 0
\(533\) 5.05004 0.218742
\(534\) 0 0
\(535\) −1.80082 −0.0778562
\(536\) 0 0
\(537\) 39.2085 1.69197
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 18.5380 0.797012 0.398506 0.917166i \(-0.369529\pi\)
0.398506 + 0.917166i \(0.369529\pi\)
\(542\) 0 0
\(543\) 3.77349 0.161936
\(544\) 0 0
\(545\) −0.604719 −0.0259033
\(546\) 0 0
\(547\) −24.6673 −1.05470 −0.527348 0.849649i \(-0.676814\pi\)
−0.527348 + 0.849649i \(0.676814\pi\)
\(548\) 0 0
\(549\) 0.0514825 0.00219722
\(550\) 0 0
\(551\) 20.0221 0.852972
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −0.968689 −0.0411186
\(556\) 0 0
\(557\) −18.8686 −0.799488 −0.399744 0.916627i \(-0.630901\pi\)
−0.399744 + 0.916627i \(0.630901\pi\)
\(558\) 0 0
\(559\) 54.7796 2.31693
\(560\) 0 0
\(561\) 20.4167 0.861993
\(562\) 0 0
\(563\) 12.0948 0.509736 0.254868 0.966976i \(-0.417968\pi\)
0.254868 + 0.966976i \(0.417968\pi\)
\(564\) 0 0
\(565\) −1.66725 −0.0701419
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 38.0776 1.59630 0.798149 0.602460i \(-0.205813\pi\)
0.798149 + 0.602460i \(0.205813\pi\)
\(570\) 0 0
\(571\) 35.3021 1.47735 0.738673 0.674064i \(-0.235453\pi\)
0.738673 + 0.674064i \(0.235453\pi\)
\(572\) 0 0
\(573\) −34.9389 −1.45959
\(574\) 0 0
\(575\) −40.3448 −1.68249
\(576\) 0 0
\(577\) 23.1430 0.963455 0.481728 0.876321i \(-0.340009\pi\)
0.481728 + 0.876321i \(0.340009\pi\)
\(578\) 0 0
\(579\) −17.4325 −0.724469
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 31.9770 1.32435
\(584\) 0 0
\(585\) −0.00506679 −0.000209486 0
\(586\) 0 0
\(587\) 8.02365 0.331172 0.165586 0.986195i \(-0.447049\pi\)
0.165586 + 0.986195i \(0.447049\pi\)
\(588\) 0 0
\(589\) −16.3092 −0.672008
\(590\) 0 0
\(591\) 4.97968 0.204837
\(592\) 0 0
\(593\) −23.8724 −0.980323 −0.490162 0.871632i \(-0.663062\pi\)
−0.490162 + 0.871632i \(0.663062\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −34.4733 −1.41090
\(598\) 0 0
\(599\) −36.0214 −1.47179 −0.735896 0.677094i \(-0.763239\pi\)
−0.735896 + 0.677094i \(0.763239\pi\)
\(600\) 0 0
\(601\) −3.67996 −0.150109 −0.0750543 0.997179i \(-0.523913\pi\)
−0.0750543 + 0.997179i \(0.523913\pi\)
\(602\) 0 0
\(603\) 0.0203307 0.000827930 0
\(604\) 0 0
\(605\) 0.518389 0.0210755
\(606\) 0 0
\(607\) 30.8608 1.25260 0.626300 0.779582i \(-0.284569\pi\)
0.626300 + 0.779582i \(0.284569\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.77614 −0.112311
\(612\) 0 0
\(613\) 6.98088 0.281955 0.140978 0.990013i \(-0.454975\pi\)
0.140978 + 0.990013i \(0.454975\pi\)
\(614\) 0 0
\(615\) −0.239341 −0.00965114
\(616\) 0 0
\(617\) 29.9068 1.20400 0.602002 0.798495i \(-0.294370\pi\)
0.602002 + 0.798495i \(0.294370\pi\)
\(618\) 0 0
\(619\) 22.2912 0.895960 0.447980 0.894044i \(-0.352144\pi\)
0.447980 + 0.894044i \(0.352144\pi\)
\(620\) 0 0
\(621\) 42.1394 1.69100
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 24.7133 0.988530
\(626\) 0 0
\(627\) −26.6997 −1.06628
\(628\) 0 0
\(629\) 17.7360 0.707183
\(630\) 0 0
\(631\) −22.9844 −0.914994 −0.457497 0.889211i \(-0.651254\pi\)
−0.457497 + 0.889211i \(0.651254\pi\)
\(632\) 0 0
\(633\) −29.8434 −1.18617
\(634\) 0 0
\(635\) 0.753911 0.0299180
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −0.105588 −0.00417699
\(640\) 0 0
\(641\) −28.7896 −1.13712 −0.568560 0.822642i \(-0.692499\pi\)
−0.568560 + 0.822642i \(0.692499\pi\)
\(642\) 0 0
\(643\) −22.1980 −0.875402 −0.437701 0.899121i \(-0.644207\pi\)
−0.437701 + 0.899121i \(0.644207\pi\)
\(644\) 0 0
\(645\) −2.59621 −0.102226
\(646\) 0 0
\(647\) −20.8413 −0.819356 −0.409678 0.912230i \(-0.634359\pi\)
−0.409678 + 0.912230i \(0.634359\pi\)
\(648\) 0 0
\(649\) −26.5404 −1.04180
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −47.8337 −1.87188 −0.935938 0.352164i \(-0.885446\pi\)
−0.935938 + 0.352164i \(0.885446\pi\)
\(654\) 0 0
\(655\) 2.92619 0.114336
\(656\) 0 0
\(657\) 0.0566505 0.00221015
\(658\) 0 0
\(659\) −3.61599 −0.140859 −0.0704296 0.997517i \(-0.522437\pi\)
−0.0704296 + 0.997517i \(0.522437\pi\)
\(660\) 0 0
\(661\) 44.0109 1.71183 0.855913 0.517119i \(-0.172996\pi\)
0.855913 + 0.517119i \(0.172996\pi\)
\(662\) 0 0
\(663\) −38.2841 −1.48683
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 28.2998 1.09577
\(668\) 0 0
\(669\) 11.6583 0.450735
\(670\) 0 0
\(671\) −19.1189 −0.738079
\(672\) 0 0
\(673\) −5.20547 −0.200656 −0.100328 0.994954i \(-0.531989\pi\)
−0.100328 + 0.994954i \(0.531989\pi\)
\(674\) 0 0
\(675\) −25.9125 −0.997372
\(676\) 0 0
\(677\) 17.8560 0.686261 0.343131 0.939288i \(-0.388513\pi\)
0.343131 + 0.939288i \(0.388513\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 3.33917 0.127957
\(682\) 0 0
\(683\) 26.6454 1.01956 0.509779 0.860305i \(-0.329727\pi\)
0.509779 + 0.860305i \(0.329727\pi\)
\(684\) 0 0
\(685\) 1.57669 0.0602424
\(686\) 0 0
\(687\) 11.0955 0.423319
\(688\) 0 0
\(689\) −59.9614 −2.28435
\(690\) 0 0
\(691\) 34.2765 1.30394 0.651969 0.758245i \(-0.273943\pi\)
0.651969 + 0.758245i \(0.273943\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.90513 −0.110198
\(696\) 0 0
\(697\) 4.38217 0.165986
\(698\) 0 0
\(699\) 8.87317 0.335614
\(700\) 0 0
\(701\) −33.0947 −1.24997 −0.624986 0.780636i \(-0.714895\pi\)
−0.624986 + 0.780636i \(0.714895\pi\)
\(702\) 0 0
\(703\) −23.1941 −0.874784
\(704\) 0 0
\(705\) 0.131572 0.00495528
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −19.8549 −0.745666 −0.372833 0.927898i \(-0.621614\pi\)
−0.372833 + 0.927898i \(0.621614\pi\)
\(710\) 0 0
\(711\) 0.0763778 0.00286439
\(712\) 0 0
\(713\) −23.0518 −0.863297
\(714\) 0 0
\(715\) 1.88164 0.0703695
\(716\) 0 0
\(717\) −5.82639 −0.217590
\(718\) 0 0
\(719\) 42.4164 1.58187 0.790933 0.611903i \(-0.209596\pi\)
0.790933 + 0.611903i \(0.209596\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4.13719 −0.153864
\(724\) 0 0
\(725\) −17.4022 −0.646302
\(726\) 0 0
\(727\) −26.0078 −0.964576 −0.482288 0.876013i \(-0.660194\pi\)
−0.482288 + 0.876013i \(0.660194\pi\)
\(728\) 0 0
\(729\) 27.0650 1.00241
\(730\) 0 0
\(731\) 47.5349 1.75814
\(732\) 0 0
\(733\) −28.9065 −1.06769 −0.533843 0.845583i \(-0.679253\pi\)
−0.533843 + 0.845583i \(0.679253\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.55017 −0.278114
\(738\) 0 0
\(739\) −3.80880 −0.140109 −0.0700546 0.997543i \(-0.522317\pi\)
−0.0700546 + 0.997543i \(0.522317\pi\)
\(740\) 0 0
\(741\) 50.0657 1.83921
\(742\) 0 0
\(743\) −11.2071 −0.411148 −0.205574 0.978642i \(-0.565906\pi\)
−0.205574 + 0.978642i \(0.565906\pi\)
\(744\) 0 0
\(745\) 0.102881 0.00376925
\(746\) 0 0
\(747\) 0.0177574 0.000649709 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.718156 0.0262059 0.0131029 0.999914i \(-0.495829\pi\)
0.0131029 + 0.999914i \(0.495829\pi\)
\(752\) 0 0
\(753\) −15.0522 −0.548533
\(754\) 0 0
\(755\) −2.93835 −0.106937
\(756\) 0 0
\(757\) −14.6357 −0.531942 −0.265971 0.963981i \(-0.585693\pi\)
−0.265971 + 0.963981i \(0.585693\pi\)
\(758\) 0 0
\(759\) −37.7381 −1.36980
\(760\) 0 0
\(761\) 8.40732 0.304765 0.152383 0.988322i \(-0.451305\pi\)
0.152383 + 0.988322i \(0.451305\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.00439670 −0.000158963 0
\(766\) 0 0
\(767\) 49.7670 1.79698
\(768\) 0 0
\(769\) −6.66726 −0.240428 −0.120214 0.992748i \(-0.538358\pi\)
−0.120214 + 0.992748i \(0.538358\pi\)
\(770\) 0 0
\(771\) −3.89441 −0.140254
\(772\) 0 0
\(773\) 19.7134 0.709040 0.354520 0.935048i \(-0.384644\pi\)
0.354520 + 0.935048i \(0.384644\pi\)
\(774\) 0 0
\(775\) 14.1751 0.509185
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.73074 −0.205325
\(780\) 0 0
\(781\) 39.2119 1.40311
\(782\) 0 0
\(783\) 18.1763 0.649567
\(784\) 0 0
\(785\) 2.34941 0.0838540
\(786\) 0 0
\(787\) 16.2381 0.578825 0.289413 0.957204i \(-0.406540\pi\)
0.289413 + 0.957204i \(0.406540\pi\)
\(788\) 0 0
\(789\) −8.35053 −0.297287
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 35.8507 1.27310
\(794\) 0 0
\(795\) 2.84180 0.100788
\(796\) 0 0
\(797\) −15.2774 −0.541152 −0.270576 0.962699i \(-0.587214\pi\)
−0.270576 + 0.962699i \(0.587214\pi\)
\(798\) 0 0
\(799\) −2.40899 −0.0852240
\(800\) 0 0
\(801\) −0.0129471 −0.000457463 0
\(802\) 0 0
\(803\) −21.0382 −0.742421
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 15.6912 0.552356
\(808\) 0 0
\(809\) −3.25997 −0.114614 −0.0573072 0.998357i \(-0.518251\pi\)
−0.0573072 + 0.998357i \(0.518251\pi\)
\(810\) 0 0
\(811\) −7.78233 −0.273275 −0.136637 0.990621i \(-0.543629\pi\)
−0.136637 + 0.990621i \(0.543629\pi\)
\(812\) 0 0
\(813\) 15.0035 0.526197
\(814\) 0 0
\(815\) 3.45104 0.120885
\(816\) 0 0
\(817\) −62.1633 −2.17482
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 4.51951 0.157732 0.0788660 0.996885i \(-0.474870\pi\)
0.0788660 + 0.996885i \(0.474870\pi\)
\(822\) 0 0
\(823\) −3.68068 −0.128301 −0.0641503 0.997940i \(-0.520434\pi\)
−0.0641503 + 0.997940i \(0.520434\pi\)
\(824\) 0 0
\(825\) 23.2060 0.807930
\(826\) 0 0
\(827\) −9.84848 −0.342465 −0.171233 0.985231i \(-0.554775\pi\)
−0.171233 + 0.985231i \(0.554775\pi\)
\(828\) 0 0
\(829\) 8.84388 0.307161 0.153580 0.988136i \(-0.450920\pi\)
0.153580 + 0.988136i \(0.450920\pi\)
\(830\) 0 0
\(831\) −46.5384 −1.61440
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −2.28125 −0.0789458
\(836\) 0 0
\(837\) −14.8056 −0.511757
\(838\) 0 0
\(839\) −3.82105 −0.131917 −0.0659587 0.997822i \(-0.521011\pi\)
−0.0659587 + 0.997822i \(0.521011\pi\)
\(840\) 0 0
\(841\) −16.7933 −0.579078
\(842\) 0 0
\(843\) 26.3833 0.908688
\(844\) 0 0
\(845\) −1.72979 −0.0595065
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 40.0562 1.37472
\(850\) 0 0
\(851\) −32.7832 −1.12379
\(852\) 0 0
\(853\) 47.3338 1.62068 0.810340 0.585960i \(-0.199283\pi\)
0.810340 + 0.585960i \(0.199283\pi\)
\(854\) 0 0
\(855\) 0.00574974 0.000196637 0
\(856\) 0 0
\(857\) −15.6208 −0.533597 −0.266798 0.963752i \(-0.585966\pi\)
−0.266798 + 0.963752i \(0.585966\pi\)
\(858\) 0 0
\(859\) 49.2078 1.67895 0.839474 0.543400i \(-0.182863\pi\)
0.839474 + 0.543400i \(0.182863\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −34.6153 −1.17832 −0.589160 0.808017i \(-0.700541\pi\)
−0.589160 + 0.808017i \(0.700541\pi\)
\(864\) 0 0
\(865\) −0.634454 −0.0215721
\(866\) 0 0
\(867\) −3.81176 −0.129454
\(868\) 0 0
\(869\) −28.3643 −0.962192
\(870\) 0 0
\(871\) 14.1576 0.479713
\(872\) 0 0
\(873\) 0.0422547 0.00143010
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −38.7040 −1.30694 −0.653471 0.756952i \(-0.726688\pi\)
−0.653471 + 0.756952i \(0.726688\pi\)
\(878\) 0 0
\(879\) −2.90849 −0.0981010
\(880\) 0 0
\(881\) 40.7943 1.37440 0.687198 0.726470i \(-0.258841\pi\)
0.687198 + 0.726470i \(0.258841\pi\)
\(882\) 0 0
\(883\) −20.4213 −0.687232 −0.343616 0.939110i \(-0.611652\pi\)
−0.343616 + 0.939110i \(0.611652\pi\)
\(884\) 0 0
\(885\) −2.35864 −0.0792850
\(886\) 0 0
\(887\) −14.9970 −0.503552 −0.251776 0.967786i \(-0.581015\pi\)
−0.251776 + 0.967786i \(0.581015\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −24.1796 −0.810049
\(892\) 0 0
\(893\) 3.15034 0.105422
\(894\) 0 0
\(895\) 3.13564 0.104813
\(896\) 0 0
\(897\) 70.7642 2.36275
\(898\) 0 0
\(899\) −9.94310 −0.331621
\(900\) 0 0
\(901\) −52.0314 −1.73342
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.301779 0.0100315
\(906\) 0 0
\(907\) −24.7950 −0.823305 −0.411652 0.911341i \(-0.635048\pi\)
−0.411652 + 0.911341i \(0.635048\pi\)
\(908\) 0 0
\(909\) −0.0745626 −0.00247308
\(910\) 0 0
\(911\) −18.8479 −0.624458 −0.312229 0.950007i \(-0.601076\pi\)
−0.312229 + 0.950007i \(0.601076\pi\)
\(912\) 0 0
\(913\) −6.59453 −0.218247
\(914\) 0 0
\(915\) −1.69910 −0.0561705
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −5.65808 −0.186643 −0.0933215 0.995636i \(-0.529748\pi\)
−0.0933215 + 0.995636i \(0.529748\pi\)
\(920\) 0 0
\(921\) −36.8286 −1.21354
\(922\) 0 0
\(923\) −73.5279 −2.42020
\(924\) 0 0
\(925\) 20.1592 0.662829
\(926\) 0 0
\(927\) −0.105770 −0.00347395
\(928\) 0 0
\(929\) −50.7518 −1.66511 −0.832556 0.553941i \(-0.813123\pi\)
−0.832556 + 0.553941i \(0.813123\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 41.5464 1.36017
\(934\) 0 0
\(935\) 1.63279 0.0533981
\(936\) 0 0
\(937\) −25.6871 −0.839162 −0.419581 0.907718i \(-0.637823\pi\)
−0.419581 + 0.907718i \(0.637823\pi\)
\(938\) 0 0
\(939\) −32.7553 −1.06893
\(940\) 0 0
\(941\) −11.9819 −0.390599 −0.195299 0.980744i \(-0.562568\pi\)
−0.195299 + 0.980744i \(0.562568\pi\)
\(942\) 0 0
\(943\) −8.09997 −0.263771
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 31.5029 1.02371 0.511854 0.859073i \(-0.328959\pi\)
0.511854 + 0.859073i \(0.328959\pi\)
\(948\) 0 0
\(949\) 39.4496 1.28059
\(950\) 0 0
\(951\) −54.6367 −1.77171
\(952\) 0 0
\(953\) 30.0320 0.972833 0.486416 0.873727i \(-0.338304\pi\)
0.486416 + 0.873727i \(0.338304\pi\)
\(954\) 0 0
\(955\) −2.79419 −0.0904177
\(956\) 0 0
\(957\) −16.2778 −0.526187
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −22.9008 −0.738735
\(962\) 0 0
\(963\) −0.0943942 −0.00304181
\(964\) 0 0
\(965\) −1.39414 −0.0448788
\(966\) 0 0
\(967\) −20.7206 −0.666328 −0.333164 0.942869i \(-0.608116\pi\)
−0.333164 + 0.942869i \(0.608116\pi\)
\(968\) 0 0
\(969\) 43.4445 1.39564
\(970\) 0 0
\(971\) 47.6630 1.52958 0.764789 0.644281i \(-0.222843\pi\)
0.764789 + 0.644281i \(0.222843\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −43.5145 −1.39358
\(976\) 0 0
\(977\) 47.2389 1.51131 0.755653 0.654973i \(-0.227320\pi\)
0.755653 + 0.654973i \(0.227320\pi\)
\(978\) 0 0
\(979\) 4.80813 0.153669
\(980\) 0 0
\(981\) −0.0316978 −0.00101203
\(982\) 0 0
\(983\) 44.7066 1.42592 0.712960 0.701204i \(-0.247354\pi\)
0.712960 + 0.701204i \(0.247354\pi\)
\(984\) 0 0
\(985\) 0.398243 0.0126891
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −87.8632 −2.79389
\(990\) 0 0
\(991\) −3.17283 −0.100788 −0.0503941 0.998729i \(-0.516048\pi\)
−0.0503941 + 0.998729i \(0.516048\pi\)
\(992\) 0 0
\(993\) −62.1235 −1.97143
\(994\) 0 0
\(995\) −2.75695 −0.0874013
\(996\) 0 0
\(997\) −1.92328 −0.0609110 −0.0304555 0.999536i \(-0.509696\pi\)
−0.0304555 + 0.999536i \(0.509696\pi\)
\(998\) 0 0
\(999\) −21.0559 −0.666178
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 \(a_p\))