Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −43.5628 | −1.92522 | −0.962610 | − | 0.270889i | \(-0.912682\pi\) | ||||
−0.962610 | + | 0.270889i | \(0.912682\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 1385.72 | 2.70648 | ||||||||
\(5\) | 1597.21 | 1.14287 | 0.571434 | − | 0.820648i | \(-0.306387\pi\) | ||||
0.571434 | + | 0.820648i | \(0.306387\pi\) | |||||||
\(6\) | −3528.58 | −1.11153 | ||||||||
\(7\) | −10966.0 | −1.72626 | −0.863132 | − | 0.504979i | \(-0.831500\pi\) | ||||
−0.863132 | + | 0.504979i | \(0.831500\pi\) | |||||||
\(8\) | −38061.5 | −3.28534 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −69578.8 | −2.20027 | ||||||||
\(11\) | 52965.0 | 1.09074 | 0.545371 | − | 0.838195i | \(-0.316389\pi\) | ||||
0.545371 | + | 0.838195i | \(0.316389\pi\) | |||||||
\(12\) | 112243. | 1.56258 | ||||||||
\(13\) | −146184. | −1.41956 | −0.709780 | − | 0.704423i | \(-0.751206\pi\) | ||||
−0.709780 | + | 0.704423i | \(0.751206\pi\) | |||||||
\(14\) | 477709. | 3.32344 | ||||||||
\(15\) | 129374. | 0.659835 | ||||||||
\(16\) | 948577. | 3.61853 | ||||||||
\(17\) | −276332. | −0.802438 | −0.401219 | − | 0.915982i | \(-0.631413\pi\) | ||||
−0.401219 | + | 0.915982i | \(0.631413\pi\) | |||||||
\(18\) | −285815. | −0.641740 | ||||||||
\(19\) | 999877. | 1.76017 | 0.880086 | − | 0.474814i | \(-0.157485\pi\) | ||||
0.880086 | + | 0.474814i | \(0.157485\pi\) | |||||||
\(20\) | 2.21327e6 | 3.09315 | ||||||||
\(21\) | −888246. | −0.996659 | ||||||||
\(22\) | −2.30730e6 | −2.09992 | ||||||||
\(23\) | 1.88611e6 | 1.40537 | 0.702686 | − | 0.711500i | \(-0.251984\pi\) | ||||
0.702686 | + | 0.711500i | \(0.251984\pi\) | |||||||
\(24\) | −3.08298e6 | −1.89679 | ||||||||
\(25\) | 597945. | 0.306148 | ||||||||
\(26\) | 6.36817e6 | 2.73297 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −1.51958e7 | −4.67209 | ||||||||
\(29\) | −6.91128e6 | −1.81454 | −0.907272 | − | 0.420543i | \(-0.861839\pi\) | ||||
−0.907272 | + | 0.420543i | \(0.861839\pi\) | |||||||
\(30\) | −5.63588e6 | −1.27033 | ||||||||
\(31\) | −1.40963e6 | −0.274143 | −0.137072 | − | 0.990561i | \(-0.543769\pi\) | ||||
−0.137072 | + | 0.990561i | \(0.543769\pi\) | |||||||
\(32\) | −2.18352e7 | −3.68114 | ||||||||
\(33\) | 4.29017e6 | 0.629740 | ||||||||
\(34\) | 1.20378e7 | 1.54487 | ||||||||
\(35\) | −1.75150e7 | −1.97289 | ||||||||
\(36\) | 9.09168e6 | 0.902159 | ||||||||
\(37\) | 4.90587e6 | 0.430337 | 0.215168 | − | 0.976577i | \(-0.430970\pi\) | ||||
0.215168 | + | 0.976577i | \(0.430970\pi\) | |||||||
\(38\) | −4.35574e7 | −3.38872 | ||||||||
\(39\) | −1.18409e7 | −0.819583 | ||||||||
\(40\) | −6.07921e7 | −3.75471 | ||||||||
\(41\) | 2.05841e7 | 1.13764 | 0.568820 | − | 0.822462i | \(-0.307400\pi\) | ||||
0.568820 | + | 0.822462i | \(0.307400\pi\) | |||||||
\(42\) | 3.86945e7 | 1.91879 | ||||||||
\(43\) | −3.94179e6 | −0.175827 | −0.0879135 | − | 0.996128i | \(-0.528020\pi\) | ||||
−0.0879135 | + | 0.996128i | \(0.528020\pi\) | |||||||
\(44\) | 7.33945e7 | 2.95207 | ||||||||
\(45\) | 1.04793e7 | 0.380956 | ||||||||
\(46\) | −8.21642e7 | −2.70565 | ||||||||
\(47\) | 6.35577e6 | 0.189989 | 0.0949943 | − | 0.995478i | \(-0.469717\pi\) | ||||
0.0949943 | + | 0.995478i | \(0.469717\pi\) | |||||||
\(48\) | 7.68347e7 | 2.08916 | ||||||||
\(49\) | 7.98995e7 | 1.97999 | ||||||||
\(50\) | −2.60481e7 | −0.589402 | ||||||||
\(51\) | −2.23829e7 | −0.463288 | ||||||||
\(52\) | −2.02569e8 | −3.84200 | ||||||||
\(53\) | −7.48000e7 | −1.30215 | −0.651074 | − | 0.759014i | \(-0.725681\pi\) | ||||
−0.651074 | + | 0.759014i | \(0.725681\pi\) | |||||||
\(54\) | −2.31510e7 | −0.370509 | ||||||||
\(55\) | 8.45961e7 | 1.24657 | ||||||||
\(56\) | 4.17382e8 | 5.67137 | ||||||||
\(57\) | 8.09900e7 | 1.01624 | ||||||||
\(58\) | 3.01075e8 | 3.49340 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 1.79275e8 | 1.78583 | ||||||||
\(61\) | −7.46185e7 | −0.690021 | −0.345010 | − | 0.938599i | \(-0.612125\pi\) | ||||
−0.345010 | + | 0.938599i | \(0.612125\pi\) | |||||||
\(62\) | 6.14074e7 | 0.527786 | ||||||||
\(63\) | −7.19479e7 | −0.575421 | ||||||||
\(64\) | 4.65530e8 | 3.46847 | ||||||||
\(65\) | −2.33486e8 | −1.62237 | ||||||||
\(66\) | −1.86892e8 | −1.21239 | ||||||||
\(67\) | 2.24949e7 | 0.136379 | 0.0681896 | − | 0.997672i | \(-0.478278\pi\) | ||||
0.0681896 | + | 0.997672i | \(0.478278\pi\) | |||||||
\(68\) | −3.82918e8 | −2.17178 | ||||||||
\(69\) | 1.52775e8 | 0.811392 | ||||||||
\(70\) | 7.63001e8 | 3.79825 | ||||||||
\(71\) | −2.63688e8 | −1.23148 | −0.615741 | − | 0.787949i | \(-0.711143\pi\) | ||||
−0.615741 | + | 0.787949i | \(0.711143\pi\) | |||||||
\(72\) | −2.49721e8 | −1.09511 | ||||||||
\(73\) | 1.35213e8 | 0.557271 | 0.278636 | − | 0.960397i | \(-0.410118\pi\) | ||||
0.278636 | + | 0.960397i | \(0.410118\pi\) | |||||||
\(74\) | −2.13714e8 | −0.828494 | ||||||||
\(75\) | 4.84335e7 | 0.176755 | ||||||||
\(76\) | 1.38554e9 | 4.76386 | ||||||||
\(77\) | −5.80815e8 | −1.88291 | ||||||||
\(78\) | 5.15821e8 | 1.57788 | ||||||||
\(79\) | 1.42336e8 | 0.411142 | 0.205571 | − | 0.978642i | \(-0.434095\pi\) | ||||
0.205571 | + | 0.978642i | \(0.434095\pi\) | |||||||
\(80\) | 1.51507e9 | 4.13551 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −8.96702e8 | −2.19021 | ||||||||
\(83\) | −1.25542e7 | −0.0290360 | −0.0145180 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145180 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(84\) | −1.23086e9 | −2.69743 | ||||||||
\(85\) | −4.41360e8 | −0.917080 | ||||||||
\(86\) | 1.71715e8 | 0.338506 | ||||||||
\(87\) | −5.59814e8 | −1.04763 | ||||||||
\(88\) | −2.01593e9 | −3.58346 | ||||||||
\(89\) | −8.08199e8 | −1.36541 | −0.682705 | − | 0.730694i | \(-0.739197\pi\) | ||||
−0.682705 | + | 0.730694i | \(0.739197\pi\) | |||||||
\(90\) | −4.56506e8 | −0.733425 | ||||||||
\(91\) | 1.60305e9 | 2.45053 | ||||||||
\(92\) | 2.61361e9 | 3.80361 | ||||||||
\(93\) | −1.14180e8 | −0.158277 | ||||||||
\(94\) | −2.76875e8 | −0.365770 | ||||||||
\(95\) | 1.59701e9 | 2.01165 | ||||||||
\(96\) | −1.76865e9 | −2.12530 | ||||||||
\(97\) | −1.04265e8 | −0.119582 | −0.0597909 | − | 0.998211i | \(-0.519043\pi\) | ||||
−0.0597909 | + | 0.998211i | \(0.519043\pi\) | |||||||
\(98\) | −3.48065e9 | −3.81191 | ||||||||
\(99\) | 3.47504e8 | 0.363581 | ||||||||
\(100\) | 8.28582e8 | 0.828582 | ||||||||
\(101\) | −1.91315e9 | −1.82938 | −0.914689 | − | 0.404159i | \(-0.867564\pi\) | ||||
−0.914689 | + | 0.404159i | \(0.867564\pi\) | |||||||
\(102\) | 9.75061e8 | 0.891931 | ||||||||
\(103\) | −3.75074e8 | −0.328359 | −0.164180 | − | 0.986430i | \(-0.552498\pi\) | ||||
−0.164180 | + | 0.986430i | \(0.552498\pi\) | |||||||
\(104\) | 5.56397e9 | 4.66374 | ||||||||
\(105\) | −1.41871e9 | −1.13905 | ||||||||
\(106\) | 3.25850e9 | 2.50692 | ||||||||
\(107\) | 3.35288e8 | 0.247281 | 0.123641 | − | 0.992327i | \(-0.460543\pi\) | ||||
0.123641 | + | 0.992327i | \(0.460543\pi\) | |||||||
\(108\) | 7.36426e8 | 0.520861 | ||||||||
\(109\) | 1.50110e9 | 1.01857 | 0.509283 | − | 0.860599i | \(-0.329911\pi\) | ||||
0.509283 | + | 0.860599i | \(0.329911\pi\) | |||||||
\(110\) | −3.68524e9 | −2.39993 | ||||||||
\(111\) | 3.97376e8 | 0.248455 | ||||||||
\(112\) | −1.04021e10 | −6.24654 | ||||||||
\(113\) | −5.24785e8 | −0.302781 | −0.151390 | − | 0.988474i | \(-0.548375\pi\) | ||||
−0.151390 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(114\) | −3.52815e9 | −1.95648 | ||||||||
\(115\) | 3.01251e9 | 1.60616 | ||||||||
\(116\) | −9.57707e9 | −4.91102 | ||||||||
\(117\) | −9.59111e8 | −0.473187 | ||||||||
\(118\) | −5.27866e8 | −0.250642 | ||||||||
\(119\) | 3.03026e9 | 1.38522 | ||||||||
\(120\) | −4.92416e9 | −2.16778 | ||||||||
\(121\) | 4.47347e8 | 0.189719 | ||||||||
\(122\) | 3.25059e9 | 1.32844 | ||||||||
\(123\) | 1.66731e9 | 0.656817 | ||||||||
\(124\) | −1.95334e9 | −0.741961 | ||||||||
\(125\) | −2.16450e9 | −0.792982 | ||||||||
\(126\) | 3.13425e9 | 1.10781 | ||||||||
\(127\) | −5.21327e8 | −0.177825 | −0.0889126 | − | 0.996039i | \(-0.528339\pi\) | ||||
−0.0889126 | + | 0.996039i | \(0.528339\pi\) | |||||||
\(128\) | −9.10015e9 | −2.99643 | ||||||||
\(129\) | −3.19285e8 | −0.101514 | ||||||||
\(130\) | 1.01713e10 | 3.12342 | ||||||||
\(131\) | 3.86658e9 | 1.14711 | 0.573557 | − | 0.819166i | \(-0.305563\pi\) | ||||
0.573557 | + | 0.819166i | \(0.305563\pi\) | |||||||
\(132\) | 5.94495e9 | 1.70438 | ||||||||
\(133\) | −1.09646e10 | −3.03852 | ||||||||
\(134\) | −9.79942e8 | −0.262560 | ||||||||
\(135\) | 8.48821e8 | 0.219945 | ||||||||
\(136\) | 1.05176e10 | 2.63628 | ||||||||
\(137\) | −1.63775e8 | −0.0397197 | −0.0198598 | − | 0.999803i | \(-0.506322\pi\) | ||||
−0.0198598 | + | 0.999803i | \(0.506322\pi\) | |||||||
\(138\) | −6.65530e9 | −1.56211 | ||||||||
\(139\) | 5.02768e9 | 1.14235 | 0.571177 | − | 0.820827i | \(-0.306487\pi\) | ||||
0.571177 | + | 0.820827i | \(0.306487\pi\) | |||||||
\(140\) | −2.42708e10 | −5.33958 | ||||||||
\(141\) | 5.14817e8 | 0.109690 | ||||||||
\(142\) | 1.14870e10 | 2.37087 | ||||||||
\(143\) | −7.74262e9 | −1.54837 | ||||||||
\(144\) | 6.22361e9 | 1.20618 | ||||||||
\(145\) | −1.10387e10 | −2.07379 | ||||||||
\(146\) | −5.89027e9 | −1.07287 | ||||||||
\(147\) | 6.47186e9 | 1.14314 | ||||||||
\(148\) | 6.79815e9 | 1.16470 | ||||||||
\(149\) | 7.02775e9 | 1.16810 | 0.584048 | − | 0.811719i | \(-0.301468\pi\) | ||||
0.584048 | + | 0.811719i | \(0.301468\pi\) | |||||||
\(150\) | −2.10990e9 | −0.340292 | ||||||||
\(151\) | −4.38989e9 | −0.687159 | −0.343580 | − | 0.939124i | \(-0.611640\pi\) | ||||
−0.343580 | + | 0.939124i | \(0.611640\pi\) | |||||||
\(152\) | −3.80568e10 | −5.78277 | ||||||||
\(153\) | −1.81302e9 | −0.267479 | ||||||||
\(154\) | 2.53019e10 | 3.62501 | ||||||||
\(155\) | −2.25147e9 | −0.313309 | ||||||||
\(156\) | −1.64081e10 | −2.21818 | ||||||||
\(157\) | 7.13429e9 | 0.937135 | 0.468568 | − | 0.883428i | \(-0.344770\pi\) | ||||
0.468568 | + | 0.883428i | \(0.344770\pi\) | |||||||
\(158\) | −6.20053e9 | −0.791538 | ||||||||
\(159\) | −6.05880e9 | −0.751796 | ||||||||
\(160\) | −3.48753e10 | −4.20705 | ||||||||
\(161\) | −2.06831e10 | −2.42604 | ||||||||
\(162\) | −1.87523e9 | −0.213913 | ||||||||
\(163\) | −1.51240e10 | −1.67812 | −0.839061 | − | 0.544038i | \(-0.816895\pi\) | ||||
−0.839061 | + | 0.544038i | \(0.816895\pi\) | |||||||
\(164\) | 2.85238e10 | 3.07900 | ||||||||
\(165\) | 6.85229e9 | 0.719710 | ||||||||
\(166\) | 5.46895e8 | 0.0559007 | ||||||||
\(167\) | −6.77132e9 | −0.673674 | −0.336837 | − | 0.941563i | \(-0.609357\pi\) | ||||
−0.336837 | + | 0.941563i | \(0.609357\pi\) | |||||||
\(168\) | 3.38080e10 | 3.27437 | ||||||||
\(169\) | 1.07652e10 | 1.01515 | ||||||||
\(170\) | 1.92269e10 | 1.76558 | ||||||||
\(171\) | 6.56019e9 | 0.586724 | ||||||||
\(172\) | −5.46220e9 | −0.475871 | ||||||||
\(173\) | −1.25124e9 | −0.106202 | −0.0531009 | − | 0.998589i | \(-0.516910\pi\) | ||||
−0.0531009 | + | 0.998589i | \(0.516910\pi\) | |||||||
\(174\) | 2.43871e10 | 2.01692 | ||||||||
\(175\) | −6.55707e9 | −0.528492 | ||||||||
\(176\) | 5.02414e10 | 3.94689 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | 3.52074e10 | 2.62872 | ||||||||
\(179\) | −1.64348e10 | −1.19653 | −0.598266 | − | 0.801297i | \(-0.704143\pi\) | ||||
−0.598266 | + | 0.801297i | \(0.704143\pi\) | |||||||
\(180\) | 1.45213e10 | 1.03105 | ||||||||
\(181\) | −4.40038e7 | −0.00304745 | −0.00152372 | − | 0.999999i | \(-0.500485\pi\) | ||||
−0.00152372 | + | 0.999999i | \(0.500485\pi\) | |||||||
\(182\) | −6.98333e10 | −4.71782 | ||||||||
\(183\) | −6.04410e9 | −0.398384 | ||||||||
\(184\) | −7.17881e10 | −4.61713 | ||||||||
\(185\) | 7.83570e9 | 0.491818 | ||||||||
\(186\) | 4.97400e9 | 0.304717 | ||||||||
\(187\) | −1.46359e10 | −0.875253 | ||||||||
\(188\) | 8.80729e9 | 0.514200 | ||||||||
\(189\) | −5.82778e9 | −0.332220 | ||||||||
\(190\) | −6.95702e10 | −3.87286 | ||||||||
\(191\) | −1.43446e10 | −0.779896 | −0.389948 | − | 0.920837i | \(-0.627507\pi\) | ||||
−0.389948 | + | 0.920837i | \(0.627507\pi\) | |||||||
\(192\) | 3.77079e10 | 2.00252 | ||||||||
\(193\) | −2.20418e10 | −1.14351 | −0.571754 | − | 0.820425i | \(-0.693737\pi\) | ||||
−0.571754 | + | 0.820425i | \(0.693737\pi\) | |||||||
\(194\) | 4.54206e9 | 0.230221 | ||||||||
\(195\) | −1.89123e10 | −0.936676 | ||||||||
\(196\) | 1.10718e11 | 5.35878 | ||||||||
\(197\) | −3.24597e10 | −1.53549 | −0.767745 | − | 0.640755i | \(-0.778621\pi\) | ||||
−0.767745 | + | 0.640755i | \(0.778621\pi\) | |||||||
\(198\) | −1.51382e10 | −0.699973 | ||||||||
\(199\) | −1.55333e10 | −0.702141 | −0.351070 | − | 0.936349i | \(-0.614182\pi\) | ||||
−0.351070 | + | 0.936349i | \(0.614182\pi\) | |||||||
\(200\) | −2.27587e10 | −1.00580 | ||||||||
\(201\) | 1.82209e9 | 0.0787386 | ||||||||
\(202\) | 8.33422e10 | 3.52196 | ||||||||
\(203\) | 7.57891e10 | 3.13238 | ||||||||
\(204\) | −3.10163e10 | −1.25388 | ||||||||
\(205\) | 3.28771e10 | 1.30017 | ||||||||
\(206\) | 1.63393e10 | 0.632164 | ||||||||
\(207\) | 1.23748e10 | 0.468458 | ||||||||
\(208\) | −1.38666e11 | −5.13673 | ||||||||
\(209\) | 5.29585e10 | 1.91989 | ||||||||
\(210\) | 6.18031e10 | 2.19292 | ||||||||
\(211\) | 7.41772e9 | 0.257632 | 0.128816 | − | 0.991669i | \(-0.458882\pi\) | ||||
0.128816 | + | 0.991669i | \(0.458882\pi\) | |||||||
\(212\) | −1.03652e11 | −3.52423 | ||||||||
\(213\) | −2.13587e10 | −0.710996 | ||||||||
\(214\) | −1.46061e10 | −0.476071 | ||||||||
\(215\) | −6.29586e9 | −0.200947 | ||||||||
\(216\) | −2.02274e10 | −0.632264 | ||||||||
\(217\) | 1.54580e10 | 0.473243 | ||||||||
\(218\) | −6.53919e10 | −1.96097 | ||||||||
\(219\) | 1.09523e10 | 0.321741 | ||||||||
\(220\) | 1.17226e11 | 3.37382 | ||||||||
\(221\) | 4.03952e10 | 1.13911 | ||||||||
\(222\) | −1.73108e10 | −0.478331 | ||||||||
\(223\) | 2.99814e10 | 0.811858 | 0.405929 | − | 0.913905i | \(-0.366948\pi\) | ||||
0.405929 | + | 0.913905i | \(0.366948\pi\) | |||||||
\(224\) | 2.39445e11 | 6.35461 | ||||||||
\(225\) | 3.92312e9 | 0.102049 | ||||||||
\(226\) | 2.28611e10 | 0.582920 | ||||||||
\(227\) | 3.94298e10 | 0.985618 | 0.492809 | − | 0.870138i | \(-0.335970\pi\) | ||||
0.492809 | + | 0.870138i | \(0.335970\pi\) | |||||||
\(228\) | 1.12229e11 | 2.75042 | ||||||||
\(229\) | −1.03992e10 | −0.249886 | −0.124943 | − | 0.992164i | \(-0.539875\pi\) | ||||
−0.124943 | + | 0.992164i | \(0.539875\pi\) | |||||||
\(230\) | −1.31233e11 | −3.09221 | ||||||||
\(231\) | −4.70460e10 | −1.08710 | ||||||||
\(232\) | 2.63054e11 | 5.96140 | ||||||||
\(233\) | −6.95843e10 | −1.54671 | −0.773356 | − | 0.633972i | \(-0.781423\pi\) | ||||
−0.773356 | + | 0.633972i | \(0.781423\pi\) | |||||||
\(234\) | 4.17815e10 | 0.910989 | ||||||||
\(235\) | 1.01515e10 | 0.217132 | ||||||||
\(236\) | 1.67912e10 | 0.352353 | ||||||||
\(237\) | 1.15292e10 | 0.237373 | ||||||||
\(238\) | −1.32006e11 | −2.66685 | ||||||||
\(239\) | −4.09211e10 | −0.811254 | −0.405627 | − | 0.914039i | \(-0.632947\pi\) | ||||
−0.405627 | + | 0.914039i | \(0.632947\pi\) | |||||||
\(240\) | 1.22721e11 | 2.38764 | ||||||||
\(241\) | −6.90087e10 | −1.31773 | −0.658866 | − | 0.752261i | \(-0.728963\pi\) | ||||
−0.658866 | + | 0.752261i | \(0.728963\pi\) | |||||||
\(242\) | −1.94877e10 | −0.365251 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | −1.03400e11 | −1.86752 | ||||||||
\(245\) | 1.27616e11 | 2.26286 | ||||||||
\(246\) | −7.26329e10 | −1.26452 | ||||||||
\(247\) | −1.46166e11 | −2.49867 | ||||||||
\(248\) | 5.36526e10 | 0.900654 | ||||||||
\(249\) | −1.01689e9 | −0.0167639 | ||||||||
\(250\) | 9.42918e10 | 1.52666 | ||||||||
\(251\) | 8.87595e10 | 1.41151 | 0.705754 | − | 0.708457i | \(-0.250609\pi\) | ||||
0.705754 | + | 0.708457i | \(0.250609\pi\) | |||||||
\(252\) | −9.96994e10 | −1.55736 | ||||||||
\(253\) | 9.98978e10 | 1.53290 | ||||||||
\(254\) | 2.27104e10 | 0.342353 | ||||||||
\(255\) | −3.57501e10 | −0.529477 | ||||||||
\(256\) | 1.58077e11 | 2.30032 | ||||||||
\(257\) | 9.45600e10 | 1.35210 | 0.676049 | − | 0.736857i | \(-0.263691\pi\) | ||||
0.676049 | + | 0.736857i | \(0.263691\pi\) | |||||||
\(258\) | 1.39089e10 | 0.195436 | ||||||||
\(259\) | −5.37978e10 | −0.742875 | ||||||||
\(260\) | −3.23545e11 | −4.39090 | ||||||||
\(261\) | −4.53449e10 | −0.604848 | ||||||||
\(262\) | −1.68439e11 | −2.20845 | ||||||||
\(263\) | −1.00500e11 | −1.29529 | −0.647644 | − | 0.761943i | \(-0.724246\pi\) | ||||
−0.647644 | + | 0.761943i | \(0.724246\pi\) | |||||||
\(264\) | −1.63290e11 | −2.06891 | ||||||||
\(265\) | −1.19471e11 | −1.48818 | ||||||||
\(266\) | 4.77650e11 | 5.84982 | ||||||||
\(267\) | −6.54641e10 | −0.788320 | ||||||||
\(268\) | 3.11716e10 | 0.369107 | ||||||||
\(269\) | −6.93801e9 | −0.0807885 | −0.0403942 | − | 0.999184i | \(-0.512861\pi\) | ||||
−0.0403942 | + | 0.999184i | \(0.512861\pi\) | |||||||
\(270\) | −3.69770e10 | −0.423443 | ||||||||
\(271\) | 9.60064e10 | 1.08128 | 0.540640 | − | 0.841254i | \(-0.318182\pi\) | ||||
0.540640 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(272\) | −2.62122e11 | −2.90365 | ||||||||
\(273\) | 1.29847e11 | 1.41482 | ||||||||
\(274\) | 7.13450e9 | 0.0764691 | ||||||||
\(275\) | 3.16702e10 | 0.333928 | ||||||||
\(276\) | 2.11702e11 | 2.19601 | ||||||||
\(277\) | −1.82037e11 | −1.85781 | −0.928905 | − | 0.370318i | \(-0.879249\pi\) | ||||
−0.928905 | + | 0.370318i | \(0.879249\pi\) | |||||||
\(278\) | −2.19020e11 | −2.19928 | ||||||||
\(279\) | −9.24858e9 | −0.0913810 | ||||||||
\(280\) | 6.66646e11 | 6.48162 | ||||||||
\(281\) | −1.73949e11 | −1.66435 | −0.832173 | − | 0.554517i | \(-0.812903\pi\) | ||||
−0.832173 | + | 0.554517i | \(0.812903\pi\) | |||||||
\(282\) | −2.24269e10 | −0.211178 | ||||||||
\(283\) | −1.91984e11 | −1.77921 | −0.889603 | − | 0.456734i | \(-0.849019\pi\) | ||||
−0.889603 | + | 0.456734i | \(0.849019\pi\) | |||||||
\(284\) | −3.65397e11 | −3.33297 | ||||||||
\(285\) | 1.29358e11 | 1.16142 | ||||||||
\(286\) | 3.37290e11 | 2.98096 | ||||||||
\(287\) | −2.25726e11 | −1.96387 | ||||||||
\(288\) | −1.43261e11 | −1.22705 | ||||||||
\(289\) | −4.22284e10 | −0.356094 | ||||||||
\(290\) | 4.80879e11 | 3.99250 | ||||||||
\(291\) | −8.44545e9 | −0.0690405 | ||||||||
\(292\) | 1.87367e11 | 1.50824 | ||||||||
\(293\) | −5.44405e10 | −0.431536 | −0.215768 | − | 0.976445i | \(-0.569226\pi\) | ||||
−0.215768 | + | 0.976445i | \(0.569226\pi\) | |||||||
\(294\) | −2.81932e11 | −2.20081 | ||||||||
\(295\) | 1.93539e10 | 0.148789 | ||||||||
\(296\) | −1.86725e11 | −1.41380 | ||||||||
\(297\) | 2.81478e10 | 0.209913 | ||||||||
\(298\) | −3.06148e11 | −2.24884 | ||||||||
\(299\) | −2.75718e11 | −1.99501 | ||||||||
\(300\) | 6.71151e10 | 0.478382 | ||||||||
\(301\) | 4.32257e10 | 0.303524 | ||||||||
\(302\) | 1.91236e11 | 1.32293 | ||||||||
\(303\) | −1.54965e11 | −1.05619 | ||||||||
\(304\) | 9.48460e11 | 6.36925 | ||||||||
\(305\) | −1.19181e11 | −0.788603 | ||||||||
\(306\) | 7.89800e10 | 0.514957 | ||||||||
\(307\) | −6.62838e10 | −0.425877 | −0.212939 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212939 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(308\) | −8.04844e11 | −5.09605 | ||||||||
\(309\) | −3.03810e10 | −0.189578 | ||||||||
\(310\) | 9.80802e10 | 0.603190 | ||||||||
\(311\) | 8.07048e9 | 0.0489190 | 0.0244595 | − | 0.999701i | \(-0.492214\pi\) | ||||
0.0244595 | + | 0.999701i | \(0.492214\pi\) | |||||||
\(312\) | 4.50681e11 | 2.69261 | ||||||||
\(313\) | 1.54810e10 | 0.0911696 | 0.0455848 | − | 0.998960i | \(-0.485485\pi\) | ||||
0.0455848 | + | 0.998960i | \(0.485485\pi\) | |||||||
\(314\) | −3.10790e11 | −1.80419 | ||||||||
\(315\) | −1.14916e11 | −0.657631 | ||||||||
\(316\) | 1.97237e11 | 1.11274 | ||||||||
\(317\) | −3.29987e11 | −1.83540 | −0.917699 | − | 0.397276i | \(-0.869956\pi\) | ||||
−0.917699 | + | 0.397276i | \(0.869956\pi\) | |||||||
\(318\) | 2.63938e11 | 1.44737 | ||||||||
\(319\) | −3.66056e11 | −1.97920 | ||||||||
\(320\) | 7.43547e11 | 3.96400 | ||||||||
\(321\) | 2.71583e10 | 0.142768 | ||||||||
\(322\) | 9.01012e11 | 4.67067 | ||||||||
\(323\) | −2.76298e11 | −1.41243 | ||||||||
\(324\) | 5.96505e10 | 0.300720 | ||||||||
\(325\) | −8.74098e10 | −0.434595 | ||||||||
\(326\) | 6.58845e11 | 3.23075 | ||||||||
\(327\) | 1.21589e11 | 0.588070 | ||||||||
\(328\) | −7.83462e11 | −3.73754 | ||||||||
\(329\) | −6.96974e10 | −0.327970 | ||||||||
\(330\) | −2.98505e11 | −1.38560 | ||||||||
\(331\) | −1.41539e11 | −0.648113 | −0.324057 | − | 0.946038i | \(-0.605047\pi\) | ||||
−0.324057 | + | 0.946038i | \(0.605047\pi\) | |||||||
\(332\) | −1.73965e10 | −0.0785853 | ||||||||
\(333\) | 3.21874e10 | 0.143446 | ||||||||
\(334\) | 2.94978e11 | 1.29697 | ||||||||
\(335\) | 3.59291e10 | 0.155863 | ||||||||
\(336\) | −8.42570e11 | −3.60644 | ||||||||
\(337\) | 7.94755e10 | 0.335659 | 0.167830 | − | 0.985816i | \(-0.446324\pi\) | ||||
0.167830 | + | 0.985816i | \(0.446324\pi\) | |||||||
\(338\) | −4.68960e11 | −1.95439 | ||||||||
\(339\) | −4.25076e10 | −0.174811 | ||||||||
\(340\) | −6.11599e11 | −2.48206 | ||||||||
\(341\) | −7.46610e10 | −0.299019 | ||||||||
\(342\) | −2.85780e11 | −1.12957 | ||||||||
\(343\) | −4.33661e11 | −1.69171 | ||||||||
\(344\) | 1.50030e11 | 0.577652 | ||||||||
\(345\) | 2.44013e11 | 0.927315 | ||||||||
\(346\) | 5.45073e10 | 0.204462 | ||||||||
\(347\) | 2.42349e11 | 0.897343 | 0.448671 | − | 0.893697i | \(-0.351897\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351897\pi\) | |||||||
\(348\) | −7.75743e11 | −2.83538 | ||||||||
\(349\) | 1.34335e11 | 0.484703 | 0.242352 | − | 0.970188i | \(-0.422081\pi\) | ||||
0.242352 | + | 0.970188i | \(0.422081\pi\) | |||||||
\(350\) | 2.85644e11 | 1.01746 | ||||||||
\(351\) | −7.76880e10 | −0.273194 | ||||||||
\(352\) | −1.15650e12 | −4.01517 | ||||||||
\(353\) | 2.89766e11 | 0.993258 | 0.496629 | − | 0.867963i | \(-0.334571\pi\) | ||||
0.496629 | + | 0.867963i | \(0.334571\pi\) | |||||||
\(354\) | −4.27571e10 | −0.144708 | ||||||||
\(355\) | −4.21164e11 | −1.40742 | ||||||||
\(356\) | −1.11993e12 | −3.69545 | ||||||||
\(357\) | 2.45451e11 | 0.799756 | ||||||||
\(358\) | 7.15943e11 | 2.30359 | ||||||||
\(359\) | 2.09948e11 | 0.667092 | 0.333546 | − | 0.942734i | \(-0.391755\pi\) | ||||
0.333546 | + | 0.942734i | \(0.391755\pi\) | |||||||
\(360\) | −3.98857e11 | −1.25157 | ||||||||
\(361\) | 6.77066e11 | 2.09821 | ||||||||
\(362\) | 1.91693e9 | 0.00586701 | ||||||||
\(363\) | 3.62351e10 | 0.109534 | ||||||||
\(364\) | 2.22137e12 | 6.63231 | ||||||||
\(365\) | 2.15964e11 | 0.636887 | ||||||||
\(366\) | 2.63298e11 | 0.766976 | ||||||||
\(367\) | 2.83366e11 | 0.815363 | 0.407681 | − | 0.913124i | \(-0.366337\pi\) | ||||
0.407681 | + | 0.913124i | \(0.366337\pi\) | |||||||
\(368\) | 1.78912e12 | 5.08539 | ||||||||
\(369\) | 1.35052e11 | 0.379214 | ||||||||
\(370\) | −3.41345e11 | −0.946859 | ||||||||
\(371\) | 8.20257e11 | 2.24785 | ||||||||
\(372\) | −1.58221e11 | −0.428372 | ||||||||
\(373\) | −2.03235e11 | −0.543636 | −0.271818 | − | 0.962349i | \(-0.587625\pi\) | ||||
−0.271818 | + | 0.962349i | \(0.587625\pi\) | |||||||
\(374\) | 6.37582e11 | 1.68505 | ||||||||
\(375\) | −1.75325e11 | −0.457828 | ||||||||
\(376\) | −2.41910e11 | −0.624178 | ||||||||
\(377\) | 1.01032e12 | 2.57586 | ||||||||
\(378\) | 2.53874e11 | 0.639596 | ||||||||
\(379\) | 7.46197e10 | 0.185771 | 0.0928853 | − | 0.995677i | \(-0.470391\pi\) | ||||
0.0928853 | + | 0.995677i | \(0.470391\pi\) | |||||||
\(380\) | 2.21300e12 | 5.44447 | ||||||||
\(381\) | −4.22275e10 | −0.102667 | ||||||||
\(382\) | 6.24889e11 | 1.50147 | ||||||||
\(383\) | −2.80797e11 | −0.666803 | −0.333401 | − | 0.942785i | \(-0.608196\pi\) | ||||
−0.333401 | + | 0.942785i | \(0.608196\pi\) | |||||||
\(384\) | −7.37112e11 | −1.72999 | ||||||||
\(385\) | −9.27681e11 | −2.15192 | ||||||||
\(386\) | 9.60203e11 | 2.20151 | ||||||||
\(387\) | −2.58621e10 | −0.0586090 | ||||||||
\(388\) | −1.44481e11 | −0.323645 | ||||||||
\(389\) | 4.02766e11 | 0.891824 | 0.445912 | − | 0.895077i | \(-0.352879\pi\) | ||||
0.445912 | + | 0.895077i | \(0.352879\pi\) | |||||||
\(390\) | 8.23874e11 | 1.80331 | ||||||||
\(391\) | −5.21193e11 | −1.12772 | ||||||||
\(392\) | −3.04109e12 | −6.50493 | ||||||||
\(393\) | 3.13193e11 | 0.662286 | ||||||||
\(394\) | 1.41404e12 | 2.95616 | ||||||||
\(395\) | 2.27339e11 | 0.469881 | ||||||||
\(396\) | 4.81541e11 | 0.984023 | ||||||||
\(397\) | −1.15594e11 | −0.233549 | −0.116775 | − | 0.993158i | \(-0.537255\pi\) | ||||
−0.116775 | + | 0.993158i | \(0.537255\pi\) | |||||||
\(398\) | 6.76673e11 | 1.35178 | ||||||||
\(399\) | −8.88136e11 | −1.75429 | ||||||||
\(400\) | 5.67197e11 | 1.10781 | ||||||||
\(401\) | −5.68027e11 | −1.09703 | −0.548516 | − | 0.836140i | \(-0.684807\pi\) | ||||
−0.548516 | + | 0.836140i | \(0.684807\pi\) | |||||||
\(402\) | −7.93753e10 | −0.151589 | ||||||||
\(403\) | 2.06065e11 | 0.389162 | ||||||||
\(404\) | −2.65108e12 | −4.95117 | ||||||||
\(405\) | 6.87545e10 | 0.126985 | ||||||||
\(406\) | −3.30159e12 | −6.03053 | ||||||||
\(407\) | 2.59840e11 | 0.469387 | ||||||||
\(408\) | 8.51926e11 | 1.52206 | ||||||||
\(409\) | −4.33352e11 | −0.765749 | −0.382874 | − | 0.923800i | \(-0.625066\pi\) | ||||
−0.382874 | + | 0.923800i | \(0.625066\pi\) | |||||||
\(410\) | −1.43222e12 | −2.50312 | ||||||||
\(411\) | −1.32658e10 | −0.0229322 | ||||||||
\(412\) | −5.19746e11 | −0.888697 | ||||||||
\(413\) | −1.32879e11 | −0.224740 | ||||||||
\(414\) | −5.39079e11 | −0.901884 | ||||||||
\(415\) | −2.00516e10 | −0.0331843 | ||||||||
\(416\) | 3.19195e12 | 5.22559 | ||||||||
\(417\) | 4.07242e11 | 0.659539 | ||||||||
\(418\) | −2.30702e12 | −3.69622 | ||||||||
\(419\) | −9.10366e11 | −1.44296 | −0.721478 | − | 0.692438i | \(-0.756537\pi\) | ||||
−0.721478 | + | 0.692438i | \(0.756537\pi\) | |||||||
\(420\) | −1.96593e12 | −3.08281 | ||||||||
\(421\) | 5.30818e11 | 0.823524 | 0.411762 | − | 0.911291i | \(-0.364913\pi\) | ||||
0.411762 | + | 0.911291i | \(0.364913\pi\) | |||||||
\(422\) | −3.23136e11 | −0.495998 | ||||||||
\(423\) | 4.17002e10 | 0.0633296 | ||||||||
\(424\) | 2.84700e12 | 4.27800 | ||||||||
\(425\) | −1.65231e11 | −0.245665 | ||||||||
\(426\) | 9.30445e11 | 1.36882 | ||||||||
\(427\) | 8.18266e11 | 1.19116 | ||||||||
\(428\) | 4.64614e11 | 0.669260 | ||||||||
\(429\) | −6.27152e11 | −0.893954 | ||||||||
\(430\) | 2.74265e11 | 0.386868 | ||||||||
\(431\) | −1.05184e12 | −1.46826 | −0.734130 | − | 0.679009i | \(-0.762410\pi\) | ||||
−0.734130 | + | 0.679009i | \(0.762410\pi\) | |||||||
\(432\) | 5.04113e11 | 0.696387 | ||||||||
\(433\) | 3.32873e11 | 0.455074 | 0.227537 | − | 0.973769i | \(-0.426933\pi\) | ||||
0.227537 | + | 0.973769i | \(0.426933\pi\) | |||||||
\(434\) | −6.73393e11 | −0.911097 | ||||||||
\(435\) | −8.94139e11 | −1.19730 | ||||||||
\(436\) | 2.08009e12 | 2.75673 | ||||||||
\(437\) | 1.88588e12 | 2.47370 | ||||||||
\(438\) | −4.77112e11 | −0.619422 | ||||||||
\(439\) | −1.34032e12 | −1.72233 | −0.861166 | − | 0.508323i | \(-0.830265\pi\) | ||||
−0.861166 | + | 0.508323i | \(0.830265\pi\) | |||||||
\(440\) | −3.21985e12 | −4.09543 | ||||||||
\(441\) | 5.24221e11 | 0.659995 | ||||||||
\(442\) | −1.75973e12 | −2.19303 | ||||||||
\(443\) | 2.01187e11 | 0.248189 | 0.124095 | − | 0.992270i | \(-0.460397\pi\) | ||||
0.124095 | + | 0.992270i | \(0.460397\pi\) | |||||||
\(444\) | 5.50650e11 | 0.672438 | ||||||||
\(445\) | −1.29086e12 | −1.56048 | ||||||||
\(446\) | −1.30607e12 | −1.56301 | ||||||||
\(447\) | 5.69248e11 | 0.674400 | ||||||||
\(448\) | −5.10500e12 | −5.98749 | ||||||||
\(449\) | −6.42787e11 | −0.746377 | −0.373189 | − | 0.927756i | \(-0.621736\pi\) | ||||
−0.373189 | + | 0.927756i | \(0.621736\pi\) | |||||||
\(450\) | −1.70902e11 | −0.196467 | ||||||||
\(451\) | 1.09024e12 | 1.24087 | ||||||||
\(452\) | −7.27203e11 | −0.819469 | ||||||||
\(453\) | −3.55581e11 | −0.396732 | ||||||||
\(454\) | −1.71767e12 | −1.89753 | ||||||||
\(455\) | 2.56040e12 | 2.80064 | ||||||||
\(456\) | −3.08260e12 | −3.33868 | ||||||||
\(457\) | 1.43216e12 | 1.53592 | 0.767959 | − | 0.640499i | \(-0.221272\pi\) | ||||
0.767959 | + | 0.640499i | \(0.221272\pi\) | |||||||
\(458\) | 4.53020e11 | 0.481086 | ||||||||
\(459\) | −1.46854e11 | −0.154429 | ||||||||
\(460\) | 4.17448e12 | 4.34702 | ||||||||
\(461\) | 4.59275e11 | 0.473607 | 0.236804 | − | 0.971558i | \(-0.423900\pi\) | ||||
0.236804 | + | 0.971558i | \(0.423900\pi\) | |||||||
\(462\) | 2.04945e12 | 2.09290 | ||||||||
\(463\) | 1.91038e12 | 1.93199 | 0.965997 | − | 0.258553i | \(-0.0832457\pi\) | ||||
0.965997 | + | 0.258553i | \(0.0832457\pi\) | |||||||
\(464\) | −6.55589e12 | −6.56599 | ||||||||
\(465\) | −1.82369e11 | −0.180889 | ||||||||
\(466\) | 3.03128e12 | 2.97776 | ||||||||
\(467\) | −4.19414e11 | −0.408053 | −0.204027 | − | 0.978965i | \(-0.565403\pi\) | ||||
−0.204027 | + | 0.978965i | \(0.565403\pi\) | |||||||
\(468\) | −1.32905e12 | −1.28067 | ||||||||
\(469\) | −2.46680e11 | −0.235426 | ||||||||
\(470\) | −4.42227e11 | −0.418027 | ||||||||
\(471\) | 5.77878e11 | 0.541055 | ||||||||
\(472\) | −4.61205e11 | −0.427715 | ||||||||
\(473\) | −2.08777e11 | −0.191782 | ||||||||
\(474\) | −5.02243e11 | −0.456995 | ||||||||
\(475\) | 5.97871e11 | 0.538873 | ||||||||
\(476\) | 4.19908e12 | 3.74906 | ||||||||
\(477\) | −4.90763e11 | −0.434049 | ||||||||
\(478\) | 1.78264e12 | 1.56184 | ||||||||
\(479\) | −2.11271e12 | −1.83371 | −0.916855 | − | 0.399220i | \(-0.869281\pi\) | ||||
−0.916855 | + | 0.399220i | \(0.869281\pi\) | |||||||
\(480\) | −2.82490e12 | −2.42894 | ||||||||
\(481\) | −7.17159e11 | −0.610889 | ||||||||
\(482\) | 3.00621e12 | 2.53692 | ||||||||
\(483\) | −1.67533e12 | −1.40068 | ||||||||
\(484\) | 6.19896e11 | 0.513469 | ||||||||
\(485\) | −1.66532e11 | −0.136666 | ||||||||
\(486\) | −1.51894e11 | −0.123503 | ||||||||
\(487\) | −5.93927e11 | −0.478468 | −0.239234 | − | 0.970962i | \(-0.576896\pi\) | ||||
−0.239234 | + | 0.970962i | \(0.576896\pi\) | |||||||
\(488\) | 2.84009e12 | 2.26695 | ||||||||
\(489\) | −1.22505e12 | −0.968864 | ||||||||
\(490\) | −5.55931e12 | −4.35651 | ||||||||
\(491\) | −6.03440e11 | −0.468562 | −0.234281 | − | 0.972169i | \(-0.575274\pi\) | ||||
−0.234281 | + | 0.972169i | \(0.575274\pi\) | |||||||
\(492\) | 2.31042e12 | 1.77766 | ||||||||
\(493\) | 1.90981e12 | 1.45606 | ||||||||
\(494\) | 6.36738e12 | 4.81049 | ||||||||
\(495\) | 5.55035e11 | 0.415525 | ||||||||
\(496\) | −1.33714e12 | −0.991996 | ||||||||
\(497\) | 2.89160e12 | 2.12586 | ||||||||
\(498\) | 4.42985e10 | 0.0322743 | ||||||||
\(499\) | −2.35555e12 | −1.70075 | −0.850375 | − | 0.526177i | \(-0.823625\pi\) | ||||
−0.850375 | + | 0.526177i | \(0.823625\pi\) | |||||||
\(500\) | −2.99939e12 | −2.14619 | ||||||||
\(501\) | −5.48477e11 | −0.388946 | ||||||||
\(502\) | −3.86661e12 | −2.71746 | ||||||||
\(503\) | 1.90452e12 | 1.32657 | 0.663285 | − | 0.748367i | \(-0.269162\pi\) | ||||
0.663285 | + | 0.748367i | \(0.269162\pi\) | |||||||
\(504\) | 2.73844e12 | 1.89046 | ||||||||
\(505\) | −3.05570e12 | −2.09074 | ||||||||
\(506\) | −4.35183e12 | −2.95117 | ||||||||
\(507\) | 8.71978e11 | 0.586097 | ||||||||
\(508\) | −7.22411e11 | −0.481280 | ||||||||
\(509\) | −1.32499e12 | −0.874951 | −0.437475 | − | 0.899230i | \(-0.644127\pi\) | ||||
−0.437475 | + | 0.899230i | \(0.644127\pi\) | |||||||
\(510\) | 1.55737e12 | 1.01936 | ||||||||
\(511\) | −1.48275e12 | −0.961997 | ||||||||
\(512\) | −2.22698e12 | −1.43219 | ||||||||
\(513\) | 5.31375e11 | 0.338745 | ||||||||
\(514\) | −4.11929e12 | −2.60309 | ||||||||
\(515\) | −5.99071e11 | −0.375272 | ||||||||
\(516\) | −4.42438e11 | −0.274744 | ||||||||
\(517\) | 3.36633e11 | 0.207229 | ||||||||
\(518\) | 2.34358e12 | 1.43020 | ||||||||
\(519\) | −1.01350e11 | −0.0613156 | ||||||||
\(520\) | 8.88680e12 | 5.33004 | ||||||||
\(521\) | 1.19512e12 | 0.710625 | 0.355312 | − | 0.934748i | \(-0.384374\pi\) | ||||
0.355312 | + | 0.934748i | \(0.384374\pi\) | |||||||
\(522\) | 1.97535e12 | 1.16447 | ||||||||
\(523\) | 1.76481e12 | 1.03143 | 0.515717 | − | 0.856759i | \(-0.327526\pi\) | ||||
0.515717 | + | 0.856759i | \(0.327526\pi\) | |||||||
\(524\) | 5.35798e12 | 3.10463 | ||||||||
\(525\) | −5.31122e11 | −0.305125 | ||||||||
\(526\) | 4.37807e12 | 2.49372 | ||||||||
\(527\) | 3.89526e11 | 0.219983 | ||||||||
\(528\) | 4.06956e12 | 2.27874 | ||||||||
\(529\) | 1.75626e12 | 0.975073 | ||||||||
\(530\) | 5.20450e12 | 2.86508 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | −1.51939e13 | −8.22368 | ||||||||
\(533\) | −3.00906e12 | −1.61495 | ||||||||
\(534\) | 2.85180e12 | 1.51769 | ||||||||
\(535\) | 5.35524e11 | 0.282610 | ||||||||
\(536\) | −8.56191e11 | −0.448052 | ||||||||
\(537\) | −1.33121e12 | −0.690818 | ||||||||
\(538\) | 3.02239e11 | 0.155536 | ||||||||
\(539\) | 4.23188e12 | 2.15965 | ||||||||
\(540\) | 1.17622e12 | 0.595276 | ||||||||
\(541\) | 1.82271e12 | 0.914807 | 0.457403 | − | 0.889259i | \(-0.348780\pi\) | ||||
0.457403 | + | 0.889259i | \(0.348780\pi\) | |||||||
\(542\) | −4.18231e12 | −2.08170 | ||||||||
\(543\) | −3.56431e9 | −0.00175945 | ||||||||
\(544\) | 6.03376e12 | 2.95388 | ||||||||
\(545\) | 2.39756e12 | 1.16409 | ||||||||
\(546\) | −5.65650e12 | −2.72383 | ||||||||
\(547\) | 8.23239e10 | 0.0393172 | 0.0196586 | − | 0.999807i | \(-0.493742\pi\) | ||||
0.0196586 | + | 0.999807i | \(0.493742\pi\) | |||||||
\(548\) | −2.26946e11 | −0.107500 | ||||||||
\(549\) | −4.89572e11 | −0.230007 | ||||||||
\(550\) | −1.37964e12 | −0.642886 | ||||||||
\(551\) | −6.91043e12 | −3.19391 | ||||||||
\(552\) | −5.81484e12 | −2.66570 | ||||||||
\(553\) | −1.56085e12 | −0.709739 | ||||||||
\(554\) | 7.93005e12 | 3.57669 | ||||||||
\(555\) | 6.34691e11 | 0.283952 | ||||||||
\(556\) | 6.96693e12 | 3.09175 | ||||||||
\(557\) | −1.73608e12 | −0.764225 | −0.382113 | − | 0.924116i | \(-0.624803\pi\) | ||||
−0.382113 | + | 0.924116i | \(0.624803\pi\) | |||||||
\(558\) | 4.02894e11 | 0.175929 | ||||||||
\(559\) | 5.76225e11 | 0.249597 | ||||||||
\(560\) | −1.66143e13 | −7.13898 | ||||||||
\(561\) | −1.18551e12 | −0.505327 | ||||||||
\(562\) | 7.57770e12 | 3.20423 | ||||||||
\(563\) | −1.36719e12 | −0.573512 | −0.286756 | − | 0.958004i | \(-0.592577\pi\) | ||||
−0.286756 | + | 0.958004i | \(0.592577\pi\) | |||||||
\(564\) | 7.13390e11 | 0.296873 | ||||||||
\(565\) | −8.38190e11 | −0.346039 | ||||||||
\(566\) | 8.36336e12 | 3.42537 | ||||||||
\(567\) | −4.72050e11 | −0.191807 | ||||||||
\(568\) | 1.00364e13 | 4.04584 | ||||||||
\(569\) | 9.42095e11 | 0.376782 | 0.188391 | − | 0.982094i | \(-0.439673\pi\) | ||||
0.188391 | + | 0.982094i | \(0.439673\pi\) | |||||||
\(570\) | −5.63519e12 | −2.23600 | ||||||||
\(571\) | 3.43206e12 | 1.35112 | 0.675558 | − | 0.737306i | \(-0.263903\pi\) | ||||
0.675558 | + | 0.737306i | \(0.263903\pi\) | |||||||
\(572\) | −1.07291e13 | −4.19064 | ||||||||
\(573\) | −1.16191e12 | −0.450273 | ||||||||
\(574\) | 9.83323e12 | 3.78088 | ||||||||
\(575\) | 1.12779e12 | 0.430252 | ||||||||
\(576\) | 3.05434e12 | 1.15616 | ||||||||
\(577\) | 2.01638e12 | 0.757322 | 0.378661 | − | 0.925535i | \(-0.376385\pi\) | ||||
0.378661 | + | 0.925535i | \(0.376385\pi\) | |||||||
\(578\) | 1.83959e12 | 0.685560 | ||||||||
\(579\) | −1.78539e12 | −0.660205 | ||||||||
\(580\) | −1.52966e13 | −5.61265 | ||||||||
\(581\) | 1.37669e11 | 0.0501238 | ||||||||
\(582\) | 3.67907e11 | 0.132918 | ||||||||
\(583\) | −3.96179e12 | −1.42031 | ||||||||
\(584\) | −5.14642e12 | −1.83083 | ||||||||
\(585\) | −1.53190e12 | −0.540790 | ||||||||
\(586\) | 2.37158e12 | 0.830803 | ||||||||
\(587\) | −5.89110e11 | −0.204797 | −0.102399 | − | 0.994743i | \(-0.532652\pi\) | ||||
−0.102399 | + | 0.994743i | \(0.532652\pi\) | |||||||
\(588\) | 8.96816e12 | 3.09389 | ||||||||
\(589\) | −1.40946e12 | −0.482539 | ||||||||
\(590\) | −8.43111e11 | −0.286451 | ||||||||
\(591\) | −2.62924e12 | −0.886516 | ||||||||
\(592\) | 4.65360e12 | 1.55719 | ||||||||
\(593\) | −2.77303e12 | −0.920893 | −0.460446 | − | 0.887687i | \(-0.652311\pi\) | ||||
−0.460446 | + | 0.887687i | \(0.652311\pi\) | |||||||
\(594\) | −1.22620e12 | −0.404130 | ||||||||
\(595\) | 4.83995e12 | 1.58312 | ||||||||
\(596\) | 9.73847e12 | 3.16142 | ||||||||
\(597\) | −1.25820e12 | −0.405381 | ||||||||
\(598\) | 1.20111e13 | 3.84084 | ||||||||
\(599\) | −1.80709e12 | −0.573533 | −0.286766 | − | 0.958001i | \(-0.592580\pi\) | ||||
−0.286766 | + | 0.958001i | \(0.592580\pi\) | |||||||
\(600\) | −1.84345e12 | −0.580699 | ||||||||
\(601\) | −1.82846e11 | −0.0571678 | −0.0285839 | − | 0.999591i | \(-0.509100\pi\) | ||||
−0.0285839 | + | 0.999591i | \(0.509100\pi\) | |||||||
\(602\) | −1.88303e12 | −0.584350 | ||||||||
\(603\) | 1.47589e11 | 0.0454597 | ||||||||
\(604\) | −6.08314e12 | −1.85978 | ||||||||
\(605\) | 7.14506e11 | 0.216824 | ||||||||
\(606\) | 6.75072e12 | 2.03340 | ||||||||
\(607\) | 3.01684e12 | 0.901994 | 0.450997 | − | 0.892526i | \(-0.351069\pi\) | ||||
0.450997 | + | 0.892526i | \(0.351069\pi\) | |||||||
\(608\) | −2.18325e13 | −6.47943 | ||||||||
\(609\) | 6.13892e12 | 1.80848 | ||||||||
\(610\) | 5.19186e12 | 1.51823 | ||||||||
\(611\) | −9.29109e11 | −0.269700 | ||||||||
\(612\) | −2.51232e12 | −0.723926 | ||||||||
\(613\) | −4.80257e12 | −1.37373 | −0.686866 | − | 0.726784i | \(-0.741014\pi\) | ||||
−0.686866 | + | 0.726784i | \(0.741014\pi\) | |||||||
\(614\) | 2.88750e12 | 0.819908 | ||||||||
\(615\) | 2.66305e12 | 0.750656 | ||||||||
\(616\) | 2.21067e13 | 6.18600 | ||||||||
\(617\) | 1.11287e12 | 0.309145 | 0.154572 | − | 0.987981i | \(-0.450600\pi\) | ||||
0.154572 | + | 0.987981i | \(0.450600\pi\) | |||||||
\(618\) | 1.32348e12 | 0.364980 | ||||||||
\(619\) | 1.60721e12 | 0.440012 | 0.220006 | − | 0.975499i | \(-0.429392\pi\) | ||||
0.220006 | + | 0.975499i | \(0.429392\pi\) | |||||||
\(620\) | −3.11990e12 | −0.847964 | ||||||||
\(621\) | 1.00236e12 | 0.270464 | ||||||||
\(622\) | −3.51572e11 | −0.0941798 | ||||||||
\(623\) | 8.86271e12 | 2.35706 | ||||||||
\(624\) | −1.12320e13 | −2.96569 | ||||||||
\(625\) | −4.62502e12 | −1.21242 | ||||||||
\(626\) | −6.74396e11 | −0.175522 | ||||||||
\(627\) | 4.28964e12 | 1.10845 | ||||||||
\(628\) | 9.88610e12 | 2.53633 | ||||||||
\(629\) | −1.35565e12 | −0.345319 | ||||||||
\(630\) | 5.00605e12 | 1.26608 | ||||||||
\(631\) | −2.45294e12 | −0.615964 | −0.307982 | − | 0.951392i | \(-0.599654\pi\) | ||||
−0.307982 | + | 0.951392i | \(0.599654\pi\) | |||||||
\(632\) | −5.41750e12 | −1.35074 | ||||||||
\(633\) | 6.00835e11 | 0.148744 | ||||||||
\(634\) | 1.43752e13 | 3.53355 | ||||||||
\(635\) | −8.32667e11 | −0.203231 | ||||||||
\(636\) | −8.39578e12 | −2.03472 | ||||||||
\(637\) | −1.16800e13 | −2.81071 | ||||||||
\(638\) | 1.59464e13 | 3.81040 | ||||||||
\(639\) | −1.73006e12 | −0.410494 | ||||||||
\(640\) | −1.45348e13 | −3.42452 | ||||||||
\(641\) | −6.74129e12 | −1.57718 | −0.788591 | − | 0.614918i | \(-0.789189\pi\) | ||||
−0.788591 | + | 0.614918i | \(0.789189\pi\) | |||||||
\(642\) | −1.18309e12 | −0.274860 | ||||||||
\(643\) | 6.95200e11 | 0.160384 | 0.0801919 | − | 0.996779i | \(-0.474447\pi\) | ||||
0.0801919 | + | 0.996779i | \(0.474447\pi\) | |||||||
\(644\) | −2.86609e13 | −6.56603 | ||||||||
\(645\) | −5.09964e11 | −0.116017 | ||||||||
\(646\) | 1.20363e13 | 2.71924 | ||||||||
\(647\) | 1.92451e11 | 0.0431769 | 0.0215884 | − | 0.999767i | \(-0.493128\pi\) | ||||
0.0215884 | + | 0.999767i | \(0.493128\pi\) | |||||||
\(648\) | −1.63842e12 | −0.365038 | ||||||||
\(649\) | 6.41796e11 | 0.142003 | ||||||||
\(650\) | 3.80781e12 | 0.836692 | ||||||||
\(651\) | 1.25210e12 | 0.273227 | ||||||||
\(652\) | −2.09576e13 | −4.54180 | ||||||||
\(653\) | −1.88242e12 | −0.405142 | −0.202571 | − | 0.979268i | \(-0.564930\pi\) | ||||
−0.202571 | + | 0.979268i | \(0.564930\pi\) | |||||||
\(654\) | −5.29675e12 | −1.13216 | ||||||||
\(655\) | 6.17573e12 | 1.31100 | ||||||||
\(656\) | 1.95256e13 | 4.11659 | ||||||||
\(657\) | 8.87134e11 | 0.185757 | ||||||||
\(658\) | 3.03621e12 | 0.631416 | ||||||||
\(659\) | 5.08014e12 | 1.04928 | 0.524640 | − | 0.851324i | \(-0.324200\pi\) | ||||
0.524640 | + | 0.851324i | \(0.324200\pi\) | |||||||
\(660\) | 9.49532e12 | 1.94788 | ||||||||
\(661\) | −1.03648e12 | −0.211181 | −0.105591 | − | 0.994410i | \(-0.533673\pi\) | ||||
−0.105591 | + | 0.994410i | \(0.533673\pi\) | |||||||
\(662\) | 6.16584e12 | 1.24776 | ||||||||
\(663\) | 3.27201e12 | 0.657664 | ||||||||
\(664\) | 4.77831e11 | 0.0953932 | ||||||||
\(665\) | −1.75128e13 | −3.47263 | ||||||||
\(666\) | −1.40217e12 | −0.276165 | ||||||||
\(667\) | −1.30354e13 | −2.55011 | ||||||||
\(668\) | −9.38313e12 | −1.82328 | ||||||||
\(669\) | 2.42849e12 | 0.468727 | ||||||||
\(670\) | −1.56517e12 | −0.300072 | ||||||||
\(671\) | −3.95217e12 | −0.752635 | ||||||||
\(672\) | 1.93950e13 | 3.66884 | ||||||||
\(673\) | 8.29211e12 | 1.55811 | 0.779053 | − | 0.626958i | \(-0.215700\pi\) | ||||
0.779053 | + | 0.626958i | \(0.215700\pi\) | |||||||
\(674\) | −3.46217e12 | −0.646218 | ||||||||
\(675\) | 3.17773e11 | 0.0589182 | ||||||||
\(676\) | 1.49174e13 | 2.74748 | ||||||||
\(677\) | 4.71501e12 | 0.862648 | 0.431324 | − | 0.902197i | \(-0.358047\pi\) | ||||
0.431324 | + | 0.902197i | \(0.358047\pi\) | |||||||
\(678\) | 1.85175e12 | 0.336549 | ||||||||
\(679\) | 1.14337e12 | 0.206430 | ||||||||
\(680\) | 1.67988e13 | 3.01292 | ||||||||
\(681\) | 3.19382e12 | 0.569047 | ||||||||
\(682\) | 3.25244e12 | 0.575678 | ||||||||
\(683\) | 4.44301e12 | 0.781240 | 0.390620 | − | 0.920552i | \(-0.372261\pi\) | ||||
0.390620 | + | 0.920552i | \(0.372261\pi\) | |||||||
\(684\) | 9.09056e12 | 1.58795 | ||||||||
\(685\) | −2.61583e11 | −0.0453943 | ||||||||
\(686\) | 1.88915e13 | 3.25692 | ||||||||
\(687\) | −8.42338e11 | −0.144272 | ||||||||
\(688\) | −3.73909e12 | −0.636236 | ||||||||
\(689\) | 1.09345e13 | 1.84848 | ||||||||
\(690\) | −1.06299e13 | −1.78529 | ||||||||
\(691\) | −8.76609e11 | −0.146270 | −0.0731349 | − | 0.997322i | \(-0.523300\pi\) | ||||
−0.0731349 | + | 0.997322i | \(0.523300\pi\) | |||||||
\(692\) | −1.73386e12 | −0.287432 | ||||||||
\(693\) | −3.81072e12 | −0.627636 | ||||||||
\(694\) | −1.05574e13 | −1.72758 | ||||||||
\(695\) | 8.03024e12 | 1.30556 | ||||||||
\(696\) | 2.13073e13 | 3.44182 | ||||||||
\(697\) | −5.68806e12 | −0.912886 | ||||||||
\(698\) | −5.85202e12 | −0.933161 | ||||||||
\(699\) | −5.63633e12 | −0.892995 | ||||||||
\(700\) | −9.08623e12 | −1.43035 | ||||||||
\(701\) | −3.11983e12 | −0.487978 | −0.243989 | − | 0.969778i | \(-0.578456\pi\) | ||||
−0.243989 | + | 0.969778i | \(0.578456\pi\) | |||||||
\(702\) | 3.38430e12 | 0.525960 | ||||||||
\(703\) | 4.90527e12 | 0.757467 | ||||||||
\(704\) | 2.46568e13 | 3.78320 | ||||||||
\(705\) | 8.22270e11 | 0.125361 | ||||||||
\(706\) | −1.26230e13 | −1.91224 | ||||||||
\(707\) | 2.09796e13 | 3.15799 | ||||||||
\(708\) | 1.36009e12 | 0.203431 | ||||||||
\(709\) | 1.64768e12 | 0.244887 | 0.122443 | − | 0.992475i | \(-0.460927\pi\) | ||||
0.122443 | + | 0.992475i | \(0.460927\pi\) | |||||||
\(710\) | 1.83471e13 | 2.70960 | ||||||||
\(711\) | 9.33863e11 | 0.137047 | ||||||||
\(712\) | 3.07612e13 | 4.48584 | ||||||||
\(713\) | −2.65871e12 | −0.385273 | ||||||||
\(714\) | −1.06925e13 | −1.53971 | ||||||||
\(715\) | −1.23666e13 | −1.76959 | ||||||||
\(716\) | −2.27739e13 | −3.23839 | ||||||||
\(717\) | −3.31461e12 | −0.468378 | ||||||||
\(718\) | −9.14590e12 | −1.28430 | ||||||||
\(719\) | 1.69332e12 | 0.236298 | 0.118149 | − | 0.992996i | \(-0.462304\pi\) | ||||
0.118149 | + | 0.992996i | \(0.462304\pi\) | |||||||
\(720\) | 9.94040e12 | 1.37850 | ||||||||
\(721\) | 4.11306e12 | 0.566835 | ||||||||
\(722\) | −2.94949e13 | −4.03951 | ||||||||
\(723\) | −5.58970e12 | −0.760793 | ||||||||
\(724\) | −6.09767e10 | −0.00824785 | ||||||||
\(725\) | −4.13257e12 | −0.555519 | ||||||||
\(726\) | −1.57850e12 | −0.210878 | ||||||||
\(727\) | −8.00586e12 | −1.06293 | −0.531463 | − | 0.847082i | \(-0.678358\pi\) | ||||
−0.531463 | + | 0.847082i | \(0.678358\pi\) | |||||||
\(728\) | −6.10144e13 | −8.05084 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −9.40797e12 | −1.22615 | ||||||||
\(731\) | 1.08924e12 | 0.141090 | ||||||||
\(732\) | −8.37540e12 | −1.07822 | ||||||||
\(733\) | 1.40134e13 | 1.79299 | 0.896493 | − | 0.443058i | \(-0.146106\pi\) | ||||
0.896493 | + | 0.443058i | \(0.146106\pi\) | |||||||
\(734\) | −1.23442e13 | −1.56975 | ||||||||
\(735\) | 1.03369e13 | 1.30646 | ||||||||
\(736\) | −4.11835e13 | −5.17337 | ||||||||
\(737\) | 1.19145e12 | 0.148755 | ||||||||
\(738\) | −5.88326e12 | −0.730070 | ||||||||
\(739\) | −1.20312e13 | −1.48392 | −0.741960 | − | 0.670444i | \(-0.766104\pi\) | ||||
−0.741960 | + | 0.670444i | \(0.766104\pi\) | |||||||
\(740\) | 1.08580e13 | 1.33109 | ||||||||
\(741\) | −1.18394e13 | −1.44261 | ||||||||
\(742\) | −3.57327e13 | −4.32761 | ||||||||
\(743\) | −6.82684e12 | −0.821808 | −0.410904 | − | 0.911679i | \(-0.634787\pi\) | ||||
−0.410904 | + | 0.911679i | \(0.634787\pi\) | |||||||
\(744\) | 4.34586e12 | 0.519993 | ||||||||
\(745\) | 1.12248e13 | 1.33498 | ||||||||
\(746\) | 8.85347e12 | 1.04662 | ||||||||
\(747\) | −8.23680e10 | −0.00967867 | ||||||||
\(748\) | −2.02813e13 | −2.36885 | ||||||||
\(749\) | −3.67677e12 | −0.426872 | ||||||||
\(750\) | 7.63763e12 | 0.881420 | ||||||||
\(751\) | 1.18371e13 | 1.35789 | 0.678944 | − | 0.734190i | \(-0.262438\pi\) | ||||
0.678944 | + | 0.734190i | \(0.262438\pi\) | |||||||
\(752\) | 6.02894e12 | 0.687481 | ||||||||
\(753\) | 7.18952e12 | 0.814934 | ||||||||
\(754\) | −4.40122e13 | −4.95909 | ||||||||
\(755\) | −7.01156e12 | −0.785332 | ||||||||
\(756\) | −8.07565e12 | −0.899144 | ||||||||
\(757\) | 5.81566e12 | 0.643676 | 0.321838 | − | 0.946795i | \(-0.395699\pi\) | ||||
0.321838 | + | 0.946795i | \(0.395699\pi\) | |||||||
\(758\) | −3.25064e12 | −0.357650 | ||||||||
\(759\) | 8.09172e12 | 0.885020 | ||||||||
\(760\) | −6.07846e13 | −6.60894 | ||||||||
\(761\) | −5.38603e12 | −0.582154 | −0.291077 | − | 0.956700i | \(-0.594014\pi\) | ||||
−0.291077 | + | 0.956700i | \(0.594014\pi\) | |||||||
\(762\) | 1.83955e12 | 0.197658 | ||||||||
\(763\) | −1.64610e13 | −1.75831 | ||||||||
\(764\) | −1.98775e13 | −2.11077 | ||||||||
\(765\) | −2.89576e12 | −0.305693 | ||||||||
\(766\) | 1.22323e13 | 1.28374 | ||||||||
\(767\) | −1.77136e12 | −0.184811 | ||||||||
\(768\) | 1.28042e13 | 1.32809 | ||||||||
\(769\) | 4.49355e12 | 0.463363 | 0.231681 | − | 0.972792i | \(-0.425577\pi\) | ||||
0.231681 | + | 0.972792i | \(0.425577\pi\) | |||||||
\(770\) | 4.04124e13 | 4.14291 | ||||||||
\(771\) | 7.65936e12 | 0.780634 | ||||||||
\(772\) | −3.05437e13 | −3.09488 | ||||||||
\(773\) | 8.71587e12 | 0.878017 | 0.439008 | − | 0.898483i | \(-0.355330\pi\) | ||||
0.439008 | + | 0.898483i | \(0.355330\pi\) | |||||||
\(774\) | 1.12662e12 | 0.112835 | ||||||||
\(775\) | −8.42881e11 | −0.0839283 | ||||||||
\(776\) | 3.96847e12 | 0.392867 | ||||||||
\(777\) | −4.35762e12 | −0.428899 | ||||||||
\(778\) | −1.75456e13 | −1.71696 | ||||||||
\(779\) | 2.05816e13 | 2.00244 | ||||||||
\(780\) | −2.62071e13 | −2.53509 | ||||||||
\(781\) | −1.39662e13 | −1.34323 | ||||||||
\(782\) | 2.27046e13 | 2.17112 | ||||||||
\(783\) | −3.67294e12 | −0.349209 | ||||||||
\(784\) | 7.57909e13 | 7.16465 | ||||||||
\(785\) | 1.13949e13 | 1.07102 | ||||||||
\(786\) | −1.36436e13 | −1.27505 | ||||||||
\(787\) | −1.99079e13 | −1.84986 | −0.924930 | − | 0.380137i | \(-0.875877\pi\) | ||||
−0.924930 | + | 0.380137i | \(0.875877\pi\) | |||||||
\(788\) | −4.49800e13 | −4.15577 | ||||||||
\(789\) | −8.14052e12 | −0.747835 | ||||||||
\(790\) | −9.90353e12 | −0.904624 | ||||||||
\(791\) | 5.75479e12 | 0.522679 | ||||||||
\(792\) | −1.32265e13 | −1.19449 | ||||||||
\(793\) | 1.09080e13 | 0.979526 | ||||||||
\(794\) | 5.03560e12 | 0.449634 | ||||||||
\(795\) | −9.67716e12 | −0.859203 | ||||||||
\(796\) | −2.15247e13 | −1.90033 | ||||||||
\(797\) | −2.67783e11 | −0.0235082 | −0.0117541 | − | 0.999931i | \(-0.503742\pi\) | ||||
−0.0117541 | + | 0.999931i | \(0.503742\pi\) | |||||||
\(798\) | 3.86897e13 | 3.37740 | ||||||||
\(799\) | −1.75630e12 | −0.152454 | ||||||||
\(800\) | −1.30562e13 | −1.12697 | ||||||||
\(801\) | −5.30259e12 | −0.455137 | ||||||||
\(802\) | 2.47448e13 | 2.11203 | ||||||||
\(803\) | 7.16158e12 | 0.607839 | ||||||||
\(804\) | 2.52490e12 | 0.213104 | ||||||||
\(805\) | −3.30351e13 | −2.77265 | ||||||||
\(806\) | −8.97675e12 | −0.749224 | ||||||||
\(807\) | −5.61979e11 | −0.0466433 | ||||||||
\(808\) | 7.28174e13 | 6.01013 | ||||||||
\(809\) | −5.14983e12 | −0.422693 | −0.211346 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211346 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(810\) | −2.99514e12 | −0.244475 | ||||||||
\(811\) | −6.19815e12 | −0.503116 | −0.251558 | − | 0.967842i | \(-0.580943\pi\) | ||||
−0.251558 | + | 0.967842i | \(0.580943\pi\) | |||||||
\(812\) | 1.05022e14 | 8.47772 | ||||||||
\(813\) | 7.77652e12 | 0.624278 | ||||||||
\(814\) | −1.13193e13 | −0.903673 | ||||||||
\(815\) | −2.41562e13 | −1.91787 | ||||||||
\(816\) | −2.12319e13 | −1.67642 | ||||||||
\(817\) | −3.94130e12 | −0.309486 | ||||||||
\(818\) | 1.88780e13 | 1.47424 | ||||||||
\(819\) | 1.05176e13 | 0.816845 | ||||||||
\(820\) | 4.55583e13 | 3.51889 | ||||||||
\(821\) | 6.20987e12 | 0.477022 | 0.238511 | − | 0.971140i | \(-0.423341\pi\) | ||||
0.238511 | + | 0.971140i | \(0.423341\pi\) | |||||||
\(822\) | 5.77895e11 | 0.0441495 | ||||||||
\(823\) | −1.59932e13 | −1.21517 | −0.607584 | − | 0.794255i | \(-0.707861\pi\) | ||||
−0.607584 | + | 0.794255i | \(0.707861\pi\) | |||||||
\(824\) | 1.42759e13 | 1.07877 | ||||||||
\(825\) | 2.56528e12 | 0.192794 | ||||||||
\(826\) | 5.78858e12 | 0.432675 | ||||||||
\(827\) | 2.11594e12 | 0.157300 | 0.0786500 | − | 0.996902i | \(-0.474939\pi\) | ||||
0.0786500 | + | 0.996902i | \(0.474939\pi\) | |||||||
\(828\) | 1.71479e13 | 1.26787 | ||||||||
\(829\) | −1.83713e13 | −1.35097 | −0.675484 | − | 0.737374i | \(-0.736065\pi\) | ||||
−0.675484 | + | 0.737374i | \(0.736065\pi\) | |||||||
\(830\) | 8.73504e11 | 0.0638872 | ||||||||
\(831\) | −1.47450e13 | −1.07261 | ||||||||
\(832\) | −6.80528e13 | −4.92369 | ||||||||
\(833\) | −2.20788e13 | −1.58881 | ||||||||
\(834\) | −1.77406e13 | −1.26976 | ||||||||
\(835\) | −1.08152e13 | −0.769920 | ||||||||
\(836\) | 7.33854e13 | 5.19615 | ||||||||
\(837\) | −7.49135e11 | −0.0527588 | ||||||||
\(838\) | 3.96581e13 | 2.77801 | ||||||||
\(839\) | −1.08393e13 | −0.755221 | −0.377611 | − | 0.925964i | \(-0.623254\pi\) | ||||
−0.377611 | + | 0.925964i | \(0.623254\pi\) | |||||||
\(840\) | 5.39983e13 | 3.74217 | ||||||||
\(841\) | 3.32587e13 | 2.29257 | ||||||||
\(842\) | −2.31239e13 | −1.58547 | ||||||||
\(843\) | −1.40899e13 | −0.960910 | ||||||||
\(844\) | 1.02788e13 | 0.697274 | ||||||||
\(845\) | 1.71942e13 | 1.16018 | ||||||||
\(846\) | −1.81658e12 | −0.121923 | ||||||||
\(847\) | −4.90561e12 | −0.327505 | ||||||||
\(848\) | −7.09536e13 | −4.71187 | ||||||||
\(849\) | −1.55507e13 | −1.02723 | ||||||||
\(850\) | 7.19794e12 | 0.472959 | ||||||||
\(851\) | 9.25301e12 | 0.604784 | ||||||||
\(852\) | −2.95971e13 | −1.92429 | ||||||||
\(853\) | 1.39415e13 | 0.901649 | 0.450825 | − | 0.892613i | \(-0.351130\pi\) | ||||
0.450825 | + | 0.892613i | \(0.351130\pi\) | |||||||
\(854\) | −3.56459e13 | −2.29324 | ||||||||
\(855\) | 1.04780e13 | 0.670548 | ||||||||
\(856\) | −1.27616e13 | −0.812403 | ||||||||
\(857\) | −4.55558e12 | −0.288489 | −0.144245 | − | 0.989542i | \(-0.546075\pi\) | ||||
−0.144245 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(858\) | 2.73205e13 | 1.72106 | ||||||||
\(859\) | 1.96628e13 | 1.23218 | 0.616092 | − | 0.787674i | \(-0.288715\pi\) | ||||
0.616092 | + | 0.787674i | \(0.288715\pi\) | |||||||
\(860\) | −8.72426e12 | −0.543858 | ||||||||
\(861\) | −1.82838e13 | −1.13384 | ||||||||
\(862\) | 4.58212e13 | 2.82673 | ||||||||
\(863\) | 1.15472e13 | 0.708644 | 0.354322 | − | 0.935123i | \(-0.384712\pi\) | ||||
0.354322 | + | 0.935123i | \(0.384712\pi\) | |||||||
\(864\) | −1.16041e13 | −0.708435 | ||||||||
\(865\) | −1.99848e12 | −0.121375 | ||||||||
\(866\) | −1.45009e13 | −0.876119 | ||||||||
\(867\) | −3.42050e12 | −0.205591 | ||||||||
\(868\) | 2.14204e13 | 1.28082 | ||||||||
\(869\) | 7.53881e12 | 0.448450 | ||||||||
\(870\) | 3.89512e13 | 2.30507 | ||||||||
\(871\) | −3.28839e12 | −0.193598 | ||||||||
\(872\) | −5.71340e13 | −3.34634 | ||||||||
\(873\) | −6.84081e11 | −0.0398606 | ||||||||
\(874\) | −8.21540e13 | −4.76242 | ||||||||
\(875\) | 2.37359e13 | 1.36890 | ||||||||
\(876\) | 1.51767e13 | 0.870783 | ||||||||
\(877\) | 2.43420e13 | 1.38950 | 0.694750 | − | 0.719251i | \(-0.255515\pi\) | ||||
0.694750 | + | 0.719251i | \(0.255515\pi\) | |||||||
\(878\) | 5.83879e13 | 3.31587 | ||||||||
\(879\) | −4.40968e12 | −0.249148 | ||||||||
\(880\) | 8.02459e13 | 4.51077 | ||||||||
\(881\) | 1.12417e13 | 0.628698 | 0.314349 | − | 0.949308i | \(-0.398214\pi\) | ||||
0.314349 | + | 0.949308i | \(0.398214\pi\) | |||||||
\(882\) | −2.28365e13 | −1.27064 | ||||||||
\(883\) | 1.39656e13 | 0.773101 | 0.386550 | − | 0.922268i | \(-0.373667\pi\) | ||||
0.386550 | + | 0.922268i | \(0.373667\pi\) | |||||||
\(884\) | 5.59763e13 | 3.08297 | ||||||||
\(885\) | 1.56767e12 | 0.0859032 | ||||||||
\(886\) | −8.76425e12 | −0.477819 | ||||||||
\(887\) | −2.71387e13 | −1.47208 | −0.736042 | − | 0.676936i | \(-0.763307\pi\) | ||||
−0.736042 | + | 0.676936i | \(0.763307\pi\) | |||||||
\(888\) | −1.51247e13 | −0.816260 | ||||||||
\(889\) | 5.71687e12 | 0.306973 | ||||||||
\(890\) | 5.62335e13 | 3.00428 | ||||||||
\(891\) | 2.27997e12 | 0.121194 | ||||||||
\(892\) | 4.15457e13 | 2.19727 | ||||||||
\(893\) | 6.35498e12 | 0.334413 | ||||||||
\(894\) | −2.47980e13 | −1.29837 | ||||||||
\(895\) | −2.62497e13 | −1.36748 | ||||||||
\(896\) | 9.97922e13 | 5.17262 | ||||||||
\(897\) | −2.23332e13 | −1.15182 | ||||||||
\(898\) | 2.80016e13 | 1.43694 | ||||||||
\(899\) | 9.74235e12 | 0.497445 | ||||||||
\(900\) | 5.43632e12 | 0.276194 | ||||||||
\(901\) | 2.06697e13 | 1.04489 | ||||||||
\(902\) | −4.74939e13 | −2.38896 | ||||||||
\(903\) | 3.50128e12 | 0.175239 | ||||||||
\(904\) | 1.99741e13 | 0.994739 | ||||||||
\(905\) | −7.02832e10 | −0.00348283 | ||||||||
\(906\) | 1.54901e13 | 0.763796 | ||||||||
\(907\) | −2.64168e13 | −1.29613 | −0.648065 | − | 0.761585i | \(-0.724421\pi\) | ||||
−0.648065 | + | 0.761585i | \(0.724421\pi\) | |||||||
\(908\) | 5.46385e13 | 2.66755 | ||||||||
\(909\) | −1.25522e13 | −0.609792 | ||||||||
\(910\) | −1.11538e14 | −5.39185 | ||||||||
\(911\) | 2.67036e13 | 1.28451 | 0.642255 | − | 0.766491i | \(-0.277999\pi\) | ||||
0.642255 | + | 0.766491i | \(0.277999\pi\) | |||||||
\(912\) | 7.68253e13 | 3.67729 | ||||||||
\(913\) | −6.64933e11 | −0.0316708 | ||||||||
\(914\) | −6.23888e13 | −2.95698 | ||||||||
\(915\) | −9.65367e12 | −0.455300 | ||||||||
\(916\) | −1.44104e13 | −0.676310 | ||||||||
\(917\) | −4.24009e13 | −1.98022 | ||||||||
\(918\) | 6.39738e12 | 0.297310 | ||||||||
\(919\) | 4.08123e12 | 0.188743 | 0.0943715 | − | 0.995537i | \(-0.469916\pi\) | ||||
0.0943715 | + | 0.995537i | \(0.469916\pi\) | |||||||
\(920\) | −1.14660e14 | −5.27677 | ||||||||
\(921\) | −5.36898e12 | −0.245880 | ||||||||
\(922\) | −2.00073e13 | −0.911799 | ||||||||
\(923\) | 3.85469e13 | 1.74816 | ||||||||
\(924\) | −6.51923e13 | −2.94220 | ||||||||
\(925\) | 2.93344e12 | 0.131747 | ||||||||
\(926\) | −8.32216e13 | −3.71952 | ||||||||
\(927\) | −2.46086e12 | −0.109453 | ||||||||
\(928\) | 1.50909e14 | 6.67959 | ||||||||
\(929\) | −6.82957e12 | −0.300831 | −0.150416 | − | 0.988623i | \(-0.548061\pi\) | ||||
−0.150416 | + | 0.988623i | \(0.548061\pi\) | |||||||
\(930\) | 7.94450e12 | 0.348252 | ||||||||
\(931\) | 7.98897e13 | 3.48512 | ||||||||
\(932\) | −9.64240e13 | −4.18614 | ||||||||
\(933\) | 6.53709e11 | 0.0282434 | ||||||||
\(934\) | 1.82708e13 | 0.785593 | ||||||||
\(935\) | −2.33766e13 | −1.00030 | ||||||||
\(936\) | 3.65052e13 | 1.55458 | ||||||||
\(937\) | 1.15809e13 | 0.490812 | 0.245406 | − | 0.969420i | \(-0.421079\pi\) | ||||
0.245406 | + | 0.969420i | \(0.421079\pi\) | |||||||
\(938\) | 1.07460e13 | 0.453248 | ||||||||
\(939\) | 1.25396e12 | 0.0526368 | ||||||||
\(940\) | 1.40671e13 | 0.587663 | ||||||||
\(941\) | 3.00051e13 | 1.24750 | 0.623752 | − | 0.781622i | \(-0.285608\pi\) | ||||
0.623752 | + | 0.781622i | \(0.285608\pi\) | |||||||
\(942\) | −2.51740e13 | −1.04165 | ||||||||
\(943\) | 3.88239e13 | 1.59881 | ||||||||
\(944\) | 1.14943e13 | 0.471093 | ||||||||
\(945\) | −9.30817e12 | −0.379683 | ||||||||
\(946\) | 9.09491e12 | 0.369223 | ||||||||
\(947\) | 3.23056e13 | 1.30528 | 0.652640 | − | 0.757668i | \(-0.273662\pi\) | ||||
0.652640 | + | 0.757668i | \(0.273662\pi\) | |||||||
\(948\) | 1.59762e13 | 0.642443 | ||||||||
\(949\) | −1.97660e13 | −0.791080 | ||||||||
\(950\) | −2.60449e13 | −1.03745 | ||||||||
\(951\) | −2.67290e13 | −1.05967 | ||||||||
\(952\) | −1.15336e14 | −4.55092 | ||||||||
\(953\) | 2.22295e13 | 0.872994 | 0.436497 | − | 0.899706i | \(-0.356219\pi\) | ||||
0.436497 | + | 0.899706i | \(0.356219\pi\) | |||||||
\(954\) | 2.13790e13 | 0.835641 | ||||||||
\(955\) | −2.29112e13 | −0.891319 | ||||||||
\(956\) | −5.67050e13 | −2.19564 | ||||||||
\(957\) | −2.96506e13 | −1.14269 | ||||||||
\(958\) | 9.20356e13 | 3.53030 | ||||||||
\(959\) | 1.79596e12 | 0.0685666 | ||||||||
\(960\) | 6.02273e13 | 2.28862 | ||||||||
\(961\) | −2.44526e13 | −0.924846 | ||||||||
\(962\) | 3.12414e13 | 1.17610 | ||||||||
\(963\) | 2.19982e12 | 0.0824270 | ||||||||
\(964\) | −9.56264e13 | −3.56641 | ||||||||
\(965\) | −3.52053e13 | −1.30688 | ||||||||
\(966\) | 7.29820e13 | 2.69661 | ||||||||
\(967\) | −3.16973e13 | −1.16574 | −0.582872 | − | 0.812564i | \(-0.698071\pi\) | ||||
−0.582872 | + | 0.812564i | \(0.698071\pi\) | |||||||
\(968\) | −1.70267e13 | −0.623291 | ||||||||
\(969\) | −2.23801e13 | −0.815466 | ||||||||
\(970\) | 7.25461e12 | 0.263113 | ||||||||
\(971\) | 3.75422e13 | 1.35529 | 0.677647 | − | 0.735387i | \(-0.263000\pi\) | ||||
0.677647 | + | 0.735387i | \(0.263000\pi\) | |||||||
\(972\) | 4.83169e12 | 0.173620 | ||||||||
\(973\) | −5.51335e13 | −1.97200 | ||||||||
\(974\) | 2.58731e13 | 0.921156 | ||||||||
\(975\) | −7.08019e12 | −0.250914 | ||||||||
\(976\) | −7.07814e13 | −2.49686 | ||||||||
\(977\) | 9.74926e11 | 0.0342331 | 0.0171166 | − | 0.999854i | \(-0.494551\pi\) | ||||
0.0171166 | + | 0.999854i | \(0.494551\pi\) | |||||||
\(978\) | 5.33664e13 | 1.86528 | ||||||||
\(979\) | −4.28063e13 | −1.48931 | ||||||||
\(980\) | 1.76840e14 | 6.12438 | ||||||||
\(981\) | 9.84870e12 | 0.339522 | ||||||||
\(982\) | 2.62875e13 | 0.902086 | ||||||||
\(983\) | −2.80063e13 | −0.956676 | −0.478338 | − | 0.878176i | \(-0.658761\pi\) | ||||
−0.478338 | + | 0.878176i | \(0.658761\pi\) | |||||||
\(984\) | −6.34605e13 | −2.15787 | ||||||||
\(985\) | −5.18449e13 | −1.75486 | ||||||||
\(986\) | −8.31966e13 | −2.80324 | ||||||||
\(987\) | −5.64549e12 | −0.189354 | ||||||||
\(988\) | −2.02544e14 | −6.76259 | ||||||||
\(989\) | −7.43465e12 | −0.247102 | ||||||||
\(990\) | −2.41789e13 | −0.799977 | ||||||||
\(991\) | 3.41237e13 | 1.12389 | 0.561947 | − | 0.827173i | \(-0.310053\pi\) | ||||
0.561947 | + | 0.827173i | \(0.310053\pi\) | |||||||
\(992\) | 3.07795e13 | 1.00916 | ||||||||
\(993\) | −1.14647e13 | −0.374188 | ||||||||
\(994\) | −1.25966e14 | −4.09275 | ||||||||
\(995\) | −2.48099e13 | −0.802455 | ||||||||
\(996\) | −1.40912e12 | −0.0453712 | ||||||||
\(997\) | 1.72440e13 | 0.552724 | 0.276362 | − | 0.961054i | \(-0.410871\pi\) | ||||
0.276362 | + | 0.961054i | \(0.410871\pi\) | |||||||
\(998\) | 1.02614e14 | 3.27432 | ||||||||
\(999\) | 2.60718e12 | 0.0828184 |
(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 | 177.10.a.a.1.2 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.2 | ✓ | 21 | 1.1 | even | 1 | trivial |