Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.57683 | −0.423240 | −0.211620 | − | 0.977352i | \(-0.567874\pi\) | ||||
−0.211620 | + | 0.977352i | \(0.567874\pi\) | |||||||
\(3\) | 3.76279 | 0.0268203 | 0.0134102 | − | 0.999910i | \(-0.495731\pi\) | ||||
0.0134102 | + | 0.999910i | \(0.495731\pi\) | |||||||
\(4\) | −420.284 | −0.820868 | ||||||||
\(5\) | −1873.25 | −1.34039 | −0.670193 | − | 0.742187i | \(-0.733789\pi\) | ||||
−0.670193 | + | 0.742187i | \(0.733789\pi\) | |||||||
\(6\) | −36.0355 | −0.0113514 | ||||||||
\(7\) | 1553.61 | 0.244568 | 0.122284 | − | 0.992495i | \(-0.460978\pi\) | ||||
0.122284 | + | 0.992495i | \(0.460978\pi\) | |||||||
\(8\) | 8928.33 | 0.770664 | ||||||||
\(9\) | −19668.8 | −0.999281 | ||||||||
\(10\) | 17939.8 | 0.567305 | ||||||||
\(11\) | −68833.5 | −1.41753 | −0.708766 | − | 0.705444i | \(-0.750748\pi\) | ||||
−0.708766 | + | 0.705444i | \(0.750748\pi\) | |||||||
\(12\) | −1581.44 | −0.0220159 | ||||||||
\(13\) | −53127.1 | −0.515906 | −0.257953 | − | 0.966157i | \(-0.583048\pi\) | ||||
−0.257953 | + | 0.966157i | \(0.583048\pi\) | |||||||
\(14\) | −14878.6 | −0.103511 | ||||||||
\(15\) | −7048.63 | −0.0359496 | ||||||||
\(16\) | 129681. | 0.494692 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 188365. | 0.422936 | ||||||||
\(19\) | 64384.8 | 0.113342 | 0.0566712 | − | 0.998393i | \(-0.481951\pi\) | ||||
0.0566712 | + | 0.998393i | \(0.481951\pi\) | |||||||
\(20\) | 787297. | 1.10028 | ||||||||
\(21\) | 5845.89 | 0.00655939 | ||||||||
\(22\) | 659207. | 0.599956 | ||||||||
\(23\) | 2.42958e6 | 1.81032 | 0.905161 | − | 0.425070i | \(-0.139750\pi\) | ||||
0.905161 | + | 0.425070i | \(0.139750\pi\) | |||||||
\(24\) | 33595.4 | 0.0206695 | ||||||||
\(25\) | 1.55593e6 | 0.796636 | ||||||||
\(26\) | 508789. | 0.218352 | ||||||||
\(27\) | −148073. | −0.0536213 | ||||||||
\(28\) | −652956. | −0.200758 | ||||||||
\(29\) | −4.67341e6 | −1.22700 | −0.613498 | − | 0.789696i | \(-0.710238\pi\) | ||||
−0.613498 | + | 0.789696i | \(0.710238\pi\) | |||||||
\(30\) | 67503.5 | 0.0152153 | ||||||||
\(31\) | −4.15669e6 | −0.808389 | −0.404194 | − | 0.914673i | \(-0.632448\pi\) | ||||
−0.404194 | + | 0.914673i | \(0.632448\pi\) | |||||||
\(32\) | −5.81323e6 | −0.980038 | ||||||||
\(33\) | −259006. | −0.0380186 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.91029e6 | −0.327816 | ||||||||
\(36\) | 8.26651e6 | 0.820277 | ||||||||
\(37\) | 9.76209e6 | 0.856318 | 0.428159 | − | 0.903704i | \(-0.359162\pi\) | ||||
0.428159 | + | 0.903704i | \(0.359162\pi\) | |||||||
\(38\) | −616602. | −0.0479710 | ||||||||
\(39\) | −199906. | −0.0138368 | ||||||||
\(40\) | −1.67250e7 | −1.03299 | ||||||||
\(41\) | 3.09207e7 | 1.70892 | 0.854459 | − | 0.519518i | \(-0.173889\pi\) | ||||
0.854459 | + | 0.519518i | \(0.173889\pi\) | |||||||
\(42\) | −55985.1 | −0.00277620 | ||||||||
\(43\) | 2.81845e7 | 1.25719 | 0.628597 | − | 0.777731i | \(-0.283630\pi\) | ||||
0.628597 | + | 0.777731i | \(0.283630\pi\) | |||||||
\(44\) | 2.89296e7 | 1.16361 | ||||||||
\(45\) | 3.68446e7 | 1.33942 | ||||||||
\(46\) | −2.32677e7 | −0.766200 | ||||||||
\(47\) | −1.87813e7 | −0.561417 | −0.280708 | − | 0.959793i | \(-0.590569\pi\) | ||||
−0.280708 | + | 0.959793i | \(0.590569\pi\) | |||||||
\(48\) | 487960. | 0.0132678 | ||||||||
\(49\) | −3.79399e7 | −0.940186 | ||||||||
\(50\) | −1.49009e7 | −0.337168 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.23285e7 | 0.423491 | ||||||||
\(53\) | 4.47911e6 | 0.0779741 | 0.0389871 | − | 0.999240i | \(-0.487587\pi\) | ||||
0.0389871 | + | 0.999240i | \(0.487587\pi\) | |||||||
\(54\) | 1.41807e6 | 0.0226947 | ||||||||
\(55\) | 1.28942e8 | 1.90004 | ||||||||
\(56\) | 1.38711e7 | 0.188480 | ||||||||
\(57\) | 242266. | 0.00303988 | ||||||||
\(58\) | 4.47565e7 | 0.519314 | ||||||||
\(59\) | 1.26323e8 | 1.35722 | 0.678609 | − | 0.734499i | \(-0.262583\pi\) | ||||
0.678609 | + | 0.734499i | \(0.262583\pi\) | |||||||
\(60\) | 2.96243e6 | 0.0295099 | ||||||||
\(61\) | −3.41770e7 | −0.316045 | −0.158023 | − | 0.987436i | \(-0.550512\pi\) | ||||
−0.158023 | + | 0.987436i | \(0.550512\pi\) | |||||||
\(62\) | 3.98079e7 | 0.342143 | ||||||||
\(63\) | −3.05576e7 | −0.244392 | ||||||||
\(64\) | −1.07241e7 | −0.0799009 | ||||||||
\(65\) | 9.95201e7 | 0.691514 | ||||||||
\(66\) | 2.48045e6 | 0.0160910 | ||||||||
\(67\) | 1.37527e8 | 0.833781 | 0.416890 | − | 0.908957i | \(-0.363120\pi\) | ||||
0.416890 | + | 0.908957i | \(0.363120\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.14198e6 | 0.0485534 | ||||||||
\(70\) | 2.78713e7 | 0.138745 | ||||||||
\(71\) | 4.06649e7 | 0.189914 | 0.0949570 | − | 0.995481i | \(-0.469729\pi\) | ||||
0.0949570 | + | 0.995481i | \(0.469729\pi\) | |||||||
\(72\) | −1.75610e8 | −0.770110 | ||||||||
\(73\) | 2.45684e8 | 1.01257 | 0.506285 | − | 0.862366i | \(-0.331018\pi\) | ||||
0.506285 | + | 0.862366i | \(0.331018\pi\) | |||||||
\(74\) | −9.34898e7 | −0.362428 | ||||||||
\(75\) | 5.85463e6 | 0.0213660 | ||||||||
\(76\) | −2.70599e7 | −0.0930391 | ||||||||
\(77\) | −1.06940e8 | −0.346683 | ||||||||
\(78\) | 1.91446e6 | 0.00585627 | ||||||||
\(79\) | −3.94690e8 | −1.14008 | −0.570039 | − | 0.821618i | \(-0.693072\pi\) | ||||
−0.570039 | + | 0.821618i | \(0.693072\pi\) | |||||||
\(80\) | −2.42924e8 | −0.663079 | ||||||||
\(81\) | 3.86585e8 | 0.997843 | ||||||||
\(82\) | −2.96122e8 | −0.723283 | ||||||||
\(83\) | 3.15697e8 | 0.730162 | 0.365081 | − | 0.930976i | \(-0.381041\pi\) | ||||
0.365081 | + | 0.930976i | \(0.381041\pi\) | |||||||
\(84\) | −2.45693e6 | −0.00538439 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.69918e8 | −0.532095 | ||||||||
\(87\) | −1.75850e7 | −0.0329084 | ||||||||
\(88\) | −6.14568e8 | −1.09244 | ||||||||
\(89\) | −4.99389e8 | −0.843693 | −0.421846 | − | 0.906667i | \(-0.638618\pi\) | ||||
−0.421846 | + | 0.906667i | \(0.638618\pi\) | |||||||
\(90\) | −3.52854e8 | −0.566897 | ||||||||
\(91\) | −8.25385e7 | −0.126174 | ||||||||
\(92\) | −1.02111e9 | −1.48603 | ||||||||
\(93\) | −1.56407e7 | −0.0216812 | ||||||||
\(94\) | 1.79865e8 | 0.237614 | ||||||||
\(95\) | −1.20609e8 | −0.151923 | ||||||||
\(96\) | −2.18739e7 | −0.0262849 | ||||||||
\(97\) | 7.84102e8 | 0.899290 | 0.449645 | − | 0.893207i | \(-0.351550\pi\) | ||||
0.449645 | + | 0.893207i | \(0.351550\pi\) | |||||||
\(98\) | 3.63344e8 | 0.397925 | ||||||||
\(99\) | 1.35388e9 | 1.41651 | ||||||||
\(100\) | −6.53933e8 | −0.653933 | ||||||||
\(101\) | 6.53522e8 | 0.624905 | 0.312452 | − | 0.949933i | \(-0.398850\pi\) | ||||
0.312452 | + | 0.949933i | \(0.398850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.02870e7 | 0.00900581 | 0.00450291 | − | 0.999990i | \(-0.498567\pi\) | ||||
0.00450291 | + | 0.999990i | \(0.498567\pi\) | |||||||
\(104\) | −4.74336e8 | −0.397590 | ||||||||
\(105\) | −1.09508e7 | −0.00879212 | ||||||||
\(106\) | −4.28957e7 | −0.0330018 | ||||||||
\(107\) | −2.80325e8 | −0.206745 | −0.103373 | − | 0.994643i | \(-0.532963\pi\) | ||||
−0.103373 | + | 0.994643i | \(0.532963\pi\) | |||||||
\(108\) | 6.22326e7 | 0.0440160 | ||||||||
\(109\) | −3.40166e8 | −0.230819 | −0.115410 | − | 0.993318i | \(-0.536818\pi\) | ||||
−0.115410 | + | 0.993318i | \(0.536818\pi\) | |||||||
\(110\) | −1.23486e9 | −0.804173 | ||||||||
\(111\) | 3.67326e7 | 0.0229667 | ||||||||
\(112\) | 2.01473e8 | 0.120986 | ||||||||
\(113\) | −1.00444e9 | −0.579523 | −0.289761 | − | 0.957099i | \(-0.593576\pi\) | ||||
−0.289761 | + | 0.957099i | \(0.593576\pi\) | |||||||
\(114\) | −2.32014e6 | −0.00128660 | ||||||||
\(115\) | −4.55120e9 | −2.42653 | ||||||||
\(116\) | 1.96416e9 | 1.00720 | ||||||||
\(117\) | 1.04495e9 | 0.515535 | ||||||||
\(118\) | −1.20978e9 | −0.574429 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.29325e7 | −0.0277051 | ||||||||
\(121\) | 2.38010e9 | 1.00940 | ||||||||
\(122\) | 3.27307e8 | 0.133763 | ||||||||
\(123\) | 1.16348e8 | 0.0458337 | ||||||||
\(124\) | 1.74699e9 | 0.663581 | ||||||||
\(125\) | 7.44044e8 | 0.272586 | ||||||||
\(126\) | 2.92645e8 | 0.103437 | ||||||||
\(127\) | 2.89317e9 | 0.986865 | 0.493432 | − | 0.869784i | \(-0.335742\pi\) | ||||
0.493432 | + | 0.869784i | \(0.335742\pi\) | |||||||
\(128\) | 3.07908e9 | 1.01385 | ||||||||
\(129\) | 1.06052e8 | 0.0337183 | ||||||||
\(130\) | −9.53087e8 | −0.292676 | ||||||||
\(131\) | 2.70866e8 | 0.0803587 | 0.0401794 | − | 0.999192i | \(-0.487207\pi\) | ||||
0.0401794 | + | 0.999192i | \(0.487207\pi\) | |||||||
\(132\) | 1.08856e8 | 0.0312083 | ||||||||
\(133\) | 1.00029e8 | 0.0277199 | ||||||||
\(134\) | −1.31707e9 | −0.352889 | ||||||||
\(135\) | 2.77376e8 | 0.0718733 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.83519e9 | −1.90023 | −0.950117 | − | 0.311894i | \(-0.899036\pi\) | ||||
−0.950117 | + | 0.311894i | \(0.899036\pi\) | |||||||
\(138\) | −8.75512e7 | −0.0205497 | ||||||||
\(139\) | 2.42960e9 | 0.552038 | 0.276019 | − | 0.961152i | \(-0.410985\pi\) | ||||
0.276019 | + | 0.961152i | \(0.410985\pi\) | |||||||
\(140\) | 1.22315e9 | 0.269093 | ||||||||
\(141\) | −7.06700e7 | −0.0150574 | ||||||||
\(142\) | −3.89441e8 | −0.0803792 | ||||||||
\(143\) | 3.65692e9 | 0.731313 | ||||||||
\(144\) | −2.55067e9 | −0.494336 | ||||||||
\(145\) | 8.75445e9 | 1.64465 | ||||||||
\(146\) | −2.35288e9 | −0.428560 | ||||||||
\(147\) | −1.42760e8 | −0.0252161 | ||||||||
\(148\) | −4.10285e9 | −0.702924 | ||||||||
\(149\) | 2.56491e9 | 0.426319 | 0.213159 | − | 0.977017i | \(-0.431625\pi\) | ||||
0.213159 | + | 0.977017i | \(0.431625\pi\) | |||||||
\(150\) | −5.60688e7 | −0.00904296 | ||||||||
\(151\) | −1.16618e10 | −1.82544 | −0.912722 | − | 0.408581i | \(-0.866024\pi\) | ||||
−0.912722 | + | 0.408581i | \(0.866024\pi\) | |||||||
\(152\) | 5.74849e8 | 0.0873489 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.02415e9 | 0.146730 | ||||||||
\(155\) | 7.78651e9 | 1.08355 | ||||||||
\(156\) | 8.40173e7 | 0.0113582 | ||||||||
\(157\) | −6.12170e9 | −0.804125 | −0.402063 | − | 0.915612i | \(-0.631707\pi\) | ||||
−0.402063 | + | 0.915612i | \(0.631707\pi\) | |||||||
\(158\) | 3.77988e9 | 0.482527 | ||||||||
\(159\) | 1.68539e7 | 0.00209129 | ||||||||
\(160\) | 1.08896e10 | 1.31363 | ||||||||
\(161\) | 3.77461e9 | 0.442747 | ||||||||
\(162\) | −3.70225e9 | −0.422327 | ||||||||
\(163\) | 7.45677e9 | 0.827382 | 0.413691 | − | 0.910417i | \(-0.364239\pi\) | ||||
0.413691 | + | 0.910417i | \(0.364239\pi\) | |||||||
\(164\) | −1.29955e10 | −1.40280 | ||||||||
\(165\) | 4.85182e8 | 0.0509597 | ||||||||
\(166\) | −3.02338e9 | −0.309034 | ||||||||
\(167\) | 9.08731e9 | 0.904089 | 0.452044 | − | 0.891995i | \(-0.350695\pi\) | ||||
0.452044 | + | 0.891995i | \(0.350695\pi\) | |||||||
\(168\) | 5.21940e7 | 0.00505509 | ||||||||
\(169\) | −7.78201e9 | −0.733841 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.26637e9 | −0.113261 | ||||||||
\(172\) | −1.18455e10 | −1.03199 | ||||||||
\(173\) | −2.09520e10 | −1.77835 | −0.889175 | − | 0.457566i | \(-0.848721\pi\) | ||||
−0.889175 | + | 0.457566i | \(0.848721\pi\) | |||||||
\(174\) | 1.68409e8 | 0.0139282 | ||||||||
\(175\) | 2.41730e9 | 0.194832 | ||||||||
\(176\) | −8.92636e9 | −0.701241 | ||||||||
\(177\) | 4.75328e8 | 0.0364010 | ||||||||
\(178\) | 4.78257e9 | 0.357084 | ||||||||
\(179\) | −1.81997e10 | −1.32503 | −0.662516 | − | 0.749048i | \(-0.730511\pi\) | ||||
−0.662516 | + | 0.749048i | \(0.730511\pi\) | |||||||
\(180\) | −1.54852e10 | −1.09949 | ||||||||
\(181\) | 4.25507e9 | 0.294682 | 0.147341 | − | 0.989086i | \(-0.452929\pi\) | ||||
0.147341 | + | 0.989086i | \(0.452929\pi\) | |||||||
\(182\) | 7.90457e8 | 0.0534020 | ||||||||
\(183\) | −1.28601e8 | −0.00847643 | ||||||||
\(184\) | 2.16921e10 | 1.39515 | ||||||||
\(185\) | −1.82868e10 | −1.14780 | ||||||||
\(186\) | 1.49789e8 | 0.00917637 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.89349e9 | 0.460849 | ||||||||
\(189\) | −2.30046e8 | −0.0131141 | ||||||||
\(190\) | 1.15505e9 | 0.0642997 | ||||||||
\(191\) | −1.04248e10 | −0.566784 | −0.283392 | − | 0.959004i | \(-0.591460\pi\) | ||||
−0.283392 | + | 0.959004i | \(0.591460\pi\) | |||||||
\(192\) | −4.03526e7 | −0.00214297 | ||||||||
\(193\) | −2.64500e9 | −0.137220 | −0.0686099 | − | 0.997644i | \(-0.521856\pi\) | ||||
−0.0686099 | + | 0.997644i | \(0.521856\pi\) | |||||||
\(194\) | −7.50921e9 | −0.380616 | ||||||||
\(195\) | 3.74473e8 | 0.0185466 | ||||||||
\(196\) | 1.59456e10 | 0.771769 | ||||||||
\(197\) | −3.57231e10 | −1.68986 | −0.844930 | − | 0.534876i | \(-0.820358\pi\) | ||||
−0.844930 | + | 0.534876i | \(0.820358\pi\) | |||||||
\(198\) | −1.29658e10 | −0.599524 | ||||||||
\(199\) | 2.74427e10 | 1.24047 | 0.620237 | − | 0.784415i | \(-0.287036\pi\) | ||||
0.620237 | + | 0.784415i | \(0.287036\pi\) | |||||||
\(200\) | 1.38919e10 | 0.613939 | ||||||||
\(201\) | 5.17485e8 | 0.0223623 | ||||||||
\(202\) | −6.25866e9 | −0.264485 | ||||||||
\(203\) | −7.26064e9 | −0.300084 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.79220e10 | −2.29061 | ||||||||
\(206\) | −9.85172e7 | −0.00381162 | ||||||||
\(207\) | −4.77870e10 | −1.80902 | ||||||||
\(208\) | −6.88955e9 | −0.255215 | ||||||||
\(209\) | −4.43183e9 | −0.160666 | ||||||||
\(210\) | 1.04874e8 | 0.00372118 | ||||||||
\(211\) | 4.93385e10 | 1.71362 | 0.856811 | − | 0.515631i | \(-0.172442\pi\) | ||||
0.856811 | + | 0.515631i | \(0.172442\pi\) | |||||||
\(212\) | −1.88250e9 | −0.0640064 | ||||||||
\(213\) | 1.53013e8 | 0.00509355 | ||||||||
\(214\) | 2.68463e9 | 0.0875028 | ||||||||
\(215\) | −5.27965e10 | −1.68513 | ||||||||
\(216\) | −1.32204e9 | −0.0413240 | ||||||||
\(217\) | −6.45786e9 | −0.197706 | ||||||||
\(218\) | 3.25771e9 | 0.0976920 | ||||||||
\(219\) | 9.24458e8 | 0.0271574 | ||||||||
\(220\) | −5.41924e10 | −1.55968 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.51782e8 | −0.00972043 | ||||||||
\(223\) | 3.12685e10 | 0.846710 | 0.423355 | − | 0.905964i | \(-0.360852\pi\) | ||||
0.423355 | + | 0.905964i | \(0.360852\pi\) | |||||||
\(224\) | −9.03147e9 | −0.239686 | ||||||||
\(225\) | −3.06033e10 | −0.796063 | ||||||||
\(226\) | 9.61934e9 | 0.245277 | ||||||||
\(227\) | 3.74858e9 | 0.0937023 | 0.0468512 | − | 0.998902i | \(-0.485081\pi\) | ||||
0.0468512 | + | 0.998902i | \(0.485081\pi\) | |||||||
\(228\) | −1.01821e8 | −0.00249534 | ||||||||
\(229\) | −4.94370e10 | −1.18793 | −0.593967 | − | 0.804489i | \(-0.702439\pi\) | ||||
−0.593967 | + | 0.804489i | \(0.702439\pi\) | |||||||
\(230\) | 4.35861e10 | 1.02700 | ||||||||
\(231\) | −4.02393e8 | −0.00929814 | ||||||||
\(232\) | −4.17257e10 | −0.945601 | ||||||||
\(233\) | 5.15582e10 | 1.14603 | 0.573015 | − | 0.819545i | \(-0.305774\pi\) | ||||
0.573015 | + | 0.819545i | \(0.305774\pi\) | |||||||
\(234\) | −1.00073e10 | −0.218195 | ||||||||
\(235\) | 3.51820e10 | 0.752516 | ||||||||
\(236\) | −5.30918e10 | −1.11410 | ||||||||
\(237\) | −1.48513e9 | −0.0305772 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.14267e10 | −1.21777 | −0.608887 | − | 0.793257i | \(-0.708384\pi\) | ||||
−0.608887 | + | 0.793257i | \(0.708384\pi\) | |||||||
\(240\) | −9.14070e8 | −0.0177840 | ||||||||
\(241\) | 8.25422e10 | 1.57616 | 0.788078 | − | 0.615575i | \(-0.211076\pi\) | ||||
0.788078 | + | 0.615575i | \(0.211076\pi\) | |||||||
\(242\) | −2.27938e10 | −0.427217 | ||||||||
\(243\) | 4.36915e9 | 0.0803838 | ||||||||
\(244\) | 1.43640e10 | 0.259431 | ||||||||
\(245\) | 7.10708e10 | 1.26021 | ||||||||
\(246\) | −1.11424e9 | −0.0193987 | ||||||||
\(247\) | −3.42058e9 | −0.0584740 | ||||||||
\(248\) | −3.71123e10 | −0.622996 | ||||||||
\(249\) | 1.18790e9 | 0.0195832 | ||||||||
\(250\) | −7.12558e9 | −0.115369 | ||||||||
\(251\) | −9.98436e10 | −1.58777 | −0.793887 | − | 0.608066i | \(-0.791946\pi\) | ||||
−0.793887 | + | 0.608066i | \(0.791946\pi\) | |||||||
\(252\) | 1.28429e10 | 0.200614 | ||||||||
\(253\) | −1.67236e11 | −2.56619 | ||||||||
\(254\) | −2.77074e10 | −0.417681 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.39970e10 | −0.349203 | ||||||||
\(257\) | −4.07145e10 | −0.582171 | −0.291085 | − | 0.956697i | \(-0.594016\pi\) | ||||
−0.291085 | + | 0.956697i | \(0.594016\pi\) | |||||||
\(258\) | −1.01564e9 | −0.0142709 | ||||||||
\(259\) | 1.51664e10 | 0.209428 | ||||||||
\(260\) | −4.18268e10 | −0.567641 | ||||||||
\(261\) | 9.19206e10 | 1.22611 | ||||||||
\(262\) | −2.59403e9 | −0.0340110 | ||||||||
\(263\) | 3.57313e10 | 0.460520 | 0.230260 | − | 0.973129i | \(-0.426042\pi\) | ||||
0.230260 | + | 0.973129i | \(0.426042\pi\) | |||||||
\(264\) | −2.31249e9 | −0.0292996 | ||||||||
\(265\) | −8.39048e9 | −0.104515 | ||||||||
\(266\) | −9.57957e8 | −0.0117322 | ||||||||
\(267\) | −1.87909e9 | −0.0226281 | ||||||||
\(268\) | −5.78005e10 | −0.684424 | ||||||||
\(269\) | 1.32773e11 | 1.54606 | 0.773028 | − | 0.634372i | \(-0.218741\pi\) | ||||
0.773028 | + | 0.634372i | \(0.218741\pi\) | |||||||
\(270\) | −2.65639e9 | −0.0304197 | ||||||||
\(271\) | −1.31223e11 | −1.47791 | −0.738956 | − | 0.673754i | \(-0.764681\pi\) | ||||
−0.738956 | + | 0.673754i | \(0.764681\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.10575e8 | −0.00338403 | ||||||||
\(274\) | 7.50363e10 | 0.804255 | ||||||||
\(275\) | −1.07100e11 | −1.12926 | ||||||||
\(276\) | −3.84223e9 | −0.0398559 | ||||||||
\(277\) | 3.70561e10 | 0.378182 | 0.189091 | − | 0.981960i | \(-0.439446\pi\) | ||||
0.189091 | + | 0.981960i | \(0.439446\pi\) | |||||||
\(278\) | −2.32679e10 | −0.233645 | ||||||||
\(279\) | 8.17573e10 | 0.807807 | ||||||||
\(280\) | −2.59840e10 | −0.252636 | ||||||||
\(281\) | 1.01765e11 | 0.973685 | 0.486843 | − | 0.873490i | \(-0.338149\pi\) | ||||
0.486843 | + | 0.873490i | \(0.338149\pi\) | |||||||
\(282\) | 6.76795e8 | 0.00637288 | ||||||||
\(283\) | −9.33903e10 | −0.865491 | −0.432746 | − | 0.901516i | \(-0.642455\pi\) | ||||
−0.432746 | + | 0.901516i | \(0.642455\pi\) | |||||||
\(284\) | −1.70908e10 | −0.155894 | ||||||||
\(285\) | −4.53825e8 | −0.00407461 | ||||||||
\(286\) | −3.50217e10 | −0.309521 | ||||||||
\(287\) | 4.80385e10 | 0.417947 | ||||||||
\(288\) | 1.14340e11 | 0.979333 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −8.38399e10 | −0.696081 | ||||||||
\(291\) | 2.95041e9 | 0.0241192 | ||||||||
\(292\) | −1.03257e11 | −0.831186 | ||||||||
\(293\) | −3.94765e10 | −0.312921 | −0.156460 | − | 0.987684i | \(-0.550008\pi\) | ||||
−0.156460 | + | 0.987684i | \(0.550008\pi\) | |||||||
\(294\) | 1.36719e9 | 0.0106725 | ||||||||
\(295\) | −2.36635e11 | −1.81920 | ||||||||
\(296\) | 8.71591e10 | 0.659933 | ||||||||
\(297\) | 1.01923e10 | 0.0760099 | ||||||||
\(298\) | −2.45637e10 | −0.180435 | ||||||||
\(299\) | −1.29076e11 | −0.933956 | ||||||||
\(300\) | −2.46061e9 | −0.0175387 | ||||||||
\(301\) | 4.37876e10 | 0.307469 | ||||||||
\(302\) | 1.11683e11 | 0.772601 | ||||||||
\(303\) | 2.45906e9 | 0.0167601 | ||||||||
\(304\) | 8.34946e9 | 0.0560696 | ||||||||
\(305\) | 6.40219e10 | 0.423623 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.10911e10 | 0.199762 | 0.0998812 | − | 0.994999i | \(-0.468154\pi\) | ||||
0.0998812 | + | 0.994999i | \(0.468154\pi\) | |||||||
\(308\) | 4.49453e10 | 0.284581 | ||||||||
\(309\) | 3.87079e7 | 0.000241539 0 | ||||||||
\(310\) | −7.45701e10 | −0.458603 | ||||||||
\(311\) | 1.33143e10 | 0.0807046 | 0.0403523 | − | 0.999186i | \(-0.487152\pi\) | ||||
0.0403523 | + | 0.999186i | \(0.487152\pi\) | |||||||
\(312\) | −1.78482e9 | −0.0106635 | ||||||||
\(313\) | −2.01278e11 | −1.18535 | −0.592674 | − | 0.805442i | \(-0.701928\pi\) | ||||
−0.592674 | + | 0.805442i | \(0.701928\pi\) | |||||||
\(314\) | 5.86265e10 | 0.340338 | ||||||||
\(315\) | 5.72420e10 | 0.327580 | ||||||||
\(316\) | 1.65882e11 | 0.935853 | ||||||||
\(317\) | −3.61827e10 | −0.201249 | −0.100625 | − | 0.994924i | \(-0.532084\pi\) | ||||
−0.100625 | + | 0.994924i | \(0.532084\pi\) | |||||||
\(318\) | −1.61407e8 | −0.000885117 0 | ||||||||
\(319\) | 3.21687e11 | 1.73930 | ||||||||
\(320\) | 2.00889e10 | 0.107098 | ||||||||
\(321\) | −1.05480e9 | −0.00554497 | ||||||||
\(322\) | −3.61488e10 | −0.187388 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.62475e11 | −0.819097 | ||||||||
\(325\) | −8.26620e10 | −0.410990 | ||||||||
\(326\) | −7.14122e10 | −0.350181 | ||||||||
\(327\) | −1.27997e9 | −0.00619064 | ||||||||
\(328\) | 2.76070e11 | 1.31700 | ||||||||
\(329\) | −2.91788e10 | −0.137305 | ||||||||
\(330\) | −4.64650e9 | −0.0215682 | ||||||||
\(331\) | 2.52419e11 | 1.15583 | 0.577917 | − | 0.816096i | \(-0.303866\pi\) | ||||
0.577917 | + | 0.816096i | \(0.303866\pi\) | |||||||
\(332\) | −1.32682e11 | −0.599366 | ||||||||
\(333\) | −1.92009e11 | −0.855702 | ||||||||
\(334\) | −8.70276e10 | −0.382646 | ||||||||
\(335\) | −2.57622e11 | −1.11759 | ||||||||
\(336\) | 7.58098e8 | 0.00324488 | ||||||||
\(337\) | 1.75954e11 | 0.743129 | 0.371564 | − | 0.928407i | \(-0.378821\pi\) | ||||
0.371564 | + | 0.928407i | \(0.378821\pi\) | |||||||
\(338\) | 7.45270e10 | 0.310591 | ||||||||
\(339\) | −3.77949e9 | −0.0155430 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.86120e11 | 1.14592 | ||||||||
\(342\) | 1.21279e10 | 0.0479365 | ||||||||
\(343\) | −1.21637e11 | −0.474508 | ||||||||
\(344\) | 2.51640e11 | 0.968874 | ||||||||
\(345\) | −1.71252e10 | −0.0650803 | ||||||||
\(346\) | 2.00653e11 | 0.752669 | ||||||||
\(347\) | −1.25482e11 | −0.464620 | −0.232310 | − | 0.972642i | \(-0.574628\pi\) | ||||
−0.232310 | + | 0.972642i | \(0.574628\pi\) | |||||||
\(348\) | 7.39072e9 | 0.0270135 | ||||||||
\(349\) | −2.12956e11 | −0.768380 | −0.384190 | − | 0.923254i | \(-0.625519\pi\) | ||||
−0.384190 | + | 0.923254i | \(0.625519\pi\) | |||||||
\(350\) | −2.31501e10 | −0.0824606 | ||||||||
\(351\) | 7.86666e9 | 0.0276636 | ||||||||
\(352\) | 4.00145e11 | 1.38923 | ||||||||
\(353\) | −4.20619e11 | −1.44179 | −0.720896 | − | 0.693043i | \(-0.756270\pi\) | ||||
−0.720896 | + | 0.693043i | \(0.756270\pi\) | |||||||
\(354\) | −4.55213e9 | −0.0154064 | ||||||||
\(355\) | −7.61754e10 | −0.254558 | ||||||||
\(356\) | 2.09886e11 | 0.692560 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.74296e11 | 0.560807 | ||||||||
\(359\) | 6.56670e9 | 0.0208652 | 0.0104326 | − | 0.999946i | \(-0.496679\pi\) | ||||
0.0104326 | + | 0.999946i | \(0.496679\pi\) | |||||||
\(360\) | 3.28961e11 | 1.03224 | ||||||||
\(361\) | −3.18542e11 | −0.987154 | ||||||||
\(362\) | −4.07501e10 | −0.124721 | ||||||||
\(363\) | 8.95581e9 | 0.0270723 | ||||||||
\(364\) | 3.46897e10 | 0.103572 | ||||||||
\(365\) | −4.60228e11 | −1.35723 | ||||||||
\(366\) | 1.23159e9 | 0.00358756 | ||||||||
\(367\) | 5.62708e11 | 1.61914 | 0.809572 | − | 0.587021i | \(-0.199699\pi\) | ||||
0.809572 | + | 0.587021i | \(0.199699\pi\) | |||||||
\(368\) | 3.15069e11 | 0.895551 | ||||||||
\(369\) | −6.08174e11 | −1.70769 | ||||||||
\(370\) | 1.75130e11 | 0.485793 | ||||||||
\(371\) | 6.95877e9 | 0.0190700 | ||||||||
\(372\) | 6.57356e9 | 0.0177974 | ||||||||
\(373\) | 3.47635e11 | 0.929896 | 0.464948 | − | 0.885338i | \(-0.346073\pi\) | ||||
0.464948 | + | 0.885338i | \(0.346073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.79968e9 | 0.00731084 | ||||||||
\(376\) | −1.67686e11 | −0.432664 | ||||||||
\(377\) | 2.48285e11 | 0.633015 | ||||||||
\(378\) | 2.20312e9 | 0.00555040 | ||||||||
\(379\) | −2.78766e11 | −0.694005 | −0.347003 | − | 0.937864i | \(-0.612801\pi\) | ||||
−0.347003 | + | 0.937864i | \(0.612801\pi\) | |||||||
\(380\) | 5.06899e10 | 0.124708 | ||||||||
\(381\) | 1.08864e10 | 0.0264680 | ||||||||
\(382\) | 9.98365e10 | 0.239886 | ||||||||
\(383\) | 5.20359e11 | 1.23569 | 0.617844 | − | 0.786301i | \(-0.288006\pi\) | ||||
0.617844 | + | 0.786301i | \(0.288006\pi\) | |||||||
\(384\) | 1.15859e10 | 0.0271919 | ||||||||
\(385\) | 2.00325e11 | 0.464689 | ||||||||
\(386\) | 2.53307e10 | 0.0580769 | ||||||||
\(387\) | −5.54356e11 | −1.25629 | ||||||||
\(388\) | −3.29546e11 | −0.738199 | ||||||||
\(389\) | 5.11901e11 | 1.13348 | 0.566738 | − | 0.823898i | \(-0.308205\pi\) | ||||
0.566738 | + | 0.823898i | \(0.308205\pi\) | |||||||
\(390\) | −3.58626e9 | −0.00784967 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.38740e11 | −0.724568 | ||||||||
\(393\) | 1.01921e9 | 0.00215525 | ||||||||
\(394\) | 3.42114e11 | 0.715217 | ||||||||
\(395\) | 7.39352e11 | 1.52815 | ||||||||
\(396\) | −5.69013e11 | −1.16277 | ||||||||
\(397\) | −2.70464e11 | −0.546452 | −0.273226 | − | 0.961950i | \(-0.588091\pi\) | ||||
−0.273226 | + | 0.961950i | \(0.588091\pi\) | |||||||
\(398\) | −2.62814e11 | −0.525018 | ||||||||
\(399\) | 3.76386e8 | 0.000743457 0 | ||||||||
\(400\) | 2.01774e11 | 0.394090 | ||||||||
\(401\) | 1.00714e11 | 0.194510 | 0.0972548 | − | 0.995260i | \(-0.468994\pi\) | ||||
0.0972548 | + | 0.995260i | \(0.468994\pi\) | |||||||
\(402\) | −4.95587e9 | −0.00946460 | ||||||||
\(403\) | 2.20833e11 | 0.417053 | ||||||||
\(404\) | −2.74665e11 | −0.512964 | ||||||||
\(405\) | −7.24169e11 | −1.33749 | ||||||||
\(406\) | 6.95339e10 | 0.127008 | ||||||||
\(407\) | −6.71958e11 | −1.21386 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.06059e11 | 0.717521 | 0.358760 | − | 0.933430i | \(-0.383199\pi\) | ||||
0.358760 | + | 0.933430i | \(0.383199\pi\) | |||||||
\(410\) | 5.54709e11 | 0.969479 | ||||||||
\(411\) | −2.94821e10 | −0.0509649 | ||||||||
\(412\) | −4.32348e9 | −0.00739258 | ||||||||
\(413\) | 1.96257e11 | 0.331932 | ||||||||
\(414\) | 4.57648e11 | 0.765649 | ||||||||
\(415\) | −5.91378e11 | −0.978699 | ||||||||
\(416\) | 3.08840e11 | 0.505607 | ||||||||
\(417\) | 9.14208e9 | 0.0148058 | ||||||||
\(418\) | 4.24429e10 | 0.0680004 | ||||||||
\(419\) | 9.21834e11 | 1.46113 | 0.730566 | − | 0.682842i | \(-0.239256\pi\) | ||||
0.730566 | + | 0.682842i | \(0.239256\pi\) | |||||||
\(420\) | 4.60245e9 | 0.00721717 | ||||||||
\(421\) | 9.29663e11 | 1.44230 | 0.721150 | − | 0.692778i | \(-0.243614\pi\) | ||||
0.721150 | + | 0.692778i | \(0.243614\pi\) | |||||||
\(422\) | −4.72506e11 | −0.725273 | ||||||||
\(423\) | 3.69407e11 | 0.561013 | ||||||||
\(424\) | 3.99910e10 | 0.0600918 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.46538e9 | −0.00215580 | ||||||||
\(427\) | −5.30975e10 | −0.0772946 | ||||||||
\(428\) | 1.17816e11 | 0.169710 | ||||||||
\(429\) | 1.37602e10 | 0.0196140 | ||||||||
\(430\) | 5.05623e11 | 0.713213 | ||||||||
\(431\) | 2.38808e11 | 0.333351 | 0.166675 | − | 0.986012i | \(-0.446697\pi\) | ||||
0.166675 | + | 0.986012i | \(0.446697\pi\) | |||||||
\(432\) | −1.92021e10 | −0.0265260 | ||||||||
\(433\) | −9.66720e11 | −1.32162 | −0.660808 | − | 0.750555i | \(-0.729786\pi\) | ||||
−0.660808 | + | 0.750555i | \(0.729786\pi\) | |||||||
\(434\) | 6.18459e10 | 0.0836771 | ||||||||
\(435\) | 3.29411e10 | 0.0441100 | ||||||||
\(436\) | 1.42967e11 | 0.189472 | ||||||||
\(437\) | 1.56428e11 | 0.205186 | ||||||||
\(438\) | −8.85337e9 | −0.0114941 | ||||||||
\(439\) | 3.49759e11 | 0.449447 | 0.224724 | − | 0.974423i | \(-0.427852\pi\) | ||||
0.224724 | + | 0.974423i | \(0.427852\pi\) | |||||||
\(440\) | 1.15124e12 | 1.46429 | ||||||||
\(441\) | 7.46234e11 | 0.939510 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.21165e11 | 0.766285 | 0.383142 | − | 0.923689i | \(-0.374842\pi\) | ||||
0.383142 | + | 0.923689i | \(0.374842\pi\) | |||||||
\(444\) | −1.54382e10 | −0.0188526 | ||||||||
\(445\) | 9.35480e11 | 1.13087 | ||||||||
\(446\) | −2.99453e11 | −0.358362 | ||||||||
\(447\) | 9.65121e9 | 0.0114340 | ||||||||
\(448\) | −1.66611e10 | −0.0195412 | ||||||||
\(449\) | −2.15975e11 | −0.250781 | −0.125390 | − | 0.992107i | \(-0.540018\pi\) | ||||
−0.125390 | + | 0.992107i | \(0.540018\pi\) | |||||||
\(450\) | 2.93083e11 | 0.336926 | ||||||||
\(451\) | −2.12838e12 | −2.42245 | ||||||||
\(452\) | 4.22150e11 | 0.475712 | ||||||||
\(453\) | −4.38808e10 | −0.0489590 | ||||||||
\(454\) | −3.58995e10 | −0.0396586 | ||||||||
\(455\) | 1.54615e11 | 0.169122 | ||||||||
\(456\) | 2.16303e9 | 0.00234272 | ||||||||
\(457\) | −4.26877e11 | −0.457804 | −0.228902 | − | 0.973449i | \(-0.573514\pi\) | ||||
−0.228902 | + | 0.973449i | \(0.573514\pi\) | |||||||
\(458\) | 4.73450e11 | 0.502781 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.91280e12 | 1.99186 | ||||||||
\(461\) | −1.33434e12 | −1.37598 | −0.687992 | − | 0.725718i | \(-0.741508\pi\) | ||||
−0.687992 | + | 0.725718i | \(0.741508\pi\) | |||||||
\(462\) | 3.85365e9 | 0.00393535 | ||||||||
\(463\) | 9.52978e11 | 0.963759 | 0.481880 | − | 0.876237i | \(-0.339954\pi\) | ||||
0.481880 | + | 0.876237i | \(0.339954\pi\) | |||||||
\(464\) | −6.06050e11 | −0.606985 | ||||||||
\(465\) | 2.92990e10 | 0.0290612 | ||||||||
\(466\) | −4.93764e11 | −0.485046 | ||||||||
\(467\) | 1.15911e12 | 1.12772 | 0.563859 | − | 0.825871i | \(-0.309316\pi\) | ||||
0.563859 | + | 0.825871i | \(0.309316\pi\) | |||||||
\(468\) | −4.39175e11 | −0.423186 | ||||||||
\(469\) | 2.13663e11 | 0.203916 | ||||||||
\(470\) | −3.36932e11 | −0.318495 | ||||||||
\(471\) | −2.30346e10 | −0.0215669 | ||||||||
\(472\) | 1.12786e12 | 1.04596 | ||||||||
\(473\) | −1.94004e12 | −1.78211 | ||||||||
\(474\) | 1.42229e10 | 0.0129415 | ||||||||
\(475\) | 1.00178e11 | 0.0902926 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.80989e10 | −0.0779180 | ||||||||
\(478\) | 5.88273e11 | 0.515411 | ||||||||
\(479\) | −9.36778e11 | −0.813068 | −0.406534 | − | 0.913636i | \(-0.633263\pi\) | ||||
−0.406534 | + | 0.913636i | \(0.633263\pi\) | |||||||
\(480\) | 4.09753e10 | 0.0352319 | ||||||||
\(481\) | −5.18631e11 | −0.441780 | ||||||||
\(482\) | −7.90493e11 | −0.667093 | ||||||||
\(483\) | 1.42030e10 | 0.0118746 | ||||||||
\(484\) | −1.00032e12 | −0.828580 | ||||||||
\(485\) | −1.46882e12 | −1.20540 | ||||||||
\(486\) | −4.18426e10 | −0.0340216 | ||||||||
\(487\) | 2.11074e12 | 1.70041 | 0.850207 | − | 0.526448i | \(-0.176477\pi\) | ||||
0.850207 | + | 0.526448i | \(0.176477\pi\) | |||||||
\(488\) | −3.05143e11 | −0.243565 | ||||||||
\(489\) | 2.80582e10 | 0.0221907 | ||||||||
\(490\) | −6.80633e11 | −0.533373 | ||||||||
\(491\) | 2.40038e12 | 1.86386 | 0.931929 | − | 0.362641i | \(-0.118125\pi\) | ||||
0.931929 | + | 0.362641i | \(0.118125\pi\) | |||||||
\(492\) | −4.88992e10 | −0.0376234 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 3.27583e10 | 0.0247485 | ||||||||
\(495\) | −2.53614e12 | −1.89867 | ||||||||
\(496\) | −5.39042e11 | −0.399904 | ||||||||
\(497\) | 6.31772e10 | 0.0464469 | ||||||||
\(498\) | −1.13763e10 | −0.00828838 | ||||||||
\(499\) | 4.49766e11 | 0.324739 | 0.162370 | − | 0.986730i | \(-0.448086\pi\) | ||||
0.162370 | + | 0.986730i | \(0.448086\pi\) | |||||||
\(500\) | −3.12710e11 | −0.223757 | ||||||||
\(501\) | 3.41936e10 | 0.0242479 | ||||||||
\(502\) | 9.56185e11 | 0.672009 | ||||||||
\(503\) | −1.01494e12 | −0.706943 | −0.353471 | − | 0.935445i | \(-0.614999\pi\) | ||||
−0.353471 | + | 0.935445i | \(0.614999\pi\) | |||||||
\(504\) | −2.72829e11 | −0.188344 | ||||||||
\(505\) | −1.22421e12 | −0.837614 | ||||||||
\(506\) | 1.60159e12 | 1.08611 | ||||||||
\(507\) | −2.92821e10 | −0.0196818 | ||||||||
\(508\) | −1.21596e12 | −0.810085 | ||||||||
\(509\) | 5.53282e11 | 0.365356 | 0.182678 | − | 0.983173i | \(-0.441523\pi\) | ||||
0.182678 | + | 0.983173i | \(0.441523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.81697e11 | 0.247642 | ||||||||
\(512\) | −1.34667e12 | −0.866058 | ||||||||
\(513\) | −9.53362e9 | −0.00607757 | ||||||||
\(514\) | 3.89916e11 | 0.246398 | ||||||||
\(515\) | −1.92702e10 | −0.0120713 | ||||||||
\(516\) | −4.45721e10 | −0.0276783 | ||||||||
\(517\) | 1.29278e12 | 0.795826 | ||||||||
\(518\) | −1.45246e11 | −0.0886383 | ||||||||
\(519\) | −7.88378e10 | −0.0476959 | ||||||||
\(520\) | 8.88548e11 | 0.532925 | ||||||||
\(521\) | 2.14089e12 | 1.27299 | 0.636493 | − | 0.771282i | \(-0.280384\pi\) | ||||
0.636493 | + | 0.771282i | \(0.280384\pi\) | |||||||
\(522\) | −8.80308e11 | −0.518940 | ||||||||
\(523\) | 3.97935e11 | 0.232570 | 0.116285 | − | 0.993216i | \(-0.462901\pi\) | ||||
0.116285 | + | 0.993216i | \(0.462901\pi\) | |||||||
\(524\) | −1.13841e11 | −0.0659639 | ||||||||
\(525\) | 9.09579e9 | 0.00522545 | ||||||||
\(526\) | −3.42193e11 | −0.194910 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.35880e10 | −0.0188075 | ||||||||
\(529\) | 4.10170e12 | 2.27726 | ||||||||
\(530\) | 8.03542e10 | 0.0442351 | ||||||||
\(531\) | −2.48463e12 | −1.35624 | ||||||||
\(532\) | −4.20405e10 | −0.0227544 | ||||||||
\(533\) | −1.64272e12 | −0.881642 | ||||||||
\(534\) | 1.79958e10 | 0.00957712 | ||||||||
\(535\) | 5.25119e11 | 0.277118 | ||||||||
\(536\) | 1.22789e12 | 0.642565 | ||||||||
\(537\) | −6.84817e10 | −0.0355378 | ||||||||
\(538\) | −1.27155e12 | −0.654353 | ||||||||
\(539\) | 2.61154e12 | 1.33274 | ||||||||
\(540\) | −1.16577e11 | −0.0589985 | ||||||||
\(541\) | −8.78322e11 | −0.440825 | −0.220412 | − | 0.975407i | \(-0.570740\pi\) | ||||
−0.220412 | + | 0.975407i | \(0.570740\pi\) | |||||||
\(542\) | 1.25670e12 | 0.625511 | ||||||||
\(543\) | 1.60109e10 | 0.00790345 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.37216e11 | 0.309387 | ||||||||
\(546\) | 2.97432e9 | 0.00143226 | ||||||||
\(547\) | 2.51249e12 | 1.19995 | 0.599973 | − | 0.800021i | \(-0.295178\pi\) | ||||
0.599973 | + | 0.800021i | \(0.295178\pi\) | |||||||
\(548\) | 3.29301e12 | 1.55984 | ||||||||
\(549\) | 6.72221e11 | 0.315818 | ||||||||
\(550\) | 1.02568e12 | 0.477947 | ||||||||
\(551\) | −3.00897e11 | −0.139071 | ||||||||
\(552\) | 8.16226e10 | 0.0374183 | ||||||||
\(553\) | −6.13193e11 | −0.278827 | ||||||||
\(554\) | −3.54880e11 | −0.160062 | ||||||||
\(555\) | −6.88093e10 | −0.0307843 | ||||||||
\(556\) | −1.02112e12 | −0.453150 | ||||||||
\(557\) | −3.99416e12 | −1.75823 | −0.879117 | − | 0.476606i | \(-0.841867\pi\) | ||||
−0.879117 | + | 0.476606i | \(0.841867\pi\) | |||||||
\(558\) | −7.82976e11 | −0.341896 | ||||||||
\(559\) | −1.49736e12 | −0.648594 | ||||||||
\(560\) | −3.77408e11 | −0.162168 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.74583e11 | −0.412103 | ||||||||
\(563\) | 3.88071e12 | 1.62789 | 0.813943 | − | 0.580945i | \(-0.197317\pi\) | ||||
0.813943 | + | 0.580945i | \(0.197317\pi\) | |||||||
\(564\) | 2.97015e10 | 0.0123601 | ||||||||
\(565\) | 1.88156e12 | 0.776785 | ||||||||
\(566\) | 8.94383e11 | 0.366311 | ||||||||
\(567\) | 6.00600e11 | 0.244040 | ||||||||
\(568\) | 3.63070e11 | 0.146360 | ||||||||
\(569\) | 1.04083e12 | 0.416270 | 0.208135 | − | 0.978100i | \(-0.433261\pi\) | ||||
0.208135 | + | 0.978100i | \(0.433261\pi\) | |||||||
\(570\) | 4.34620e9 | 0.00172454 | ||||||||
\(571\) | 3.42931e12 | 1.35003 | 0.675017 | − | 0.737802i | \(-0.264136\pi\) | ||||
0.675017 | + | 0.737802i | \(0.264136\pi\) | |||||||
\(572\) | −1.53695e12 | −0.600312 | ||||||||
\(573\) | −3.92263e10 | −0.0152013 | ||||||||
\(574\) | −4.60057e11 | −0.176892 | ||||||||
\(575\) | 3.78025e12 | 1.44217 | ||||||||
\(576\) | 2.10931e11 | 0.0798434 | ||||||||
\(577\) | −2.26487e12 | −0.850652 | −0.425326 | − | 0.905040i | \(-0.639841\pi\) | ||||
−0.425326 | + | 0.905040i | \(0.639841\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.95255e9 | −0.00368028 | ||||||||
\(580\) | −3.67936e12 | −1.35004 | ||||||||
\(581\) | 4.90469e11 | 0.178574 | ||||||||
\(582\) | −2.82556e10 | −0.0102082 | ||||||||
\(583\) | −3.08313e11 | −0.110531 | ||||||||
\(584\) | 2.19355e12 | 0.780351 | ||||||||
\(585\) | −1.95745e12 | −0.691016 | ||||||||
\(586\) | 3.78060e11 | 0.132441 | ||||||||
\(587\) | 2.23470e12 | 0.776870 | 0.388435 | − | 0.921476i | \(-0.373016\pi\) | ||||
0.388435 | + | 0.921476i | \(0.373016\pi\) | |||||||
\(588\) | 5.99997e10 | 0.0206991 | ||||||||
\(589\) | −2.67628e11 | −0.0916247 | ||||||||
\(590\) | 2.26621e12 | 0.769957 | ||||||||
\(591\) | −1.34418e11 | −0.0453226 | ||||||||
\(592\) | 1.26595e12 | 0.423613 | ||||||||
\(593\) | −3.12521e12 | −1.03785 | −0.518923 | − | 0.854821i | \(-0.673667\pi\) | ||||
−0.518923 | + | 0.854821i | \(0.673667\pi\) | |||||||
\(594\) | −9.76104e10 | −0.0321704 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.07799e12 | −0.349951 | ||||||||
\(597\) | 1.03261e11 | 0.0332699 | ||||||||
\(598\) | 1.23614e12 | 0.395287 | ||||||||
\(599\) | −4.98049e12 | −1.58071 | −0.790353 | − | 0.612652i | \(-0.790103\pi\) | ||||
−0.790353 | + | 0.612652i | \(0.790103\pi\) | |||||||
\(600\) | 5.22721e10 | 0.0164660 | ||||||||
\(601\) | 1.92193e12 | 0.600901 | 0.300451 | − | 0.953797i | \(-0.402863\pi\) | ||||
0.300451 | + | 0.953797i | \(0.402863\pi\) | |||||||
\(602\) | −4.19346e11 | −0.130133 | ||||||||
\(603\) | −2.70500e12 | −0.833181 | ||||||||
\(604\) | 4.90126e12 | 1.49845 | ||||||||
\(605\) | −4.45852e12 | −1.35298 | ||||||||
\(606\) | −2.35500e10 | −0.00709356 | ||||||||
\(607\) | −1.10595e12 | −0.330662 | −0.165331 | − | 0.986238i | \(-0.552869\pi\) | ||||
−0.165331 | + | 0.986238i | \(0.552869\pi\) | |||||||
\(608\) | −3.74284e11 | −0.111080 | ||||||||
\(609\) | −2.73202e10 | −0.00804835 | ||||||||
\(610\) | −6.13127e11 | −0.179294 | ||||||||
\(611\) | 9.97796e11 | 0.289638 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.38242e12 | −0.967511 | −0.483755 | − | 0.875203i | \(-0.660728\pi\) | ||||
−0.483755 | + | 0.875203i | \(0.660728\pi\) | |||||||
\(614\) | −2.97754e11 | −0.0845474 | ||||||||
\(615\) | −2.17948e11 | −0.0614349 | ||||||||
\(616\) | −9.54797e11 | −0.267176 | ||||||||
\(617\) | −1.73474e12 | −0.481893 | −0.240947 | − | 0.970538i | \(-0.577458\pi\) | ||||
−0.240947 | + | 0.970538i | \(0.577458\pi\) | |||||||
\(618\) | −3.70699e8 | −0.000102229 0 | ||||||||
\(619\) | 4.13205e12 | 1.13125 | 0.565624 | − | 0.824663i | \(-0.308635\pi\) | ||||
0.565624 | + | 0.824663i | \(0.308635\pi\) | |||||||
\(620\) | −3.27255e12 | −0.889454 | ||||||||
\(621\) | −3.59754e11 | −0.0970718 | ||||||||
\(622\) | −1.27509e11 | −0.0341574 | ||||||||
\(623\) | −7.75854e11 | −0.206340 | ||||||||
\(624\) | −2.59239e10 | −0.00684494 | ||||||||
\(625\) | −4.43270e12 | −1.16201 | ||||||||
\(626\) | 1.92760e12 | 0.501687 | ||||||||
\(627\) | −1.66760e10 | −0.00430912 | ||||||||
\(628\) | 2.57286e12 | 0.660081 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −5.48197e11 | −0.138645 | ||||||||
\(631\) | −1.18926e12 | −0.298637 | −0.149318 | − | 0.988789i | \(-0.547708\pi\) | ||||
−0.149318 | + | 0.988789i | \(0.547708\pi\) | |||||||
\(632\) | −3.52392e12 | −0.878617 | ||||||||
\(633\) | 1.85650e11 | 0.0459599 | ||||||||
\(634\) | 3.46516e11 | 0.0851768 | ||||||||
\(635\) | −5.41963e12 | −1.32278 | ||||||||
\(636\) | −7.08344e9 | −0.00171667 | ||||||||
\(637\) | 2.01564e12 | 0.485048 | ||||||||
\(638\) | −3.08074e12 | −0.736143 | ||||||||
\(639\) | −7.99831e11 | −0.189777 | ||||||||
\(640\) | −5.76787e12 | −1.35896 | ||||||||
\(641\) | −1.36967e12 | −0.320447 | −0.160224 | − | 0.987081i | \(-0.551221\pi\) | ||||
−0.160224 | + | 0.987081i | \(0.551221\pi\) | |||||||
\(642\) | 1.01017e10 | 0.00234685 | ||||||||
\(643\) | 4.23668e12 | 0.977409 | 0.488705 | − | 0.872449i | \(-0.337470\pi\) | ||||
0.488705 | + | 0.872449i | \(0.337470\pi\) | |||||||
\(644\) | −1.58641e12 | −0.363437 | ||||||||
\(645\) | −1.98662e11 | −0.0451956 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.27863e12 | −1.63298 | −0.816489 | − | 0.577361i | \(-0.804082\pi\) | ||||
−0.816489 | + | 0.577361i | \(0.804082\pi\) | |||||||
\(648\) | 3.45155e12 | 0.769001 | ||||||||
\(649\) | −8.69528e12 | −1.92390 | ||||||||
\(650\) | 7.91640e11 | 0.173947 | ||||||||
\(651\) | −2.42996e10 | −0.00530254 | ||||||||
\(652\) | −3.13396e12 | −0.679172 | ||||||||
\(653\) | −2.58771e12 | −0.556937 | −0.278468 | − | 0.960445i | \(-0.589827\pi\) | ||||
−0.278468 | + | 0.960445i | \(0.589827\pi\) | |||||||
\(654\) | 1.22581e10 | 0.00262013 | ||||||||
\(655\) | −5.07398e11 | −0.107712 | ||||||||
\(656\) | 4.00981e12 | 0.845388 | ||||||||
\(657\) | −4.83233e12 | −1.01184 | ||||||||
\(658\) | 2.79440e11 | 0.0581128 | ||||||||
\(659\) | 3.62332e12 | 0.748381 | 0.374190 | − | 0.927352i | \(-0.377921\pi\) | ||||
0.374190 | + | 0.927352i | \(0.377921\pi\) | |||||||
\(660\) | −2.03914e11 | −0.0418312 | ||||||||
\(661\) | 1.90260e11 | 0.0387651 | 0.0193826 | − | 0.999812i | \(-0.493830\pi\) | ||||
0.0193826 | + | 0.999812i | \(0.493830\pi\) | |||||||
\(662\) | −2.41737e12 | −0.489195 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.81865e12 | 0.562709 | ||||||||
\(665\) | −1.87378e11 | −0.0371554 | ||||||||
\(666\) | 1.83884e12 | 0.362167 | ||||||||
\(667\) | −1.13544e13 | −2.22126 | ||||||||
\(668\) | −3.81925e12 | −0.742137 | ||||||||
\(669\) | 1.17657e11 | 0.0227090 | ||||||||
\(670\) | 2.46721e12 | 0.473008 | ||||||||
\(671\) | 2.35252e12 | 0.448004 | ||||||||
\(672\) | −3.39835e10 | −0.00642845 | ||||||||
\(673\) | −1.03919e13 | −1.95266 | −0.976332 | − | 0.216278i | \(-0.930608\pi\) | ||||
−0.976332 | + | 0.216278i | \(0.930608\pi\) | |||||||
\(674\) | −1.68508e12 | −0.314522 | ||||||||
\(675\) | −2.30391e11 | −0.0427167 | ||||||||
\(676\) | 3.27066e12 | 0.602386 | ||||||||
\(677\) | 5.50581e12 | 1.00733 | 0.503666 | − | 0.863899i | \(-0.331984\pi\) | ||||
0.503666 | + | 0.863899i | \(0.331984\pi\) | |||||||
\(678\) | 3.61955e10 | 0.00657841 | ||||||||
\(679\) | 1.21819e12 | 0.219938 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41051e10 | 0.00251313 | ||||||||
\(682\) | −2.74012e12 | −0.484998 | ||||||||
\(683\) | −1.92719e12 | −0.338869 | −0.169434 | − | 0.985541i | \(-0.554194\pi\) | ||||
−0.169434 | + | 0.985541i | \(0.554194\pi\) | |||||||
\(684\) | 5.32237e11 | 0.0929722 | ||||||||
\(685\) | 1.46772e13 | 2.54705 | ||||||||
\(686\) | 1.16490e12 | 0.200831 | ||||||||
\(687\) | −1.86021e11 | −0.0318608 | ||||||||
\(688\) | 3.65498e12 | 0.621924 | ||||||||
\(689\) | −2.37962e11 | −0.0402273 | ||||||||
\(690\) | 1.64005e11 | 0.0275446 | ||||||||
\(691\) | 1.24650e12 | 0.207989 | 0.103994 | − | 0.994578i | \(-0.466838\pi\) | ||||
0.103994 | + | 0.994578i | \(0.466838\pi\) | |||||||
\(692\) | 8.80579e12 | 1.45979 | ||||||||
\(693\) | 2.10339e12 | 0.346434 | ||||||||
\(694\) | 1.20172e12 | 0.196646 | ||||||||
\(695\) | −4.55125e12 | −0.739944 | ||||||||
\(696\) | −1.57005e11 | −0.0253613 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.03944e12 | 0.325209 | ||||||||
\(699\) | 1.94002e11 | 0.0307369 | ||||||||
\(700\) | −1.01595e12 | −0.159931 | ||||||||
\(701\) | 9.42697e12 | 1.47449 | 0.737244 | − | 0.675627i | \(-0.236127\pi\) | ||||
0.737244 | + | 0.675627i | \(0.236127\pi\) | |||||||
\(702\) | −7.53376e10 | −0.0117083 | ||||||||
\(703\) | 6.28530e11 | 0.0970570 | ||||||||
\(704\) | 7.38178e11 | 0.113262 | ||||||||
\(705\) | 1.32382e11 | 0.0201827 | ||||||||
\(706\) | 4.02820e12 | 0.610224 | ||||||||
\(707\) | 1.01532e12 | 0.152832 | ||||||||
\(708\) | −1.99773e11 | −0.0298804 | ||||||||
\(709\) | −1.44728e12 | −0.215103 | −0.107551 | − | 0.994200i | \(-0.534301\pi\) | ||||
−0.107551 | + | 0.994200i | \(0.534301\pi\) | |||||||
\(710\) | 7.29519e11 | 0.107739 | ||||||||
\(711\) | 7.76310e12 | 1.13926 | ||||||||
\(712\) | −4.45871e12 | −0.650204 | ||||||||
\(713\) | −1.00990e13 | −1.46344 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.85032e12 | −0.980243 | ||||||||
\(716\) | 7.64907e12 | 1.08768 | ||||||||
\(717\) | −2.31136e11 | −0.0326611 | ||||||||
\(718\) | −6.28882e10 | −0.00883098 | ||||||||
\(719\) | 7.25929e12 | 1.01301 | 0.506506 | − | 0.862237i | \(-0.330937\pi\) | ||||
0.506506 | + | 0.862237i | \(0.330937\pi\) | |||||||
\(720\) | 4.77803e12 | 0.662602 | ||||||||
\(721\) | 1.59820e10 | 0.00220253 | ||||||||
\(722\) | 3.05062e12 | 0.417803 | ||||||||
\(723\) | 3.10589e11 | 0.0422730 | ||||||||
\(724\) | −1.78834e12 | −0.241895 | ||||||||
\(725\) | −7.27150e12 | −0.977469 | ||||||||
\(726\) | −8.57683e10 | −0.0114581 | ||||||||
\(727\) | −3.08455e12 | −0.409531 | −0.204765 | − | 0.978811i | \(-0.565643\pi\) | ||||
−0.204765 | + | 0.978811i | \(0.565643\pi\) | |||||||
\(728\) | −7.36931e11 | −0.0972379 | ||||||||
\(729\) | −7.59271e12 | −0.995687 | ||||||||
\(730\) | 4.40752e12 | 0.574436 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 5.40488e10 | 0.00695803 | ||||||||
\(733\) | 3.11662e12 | 0.398764 | 0.199382 | − | 0.979922i | \(-0.436106\pi\) | ||||
0.199382 | + | 0.979922i | \(0.436106\pi\) | |||||||
\(734\) | −5.38895e12 | −0.685286 | ||||||||
\(735\) | 2.67424e11 | 0.0337993 | ||||||||
\(736\) | −1.41237e13 | −1.77418 | ||||||||
\(737\) | −9.46648e12 | −1.18191 | ||||||||
\(738\) | 5.82437e12 | 0.722762 | ||||||||
\(739\) | 4.75055e12 | 0.585927 | 0.292964 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292964 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(740\) | 7.68566e12 | 0.942189 | ||||||||
\(741\) | −1.28709e10 | −0.00156829 | ||||||||
\(742\) | −6.66430e10 | −0.00807118 | ||||||||
\(743\) | −7.29991e12 | −0.878755 | −0.439377 | − | 0.898303i | \(-0.644801\pi\) | ||||
−0.439377 | + | 0.898303i | \(0.644801\pi\) | |||||||
\(744\) | −1.39646e11 | −0.0167090 | ||||||||
\(745\) | −4.80471e12 | −0.571432 | ||||||||
\(746\) | −3.32925e12 | −0.393569 | ||||||||
\(747\) | −6.20939e12 | −0.729636 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.35515e11 | −0.0505633 | ||||||||
\(750\) | −2.68120e10 | −0.00309424 | ||||||||
\(751\) | 2.03675e12 | 0.233646 | 0.116823 | − | 0.993153i | \(-0.462729\pi\) | ||||
0.116823 | + | 0.993153i | \(0.462729\pi\) | |||||||
\(752\) | −2.43557e12 | −0.277728 | ||||||||
\(753\) | −3.75690e11 | −0.0425846 | ||||||||
\(754\) | −2.37778e12 | −0.267917 | ||||||||
\(755\) | 2.18454e13 | 2.44680 | ||||||||
\(756\) | 9.66849e10 | 0.0107649 | ||||||||
\(757\) | −6.50159e12 | −0.719595 | −0.359798 | − | 0.933030i | \(-0.617154\pi\) | ||||
−0.359798 | + | 0.933030i | \(0.617154\pi\) | |||||||
\(758\) | 2.66969e12 | 0.293731 | ||||||||
\(759\) | −6.29274e11 | −0.0688259 | ||||||||
\(760\) | −1.07683e12 | −0.117081 | ||||||||
\(761\) | −9.68338e12 | −1.04664 | −0.523318 | − | 0.852137i | \(-0.675306\pi\) | ||||
−0.523318 | + | 0.852137i | \(0.675306\pi\) | |||||||
\(762\) | −1.04257e11 | −0.0112023 | ||||||||
\(763\) | −5.28485e11 | −0.0564510 | ||||||||
\(764\) | 4.38138e12 | 0.465255 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.98339e12 | −0.522992 | ||||||||
\(767\) | −6.71119e12 | −0.700197 | ||||||||
\(768\) | −9.02957e10 | −0.00936573 | ||||||||
\(769\) | −3.78295e12 | −0.390088 | −0.195044 | − | 0.980795i | \(-0.562485\pi\) | ||||
−0.195044 | + | 0.980795i | \(0.562485\pi\) | |||||||
\(770\) | −1.91848e12 | −0.196675 | ||||||||
\(771\) | −1.53200e11 | −0.0156140 | ||||||||
\(772\) | 1.11165e12 | 0.112639 | ||||||||
\(773\) | −1.52760e13 | −1.53887 | −0.769435 | − | 0.638726i | \(-0.779462\pi\) | ||||
−0.769435 | + | 0.638726i | \(0.779462\pi\) | |||||||
\(774\) | 5.30898e12 | 0.531712 | ||||||||
\(775\) | −6.46753e12 | −0.643992 | ||||||||
\(776\) | 7.00072e12 | 0.693051 | ||||||||
\(777\) | 5.70681e10 | 0.00561692 | ||||||||
\(778\) | −4.90238e12 | −0.479732 | ||||||||
\(779\) | 1.99082e12 | 0.193693 | ||||||||
\(780\) | −1.57385e11 | −0.0152243 | ||||||||
\(781\) | −2.79911e12 | −0.269209 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.92004e11 | 0.0657931 | ||||||||
\(784\) | −4.92007e12 | −0.465103 | ||||||||
\(785\) | 1.14675e13 | 1.07784 | ||||||||
\(786\) | −9.76079e9 | −0.000912186 0 | ||||||||
\(787\) | −1.49696e12 | −0.139099 | −0.0695497 | − | 0.997578i | \(-0.522156\pi\) | ||||
−0.0695497 | + | 0.997578i | \(0.522156\pi\) | |||||||
\(788\) | 1.50139e13 | 1.38715 | ||||||||
\(789\) | 1.34449e11 | 0.0123513 | ||||||||
\(790\) | −7.08065e12 | −0.646772 | ||||||||
\(791\) | −1.56050e12 | −0.141733 | ||||||||
\(792\) | 1.20878e13 | 1.09165 | ||||||||
\(793\) | 1.81572e12 | 0.163050 | ||||||||
\(794\) | 2.59018e12 | 0.231280 | ||||||||
\(795\) | −3.15716e10 | −0.00280314 | ||||||||
\(796\) | −1.15337e13 | −1.01827 | ||||||||
\(797\) | −9.20364e12 | −0.807974 | −0.403987 | − | 0.914765i | \(-0.632376\pi\) | ||||
−0.403987 | + | 0.914765i | \(0.632376\pi\) | |||||||
\(798\) | −3.60459e9 | −0.000314661 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −9.04498e12 | −0.780734 | ||||||||
\(801\) | 9.82241e12 | 0.843086 | ||||||||
\(802\) | −9.64523e11 | −0.0823242 | ||||||||
\(803\) | −1.69113e13 | −1.43535 | ||||||||
\(804\) | −2.17491e11 | −0.0183565 | ||||||||
\(805\) | −7.07077e12 | −0.593452 | ||||||||
\(806\) | −2.11488e12 | −0.176513 | ||||||||
\(807\) | 4.99597e11 | 0.0414657 | ||||||||
\(808\) | 5.83485e12 | 0.481592 | ||||||||
\(809\) | −1.38525e13 | −1.13700 | −0.568498 | − | 0.822684i | \(-0.692475\pi\) | ||||
−0.568498 | + | 0.822684i | \(0.692475\pi\) | |||||||
\(810\) | 6.93524e12 | 0.566081 | ||||||||
\(811\) | −7.80849e12 | −0.633831 | −0.316915 | − | 0.948454i | \(-0.602647\pi\) | ||||
−0.316915 | + | 0.948454i | \(0.602647\pi\) | |||||||
\(812\) | 3.05153e12 | 0.246329 | ||||||||
\(813\) | −4.93764e11 | −0.0396380 | ||||||||
\(814\) | 6.43523e12 | 0.513753 | ||||||||
\(815\) | −1.39684e13 | −1.10901 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.81465e12 | 0.142493 | ||||||||
\(818\) | −3.88876e12 | −0.303684 | ||||||||
\(819\) | 1.62344e12 | 0.126083 | ||||||||
\(820\) | 2.43437e13 | 1.88029 | ||||||||
\(821\) | 4.91660e12 | 0.377677 | 0.188838 | − | 0.982008i | \(-0.439528\pi\) | ||||
0.188838 | + | 0.982008i | \(0.439528\pi\) | |||||||
\(822\) | 2.82345e11 | 0.0215704 | ||||||||
\(823\) | −1.09549e13 | −0.832360 | −0.416180 | − | 0.909282i | \(-0.636631\pi\) | ||||
−0.416180 | + | 0.909282i | \(0.636631\pi\) | |||||||
\(824\) | 9.18461e10 | 0.00694046 | ||||||||
\(825\) | −4.02995e11 | −0.0302870 | ||||||||
\(826\) | −1.87952e12 | −0.140487 | ||||||||
\(827\) | −2.82911e12 | −0.210317 | −0.105159 | − | 0.994455i | \(-0.533535\pi\) | ||||
−0.105159 | + | 0.994455i | \(0.533535\pi\) | |||||||
\(828\) | 2.00841e13 | 1.48497 | ||||||||
\(829\) | −2.90839e12 | −0.213873 | −0.106937 | − | 0.994266i | \(-0.534104\pi\) | ||||
−0.106937 | + | 0.994266i | \(0.534104\pi\) | |||||||
\(830\) | 5.66353e12 | 0.414225 | ||||||||
\(831\) | 1.39434e11 | 0.0101430 | ||||||||
\(832\) | 5.69741e11 | 0.0412214 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.75521e10 | −0.00626642 | ||||||||
\(835\) | −1.70228e13 | −1.21183 | ||||||||
\(836\) | 1.86263e12 | 0.131886 | ||||||||
\(837\) | 6.15492e11 | 0.0433469 | ||||||||
\(838\) | −8.82825e12 | −0.618410 | ||||||||
\(839\) | 2.60868e13 | 1.81757 | 0.908787 | − | 0.417259i | \(-0.137009\pi\) | ||||
0.908787 | + | 0.417259i | \(0.137009\pi\) | |||||||
\(840\) | −9.77723e10 | −0.00677577 | ||||||||
\(841\) | 7.33362e12 | 0.505518 | ||||||||
\(842\) | −8.90322e12 | −0.610439 | ||||||||
\(843\) | 3.82919e11 | 0.0261145 | ||||||||
\(844\) | −2.07362e13 | −1.40666 | ||||||||
\(845\) | 1.45776e13 | 0.983630 | ||||||||
\(846\) | −3.53774e12 | −0.237443 | ||||||||
\(847\) | 3.69774e12 | 0.246866 | ||||||||
\(848\) | 5.80854e11 | 0.0385732 | ||||||||
\(849\) | −3.51408e11 | −0.0232127 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.37177e13 | 1.55021 | ||||||||
\(852\) | −6.43091e10 | −0.00418114 | ||||||||
\(853\) | −4.84767e12 | −0.313518 | −0.156759 | − | 0.987637i | \(-0.550105\pi\) | ||||
−0.156759 | + | 0.987637i | \(0.550105\pi\) | |||||||
\(854\) | 5.08506e11 | 0.0327141 | ||||||||
\(855\) | 2.37223e12 | 0.151813 | ||||||||
\(856\) | −2.50284e12 | −0.159331 | ||||||||
\(857\) | −2.06896e13 | −1.31020 | −0.655101 | − | 0.755541i | \(-0.727374\pi\) | ||||
−0.655101 | + | 0.755541i | \(0.727374\pi\) | |||||||
\(858\) | −1.31779e11 | −0.00830145 | ||||||||
\(859\) | −2.50372e13 | −1.56898 | −0.784488 | − | 0.620144i | \(-0.787074\pi\) | ||||
−0.784488 | + | 0.620144i | \(0.787074\pi\) | |||||||
\(860\) | 2.21896e13 | 1.38327 | ||||||||
\(861\) | 1.80759e11 | 0.0112095 | ||||||||
\(862\) | −2.28703e12 | −0.141087 | ||||||||
\(863\) | 1.89430e13 | 1.16252 | 0.581260 | − | 0.813718i | \(-0.302560\pi\) | ||||
0.581260 | + | 0.813718i | \(0.302560\pi\) | |||||||
\(864\) | 8.60780e11 | 0.0525509 | ||||||||
\(865\) | 3.92482e13 | 2.38368 | ||||||||
\(866\) | 9.25811e12 | 0.559361 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.71414e12 | 0.162291 | ||||||||
\(869\) | 2.71679e13 | 1.61610 | ||||||||
\(870\) | −3.15472e11 | −0.0186691 | ||||||||
\(871\) | −7.30642e12 | −0.430153 | ||||||||
\(872\) | −3.03712e12 | −0.177884 | ||||||||
\(873\) | −1.54224e13 | −0.898643 | ||||||||
\(874\) | −1.49808e12 | −0.0868429 | ||||||||
\(875\) | 1.15595e12 | 0.0666658 | ||||||||
\(876\) | −3.88535e11 | −0.0222927 | ||||||||
\(877\) | −1.70384e13 | −0.972591 | −0.486295 | − | 0.873794i | \(-0.661652\pi\) | ||||
−0.486295 | + | 0.873794i | \(0.661652\pi\) | |||||||
\(878\) | −3.34958e12 | −0.190224 | ||||||||
\(879\) | −1.48542e11 | −0.00839263 | ||||||||
\(880\) | 1.67213e13 | 0.939935 | ||||||||
\(881\) | −2.66051e13 | −1.48790 | −0.743950 | − | 0.668235i | \(-0.767050\pi\) | ||||
−0.743950 | + | 0.668235i | \(0.767050\pi\) | |||||||
\(882\) | −7.14656e12 | −0.397638 | ||||||||
\(883\) | 1.28352e13 | 0.710525 | 0.355263 | − | 0.934767i | \(-0.384391\pi\) | ||||
0.355263 | + | 0.934767i | \(0.384391\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.90407e11 | −0.0487914 | ||||||||
\(886\) | −5.94879e12 | −0.324322 | ||||||||
\(887\) | 1.18450e12 | 0.0642511 | 0.0321255 | − | 0.999484i | \(-0.489772\pi\) | ||||
0.0321255 | + | 0.999484i | \(0.489772\pi\) | |||||||
\(888\) | 3.27961e11 | 0.0176996 | ||||||||
\(889\) | 4.49485e12 | 0.241356 | ||||||||
\(890\) | −8.95893e12 | −0.478631 | ||||||||
\(891\) | −2.66100e13 | −1.41447 | ||||||||
\(892\) | −1.31417e13 | −0.695037 | ||||||||
\(893\) | −1.20923e12 | −0.0636323 | ||||||||
\(894\) | −9.24280e10 | −0.00483933 | ||||||||
\(895\) | 3.40926e13 | 1.77606 | ||||||||
\(896\) | 4.78367e12 | 0.247957 | ||||||||
\(897\) | −4.85687e11 | −0.0250490 | ||||||||
\(898\) | 2.06835e12 | 0.106140 | ||||||||
\(899\) | 1.94259e13 | 0.991890 | ||||||||
\(900\) | 1.28621e13 | 0.653463 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.03831e13 | 1.02528 | ||||||||
\(903\) | 1.64763e11 | 0.00824643 | ||||||||
\(904\) | −8.96796e12 | −0.446617 | ||||||||
\(905\) | −7.97079e12 | −0.394987 | ||||||||
\(906\) | 4.20239e11 | 0.0207214 | ||||||||
\(907\) | −4.15423e12 | −0.203825 | −0.101913 | − | 0.994793i | \(-0.532496\pi\) | ||||
−0.101913 | + | 0.994793i | \(0.532496\pi\) | |||||||
\(908\) | −1.57547e12 | −0.0769172 | ||||||||
\(909\) | −1.28540e13 | −0.624455 | ||||||||
\(910\) | −1.48072e12 | −0.0715793 | ||||||||
\(911\) | −7.95629e12 | −0.382717 | −0.191359 | − | 0.981520i | \(-0.561289\pi\) | ||||
−0.191359 | + | 0.981520i | \(0.561289\pi\) | |||||||
\(912\) | 3.14172e10 | 0.00150380 | ||||||||
\(913\) | −2.17305e13 | −1.03503 | ||||||||
\(914\) | 4.08812e12 | 0.193761 | ||||||||
\(915\) | 2.40901e11 | 0.0113617 | ||||||||
\(916\) | 2.07776e13 | 0.975137 | ||||||||
\(917\) | 4.20819e11 | 0.0196532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.01245e13 | −0.468225 | −0.234112 | − | 0.972210i | \(-0.575218\pi\) | ||||
−0.234112 | + | 0.972210i | \(0.575218\pi\) | |||||||
\(920\) | −4.06346e13 | −1.87004 | ||||||||
\(921\) | 1.16989e11 | 0.00535769 | ||||||||
\(922\) | 1.27788e13 | 0.582372 | ||||||||
\(923\) | −2.16041e12 | −0.0979778 | ||||||||
\(924\) | 1.69119e11 | 0.00763255 | ||||||||
\(925\) | 1.51891e13 | 0.682174 | ||||||||
\(926\) | −9.12651e12 | −0.407901 | ||||||||
\(927\) | −2.02334e11 | −0.00899934 | ||||||||
\(928\) | 2.71676e13 | 1.20250 | ||||||||
\(929\) | 3.17571e13 | 1.39885 | 0.699424 | − | 0.714707i | \(-0.253440\pi\) | ||||
0.699424 | + | 0.714707i | \(0.253440\pi\) | |||||||
\(930\) | −2.80591e11 | −0.0122999 | ||||||||
\(931\) | −2.44275e12 | −0.106563 | ||||||||
\(932\) | −2.16691e13 | −0.940739 | ||||||||
\(933\) | 5.00990e10 | 0.00216452 | ||||||||
\(934\) | −1.11006e13 | −0.477295 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.32964e12 | 0.397304 | ||||||||
\(937\) | 1.04267e13 | 0.441897 | 0.220948 | − | 0.975286i | \(-0.429085\pi\) | ||||
0.220948 | + | 0.975286i | \(0.429085\pi\) | |||||||
\(938\) | −2.04621e12 | −0.0863055 | ||||||||
\(939\) | −7.57364e11 | −0.0317914 | ||||||||
\(940\) | −1.47865e13 | −0.617716 | ||||||||
\(941\) | −1.39589e13 | −0.580359 | −0.290180 | − | 0.956972i | \(-0.593715\pi\) | ||||
−0.290180 | + | 0.956972i | \(0.593715\pi\) | |||||||
\(942\) | 2.20599e11 | 0.00912797 | ||||||||
\(943\) | 7.51242e13 | 3.09369 | ||||||||
\(944\) | 1.63817e13 | 0.671405 | ||||||||
\(945\) | 4.30934e11 | 0.0175779 | ||||||||
\(946\) | 1.85794e13 | 0.754261 | ||||||||
\(947\) | −3.37968e13 | −1.36553 | −0.682764 | − | 0.730639i | \(-0.739222\pi\) | ||||
−0.682764 | + | 0.730639i | \(0.739222\pi\) | |||||||
\(948\) | 6.24179e11 | 0.0250999 | ||||||||
\(949\) | −1.30525e13 | −0.522391 | ||||||||
\(950\) | −9.59390e11 | −0.0382155 | ||||||||
\(951\) | −1.36148e11 | −0.00539757 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.89333e12 | 0.152898 | 0.0764492 | − | 0.997073i | \(-0.475642\pi\) | ||||
0.0764492 | + | 0.997073i | \(0.475642\pi\) | |||||||
\(954\) | 8.43708e11 | 0.0329780 | ||||||||
\(955\) | 1.95282e13 | 0.759709 | ||||||||
\(956\) | 2.58167e13 | 0.999632 | ||||||||
\(957\) | 1.21044e12 | 0.0466487 | ||||||||
\(958\) | 8.97136e12 | 0.344123 | ||||||||
\(959\) | −1.21728e13 | −0.464736 | ||||||||
\(960\) | 7.55903e10 | 0.00287240 | ||||||||
\(961\) | −9.16152e12 | −0.346507 | ||||||||
\(962\) | 4.96684e12 | 0.186979 | ||||||||
\(963\) | 5.51367e12 | 0.206596 | ||||||||
\(964\) | −3.46912e13 | −1.29382 | ||||||||
\(965\) | 4.95473e12 | 0.183928 | ||||||||
\(966\) | −1.36020e11 | −0.00502581 | ||||||||
\(967\) | −2.13333e13 | −0.784584 | −0.392292 | − | 0.919841i | \(-0.628318\pi\) | ||||
−0.392292 | + | 0.919841i | \(0.628318\pi\) | |||||||
\(968\) | 2.12503e13 | 0.777905 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.40666e13 | 0.510172 | ||||||||
\(971\) | 6.06046e12 | 0.218786 | 0.109393 | − | 0.993999i | \(-0.465109\pi\) | ||||
0.109393 | + | 0.993999i | \(0.465109\pi\) | |||||||
\(972\) | −1.83628e12 | −0.0659845 | ||||||||
\(973\) | 3.77465e12 | 0.135011 | ||||||||
\(974\) | −2.02142e13 | −0.719683 | ||||||||
\(975\) | −3.11039e11 | −0.0110229 | ||||||||
\(976\) | −4.43209e12 | −0.156345 | ||||||||
\(977\) | −3.07781e13 | −1.08073 | −0.540363 | − | 0.841432i | \(-0.681713\pi\) | ||||
−0.540363 | + | 0.841432i | \(0.681713\pi\) | |||||||
\(978\) | −2.68709e11 | −0.00939197 | ||||||||
\(979\) | 3.43747e13 | 1.19596 | ||||||||
\(980\) | −2.98700e13 | −1.03447 | ||||||||
\(981\) | 6.69068e12 | 0.230653 | ||||||||
\(982\) | −2.29880e13 | −0.788859 | ||||||||
\(983\) | −1.64085e13 | −0.560504 | −0.280252 | − | 0.959927i | \(-0.590418\pi\) | ||||
−0.280252 | + | 0.959927i | \(0.590418\pi\) | |||||||
\(984\) | 1.03879e12 | 0.0353224 | ||||||||
\(985\) | 6.69182e13 | 2.26507 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.09793e11 | −0.00368255 | ||||||||
\(988\) | 1.43761e12 | 0.0479994 | ||||||||
\(989\) | 6.84764e13 | 2.27592 | ||||||||
\(990\) | 2.42882e13 | 0.803595 | ||||||||
\(991\) | 4.00736e13 | 1.31986 | 0.659928 | − | 0.751329i | \(-0.270587\pi\) | ||||
0.659928 | + | 0.751329i | \(0.270587\pi\) | |||||||
\(992\) | 2.41638e13 | 0.792252 | ||||||||
\(993\) | 9.49797e11 | 0.0309998 | ||||||||
\(994\) | −6.05038e11 | −0.0196582 | ||||||||
\(995\) | −5.14069e13 | −1.66271 | ||||||||
\(996\) | −4.99256e11 | −0.0160752 | ||||||||
\(997\) | 5.15990e13 | 1.65391 | 0.826957 | − | 0.562266i | \(-0.190070\pi\) | ||||
0.826957 | + | 0.562266i | \(0.190070\pi\) | |||||||
\(998\) | −4.30734e12 | −0.137443 | ||||||||
\(999\) | −1.44550e12 | −0.0459169 |
(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 | 289.10.a.f.1.12 | 24 | ||
17.8 | even | 8 | 17.10.c.a.13.7 | yes | 24 | ||
17.15 | even | 8 | 17.10.c.a.4.6 | ✓ | 24 | ||
17.16 | even | 2 | inner | 289.10.a.f.1.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.c.a.4.6 | ✓ | 24 | 17.15 | even | 8 | ||
17.10.c.a.13.7 | yes | 24 | 17.8 | even | 8 | ||
289.10.a.f.1.11 | 24 | 17.16 | even | 2 | inner | ||
289.10.a.f.1.12 | 24 | 1.1 | even | 1 | trivial |