Properties

Label 72.14.a.a.1.1
Level $72$
Weight $14$
Character 72.1
Self dual yes
Analytic conductor $77.206$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 72.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(77.2062688454\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 8)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 72.1

$q$-expansion

\(f(q)\) \(=\) \(q+4330.00 q^{5} -139992. q^{7} +O(q^{10})\) \(q+4330.00 q^{5} -139992. q^{7} +6.48432e6 q^{11} -2.25880e7 q^{13} +2.37323e7 q^{17} +3.25345e8 q^{19} -9.21601e8 q^{23} -1.20195e9 q^{25} +3.86588e9 q^{29} -2.25340e9 q^{31} -6.06165e8 q^{35} +1.82504e10 q^{37} -3.44228e10 q^{41} -1.71925e10 q^{43} +6.73717e10 q^{47} -7.72913e10 q^{49} +8.72812e10 q^{53} +2.80771e10 q^{55} -5.40215e11 q^{59} -5.12766e10 q^{61} -9.78062e10 q^{65} +2.55199e10 q^{67} +1.38750e12 q^{71} -8.19049e11 q^{73} -9.07753e11 q^{77} -4.03094e12 q^{79} -4.18082e12 q^{83} +1.02761e11 q^{85} -2.67703e12 q^{89} +3.16214e12 q^{91} +1.40874e12 q^{95} -1.40395e13 q^{97} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 4330.00 0.123932 0.0619659 0.998078i \(-0.480263\pi\)
0.0619659 + 0.998078i \(0.480263\pi\)
\(6\) 0 0
\(7\) −139992. −0.449745 −0.224872 0.974388i \(-0.572196\pi\)
−0.224872 + 0.974388i \(0.572196\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.48432e6 1.10360 0.551801 0.833976i \(-0.313941\pi\)
0.551801 + 0.833976i \(0.313941\pi\)
\(12\) 0 0
\(13\) −2.25880e7 −1.29792 −0.648958 0.760824i \(-0.724795\pi\)
−0.648958 + 0.760824i \(0.724795\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.37323e7 0.238463 0.119232 0.992866i \(-0.461957\pi\)
0.119232 + 0.992866i \(0.461957\pi\)
\(18\) 0 0
\(19\) 3.25345e8 1.58652 0.793260 0.608883i \(-0.208382\pi\)
0.793260 + 0.608883i \(0.208382\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −9.21601e8 −1.29811 −0.649055 0.760741i \(-0.724836\pi\)
−0.649055 + 0.760741i \(0.724836\pi\)
\(24\) 0 0
\(25\) −1.20195e9 −0.984641
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.86588e9 1.20687 0.603436 0.797411i \(-0.293798\pi\)
0.603436 + 0.797411i \(0.293798\pi\)
\(30\) 0 0
\(31\) −2.25340e9 −0.456024 −0.228012 0.973658i \(-0.573223\pi\)
−0.228012 + 0.973658i \(0.573223\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −6.06165e8 −0.0557377
\(36\) 0 0
\(37\) 1.82504e10 1.16939 0.584697 0.811252i \(-0.301213\pi\)
0.584697 + 0.811252i \(0.301213\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.44228e10 −1.13175 −0.565877 0.824490i \(-0.691462\pi\)
−0.565877 + 0.824490i \(0.691462\pi\)
\(42\) 0 0
\(43\) −1.71925e10 −0.414757 −0.207379 0.978261i \(-0.566493\pi\)
−0.207379 + 0.978261i \(0.566493\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.73717e10 0.911679 0.455839 0.890062i \(-0.349339\pi\)
0.455839 + 0.890062i \(0.349339\pi\)
\(48\) 0 0
\(49\) −7.72913e10 −0.797730
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.72812e10 0.540913 0.270457 0.962732i \(-0.412825\pi\)
0.270457 + 0.962732i \(0.412825\pi\)
\(54\) 0 0
\(55\) 2.80771e10 0.136771
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.40215e11 −1.66736 −0.833678 0.552251i \(-0.813769\pi\)
−0.833678 + 0.552251i \(0.813769\pi\)
\(60\) 0 0
\(61\) −5.12766e10 −0.127431 −0.0637155 0.997968i \(-0.520295\pi\)
−0.0637155 + 0.997968i \(0.520295\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9.78062e10 −0.160853
\(66\) 0 0
\(67\) 2.55199e10 0.0344662 0.0172331 0.999851i \(-0.494514\pi\)
0.0172331 + 0.999851i \(0.494514\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.38750e12 1.28545 0.642723 0.766099i \(-0.277805\pi\)
0.642723 + 0.766099i \(0.277805\pi\)
\(72\) 0 0
\(73\) −8.19049e11 −0.633449 −0.316724 0.948518i \(-0.602583\pi\)
−0.316724 + 0.948518i \(0.602583\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.07753e11 −0.496339
\(78\) 0 0
\(79\) −4.03094e12 −1.86565 −0.932824 0.360332i \(-0.882663\pi\)
−0.932824 + 0.360332i \(0.882663\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.18082e12 −1.40364 −0.701818 0.712357i \(-0.747628\pi\)
−0.701818 + 0.712357i \(0.747628\pi\)
\(84\) 0 0
\(85\) 1.02761e11 0.0295532
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.67703e12 −0.570976 −0.285488 0.958382i \(-0.592156\pi\)
−0.285488 + 0.958382i \(0.592156\pi\)
\(90\) 0 0
\(91\) 3.16214e12 0.583731
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.40874e12 0.196620
\(96\) 0 0
\(97\) −1.40395e13 −1.71133 −0.855666 0.517528i \(-0.826852\pi\)
−0.855666 + 0.517528i \(0.826852\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.22392e12 0.583411 0.291706 0.956508i \(-0.405777\pi\)
0.291706 + 0.956508i \(0.405777\pi\)
\(102\) 0 0
\(103\) −2.11756e13 −1.74740 −0.873702 0.486461i \(-0.838288\pi\)
−0.873702 + 0.486461i \(0.838288\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.87895e13 −1.21038 −0.605188 0.796083i \(-0.706902\pi\)
−0.605188 + 0.796083i \(0.706902\pi\)
\(108\) 0 0
\(109\) −9.95159e12 −0.568356 −0.284178 0.958772i \(-0.591721\pi\)
−0.284178 + 0.958772i \(0.591721\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.08879e13 −0.943812 −0.471906 0.881649i \(-0.656434\pi\)
−0.471906 + 0.881649i \(0.656434\pi\)
\(114\) 0 0
\(115\) −3.99053e12 −0.160877
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.32233e12 −0.107248
\(120\) 0 0
\(121\) 7.52375e12 0.217936
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.04901e13 −0.245960
\(126\) 0 0
\(127\) −6.26814e13 −1.32561 −0.662803 0.748794i \(-0.730633\pi\)
−0.662803 + 0.748794i \(0.730633\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.97773e12 0.120629 0.0603144 0.998179i \(-0.480790\pi\)
0.0603144 + 0.998179i \(0.480790\pi\)
\(132\) 0 0
\(133\) −4.55457e13 −0.713529
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.78591e13 0.747632 0.373816 0.927503i \(-0.378049\pi\)
0.373816 + 0.927503i \(0.378049\pi\)
\(138\) 0 0
\(139\) −3.93498e13 −0.462750 −0.231375 0.972865i \(-0.574322\pi\)
−0.231375 + 0.972865i \(0.574322\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.46468e14 −1.43238
\(144\) 0 0
\(145\) 1.67393e13 0.149570
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.31370e13 0.322953 0.161476 0.986877i \(-0.448374\pi\)
0.161476 + 0.986877i \(0.448374\pi\)
\(150\) 0 0
\(151\) 2.19599e14 1.50758 0.753788 0.657117i \(-0.228224\pi\)
0.753788 + 0.657117i \(0.228224\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.75723e12 −0.0565159
\(156\) 0 0
\(157\) 6.61866e13 0.352714 0.176357 0.984326i \(-0.443569\pi\)
0.176357 + 0.984326i \(0.443569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.29017e14 0.583818
\(162\) 0 0
\(163\) −2.47622e14 −1.03412 −0.517058 0.855950i \(-0.672973\pi\)
−0.517058 + 0.855950i \(0.672973\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.05226e13 0.215904 0.107952 0.994156i \(-0.465571\pi\)
0.107952 + 0.994156i \(0.465571\pi\)
\(168\) 0 0
\(169\) 2.07344e14 0.684586
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.82357e14 0.800752 0.400376 0.916351i \(-0.368879\pi\)
0.400376 + 0.916351i \(0.368879\pi\)
\(174\) 0 0
\(175\) 1.68264e14 0.442837
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.65618e14 0.376324 0.188162 0.982138i \(-0.439747\pi\)
0.188162 + 0.982138i \(0.439747\pi\)
\(180\) 0 0
\(181\) 8.52134e14 1.80135 0.900673 0.434497i \(-0.143074\pi\)
0.900673 + 0.434497i \(0.143074\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.90242e13 0.144925
\(186\) 0 0
\(187\) 1.53888e14 0.263168
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.30990e14 −1.38748 −0.693742 0.720223i \(-0.744039\pi\)
−0.693742 + 0.720223i \(0.744039\pi\)
\(192\) 0 0
\(193\) 4.17870e14 0.581994 0.290997 0.956724i \(-0.406013\pi\)
0.290997 + 0.956724i \(0.406013\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.17420e15 1.43124 0.715621 0.698489i \(-0.246144\pi\)
0.715621 + 0.698489i \(0.246144\pi\)
\(198\) 0 0
\(199\) 9.52478e13 0.108720 0.0543601 0.998521i \(-0.482688\pi\)
0.0543601 + 0.998521i \(0.482688\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.41192e14 −0.542784
\(204\) 0 0
\(205\) −1.49051e14 −0.140260
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.10964e15 1.75089
\(210\) 0 0
\(211\) 7.61637e14 0.594172 0.297086 0.954851i \(-0.403985\pi\)
0.297086 + 0.954851i \(0.403985\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7.44435e13 −0.0514016
\(216\) 0 0
\(217\) 3.15458e14 0.205094
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −5.36065e14 −0.309505
\(222\) 0 0
\(223\) −1.62673e15 −0.885796 −0.442898 0.896572i \(-0.646050\pi\)
−0.442898 + 0.896572i \(0.646050\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.50895e15 −0.731991 −0.365996 0.930617i \(-0.619271\pi\)
−0.365996 + 0.930617i \(0.619271\pi\)
\(228\) 0 0
\(229\) 1.69644e15 0.777334 0.388667 0.921378i \(-0.372936\pi\)
0.388667 + 0.921378i \(0.372936\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.27819e15 −0.523339 −0.261670 0.965158i \(-0.584273\pi\)
−0.261670 + 0.965158i \(0.584273\pi\)
\(234\) 0 0
\(235\) 2.91720e14 0.112986
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.10138e15 0.382252 0.191126 0.981566i \(-0.438786\pi\)
0.191126 + 0.981566i \(0.438786\pi\)
\(240\) 0 0
\(241\) 9.15325e14 0.300929 0.150465 0.988615i \(-0.451923\pi\)
0.150465 + 0.988615i \(0.451923\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.34671e14 −0.0988641
\(246\) 0 0
\(247\) −7.34890e15 −2.05917
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.68301e15 −1.43450 −0.717248 0.696818i \(-0.754598\pi\)
−0.717248 + 0.696818i \(0.754598\pi\)
\(252\) 0 0
\(253\) −5.97596e15 −1.43260
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.40938e15 1.60404 0.802022 0.597294i \(-0.203758\pi\)
0.802022 + 0.597294i \(0.203758\pi\)
\(258\) 0 0
\(259\) −2.55491e15 −0.525929
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.44830e15 −0.828861 −0.414431 0.910081i \(-0.636019\pi\)
−0.414431 + 0.910081i \(0.636019\pi\)
\(264\) 0 0
\(265\) 3.77928e14 0.0670364
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.99525e15 0.642916 0.321458 0.946924i \(-0.395827\pi\)
0.321458 + 0.946924i \(0.395827\pi\)
\(270\) 0 0
\(271\) 5.58778e15 0.856917 0.428458 0.903562i \(-0.359057\pi\)
0.428458 + 0.903562i \(0.359057\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.79386e15 −1.08665
\(276\) 0 0
\(277\) −9.01343e14 −0.119887 −0.0599435 0.998202i \(-0.519092\pi\)
−0.0599435 + 0.998202i \(0.519092\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.24836e16 −1.51268 −0.756342 0.654176i \(-0.773015\pi\)
−0.756342 + 0.654176i \(0.773015\pi\)
\(282\) 0 0
\(283\) −5.47980e15 −0.634093 −0.317046 0.948410i \(-0.602691\pi\)
−0.317046 + 0.948410i \(0.602691\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.81892e15 0.509000
\(288\) 0 0
\(289\) −9.34136e15 −0.943135
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.61630e15 −0.426240 −0.213120 0.977026i \(-0.568363\pi\)
−0.213120 + 0.977026i \(0.568363\pi\)
\(294\) 0 0
\(295\) −2.33913e15 −0.206638
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.08171e16 1.68484
\(300\) 0 0
\(301\) 2.40681e15 0.186535
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.22028e14 −0.0157928
\(306\) 0 0
\(307\) −2.22392e16 −1.51607 −0.758037 0.652211i \(-0.773842\pi\)
−0.758037 + 0.652211i \(0.773842\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.51173e16 −0.947393 −0.473697 0.880688i \(-0.657081\pi\)
−0.473697 + 0.880688i \(0.657081\pi\)
\(312\) 0 0
\(313\) 8.36531e15 0.502856 0.251428 0.967876i \(-0.419100\pi\)
0.251428 + 0.967876i \(0.419100\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.34425e15 0.517201 0.258600 0.965984i \(-0.416739\pi\)
0.258600 + 0.965984i \(0.416739\pi\)
\(318\) 0 0
\(319\) 2.50676e16 1.33191
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.72117e15 0.378327
\(324\) 0 0
\(325\) 2.71498e16 1.27798
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9.43151e15 −0.410023
\(330\) 0 0
\(331\) 3.92466e16 1.64029 0.820144 0.572157i \(-0.193893\pi\)
0.820144 + 0.572157i \(0.193893\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.10501e14 0.00427146
\(336\) 0 0
\(337\) −3.01727e16 −1.12207 −0.561036 0.827792i \(-0.689597\pi\)
−0.561036 + 0.827792i \(0.689597\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.46118e16 −0.503269
\(342\) 0 0
\(343\) 2.43838e16 0.808519
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.02701e16 1.23834 0.619172 0.785255i \(-0.287468\pi\)
0.619172 + 0.785255i \(0.287468\pi\)
\(348\) 0 0
\(349\) −4.36418e16 −1.29282 −0.646409 0.762991i \(-0.723730\pi\)
−0.646409 + 0.762991i \(0.723730\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.08122e16 0.847593 0.423796 0.905758i \(-0.360697\pi\)
0.423796 + 0.905758i \(0.360697\pi\)
\(354\) 0 0
\(355\) 6.00788e15 0.159308
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.06926e16 1.00323 0.501616 0.865090i \(-0.332739\pi\)
0.501616 + 0.865090i \(0.332739\pi\)
\(360\) 0 0
\(361\) 6.37963e16 1.51705
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.54648e15 −0.0785045
\(366\) 0 0
\(367\) −1.06190e16 −0.226857 −0.113429 0.993546i \(-0.536183\pi\)
−0.113429 + 0.993546i \(0.536183\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.22187e16 −0.243273
\(372\) 0 0
\(373\) 7.41221e16 1.42508 0.712542 0.701630i \(-0.247544\pi\)
0.712542 + 0.701630i \(0.247544\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.73226e16 −1.56642
\(378\) 0 0
\(379\) 4.60131e16 0.797493 0.398746 0.917061i \(-0.369445\pi\)
0.398746 + 0.917061i \(0.369445\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.36970e16 1.19305 0.596524 0.802595i \(-0.296548\pi\)
0.596524 + 0.802595i \(0.296548\pi\)
\(384\) 0 0
\(385\) −3.93057e15 −0.0615122
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.03726e16 −1.02975 −0.514874 0.857266i \(-0.672161\pi\)
−0.514874 + 0.857266i \(0.672161\pi\)
\(390\) 0 0
\(391\) −2.18717e16 −0.309552
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.74540e16 −0.231213
\(396\) 0 0
\(397\) −1.07601e17 −1.37936 −0.689680 0.724115i \(-0.742249\pi\)
−0.689680 + 0.724115i \(0.742249\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.85722e16 0.463272 0.231636 0.972802i \(-0.425592\pi\)
0.231636 + 0.972802i \(0.425592\pi\)
\(402\) 0 0
\(403\) 5.08999e16 0.591881
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.18341e17 1.29054
\(408\) 0 0
\(409\) −5.34639e16 −0.564753 −0.282377 0.959304i \(-0.591123\pi\)
−0.282377 + 0.959304i \(0.591123\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.56257e16 0.749884
\(414\) 0 0
\(415\) −1.81030e16 −0.173955
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.04340e17 −0.942016 −0.471008 0.882129i \(-0.656110\pi\)
−0.471008 + 0.882129i \(0.656110\pi\)
\(420\) 0 0
\(421\) −7.03173e16 −0.615500 −0.307750 0.951467i \(-0.599576\pi\)
−0.307750 + 0.951467i \(0.599576\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.85251e16 −0.234801
\(426\) 0 0
\(427\) 7.17831e15 0.0573114
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.40437e16 −0.481254 −0.240627 0.970618i \(-0.577353\pi\)
−0.240627 + 0.970618i \(0.577353\pi\)
\(432\) 0 0
\(433\) −1.12484e17 −0.820201 −0.410101 0.912040i \(-0.634506\pi\)
−0.410101 + 0.912040i \(0.634506\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.99838e17 −2.05948
\(438\) 0 0
\(439\) −3.14978e16 −0.210020 −0.105010 0.994471i \(-0.533487\pi\)
−0.105010 + 0.994471i \(0.533487\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.14104e17 −0.717261 −0.358631 0.933480i \(-0.616756\pi\)
−0.358631 + 0.933480i \(0.616756\pi\)
\(444\) 0 0
\(445\) −1.15915e16 −0.0707621
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.86758e16 0.453148 0.226574 0.973994i \(-0.427247\pi\)
0.226574 + 0.973994i \(0.427247\pi\)
\(450\) 0 0
\(451\) −2.23209e17 −1.24900
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.36921e16 0.0723428
\(456\) 0 0
\(457\) 2.35679e17 1.21022 0.605112 0.796140i \(-0.293128\pi\)
0.605112 + 0.796140i \(0.293128\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.33465e17 1.13283 0.566415 0.824120i \(-0.308330\pi\)
0.566415 + 0.824120i \(0.308330\pi\)
\(462\) 0 0
\(463\) −1.43911e17 −0.678920 −0.339460 0.940620i \(-0.610244\pi\)
−0.339460 + 0.940620i \(0.610244\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.72838e17 1.21715 0.608576 0.793496i \(-0.291741\pi\)
0.608576 + 0.793496i \(0.291741\pi\)
\(468\) 0 0
\(469\) −3.57259e15 −0.0155010
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.11482e17 −0.457727
\(474\) 0 0
\(475\) −3.91050e17 −1.56215
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.61844e17 −1.36880 −0.684401 0.729106i \(-0.739936\pi\)
−0.684401 + 0.729106i \(0.739936\pi\)
\(480\) 0 0
\(481\) −4.12240e17 −1.51778
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.07909e16 −0.212089
\(486\) 0 0
\(487\) 3.33934e17 1.13429 0.567143 0.823619i \(-0.308049\pi\)
0.567143 + 0.823619i \(0.308049\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.79534e16 0.0578251 0.0289125 0.999582i \(-0.490796\pi\)
0.0289125 + 0.999582i \(0.490796\pi\)
\(492\) 0 0
\(493\) 9.17461e16 0.287795
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.94239e17 −0.578123
\(498\) 0 0
\(499\) 4.21623e17 1.22256 0.611281 0.791414i \(-0.290655\pi\)
0.611281 + 0.791414i \(0.290655\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.53513e17 −0.973225 −0.486612 0.873618i \(-0.661768\pi\)
−0.486612 + 0.873618i \(0.661768\pi\)
\(504\) 0 0
\(505\) 2.69496e16 0.0723032
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.95547e17 1.51792 0.758962 0.651135i \(-0.225707\pi\)
0.758962 + 0.651135i \(0.225707\pi\)
\(510\) 0 0
\(511\) 1.14660e17 0.284890
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.16903e16 −0.216559
\(516\) 0 0
\(517\) 4.36860e17 1.00613
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.18807e17 1.35553 0.677767 0.735277i \(-0.262948\pi\)
0.677767 + 0.735277i \(0.262948\pi\)
\(522\) 0 0
\(523\) −3.97661e17 −0.849674 −0.424837 0.905270i \(-0.639669\pi\)
−0.424837 + 0.905270i \(0.639669\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.34783e16 −0.108745
\(528\) 0 0
\(529\) 3.45311e17 0.685092
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7.77544e17 1.46892
\(534\) 0 0
\(535\) −8.13584e16 −0.150004
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −5.01182e17 −0.880376
\(540\) 0 0
\(541\) 4.06842e17 0.697660 0.348830 0.937186i \(-0.386579\pi\)
0.348830 + 0.937186i \(0.386579\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −4.30904e16 −0.0704374
\(546\) 0 0
\(547\) −2.81721e17 −0.449678 −0.224839 0.974396i \(-0.572186\pi\)
−0.224839 + 0.974396i \(0.572186\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.25774e18 1.91473
\(552\) 0 0
\(553\) 5.64299e17 0.839065
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.23400e18 −1.75088 −0.875442 0.483324i \(-0.839429\pi\)
−0.875442 + 0.483324i \(0.839429\pi\)
\(558\) 0 0
\(559\) 3.88345e17 0.538320
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.42261e18 −1.88270 −0.941348 0.337437i \(-0.890440\pi\)
−0.941348 + 0.337437i \(0.890440\pi\)
\(564\) 0 0
\(565\) −9.04448e16 −0.116968
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.50797e17 0.556866 0.278433 0.960456i \(-0.410185\pi\)
0.278433 + 0.960456i \(0.410185\pi\)
\(570\) 0 0
\(571\) 7.13748e17 0.861807 0.430904 0.902398i \(-0.358195\pi\)
0.430904 + 0.902398i \(0.358195\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.10772e18 1.27817
\(576\) 0 0
\(577\) 1.28447e18 1.44905 0.724524 0.689250i \(-0.242060\pi\)
0.724524 + 0.689250i \(0.242060\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.85282e17 0.631277
\(582\) 0 0
\(583\) 5.65960e17 0.596953
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.80690e16 0.0585864 0.0292932 0.999571i \(-0.490674\pi\)
0.0292932 + 0.999571i \(0.490674\pi\)
\(588\) 0 0
\(589\) −7.33133e17 −0.723491
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.39716e18 1.31944 0.659722 0.751509i \(-0.270674\pi\)
0.659722 + 0.751509i \(0.270674\pi\)
\(594\) 0 0
\(595\) −1.43857e16 −0.0132914
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.23231e17 −0.462827 −0.231414 0.972855i \(-0.574335\pi\)
−0.231414 + 0.972855i \(0.574335\pi\)
\(600\) 0 0
\(601\) −1.51221e18 −1.30897 −0.654484 0.756076i \(-0.727114\pi\)
−0.654484 + 0.756076i \(0.727114\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.25778e16 0.0270092
\(606\) 0 0
\(607\) −1.70314e18 −1.38205 −0.691024 0.722832i \(-0.742840\pi\)
−0.691024 + 0.722832i \(0.742840\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.52180e18 −1.18328
\(612\) 0 0
\(613\) −6.08885e17 −0.463492 −0.231746 0.972776i \(-0.574444\pi\)
−0.231746 + 0.972776i \(0.574444\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.93917e17 −0.433383 −0.216692 0.976240i \(-0.569527\pi\)
−0.216692 + 0.976240i \(0.569527\pi\)
\(618\) 0 0
\(619\) 1.00496e18 0.718055 0.359028 0.933327i \(-0.383108\pi\)
0.359028 + 0.933327i \(0.383108\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.74762e17 0.256793
\(624\) 0 0
\(625\) 1.42181e18 0.954159
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.33123e17 0.278857
\(630\) 0 0
\(631\) −7.35349e16 −0.0463770 −0.0231885 0.999731i \(-0.507382\pi\)
−0.0231885 + 0.999731i \(0.507382\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.71410e17 −0.164285
\(636\) 0 0
\(637\) 1.74586e18 1.03539
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.82655e18 −1.60946 −0.804728 0.593644i \(-0.797689\pi\)
−0.804728 + 0.593644i \(0.797689\pi\)
\(642\) 0 0
\(643\) −1.57731e18 −0.880126 −0.440063 0.897967i \(-0.645044\pi\)
−0.440063 + 0.897967i \(0.645044\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.78710e18 0.957789 0.478895 0.877872i \(-0.341038\pi\)
0.478895 + 0.877872i \(0.341038\pi\)
\(648\) 0 0
\(649\) −3.50293e18 −1.84010
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.34506e18 −1.68837 −0.844185 0.536051i \(-0.819915\pi\)
−0.844185 + 0.536051i \(0.819915\pi\)
\(654\) 0 0
\(655\) 3.02136e16 0.0149497
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.69802e18 0.807584 0.403792 0.914851i \(-0.367692\pi\)
0.403792 + 0.914851i \(0.367692\pi\)
\(660\) 0 0
\(661\) −1.72815e18 −0.805883 −0.402942 0.915226i \(-0.632012\pi\)
−0.402942 + 0.915226i \(0.632012\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.97213e17 −0.0884289
\(666\) 0 0
\(667\) −3.56280e18 −1.56665
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.32494e17 −0.140633
\(672\) 0 0
\(673\) −1.82377e18 −0.756608 −0.378304 0.925681i \(-0.623493\pi\)
−0.378304 + 0.925681i \(0.623493\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.09138e18 1.23403 0.617014 0.786952i \(-0.288342\pi\)
0.617014 + 0.786952i \(0.288342\pi\)
\(678\) 0 0
\(679\) 1.96541e18 0.769662
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3.14496e17 −0.118544 −0.0592722 0.998242i \(-0.518878\pi\)
−0.0592722 + 0.998242i \(0.518878\pi\)
\(684\) 0 0
\(685\) 2.50530e17 0.0926554
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.97151e18 −0.702060
\(690\) 0 0
\(691\) −4.48311e17 −0.156665 −0.0783325 0.996927i \(-0.524960\pi\)
−0.0783325 + 0.996927i \(0.524960\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.70385e17 −0.0573494
\(696\) 0 0
\(697\) −8.16932e17 −0.269881
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.21704e18 −1.02398 −0.511988 0.858992i \(-0.671091\pi\)
−0.511988 + 0.858992i \(0.671091\pi\)
\(702\) 0 0
\(703\) 5.93767e18 1.85527
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.71299e17 −0.262386
\(708\) 0 0
\(709\) −3.21328e18 −0.950053 −0.475026 0.879971i \(-0.657562\pi\)
−0.475026 + 0.879971i \(0.657562\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.07674e18 0.591970
\(714\) 0 0
\(715\) −6.34207e17 −0.177518
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.51628e18 0.679237 0.339619 0.940563i \(-0.389702\pi\)
0.339619 + 0.940563i \(0.389702\pi\)
\(720\) 0 0
\(721\) 2.96441e18 0.785886
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.64661e18 −1.18834
\(726\) 0 0
\(727\) −1.20284e18 −0.302157 −0.151078 0.988522i \(-0.548275\pi\)
−0.151078 + 0.988522i \(0.548275\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −4.08017e17 −0.0989044
\(732\) 0 0
\(733\) −1.79874e18 −0.428345 −0.214173 0.976796i \(-0.568705\pi\)
−0.214173 + 0.976796i \(0.568705\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.65479e17 0.0380369
\(738\) 0 0
\(739\) −2.14261e18 −0.483898 −0.241949 0.970289i \(-0.577787\pi\)
−0.241949 + 0.970289i \(0.577787\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.34550e18 1.16563 0.582816 0.812604i \(-0.301951\pi\)
0.582816 + 0.812604i \(0.301951\pi\)
\(744\) 0 0
\(745\) 1.86783e17 0.0400241
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.63038e18 0.544360
\(750\) 0 0
\(751\) 3.42693e18 0.697021 0.348511 0.937305i \(-0.386688\pi\)
0.348511 + 0.937305i \(0.386688\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.50862e17 0.186837
\(756\) 0 0
\(757\) 1.77769e18 0.343347 0.171674 0.985154i \(-0.445083\pi\)
0.171674 + 0.985154i \(0.445083\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −4.61017e18 −0.860432 −0.430216 0.902726i \(-0.641563\pi\)
−0.430216 + 0.902726i \(0.641563\pi\)
\(762\) 0 0
\(763\) 1.39314e18 0.255615
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.22024e19 2.16409
\(768\) 0 0
\(769\) 4.06261e18 0.708409 0.354204 0.935168i \(-0.384752\pi\)
0.354204 + 0.935168i \(0.384752\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.77091e18 0.467149 0.233574 0.972339i \(-0.424958\pi\)
0.233574 + 0.972339i \(0.424958\pi\)
\(774\) 0 0
\(775\) 2.70849e18 0.449020
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.11993e19 −1.79555
\(780\) 0 0
\(781\) 8.99700e18 1.41862
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.86588e17 0.0437125
\(786\) 0 0
\(787\) 4.81906e18 0.722980 0.361490 0.932376i \(-0.382268\pi\)
0.361490 + 0.932376i \(0.382268\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.92414e18 0.424475
\(792\) 0 0
\(793\) 1.15824e18 0.165395
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 8.13421e17 0.112418 0.0562090 0.998419i \(-0.482099\pi\)
0.0562090 + 0.998419i \(0.482099\pi\)
\(798\) 0 0
\(799\) 1.59888e18 0.217402
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5.31098e18 −0.699075
\(804\) 0 0
\(805\) 5.58642e17 0.0723537
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 6.03069e18 0.756313 0.378156 0.925742i \(-0.376558\pi\)
0.378156 + 0.925742i \(0.376558\pi\)
\(810\) 0 0
\(811\) 3.20788e18 0.395897 0.197948 0.980212i \(-0.436572\pi\)
0.197948 + 0.980212i \(0.436572\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.07220e18 −0.128160
\(816\) 0 0
\(817\) −5.59349e18 −0.658021
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1.08418e19 1.23558 0.617789 0.786344i \(-0.288029\pi\)
0.617789 + 0.786344i \(0.288029\pi\)
\(822\) 0 0
\(823\) −3.62368e18 −0.406491 −0.203246 0.979128i \(-0.565149\pi\)
−0.203246 + 0.979128i \(0.565149\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5.78670e18 −0.628992 −0.314496 0.949259i \(-0.601836\pi\)
−0.314496 + 0.949259i \(0.601836\pi\)
\(828\) 0 0
\(829\) −8.10871e18 −0.867655 −0.433828 0.900996i \(-0.642837\pi\)
−0.433828 + 0.900996i \(0.642837\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.83430e18 −0.190229
\(834\) 0 0
\(835\) 2.62063e17 0.0267573
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.53236e19 1.51673 0.758365 0.651830i \(-0.225998\pi\)
0.758365 + 0.651830i \(0.225998\pi\)
\(840\) 0 0
\(841\) 4.68439e18 0.456541
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.97800e17 0.0848420
\(846\) 0 0
\(847\) −1.05326e18 −0.0980156
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.68196e19 −1.51800
\(852\) 0 0
\(853\) 9.91139e18 0.880979 0.440490 0.897758i \(-0.354805\pi\)
0.440490 + 0.897758i \(0.354805\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.72370e18 0.321069 0.160535 0.987030i \(-0.448678\pi\)
0.160535 + 0.987030i \(0.448678\pi\)
\(858\) 0 0
\(859\) −3.07811e18 −0.261414 −0.130707 0.991421i \(-0.541725\pi\)
−0.130707 + 0.991421i \(0.541725\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 4.68138e18 0.385748 0.192874 0.981224i \(-0.438219\pi\)
0.192874 + 0.981224i \(0.438219\pi\)
\(864\) 0 0
\(865\) 1.22260e18 0.0992387
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.61379e19 −2.05893
\(870\) 0 0
\(871\) −5.76445e17 −0.0447342
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.46853e18 0.110619
\(876\) 0 0
\(877\) −3.27869e18 −0.243334 −0.121667 0.992571i \(-0.538824\pi\)
−0.121667 + 0.992571i \(0.538824\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 8.02437e18 0.578186 0.289093 0.957301i \(-0.406646\pi\)
0.289093 + 0.957301i \(0.406646\pi\)
\(882\) 0 0
\(883\) −2.07925e19 −1.47626 −0.738128 0.674661i \(-0.764290\pi\)
−0.738128 + 0.674661i \(0.764290\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.61191e19 −1.80075 −0.900376 0.435112i \(-0.856709\pi\)
−0.900376 + 0.435112i \(0.856709\pi\)
\(888\) 0 0
\(889\) 8.77489e18 0.596184
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.19191e19 1.44640
\(894\) 0 0
\(895\) 7.17124e17 0.0466385
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −8.71138e18 −0.550363
\(900\) 0 0
\(901\) 2.07138e18 0.128988
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.68974e18 0.223244
\(906\) 0 0
\(907\) −2.55190e19 −1.52201 −0.761004 0.648747i \(-0.775293\pi\)
−0.761004 + 0.648747i \(0.775293\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.62951e19 0.944466 0.472233 0.881474i \(-0.343448\pi\)
0.472233 + 0.881474i \(0.343448\pi\)
\(912\) 0 0
\(913\) −2.71098e19 −1.54905
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −9.76826e17 −0.0542521
\(918\) 0 0
\(919\) −2.25963e18 −0.123733 −0.0618667 0.998084i \(-0.519705\pi\)
−0.0618667 + 0.998084i \(0.519705\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.13409e19 −1.66840
\(924\) 0 0
\(925\) −2.19361e19 −1.15143
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.38768e19 0.708250 0.354125 0.935198i \(-0.384779\pi\)
0.354125 + 0.935198i \(0.384779\pi\)
\(930\) 0 0
\(931\) −2.51463e19 −1.26561
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 6.66334e17 0.0326149
\(936\) 0 0
\(937\) 1.27938e19 0.617578 0.308789 0.951131i \(-0.400076\pi\)
0.308789 + 0.951131i \(0.400076\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.00758e19 0.473093 0.236547 0.971620i \(-0.423984\pi\)
0.236547 + 0.971620i \(0.423984\pi\)
\(942\) 0 0
\(943\) 3.17241e19 1.46914
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.66672e19 −0.750912 −0.375456 0.926840i \(-0.622514\pi\)
−0.375456 + 0.926840i \(0.622514\pi\)
\(948\) 0 0
\(949\) 1.85007e19 0.822163
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.79060e19 −1.20668 −0.603341 0.797483i \(-0.706164\pi\)
−0.603341 + 0.797483i \(0.706164\pi\)
\(954\) 0 0
\(955\) −4.03119e18 −0.171954
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −8.09981e18 −0.336243
\(960\) 0 0
\(961\) −1.93397e19 −0.792042
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.80938e18 0.0721276
\(966\) 0 0
\(967\) 4.06377e19 1.59829 0.799147 0.601136i \(-0.205285\pi\)
0.799147 + 0.601136i \(0.205285\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.91648e18 −0.149958 −0.0749792 0.997185i \(-0.523889\pi\)
−0.0749792 + 0.997185i \(0.523889\pi\)
\(972\) 0 0
\(973\) 5.50865e18 0.208119
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −8.91758e18 −0.328044 −0.164022 0.986457i \(-0.552447\pi\)
−0.164022 + 0.986457i \(0.552447\pi\)
\(978\) 0 0
\(979\) −1.73587e19 −0.630130
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.03354e19 1.07239 0.536194 0.844095i \(-0.319862\pi\)
0.536194 + 0.844095i \(0.319862\pi\)
\(984\) 0 0
\(985\) 5.08430e18 0.177376
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.58446e19 0.538401
\(990\) 0 0
\(991\) −4.90085e19 −1.64359 −0.821794 0.569785i \(-0.807027\pi\)
−0.821794 + 0.569785i \(0.807027\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4.12423e17 0.0134739
\(996\) 0 0
\(997\) −1.57448e19 −0.507715 −0.253857 0.967242i \(-0.581699\pi\)
−0.253857 + 0.967242i \(0.581699\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 72.14.a.a.1.1 1
3.2 odd 2 8.14.a.a.1.1 1
4.3 odd 2 144.14.a.f.1.1 1
12.11 even 2 16.14.a.c.1.1 1
15.2 even 4 200.14.c.a.49.2 2
15.8 even 4 200.14.c.a.49.1 2
15.14 odd 2 200.14.a.a.1.1 1
24.5 odd 2 64.14.a.f.1.1 1
24.11 even 2 64.14.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.14.a.a.1.1 1 3.2 odd 2
16.14.a.c.1.1 1 12.11 even 2
64.14.a.d.1.1 1 24.11 even 2
64.14.a.f.1.1 1 24.5 odd 2
72.14.a.a.1.1 1 1.1 even 1 trivial
144.14.a.f.1.1 1 4.3 odd 2
200.14.a.a.1.1 1 15.14 odd 2
200.14.c.a.49.1 2 15.8 even 4
200.14.c.a.49.2 2 15.2 even 4