Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,12,Mod(1,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(3.07337272224\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −516.000 | −1.22598 | −0.612989 | − | 0.790091i | \(-0.710033\pi\) | ||||
−0.612989 | + | 0.790091i | \(0.710033\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10530.0 | −1.50693 | −0.753465 | − | 0.657487i | \(-0.771619\pi\) | ||||
−0.753465 | + | 0.657487i | \(0.771619\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49304.0 | 1.10877 | 0.554387 | − | 0.832259i | \(-0.312953\pi\) | ||||
0.554387 | + | 0.832259i | \(0.312953\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 89109.0 | 0.503023 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −309420. | −0.579280 | −0.289640 | − | 0.957136i | \(-0.593536\pi\) | ||||
−0.289640 | + | 0.957136i | \(0.593536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.72359e6 | −1.28750 | −0.643749 | − | 0.765237i | \(-0.722622\pi\) | ||||
−0.643749 | + | 0.765237i | \(0.722622\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.43348e6 | 1.84746 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.27950e6 | −0.389378 | −0.194689 | − | 0.980865i | \(-0.562370\pi\) | ||||
−0.194689 | + | 0.980865i | \(0.562370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.55044e6 | 0.421608 | 0.210804 | − | 0.977528i | \(-0.432392\pi\) | ||||
0.210804 | + | 0.977528i | \(0.432392\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.54409e7 | −1.35933 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.28287e6 | −0.235939 | −0.117969 | − | 0.993017i | \(-0.537638\pi\) | ||||
−0.117969 | + | 0.993017i | \(0.537638\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.20528e7 | 1.27084 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.54276e7 | 0.609283 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.90400e7 | −0.625046 | −0.312523 | − | 0.949910i | \(-0.601174\pi\) | ||||
−0.312523 | + | 0.949910i | \(0.601174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.41741e8 | −0.889212 | −0.444606 | − | 0.895726i | \(-0.646656\pi\) | ||||
−0.444606 | + | 0.895726i | \(0.646656\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.59661e8 | 0.710185 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.19171e8 | −1.67085 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.11367e8 | 1.68649 | 0.843246 | − | 0.537528i | \(-0.180642\pi\) | ||||
0.843246 | + | 0.537528i | \(0.180642\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.89375e8 | 1.57844 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.22526e9 | −1.65165 | −0.825825 | − | 0.563927i | \(-0.809290\pi\) | ||||
−0.825825 | + | 0.563927i | \(0.809290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.36062e7 | −0.0348613 | −0.0174306 | − | 0.999848i | \(-0.505549\pi\) | ||||
−0.0174306 | + | 0.999848i | \(0.505549\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.38318e8 | −0.758021 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.23215e8 | 0.0783653 | 0.0391827 | − | 0.999232i | \(-0.487525\pi\) | ||||
0.0391827 | + | 0.999232i | \(0.487525\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.53558e8 | 0.229379 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17622e9 | 0.477368 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.10612e9 | 0.363317 | 0.181658 | − | 0.983362i | \(-0.441853\pi\) | ||||
0.181658 | + | 0.983362i | \(0.441853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.25819e9 | 0.872935 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.34803e9 | −0.516882 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.06278e9 | −1.65035 | −0.825174 | − | 0.564879i | \(-0.808923\pi\) | ||||
−0.825174 | + | 0.564879i | \(0.808923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.85415e9 | −0.584271 | −0.292136 | − | 0.956377i | \(-0.594366\pi\) | ||||
−0.292136 | + | 0.956377i | \(0.594366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.39343e9 | 0.557739 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.81494e10 | 1.94017 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.53138e10 | −1.38570 | −0.692852 | − | 0.721080i | \(-0.743646\pi\) | ||||
−0.692852 | + | 0.721080i | \(0.743646\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.75796e9 | 0.289256 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.06196e10 | 1.35631 | 0.678156 | − | 0.734918i | \(-0.262779\pi\) | ||||
0.678156 | + | 0.734918i | \(0.262779\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.06372e9 | −0.116513 | −0.0582566 | − | 0.998302i | \(-0.518554\pi\) | ||||
−0.0582566 | + | 0.998302i | \(0.518554\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.20192e10 | −1.55802 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.52556e10 | −0.642291 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.36899e10 | 0.500553 | 0.250277 | − | 0.968174i | \(-0.419478\pi\) | ||||
0.250277 | + | 0.968174i | \(0.419478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.92260e10 | −1.24999 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.55704e10 | 1.82717 | 0.913584 | − | 0.406650i | \(-0.133303\pi\) | ||||
0.913584 | + | 0.406650i | \(0.133303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.40032e10 | 0.586765 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.56247e10 | 0.766293 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.97155e10 | −0.564077 | −0.282038 | − | 0.959403i | \(-0.591011\pi\) | ||||
−0.282038 | + | 0.959403i | \(0.591011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.49801e10 | −1.42754 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.31382e10 | 1.09015 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.79162e10 | −0.635334 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.34396e10 | −0.277144 | −0.138572 | − | 0.990352i | \(-0.544251\pi\) | ||||
−0.138572 | + | 0.990352i | \(0.544251\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.75721e10 | −0.291391 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.52020e11 | −1.43924 | −0.719620 | − | 0.694368i | \(-0.755684\pi\) | ||||
−0.719620 | + | 0.694368i | \(0.755684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.69858e11 | 1.44371 | 0.721856 | − | 0.692043i | \(-0.243289\pi\) | ||||
0.721856 | + | 0.692043i | \(0.243289\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.67892e11 | 2.04842 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.39932e10 | −0.234305 | −0.117153 | − | 0.993114i | \(-0.537377\pi\) | ||||
−0.117153 | + | 0.993114i | \(0.537377\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.20016e11 | 0.747127 | 0.373563 | − | 0.927605i | \(-0.378136\pi\) | ||||
0.373563 | + | 0.927605i | \(0.378136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.67065e11 | −2.06760 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.17612e10 | −0.0600510 | −0.0300255 | − | 0.999549i | \(-0.509559\pi\) | ||||
−0.0300255 | + | 0.999549i | \(0.509559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.66886e10 | 0.355544 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.53588e11 | −0.647641 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.12389e11 | −0.431732 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.89571e11 | −0.664435 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.32235e11 | 2.02489 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.39256e11 | −0.408138 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.54679e10 | −0.202694 | −0.101347 | − | 0.994851i | \(-0.532315\pi\) | ||||
−0.101347 | + | 0.994851i | \(0.532315\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.73408e10 | 0.0427392 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.60244e11 | 1.72171 | 0.860857 | − | 0.508847i | \(-0.169928\pi\) | ||||
0.860857 | + | 0.508847i | \(0.169928\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.24355e11 | 0.467468 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.78353e11 | −0.918148 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.83847e11 | −1.21059 | −0.605293 | − | 0.796003i | \(-0.706944\pi\) | ||||
−0.605293 | + | 0.796003i | \(0.706944\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.47422e11 | −1.54868 | −0.774341 | − | 0.632769i | \(-0.781918\pi\) | ||||
−0.774341 | + | 0.632769i | \(0.781918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.35787e10 | −0.0960742 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.33314e11 | 0.745822 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.26991e11 | 0.941901 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.34036e11 | −0.281214 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.07160e12 | 1.19539 | 0.597693 | − | 0.801725i | \(-0.296084\pi\) | ||||
0.597693 | + | 0.801725i | \(0.296084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94017e11 | −0.926771 | −0.463386 | − | 0.886157i | \(-0.653365\pi\) | ||||
−0.463386 | + | 0.886157i | \(0.653365\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.03124e11 | −0.195866 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.49253e12 | 1.33998 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.55657e11 | 0.381233 | 0.190616 | − | 0.981665i | \(-0.438951\pi\) | ||||
0.190616 | + | 0.981665i | \(0.438951\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.70759e11 | −0.445419 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.59075e11 | −0.261603 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.45519e12 | −0.990575 | −0.495287 | − | 0.868729i | \(-0.664937\pi\) | ||||
−0.495287 | + | 0.868729i | \(0.664937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.68123e12 | −1.07020 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.63036e11 | −0.216277 | −0.108138 | − | 0.994136i | \(-0.534489\pi\) | ||||
−0.108138 | + | 0.994136i | \(0.534489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.17862e12 | 0.657651 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.05486e11 | 0.212079 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.79133e12 | −0.878866 | −0.439433 | − | 0.898275i | \(-0.644821\pi\) | ||||
−0.439433 | + | 0.898275i | \(0.644821\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.05945e12 | 1.40907 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.67639e12 | 2.02329 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.17420e11 | −0.291798 | −0.145899 | − | 0.989300i | \(-0.546607\pi\) | ||||
−0.145899 | + | 0.989300i | \(0.546607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.81682e12 | −0.695153 | −0.347576 | − | 0.937652i | \(-0.612995\pi\) | ||||
−0.347576 | + | 0.937652i | \(0.612995\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.98874e12 | 0.716304 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.49069e12 | −2.54143 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.05324e11 | 0.225559 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.23976e12 | 0.675557 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.65644e12 | 1.32547 | 0.662736 | − | 0.748853i | \(-0.269395\pi\) | ||||
0.662736 | + | 0.748853i | \(0.269395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.54446e12 | −0.952762 | −0.476381 | − | 0.879239i | \(-0.658052\pi\) | ||||
−0.476381 | + | 0.879239i | \(0.658052\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.36511e12 | −2.37861 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.66061e11 | 0.207962 | 0.103981 | − | 0.994579i | \(-0.466842\pi\) | ||||
0.103981 | + | 0.994579i | \(0.466842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.22516e8 | 0.000118688 0 | 5.93441e−5 | − | 1.00000i | \(-0.499981\pi\) | ||||
5.93441e−5 | 1.00000i | \(0.499981\pi\) | ||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.90190e12 | 1.69884 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.40395e12 | −0.693035 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.29020e13 | 2.48892 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.48969e11 | −0.118683 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.40800e12 | −0.244229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51292e12 | 0.578248 | 0.289124 | − | 0.957292i | \(-0.406636\pi\) | ||||
0.289124 | + | 0.957292i | \(0.406636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.06397e13 | −1.66281 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.53873e11 | 0.0525335 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.98838e12 | −0.985935 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.06488e12 | 0.142843 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.92894e12 | 0.501323 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.34171e13 | −1.62923 | −0.814616 | − | 0.580000i | \(-0.803052\pi\) | ||||
−0.814616 | + | 0.580000i | \(0.803052\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.52946e12 | 0.639262 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.80436e12 | 0.749281 | 0.374641 | − | 0.927170i | \(-0.377766\pi\) | ||||
0.374641 | + | 0.927170i | \(0.377766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.91721e12 | −0.725832 | −0.362916 | − | 0.931822i | \(-0.618219\pi\) | ||||
−0.362916 | + | 0.931822i | \(0.618219\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.87191e12 | 0.787434 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.43160e12 | 0.708965 | 0.354483 | − | 0.935063i | \(-0.384657\pi\) | ||||
0.354483 | + | 0.935063i | \(0.384657\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.29745e12 | −0.118091 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.06397e12 | −0.613668 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.24747e13 | 1.03477 | 0.517383 | − | 0.855754i | \(-0.326906\pi\) | ||||
0.517383 | + | 0.855754i | \(0.326906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.40984e12 | 0.507871 | 0.253936 | − | 0.967221i | \(-0.418275\pi\) | ||||
0.253936 | + | 0.967221i | \(0.418275\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.21933e13 | 0.923179 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.77596e12 | −0.345659 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.84312e12 | −0.542820 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.38343e13 | −2.24007 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.80663e13 | −1.14463 | −0.572314 | − | 0.820035i | \(-0.693954\pi\) | ||||
−0.572314 | + | 0.820035i | \(0.693954\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.25347e12 | 0.136675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.23856e13 | −0.719361 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.99754e13 | 1.66775 | 0.833877 | − | 0.551950i | \(-0.186116\pi\) | ||||
0.833877 | + | 0.551950i | \(0.186116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50732e13 | 1.86994 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.15209e12 | −0.314412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.35042e13 | −0.661777 | −0.330888 | − | 0.943670i | \(-0.607348\pi\) | ||||
−0.330888 | + | 0.943670i | \(0.607348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.16475e13 | −0.547493 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.53332e13 | 0.691546 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.82116e13 | 1.22121 | 0.610605 | − | 0.791935i | \(-0.290926\pi\) | ||||
0.610605 | + | 0.791935i | \(0.290926\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.01156e13 | −1.25158 | −0.625792 | − | 0.779990i | \(-0.715224\pi\) | ||||
−0.625792 | + | 0.779990i | \(0.715224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.38497e13 | 1.75014 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.92004e13 | −0.736173 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.74924e12 | 0.322353 | 0.161176 | − | 0.986926i | \(-0.448471\pi\) | ||||
0.161176 | + | 0.986926i | \(0.448471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.26304e13 | −0.447294 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.09851e13 | −1.73603 | −0.868017 | − | 0.496534i | \(-0.834606\pi\) | ||||
−0.868017 | + | 0.496534i | \(0.834606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.57604e13 | 0.516109 | 0.258055 | − | 0.966130i | \(-0.416919\pi\) | ||||
0.258055 | + | 0.966130i | \(0.416919\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.47247e13 | 0.778906 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.04103e13 | −1.83131 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.90758e13 | −0.848385 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.20948e13 | 0.339773 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.05220e13 | −0.284659 | −0.142329 | − | 0.989819i | \(-0.545459\pi\) | ||||
−0.142329 | + | 0.989819i | \(0.545459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.54311e13 | 2.48696 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.40562e13 | −0.352946 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.25527e13 | 0.303771 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.65692e12 | −0.0386533 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.84423e13 | 1.76448 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.05842e13 | 0.880457 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.62241e13 | −1.17669 | −0.588344 | − | 0.808611i | \(-0.700220\pi\) | ||||
−0.588344 | + | 0.808611i | \(0.700220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.76466e13 | −1.76996 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.94567e13 | −0.379216 | −0.189608 | − | 0.981860i | \(-0.560722\pi\) | ||||
−0.189608 | + | 0.981860i | \(0.560722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.61189e13 | 0.491430 | 0.245715 | − | 0.969342i | \(-0.420977\pi\) | ||||
0.245715 | + | 0.969342i | \(0.420977\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.62628e13 | −0.840474 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.21160e13 | 0.563503 | 0.281751 | − | 0.959487i | \(-0.409085\pi\) | ||||
0.281751 | + | 0.959487i | \(0.409085\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.13624e13 | 0.362077 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75405e13 | 0.287253 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.03727e13 | −0.164165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.06954e14 | −1.63620 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.19284e13 | −0.915961 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.07497e12 | 0.0868894 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.69111e13 | 0.372287 | 0.186143 | − | 0.982523i | \(-0.440401\pi\) | ||||
0.186143 | + | 0.982523i | \(0.440401\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.33892e13 | 0.848344 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.61254e14 | 2.08816 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.37528e13 | 0.548329 | 0.274164 | − | 0.961683i | \(-0.411599\pi\) | ||||
0.274164 | + | 0.961683i | \(0.411599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.06878e12 | 0.0736213 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.38574e13 | 0.515103 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.51279e13 | −0.854444 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.95713e13 | −0.435889 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.17892e13 | −0.979443 | −0.489722 | − | 0.871879i | \(-0.662902\pi\) | ||||
−0.489722 | + | 0.871879i | \(0.662902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.10757e14 | 1.14507 | 0.572534 | − | 0.819881i | \(-0.305960\pi\) | ||||
0.572534 | + | 0.819881i | \(0.305960\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.82988e13 | −0.784451 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.25419e12 | −0.0607310 | −0.0303655 | − | 0.999539i | \(-0.509667\pi\) | ||||
−0.0303655 | + | 0.999539i | \(0.509667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.17125e14 | −2.04387 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.79925e13 | 0.529294 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.07090e13 | 0.183291 | 0.0916453 | − | 0.995792i | \(-0.470787\pi\) | ||||
0.0916453 | + | 0.995792i | \(0.470787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.57837e13 | −0.822247 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.78186e13 | 0.814582 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.17310e13 | 0.175577 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.05329e14 | 1.60985 | 0.804926 | − | 0.593375i | \(-0.202205\pi\) | ||||
0.804926 | + | 0.593375i | \(0.202205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.09182e14 | −0.830817 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.45362e13 | 0.402836 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.65041e14 | −1.18357 | −0.591783 | − | 0.806097i | \(-0.701576\pi\) | ||||
−0.591783 | + | 0.806097i | \(0.701576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.18559e13 | 0.500369 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.18997e14 | 0.804745 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.19092e14 | 0.782289 | 0.391144 | − | 0.920329i | \(-0.372079\pi\) | ||||
0.391144 | + | 0.920329i | \(0.372079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.89414e13 | 0.248499 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.97765e13 | −0.308625 | −0.154313 | − | 0.988022i | \(-0.549316\pi\) | ||||
−0.154313 | + | 0.988022i | \(0.549316\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.60642e14 | 0.967888 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.99462e12 | −0.0175360 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.93513e14 | −1.10151 | −0.550754 | − | 0.834667i | \(-0.685660\pi\) | ||||
−0.550754 | + | 0.834667i | \(0.685660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.66013e13 | 0.0918693 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.92286e14 | −2.11078 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.44154e14 | −0.754299 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.07502e13 | −0.207387 | −0.103694 | − | 0.994609i | \(-0.533066\pi\) | ||||
−0.103694 | + | 0.994609i | \(0.533066\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.15767e14 | −0.573106 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.55462e13 | −0.0748740 | −0.0374370 | − | 0.999299i | \(-0.511919\pi\) | ||||
−0.0374370 | + | 0.999299i | \(0.511919\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.44303e14 | 1.14486 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.13050e14 | 1.88365 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.20111e14 | −0.976951 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.61195e14 | 1.56050 | 0.780250 | − | 0.625468i | \(-0.215092\pi\) | ||||
0.780250 | + | 0.625468i | \(0.215092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.52865e14 | 1.48415 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.46831e14 | −1.82986 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.90457e14 | −2.75342 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.88870e14 | 1.89865 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.11674e14 | 1.17902 | 0.589512 | − | 0.807760i | \(-0.299320\pi\) | ||||
0.589512 | + | 0.807760i | \(0.299320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.62039e14 | 0.965636 | 0.482818 | − | 0.875721i | \(-0.339613\pi\) | ||||
0.482818 | + | 0.875721i | \(0.339613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.09795e13 | 0.0394196 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.41449e14 | −0.494837 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.90025e14 | −0.647825 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.75190e14 | −0.914362 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.81245e14 | 1.23475 | 0.617376 | − | 0.786668i | \(-0.288196\pi\) | ||||
0.617376 | + | 0.786668i | \(0.288196\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.90598e14 | −0.917505 | −0.458753 | − | 0.888564i | \(-0.651704\pi\) | ||||
−0.458753 | + | 0.888564i | \(0.651704\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.75128e14 | −1.15475 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.31403e13 | −0.0994738 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.51507e13 | −0.161434 | −0.0807172 | − | 0.996737i | \(-0.525721\pi\) | ||||
−0.0807172 | + | 0.996737i | \(0.525721\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.04161e13 | 0.115383 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.24887e14 | −0.347774 | −0.173887 | − | 0.984766i | \(-0.555633\pi\) | ||||
−0.173887 | + | 0.984766i | \(0.555633\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.12904e14 | 0.850025 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.52946e14 | −1.46552 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.82240e14 | −0.471290 | −0.235645 | − | 0.971839i | \(-0.575720\pi\) | ||||
−0.235645 | + | 0.971839i | \(0.575720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.79121e14 | 0.956768 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.61313e14 | 1.13620 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.94840e14 | 2.15121 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.77455e14 | 0.651110 | 0.325555 | − | 0.945523i | \(-0.394449\pi\) | ||||
0.325555 | + | 0.945523i | \(0.394449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.03552e14 | −0.237241 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.08550e13 | 0.113757 | 0.0568785 | − | 0.998381i | \(-0.481885\pi\) | ||||
0.0568785 | + | 0.998381i | \(0.481885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.59886e12 | −0.0100451 | −0.00502255 | − | 0.999987i | \(-0.501599\pi\) | ||||
−0.00502255 | + | 0.999987i | \(0.501599\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.70145e14 | −1.64279 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.85607e14 | 0.595012 | 0.297506 | − | 0.954720i | \(-0.403845\pi\) | ||||
0.297506 | + | 0.954720i | \(0.403845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.55030e14 | −1.53643 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.35119e14 | −0.467383 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.03984e13 | 0.0201944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.82368e14 | 0.535797 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.85654e13 | 0.182757 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.32901e14 | 1.14681 | 0.573403 | − | 0.819273i | \(-0.305623\pi\) | ||||
0.573403 | + | 0.819273i | \(0.305623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.22611e15 | −2.17135 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.85283e14 | 0.320719 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.46819e14 | 0.417638 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.43316e14 | −1.22960 | −0.614800 | − | 0.788683i | \(-0.710763\pi\) | ||||
−0.614800 | + | 0.788683i | \(0.710763\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.50877e14 | 1.21442 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.26044e15 | −1.99330 | −0.996652 | − | 0.0817625i | \(-0.973945\pi\) | ||||
−0.996652 | + | 0.0817625i | \(0.973945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.57377e14 | 0.243379 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.90334e14 | 0.439106 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.01663e15 | 1.50384 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.48550e14 | 0.649019 | 0.324510 | − | 0.945882i | \(-0.394801\pi\) | ||||
0.324510 | + | 0.945882i | \(0.394801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.87327e14 | 0.265150 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.23495e14 | 0.586441 | 0.293221 | − | 0.956045i | \(-0.405273\pi\) | ||||
0.293221 | + | 0.956045i | \(0.405273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.60077e15 | 2.16884 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.08166e14 | −0.806266 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.69213e14 | −1.25739 | −0.628697 | − | 0.777650i | \(-0.716412\pi\) | ||||
−0.628697 | + | 0.777650i | \(0.716412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.01750e14 | −0.129187 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.06716e14 | 0.256879 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.78860e15 | −2.17558 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.81251e13 | −0.0453955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.24327e14 | 1.07747 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.74209e14 | −0.769462 | −0.384731 | − | 0.923029i | \(-0.625706\pi\) | ||||
−0.384731 | + | 0.923029i | \(0.625706\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.55642e14 | 0.509172 | 0.254586 | − | 0.967050i | \(-0.418061\pi\) | ||||
0.254586 | + | 0.967050i | \(0.418061\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.57868e15 | −1.72750 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.23098e14 | 0.346239 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.99770e14 | −0.944333 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.07575e14 | −0.830163 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.11185e15 | 2.12649 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.57949e14 | 0.353081 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.70189e14 | 0.357738 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.40340e14 | −0.132875 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.14966e15 | 1.06655 | 0.533277 | − | 0.845941i | \(-0.320960\pi\) | ||||
0.533277 | + | 0.845941i | \(0.320960\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.37480e14 | 0.852242 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.26377e15 | −1.12587 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.71517e14 | −0.760931 | −0.380466 | − | 0.924795i | \(-0.624236\pi\) | ||||
−0.380466 | + | 0.924795i | \(0.624236\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.43439e14 | −0.293902 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.14163e14 | −0.263524 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.74965e14 | 0.555000 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.86520e15 | 3.11573 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.80516e14 | −0.537818 | −0.268909 | − | 0.963166i | \(-0.586663\pi\) | ||||
−0.268909 | + | 0.963166i | \(0.586663\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.79235e13 | 0.0448838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.63947e14 | −0.276530 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.84626e14 | −0.659119 | −0.329559 | − | 0.944135i | \(-0.606900\pi\) | ||||
−0.329559 | + | 0.944135i | \(0.606900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.23846e14 | 0.0904927 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.93400e15 | −1.38596 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.85892e15 | −1.30660 | −0.653300 | − | 0.757099i | \(-0.726616\pi\) | ||||
−0.653300 | + | 0.757099i | \(0.726616\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.74453e14 | 0.120276 | 0.0601382 | − | 0.998190i | \(-0.480846\pi\) | ||||
0.0601382 | + | 0.998190i | \(0.480846\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.40272e15 | −1.62500 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.51922e14 | −0.299841 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.79199e14 | −0.442110 | −0.221055 | − | 0.975261i | \(-0.570950\pi\) | ||||
−0.221055 | + | 0.975261i | \(0.570950\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.82894e15 | 1.16807 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.23288e15 | 2.02592 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.42256e14 | −0.210462 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.61728e15 | 0.975950 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.34702e14 | −0.198221 | −0.0991104 | − | 0.995076i | \(-0.531600\pi\) | ||||
−0.0991104 | + | 0.995076i | \(0.531600\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.44983e14 | −0.374899 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.46888e14 | −0.254957 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.98542e15 | 1.11186 | 0.555931 | − | 0.831228i | \(-0.312362\pi\) | ||||
0.555931 | + | 0.831228i | \(0.312362\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.18345e15 | 0.650590 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.69618e11 | −0.000145509 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.19216e14 | 0.222121 | 0.111061 | − | 0.993814i | \(-0.464575\pi\) | ||||
0.111061 | + | 0.993814i | \(0.464575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.53284e15 | −1.31764 | −0.658822 | − | 0.752299i | \(-0.728945\pi\) | ||||
−0.658822 | + | 0.752299i | \(0.728945\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.36459e15 | −0.697041 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.99618e15 | 1.00126 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.43383e14 | 0.464676 | 0.232338 | − | 0.972635i | \(-0.425362\pi\) | ||||
0.232338 | + | 0.972635i | \(0.425362\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.75644e15 | 0.849645 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.12372e14 | −0.100895 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.26745e15 | −0.591422 | −0.295711 | − | 0.955277i | \(-0.595557\pi\) | ||||
−0.295711 | + | 0.955277i | \(0.595557\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.65744e15 | −3.05136 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.35186e15 | 1.95933 | 0.979663 | − | 0.200649i | \(-0.0643051\pi\) | ||||
0.979663 | + | 0.200649i | \(0.0643051\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.26851e15 | −0.561040 | −0.280520 | − | 0.959848i | \(-0.590507\pi\) | ||||
−0.280520 | + | 0.959848i | \(0.590507\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.30843e14 | −0.143754 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.46509e15 | −0.625433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.56356e15 | −0.655804 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.26527e14 | 0.299420 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.62156e15 | −0.656682 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.34776e15 | 1.33227 | 0.666137 | − | 0.745830i | \(-0.267947\pi\) | ||||
0.666137 | + | 0.745830i | \(0.267947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.81266e15 | −0.708920 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.94677e14 | 0.305447 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.81749e14 | −0.295325 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.83739e15 | 0.682256 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.75533e14 | −0.173565 | −0.0867825 | − | 0.996227i | \(-0.527659\pi\) | ||||
−0.0867825 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.59955e15 | 1.65027 | 0.825135 | − | 0.564935i | \(-0.191099\pi\) | ||||
0.825135 | + | 0.564935i | \(0.191099\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.82599e14 | −0.0644050 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.98217e15 | 1.72761 | 0.863803 | − | 0.503830i | \(-0.168076\pi\) | ||||
0.863803 | + | 0.503830i | \(0.168076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.80421e15 | 0.956013 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.60601e15 | 1.20873 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.59598e15 | −1.18521 | −0.592605 | − | 0.805493i | \(-0.701900\pi\) | ||||
−0.592605 | + | 0.805493i | \(0.701900\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00537e15 | −2.59450 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.83896e14 | −0.0586088 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.26177e15 | −1.02231 | −0.511156 | − | 0.859488i | \(-0.670783\pi\) | ||||
−0.511156 | + | 0.859488i | \(0.670783\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.94481e14 | −0.0907714 | −0.0453857 | − | 0.998970i | \(-0.514452\pi\) | ||||
−0.0453857 | + | 0.998970i | \(0.514452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.02733e15 | −0.614611 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.36246e15 | −0.704442 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.02810e14 | 0.147473 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.92324e15 | 1.99740 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.19255e15 | 0.338457 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.07023e15 | −0.857211 | −0.428606 | − | 0.903492i | \(-0.640995\pi\) | ||||
−0.428606 | + | 0.903492i | \(0.640995\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.81891e15 | 0.774302 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.04157e15 | −1.09223 | −0.546113 | − | 0.837712i | \(-0.683893\pi\) | ||||
−0.546113 | + | 0.837712i | \(0.683893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.15567e15 | −0.307290 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.51105e15 | −0.918603 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.60126e15 | −1.69947 | −0.849734 | − | 0.527211i | \(-0.823238\pi\) | ||||
−0.849734 | + | 0.527211i | \(0.823238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.20091e15 | 1.82427 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.56928e15 | 0.889854 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.90650e15 | −0.467770 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.73449e14 | 0.235063 | 0.117531 | − | 0.993069i | \(-0.462502\pi\) | ||||
0.117531 | + | 0.993069i | \(0.462502\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.35942e15 | −0.323087 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.97636e15 | 2.33376 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.79299e15 | 0.643115 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.83471e15 | −0.869176 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.39327e15 | 0.980255 | 0.490127 | − | 0.871651i | \(-0.336950\pi\) | ||||
0.490127 | + | 0.871651i | \(0.336950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.23704e15 | 0.711039 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.69484e14 | 0.144777 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.49519e15 | −1.59579 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.72732e15 | 0.362091 | 0.181046 | − | 0.983475i | \(-0.442052\pi\) | ||||
0.181046 | + | 0.983475i | \(0.442052\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.21989e15 | 0.251790 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.03228e15 | 0.209800 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.61580e15 | −1.12390 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.43696e15 | −1.26860 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.55073e15 | −1.27140 | −0.635698 | − | 0.771938i | \(-0.719288\pi\) | ||||
−0.635698 | + | 0.771938i | \(0.719288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.37467e15 | 1.60075 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.30748e15 | −0.622639 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.28413e15 | −0.794334 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.68611e15 | −0.490552 | −0.245276 | − | 0.969453i | \(-0.578879\pi\) | ||||
−0.245276 | + | 0.969453i | \(0.578879\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.57047e14 | 0.118194 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.66054e13 | 0.0135742 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.79856e14 | −0.0663052 | −0.0331526 | − | 0.999450i | \(-0.510555\pi\) | ||||
−0.0331526 | + | 0.999450i | \(0.510555\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.46440e15 | 0.423770 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.73839e15 | 0.802711 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.97557e15 | 0.329722 | 0.164861 | − | 0.986317i | \(-0.447282\pi\) | ||||
0.164861 | + | 0.986317i | \(0.447282\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.04705e15 | 0.665485 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.86579e15 | 1.27439 | 0.637197 | − | 0.770701i | \(-0.280094\pi\) | ||||
0.637197 | + | 0.770701i | \(0.280094\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.12839e16 | −1.80136 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.84292e15 | 0.919107 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.67600e15 | −0.259791 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.45429e15 | −0.833141 | −0.416571 | − | 0.909103i | \(-0.636768\pi\) | ||||
−0.416571 | + | 0.909103i | \(0.636768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.32223e15 | 1.40329 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.41400e15 | 1.39658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.14636e16 | −1.67608 | −0.838039 | − | 0.545611i | \(-0.816298\pi\) | ||||
−0.838039 | + | 0.545611i | \(0.816298\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.16279e15 | −0.167560 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.25092e15 | −1.02986 | −0.514929 | − | 0.857233i | \(-0.672182\pi\) | ||||
−0.514929 | + | 0.857233i | \(0.672182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.91728e15 | 0.828394 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.13890e15 | 0.295156 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.56206e16 | 2.12482 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.06294e16 | 1.42533 | 0.712664 | − | 0.701506i | \(-0.247488\pi\) | ||||
0.712664 | + | 0.701506i | \(0.247488\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.54673e16 | −2.04463 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.37768e14 | −0.0440181 | −0.0220090 | − | 0.999758i | \(-0.507006\pi\) | ||||
−0.0220090 | + | 0.999758i | \(0.507006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.79540e15 | −1.13005 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.80978e16 | −2.29250 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.57549e15 | −0.696349 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.38012e15 | −0.785685 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.13632e15 | −0.380830 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.79807e15 | −0.574491 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.05334e16 | 1.24368 | 0.621839 | − | 0.783145i | \(-0.286386\pi\) | ||||
0.621839 | + | 0.783145i | \(0.286386\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.96816e15 | 0.811324 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.79875e14 | −0.0665830 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.64299e15 | 0.752248 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.01009e15 | 0.671215 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.44072e16 | 1.58693 | 0.793467 | − | 0.608613i | \(-0.208274\pi\) | ||||
0.793467 | + | 0.608613i | \(0.208274\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.80868e14 | −0.0305137 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.64792e15 | −0.283743 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.38556e14 | 0.0674937 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.78106e15 | 0.394217 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.45572e16 | −1.49718 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.25295e15 | 0.330036 | 0.165018 | − | 0.986291i | \(-0.447232\pi\) | ||||
0.165018 | + | 0.986291i | \(0.447232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.71598e15 | −0.371928 | −0.185964 | − | 0.982557i | \(-0.559541\pi\) | ||||
−0.185964 | + | 0.982557i | \(0.559541\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.55396e16 | 1.53442 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.53231e16 | 1.49273 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.52923e14 | −0.0146978 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.57249e15 | −0.718087 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.73451e16 | −1.62289 | −0.811444 | − | 0.584430i | \(-0.801318\pi\) | ||||
−0.811444 | + | 0.584430i | \(0.801318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.13360e16 | −1.04655 | −0.523274 | − | 0.852165i | \(-0.675290\pi\) | ||||
−0.523274 | + | 0.852165i | \(0.675290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.90739e15 | 0.902532 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.73855e14 | 0.0246173 | 0.0123086 | − | 0.999924i | \(-0.496082\pi\) | ||||
0.0123086 | + | 0.999924i | \(0.496082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.81354e14 | −0.0604398 | −0.0302199 | − | 0.999543i | \(-0.509621\pi\) | ||||
−0.0302199 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.51461e15 | −0.395198 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.03389e15 | −0.0893151 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.82277e15 | 0.325914 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.43894e15 | −0.541782 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.25824e16 | −1.04489 | −0.522447 | − | 0.852672i | \(-0.674981\pi\) | ||||
−0.522447 | + | 0.852672i | \(0.674981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.43398e15 | −0.609318 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.63083e16 | 2.12834 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.24108e16 | −0.991034 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.34661e15 | −0.736708 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.13237e15 | −0.632739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.18079e15 | −0.397909 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.74651e16 | 1.32419 | 0.662097 | − | 0.749418i | \(-0.269667\pi\) | ||||
0.662097 | + | 0.749418i | \(0.269667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.26976e15 | −0.319588 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.42451e14 | 0.0105262 | 0.00526310 | − | 0.999986i | \(-0.498325\pi\) | ||||
0.00526310 | + | 0.999986i | \(0.498325\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.42828e16 | 1.04196 | 0.520981 | − | 0.853569i | \(-0.325566\pi\) | ||||
0.520981 | + | 0.853569i | \(0.325566\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.11717e16 | 2.24514 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.56691e16 | −1.82537 | −0.912684 | − | 0.408666i | \(-0.865994\pi\) | ||||
−0.912684 | + | 0.408666i | \(0.865994\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.88627e16 | 1.32439 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.50031e16 | 1.04010 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.23592e15 | −0.289961 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.63947e16 | 1.78409 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.08868e15 | −0.139410 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.86586e15 | −0.452533 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.75472e16 | −1.79300 | −0.896500 | − | 0.443043i | \(-0.853899\pi\) | ||||
−0.896500 | + | 0.443043i | \(0.853899\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.42933e15 | 0.348985 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.19012e14 | −0.0392945 | −0.0196472 | − | 0.999807i | \(-0.506254\pi\) | ||||
−0.0196472 | + | 0.999807i | \(0.506254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.45657e16 | −0.913162 | −0.456581 | − | 0.889682i | \(-0.650926\pi\) | ||||
−0.456581 | + | 0.889682i | \(0.650926\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.92424e16 | −3.04896 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.37845e16 | 0.842971 | 0.421485 | − | 0.906835i | \(-0.361509\pi\) | ||||
0.421485 | + | 0.906835i | \(0.361509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.72087e15 | −0.224742 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.21373e16 | 0.724095 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.60681e14 | 0.0330395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.55443e15 | 0.439719 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.47720e15 | −0.372417 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.78578e15 | 0.555798 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.52141e15 | −0.141467 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.54971e14 | 0.0473881 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.91311e16 | 1.04755 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.60515e16 | −0.868312 | −0.434156 | − | 0.900838i | \(-0.642953\pi\) | ||||
−0.434156 | + | 0.900838i | \(0.642953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.35464e16 | −0.723971 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.36888e15 | −0.283487 | −0.141743 | − | 0.989903i | \(-0.545271\pi\) | ||||
−0.141743 | + | 0.989903i | \(0.545271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.02888e16 | −1.05844 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.09414e16 | −1.07942 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.74831e16 | 1.90899 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.82347e16 | 0.917621 | 0.458811 | − | 0.888534i | \(-0.348276\pi\) | ||||
0.458811 | + | 0.888534i | \(0.348276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.90116e16 | 1.44259 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.55399e16 | −1.74625 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.41423e16 | 2.14326 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.51359e16 | 0.726221 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.38866e16 | 0.658429 | 0.329214 | − | 0.944255i | \(-0.393216\pi\) | ||||
0.329214 | + | 0.944255i | \(0.393216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.06389e15 | 0.0967081 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.00396e16 | 0.464911 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.42706e15 | −0.339901 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.44922e16 | −1.56010 | −0.780051 | − | 0.625716i | \(-0.784807\pi\) | ||||
−0.780051 | + | 0.625716i | \(0.784807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.34774e16 | −0.602483 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.72679e15 | −0.164662 | −0.0823308 | − | 0.996605i | \(-0.526236\pi\) | ||||
−0.0823308 | + | 0.996605i | \(0.526236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.92343e15 | 0.389688 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.35847e16 | −1.01802 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.18404e16 | 1.35848 | 0.679240 | − | 0.733916i | \(-0.262310\pi\) | ||||
0.679240 | + | 0.733916i | \(0.262310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.55701e15 | 0.150010 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.65719e16 | −0.690842 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.83117e15 | −0.116669 | −0.0583344 | − | 0.998297i | \(-0.518579\pi\) | ||||
−0.0583344 | + | 0.998297i | \(0.518579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.90323e16 | −1.99739 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.10230e16 | −0.443898 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.37164e16 | −1.34227 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.31805e15 | −0.209302 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.02910e15 | −0.117861 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.73231e16 | 1.43575 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.32651e16 | 0.884827 | 0.442414 | − | 0.896811i | \(-0.354122\pi\) | ||||
0.442414 | + | 0.896811i | \(0.354122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.35234e15 | 0.201262 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.26973e16 | 0.843857 | 0.421928 | − | 0.906629i | \(-0.361353\pi\) | ||||
0.421928 | + | 0.906629i | \(0.361353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.67117e16 | −1.71714 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.51882e16 | 2.00595 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.97456e16 | 0.709660 | 0.354830 | − | 0.934931i | \(-0.384539\pi\) | ||||
0.354830 | + | 0.934931i | \(0.384539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.19457e15 | 0.326758 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.06945e16 | 0.375822 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.32703e15 | −0.289365 | −0.144682 | − | 0.989478i | \(-0.546216\pi\) | ||||
−0.144682 | + | 0.989478i | \(0.546216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.11963e15 | −0.313385 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.13469e15 | −0.106525 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.44750e14 | 0.00822513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.72947e16 | −0.907138 | −0.453569 | − | 0.891221i | \(-0.649849\pi\) | ||||
−0.453569 | + | 0.891221i | \(0.649849\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.38861e16 | −0.456416 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.50209e12 | −0.000178855 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.85037e16 | 1.23788 | 0.618941 | − | 0.785437i | \(-0.287562\pi\) | ||||
0.618941 | + | 0.785437i | \(0.287562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.23157e16 | 1.02755 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 4.12.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 36.12.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 16.12.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 100.12.c.a.49.2 | 2 | |||
5.3 | odd | 4 | 100.12.c.a.49.1 | 2 | |||
5.4 | even | 2 | 100.12.a.b.1.1 | 1 | |||
7.2 | even | 3 | 196.12.e.b.165.1 | 2 | |||
7.3 | odd | 6 | 196.12.e.a.177.1 | 2 | |||
7.4 | even | 3 | 196.12.e.b.177.1 | 2 | |||
7.5 | odd | 6 | 196.12.e.a.165.1 | 2 | |||
7.6 | odd | 2 | 196.12.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 64.12.a.a.1.1 | 1 | |||
8.5 | even | 2 | 64.12.a.g.1.1 | 1 | |||
12.11 | even | 2 | 144.12.a.n.1.1 | 1 | |||
16.3 | odd | 4 | 256.12.b.f.129.2 | 2 | |||
16.5 | even | 4 | 256.12.b.b.129.2 | 2 | |||
16.11 | odd | 4 | 256.12.b.f.129.1 | 2 | |||
16.13 | even | 4 | 256.12.b.b.129.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.12.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.12.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
36.12.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
64.12.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
64.12.a.g.1.1 | 1 | 8.5 | even | 2 | |||
100.12.a.b.1.1 | 1 | 5.4 | even | 2 | |||
100.12.c.a.49.1 | 2 | 5.3 | odd | 4 | |||
100.12.c.a.49.2 | 2 | 5.2 | odd | 4 | |||
144.12.a.n.1.1 | 1 | 12.11 | even | 2 | |||
196.12.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
196.12.e.a.165.1 | 2 | 7.5 | odd | 6 | |||
196.12.e.a.177.1 | 2 | 7.3 | odd | 6 | |||
196.12.e.b.165.1 | 2 | 7.2 | even | 3 | |||
196.12.e.b.177.1 | 2 | 7.4 | even | 3 | |||
256.12.b.b.129.1 | 2 | 16.13 | even | 4 | |||
256.12.b.b.129.2 | 2 | 16.5 | even | 4 | |||
256.12.b.f.129.1 | 2 | 16.11 | odd | 4 | |||
256.12.b.f.129.2 | 2 | 16.3 | odd | 4 |