Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [272,10,Mod(1,272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(272, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("272.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 272.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: | \(140.089747437\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(16.8116\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 272.1 |
$q$-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 | ||||||||
\(3\) | 116.887 | 0.833144 | 0.416572 | − | 0.909103i | \(-0.363231\pi\) | ||||
0.416572 | + | 0.909103i | \(0.363231\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1103.40 | −0.789528 | −0.394764 | − | 0.918783i | \(-0.629174\pi\) | ||||
−0.394764 | + | 0.918783i | \(0.629174\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5164.29 | 0.812961 | 0.406480 | − | 0.913660i | \(-0.366756\pi\) | ||||
0.406480 | + | 0.913660i | \(0.366756\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6020.47 | −0.305872 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −44537.1 | −0.917180 | −0.458590 | − | 0.888648i | \(-0.651645\pi\) | ||||
−0.458590 | + | 0.888648i | \(0.651645\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 69656.8 | 0.676424 | 0.338212 | − | 0.941070i | \(-0.390178\pi\) | ||||
0.338212 | + | 0.941070i | \(0.390178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −128973. | −0.657790 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 83521.0 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 170217. | 0.299648 | 0.149824 | − | 0.988713i | \(-0.452129\pi\) | ||||
0.149824 | + | 0.988713i | \(0.452129\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 603638. | 0.677313 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00737e6 | 1.49572 | 0.747861 | − | 0.663855i | \(-0.231081\pi\) | ||||
0.747861 | + | 0.663855i | \(0.231081\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −735637. | −0.376646 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.00440e6 | −1.08798 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 155688. | 0.0408755 | 0.0204378 | − | 0.999791i | \(-0.493494\pi\) | ||||
0.0204378 | + | 0.999791i | \(0.493494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.27490e6 | −0.831379 | −0.415689 | − | 0.909507i | \(-0.636460\pi\) | ||||
−0.415689 | + | 0.909507i | \(0.636460\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.20580e6 | −0.764143 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.69827e6 | −0.641855 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.51022e7 | 1.32474 | 0.662371 | − | 0.749176i | \(-0.269550\pi\) | ||||
0.662371 | + | 0.749176i | \(0.269550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.14197e6 | 0.563558 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.59320e7 | 0.880526 | 0.440263 | − | 0.897869i | \(-0.354885\pi\) | ||||
0.440263 | + | 0.897869i | \(0.354885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.49261e7 | −0.665790 | −0.332895 | − | 0.942964i | \(-0.608025\pi\) | ||||
−0.332895 | + | 0.942964i | \(0.608025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.64298e6 | 0.241494 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.36137e7 | −1.00479 | −0.502396 | − | 0.864638i | \(-0.667548\pi\) | ||||
−0.502396 | + | 0.864638i | \(0.667548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.36837e7 | −0.339095 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.76250e6 | 0.202067 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.50379e7 | −0.958121 | −0.479060 | − | 0.877782i | \(-0.659023\pi\) | ||||
−0.479060 | + | 0.877782i | \(0.659023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.91421e7 | 0.724139 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.98961e7 | 0.249650 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.94611e7 | 0.853730 | 0.426865 | − | 0.904315i | \(-0.359618\pi\) | ||||
0.426865 | + | 0.904315i | \(0.359618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.27852e7 | 0.118229 | 0.0591146 | − | 0.998251i | \(-0.481172\pi\) | ||||
0.0591146 | + | 0.998251i | \(0.481172\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.10915e7 | −0.248662 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.68593e7 | −0.534055 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.73169e8 | −1.65613 | −0.828066 | − | 0.560631i | \(-0.810559\pi\) | ||||
−0.828066 | + | 0.560631i | \(0.810559\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.34635e8 | 1.24615 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.88392e6 | −0.0181388 | −0.00906938 | − | 0.999959i | \(-0.502887\pi\) | ||||
−0.00906938 | + | 0.999959i | \(0.502887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.32369e8 | 0.957690 | 0.478845 | − | 0.877900i | \(-0.341056\pi\) | ||||
0.478845 | + | 0.877900i | \(0.341056\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.59862e7 | −0.313800 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.30002e8 | −0.745631 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.38948e8 | −0.979064 | −0.489532 | − | 0.871985i | \(-0.662832\pi\) | ||||
−0.489532 | + | 0.871985i | \(0.662832\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.32673e8 | −0.600571 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.74624e8 | −1.32902 | −0.664511 | − | 0.747278i | \(-0.731360\pi\) | ||||
−0.664511 | + | 0.747278i | \(0.731360\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.21569e7 | −0.191489 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.81978e7 | 0.0340552 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.82429e8 | −1.65976 | −0.829882 | − | 0.557940i | \(-0.811592\pi\) | ||||
−0.829882 | + | 0.557940i | \(0.811592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.59728e8 | 0.549906 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.99680e8 | −0.692658 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.87817e8 | −0.236581 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.03147e9 | −1.18300 | −0.591500 | − | 0.806305i | \(-0.701464\pi\) | ||||
−0.591500 | + | 0.806305i | \(0.701464\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.68134e8 | 0.280539 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.23482e7 | −0.0500559 | −0.0250280 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250280 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.65791e8 | −0.407778 | −0.203889 | − | 0.978994i | \(-0.565358\pi\) | ||||
−0.203889 | + | 0.978994i | \(0.565358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.66053e8 | −0.534757 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.44228e9 | 1.06371 | 0.531854 | − | 0.846836i | \(-0.321496\pi\) | ||||
0.531854 | + | 0.846836i | \(0.321496\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.37882e9 | 1.61414 | 0.807072 | − | 0.590453i | \(-0.201051\pi\) | ||||
0.807072 | + | 0.590453i | \(0.201051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.76524e9 | 1.10370 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.54552e8 | −0.319955 | −0.159978 | − | 0.987121i | \(-0.551142\pi\) | ||||
−0.159978 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.21492e9 | −1.18091 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.19367e8 | −0.206899 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.31327e8 | 0.197172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.74397e8 | −0.158781 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.86224e9 | 0.733605 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.96678e9 | 1.08690 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.25473e9 | −1.11019 | −0.555097 | − | 0.831786i | \(-0.687319\pi\) | ||||
−0.555097 | + | 0.831786i | \(0.687319\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.74466e9 | −0.554699 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.29117e9 | 0.679731 | 0.339865 | − | 0.940474i | \(-0.389618\pi\) | ||||
0.339865 | + | 0.940474i | \(0.389618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.79051e8 | 0.243602 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.31505e9 | 0.858989 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.07071e9 | 1.71483 | 0.857413 | − | 0.514628i | \(-0.172070\pi\) | ||||
0.857413 | + | 0.514628i | \(0.172070\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.13323e9 | 0.484697 | 0.242349 | − | 0.970189i | \(-0.422082\pi\) | ||||
0.242349 | + | 0.970189i | \(0.422082\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.92900e9 | −0.837136 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.10231e9 | −0.620402 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.71786e8 | −0.0322724 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.59944e9 | −0.282515 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.98904e9 | −1.49408 | −0.747042 | − | 0.664777i | \(-0.768527\pi\) | ||||
−0.747042 | + | 0.664777i | \(0.768527\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.53054e9 | −0.709175 | −0.354588 | − | 0.935023i | \(-0.615379\pi\) | ||||
−0.354588 | + | 0.935023i | \(0.615379\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.02836e8 | −0.0741848 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.71692e9 | 0.656396 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.69961e9 | −0.485967 | −0.242984 | − | 0.970030i | \(-0.578126\pi\) | ||||
−0.242984 | + | 0.970030i | \(0.578126\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.43320e9 | −0.798252 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.03666e10 | 1.21596 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.71522e10 | −1.90317 | −0.951583 | − | 0.307393i | \(-0.900544\pi\) | ||||
−0.951583 | + | 0.307393i | \(0.900544\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.74407e9 | 0.603312 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.39036e10 | −1.38326 | −0.691628 | − | 0.722254i | \(-0.743106\pi\) | ||||
−0.691628 | + | 0.722254i | \(0.743106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.75242e9 | −0.542451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.02479e9 | −0.0916540 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.51288e9 | 0.128409 | 0.0642047 | − | 0.997937i | \(-0.479549\pi\) | ||||
0.0642047 | + | 0.997937i | \(0.479549\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.79904e9 | −0.306198 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.28796e9 | 0.711280 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.09830e10 | 1.52767 | 0.763835 | − | 0.645411i | \(-0.223314\pi\) | ||||
0.763835 | + | 0.645411i | \(0.223314\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.75141e10 | −1.21293 | −0.606464 | − | 0.795111i | \(-0.707413\pi\) | ||||
−0.606464 | + | 0.795111i | \(0.707413\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.49443e9 | 0.0985018 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.66637e10 | −1.04592 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.71978e9 | −0.222449 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.55156e10 | −0.884484 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.64385e10 | −0.893741 | −0.446871 | − | 0.894599i | \(-0.647462\pi\) | ||||
−0.446871 | + | 0.894599i | \(0.647462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.12709e9 | −0.473505 | −0.236753 | − | 0.971570i | \(-0.576083\pi\) | ||||
−0.236753 | + | 0.971570i | \(0.576083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.98383e9 | −0.444945 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.53151e9 | 0.0724472 | 0.0362236 | − | 0.999344i | \(-0.488467\pi\) | ||||
0.0362236 | + | 0.999344i | \(0.488467\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.77679e10 | −0.803152 | −0.401576 | − | 0.915826i | \(-0.631537\pi\) | ||||
−0.401576 | + | 0.915826i | \(0.631537\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.19299e10 | −1.37980 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.04017e8 | 0.0332302 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.75793e10 | −0.695200 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.20853e10 | −0.457499 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.58097e9 | −0.274832 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.19005e10 | −1.80260 | −0.901302 | − | 0.433192i | \(-0.857387\pi\) | ||||
−0.901302 | + | 0.433192i | \(0.857387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.53979e8 | −0.0151122 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.64694e10 | 0.525660 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.20769e10 | −0.675878 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.71608e10 | 0.797893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.81781e9 | 0.164057 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.09533e10 | 1.65054 | 0.825269 | − | 0.564740i | \(-0.191024\pi\) | ||||
0.825269 | + | 0.564740i | \(0.191024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.42888e9 | 0.115205 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.35858e10 | −1.58944 | −0.794720 | − | 0.606977i | \(-0.792382\pi\) | ||||
−0.794720 | + | 0.606977i | \(0.792382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.22903e10 | −1.49679 | −0.748395 | − | 0.663254i | \(-0.769175\pi\) | ||||
−0.748395 | + | 0.663254i | \(0.769175\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.68842e10 | −0.621218 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.69026e10 | 1.93166 | 0.965831 | − | 0.259172i | \(-0.0834496\pi\) | ||||
0.965831 | + | 0.259172i | \(0.0834496\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.70893e10 | 0.793311 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.96186e10 | −0.815701 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.04686e10 | −1.39703 | −0.698514 | − | 0.715597i | \(-0.746155\pi\) | ||||
−0.698514 | + | 0.715597i | \(0.746155\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.25058e10 | 1.19356 | 0.596779 | − | 0.802405i | \(-0.296447\pi\) | ||||
0.596779 | + | 0.802405i | \(0.296447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.19391e10 | 0.587617 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.50986e10 | 0.267725 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.18568e10 | 0.202689 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.71660e10 | −1.10727 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.26518e9 | 0.115535 | 0.0577676 | − | 0.998330i | \(-0.481602\pi\) | ||||
0.0577676 | + | 0.998330i | \(0.481602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.94022e10 | −1.37185 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.07719e10 | −0.159538 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.23779e10 | −1.17791 | −0.588955 | − | 0.808166i | \(-0.700460\pi\) | ||||
−0.588955 | + | 0.808166i | \(0.700460\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.79920e10 | 1.07696 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.37314e8 | −0.0125027 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.05229e10 | −1.03781 | −0.518906 | − | 0.854831i | \(-0.673660\pi\) | ||||
−0.518906 | + | 0.854831i | \(0.673660\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.07287e10 | 0.756463 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.14833e11 | −1.38282 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.37804e10 | 0.393350 | 0.196675 | − | 0.980469i | \(-0.436986\pi\) | ||||
0.196675 | + | 0.980469i | \(0.436986\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.31396e10 | −0.598489 | −0.299245 | − | 0.954176i | \(-0.596735\pi\) | ||||
−0.299245 | + | 0.954176i | \(0.596735\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.20475e10 | 0.458150 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.27631e10 | 0.345452 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.33887e11 | −1.36640 | −0.683201 | − | 0.730231i | \(-0.739413\pi\) | ||||
−0.683201 | + | 0.730231i | \(0.739413\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.57369e10 | 0.254295 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.71427e10 | −0.642422 | −0.321211 | − | 0.947008i | \(-0.604090\pi\) | ||||
−0.321211 | + | 0.947008i | \(0.604090\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.11880e11 | −1.03684 | −0.518420 | − | 0.855126i | \(-0.673480\pi\) | ||||
−0.518420 | + | 0.855126i | \(0.673480\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.19534e10 | −0.197106 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.22774e10 | 0.715833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.20566e11 | −0.985609 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.51192e11 | 1.19846 | 0.599230 | − | 0.800577i | \(-0.295474\pi\) | ||||
0.599230 | + | 0.800577i | \(0.295474\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.76773e10 | −0.674044 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.33807e11 | 0.997872 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.39827e11 | 1.01174 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.70825e10 | −0.541261 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.11881e9 | −0.0417038 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.41072e10 | −0.0933452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.62355e10 | −0.425567 | −0.212784 | − | 0.977099i | \(-0.568253\pi\) | ||||
−0.212784 | + | 0.977099i | \(0.568253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.44449e10 | −0.339738 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.27102e10 | 0.561960 | 0.280980 | − | 0.959714i | \(-0.409340\pi\) | ||||
0.280980 | + | 0.959714i | \(0.409340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.58675e11 | 1.52337 | 0.761684 | − | 0.647949i | \(-0.224373\pi\) | ||||
0.761684 | + | 0.647949i | \(0.224373\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.43063e10 | 0.196325 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.47169e10 | −0.248717 | −0.124358 | − | 0.992237i | \(-0.539687\pi\) | ||||
−0.124358 | + | 0.992237i | \(0.539687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.93388e9 | −0.0374902 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.68583e11 | 0.886221 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.42167e10 | 0.0726754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.12421e10 | −0.254772 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.78053e11 | 1.34481 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.73591e11 | −0.816856 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.78159e10 | −0.218951 | −0.109475 | − | 0.993990i | \(-0.534917\pi\) | ||||
−0.109475 | + | 0.993990i | \(0.534917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.09221e10 | −0.405201 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.01414e11 | 1.30756 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.76342e11 | 1.58945 | 0.794727 | − | 0.606968i | \(-0.207614\pi\) | ||||
0.794727 | + | 0.606968i | \(0.207614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.48198e10 | −0.266569 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.90392e11 | 0.762524 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.79064e11 | −1.08863 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.58895e11 | −0.983872 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.77078e11 | 0.655665 | 0.327833 | − | 0.944736i | \(-0.393682\pi\) | ||||
0.327833 | + | 0.944736i | \(0.393682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.43883e11 | 0.879967 | 0.439984 | − | 0.898006i | \(-0.354984\pi\) | ||||
0.439984 | + | 0.898006i | \(0.354984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.09277e11 | −0.735934 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.91758e11 | 0.657304 | 0.328652 | − | 0.944451i | \(-0.393406\pi\) | ||||
0.328652 | + | 0.944451i | \(0.393406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.28551e9 | 0.0143211 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.04164e10 | 0.164273 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.43139e10 | 0.204352 | 0.102176 | − | 0.994766i | \(-0.467419\pi\) | ||||
0.102176 | + | 0.994766i | \(0.467419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.93714e11 | −0.910211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.37621e10 | −0.132287 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.56395e11 | −0.756123 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.24947e10 | −0.208597 | −0.104299 | − | 0.994546i | \(-0.533260\pi\) | ||||
−0.104299 | + | 0.994546i | \(0.533260\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.59180e10 | −0.269328 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.84232e11 | −0.778914 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.44526e10 | −0.145656 | −0.0728281 | − | 0.997345i | \(-0.523202\pi\) | ||||
−0.0728281 | + | 0.997345i | \(0.523202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.46777e11 | 0.905544 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.08447e10 | 0.0276492 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.15005e11 | 0.535270 | 0.267635 | − | 0.963520i | \(-0.413758\pi\) | ||||
0.267635 | + | 0.963520i | \(0.413758\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.80435e11 | −0.924951 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.29189e11 | 1.01919 | 0.509594 | − | 0.860415i | \(-0.329796\pi\) | ||||
0.509594 | + | 0.860415i | \(0.329796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.53784e11 | 0.588696 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.98619e10 | 0.203646 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.02217e11 | −0.447760 | −0.223880 | − | 0.974617i | \(-0.571872\pi\) | ||||
−0.223880 | + | 0.974617i | \(0.571872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.67657e11 | 0.362766 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.67808e11 | 0.566313 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.73995e11 | 0.772998 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.81106e11 | 0.365911 | 0.182955 | − | 0.983121i | \(-0.441434\pi\) | ||||
0.182955 | + | 0.983121i | \(0.441434\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.02749e11 | 0.202956 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.40602e11 | −0.271545 | −0.135772 | − | 0.990740i | \(-0.543352\pi\) | ||||
−0.135772 | + | 0.990740i | \(0.543352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.97776e11 | −0.562364 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.56732e11 | 0.474167 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.72606e11 | −1.21503 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.11843e11 | −1.08115 | −0.540574 | − | 0.841297i | \(-0.681793\pi\) | ||||
−0.540574 | + | 0.841297i | \(0.681793\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.26472e11 | 1.42870 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.10360e11 | 0.694049 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.34039e11 | 1.04930 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.49346e11 | 0.403822 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.89071e10 | −0.0458186 | −0.0229093 | − | 0.999738i | \(-0.507293\pi\) | ||||
−0.0229093 | + | 0.999738i | \(0.507293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.06260e12 | 1.64854 | 0.824272 | − | 0.566193i | \(-0.191584\pi\) | ||||
0.824272 | + | 0.566193i | \(0.191584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.02370e11 | 0.307337 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.14411e10 | −0.0913501 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.60267e10 | 0.0961156 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.62619e11 | −0.516884 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.09485e10 | 0.0711187 | 0.0355594 | − | 0.999368i | \(-0.488679\pi\) | ||||
0.0355594 | + | 0.999368i | \(0.488679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.02428e12 | −1.40030 | −0.700152 | − | 0.713994i | \(-0.746885\pi\) | ||||
−0.700152 | + | 0.713994i | \(0.746885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00795e10 | −0.0268875 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.41688e11 | 0.448191 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.70271e11 | −0.475805 | −0.237903 | − | 0.971289i | \(-0.576460\pi\) | ||||
−0.237903 | + | 0.971289i | \(0.576460\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.23824e10 | 0.103720 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.17113e12 | 1.44473 | 0.722366 | − | 0.691511i | \(-0.243054\pi\) | ||||
0.722366 | + | 0.691511i | \(0.243054\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.08401e12 | 1.31043 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.05070e12 | −1.24479 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.79800e10 | 0.0789355 | 0.0394678 | − | 0.999221i | \(-0.487434\pi\) | ||||
0.0394678 | + | 0.999221i | \(0.487434\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.09563e11 | −0.807601 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.29560e11 | −0.590845 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.96924e11 | −0.434166 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.72167e12 | 1.84640 | 0.923202 | − | 0.384315i | \(-0.125562\pi\) | ||||
0.923202 | + | 0.384315i | \(0.125562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.50930e11 | −0.263874 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.42332e12 | 1.46774 | 0.733868 | − | 0.679292i | \(-0.237713\pi\) | ||||
0.733868 | + | 0.679292i | \(0.237713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.62089e12 | −1.63922 | −0.819611 | − | 0.572920i | \(-0.805811\pi\) | ||||
−0.819611 | + | 0.572920i | \(0.805811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.51346e11 | 0.546873 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.13569e12 | 1.10493 | 0.552465 | − | 0.833536i | \(-0.313687\pi\) | ||||
0.552465 | + | 0.833536i | \(0.313687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.41072e12 | −1.34637 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.32435e11 | −0.404881 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.64763e11 | 0.610649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.25218e11 | −0.112861 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.31354e11 | 0.293062 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.54480e11 | −0.134080 | −0.0670398 | − | 0.997750i | \(-0.521355\pi\) | ||||
−0.0670398 | + | 0.997750i | \(0.521355\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05197e12 | 0.896087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.21172e12 | 1.01307 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.13813e12 | 0.934011 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.40063e11 | 0.757315 | 0.378657 | − | 0.925537i | \(-0.376386\pi\) | ||||
0.378657 | + | 0.925537i | \(0.376386\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.00487e12 | −1.58561 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.38393e11 | 0.418055 | 0.209027 | − | 0.977910i | \(-0.432970\pi\) | ||||
0.209027 | + | 0.977910i | \(0.432970\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.30032e10 | 0.00991377 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.95859e11 | −0.221494 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.00577e10 | −0.0147461 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.12934e11 | 0.442549 | 0.221274 | − | 0.975212i | \(-0.428978\pi\) | ||||
0.221274 | + | 0.975212i | \(0.428978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.62514e12 | −1.15245 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.31510e12 | 1.61255 | 0.806277 | − | 0.591538i | \(-0.201479\pi\) | ||||
0.806277 | + | 0.591538i | \(0.201479\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.77609e10 | 0.0395205 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.72382e11 | −0.451940 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.48597e12 | −0.981249 | −0.490625 | − | 0.871371i | \(-0.663231\pi\) | ||||
−0.490625 | + | 0.871371i | \(0.663231\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.20002e12 | 0.778564 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.11400e11 | −0.326011 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.13954e11 | 0.321952 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.49706e12 | 0.921575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.76836e11 | 0.106984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.26648e11 | −0.134766 | −0.0673832 | − | 0.997727i | \(-0.521465\pi\) | ||||
−0.0673832 | + | 0.997727i | \(0.521465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.52624e12 | 0.891998 | 0.445999 | − | 0.895033i | \(-0.352848\pi\) | ||||
0.445999 | + | 0.895033i | \(0.352848\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.44058e11 | −0.255107 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.57044e11 | −0.201639 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.22836e12 | 1.23719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.78393e11 | −0.261132 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.10977e12 | 0.595609 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.59141e12 | −0.839827 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.45264e12 | 1.27277 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.09432e11 | 0.311011 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.24488e11 | 0.413806 | 0.206903 | − | 0.978361i | \(-0.433662\pi\) | ||||
0.206903 | + | 0.978361i | \(0.433662\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.04717e12 | −1.01054 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.62479e12 | −1.27441 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.27510e11 | 0.156416 | 0.0782082 | − | 0.996937i | \(-0.475080\pi\) | ||||
0.0782082 | + | 0.996937i | \(0.475080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.69731e10 | −0.0361629 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.65007e10 | 0.0122483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.75043e12 | −0.795941 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.94777e12 | −0.871402 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.54333e11 | 0.288038 | 0.144019 | − | 0.989575i | \(-0.453997\pi\) | ||||
0.144019 | + | 0.989575i | \(0.453997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.03970e12 | −0.450356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.34793e11 | −0.185332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.05130e12 | 0.860483 | 0.430242 | − | 0.902714i | \(-0.358428\pi\) | ||||
0.430242 | + | 0.902714i | \(0.358428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.11892e11 | 0.252614 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.20159e12 | −0.488241 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.21470e11 | 0.368533 | 0.184266 | − | 0.982876i | \(-0.441009\pi\) | ||||
0.184266 | + | 0.982876i | \(0.441009\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.70877e12 | 0.672701 | 0.336351 | − | 0.941737i | \(-0.390807\pi\) | ||||
0.336351 | + | 0.941737i | \(0.390807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.92144e12 | −0.744615 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.47669e12 | −0.563358 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50384e12 | −0.564820 | −0.282410 | − | 0.959294i | \(-0.591134\pi\) | ||||
−0.282410 | + | 0.959294i | \(0.591134\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.06684e12 | −0.394498 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.96753e12 | −1.08044 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.45123e12 | 0.878769 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.62729e11 | 0.163352 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.06312e12 | 1.06486 | 0.532430 | − | 0.846474i | \(-0.321279\pi\) | ||||
0.532430 | + | 0.846474i | \(0.321279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.27662e11 | −0.249121 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.79013e11 | 0.0603589 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.03492e11 | −0.233622 | −0.116811 | − | 0.993154i | \(-0.537267\pi\) | ||||
−0.116811 | + | 0.993154i | \(0.537267\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.75925e11 | −0.155673 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.07683e12 | −0.669141 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.22780e12 | −0.707060 | −0.353530 | − | 0.935423i | \(-0.615019\pi\) | ||||
−0.353530 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.12659e12 | −0.977541 | −0.488771 | − | 0.872412i | \(-0.662555\pi\) | ||||
−0.488771 | + | 0.872412i | \(0.662555\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.64461e12 | 0.506564 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.13109e11 | 0.125362 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.02028e11 | −0.239795 | −0.119898 | − | 0.992786i | \(-0.538257\pi\) | ||||
−0.119898 | + | 0.992786i | \(0.538257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.39790e10 | 0.0276855 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.34143e12 | −0.679665 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.27823e12 | 1.22375 | 0.611874 | − | 0.790955i | \(-0.290416\pi\) | ||||
0.611874 | + | 0.790955i | \(0.290416\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.05479e12 | −0.579201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.33959e12 | −0.649914 | −0.324957 | − | 0.945729i | \(-0.605350\pi\) | ||||
−0.324957 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.17485e12 | −1.96429 | −0.982144 | − | 0.188131i | \(-0.939757\pi\) | ||||
−0.982144 | + | 0.188131i | \(0.939757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.03092e12 | −1.62731 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.07355e12 | −1.34932 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.83675e12 | −0.481492 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.86116e11 | −0.228974 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.26135e12 | 0.321297 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.21641e12 | −0.556567 | −0.278283 | − | 0.960499i | \(-0.589765\pi\) | ||||
−0.278283 | + | 0.960499i | \(0.589765\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.06648e12 | −1.50183 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.59127e12 | 0.876528 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.53164e11 | −0.229372 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.33830e10 | 0.00554813 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.69709e10 | 0.0133288 | 0.00666442 | − | 0.999978i | \(-0.497879\pi\) | ||||
0.00666442 | + | 0.999978i | \(0.497879\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.26271e12 | 0.752713 | 0.376356 | − | 0.926475i | \(-0.377177\pi\) | ||||
0.376356 | + | 0.926475i | \(0.377177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.92506e12 | 0.437950 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.42290e12 | −0.992289 | −0.496144 | − | 0.868240i | \(-0.665251\pi\) | ||||
−0.496144 | + | 0.868240i | \(0.665251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.53897e12 | −0.783024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.58049e12 | −0.563104 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.99365e12 | 1.07475 | 0.537376 | − | 0.843343i | \(-0.319416\pi\) | ||||
0.537376 | + | 0.843343i | \(0.319416\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.52808e12 | −0.536666 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.39897e12 | −0.292930 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.68196e12 | −0.347401 | −0.173701 | − | 0.984799i | \(-0.555572\pi\) | ||||
−0.173701 | + | 0.984799i | \(0.555572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.83788e12 | 1.80070 | 0.900351 | − | 0.435165i | \(-0.143310\pi\) | ||||
0.900351 | + | 0.435165i | \(0.143310\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.80025e11 | 0.136683 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.69943e11 | −0.192331 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.12522e11 | 0.0611385 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.12464e12 | 1.37514 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.69417e11 | −0.108437 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.41749e12 | 0.830057 | 0.415029 | − | 0.909808i | \(-0.363772\pi\) | ||||
0.415029 | + | 0.909808i | \(0.363772\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.21014e12 | 0.409783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.50941e12 | −1.55686 | −0.778431 | − | 0.627730i | \(-0.783984\pi\) | ||||
−0.778431 | + | 0.627730i | \(0.783984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.32682e12 | −0.961733 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.43235e12 | −1.32423 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.49030e12 | −0.613719 | −0.306859 | − | 0.951755i | \(-0.599278\pi\) | ||||
−0.306859 | + | 0.951755i | \(0.599278\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.80181e12 | −1.35390 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.28092e12 | −1.24704 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.83376e12 | −0.648095 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.30831e12 | −0.552019 | −0.276010 | − | 0.961155i | \(-0.589012\pi\) | ||||
−0.276010 | + | 0.961155i | \(0.589012\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.38472e12 | 0.228067 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.35380e12 | −0.382682 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.33065e12 | 0.213559 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.01578e13 | 1.60935 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.72300e12 | 0.269497 | 0.134749 | − | 0.990880i | \(-0.456977\pi\) | ||||
0.134749 | + | 0.990880i | \(0.456977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.57065e12 | 0.396957 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.33525e12 | 0.660942 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.70341e11 | −0.0406935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.11666e12 | 1.20634 | 0.603169 | − | 0.797613i | \(-0.293904\pi\) | ||||
0.603169 | + | 0.797613i | \(0.293904\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.04063e12 | 0.299468 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.58130e12 | −1.24351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.42309e12 | 0.489825 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.23685e12 | −1.16392 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.41170e12 | 0.476092 | 0.238046 | − | 0.971254i | \(-0.423493\pi\) | ||||
0.238046 | + | 0.971254i | \(0.423493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.40548e12 | −0.331508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.30611e12 | 0.994406 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.14530e11 | −0.0153956 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.77588e12 | 0.899624 | 0.449812 | − | 0.893123i | \(-0.351491\pi\) | ||||
0.449812 | + | 0.893123i | \(0.351491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.31297e12 | 1.09014 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.24664e12 | −0.161478 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.34191e13 | −1.71694 | −0.858469 | − | 0.512866i | \(-0.828584\pi\) | ||||
−0.858469 | + | 0.512866i | \(0.828584\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.76483e12 | 0.223053 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.21661e13 | 1.51897 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.85851e12 | −1.21594 | −0.607969 | − | 0.793961i | \(-0.708016\pi\) | ||||
−0.607969 | + | 0.793961i | \(0.708016\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.38590e12 | 0.168869 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.66107e12 | −0.801853 | −0.400926 | − | 0.916110i | \(-0.631312\pi\) | ||||
−0.400926 | + | 0.916110i | \(0.631312\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.91849e12 | 1.17962 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.45951e12 | 0.406510 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.44835e12 | 0.864752 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.09306e12 | −0.240106 | −0.120053 | − | 0.992767i | \(-0.538306\pi\) | ||||
−0.120053 | + | 0.992767i | \(0.538306\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.49203e11 | 0.0962575 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.99899e12 | 0.559913 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.26189e13 | 1.39666 | 0.698330 | − | 0.715776i | \(-0.253927\pi\) | ||||
0.698330 | + | 0.715776i | \(0.253927\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.04499e13 | −1.14295 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.62893e12 | −0.716494 | −0.358247 | − | 0.933627i | \(-0.616625\pi\) | ||||
−0.358247 | + | 0.933627i | \(0.616625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.22849e13 | 1.31224 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.54828e11 | 0.0585709 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.53501e12 | 0.577483 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.47382e12 | 0.358210 | 0.179105 | − | 0.983830i | \(-0.442680\pi\) | ||||
0.179105 | + | 0.983830i | \(0.442680\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.62889e12 | −0.981368 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.16131e13 | −1.16988 | −0.584941 | − | 0.811076i | \(-0.698882\pi\) | ||||
−0.584941 | + | 0.811076i | \(0.698882\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.14478e12 | 0.313135 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.11623e12 | 0.897265 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.71190e12 | 0.263848 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.72978e11 | 0.0166365 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.67748e11 | −0.0444717 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.08214e12 | 0.383685 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50665e13 | 1.39999 | 0.699997 | − | 0.714146i | \(-0.253185\pi\) | ||||
0.699997 | + | 0.714146i | \(0.253185\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.41207e12 | −0.864646 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.86387e12 | −0.260111 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.90579e11 | 0.0799730 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.09839e12 | 0.630242 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.67142e12 | −0.673463 | −0.336731 | − | 0.941601i | \(-0.609321\pi\) | ||||
−0.336731 | + | 0.941601i | \(0.609321\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.80745e12 | −0.243698 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.91468e12 | 0.507674 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.03490e13 | −0.878374 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.14385e13 | −0.960037 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.94848e12 | 0.327717 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00907e12 | −0.493218 | −0.246609 | − | 0.969115i | \(-0.579316\pi\) | ||||
−0.246609 | + | 0.969115i | \(0.579316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.51786e13 | 1.23208 | 0.616038 | − | 0.787717i | \(-0.288737\pi\) | ||||
0.616038 | + | 0.787717i | \(0.288737\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.21132e12 | −0.498627 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.89258e13 | 1.50260 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.54067e12 | −0.199503 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.16573e12 | −0.168201 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.51618e13 | 1.16468 | 0.582339 | − | 0.812946i | \(-0.302138\pi\) | ||||
0.582339 | + | 0.812946i | \(0.302138\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.88314e12 | 0.674943 | 0.337472 | − | 0.941336i | \(-0.390428\pi\) | ||||
0.337472 | + | 0.941336i | \(0.390428\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.82958e12 | 0.287811 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.71703e9 | −0.000722368 0 | −0.000361184 | − | 1.00000i | \(-0.500115\pi\) | ||||
−0.000361184 | 1.00000i | \(0.500115\pi\) | ||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.15249e12 | −0.452434 | −0.226217 | − | 0.974077i | \(-0.572636\pi\) | ||||
−0.226217 | + | 0.974077i | \(0.572636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.56496e13 | −1.13841 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.14288e12 | −0.0822426 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53412e13 | 1.09212 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.28435e13 | 0.904522 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.01899e13 | −1.40671 | −0.703355 | − | 0.710839i | \(-0.748316\pi\) | ||||
−0.703355 | + | 0.710839i | \(0.748316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.44829e13 | −0.998329 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.84810e12 | −0.535230 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.34722e12 | 0.428280 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.93350e12 | −0.129083 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.30773e13 | −0.863837 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.03156e13 | 1.98145 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.71140e13 | −1.75357 | −0.876784 | − | 0.480885i | \(-0.840315\pi\) | ||||
−0.876784 | + | 0.480885i | \(0.840315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.13075e12 | 0.0723633 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.66987e13 | 1.69074 | 0.845371 | − | 0.534180i | \(-0.179380\pi\) | ||||
0.845371 | + | 0.534180i | \(0.179380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.62702e13 | −1.64624 | −0.823122 | − | 0.567864i | \(-0.807770\pi\) | ||||
−0.823122 | + | 0.567864i | \(0.807770\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.61714e12 | 0.596392 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.34256e13 | −1.43761 | −0.718806 | − | 0.695211i | \(-0.755311\pi\) | ||||
−0.718806 | + | 0.695211i | \(0.755311\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.66931e12 | −0.101383 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.15374e11 | 0.0490085 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.50958e13 | 0.897978 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.90281e13 | −1.12025 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.20995e12 | 0.361846 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.53213e13 | 0.883607 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.84217e12 | −0.276402 | −0.138201 | − | 0.990404i | \(-0.544132\pi\) | ||||
−0.138201 | + | 0.990404i | \(0.544132\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.76723e13 | 0.998489 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.59269e13 | 0.890718 | 0.445359 | − | 0.895352i | \(-0.353076\pi\) | ||||
0.445359 | + | 0.895352i | \(0.353076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.71830e12 | −0.261194 | −0.130597 | − | 0.991436i | \(-0.541689\pi\) | ||||
−0.130597 | + | 0.991436i | \(0.541689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.02483e13 | −0.561575 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.26007e13 | −0.683502 | −0.341751 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341751 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.68084e13 | −0.902544 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.03626e13 | 0.550832 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.72163e12 | −0.301084 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.31527e13 | −1.20614 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.63439e13 | 0.842927 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.65550e11 | −0.0339830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.59682e12 | −0.232378 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.00993e12 | −0.450948 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.93251e13 | 0.957640 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.04459e13 | 1.00317 | 0.501584 | − | 0.865109i | \(-0.332751\pi\) | ||||
0.501584 | + | 0.865109i | \(0.332751\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.15161e11 | 0.0153107 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.21126e12 | −0.298777 | −0.149388 | − | 0.988779i | \(-0.547730\pi\) | ||||
−0.149388 | + | 0.988779i | \(0.547730\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.55921e13 | 1.21895 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.64895e12 | −0.0777699 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.18323e13 | 0.552594 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.32576e12 | 0.431285 | 0.215642 | − | 0.976472i | \(-0.430815\pi\) | ||||
0.215642 | + | 0.976472i | \(0.430815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.74206e12 | −0.354559 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.70542e11 | −0.0122695 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.11097e13 | −0.498959 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.80428e12 | 0.124728 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.57119e13 | 1.13256 | 0.566282 | − | 0.824211i | \(-0.308381\pi\) | ||||
0.566282 | + | 0.824211i | \(0.308381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.32920e12 | −0.101609 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.08366e13 | 0.468194 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.10440e12 | 0.175629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.29891e12 | 0.309336 | 0.154668 | − | 0.987967i | \(-0.450569\pi\) | ||||
0.154668 | + | 0.987967i | \(0.450569\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.02357e13 | 1.26918 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.10493e13 | −0.459389 | −0.229695 | − | 0.973263i | \(-0.573773\pi\) | ||||
−0.229695 | + | 0.973263i | \(0.573773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.19813e13 | 1.31702 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.71199e13 | 0.698324 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.10292e12 | 0.367795 | 0.183898 | − | 0.982945i | \(-0.441129\pi\) | ||||
0.183898 | + | 0.982945i | \(0.441129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.61861e13 | 0.647804 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.22681e12 | −0.207217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.09267e13 | 1.60727 | 0.803635 | − | 0.595123i | \(-0.202896\pi\) | ||||
0.803635 | + | 0.595123i | \(0.202896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.81382e13 | 0.705633 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.10479e11 | −0.0312347 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.65152e13 | 1.39409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.16481e12 | −0.308810 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.68320e12 | −0.325358 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00708e13 | 0.373845 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.16443e13 | −1.89934 | −0.949671 | − | 0.313248i | \(-0.898583\pi\) | ||||
−0.949671 | + | 0.313248i | \(0.898583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.66175e12 | 0.0605491 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.69234e13 | 1.69396 | 0.846979 | − | 0.531627i | \(-0.178419\pi\) | ||||
0.846979 | + | 0.531627i | \(0.178419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.10166e13 | 0.394040 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.98953e12 | −0.212262 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.71530e13 | −1.65571 | −0.827854 | − | 0.560944i | \(-0.810438\pi\) | ||||
−0.827854 | + | 0.560944i | \(0.810438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.37545e13 | 1.52230 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.43216e13 | −0.493721 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.10494e13 | −1.40222 | −0.701110 | − | 0.713053i | \(-0.747312\pi\) | ||||
−0.701110 | + | 0.713053i | \(0.747312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.68986e12 | −0.0571990 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.02905e13 | −0.680559 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.99621e13 | −0.995837 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.40949e12 | −0.276973 | −0.138487 | − | 0.990364i | \(-0.544224\pi\) | ||||
−0.138487 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.58905e12 | −0.182417 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.96051e13 | 0.634110 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.54531e13 | 0.815854 | 0.407927 | − | 0.913015i | \(-0.366252\pi\) | ||||
0.407927 | + | 0.913015i | \(0.366252\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.53729e13 | −1.44129 |
(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 | 272.10.a.g.1.5 | 7 | ||
4.3 | odd | 2 | 17.10.a.b.1.3 | ✓ | 7 | ||
12.11 | even | 2 | 153.10.a.f.1.5 | 7 | |||
68.67 | odd | 2 | 289.10.a.b.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.b.1.3 | ✓ | 7 | 4.3 | odd | 2 | ||
153.10.a.f.1.5 | 7 | 12.11 | even | 2 | |||
272.10.a.g.1.5 | 7 | 1.1 | even | 1 | trivial | ||
289.10.a.b.1.3 | 7 | 68.67 | odd | 2 |