Properties

Label 8036.2.a.t.1.5
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 1.5
Root \(-1.77641\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.77641 q^{3}\) \(-0.716761 q^{5}\) \(+0.155650 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.77641 q^{3}\) \(-0.716761 q^{5}\) \(+0.155650 q^{9}\) \(+1.69774 q^{11}\) \(-4.41385 q^{13}\) \(+1.27327 q^{15}\) \(+1.35813 q^{17}\) \(+6.61457 q^{19}\) \(-4.94432 q^{23}\) \(-4.48625 q^{25}\) \(+5.05275 q^{27}\) \(-0.711000 q^{29}\) \(+3.41573 q^{31}\) \(-3.01588 q^{33}\) \(-5.21830 q^{37}\) \(+7.84083 q^{39}\) \(-1.00000 q^{41}\) \(-6.26787 q^{43}\) \(-0.111564 q^{45}\) \(+7.29375 q^{47}\) \(-2.41260 q^{51}\) \(-12.1698 q^{53}\) \(-1.21687 q^{55}\) \(-11.7502 q^{57}\) \(-1.69715 q^{59}\) \(+7.76380 q^{61}\) \(+3.16368 q^{65}\) \(+3.13992 q^{67}\) \(+8.78317 q^{69}\) \(+3.54572 q^{71}\) \(+11.4366 q^{73}\) \(+7.96945 q^{75}\) \(+8.90590 q^{79}\) \(-9.44272 q^{81}\) \(-12.4174 q^{83}\) \(-0.973454 q^{85}\) \(+1.26303 q^{87}\) \(-6.08357 q^{89}\) \(-6.06775 q^{93}\) \(-4.74107 q^{95}\) \(-15.9366 q^{97}\) \(+0.264252 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.77641 −1.02561 −0.512807 0.858504i \(-0.671394\pi\)
−0.512807 + 0.858504i \(0.671394\pi\)
\(4\) 0 0
\(5\) −0.716761 −0.320545 −0.160273 0.987073i \(-0.551237\pi\)
−0.160273 + 0.987073i \(0.551237\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.155650 0.0518832
\(10\) 0 0
\(11\) 1.69774 0.511887 0.255943 0.966692i \(-0.417614\pi\)
0.255943 + 0.966692i \(0.417614\pi\)
\(12\) 0 0
\(13\) −4.41385 −1.22418 −0.612091 0.790787i \(-0.709671\pi\)
−0.612091 + 0.790787i \(0.709671\pi\)
\(14\) 0 0
\(15\) 1.27327 0.328756
\(16\) 0 0
\(17\) 1.35813 0.329394 0.164697 0.986344i \(-0.447335\pi\)
0.164697 + 0.986344i \(0.447335\pi\)
\(18\) 0 0
\(19\) 6.61457 1.51749 0.758743 0.651390i \(-0.225814\pi\)
0.758743 + 0.651390i \(0.225814\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.94432 −1.03096 −0.515481 0.856901i \(-0.672387\pi\)
−0.515481 + 0.856901i \(0.672387\pi\)
\(24\) 0 0
\(25\) −4.48625 −0.897251
\(26\) 0 0
\(27\) 5.05275 0.972401
\(28\) 0 0
\(29\) −0.711000 −0.132029 −0.0660147 0.997819i \(-0.521028\pi\)
−0.0660147 + 0.997819i \(0.521028\pi\)
\(30\) 0 0
\(31\) 3.41573 0.613483 0.306742 0.951793i \(-0.400761\pi\)
0.306742 + 0.951793i \(0.400761\pi\)
\(32\) 0 0
\(33\) −3.01588 −0.524998
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.21830 −0.857883 −0.428942 0.903332i \(-0.641113\pi\)
−0.428942 + 0.903332i \(0.641113\pi\)
\(38\) 0 0
\(39\) 7.84083 1.25554
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −6.26787 −0.955841 −0.477921 0.878403i \(-0.658609\pi\)
−0.477921 + 0.878403i \(0.658609\pi\)
\(44\) 0 0
\(45\) −0.111564 −0.0166309
\(46\) 0 0
\(47\) 7.29375 1.06390 0.531952 0.846775i \(-0.321459\pi\)
0.531952 + 0.846775i \(0.321459\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.41260 −0.337831
\(52\) 0 0
\(53\) −12.1698 −1.67165 −0.835827 0.548994i \(-0.815011\pi\)
−0.835827 + 0.548994i \(0.815011\pi\)
\(54\) 0 0
\(55\) −1.21687 −0.164083
\(56\) 0 0
\(57\) −11.7502 −1.55635
\(58\) 0 0
\(59\) −1.69715 −0.220950 −0.110475 0.993879i \(-0.535237\pi\)
−0.110475 + 0.993879i \(0.535237\pi\)
\(60\) 0 0
\(61\) 7.76380 0.994053 0.497027 0.867735i \(-0.334425\pi\)
0.497027 + 0.867735i \(0.334425\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.16368 0.392406
\(66\) 0 0
\(67\) 3.13992 0.383602 0.191801 0.981434i \(-0.438567\pi\)
0.191801 + 0.981434i \(0.438567\pi\)
\(68\) 0 0
\(69\) 8.78317 1.05737
\(70\) 0 0
\(71\) 3.54572 0.420799 0.210400 0.977615i \(-0.432523\pi\)
0.210400 + 0.977615i \(0.432523\pi\)
\(72\) 0 0
\(73\) 11.4366 1.33856 0.669278 0.743012i \(-0.266603\pi\)
0.669278 + 0.743012i \(0.266603\pi\)
\(74\) 0 0
\(75\) 7.96945 0.920232
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 8.90590 1.00199 0.500996 0.865450i \(-0.332967\pi\)
0.500996 + 0.865450i \(0.332967\pi\)
\(80\) 0 0
\(81\) −9.44272 −1.04919
\(82\) 0 0
\(83\) −12.4174 −1.36299 −0.681494 0.731824i \(-0.738669\pi\)
−0.681494 + 0.731824i \(0.738669\pi\)
\(84\) 0 0
\(85\) −0.973454 −0.105586
\(86\) 0 0
\(87\) 1.26303 0.135411
\(88\) 0 0
\(89\) −6.08357 −0.644857 −0.322429 0.946594i \(-0.604499\pi\)
−0.322429 + 0.946594i \(0.604499\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −6.06775 −0.629197
\(94\) 0 0
\(95\) −4.74107 −0.486423
\(96\) 0 0
\(97\) −15.9366 −1.61812 −0.809059 0.587728i \(-0.800023\pi\)
−0.809059 + 0.587728i \(0.800023\pi\)
\(98\) 0 0
\(99\) 0.264252 0.0265583
\(100\) 0 0
\(101\) 15.1504 1.50752 0.753759 0.657151i \(-0.228239\pi\)
0.753759 + 0.657151i \(0.228239\pi\)
\(102\) 0 0
\(103\) −18.4235 −1.81532 −0.907662 0.419702i \(-0.862134\pi\)
−0.907662 + 0.419702i \(0.862134\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.0184 −1.54855 −0.774277 0.632847i \(-0.781886\pi\)
−0.774277 + 0.632847i \(0.781886\pi\)
\(108\) 0 0
\(109\) 5.59424 0.535831 0.267916 0.963442i \(-0.413665\pi\)
0.267916 + 0.963442i \(0.413665\pi\)
\(110\) 0 0
\(111\) 9.26986 0.879856
\(112\) 0 0
\(113\) −14.8004 −1.39231 −0.696153 0.717893i \(-0.745107\pi\)
−0.696153 + 0.717893i \(0.745107\pi\)
\(114\) 0 0
\(115\) 3.54390 0.330470
\(116\) 0 0
\(117\) −0.687014 −0.0635145
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.11769 −0.737972
\(122\) 0 0
\(123\) 1.77641 0.160174
\(124\) 0 0
\(125\) 6.79938 0.608155
\(126\) 0 0
\(127\) −2.17883 −0.193340 −0.0966700 0.995316i \(-0.530819\pi\)
−0.0966700 + 0.995316i \(0.530819\pi\)
\(128\) 0 0
\(129\) 11.1343 0.980324
\(130\) 0 0
\(131\) 6.33225 0.553251 0.276625 0.960978i \(-0.410784\pi\)
0.276625 + 0.960978i \(0.410784\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −3.62161 −0.311699
\(136\) 0 0
\(137\) 21.0536 1.79873 0.899365 0.437198i \(-0.144029\pi\)
0.899365 + 0.437198i \(0.144029\pi\)
\(138\) 0 0
\(139\) −7.86444 −0.667053 −0.333526 0.942741i \(-0.608239\pi\)
−0.333526 + 0.942741i \(0.608239\pi\)
\(140\) 0 0
\(141\) −12.9567 −1.09115
\(142\) 0 0
\(143\) −7.49356 −0.626643
\(144\) 0 0
\(145\) 0.509617 0.0423214
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.33573 0.764813 0.382407 0.923994i \(-0.375095\pi\)
0.382407 + 0.923994i \(0.375095\pi\)
\(150\) 0 0
\(151\) −1.50195 −0.122227 −0.0611135 0.998131i \(-0.519465\pi\)
−0.0611135 + 0.998131i \(0.519465\pi\)
\(152\) 0 0
\(153\) 0.211392 0.0170900
\(154\) 0 0
\(155\) −2.44826 −0.196649
\(156\) 0 0
\(157\) 13.5894 1.08455 0.542276 0.840201i \(-0.317563\pi\)
0.542276 + 0.840201i \(0.317563\pi\)
\(158\) 0 0
\(159\) 21.6186 1.71447
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 14.1671 1.10966 0.554828 0.831965i \(-0.312784\pi\)
0.554828 + 0.831965i \(0.312784\pi\)
\(164\) 0 0
\(165\) 2.16167 0.168286
\(166\) 0 0
\(167\) −7.61946 −0.589611 −0.294806 0.955557i \(-0.595255\pi\)
−0.294806 + 0.955557i \(0.595255\pi\)
\(168\) 0 0
\(169\) 6.48208 0.498621
\(170\) 0 0
\(171\) 1.02955 0.0787320
\(172\) 0 0
\(173\) 6.78468 0.515830 0.257915 0.966168i \(-0.416965\pi\)
0.257915 + 0.966168i \(0.416965\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.01484 0.226609
\(178\) 0 0
\(179\) 13.4212 1.00315 0.501575 0.865114i \(-0.332754\pi\)
0.501575 + 0.865114i \(0.332754\pi\)
\(180\) 0 0
\(181\) −23.4891 −1.74593 −0.872964 0.487784i \(-0.837805\pi\)
−0.872964 + 0.487784i \(0.837805\pi\)
\(182\) 0 0
\(183\) −13.7917 −1.01951
\(184\) 0 0
\(185\) 3.74027 0.274990
\(186\) 0 0
\(187\) 2.30574 0.168613
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.74296 0.270831 0.135416 0.990789i \(-0.456763\pi\)
0.135416 + 0.990789i \(0.456763\pi\)
\(192\) 0 0
\(193\) 22.3013 1.60528 0.802640 0.596464i \(-0.203428\pi\)
0.802640 + 0.596464i \(0.203428\pi\)
\(194\) 0 0
\(195\) −5.62000 −0.402457
\(196\) 0 0
\(197\) 12.1467 0.865415 0.432708 0.901534i \(-0.357558\pi\)
0.432708 + 0.901534i \(0.357558\pi\)
\(198\) 0 0
\(199\) 12.7447 0.903445 0.451722 0.892159i \(-0.350810\pi\)
0.451722 + 0.892159i \(0.350810\pi\)
\(200\) 0 0
\(201\) −5.57780 −0.393427
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.716761 0.0500608
\(206\) 0 0
\(207\) −0.769582 −0.0534896
\(208\) 0 0
\(209\) 11.2298 0.776781
\(210\) 0 0
\(211\) 2.56860 0.176830 0.0884149 0.996084i \(-0.471820\pi\)
0.0884149 + 0.996084i \(0.471820\pi\)
\(212\) 0 0
\(213\) −6.29866 −0.431577
\(214\) 0 0
\(215\) 4.49257 0.306391
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −20.3162 −1.37284
\(220\) 0 0
\(221\) −5.99458 −0.403239
\(222\) 0 0
\(223\) −20.3812 −1.36483 −0.682413 0.730967i \(-0.739069\pi\)
−0.682413 + 0.730967i \(0.739069\pi\)
\(224\) 0 0
\(225\) −0.698283 −0.0465522
\(226\) 0 0
\(227\) −25.8696 −1.71703 −0.858513 0.512792i \(-0.828611\pi\)
−0.858513 + 0.512792i \(0.828611\pi\)
\(228\) 0 0
\(229\) 23.2042 1.53338 0.766689 0.642018i \(-0.221903\pi\)
0.766689 + 0.642018i \(0.221903\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 17.8849 1.17168 0.585838 0.810428i \(-0.300765\pi\)
0.585838 + 0.810428i \(0.300765\pi\)
\(234\) 0 0
\(235\) −5.22788 −0.341029
\(236\) 0 0
\(237\) −15.8206 −1.02766
\(238\) 0 0
\(239\) −9.03234 −0.584254 −0.292127 0.956380i \(-0.594363\pi\)
−0.292127 + 0.956380i \(0.594363\pi\)
\(240\) 0 0
\(241\) −3.99359 −0.257250 −0.128625 0.991693i \(-0.541056\pi\)
−0.128625 + 0.991693i \(0.541056\pi\)
\(242\) 0 0
\(243\) 1.61595 0.103663
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −29.1957 −1.85768
\(248\) 0 0
\(249\) 22.0585 1.39790
\(250\) 0 0
\(251\) 25.9887 1.64039 0.820195 0.572084i \(-0.193865\pi\)
0.820195 + 0.572084i \(0.193865\pi\)
\(252\) 0 0
\(253\) −8.39416 −0.527736
\(254\) 0 0
\(255\) 1.72926 0.108290
\(256\) 0 0
\(257\) 24.1578 1.50692 0.753460 0.657494i \(-0.228384\pi\)
0.753460 + 0.657494i \(0.228384\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.110667 −0.00685010
\(262\) 0 0
\(263\) −15.3693 −0.947712 −0.473856 0.880602i \(-0.657138\pi\)
−0.473856 + 0.880602i \(0.657138\pi\)
\(264\) 0 0
\(265\) 8.72286 0.535841
\(266\) 0 0
\(267\) 10.8069 0.661374
\(268\) 0 0
\(269\) −13.8438 −0.844074 −0.422037 0.906579i \(-0.638685\pi\)
−0.422037 + 0.906579i \(0.638685\pi\)
\(270\) 0 0
\(271\) 17.5459 1.06584 0.532919 0.846167i \(-0.321095\pi\)
0.532919 + 0.846167i \(0.321095\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.61648 −0.459291
\(276\) 0 0
\(277\) −14.9385 −0.897568 −0.448784 0.893640i \(-0.648143\pi\)
−0.448784 + 0.893640i \(0.648143\pi\)
\(278\) 0 0
\(279\) 0.531657 0.0318295
\(280\) 0 0
\(281\) −17.8574 −1.06529 −0.532643 0.846340i \(-0.678801\pi\)
−0.532643 + 0.846340i \(0.678801\pi\)
\(282\) 0 0
\(283\) 10.5195 0.625317 0.312658 0.949866i \(-0.398780\pi\)
0.312658 + 0.949866i \(0.398780\pi\)
\(284\) 0 0
\(285\) 8.42210 0.498882
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.1555 −0.891499
\(290\) 0 0
\(291\) 28.3100 1.65956
\(292\) 0 0
\(293\) −2.08524 −0.121821 −0.0609105 0.998143i \(-0.519400\pi\)
−0.0609105 + 0.998143i \(0.519400\pi\)
\(294\) 0 0
\(295\) 1.21645 0.0708244
\(296\) 0 0
\(297\) 8.57823 0.497760
\(298\) 0 0
\(299\) 21.8235 1.26209
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −26.9133 −1.54613
\(304\) 0 0
\(305\) −5.56480 −0.318639
\(306\) 0 0
\(307\) 31.1415 1.77734 0.888669 0.458549i \(-0.151631\pi\)
0.888669 + 0.458549i \(0.151631\pi\)
\(308\) 0 0
\(309\) 32.7278 1.86182
\(310\) 0 0
\(311\) 1.29468 0.0734144 0.0367072 0.999326i \(-0.488313\pi\)
0.0367072 + 0.999326i \(0.488313\pi\)
\(312\) 0 0
\(313\) 3.26088 0.184316 0.0921580 0.995744i \(-0.470624\pi\)
0.0921580 + 0.995744i \(0.470624\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 26.6758 1.49826 0.749131 0.662422i \(-0.230472\pi\)
0.749131 + 0.662422i \(0.230472\pi\)
\(318\) 0 0
\(319\) −1.20709 −0.0675841
\(320\) 0 0
\(321\) 28.4553 1.58822
\(322\) 0 0
\(323\) 8.98343 0.499852
\(324\) 0 0
\(325\) 19.8017 1.09840
\(326\) 0 0
\(327\) −9.93769 −0.549556
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −15.3959 −0.846237 −0.423118 0.906074i \(-0.639065\pi\)
−0.423118 + 0.906074i \(0.639065\pi\)
\(332\) 0 0
\(333\) −0.812226 −0.0445097
\(334\) 0 0
\(335\) −2.25057 −0.122962
\(336\) 0 0
\(337\) 9.41514 0.512875 0.256438 0.966561i \(-0.417451\pi\)
0.256438 + 0.966561i \(0.417451\pi\)
\(338\) 0 0
\(339\) 26.2917 1.42797
\(340\) 0 0
\(341\) 5.79901 0.314034
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −6.29544 −0.338935
\(346\) 0 0
\(347\) 17.8029 0.955707 0.477854 0.878440i \(-0.341415\pi\)
0.477854 + 0.878440i \(0.341415\pi\)
\(348\) 0 0
\(349\) 8.62781 0.461836 0.230918 0.972973i \(-0.425827\pi\)
0.230918 + 0.972973i \(0.425827\pi\)
\(350\) 0 0
\(351\) −22.3021 −1.19040
\(352\) 0 0
\(353\) 5.87764 0.312835 0.156418 0.987691i \(-0.450005\pi\)
0.156418 + 0.987691i \(0.450005\pi\)
\(354\) 0 0
\(355\) −2.54143 −0.134885
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.18050 0.220638 0.110319 0.993896i \(-0.464813\pi\)
0.110319 + 0.993896i \(0.464813\pi\)
\(360\) 0 0
\(361\) 24.7525 1.30276
\(362\) 0 0
\(363\) 14.4204 0.756874
\(364\) 0 0
\(365\) −8.19734 −0.429068
\(366\) 0 0
\(367\) −12.3369 −0.643980 −0.321990 0.946743i \(-0.604352\pi\)
−0.321990 + 0.946743i \(0.604352\pi\)
\(368\) 0 0
\(369\) −0.155650 −0.00810279
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −10.6356 −0.550690 −0.275345 0.961345i \(-0.588792\pi\)
−0.275345 + 0.961345i \(0.588792\pi\)
\(374\) 0 0
\(375\) −12.0785 −0.623732
\(376\) 0 0
\(377\) 3.13825 0.161628
\(378\) 0 0
\(379\) 10.0037 0.513857 0.256929 0.966430i \(-0.417289\pi\)
0.256929 + 0.966430i \(0.417289\pi\)
\(380\) 0 0
\(381\) 3.87051 0.198292
\(382\) 0 0
\(383\) 8.42654 0.430576 0.215288 0.976551i \(-0.430931\pi\)
0.215288 + 0.976551i \(0.430931\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.975591 −0.0495921
\(388\) 0 0
\(389\) 21.0941 1.06951 0.534756 0.845007i \(-0.320404\pi\)
0.534756 + 0.845007i \(0.320404\pi\)
\(390\) 0 0
\(391\) −6.71502 −0.339593
\(392\) 0 0
\(393\) −11.2487 −0.567422
\(394\) 0 0
\(395\) −6.38340 −0.321184
\(396\) 0 0
\(397\) −7.46045 −0.374429 −0.187215 0.982319i \(-0.559946\pi\)
−0.187215 + 0.982319i \(0.559946\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.2028 −0.958940 −0.479470 0.877558i \(-0.659171\pi\)
−0.479470 + 0.877558i \(0.659171\pi\)
\(402\) 0 0
\(403\) −15.0765 −0.751015
\(404\) 0 0
\(405\) 6.76818 0.336313
\(406\) 0 0
\(407\) −8.85930 −0.439139
\(408\) 0 0
\(409\) 18.7835 0.928784 0.464392 0.885630i \(-0.346273\pi\)
0.464392 + 0.885630i \(0.346273\pi\)
\(410\) 0 0
\(411\) −37.3999 −1.84480
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 8.90031 0.436899
\(416\) 0 0
\(417\) 13.9705 0.684139
\(418\) 0 0
\(419\) −2.94543 −0.143894 −0.0719469 0.997408i \(-0.522921\pi\)
−0.0719469 + 0.997408i \(0.522921\pi\)
\(420\) 0 0
\(421\) −24.1692 −1.17793 −0.588967 0.808157i \(-0.700465\pi\)
−0.588967 + 0.808157i \(0.700465\pi\)
\(422\) 0 0
\(423\) 1.13527 0.0551987
\(424\) 0 0
\(425\) −6.09291 −0.295549
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 13.3117 0.642693
\(430\) 0 0
\(431\) 19.2317 0.926359 0.463179 0.886265i \(-0.346709\pi\)
0.463179 + 0.886265i \(0.346709\pi\)
\(432\) 0 0
\(433\) 25.3115 1.21639 0.608196 0.793787i \(-0.291894\pi\)
0.608196 + 0.793787i \(0.291894\pi\)
\(434\) 0 0
\(435\) −0.905291 −0.0434054
\(436\) 0 0
\(437\) −32.7046 −1.56447
\(438\) 0 0
\(439\) 21.2047 1.01205 0.506023 0.862520i \(-0.331115\pi\)
0.506023 + 0.862520i \(0.331115\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −30.2976 −1.43948 −0.719741 0.694242i \(-0.755740\pi\)
−0.719741 + 0.694242i \(0.755740\pi\)
\(444\) 0 0
\(445\) 4.36047 0.206706
\(446\) 0 0
\(447\) −16.5841 −0.784403
\(448\) 0 0
\(449\) −7.56127 −0.356838 −0.178419 0.983955i \(-0.557098\pi\)
−0.178419 + 0.983955i \(0.557098\pi\)
\(450\) 0 0
\(451\) −1.69774 −0.0799433
\(452\) 0 0
\(453\) 2.66809 0.125358
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 32.5520 1.52272 0.761360 0.648329i \(-0.224532\pi\)
0.761360 + 0.648329i \(0.224532\pi\)
\(458\) 0 0
\(459\) 6.86228 0.320304
\(460\) 0 0
\(461\) 20.1030 0.936289 0.468145 0.883652i \(-0.344923\pi\)
0.468145 + 0.883652i \(0.344923\pi\)
\(462\) 0 0
\(463\) −9.92239 −0.461133 −0.230566 0.973057i \(-0.574058\pi\)
−0.230566 + 0.973057i \(0.574058\pi\)
\(464\) 0 0
\(465\) 4.34913 0.201686
\(466\) 0 0
\(467\) −5.88181 −0.272178 −0.136089 0.990697i \(-0.543453\pi\)
−0.136089 + 0.990697i \(0.543453\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −24.1404 −1.11233
\(472\) 0 0
\(473\) −10.6412 −0.489283
\(474\) 0 0
\(475\) −29.6746 −1.36157
\(476\) 0 0
\(477\) −1.89423 −0.0867307
\(478\) 0 0
\(479\) −14.5129 −0.663109 −0.331555 0.943436i \(-0.607573\pi\)
−0.331555 + 0.943436i \(0.607573\pi\)
\(480\) 0 0
\(481\) 23.0328 1.05020
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 11.4227 0.518680
\(486\) 0 0
\(487\) 31.8829 1.44475 0.722375 0.691501i \(-0.243050\pi\)
0.722375 + 0.691501i \(0.243050\pi\)
\(488\) 0 0
\(489\) −25.1667 −1.13808
\(490\) 0 0
\(491\) 29.3079 1.32265 0.661323 0.750101i \(-0.269995\pi\)
0.661323 + 0.750101i \(0.269995\pi\)
\(492\) 0 0
\(493\) −0.965629 −0.0434897
\(494\) 0 0
\(495\) −0.189406 −0.00851315
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 21.4677 0.961024 0.480512 0.876988i \(-0.340451\pi\)
0.480512 + 0.876988i \(0.340451\pi\)
\(500\) 0 0
\(501\) 13.5353 0.604713
\(502\) 0 0
\(503\) −4.79250 −0.213687 −0.106844 0.994276i \(-0.534074\pi\)
−0.106844 + 0.994276i \(0.534074\pi\)
\(504\) 0 0
\(505\) −10.8592 −0.483228
\(506\) 0 0
\(507\) −11.5149 −0.511393
\(508\) 0 0
\(509\) 5.25958 0.233127 0.116563 0.993183i \(-0.462812\pi\)
0.116563 + 0.993183i \(0.462812\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 33.4217 1.47561
\(514\) 0 0
\(515\) 13.2053 0.581894
\(516\) 0 0
\(517\) 12.3829 0.544598
\(518\) 0 0
\(519\) −12.0524 −0.529042
\(520\) 0 0
\(521\) −0.492973 −0.0215976 −0.0107988 0.999942i \(-0.503437\pi\)
−0.0107988 + 0.999942i \(0.503437\pi\)
\(522\) 0 0
\(523\) 10.1976 0.445908 0.222954 0.974829i \(-0.428430\pi\)
0.222954 + 0.974829i \(0.428430\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.63900 0.202078
\(528\) 0 0
\(529\) 1.44633 0.0628840
\(530\) 0 0
\(531\) −0.264160 −0.0114636
\(532\) 0 0
\(533\) 4.41385 0.191185
\(534\) 0 0
\(535\) 11.4813 0.496382
\(536\) 0 0
\(537\) −23.8417 −1.02884
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −5.80961 −0.249775 −0.124887 0.992171i \(-0.539857\pi\)
−0.124887 + 0.992171i \(0.539857\pi\)
\(542\) 0 0
\(543\) 41.7263 1.79065
\(544\) 0 0
\(545\) −4.00974 −0.171758
\(546\) 0 0
\(547\) 44.3728 1.89724 0.948621 0.316413i \(-0.102479\pi\)
0.948621 + 0.316413i \(0.102479\pi\)
\(548\) 0 0
\(549\) 1.20843 0.0515746
\(550\) 0 0
\(551\) −4.70296 −0.200353
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −6.64428 −0.282034
\(556\) 0 0
\(557\) 28.2088 1.19525 0.597624 0.801777i \(-0.296112\pi\)
0.597624 + 0.801777i \(0.296112\pi\)
\(558\) 0 0
\(559\) 27.6654 1.17012
\(560\) 0 0
\(561\) −4.09596 −0.172931
\(562\) 0 0
\(563\) 43.1476 1.81845 0.909226 0.416302i \(-0.136674\pi\)
0.909226 + 0.416302i \(0.136674\pi\)
\(564\) 0 0
\(565\) 10.6084 0.446298
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 23.4484 0.983009 0.491504 0.870875i \(-0.336447\pi\)
0.491504 + 0.870875i \(0.336447\pi\)
\(570\) 0 0
\(571\) 15.7679 0.659865 0.329933 0.944005i \(-0.392974\pi\)
0.329933 + 0.944005i \(0.392974\pi\)
\(572\) 0 0
\(573\) −6.64905 −0.277768
\(574\) 0 0
\(575\) 22.1815 0.925032
\(576\) 0 0
\(577\) 34.7488 1.44661 0.723306 0.690528i \(-0.242622\pi\)
0.723306 + 0.690528i \(0.242622\pi\)
\(578\) 0 0
\(579\) −39.6163 −1.64640
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −20.6611 −0.855697
\(584\) 0 0
\(585\) 0.492425 0.0203593
\(586\) 0 0
\(587\) 9.23176 0.381036 0.190518 0.981684i \(-0.438983\pi\)
0.190518 + 0.981684i \(0.438983\pi\)
\(588\) 0 0
\(589\) 22.5936 0.930952
\(590\) 0 0
\(591\) −21.5775 −0.887581
\(592\) 0 0
\(593\) 42.6848 1.75285 0.876427 0.481535i \(-0.159920\pi\)
0.876427 + 0.481535i \(0.159920\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −22.6398 −0.926585
\(598\) 0 0
\(599\) −30.3442 −1.23983 −0.619915 0.784669i \(-0.712833\pi\)
−0.619915 + 0.784669i \(0.712833\pi\)
\(600\) 0 0
\(601\) 18.9452 0.772792 0.386396 0.922333i \(-0.373720\pi\)
0.386396 + 0.922333i \(0.373720\pi\)
\(602\) 0 0
\(603\) 0.488727 0.0199025
\(604\) 0 0
\(605\) 5.81845 0.236554
\(606\) 0 0
\(607\) 24.6141 0.999057 0.499529 0.866297i \(-0.333507\pi\)
0.499529 + 0.866297i \(0.333507\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −32.1935 −1.30241
\(612\) 0 0
\(613\) −26.3723 −1.06517 −0.532583 0.846378i \(-0.678779\pi\)
−0.532583 + 0.846378i \(0.678779\pi\)
\(614\) 0 0
\(615\) −1.27327 −0.0513430
\(616\) 0 0
\(617\) 17.8189 0.717361 0.358681 0.933460i \(-0.383227\pi\)
0.358681 + 0.933460i \(0.383227\pi\)
\(618\) 0 0
\(619\) −7.78205 −0.312787 −0.156393 0.987695i \(-0.549987\pi\)
−0.156393 + 0.987695i \(0.549987\pi\)
\(620\) 0 0
\(621\) −24.9824 −1.00251
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 17.5577 0.702309
\(626\) 0 0
\(627\) −19.9488 −0.796677
\(628\) 0 0
\(629\) −7.08712 −0.282582
\(630\) 0 0
\(631\) 38.4583 1.53100 0.765499 0.643437i \(-0.222492\pi\)
0.765499 + 0.643437i \(0.222492\pi\)
\(632\) 0 0
\(633\) −4.56290 −0.181359
\(634\) 0 0
\(635\) 1.56170 0.0619743
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.551889 0.0218324
\(640\) 0 0
\(641\) 27.2535 1.07645 0.538224 0.842802i \(-0.319096\pi\)
0.538224 + 0.842802i \(0.319096\pi\)
\(642\) 0 0
\(643\) 24.3283 0.959414 0.479707 0.877429i \(-0.340743\pi\)
0.479707 + 0.877429i \(0.340743\pi\)
\(644\) 0 0
\(645\) −7.98066 −0.314238
\(646\) 0 0
\(647\) −7.86154 −0.309069 −0.154535 0.987987i \(-0.549388\pi\)
−0.154535 + 0.987987i \(0.549388\pi\)
\(648\) 0 0
\(649\) −2.88131 −0.113101
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −44.8914 −1.75674 −0.878368 0.477986i \(-0.841367\pi\)
−0.878368 + 0.477986i \(0.841367\pi\)
\(654\) 0 0
\(655\) −4.53871 −0.177342
\(656\) 0 0
\(657\) 1.78011 0.0694486
\(658\) 0 0
\(659\) −32.8974 −1.28150 −0.640750 0.767750i \(-0.721376\pi\)
−0.640750 + 0.767750i \(0.721376\pi\)
\(660\) 0 0
\(661\) −27.4082 −1.06606 −0.533028 0.846098i \(-0.678946\pi\)
−0.533028 + 0.846098i \(0.678946\pi\)
\(662\) 0 0
\(663\) 10.6489 0.413567
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3.51541 0.136117
\(668\) 0 0
\(669\) 36.2055 1.39978
\(670\) 0 0
\(671\) 13.1809 0.508843
\(672\) 0 0
\(673\) −11.7433 −0.452673 −0.226336 0.974049i \(-0.572675\pi\)
−0.226336 + 0.974049i \(0.572675\pi\)
\(674\) 0 0
\(675\) −22.6679 −0.872488
\(676\) 0 0
\(677\) 34.8790 1.34051 0.670255 0.742131i \(-0.266185\pi\)
0.670255 + 0.742131i \(0.266185\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 45.9552 1.76101
\(682\) 0 0
\(683\) 28.1265 1.07623 0.538115 0.842871i \(-0.319137\pi\)
0.538115 + 0.842871i \(0.319137\pi\)
\(684\) 0 0
\(685\) −15.0904 −0.576575
\(686\) 0 0
\(687\) −41.2203 −1.57265
\(688\) 0 0
\(689\) 53.7158 2.04641
\(690\) 0 0
\(691\) −22.0866 −0.840216 −0.420108 0.907474i \(-0.638008\pi\)
−0.420108 + 0.907474i \(0.638008\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.63693 0.213821
\(696\) 0 0
\(697\) −1.35813 −0.0514428
\(698\) 0 0
\(699\) −31.7709 −1.20169
\(700\) 0 0
\(701\) 19.4355 0.734067 0.367034 0.930208i \(-0.380373\pi\)
0.367034 + 0.930208i \(0.380373\pi\)
\(702\) 0 0
\(703\) −34.5168 −1.30183
\(704\) 0 0
\(705\) 9.28688 0.349764
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 28.3317 1.06402 0.532010 0.846738i \(-0.321437\pi\)
0.532010 + 0.846738i \(0.321437\pi\)
\(710\) 0 0
\(711\) 1.38620 0.0519865
\(712\) 0 0
\(713\) −16.8885 −0.632478
\(714\) 0 0
\(715\) 5.37109 0.200867
\(716\) 0 0
\(717\) 16.0452 0.599218
\(718\) 0 0
\(719\) −39.2419 −1.46348 −0.731738 0.681586i \(-0.761291\pi\)
−0.731738 + 0.681586i \(0.761291\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 7.09428 0.263839
\(724\) 0 0
\(725\) 3.18972 0.118463
\(726\) 0 0
\(727\) 34.1234 1.26557 0.632784 0.774328i \(-0.281912\pi\)
0.632784 + 0.774328i \(0.281912\pi\)
\(728\) 0 0
\(729\) 25.4576 0.942873
\(730\) 0 0
\(731\) −8.51257 −0.314849
\(732\) 0 0
\(733\) 20.4573 0.755607 0.377804 0.925886i \(-0.376679\pi\)
0.377804 + 0.925886i \(0.376679\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.33075 0.196361
\(738\) 0 0
\(739\) 17.2786 0.635603 0.317801 0.948157i \(-0.397056\pi\)
0.317801 + 0.948157i \(0.397056\pi\)
\(740\) 0 0
\(741\) 51.8637 1.90526
\(742\) 0 0
\(743\) −40.0023 −1.46754 −0.733771 0.679397i \(-0.762241\pi\)
−0.733771 + 0.679397i \(0.762241\pi\)
\(744\) 0 0
\(745\) −6.69149 −0.245157
\(746\) 0 0
\(747\) −1.93276 −0.0707161
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −23.8954 −0.871955 −0.435977 0.899958i \(-0.643597\pi\)
−0.435977 + 0.899958i \(0.643597\pi\)
\(752\) 0 0
\(753\) −46.1667 −1.68241
\(754\) 0 0
\(755\) 1.07654 0.0391793
\(756\) 0 0
\(757\) 18.8809 0.686239 0.343120 0.939292i \(-0.388516\pi\)
0.343120 + 0.939292i \(0.388516\pi\)
\(758\) 0 0
\(759\) 14.9115 0.541253
\(760\) 0 0
\(761\) −36.3709 −1.31844 −0.659222 0.751949i \(-0.729114\pi\)
−0.659222 + 0.751949i \(0.729114\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.151518 −0.00547813
\(766\) 0 0
\(767\) 7.49095 0.270483
\(768\) 0 0
\(769\) 19.8688 0.716488 0.358244 0.933628i \(-0.383376\pi\)
0.358244 + 0.933628i \(0.383376\pi\)
\(770\) 0 0
\(771\) −42.9142 −1.54552
\(772\) 0 0
\(773\) −52.9289 −1.90372 −0.951860 0.306533i \(-0.900831\pi\)
−0.951860 + 0.306533i \(0.900831\pi\)
\(774\) 0 0
\(775\) −15.3238 −0.550448
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.61457 −0.236992
\(780\) 0 0
\(781\) 6.01969 0.215402
\(782\) 0 0
\(783\) −3.59250 −0.128386
\(784\) 0 0
\(785\) −9.74035 −0.347648
\(786\) 0 0
\(787\) −33.5636 −1.19641 −0.598207 0.801341i \(-0.704120\pi\)
−0.598207 + 0.801341i \(0.704120\pi\)
\(788\) 0 0
\(789\) 27.3023 0.971986
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −34.2683 −1.21690
\(794\) 0 0
\(795\) −15.4954 −0.549566
\(796\) 0 0
\(797\) −1.71633 −0.0607957 −0.0303978 0.999538i \(-0.509677\pi\)
−0.0303978 + 0.999538i \(0.509677\pi\)
\(798\) 0 0
\(799\) 9.90585 0.350444
\(800\) 0 0
\(801\) −0.946905 −0.0334572
\(802\) 0 0
\(803\) 19.4164 0.685189
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 24.5924 0.865694
\(808\) 0 0
\(809\) 19.5588 0.687650 0.343825 0.939034i \(-0.388277\pi\)
0.343825 + 0.939034i \(0.388277\pi\)
\(810\) 0 0
\(811\) −9.68156 −0.339966 −0.169983 0.985447i \(-0.554371\pi\)
−0.169983 + 0.985447i \(0.554371\pi\)
\(812\) 0 0
\(813\) −31.1688 −1.09314
\(814\) 0 0
\(815\) −10.1545 −0.355695
\(816\) 0 0
\(817\) −41.4593 −1.45048
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 31.1857 1.08839 0.544195 0.838959i \(-0.316835\pi\)
0.544195 + 0.838959i \(0.316835\pi\)
\(822\) 0 0
\(823\) 19.1768 0.668462 0.334231 0.942491i \(-0.391523\pi\)
0.334231 + 0.942491i \(0.391523\pi\)
\(824\) 0 0
\(825\) 13.5300 0.471055
\(826\) 0 0
\(827\) 11.5616 0.402037 0.201018 0.979587i \(-0.435575\pi\)
0.201018 + 0.979587i \(0.435575\pi\)
\(828\) 0 0
\(829\) 33.7231 1.17125 0.585626 0.810582i \(-0.300849\pi\)
0.585626 + 0.810582i \(0.300849\pi\)
\(830\) 0 0
\(831\) 26.5370 0.920557
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 5.46133 0.188997
\(836\) 0 0
\(837\) 17.2588 0.596552
\(838\) 0 0
\(839\) 6.17987 0.213353 0.106676 0.994294i \(-0.465979\pi\)
0.106676 + 0.994294i \(0.465979\pi\)
\(840\) 0 0
\(841\) −28.4945 −0.982568
\(842\) 0 0
\(843\) 31.7222 1.09257
\(844\) 0 0
\(845\) −4.64610 −0.159831
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −18.6869 −0.641333
\(850\) 0 0
\(851\) 25.8010 0.884445
\(852\) 0 0
\(853\) −1.00381 −0.0343698 −0.0171849 0.999852i \(-0.505470\pi\)
−0.0171849 + 0.999852i \(0.505470\pi\)
\(854\) 0 0
\(855\) −0.737945 −0.0252372
\(856\) 0 0
\(857\) 38.1622 1.30360 0.651798 0.758393i \(-0.274015\pi\)
0.651798 + 0.758393i \(0.274015\pi\)
\(858\) 0 0
\(859\) 26.2597 0.895970 0.447985 0.894041i \(-0.352142\pi\)
0.447985 + 0.894041i \(0.352142\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −5.57453 −0.189759 −0.0948796 0.995489i \(-0.530247\pi\)
−0.0948796 + 0.995489i \(0.530247\pi\)
\(864\) 0 0
\(865\) −4.86300 −0.165347
\(866\) 0 0
\(867\) 26.9224 0.914334
\(868\) 0 0
\(869\) 15.1199 0.512906
\(870\) 0 0
\(871\) −13.8591 −0.469599
\(872\) 0 0
\(873\) −2.48053 −0.0839531
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −21.2734 −0.718353 −0.359177 0.933270i \(-0.616942\pi\)
−0.359177 + 0.933270i \(0.616942\pi\)
\(878\) 0 0
\(879\) 3.70425 0.124941
\(880\) 0 0
\(881\) 15.3317 0.516538 0.258269 0.966073i \(-0.416848\pi\)
0.258269 + 0.966073i \(0.416848\pi\)
\(882\) 0 0
\(883\) 46.6633 1.57034 0.785172 0.619278i \(-0.212574\pi\)
0.785172 + 0.619278i \(0.212574\pi\)
\(884\) 0 0
\(885\) −2.16092 −0.0726385
\(886\) 0 0
\(887\) −48.3270 −1.62266 −0.811332 0.584586i \(-0.801257\pi\)
−0.811332 + 0.584586i \(0.801257\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −16.0313 −0.537067
\(892\) 0 0
\(893\) 48.2450 1.61446
\(894\) 0 0
\(895\) −9.61982 −0.321555
\(896\) 0 0
\(897\) −38.7676 −1.29441
\(898\) 0 0
\(899\) −2.42858 −0.0809978
\(900\) 0 0
\(901\) −16.5282 −0.550633
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 16.8361 0.559649
\(906\) 0 0
\(907\) −41.4253 −1.37550 −0.687752 0.725946i \(-0.741402\pi\)
−0.687752 + 0.725946i \(0.741402\pi\)
\(908\) 0 0
\(909\) 2.35815 0.0782148
\(910\) 0 0
\(911\) 16.6815 0.552682 0.276341 0.961060i \(-0.410878\pi\)
0.276341 + 0.961060i \(0.410878\pi\)
\(912\) 0 0
\(913\) −21.0815 −0.697695
\(914\) 0 0
\(915\) 9.88538 0.326801
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 26.0748 0.860128 0.430064 0.902798i \(-0.358491\pi\)
0.430064 + 0.902798i \(0.358491\pi\)
\(920\) 0 0
\(921\) −55.3202 −1.82286
\(922\) 0 0
\(923\) −15.6503 −0.515135
\(924\) 0 0
\(925\) 23.4106 0.769736
\(926\) 0 0
\(927\) −2.86761 −0.0941848
\(928\) 0 0
\(929\) −5.10830 −0.167598 −0.0837990 0.996483i \(-0.526705\pi\)
−0.0837990 + 0.996483i \(0.526705\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −2.29988 −0.0752948
\(934\) 0 0
\(935\) −1.65267 −0.0540480
\(936\) 0 0
\(937\) 28.5517 0.932743 0.466372 0.884589i \(-0.345561\pi\)
0.466372 + 0.884589i \(0.345561\pi\)
\(938\) 0 0
\(939\) −5.79268 −0.189037
\(940\) 0 0
\(941\) 25.2333 0.822582 0.411291 0.911504i \(-0.365078\pi\)
0.411291 + 0.911504i \(0.365078\pi\)
\(942\) 0 0
\(943\) 4.94432 0.161009
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −14.8090 −0.481226 −0.240613 0.970621i \(-0.577349\pi\)
−0.240613 + 0.970621i \(0.577349\pi\)
\(948\) 0 0
\(949\) −50.4796 −1.63864
\(950\) 0 0
\(951\) −47.3872 −1.53664
\(952\) 0 0
\(953\) −33.0779 −1.07150 −0.535750 0.844377i \(-0.679971\pi\)
−0.535750 + 0.844377i \(0.679971\pi\)
\(954\) 0 0
\(955\) −2.68281 −0.0868137
\(956\) 0 0
\(957\) 2.14429 0.0693152
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −19.3328 −0.623638
\(962\) 0 0
\(963\) −2.49325 −0.0803439
\(964\) 0 0
\(965\) −15.9847 −0.514565
\(966\) 0 0
\(967\) −28.0778 −0.902920 −0.451460 0.892291i \(-0.649097\pi\)
−0.451460 + 0.892291i \(0.649097\pi\)
\(968\) 0 0
\(969\) −15.9583 −0.512655
\(970\) 0 0
\(971\) 37.1577 1.19245 0.596224 0.802818i \(-0.296667\pi\)
0.596224 + 0.802818i \(0.296667\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −35.1759 −1.12653
\(976\) 0 0
\(977\) −53.9199 −1.72505 −0.862526 0.506013i \(-0.831119\pi\)
−0.862526 + 0.506013i \(0.831119\pi\)
\(978\) 0 0
\(979\) −10.3283 −0.330094
\(980\) 0 0
\(981\) 0.870741 0.0278006
\(982\) 0 0
\(983\) −18.1739 −0.579658 −0.289829 0.957078i \(-0.593598\pi\)
−0.289829 + 0.957078i \(0.593598\pi\)
\(984\) 0 0
\(985\) −8.70627 −0.277405
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 30.9904 0.985437
\(990\) 0 0
\(991\) −61.2275 −1.94496 −0.972478 0.232996i \(-0.925147\pi\)
−0.972478 + 0.232996i \(0.925147\pi\)
\(992\) 0 0
\(993\) 27.3496 0.867912
\(994\) 0 0
\(995\) −9.13488 −0.289595
\(996\) 0 0
\(997\) 38.0328 1.20451 0.602256 0.798303i \(-0.294269\pi\)
0.602256 + 0.798303i \(0.294269\pi\)
\(998\) 0 0
\(999\) −26.3667 −0.834207
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 \(a_p\))