Properties

Label 24.8.a.c.1.1
Level 24
Weight 8
Character 24.1
Self dual Yes
Analytic conductor 7.497
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 24.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.49724061162\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 24.1

$q$-expansion

\(f(q)\) \(=\) \(q+27.0000 q^{3} +110.000 q^{5} +504.000 q^{7} +729.000 q^{9} +O(q^{10})\) \(q+27.0000 q^{3} +110.000 q^{5} +504.000 q^{7} +729.000 q^{9} +3812.00 q^{11} +9574.00 q^{13} +2970.00 q^{15} +26098.0 q^{17} -38308.0 q^{19} +13608.0 q^{21} -71128.0 q^{23} -66025.0 q^{25} +19683.0 q^{27} +74262.0 q^{29} -275680. q^{31} +102924. q^{33} +55440.0 q^{35} -266610. q^{37} +258498. q^{39} +684762. q^{41} +245956. q^{43} +80190.0 q^{45} +478800. q^{47} -569527. q^{49} +704646. q^{51} -569410. q^{53} +419320. q^{55} -1.03432e6 q^{57} -1.52532e6 q^{59} -2.64046e6 q^{61} +367416. q^{63} +1.05314e6 q^{65} +1.41624e6 q^{67} -1.92046e6 q^{69} -3.51130e6 q^{71} +4.73862e6 q^{73} -1.78268e6 q^{75} +1.92125e6 q^{77} +4.66149e6 q^{79} +531441. q^{81} -5.72925e6 q^{83} +2.87078e6 q^{85} +2.00507e6 q^{87} +1.19935e7 q^{89} +4.82530e6 q^{91} -7.44336e6 q^{93} -4.21388e6 q^{95} +7.15075e6 q^{97} +2.77895e6 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 27.0000 0.577350
\(4\) 0 0
\(5\) 110.000 0.393548 0.196774 0.980449i \(-0.436953\pi\)
0.196774 + 0.980449i \(0.436953\pi\)
\(6\) 0 0
\(7\) 504.000 0.555376 0.277688 0.960671i \(-0.410432\pi\)
0.277688 + 0.960671i \(0.410432\pi\)
\(8\) 0 0
\(9\) 729.000 0.333333
\(10\) 0 0
\(11\) 3812.00 0.863532 0.431766 0.901986i \(-0.357891\pi\)
0.431766 + 0.901986i \(0.357891\pi\)
\(12\) 0 0
\(13\) 9574.00 1.20863 0.604313 0.796747i \(-0.293448\pi\)
0.604313 + 0.796747i \(0.293448\pi\)
\(14\) 0 0
\(15\) 2970.00 0.227215
\(16\) 0 0
\(17\) 26098.0 1.28836 0.644178 0.764875i \(-0.277200\pi\)
0.644178 + 0.764875i \(0.277200\pi\)
\(18\) 0 0
\(19\) −38308.0 −1.28130 −0.640652 0.767832i \(-0.721336\pi\)
−0.640652 + 0.767832i \(0.721336\pi\)
\(20\) 0 0
\(21\) 13608.0 0.320647
\(22\) 0 0
\(23\) −71128.0 −1.21897 −0.609485 0.792797i \(-0.708624\pi\)
−0.609485 + 0.792797i \(0.708624\pi\)
\(24\) 0 0
\(25\) −66025.0 −0.845120
\(26\) 0 0
\(27\) 19683.0 0.192450
\(28\) 0 0
\(29\) 74262.0 0.565423 0.282712 0.959205i \(-0.408766\pi\)
0.282712 + 0.959205i \(0.408766\pi\)
\(30\) 0 0
\(31\) −275680. −1.66203 −0.831016 0.556249i \(-0.812240\pi\)
−0.831016 + 0.556249i \(0.812240\pi\)
\(32\) 0 0
\(33\) 102924. 0.498560
\(34\) 0 0
\(35\) 55440.0 0.218567
\(36\) 0 0
\(37\) −266610. −0.865307 −0.432654 0.901560i \(-0.642423\pi\)
−0.432654 + 0.901560i \(0.642423\pi\)
\(38\) 0 0
\(39\) 258498. 0.697800
\(40\) 0 0
\(41\) 684762. 1.55166 0.775829 0.630943i \(-0.217332\pi\)
0.775829 + 0.630943i \(0.217332\pi\)
\(42\) 0 0
\(43\) 245956. 0.471756 0.235878 0.971783i \(-0.424203\pi\)
0.235878 + 0.971783i \(0.424203\pi\)
\(44\) 0 0
\(45\) 80190.0 0.131183
\(46\) 0 0
\(47\) 478800. 0.672685 0.336342 0.941740i \(-0.390810\pi\)
0.336342 + 0.941740i \(0.390810\pi\)
\(48\) 0 0
\(49\) −569527. −0.691557
\(50\) 0 0
\(51\) 704646. 0.743833
\(52\) 0 0
\(53\) −569410. −0.525363 −0.262682 0.964883i \(-0.584607\pi\)
−0.262682 + 0.964883i \(0.584607\pi\)
\(54\) 0 0
\(55\) 419320. 0.339841
\(56\) 0 0
\(57\) −1.03432e6 −0.739761
\(58\) 0 0
\(59\) −1.52532e6 −0.966897 −0.483448 0.875373i \(-0.660616\pi\)
−0.483448 + 0.875373i \(0.660616\pi\)
\(60\) 0 0
\(61\) −2.64046e6 −1.48945 −0.744723 0.667374i \(-0.767418\pi\)
−0.744723 + 0.667374i \(0.767418\pi\)
\(62\) 0 0
\(63\) 367416. 0.185125
\(64\) 0 0
\(65\) 1.05314e6 0.475652
\(66\) 0 0
\(67\) 1.41624e6 0.575273 0.287636 0.957740i \(-0.407131\pi\)
0.287636 + 0.957740i \(0.407131\pi\)
\(68\) 0 0
\(69\) −1.92046e6 −0.703773
\(70\) 0 0
\(71\) −3.51130e6 −1.16430 −0.582149 0.813082i \(-0.697788\pi\)
−0.582149 + 0.813082i \(0.697788\pi\)
\(72\) 0 0
\(73\) 4.73862e6 1.42568 0.712839 0.701327i \(-0.247409\pi\)
0.712839 + 0.701327i \(0.247409\pi\)
\(74\) 0 0
\(75\) −1.78268e6 −0.487930
\(76\) 0 0
\(77\) 1.92125e6 0.479585
\(78\) 0 0
\(79\) 4.66149e6 1.06373 0.531863 0.846830i \(-0.321492\pi\)
0.531863 + 0.846830i \(0.321492\pi\)
\(80\) 0 0
\(81\) 531441. 0.111111
\(82\) 0 0
\(83\) −5.72925e6 −1.09983 −0.549914 0.835221i \(-0.685339\pi\)
−0.549914 + 0.835221i \(0.685339\pi\)
\(84\) 0 0
\(85\) 2.87078e6 0.507030
\(86\) 0 0
\(87\) 2.00507e6 0.326447
\(88\) 0 0
\(89\) 1.19935e7 1.80336 0.901678 0.432408i \(-0.142336\pi\)
0.901678 + 0.432408i \(0.142336\pi\)
\(90\) 0 0
\(91\) 4.82530e6 0.671242
\(92\) 0 0
\(93\) −7.44336e6 −0.959575
\(94\) 0 0
\(95\) −4.21388e6 −0.504254
\(96\) 0 0
\(97\) 7.15075e6 0.795519 0.397760 0.917490i \(-0.369788\pi\)
0.397760 + 0.917490i \(0.369788\pi\)
\(98\) 0 0
\(99\) 2.77895e6 0.287844
\(100\) 0 0
\(101\) −8.78373e6 −0.848309 −0.424155 0.905590i \(-0.639429\pi\)
−0.424155 + 0.905590i \(0.639429\pi\)
\(102\) 0 0
\(103\) −8.01610e6 −0.722825 −0.361412 0.932406i \(-0.617705\pi\)
−0.361412 + 0.932406i \(0.617705\pi\)
\(104\) 0 0
\(105\) 1.49688e6 0.126190
\(106\) 0 0
\(107\) −5.15123e6 −0.406507 −0.203253 0.979126i \(-0.565151\pi\)
−0.203253 + 0.979126i \(0.565151\pi\)
\(108\) 0 0
\(109\) −2.41280e7 −1.78455 −0.892274 0.451493i \(-0.850891\pi\)
−0.892274 + 0.451493i \(0.850891\pi\)
\(110\) 0 0
\(111\) −7.19847e6 −0.499585
\(112\) 0 0
\(113\) 2.04827e6 0.133541 0.0667703 0.997768i \(-0.478731\pi\)
0.0667703 + 0.997768i \(0.478731\pi\)
\(114\) 0 0
\(115\) −7.82408e6 −0.479723
\(116\) 0 0
\(117\) 6.97945e6 0.402875
\(118\) 0 0
\(119\) 1.31534e7 0.715523
\(120\) 0 0
\(121\) −4.95583e6 −0.254312
\(122\) 0 0
\(123\) 1.84886e7 0.895850
\(124\) 0 0
\(125\) −1.58565e7 −0.726143
\(126\) 0 0
\(127\) 1.36634e6 0.0591895 0.0295947 0.999562i \(-0.490578\pi\)
0.0295947 + 0.999562i \(0.490578\pi\)
\(128\) 0 0
\(129\) 6.64081e6 0.272369
\(130\) 0 0
\(131\) 3.84645e7 1.49489 0.747447 0.664321i \(-0.231279\pi\)
0.747447 + 0.664321i \(0.231279\pi\)
\(132\) 0 0
\(133\) −1.93072e7 −0.711605
\(134\) 0 0
\(135\) 2.16513e6 0.0757383
\(136\) 0 0
\(137\) 7.62585e6 0.253376 0.126688 0.991943i \(-0.459565\pi\)
0.126688 + 0.991943i \(0.459565\pi\)
\(138\) 0 0
\(139\) 5.32324e6 0.168122 0.0840609 0.996461i \(-0.473211\pi\)
0.0840609 + 0.996461i \(0.473211\pi\)
\(140\) 0 0
\(141\) 1.29276e7 0.388375
\(142\) 0 0
\(143\) 3.64961e7 1.04369
\(144\) 0 0
\(145\) 8.16882e6 0.222521
\(146\) 0 0
\(147\) −1.53772e7 −0.399271
\(148\) 0 0
\(149\) 7.61366e6 0.188557 0.0942783 0.995546i \(-0.469946\pi\)
0.0942783 + 0.995546i \(0.469946\pi\)
\(150\) 0 0
\(151\) −2.50221e7 −0.591432 −0.295716 0.955276i \(-0.595558\pi\)
−0.295716 + 0.955276i \(0.595558\pi\)
\(152\) 0 0
\(153\) 1.90254e7 0.429452
\(154\) 0 0
\(155\) −3.03248e7 −0.654089
\(156\) 0 0
\(157\) 3.93145e7 0.810782 0.405391 0.914143i \(-0.367135\pi\)
0.405391 + 0.914143i \(0.367135\pi\)
\(158\) 0 0
\(159\) −1.53741e7 −0.303319
\(160\) 0 0
\(161\) −3.58485e7 −0.676987
\(162\) 0 0
\(163\) −6.28387e7 −1.13650 −0.568252 0.822855i \(-0.692380\pi\)
−0.568252 + 0.822855i \(0.692380\pi\)
\(164\) 0 0
\(165\) 1.13216e7 0.196207
\(166\) 0 0
\(167\) 1.04133e7 0.173014 0.0865072 0.996251i \(-0.472429\pi\)
0.0865072 + 0.996251i \(0.472429\pi\)
\(168\) 0 0
\(169\) 2.89130e7 0.460775
\(170\) 0 0
\(171\) −2.79265e7 −0.427101
\(172\) 0 0
\(173\) −8.03551e7 −1.17992 −0.589959 0.807433i \(-0.700856\pi\)
−0.589959 + 0.807433i \(0.700856\pi\)
\(174\) 0 0
\(175\) −3.32766e7 −0.469360
\(176\) 0 0
\(177\) −4.11837e7 −0.558238
\(178\) 0 0
\(179\) −8.40084e7 −1.09481 −0.547403 0.836869i \(-0.684383\pi\)
−0.547403 + 0.836869i \(0.684383\pi\)
\(180\) 0 0
\(181\) 1.15469e8 1.44741 0.723703 0.690112i \(-0.242439\pi\)
0.723703 + 0.690112i \(0.242439\pi\)
\(182\) 0 0
\(183\) −7.12924e7 −0.859932
\(184\) 0 0
\(185\) −2.93271e7 −0.340540
\(186\) 0 0
\(187\) 9.94856e7 1.11254
\(188\) 0 0
\(189\) 9.92023e6 0.106882
\(190\) 0 0
\(191\) 9.97154e7 1.03549 0.517744 0.855535i \(-0.326772\pi\)
0.517744 + 0.855535i \(0.326772\pi\)
\(192\) 0 0
\(193\) −1.86157e7 −0.186393 −0.0931965 0.995648i \(-0.529708\pi\)
−0.0931965 + 0.995648i \(0.529708\pi\)
\(194\) 0 0
\(195\) 2.84348e7 0.274618
\(196\) 0 0
\(197\) 9.30384e7 0.867022 0.433511 0.901148i \(-0.357274\pi\)
0.433511 + 0.901148i \(0.357274\pi\)
\(198\) 0 0
\(199\) 7.39686e7 0.665367 0.332684 0.943038i \(-0.392046\pi\)
0.332684 + 0.943038i \(0.392046\pi\)
\(200\) 0 0
\(201\) 3.82384e7 0.332134
\(202\) 0 0
\(203\) 3.74280e7 0.314023
\(204\) 0 0
\(205\) 7.53238e7 0.610652
\(206\) 0 0
\(207\) −5.18523e7 −0.406323
\(208\) 0 0
\(209\) −1.46030e8 −1.10645
\(210\) 0 0
\(211\) 1.85163e8 1.35695 0.678476 0.734623i \(-0.262641\pi\)
0.678476 + 0.734623i \(0.262641\pi\)
\(212\) 0 0
\(213\) −9.48052e7 −0.672208
\(214\) 0 0
\(215\) 2.70552e7 0.185659
\(216\) 0 0
\(217\) −1.38943e8 −0.923053
\(218\) 0 0
\(219\) 1.27943e8 0.823116
\(220\) 0 0
\(221\) 2.49862e8 1.55714
\(222\) 0 0
\(223\) −1.20862e8 −0.729830 −0.364915 0.931041i \(-0.618902\pi\)
−0.364915 + 0.931041i \(0.618902\pi\)
\(224\) 0 0
\(225\) −4.81322e7 −0.281707
\(226\) 0 0
\(227\) −2.82315e8 −1.60193 −0.800966 0.598710i \(-0.795680\pi\)
−0.800966 + 0.598710i \(0.795680\pi\)
\(228\) 0 0
\(229\) −8.91913e7 −0.490793 −0.245397 0.969423i \(-0.578918\pi\)
−0.245397 + 0.969423i \(0.578918\pi\)
\(230\) 0 0
\(231\) 5.18737e7 0.276889
\(232\) 0 0
\(233\) −2.32240e8 −1.20279 −0.601396 0.798951i \(-0.705389\pi\)
−0.601396 + 0.798951i \(0.705389\pi\)
\(234\) 0 0
\(235\) 5.26680e7 0.264734
\(236\) 0 0
\(237\) 1.25860e8 0.614142
\(238\) 0 0
\(239\) 3.21986e8 1.52561 0.762807 0.646626i \(-0.223821\pi\)
0.762807 + 0.646626i \(0.223821\pi\)
\(240\) 0 0
\(241\) −2.00366e8 −0.922072 −0.461036 0.887381i \(-0.652522\pi\)
−0.461036 + 0.887381i \(0.652522\pi\)
\(242\) 0 0
\(243\) 1.43489e7 0.0641500
\(244\) 0 0
\(245\) −6.26480e7 −0.272161
\(246\) 0 0
\(247\) −3.66761e8 −1.54862
\(248\) 0 0
\(249\) −1.54690e8 −0.634986
\(250\) 0 0
\(251\) −8.70560e7 −0.347489 −0.173744 0.984791i \(-0.555587\pi\)
−0.173744 + 0.984791i \(0.555587\pi\)
\(252\) 0 0
\(253\) −2.71140e8 −1.05262
\(254\) 0 0
\(255\) 7.75111e7 0.292734
\(256\) 0 0
\(257\) 5.22879e8 1.92148 0.960738 0.277457i \(-0.0894915\pi\)
0.960738 + 0.277457i \(0.0894915\pi\)
\(258\) 0 0
\(259\) −1.34371e8 −0.480571
\(260\) 0 0
\(261\) 5.41370e7 0.188474
\(262\) 0 0
\(263\) −4.06215e8 −1.37693 −0.688464 0.725270i \(-0.741715\pi\)
−0.688464 + 0.725270i \(0.741715\pi\)
\(264\) 0 0
\(265\) −6.26351e7 −0.206756
\(266\) 0 0
\(267\) 3.23825e8 1.04117
\(268\) 0 0
\(269\) 3.82347e8 1.19764 0.598818 0.800885i \(-0.295637\pi\)
0.598818 + 0.800885i \(0.295637\pi\)
\(270\) 0 0
\(271\) 2.84165e8 0.867317 0.433658 0.901077i \(-0.357222\pi\)
0.433658 + 0.901077i \(0.357222\pi\)
\(272\) 0 0
\(273\) 1.30283e8 0.387542
\(274\) 0 0
\(275\) −2.51687e8 −0.729788
\(276\) 0 0
\(277\) 2.93752e8 0.830427 0.415213 0.909724i \(-0.363707\pi\)
0.415213 + 0.909724i \(0.363707\pi\)
\(278\) 0 0
\(279\) −2.00971e8 −0.554011
\(280\) 0 0
\(281\) 4.15399e8 1.11685 0.558424 0.829556i \(-0.311406\pi\)
0.558424 + 0.829556i \(0.311406\pi\)
\(282\) 0 0
\(283\) 5.06429e7 0.132821 0.0664104 0.997792i \(-0.478845\pi\)
0.0664104 + 0.997792i \(0.478845\pi\)
\(284\) 0 0
\(285\) −1.13775e8 −0.291131
\(286\) 0 0
\(287\) 3.45120e8 0.861754
\(288\) 0 0
\(289\) 2.70767e8 0.659862
\(290\) 0 0
\(291\) 1.93070e8 0.459293
\(292\) 0 0
\(293\) 7.47714e7 0.173660 0.0868298 0.996223i \(-0.472326\pi\)
0.0868298 + 0.996223i \(0.472326\pi\)
\(294\) 0 0
\(295\) −1.67786e8 −0.380520
\(296\) 0 0
\(297\) 7.50316e7 0.166187
\(298\) 0 0
\(299\) −6.80979e8 −1.47328
\(300\) 0 0
\(301\) 1.23962e8 0.262002
\(302\) 0 0
\(303\) −2.37161e8 −0.489772
\(304\) 0 0
\(305\) −2.90450e8 −0.586169
\(306\) 0 0
\(307\) 8.52577e7 0.168170 0.0840851 0.996459i \(-0.473203\pi\)
0.0840851 + 0.996459i \(0.473203\pi\)
\(308\) 0 0
\(309\) −2.16435e8 −0.417323
\(310\) 0 0
\(311\) 9.39129e8 1.77037 0.885184 0.465240i \(-0.154032\pi\)
0.885184 + 0.465240i \(0.154032\pi\)
\(312\) 0 0
\(313\) −3.43040e8 −0.632323 −0.316162 0.948705i \(-0.602394\pi\)
−0.316162 + 0.948705i \(0.602394\pi\)
\(314\) 0 0
\(315\) 4.04158e7 0.0728557
\(316\) 0 0
\(317\) −1.03960e9 −1.83298 −0.916492 0.400054i \(-0.868991\pi\)
−0.916492 + 0.400054i \(0.868991\pi\)
\(318\) 0 0
\(319\) 2.83087e8 0.488261
\(320\) 0 0
\(321\) −1.39083e8 −0.234697
\(322\) 0 0
\(323\) −9.99762e8 −1.65077
\(324\) 0 0
\(325\) −6.32123e8 −1.02143
\(326\) 0 0
\(327\) −6.51456e8 −1.03031
\(328\) 0 0
\(329\) 2.41315e8 0.373593
\(330\) 0 0
\(331\) 1.10022e9 1.66756 0.833779 0.552098i \(-0.186173\pi\)
0.833779 + 0.552098i \(0.186173\pi\)
\(332\) 0 0
\(333\) −1.94359e8 −0.288436
\(334\) 0 0
\(335\) 1.55786e8 0.226397
\(336\) 0 0
\(337\) 1.28272e9 1.82569 0.912847 0.408302i \(-0.133879\pi\)
0.912847 + 0.408302i \(0.133879\pi\)
\(338\) 0 0
\(339\) 5.53034e7 0.0770997
\(340\) 0 0
\(341\) −1.05089e9 −1.43522
\(342\) 0 0
\(343\) −7.02107e8 −0.939451
\(344\) 0 0
\(345\) −2.11250e8 −0.276968
\(346\) 0 0
\(347\) 1.25822e9 1.61660 0.808301 0.588770i \(-0.200388\pi\)
0.808301 + 0.588770i \(0.200388\pi\)
\(348\) 0 0
\(349\) 1.35371e8 0.170465 0.0852327 0.996361i \(-0.472837\pi\)
0.0852327 + 0.996361i \(0.472837\pi\)
\(350\) 0 0
\(351\) 1.88445e8 0.232600
\(352\) 0 0
\(353\) −8.49221e8 −1.02756 −0.513782 0.857921i \(-0.671756\pi\)
−0.513782 + 0.857921i \(0.671756\pi\)
\(354\) 0 0
\(355\) −3.86243e8 −0.458207
\(356\) 0 0
\(357\) 3.55142e8 0.413107
\(358\) 0 0
\(359\) 2.20121e8 0.251091 0.125546 0.992088i \(-0.459932\pi\)
0.125546 + 0.992088i \(0.459932\pi\)
\(360\) 0 0
\(361\) 5.73631e8 0.641738
\(362\) 0 0
\(363\) −1.33807e8 −0.146827
\(364\) 0 0
\(365\) 5.21248e8 0.561073
\(366\) 0 0
\(367\) 4.66505e8 0.492635 0.246317 0.969189i \(-0.420779\pi\)
0.246317 + 0.969189i \(0.420779\pi\)
\(368\) 0 0
\(369\) 4.99191e8 0.517220
\(370\) 0 0
\(371\) −2.86983e8 −0.291774
\(372\) 0 0
\(373\) −2.98453e8 −0.297780 −0.148890 0.988854i \(-0.547570\pi\)
−0.148890 + 0.988854i \(0.547570\pi\)
\(374\) 0 0
\(375\) −4.28125e8 −0.419239
\(376\) 0 0
\(377\) 7.10984e8 0.683385
\(378\) 0 0
\(379\) 1.46218e9 1.37964 0.689818 0.723983i \(-0.257691\pi\)
0.689818 + 0.723983i \(0.257691\pi\)
\(380\) 0 0
\(381\) 3.68911e7 0.0341731
\(382\) 0 0
\(383\) 1.58702e9 1.44340 0.721700 0.692206i \(-0.243361\pi\)
0.721700 + 0.692206i \(0.243361\pi\)
\(384\) 0 0
\(385\) 2.11337e8 0.188740
\(386\) 0 0
\(387\) 1.79302e8 0.157252
\(388\) 0 0
\(389\) −3.14439e8 −0.270840 −0.135420 0.990788i \(-0.543238\pi\)
−0.135420 + 0.990788i \(0.543238\pi\)
\(390\) 0 0
\(391\) −1.85630e9 −1.57047
\(392\) 0 0
\(393\) 1.03854e9 0.863078
\(394\) 0 0
\(395\) 5.12764e8 0.418627
\(396\) 0 0
\(397\) −8.52757e8 −0.684004 −0.342002 0.939699i \(-0.611105\pi\)
−0.342002 + 0.939699i \(0.611105\pi\)
\(398\) 0 0
\(399\) −5.21295e8 −0.410846
\(400\) 0 0
\(401\) 6.92522e8 0.536325 0.268163 0.963374i \(-0.413584\pi\)
0.268163 + 0.963374i \(0.413584\pi\)
\(402\) 0 0
\(403\) −2.63936e9 −2.00877
\(404\) 0 0
\(405\) 5.84585e7 0.0437276
\(406\) 0 0
\(407\) −1.01632e9 −0.747221
\(408\) 0 0
\(409\) 6.17357e8 0.446174 0.223087 0.974799i \(-0.428387\pi\)
0.223087 + 0.974799i \(0.428387\pi\)
\(410\) 0 0
\(411\) 2.05898e8 0.146287
\(412\) 0 0
\(413\) −7.68763e8 −0.536992
\(414\) 0 0
\(415\) −6.30218e8 −0.432835
\(416\) 0 0
\(417\) 1.43727e8 0.0970651
\(418\) 0 0
\(419\) −1.65512e9 −1.09921 −0.549604 0.835425i \(-0.685221\pi\)
−0.549604 + 0.835425i \(0.685221\pi\)
\(420\) 0 0
\(421\) 7.01472e7 0.0458166 0.0229083 0.999738i \(-0.492707\pi\)
0.0229083 + 0.999738i \(0.492707\pi\)
\(422\) 0 0
\(423\) 3.49045e8 0.224228
\(424\) 0 0
\(425\) −1.72312e9 −1.08882
\(426\) 0 0
\(427\) −1.33079e9 −0.827203
\(428\) 0 0
\(429\) 9.85394e8 0.602573
\(430\) 0 0
\(431\) 1.81387e9 1.09128 0.545640 0.838020i \(-0.316287\pi\)
0.545640 + 0.838020i \(0.316287\pi\)
\(432\) 0 0
\(433\) −2.59970e9 −1.53892 −0.769460 0.638695i \(-0.779475\pi\)
−0.769460 + 0.638695i \(0.779475\pi\)
\(434\) 0 0
\(435\) 2.20558e8 0.128473
\(436\) 0 0
\(437\) 2.72477e9 1.56187
\(438\) 0 0
\(439\) −1.67431e9 −0.944517 −0.472258 0.881460i \(-0.656561\pi\)
−0.472258 + 0.881460i \(0.656561\pi\)
\(440\) 0 0
\(441\) −4.15185e8 −0.230519
\(442\) 0 0
\(443\) −2.52711e8 −0.138105 −0.0690527 0.997613i \(-0.521998\pi\)
−0.0690527 + 0.997613i \(0.521998\pi\)
\(444\) 0 0
\(445\) 1.31929e9 0.709707
\(446\) 0 0
\(447\) 2.05569e8 0.108863
\(448\) 0 0
\(449\) 7.55311e8 0.393789 0.196895 0.980425i \(-0.436914\pi\)
0.196895 + 0.980425i \(0.436914\pi\)
\(450\) 0 0
\(451\) 2.61031e9 1.33991
\(452\) 0 0
\(453\) −6.75597e8 −0.341463
\(454\) 0 0
\(455\) 5.30783e8 0.264166
\(456\) 0 0
\(457\) −1.51584e8 −0.0742928 −0.0371464 0.999310i \(-0.511827\pi\)
−0.0371464 + 0.999310i \(0.511827\pi\)
\(458\) 0 0
\(459\) 5.13687e8 0.247944
\(460\) 0 0
\(461\) −7.78405e8 −0.370043 −0.185022 0.982734i \(-0.559236\pi\)
−0.185022 + 0.982734i \(0.559236\pi\)
\(462\) 0 0
\(463\) 2.41052e9 1.12870 0.564349 0.825536i \(-0.309127\pi\)
0.564349 + 0.825536i \(0.309127\pi\)
\(464\) 0 0
\(465\) −8.18770e8 −0.377639
\(466\) 0 0
\(467\) −1.76192e9 −0.800527 −0.400264 0.916400i \(-0.631081\pi\)
−0.400264 + 0.916400i \(0.631081\pi\)
\(468\) 0 0
\(469\) 7.13783e8 0.319493
\(470\) 0 0
\(471\) 1.06149e9 0.468105
\(472\) 0 0
\(473\) 9.37584e8 0.407377
\(474\) 0 0
\(475\) 2.52929e9 1.08285
\(476\) 0 0
\(477\) −4.15100e8 −0.175121
\(478\) 0 0
\(479\) 6.43811e8 0.267661 0.133830 0.991004i \(-0.457272\pi\)
0.133830 + 0.991004i \(0.457272\pi\)
\(480\) 0 0
\(481\) −2.55252e9 −1.04583
\(482\) 0 0
\(483\) −9.67910e8 −0.390859
\(484\) 0 0
\(485\) 7.86583e8 0.313075
\(486\) 0 0
\(487\) 3.16421e9 1.24141 0.620704 0.784045i \(-0.286847\pi\)
0.620704 + 0.784045i \(0.286847\pi\)
\(488\) 0 0
\(489\) −1.69665e9 −0.656160
\(490\) 0 0
\(491\) 3.62406e9 1.38169 0.690844 0.723004i \(-0.257239\pi\)
0.690844 + 0.723004i \(0.257239\pi\)
\(492\) 0 0
\(493\) 1.93809e9 0.728467
\(494\) 0 0
\(495\) 3.05684e8 0.113280
\(496\) 0 0
\(497\) −1.76970e9 −0.646624
\(498\) 0 0
\(499\) −1.35483e9 −0.488128 −0.244064 0.969759i \(-0.578481\pi\)
−0.244064 + 0.969759i \(0.578481\pi\)
\(500\) 0 0
\(501\) 2.81160e8 0.0998899
\(502\) 0 0
\(503\) −4.66389e9 −1.63403 −0.817015 0.576616i \(-0.804373\pi\)
−0.817015 + 0.576616i \(0.804373\pi\)
\(504\) 0 0
\(505\) −9.66210e8 −0.333850
\(506\) 0 0
\(507\) 7.80650e8 0.266029
\(508\) 0 0
\(509\) −1.34292e9 −0.451376 −0.225688 0.974200i \(-0.572463\pi\)
−0.225688 + 0.974200i \(0.572463\pi\)
\(510\) 0 0
\(511\) 2.38826e9 0.791788
\(512\) 0 0
\(513\) −7.54016e8 −0.246587
\(514\) 0 0
\(515\) −8.81771e8 −0.284466
\(516\) 0 0
\(517\) 1.82519e9 0.580885
\(518\) 0 0
\(519\) −2.16959e9 −0.681226
\(520\) 0 0
\(521\) −1.45400e9 −0.450435 −0.225217 0.974309i \(-0.572309\pi\)
−0.225217 + 0.974309i \(0.572309\pi\)
\(522\) 0 0
\(523\) 4.90309e8 0.149870 0.0749349 0.997188i \(-0.476125\pi\)
0.0749349 + 0.997188i \(0.476125\pi\)
\(524\) 0 0
\(525\) −8.98468e8 −0.270985
\(526\) 0 0
\(527\) −7.19470e9 −2.14129
\(528\) 0 0
\(529\) 1.65437e9 0.485889
\(530\) 0 0
\(531\) −1.11196e9 −0.322299
\(532\) 0 0
\(533\) 6.55591e9 1.87537
\(534\) 0 0
\(535\) −5.66635e8 −0.159980
\(536\) 0 0
\(537\) −2.26823e9 −0.632086
\(538\) 0 0
\(539\) −2.17104e9 −0.597182
\(540\) 0 0
\(541\) −4.82889e9 −1.31116 −0.655582 0.755124i \(-0.727577\pi\)
−0.655582 + 0.755124i \(0.727577\pi\)
\(542\) 0 0
\(543\) 3.11766e9 0.835660
\(544\) 0 0
\(545\) −2.65408e9 −0.702306
\(546\) 0 0
\(547\) −3.08793e9 −0.806698 −0.403349 0.915046i \(-0.632154\pi\)
−0.403349 + 0.915046i \(0.632154\pi\)
\(548\) 0 0
\(549\) −1.92489e9 −0.496482
\(550\) 0 0
\(551\) −2.84483e9 −0.724479
\(552\) 0 0
\(553\) 2.34939e9 0.590768
\(554\) 0 0
\(555\) −7.91832e8 −0.196611
\(556\) 0 0
\(557\) 4.09889e9 1.00502 0.502508 0.864573i \(-0.332411\pi\)
0.502508 + 0.864573i \(0.332411\pi\)
\(558\) 0 0
\(559\) 2.35478e9 0.570177
\(560\) 0 0
\(561\) 2.68611e9 0.642324
\(562\) 0 0
\(563\) 4.97105e9 1.17400 0.587001 0.809587i \(-0.300309\pi\)
0.587001 + 0.809587i \(0.300309\pi\)
\(564\) 0 0
\(565\) 2.25310e8 0.0525547
\(566\) 0 0
\(567\) 2.67846e8 0.0617085
\(568\) 0 0
\(569\) 3.71316e9 0.844988 0.422494 0.906366i \(-0.361155\pi\)
0.422494 + 0.906366i \(0.361155\pi\)
\(570\) 0 0
\(571\) −2.36205e9 −0.530961 −0.265481 0.964116i \(-0.585531\pi\)
−0.265481 + 0.964116i \(0.585531\pi\)
\(572\) 0 0
\(573\) 2.69232e9 0.597840
\(574\) 0 0
\(575\) 4.69623e9 1.03018
\(576\) 0 0
\(577\) −1.81146e8 −0.0392566 −0.0196283 0.999807i \(-0.506248\pi\)
−0.0196283 + 0.999807i \(0.506248\pi\)
\(578\) 0 0
\(579\) −5.02625e8 −0.107614
\(580\) 0 0
\(581\) −2.88754e9 −0.610818
\(582\) 0 0
\(583\) −2.17059e9 −0.453668
\(584\) 0 0
\(585\) 7.67739e8 0.158551
\(586\) 0 0
\(587\) 2.31976e9 0.473380 0.236690 0.971585i \(-0.423937\pi\)
0.236690 + 0.971585i \(0.423937\pi\)
\(588\) 0 0
\(589\) 1.05607e10 2.12957
\(590\) 0 0
\(591\) 2.51204e9 0.500576
\(592\) 0 0
\(593\) 2.27806e9 0.448615 0.224308 0.974518i \(-0.427988\pi\)
0.224308 + 0.974518i \(0.427988\pi\)
\(594\) 0 0
\(595\) 1.44687e9 0.281592
\(596\) 0 0
\(597\) 1.99715e9 0.384150
\(598\) 0 0
\(599\) −4.88253e9 −0.928220 −0.464110 0.885778i \(-0.653626\pi\)
−0.464110 + 0.885778i \(0.653626\pi\)
\(600\) 0 0
\(601\) −6.74758e9 −1.26791 −0.633954 0.773371i \(-0.718569\pi\)
−0.633954 + 0.773371i \(0.718569\pi\)
\(602\) 0 0
\(603\) 1.03244e9 0.191758
\(604\) 0 0
\(605\) −5.45141e8 −0.100084
\(606\) 0 0
\(607\) −9.05928e9 −1.64412 −0.822060 0.569401i \(-0.807175\pi\)
−0.822060 + 0.569401i \(0.807175\pi\)
\(608\) 0 0
\(609\) 1.01056e9 0.181301
\(610\) 0 0
\(611\) 4.58403e9 0.813024
\(612\) 0 0
\(613\) −8.48777e9 −1.48827 −0.744135 0.668029i \(-0.767138\pi\)
−0.744135 + 0.668029i \(0.767138\pi\)
\(614\) 0 0
\(615\) 2.03374e9 0.352560
\(616\) 0 0
\(617\) 2.34407e9 0.401766 0.200883 0.979615i \(-0.435619\pi\)
0.200883 + 0.979615i \(0.435619\pi\)
\(618\) 0 0
\(619\) −1.01541e9 −0.172077 −0.0860384 0.996292i \(-0.527421\pi\)
−0.0860384 + 0.996292i \(0.527421\pi\)
\(620\) 0 0
\(621\) −1.40001e9 −0.234591
\(622\) 0 0
\(623\) 6.04473e9 1.00154
\(624\) 0 0
\(625\) 3.41399e9 0.559348
\(626\) 0 0
\(627\) −3.94281e9 −0.638807
\(628\) 0 0
\(629\) −6.95799e9 −1.11482
\(630\) 0 0
\(631\) 7.01911e9 1.11219 0.556095 0.831119i \(-0.312299\pi\)
0.556095 + 0.831119i \(0.312299\pi\)
\(632\) 0 0
\(633\) 4.99939e9 0.783437
\(634\) 0 0
\(635\) 1.50297e8 0.0232939
\(636\) 0 0
\(637\) −5.45265e9 −0.835833
\(638\) 0 0
\(639\) −2.55974e9 −0.388099
\(640\) 0 0
\(641\) −4.52776e9 −0.679016 −0.339508 0.940603i \(-0.610261\pi\)
−0.339508 + 0.940603i \(0.610261\pi\)
\(642\) 0 0
\(643\) −8.63094e9 −1.28032 −0.640162 0.768240i \(-0.721133\pi\)
−0.640162 + 0.768240i \(0.721133\pi\)
\(644\) 0 0
\(645\) 7.30489e8 0.107190
\(646\) 0 0
\(647\) 2.57401e9 0.373632 0.186816 0.982395i \(-0.440183\pi\)
0.186816 + 0.982395i \(0.440183\pi\)
\(648\) 0 0
\(649\) −5.81454e9 −0.834946
\(650\) 0 0
\(651\) −3.75145e9 −0.532925
\(652\) 0 0
\(653\) −9.31827e9 −1.30960 −0.654800 0.755802i \(-0.727247\pi\)
−0.654800 + 0.755802i \(0.727247\pi\)
\(654\) 0 0
\(655\) 4.23109e9 0.588313
\(656\) 0 0
\(657\) 3.45445e9 0.475226
\(658\) 0 0
\(659\) 1.04422e10 1.42133 0.710663 0.703532i \(-0.248395\pi\)
0.710663 + 0.703532i \(0.248395\pi\)
\(660\) 0 0
\(661\) −1.04761e10 −1.41090 −0.705449 0.708761i \(-0.749254\pi\)
−0.705449 + 0.708761i \(0.749254\pi\)
\(662\) 0 0
\(663\) 6.74628e9 0.899015
\(664\) 0 0
\(665\) −2.12380e9 −0.280051
\(666\) 0 0
\(667\) −5.28211e9 −0.689234
\(668\) 0 0
\(669\) −3.26327e9 −0.421368
\(670\) 0 0
\(671\) −1.00654e10 −1.28618
\(672\) 0 0
\(673\) 1.38891e10 1.75639 0.878197 0.478299i \(-0.158746\pi\)
0.878197 + 0.478299i \(0.158746\pi\)
\(674\) 0 0
\(675\) −1.29957e9 −0.162643
\(676\) 0 0
\(677\) −7.48893e8 −0.0927598 −0.0463799 0.998924i \(-0.514768\pi\)
−0.0463799 + 0.998924i \(0.514768\pi\)
\(678\) 0 0
\(679\) 3.60398e9 0.441813
\(680\) 0 0
\(681\) −7.62251e9 −0.924875
\(682\) 0 0
\(683\) 1.15581e10 1.38808 0.694038 0.719938i \(-0.255830\pi\)
0.694038 + 0.719938i \(0.255830\pi\)
\(684\) 0 0
\(685\) 8.38844e8 0.0997158
\(686\) 0 0
\(687\) −2.40817e9 −0.283360
\(688\) 0 0
\(689\) −5.45153e9 −0.634967
\(690\) 0 0
\(691\) 3.34337e8 0.0385489 0.0192744 0.999814i \(-0.493864\pi\)
0.0192744 + 0.999814i \(0.493864\pi\)
\(692\) 0 0
\(693\) 1.40059e9 0.159862
\(694\) 0 0
\(695\) 5.85556e8 0.0661640
\(696\) 0 0
\(697\) 1.78709e10 1.99909
\(698\) 0 0
\(699\) −6.27047e9 −0.694433
\(700\) 0 0
\(701\) −5.55383e9 −0.608948 −0.304474 0.952521i \(-0.598481\pi\)
−0.304474 + 0.952521i \(0.598481\pi\)
\(702\) 0 0
\(703\) 1.02133e10 1.10872
\(704\) 0 0
\(705\) 1.42204e9 0.152844
\(706\) 0 0
\(707\) −4.42700e9 −0.471131
\(708\) 0 0
\(709\) 1.30817e10 1.37849 0.689243 0.724530i \(-0.257943\pi\)
0.689243 + 0.724530i \(0.257943\pi\)
\(710\) 0 0
\(711\) 3.39822e9 0.354575
\(712\) 0 0
\(713\) 1.96086e10 2.02597
\(714\) 0 0
\(715\) 4.01457e9 0.410741
\(716\) 0 0
\(717\) 8.69363e9 0.880814
\(718\) 0 0
\(719\) −1.10847e10 −1.11217 −0.556085 0.831125i \(-0.687697\pi\)
−0.556085 + 0.831125i \(0.687697\pi\)
\(720\) 0 0
\(721\) −4.04012e9 −0.401440
\(722\) 0 0
\(723\) −5.40989e9 −0.532358
\(724\) 0 0
\(725\) −4.90315e9 −0.477850
\(726\) 0 0
\(727\) −7.79416e9 −0.752314 −0.376157 0.926556i \(-0.622755\pi\)
−0.376157 + 0.926556i \(0.622755\pi\)
\(728\) 0 0
\(729\) 3.87420e8 0.0370370
\(730\) 0 0
\(731\) 6.41896e9 0.607790
\(732\) 0 0
\(733\) 6.83552e9 0.641073 0.320537 0.947236i \(-0.396137\pi\)
0.320537 + 0.947236i \(0.396137\pi\)
\(734\) 0 0
\(735\) −1.69150e9 −0.157132
\(736\) 0 0
\(737\) 5.39869e9 0.496767
\(738\) 0 0
\(739\) 1.73862e10 1.58471 0.792356 0.610059i \(-0.208854\pi\)
0.792356 + 0.610059i \(0.208854\pi\)
\(740\) 0 0
\(741\) −9.90254e9 −0.894094
\(742\) 0 0
\(743\) 2.25537e9 0.201724 0.100862 0.994900i \(-0.467840\pi\)
0.100862 + 0.994900i \(0.467840\pi\)
\(744\) 0 0
\(745\) 8.37503e8 0.0742061
\(746\) 0 0
\(747\) −4.17662e9 −0.366609
\(748\) 0 0
\(749\) −2.59622e9 −0.225764
\(750\) 0 0
\(751\) −2.05027e10 −1.76632 −0.883162 0.469068i \(-0.844590\pi\)
−0.883162 + 0.469068i \(0.844590\pi\)
\(752\) 0 0
\(753\) −2.35051e9 −0.200623
\(754\) 0 0
\(755\) −2.75243e9 −0.232757
\(756\) 0 0
\(757\) −2.57872e8 −0.0216057 −0.0108029 0.999942i \(-0.503439\pi\)
−0.0108029 + 0.999942i \(0.503439\pi\)
\(758\) 0 0
\(759\) −7.32078e9 −0.607731
\(760\) 0 0
\(761\) −1.34452e10 −1.10591 −0.552957 0.833210i \(-0.686501\pi\)
−0.552957 + 0.833210i \(0.686501\pi\)
\(762\) 0 0
\(763\) −1.21605e10 −0.991096
\(764\) 0 0
\(765\) 2.09280e9 0.169010
\(766\) 0 0
\(767\) −1.46035e10 −1.16862
\(768\) 0 0
\(769\) 8.28541e9 0.657009 0.328505 0.944502i \(-0.393455\pi\)
0.328505 + 0.944502i \(0.393455\pi\)
\(770\) 0 0
\(771\) 1.41177e10 1.10936
\(772\) 0 0
\(773\) 1.43430e10 1.11689 0.558447 0.829540i \(-0.311397\pi\)
0.558447 + 0.829540i \(0.311397\pi\)
\(774\) 0 0
\(775\) 1.82018e10 1.40462
\(776\) 0 0
\(777\) −3.62803e9 −0.277458
\(778\) 0 0
\(779\) −2.62319e10 −1.98814
\(780\) 0 0
\(781\) −1.33851e10 −1.00541
\(782\) 0 0
\(783\) 1.46170e9 0.108816
\(784\) 0 0
\(785\) 4.32460e9 0.319082
\(786\) 0 0
\(787\) −3.83137e9 −0.280184 −0.140092 0.990139i \(-0.544740\pi\)
−0.140092 + 0.990139i \(0.544740\pi\)
\(788\) 0 0
\(789\) −1.09678e10 −0.794970
\(790\) 0 0
\(791\) 1.03233e9 0.0741653
\(792\) 0 0
\(793\) −2.52797e10 −1.80018
\(794\) 0 0
\(795\) −1.69115e9 −0.119370
\(796\) 0 0
\(797\) −1.95859e9 −0.137038 −0.0685188 0.997650i \(-0.521827\pi\)
−0.0685188 + 0.997650i \(0.521827\pi\)
\(798\) 0 0
\(799\) 1.24957e10 0.866658
\(800\) 0 0
\(801\) 8.74327e9 0.601119
\(802\) 0 0
\(803\) 1.80636e10 1.23112
\(804\) 0 0
\(805\) −3.94334e9 −0.266427
\(806\) 0 0
\(807\) 1.03234e10 0.691455
\(808\) 0 0
\(809\) 2.07415e9 0.137727 0.0688637 0.997626i \(-0.478063\pi\)
0.0688637 + 0.997626i \(0.478063\pi\)
\(810\) 0 0
\(811\) −5.71508e9 −0.376227 −0.188113 0.982147i \(-0.560237\pi\)
−0.188113 + 0.982147i \(0.560237\pi\)
\(812\) 0 0
\(813\) 7.67245e9 0.500746
\(814\) 0 0
\(815\) −6.91226e9 −0.447268
\(816\) 0 0
\(817\) −9.42208e9 −0.604463
\(818\) 0 0
\(819\) 3.51764e9 0.223747
\(820\) 0 0
\(821\) 2.82748e10 1.78319 0.891596 0.452832i \(-0.149586\pi\)
0.891596 + 0.452832i \(0.149586\pi\)
\(822\) 0 0
\(823\) −2.09283e9 −0.130868 −0.0654342 0.997857i \(-0.520843\pi\)
−0.0654342 + 0.997857i \(0.520843\pi\)
\(824\) 0 0
\(825\) −6.79556e9 −0.421343
\(826\) 0 0
\(827\) −3.71453e9 −0.228368 −0.114184 0.993460i \(-0.536425\pi\)
−0.114184 + 0.993460i \(0.536425\pi\)
\(828\) 0 0
\(829\) 3.37924e9 0.206005 0.103003 0.994681i \(-0.467155\pi\)
0.103003 + 0.994681i \(0.467155\pi\)
\(830\) 0 0
\(831\) 7.93130e9 0.479447
\(832\) 0 0
\(833\) −1.48635e10 −0.890972
\(834\) 0 0
\(835\) 1.14547e9 0.0680895
\(836\) 0 0
\(837\) −5.42621e9 −0.319858
\(838\) 0 0
\(839\) 1.64907e10 0.963990 0.481995 0.876174i \(-0.339912\pi\)
0.481995 + 0.876174i \(0.339912\pi\)
\(840\) 0 0
\(841\) −1.17350e10 −0.680297
\(842\) 0 0
\(843\) 1.12158e10 0.644812
\(844\) 0 0
\(845\) 3.18043e9 0.181337
\(846\) 0 0
\(847\) −2.49774e9 −0.141239
\(848\) 0 0
\(849\) 1.36736e9 0.0766841
\(850\) 0 0
\(851\) 1.89634e10 1.05478
\(852\) 0 0
\(853\) −4.77028e9 −0.263162 −0.131581 0.991305i \(-0.542005\pi\)
−0.131581 + 0.991305i \(0.542005\pi\)
\(854\) 0 0
\(855\) −3.07192e9 −0.168085
\(856\) 0 0
\(857\) 1.61514e10 0.876554 0.438277 0.898840i \(-0.355589\pi\)
0.438277 + 0.898840i \(0.355589\pi\)
\(858\) 0 0
\(859\) −3.41593e8 −0.0183879 −0.00919397 0.999958i \(-0.502927\pi\)
−0.00919397 + 0.999958i \(0.502927\pi\)
\(860\) 0 0
\(861\) 9.31824e9 0.497534
\(862\) 0 0
\(863\) 6.07878e9 0.321943 0.160971 0.986959i \(-0.448537\pi\)
0.160971 + 0.986959i \(0.448537\pi\)
\(864\) 0 0
\(865\) −8.83906e9 −0.464354
\(866\) 0 0
\(867\) 7.31071e9 0.380972
\(868\) 0 0
\(869\) 1.77696e10 0.918562
\(870\) 0 0
\(871\) 1.35590e10 0.695289
\(872\) 0 0
\(873\) 5.21290e9 0.265173
\(874\) 0 0
\(875\) −7.99168e9 −0.403283
\(876\) 0 0
\(877\) 1.23852e10 0.620020 0.310010 0.950733i \(-0.399668\pi\)
0.310010 + 0.950733i \(0.399668\pi\)
\(878\) 0 0
\(879\) 2.01883e9 0.100262
\(880\) 0 0
\(881\) −1.37801e10 −0.678949 −0.339475 0.940615i \(-0.610249\pi\)
−0.339475 + 0.940615i \(0.610249\pi\)
\(882\) 0 0
\(883\) 1.89296e9 0.0925292 0.0462646 0.998929i \(-0.485268\pi\)
0.0462646 + 0.998929i \(0.485268\pi\)
\(884\) 0 0
\(885\) −4.53021e9 −0.219693
\(886\) 0 0
\(887\) 4.23912e9 0.203959 0.101979 0.994787i \(-0.467482\pi\)
0.101979 + 0.994787i \(0.467482\pi\)
\(888\) 0 0
\(889\) 6.88633e8 0.0328724
\(890\) 0 0
\(891\) 2.02585e9 0.0959480
\(892\) 0 0
\(893\) −1.83419e10 −0.861913
\(894\) 0 0
\(895\) −9.24092e9 −0.430859
\(896\) 0 0
\(897\) −1.83864e10 −0.850598
\(898\) 0 0
\(899\) −2.04725e10 −0.939751
\(900\) 0 0
\(901\) −1.48605e10 −0.676855
\(902\) 0 0
\(903\) 3.34697e9 0.151267
\(904\) 0 0
\(905\) 1.27016e10 0.569623
\(906\) 0 0
\(907\) −9.51367e9 −0.423372 −0.211686 0.977338i \(-0.567895\pi\)
−0.211686 + 0.977338i \(0.567895\pi\)
\(908\) 0 0
\(909\) −6.40334e9 −0.282770
\(910\) 0 0
\(911\) −1.16235e10 −0.509359 −0.254680 0.967025i \(-0.581970\pi\)
−0.254680 + 0.967025i \(0.581970\pi\)
\(912\) 0 0
\(913\) −2.18399e10 −0.949736
\(914\) 0 0
\(915\) −7.84216e9 −0.338425
\(916\) 0 0
\(917\) 1.93861e10 0.830229
\(918\) 0 0
\(919\) −9.22943e9 −0.392257 −0.196128 0.980578i \(-0.562837\pi\)
−0.196128 + 0.980578i \(0.562837\pi\)
\(920\) 0 0
\(921\) 2.30196e9 0.0970931
\(922\) 0 0
\(923\) −3.36172e10 −1.40720
\(924\) 0 0
\(925\) 1.76029e10 0.731289
\(926\) 0 0
\(927\) −5.84374e9 −0.240942
\(928\) 0 0
\(929\) −4.09353e10 −1.67511 −0.837555 0.546353i \(-0.816016\pi\)
−0.837555 + 0.546353i \(0.816016\pi\)
\(930\) 0 0
\(931\) 2.18174e10 0.886094
\(932\) 0 0
\(933\) 2.53565e10 1.02212
\(934\) 0 0
\(935\) 1.09434e10 0.437837
\(936\) 0 0
\(937\) −1.75085e9 −0.0695281 −0.0347641 0.999396i \(-0.511068\pi\)
−0.0347641 + 0.999396i \(0.511068\pi\)
\(938\) 0 0
\(939\) −9.26207e9 −0.365072
\(940\) 0 0
\(941\) 5.91102e9 0.231259 0.115630 0.993292i \(-0.463111\pi\)
0.115630 + 0.993292i \(0.463111\pi\)
\(942\) 0 0
\(943\) −4.87058e10 −1.89143
\(944\) 0 0
\(945\) 1.09123e9 0.0420633
\(946\) 0 0
\(947\) −2.26089e10 −0.865077 −0.432538 0.901616i \(-0.642382\pi\)
−0.432538 + 0.901616i \(0.642382\pi\)
\(948\) 0 0
\(949\) 4.53675e10 1.72311
\(950\) 0 0
\(951\) −2.80692e10 −1.05827
\(952\) 0 0
\(953\) 1.11773e10 0.418322 0.209161 0.977881i \(-0.432927\pi\)
0.209161 + 0.977881i \(0.432927\pi\)
\(954\) 0 0
\(955\) 1.09687e10 0.407515
\(956\) 0 0
\(957\) 7.64334e9 0.281898
\(958\) 0 0
\(959\) 3.84343e9 0.140719
\(960\) 0 0
\(961\) 4.84868e10 1.76235
\(962\) 0 0
\(963\) −3.75525e9 −0.135502
\(964\) 0 0
\(965\) −2.04773e9 −0.0733546
\(966\) 0 0
\(967\) 1.55518e10 0.553078 0.276539 0.961003i \(-0.410812\pi\)
0.276539 + 0.961003i \(0.410812\pi\)
\(968\) 0 0
\(969\) −2.69936e10 −0.953075
\(970\) 0 0
\(971\) 8.34508e9 0.292525 0.146263 0.989246i \(-0.453276\pi\)
0.146263 + 0.989246i \(0.453276\pi\)
\(972\) 0 0
\(973\) 2.68291e9 0.0933709
\(974\) 0 0
\(975\) −1.70673e10 −0.589725
\(976\) 0 0
\(977\) −9.85180e9 −0.337975 −0.168988 0.985618i \(-0.554050\pi\)
−0.168988 + 0.985618i \(0.554050\pi\)
\(978\) 0 0
\(979\) 4.57193e10 1.55726
\(980\) 0 0
\(981\) −1.75893e10 −0.594850
\(982\) 0 0
\(983\) 3.70884e10 1.24538 0.622688 0.782470i \(-0.286041\pi\)
0.622688 + 0.782470i \(0.286041\pi\)
\(984\) 0 0
\(985\) 1.02342e10 0.341215
\(986\) 0 0
\(987\) 6.51551e9 0.215694
\(988\) 0 0
\(989\) −1.74944e10 −0.575057
\(990\) 0 0
\(991\) 6.43526e9 0.210043 0.105022 0.994470i \(-0.466509\pi\)
0.105022 + 0.994470i \(0.466509\pi\)
\(992\) 0 0
\(993\) 2.97059e10 0.962765
\(994\) 0 0
\(995\) 8.13654e9 0.261854
\(996\) 0 0
\(997\) −1.23071e10 −0.393299 −0.196650 0.980474i \(-0.563006\pi\)
−0.196650 + 0.980474i \(0.563006\pi\)
\(998\) 0 0
\(999\) −5.24768e9 −0.166528
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 \(a_p\))