Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
Defining polynomial: | \(x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + 50741131904 x^{8} - 7480805165760 x^{7} - 10751966150272 x^{6} + 413177144536320 x^{5} + 886760582981376 x^{4} - 10454479722123264 x^{3} - 29180140031461376 x^{2} + 79787300207378432 x + 248723246810300416\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-5.66556\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.66556 | −0.500770 | −0.250385 | − | 0.968146i | \(-0.580557\pi\) | ||||
−0.250385 | + | 0.968146i | \(0.580557\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | −95.9014 | −0.749230 | ||||||||
\(5\) | 117.894 | 0.421791 | 0.210896 | − | 0.977509i | \(-0.432362\pi\) | ||||
0.210896 | + | 0.977509i | \(0.432362\pi\) | |||||||
\(6\) | 152.970 | 0.289120 | ||||||||
\(7\) | 1197.66 | 1.31975 | 0.659874 | − | 0.751376i | \(-0.270609\pi\) | ||||
0.659874 | + | 0.751376i | \(0.270609\pi\) | |||||||
\(8\) | 1268.53 | 0.875961 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −667.937 | −0.211220 | ||||||||
\(11\) | −6536.63 | −1.48074 | −0.740371 | − | 0.672199i | \(-0.765350\pi\) | ||||
−0.740371 | + | 0.672199i | \(0.765350\pi\) | |||||||
\(12\) | 2589.34 | 0.432568 | ||||||||
\(13\) | 11916.5 | 1.50435 | 0.752175 | − | 0.658964i | \(-0.229005\pi\) | ||||
0.752175 | + | 0.658964i | \(0.229005\pi\) | |||||||
\(14\) | −6785.43 | −0.660890 | ||||||||
\(15\) | −3183.14 | −0.243521 | ||||||||
\(16\) | 5088.45 | 0.310574 | ||||||||
\(17\) | 29402.4 | 1.45148 | 0.725741 | − | 0.687968i | \(-0.241497\pi\) | ||||
0.725741 | + | 0.687968i | \(0.241497\pi\) | |||||||
\(18\) | −4130.20 | −0.166923 | ||||||||
\(19\) | 3457.38 | 0.115640 | 0.0578202 | − | 0.998327i | \(-0.481585\pi\) | ||||
0.0578202 | + | 0.998327i | \(0.481585\pi\) | |||||||
\(20\) | −11306.2 | −0.316018 | ||||||||
\(21\) | −32336.9 | −0.761957 | ||||||||
\(22\) | 37033.7 | 0.741511 | ||||||||
\(23\) | −37722.6 | −0.646479 | −0.323239 | − | 0.946317i | \(-0.604772\pi\) | ||||
−0.323239 | + | 0.946317i | \(0.604772\pi\) | |||||||
\(24\) | −34250.2 | −0.505737 | ||||||||
\(25\) | −64225.9 | −0.822092 | ||||||||
\(26\) | −67514.0 | −0.753333 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −114857. | −0.988795 | ||||||||
\(29\) | −207751. | −1.58179 | −0.790896 | − | 0.611951i | \(-0.790385\pi\) | ||||
−0.790896 | + | 0.611951i | \(0.790385\pi\) | |||||||
\(30\) | 18034.3 | 0.121948 | ||||||||
\(31\) | 111488. | 0.672141 | 0.336071 | − | 0.941837i | \(-0.390902\pi\) | ||||
0.336071 | + | 0.941837i | \(0.390902\pi\) | |||||||
\(32\) | −191200. | −1.03149 | ||||||||
\(33\) | 176489. | 0.854907 | ||||||||
\(34\) | −166581. | −0.726858 | ||||||||
\(35\) | 141197. | 0.556658 | ||||||||
\(36\) | −69912.1 | −0.249743 | ||||||||
\(37\) | −49565.3 | −0.160869 | −0.0804344 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804344 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(38\) | −19588.0 | −0.0579092 | ||||||||
\(39\) | −321747. | −0.868536 | ||||||||
\(40\) | 149552. | 0.369473 | ||||||||
\(41\) | 112884. | 0.255793 | 0.127896 | − | 0.991788i | \(-0.459177\pi\) | ||||
0.127896 | + | 0.991788i | \(0.459177\pi\) | |||||||
\(42\) | 183207. | 0.381565 | ||||||||
\(43\) | −38995.6 | −0.0747956 | −0.0373978 | − | 0.999300i | \(-0.511907\pi\) | ||||
−0.0373978 | + | 0.999300i | \(0.511907\pi\) | |||||||
\(44\) | 626872. | 1.10942 | ||||||||
\(45\) | 85944.9 | 0.140597 | ||||||||
\(46\) | 213720. | 0.323737 | ||||||||
\(47\) | 1.22368e6 | 1.71919 | 0.859597 | − | 0.510972i | \(-0.170715\pi\) | ||||
0.859597 | + | 0.510972i | \(0.170715\pi\) | |||||||
\(48\) | −137388. | −0.179310 | ||||||||
\(49\) | 610852. | 0.741737 | ||||||||
\(50\) | 363876. | 0.411679 | ||||||||
\(51\) | −793865. | −0.838013 | ||||||||
\(52\) | −1.14281e6 | −1.12710 | ||||||||
\(53\) | −475269. | −0.438504 | −0.219252 | − | 0.975668i | \(-0.570362\pi\) | ||||
−0.219252 | + | 0.975668i | \(0.570362\pi\) | |||||||
\(54\) | 111515. | 0.0963732 | ||||||||
\(55\) | −770631. | −0.624564 | ||||||||
\(56\) | 1.51927e6 | 1.15605 | ||||||||
\(57\) | −93349.3 | −0.0667650 | ||||||||
\(58\) | 1.17702e6 | 0.792114 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 305268. | 0.182453 | ||||||||
\(61\) | 699413. | 0.394529 | 0.197265 | − | 0.980350i | \(-0.436794\pi\) | ||||
0.197265 | + | 0.980350i | \(0.436794\pi\) | |||||||
\(62\) | −631640. | −0.336588 | ||||||||
\(63\) | 873096. | 0.439916 | ||||||||
\(64\) | 431937. | 0.205964 | ||||||||
\(65\) | 1.40489e6 | 0.634521 | ||||||||
\(66\) | −999909. | −0.428111 | ||||||||
\(67\) | −3.23969e6 | −1.31596 | −0.657979 | − | 0.753036i | \(-0.728589\pi\) | ||||
−0.657979 | + | 0.753036i | \(0.728589\pi\) | |||||||
\(68\) | −2.81973e6 | −1.08749 | ||||||||
\(69\) | 1.01851e6 | 0.373245 | ||||||||
\(70\) | −799963. | −0.278758 | ||||||||
\(71\) | 5.13542e6 | 1.70283 | 0.851417 | − | 0.524490i | \(-0.175744\pi\) | ||||
0.851417 | + | 0.524490i | \(0.175744\pi\) | |||||||
\(72\) | 924757. | 0.291987 | ||||||||
\(73\) | 5.08296e6 | 1.52928 | 0.764639 | − | 0.644459i | \(-0.222917\pi\) | ||||
0.764639 | + | 0.644459i | \(0.222917\pi\) | |||||||
\(74\) | 280816. | 0.0805583 | ||||||||
\(75\) | 1.73410e6 | 0.474635 | ||||||||
\(76\) | −331568. | −0.0866412 | ||||||||
\(77\) | −7.82867e6 | −1.95421 | ||||||||
\(78\) | 1.82288e6 | 0.434937 | ||||||||
\(79\) | 7.01416e6 | 1.60059 | 0.800296 | − | 0.599605i | \(-0.204675\pi\) | ||||
0.800296 | + | 0.599605i | \(0.204675\pi\) | |||||||
\(80\) | 599899. | 0.130998 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −639551. | −0.128093 | ||||||||
\(83\) | 6.20880e6 | 1.19188 | 0.595942 | − | 0.803027i | \(-0.296779\pi\) | ||||
0.595942 | + | 0.803027i | \(0.296779\pi\) | |||||||
\(84\) | 3.10115e6 | 0.570881 | ||||||||
\(85\) | 3.46637e6 | 0.612222 | ||||||||
\(86\) | 220932. | 0.0374554 | ||||||||
\(87\) | 5.60927e6 | 0.913248 | ||||||||
\(88\) | −8.29189e6 | −1.29707 | ||||||||
\(89\) | 1.44794e6 | 0.217714 | 0.108857 | − | 0.994057i | \(-0.465281\pi\) | ||||
0.108857 | + | 0.994057i | \(0.465281\pi\) | |||||||
\(90\) | −486926. | −0.0704068 | ||||||||
\(91\) | 1.42720e7 | 1.98536 | ||||||||
\(92\) | 3.61765e6 | 0.484361 | ||||||||
\(93\) | −3.01017e6 | −0.388061 | ||||||||
\(94\) | −6.93283e6 | −0.860921 | ||||||||
\(95\) | 407605. | 0.0487761 | ||||||||
\(96\) | 5.16241e6 | 0.595530 | ||||||||
\(97\) | −1.19209e7 | −1.32620 | −0.663098 | − | 0.748532i | \(-0.730759\pi\) | ||||
−0.663098 | + | 0.748532i | \(0.730759\pi\) | |||||||
\(98\) | −3.46082e6 | −0.371439 | ||||||||
\(99\) | −4.76520e6 | −0.493581 | ||||||||
\(100\) | 6.15936e6 | 0.615936 | ||||||||
\(101\) | −1.33614e7 | −1.29041 | −0.645205 | − | 0.764009i | \(-0.723228\pi\) | ||||
−0.645205 | + | 0.764009i | \(0.723228\pi\) | |||||||
\(102\) | 4.49769e6 | 0.419652 | ||||||||
\(103\) | 2.58316e6 | 0.232928 | 0.116464 | − | 0.993195i | \(-0.462844\pi\) | ||||
0.116464 | + | 0.993195i | \(0.462844\pi\) | |||||||
\(104\) | 1.51165e7 | 1.31775 | ||||||||
\(105\) | −3.81233e6 | −0.321387 | ||||||||
\(106\) | 2.69266e6 | 0.219590 | ||||||||
\(107\) | −4.52462e6 | −0.357058 | −0.178529 | − | 0.983935i | \(-0.557134\pi\) | ||||
−0.178529 | + | 0.983935i | \(0.557134\pi\) | |||||||
\(108\) | 1.88763e6 | 0.144189 | ||||||||
\(109\) | −312613. | −0.0231214 | −0.0115607 | − | 0.999933i | \(-0.503680\pi\) | ||||
−0.0115607 | + | 0.999933i | \(0.503680\pi\) | |||||||
\(110\) | 4.36606e6 | 0.312763 | ||||||||
\(111\) | 1.33826e6 | 0.0928777 | ||||||||
\(112\) | 6.09425e6 | 0.409880 | ||||||||
\(113\) | 4.97336e6 | 0.324246 | 0.162123 | − | 0.986771i | \(-0.448166\pi\) | ||||
0.162123 | + | 0.986771i | \(0.448166\pi\) | |||||||
\(114\) | 528876. | 0.0334339 | ||||||||
\(115\) | −4.44728e6 | −0.272679 | ||||||||
\(116\) | 1.99236e7 | 1.18513 | ||||||||
\(117\) | 8.68716e6 | 0.501450 | ||||||||
\(118\) | 1.16359e6 | 0.0651947 | ||||||||
\(119\) | 3.52141e7 | 1.91559 | ||||||||
\(120\) | −4.03791e6 | −0.213315 | ||||||||
\(121\) | 2.32403e7 | 1.19260 | ||||||||
\(122\) | −3.96257e6 | −0.197568 | ||||||||
\(123\) | −3.04786e6 | −0.147682 | ||||||||
\(124\) | −1.06918e7 | −0.503588 | ||||||||
\(125\) | −1.67824e7 | −0.768543 | ||||||||
\(126\) | −4.94658e6 | −0.220297 | ||||||||
\(127\) | 4.34322e7 | 1.88148 | 0.940738 | − | 0.339134i | \(-0.110134\pi\) | ||||
0.940738 | + | 0.339134i | \(0.110134\pi\) | |||||||
\(128\) | 2.20265e7 | 0.928347 | ||||||||
\(129\) | 1.05288e6 | 0.0431833 | ||||||||
\(130\) | −7.95951e6 | −0.317749 | ||||||||
\(131\) | −3.43447e7 | −1.33478 | −0.667391 | − | 0.744707i | \(-0.732589\pi\) | ||||
−0.667391 | + | 0.744707i | \(0.732589\pi\) | |||||||
\(132\) | −1.69255e7 | −0.640521 | ||||||||
\(133\) | 4.14077e6 | 0.152616 | ||||||||
\(134\) | 1.83547e7 | 0.658992 | ||||||||
\(135\) | −2.32051e6 | −0.0811738 | ||||||||
\(136\) | 3.72978e7 | 1.27144 | ||||||||
\(137\) | −5.15704e7 | −1.71348 | −0.856738 | − | 0.515752i | \(-0.827513\pi\) | ||||
−0.856738 | + | 0.515752i | \(0.827513\pi\) | |||||||
\(138\) | −5.77044e6 | −0.186910 | ||||||||
\(139\) | 6.25955e7 | 1.97693 | 0.988466 | − | 0.151444i | \(-0.0483924\pi\) | ||||
0.988466 | + | 0.151444i | \(0.0483924\pi\) | |||||||
\(140\) | −1.35410e7 | −0.417065 | ||||||||
\(141\) | −3.30393e7 | −0.992577 | ||||||||
\(142\) | −2.90951e7 | −0.852728 | ||||||||
\(143\) | −7.78940e7 | −2.22755 | ||||||||
\(144\) | 3.70948e6 | 0.103525 | ||||||||
\(145\) | −2.44926e7 | −0.667186 | ||||||||
\(146\) | −2.87978e7 | −0.765816 | ||||||||
\(147\) | −1.64930e7 | −0.428242 | ||||||||
\(148\) | 4.75338e6 | 0.120528 | ||||||||
\(149\) | −4.84710e6 | −0.120041 | −0.0600206 | − | 0.998197i | \(-0.519117\pi\) | ||||
−0.0600206 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(150\) | −9.82466e6 | −0.237683 | ||||||||
\(151\) | 7.66941e7 | 1.81277 | 0.906385 | − | 0.422452i | \(-0.138831\pi\) | ||||
0.906385 | + | 0.422452i | \(0.138831\pi\) | |||||||
\(152\) | 4.38578e6 | 0.101297 | ||||||||
\(153\) | 2.14344e7 | 0.483827 | ||||||||
\(154\) | 4.43538e7 | 0.978608 | ||||||||
\(155\) | 1.31437e7 | 0.283503 | ||||||||
\(156\) | 3.08560e7 | 0.650733 | ||||||||
\(157\) | −4.97181e6 | −0.102534 | −0.0512668 | − | 0.998685i | \(-0.516326\pi\) | ||||
−0.0512668 | + | 0.998685i | \(0.516326\pi\) | |||||||
\(158\) | −3.97392e7 | −0.801529 | ||||||||
\(159\) | 1.28323e7 | 0.253170 | ||||||||
\(160\) | −2.25414e7 | −0.435073 | ||||||||
\(161\) | −4.51790e7 | −0.853190 | ||||||||
\(162\) | −3.01091e6 | −0.0556411 | ||||||||
\(163\) | 1.80568e7 | 0.326577 | 0.163288 | − | 0.986578i | \(-0.447790\pi\) | ||||
0.163288 | + | 0.986578i | \(0.447790\pi\) | |||||||
\(164\) | −1.08257e7 | −0.191648 | ||||||||
\(165\) | 2.08070e7 | 0.360592 | ||||||||
\(166\) | −3.51763e7 | −0.596860 | ||||||||
\(167\) | −3.89288e7 | −0.646790 | −0.323395 | − | 0.946264i | \(-0.604824\pi\) | ||||
−0.323395 | + | 0.946264i | \(0.604824\pi\) | |||||||
\(168\) | −4.10202e7 | −0.667445 | ||||||||
\(169\) | 7.92556e7 | 1.26307 | ||||||||
\(170\) | −1.96390e7 | −0.306582 | ||||||||
\(171\) | 2.52043e6 | 0.0385468 | ||||||||
\(172\) | 3.73973e6 | 0.0560391 | ||||||||
\(173\) | 9.04299e7 | 1.32786 | 0.663928 | − | 0.747797i | \(-0.268888\pi\) | ||||
0.663928 | + | 0.747797i | \(0.268888\pi\) | |||||||
\(174\) | −3.17797e7 | −0.457327 | ||||||||
\(175\) | −7.69210e7 | −1.08496 | ||||||||
\(176\) | −3.32613e7 | −0.459881 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −8.20342e6 | −0.109025 | ||||||||
\(179\) | 1.14493e7 | 0.149208 | 0.0746042 | − | 0.997213i | \(-0.476231\pi\) | ||||
0.0746042 | + | 0.997213i | \(0.476231\pi\) | |||||||
\(180\) | −8.24223e6 | −0.105339 | ||||||||
\(181\) | −9.25112e7 | −1.15963 | −0.579815 | − | 0.814748i | \(-0.696875\pi\) | ||||
−0.579815 | + | 0.814748i | \(0.696875\pi\) | |||||||
\(182\) | −8.08589e7 | −0.994210 | ||||||||
\(183\) | −1.88841e7 | −0.227781 | ||||||||
\(184\) | −4.78522e7 | −0.566291 | ||||||||
\(185\) | −5.84347e6 | −0.0678531 | ||||||||
\(186\) | 1.70543e7 | 0.194329 | ||||||||
\(187\) | −1.92193e8 | −2.14927 | ||||||||
\(188\) | −1.17353e8 | −1.28807 | ||||||||
\(189\) | −2.35736e7 | −0.253986 | ||||||||
\(190\) | −2.30931e6 | −0.0244256 | ||||||||
\(191\) | 2.78323e7 | 0.289023 | 0.144511 | − | 0.989503i | \(-0.453839\pi\) | ||||
0.144511 | + | 0.989503i | \(0.453839\pi\) | |||||||
\(192\) | −1.16623e7 | −0.118913 | ||||||||
\(193\) | −3.52675e7 | −0.353122 | −0.176561 | − | 0.984290i | \(-0.556497\pi\) | ||||
−0.176561 | + | 0.984290i | \(0.556497\pi\) | |||||||
\(194\) | 6.75386e7 | 0.664119 | ||||||||
\(195\) | −3.79321e7 | −0.366341 | ||||||||
\(196\) | −5.85816e7 | −0.555731 | ||||||||
\(197\) | 1.76100e8 | 1.64107 | 0.820536 | − | 0.571595i | \(-0.193675\pi\) | ||||
0.820536 | + | 0.571595i | \(0.193675\pi\) | |||||||
\(198\) | 2.69976e7 | 0.247170 | ||||||||
\(199\) | 1.94813e8 | 1.75239 | 0.876196 | − | 0.481954i | \(-0.160073\pi\) | ||||
0.876196 | + | 0.481954i | \(0.160073\pi\) | |||||||
\(200\) | −8.14724e7 | −0.720121 | ||||||||
\(201\) | 8.74717e7 | 0.759769 | ||||||||
\(202\) | 7.57000e7 | 0.646199 | ||||||||
\(203\) | −2.48815e8 | −2.08757 | ||||||||
\(204\) | 7.61327e7 | 0.627864 | ||||||||
\(205\) | 1.33084e7 | 0.107891 | ||||||||
\(206\) | −1.46351e7 | −0.116643 | ||||||||
\(207\) | −2.74998e7 | −0.215493 | ||||||||
\(208\) | 6.06368e7 | 0.467212 | ||||||||
\(209\) | −2.25996e7 | −0.171234 | ||||||||
\(210\) | 2.15990e7 | 0.160941 | ||||||||
\(211\) | 9.43223e7 | 0.691235 | 0.345617 | − | 0.938376i | \(-0.387670\pi\) | ||||
0.345617 | + | 0.938376i | \(0.387670\pi\) | |||||||
\(212\) | 4.55789e7 | 0.328540 | ||||||||
\(213\) | −1.38656e8 | −0.983131 | ||||||||
\(214\) | 2.56345e7 | 0.178804 | ||||||||
\(215\) | −4.59736e6 | −0.0315481 | ||||||||
\(216\) | −2.49684e7 | −0.168579 | ||||||||
\(217\) | 1.33525e8 | 0.887058 | ||||||||
\(218\) | 1.77113e6 | 0.0115785 | ||||||||
\(219\) | −1.37240e8 | −0.882929 | ||||||||
\(220\) | 7.39045e7 | 0.467942 | ||||||||
\(221\) | 3.50375e8 | 2.18354 | ||||||||
\(222\) | −7.58202e6 | −0.0465103 | ||||||||
\(223\) | −3.04202e8 | −1.83694 | −0.918470 | − | 0.395492i | \(-0.870574\pi\) | ||||
−0.918470 | + | 0.395492i | \(0.870574\pi\) | |||||||
\(224\) | −2.28994e8 | −1.36130 | ||||||||
\(225\) | −4.68207e7 | −0.274031 | ||||||||
\(226\) | −2.81769e7 | −0.162373 | ||||||||
\(227\) | 1.54534e8 | 0.876866 | 0.438433 | − | 0.898764i | \(-0.355534\pi\) | ||||
0.438433 | + | 0.898764i | \(0.355534\pi\) | |||||||
\(228\) | 8.95232e6 | 0.0500223 | ||||||||
\(229\) | 1.18030e8 | 0.649485 | 0.324742 | − | 0.945803i | \(-0.394722\pi\) | ||||
0.324742 | + | 0.945803i | \(0.394722\pi\) | |||||||
\(230\) | 2.51963e7 | 0.136550 | ||||||||
\(231\) | 2.11374e8 | 1.12826 | ||||||||
\(232\) | −2.63537e8 | −1.38559 | ||||||||
\(233\) | −6.82032e7 | −0.353231 | −0.176615 | − | 0.984280i | \(-0.556515\pi\) | ||||
−0.176615 | + | 0.984280i | \(0.556515\pi\) | |||||||
\(234\) | −4.92177e7 | −0.251111 | ||||||||
\(235\) | 1.44265e8 | 0.725141 | ||||||||
\(236\) | 1.96961e7 | 0.0975414 | ||||||||
\(237\) | −1.89382e8 | −0.924103 | ||||||||
\(238\) | −1.99508e8 | −0.959270 | ||||||||
\(239\) | −8.01024e7 | −0.379536 | −0.189768 | − | 0.981829i | \(-0.560774\pi\) | ||||
−0.189768 | + | 0.981829i | \(0.560774\pi\) | |||||||
\(240\) | −1.61973e7 | −0.0756315 | ||||||||
\(241\) | 9.44904e7 | 0.434839 | 0.217419 | − | 0.976078i | \(-0.430236\pi\) | ||||
0.217419 | + | 0.976078i | \(0.430236\pi\) | |||||||
\(242\) | −1.31670e8 | −0.597216 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −6.70746e7 | −0.295593 | ||||||||
\(245\) | 7.20159e7 | 0.312858 | ||||||||
\(246\) | 1.72679e7 | 0.0739547 | ||||||||
\(247\) | 4.12000e7 | 0.173964 | ||||||||
\(248\) | 1.41425e8 | 0.588770 | ||||||||
\(249\) | −1.67638e8 | −0.688135 | ||||||||
\(250\) | 9.50815e7 | 0.384863 | ||||||||
\(251\) | −2.37800e8 | −0.949191 | −0.474596 | − | 0.880204i | \(-0.657406\pi\) | ||||
−0.474596 | + | 0.880204i | \(0.657406\pi\) | |||||||
\(252\) | −8.37311e7 | −0.329598 | ||||||||
\(253\) | 2.46579e8 | 0.957268 | ||||||||
\(254\) | −2.46068e8 | −0.942187 | ||||||||
\(255\) | −9.35921e7 | −0.353467 | ||||||||
\(256\) | −1.80080e8 | −0.670852 | ||||||||
\(257\) | 673684. | 0.00247566 | 0.00123783 | − | 0.999999i | \(-0.499606\pi\) | ||||
0.00123783 | + | 0.999999i | \(0.499606\pi\) | |||||||
\(258\) | −5.96517e6 | −0.0216249 | ||||||||
\(259\) | −5.93625e7 | −0.212307 | ||||||||
\(260\) | −1.34731e8 | −0.475402 | ||||||||
\(261\) | −1.51450e8 | −0.527264 | ||||||||
\(262\) | 1.94582e8 | 0.668419 | ||||||||
\(263\) | −3.23561e7 | −0.109676 | −0.0548380 | − | 0.998495i | \(-0.517464\pi\) | ||||
−0.0548380 | + | 0.998495i | \(0.517464\pi\) | |||||||
\(264\) | 2.23881e8 | 0.748865 | ||||||||
\(265\) | −5.60314e7 | −0.184957 | ||||||||
\(266\) | −2.34598e7 | −0.0764256 | ||||||||
\(267\) | −3.90945e7 | −0.125697 | ||||||||
\(268\) | 3.10691e8 | 0.985955 | ||||||||
\(269\) | 2.61753e8 | 0.819896 | 0.409948 | − | 0.912109i | \(-0.365547\pi\) | ||||
0.409948 | + | 0.912109i | \(0.365547\pi\) | |||||||
\(270\) | 1.31470e7 | 0.0406494 | ||||||||
\(271\) | 6.21861e8 | 1.89802 | 0.949011 | − | 0.315244i | \(-0.102086\pi\) | ||||
0.949011 | + | 0.315244i | \(0.102086\pi\) | |||||||
\(272\) | 1.49613e8 | 0.450793 | ||||||||
\(273\) | −3.85344e8 | −1.14625 | ||||||||
\(274\) | 2.92175e8 | 0.858057 | ||||||||
\(275\) | 4.19821e8 | 1.21731 | ||||||||
\(276\) | −9.76766e7 | −0.279646 | ||||||||
\(277\) | 2.81765e8 | 0.796541 | 0.398270 | − | 0.917268i | \(-0.369611\pi\) | ||||
0.398270 | + | 0.917268i | \(0.369611\pi\) | |||||||
\(278\) | −3.54639e8 | −0.989988 | ||||||||
\(279\) | 8.12745e7 | 0.224047 | ||||||||
\(280\) | 1.79113e8 | 0.487611 | ||||||||
\(281\) | 2.34019e8 | 0.629186 | 0.314593 | − | 0.949227i | \(-0.398132\pi\) | ||||
0.314593 | + | 0.949227i | \(0.398132\pi\) | |||||||
\(282\) | 1.87186e8 | 0.497053 | ||||||||
\(283\) | −3.59081e8 | −0.941759 | −0.470879 | − | 0.882198i | \(-0.656063\pi\) | ||||
−0.470879 | + | 0.882198i | \(0.656063\pi\) | |||||||
\(284\) | −4.92494e8 | −1.27581 | ||||||||
\(285\) | −1.10053e7 | −0.0281609 | ||||||||
\(286\) | 4.41314e8 | 1.11549 | ||||||||
\(287\) | 1.35197e8 | 0.337582 | ||||||||
\(288\) | −1.39385e8 | −0.343829 | ||||||||
\(289\) | 4.54163e8 | 1.10680 | ||||||||
\(290\) | 1.38764e8 | 0.334107 | ||||||||
\(291\) | 3.21864e8 | 0.765680 | ||||||||
\(292\) | −4.87463e8 | −1.14578 | ||||||||
\(293\) | 2.48310e8 | 0.576711 | 0.288355 | − | 0.957523i | \(-0.406892\pi\) | ||||
0.288355 | + | 0.957523i | \(0.406892\pi\) | |||||||
\(294\) | 9.34422e7 | 0.214451 | ||||||||
\(295\) | −2.42130e7 | −0.0549125 | ||||||||
\(296\) | −6.28750e7 | −0.140915 | ||||||||
\(297\) | 1.28660e8 | 0.284969 | ||||||||
\(298\) | 2.74616e7 | 0.0601130 | ||||||||
\(299\) | −4.49523e8 | −0.972530 | ||||||||
\(300\) | −1.66303e8 | −0.355611 | ||||||||
\(301\) | −4.67036e7 | −0.0987114 | ||||||||
\(302\) | −4.34516e8 | −0.907781 | ||||||||
\(303\) | 3.60758e8 | 0.745019 | ||||||||
\(304\) | 1.75927e7 | 0.0359150 | ||||||||
\(305\) | 8.24567e7 | 0.166409 | ||||||||
\(306\) | −1.21438e8 | −0.242286 | ||||||||
\(307\) | 1.92429e8 | 0.379566 | 0.189783 | − | 0.981826i | \(-0.439222\pi\) | ||||
0.189783 | + | 0.981826i | \(0.439222\pi\) | |||||||
\(308\) | 7.50780e8 | 1.46415 | ||||||||
\(309\) | −6.97454e7 | −0.134481 | ||||||||
\(310\) | −7.44667e7 | −0.141970 | ||||||||
\(311\) | −4.80733e8 | −0.906238 | −0.453119 | − | 0.891450i | \(-0.649689\pi\) | ||||
−0.453119 | + | 0.891450i | \(0.649689\pi\) | |||||||
\(312\) | −4.08145e8 | −0.760804 | ||||||||
\(313\) | 7.85937e8 | 1.44871 | 0.724357 | − | 0.689425i | \(-0.242137\pi\) | ||||
0.724357 | + | 0.689425i | \(0.242137\pi\) | |||||||
\(314\) | 2.81681e7 | 0.0513457 | ||||||||
\(315\) | 1.02933e8 | 0.185553 | ||||||||
\(316\) | −6.72668e8 | −1.19921 | ||||||||
\(317\) | −2.09039e8 | −0.368570 | −0.184285 | − | 0.982873i | \(-0.558997\pi\) | ||||
−0.184285 | + | 0.982873i | \(0.558997\pi\) | |||||||
\(318\) | −7.27019e7 | −0.126780 | ||||||||
\(319\) | 1.35799e9 | 2.34222 | ||||||||
\(320\) | 5.09229e7 | 0.0868736 | ||||||||
\(321\) | 1.22165e8 | 0.206148 | ||||||||
\(322\) | 2.55964e8 | 0.427252 | ||||||||
\(323\) | 1.01655e8 | 0.167850 | ||||||||
\(324\) | −5.09659e7 | −0.0832477 | ||||||||
\(325\) | −7.65351e8 | −1.23671 | ||||||||
\(326\) | −1.02302e8 | −0.163540 | ||||||||
\(327\) | 8.44054e6 | 0.0133491 | ||||||||
\(328\) | 1.43196e8 | 0.224065 | ||||||||
\(329\) | 1.46555e9 | 2.26890 | ||||||||
\(330\) | −1.17884e8 | −0.180574 | ||||||||
\(331\) | 7.95790e8 | 1.20615 | 0.603074 | − | 0.797685i | \(-0.293942\pi\) | ||||
0.603074 | + | 0.797685i | \(0.293942\pi\) | |||||||
\(332\) | −5.95432e8 | −0.892995 | ||||||||
\(333\) | −3.61331e7 | −0.0536230 | ||||||||
\(334\) | 2.20554e8 | 0.323893 | ||||||||
\(335\) | −3.81941e8 | −0.555060 | ||||||||
\(336\) | −1.64545e8 | −0.236644 | ||||||||
\(337\) | 2.75834e8 | 0.392593 | 0.196297 | − | 0.980545i | \(-0.437108\pi\) | ||||
0.196297 | + | 0.980545i | \(0.437108\pi\) | |||||||
\(338\) | −4.49027e8 | −0.632506 | ||||||||
\(339\) | −1.34281e8 | −0.187204 | ||||||||
\(340\) | −3.32430e8 | −0.458695 | ||||||||
\(341\) | −7.28753e8 | −0.995268 | ||||||||
\(342\) | −1.42797e7 | −0.0193031 | ||||||||
\(343\) | −2.54732e8 | −0.340843 | ||||||||
\(344\) | −4.94670e7 | −0.0655181 | ||||||||
\(345\) | 1.20077e8 | 0.157431 | ||||||||
\(346\) | −5.12337e8 | −0.664950 | ||||||||
\(347\) | 4.81631e8 | 0.618816 | 0.309408 | − | 0.950929i | \(-0.399869\pi\) | ||||
0.309408 | + | 0.950929i | \(0.399869\pi\) | |||||||
\(348\) | −5.37936e8 | −0.684232 | ||||||||
\(349\) | −3.21673e8 | −0.405066 | −0.202533 | − | 0.979275i | \(-0.564917\pi\) | ||||
−0.202533 | + | 0.979275i | \(0.564917\pi\) | |||||||
\(350\) | 4.35801e8 | 0.543313 | ||||||||
\(351\) | −2.34553e8 | −0.289512 | ||||||||
\(352\) | 1.24981e9 | 1.52737 | ||||||||
\(353\) | 1.17516e9 | 1.42195 | 0.710977 | − | 0.703216i | \(-0.248253\pi\) | ||||
0.710977 | + | 0.703216i | \(0.248253\pi\) | |||||||
\(354\) | −3.14169e7 | −0.0376402 | ||||||||
\(355\) | 6.05437e8 | 0.718240 | ||||||||
\(356\) | −1.38860e8 | −0.163118 | ||||||||
\(357\) | −9.50782e8 | −1.10597 | ||||||||
\(358\) | −6.48668e7 | −0.0747191 | ||||||||
\(359\) | 3.28816e8 | 0.375079 | 0.187539 | − | 0.982257i | \(-0.439949\pi\) | ||||
0.187539 | + | 0.982257i | \(0.439949\pi\) | |||||||
\(360\) | 1.09023e8 | 0.123158 | ||||||||
\(361\) | −8.81918e8 | −0.986627 | ||||||||
\(362\) | 5.24128e8 | 0.580707 | ||||||||
\(363\) | −6.27489e8 | −0.688546 | ||||||||
\(364\) | −1.36870e9 | −1.48749 | ||||||||
\(365\) | 5.99251e8 | 0.645036 | ||||||||
\(366\) | 1.06989e8 | 0.114066 | ||||||||
\(367\) | −6.95555e8 | −0.734515 | −0.367257 | − | 0.930119i | \(-0.619703\pi\) | ||||
−0.367257 | + | 0.930119i | \(0.619703\pi\) | |||||||
\(368\) | −1.91950e8 | −0.200780 | ||||||||
\(369\) | 8.22923e7 | 0.0852643 | ||||||||
\(370\) | 3.31065e7 | 0.0339788 | ||||||||
\(371\) | −5.69211e8 | −0.578715 | ||||||||
\(372\) | 2.88679e8 | 0.290747 | ||||||||
\(373\) | 1.04776e9 | 1.04540 | 0.522699 | − | 0.852517i | \(-0.324925\pi\) | ||||
0.522699 | + | 0.852517i | \(0.324925\pi\) | |||||||
\(374\) | 1.08888e9 | 1.07629 | ||||||||
\(375\) | 4.53124e8 | 0.443718 | ||||||||
\(376\) | 1.55227e9 | 1.50595 | ||||||||
\(377\) | −2.47567e9 | −2.37957 | ||||||||
\(378\) | 1.33558e8 | 0.127188 | ||||||||
\(379\) | 9.05666e8 | 0.854537 | 0.427268 | − | 0.904125i | \(-0.359476\pi\) | ||||
0.427268 | + | 0.904125i | \(0.359476\pi\) | |||||||
\(380\) | −3.90899e7 | −0.0365445 | ||||||||
\(381\) | −1.17267e9 | −1.08627 | ||||||||
\(382\) | −1.57686e8 | −0.144734 | ||||||||
\(383\) | 1.13004e9 | 1.02777 | 0.513887 | − | 0.857858i | \(-0.328205\pi\) | ||||
0.513887 | + | 0.857858i | \(0.328205\pi\) | |||||||
\(384\) | −5.94715e8 | −0.535982 | ||||||||
\(385\) | −9.22955e8 | −0.824267 | ||||||||
\(386\) | 1.99810e8 | 0.176833 | ||||||||
\(387\) | −2.84278e7 | −0.0249319 | ||||||||
\(388\) | 1.14323e9 | 0.993626 | ||||||||
\(389\) | −9.69975e8 | −0.835482 | −0.417741 | − | 0.908566i | \(-0.637178\pi\) | ||||
−0.417741 | + | 0.908566i | \(0.637178\pi\) | |||||||
\(390\) | 2.14907e8 | 0.183453 | ||||||||
\(391\) | −1.10914e9 | −0.938352 | ||||||||
\(392\) | 7.74883e8 | 0.649733 | ||||||||
\(393\) | 9.27307e8 | 0.770637 | ||||||||
\(394\) | −9.97706e8 | −0.821799 | ||||||||
\(395\) | 8.26929e8 | 0.675116 | ||||||||
\(396\) | 4.56989e8 | 0.369805 | ||||||||
\(397\) | −1.37378e9 | −1.10192 | −0.550961 | − | 0.834531i | \(-0.685739\pi\) | ||||
−0.550961 | + | 0.834531i | \(0.685739\pi\) | |||||||
\(398\) | −1.10372e9 | −0.877546 | ||||||||
\(399\) | −1.11801e8 | −0.0881130 | ||||||||
\(400\) | −3.26811e8 | −0.255321 | ||||||||
\(401\) | 5.72339e8 | 0.443249 | 0.221625 | − | 0.975132i | \(-0.428864\pi\) | ||||
0.221625 | + | 0.975132i | \(0.428864\pi\) | |||||||
\(402\) | −4.95577e8 | −0.380469 | ||||||||
\(403\) | 1.32855e9 | 1.01114 | ||||||||
\(404\) | 1.28138e9 | 0.966813 | ||||||||
\(405\) | 6.26538e7 | 0.0468657 | ||||||||
\(406\) | 1.40968e9 | 1.04539 | ||||||||
\(407\) | 3.23990e8 | 0.238205 | ||||||||
\(408\) | −1.00704e9 | −0.734067 | ||||||||
\(409\) | 1.07412e8 | 0.0776286 | 0.0388143 | − | 0.999246i | \(-0.487642\pi\) | ||||
0.0388143 | + | 0.999246i | \(0.487642\pi\) | |||||||
\(410\) | −7.53994e7 | −0.0540287 | ||||||||
\(411\) | 1.39240e9 | 0.989276 | ||||||||
\(412\) | −2.47729e8 | −0.174516 | ||||||||
\(413\) | −2.45975e8 | −0.171817 | ||||||||
\(414\) | 1.55802e8 | 0.107912 | ||||||||
\(415\) | 7.31982e8 | 0.502727 | ||||||||
\(416\) | −2.27845e9 | −1.55172 | ||||||||
\(417\) | −1.69008e9 | −1.14138 | ||||||||
\(418\) | 1.28040e8 | 0.0857486 | ||||||||
\(419\) | 4.96522e8 | 0.329753 | 0.164877 | − | 0.986314i | \(-0.447277\pi\) | ||||
0.164877 | + | 0.986314i | \(0.447277\pi\) | |||||||
\(420\) | 3.65608e8 | 0.240793 | ||||||||
\(421\) | 2.13271e9 | 1.39298 | 0.696490 | − | 0.717566i | \(-0.254744\pi\) | ||||
0.696490 | + | 0.717566i | \(0.254744\pi\) | |||||||
\(422\) | −5.34389e8 | −0.346150 | ||||||||
\(423\) | 8.92062e8 | 0.573065 | ||||||||
\(424\) | −6.02891e8 | −0.384113 | ||||||||
\(425\) | −1.88840e9 | −1.19325 | ||||||||
\(426\) | 7.85567e8 | 0.492323 | ||||||||
\(427\) | 8.37660e8 | 0.520679 | ||||||||
\(428\) | 4.33918e8 | 0.267519 | ||||||||
\(429\) | 2.10314e9 | 1.28608 | ||||||||
\(430\) | 2.60466e7 | 0.0157984 | ||||||||
\(431\) | −2.75546e8 | −0.165777 | −0.0828885 | − | 0.996559i | \(-0.526415\pi\) | ||||
−0.0828885 | + | 0.996559i | \(0.526415\pi\) | |||||||
\(432\) | −1.00156e8 | −0.0597701 | ||||||||
\(433\) | 1.42964e9 | 0.846289 | 0.423144 | − | 0.906062i | \(-0.360926\pi\) | ||||
0.423144 | + | 0.906062i | \(0.360926\pi\) | |||||||
\(434\) | −7.56492e8 | −0.444212 | ||||||||
\(435\) | 6.61300e8 | 0.385200 | ||||||||
\(436\) | 2.99800e7 | 0.0173232 | ||||||||
\(437\) | −1.30421e8 | −0.0747591 | ||||||||
\(438\) | 7.77541e8 | 0.442144 | ||||||||
\(439\) | −2.29794e9 | −1.29632 | −0.648161 | − | 0.761503i | \(-0.724462\pi\) | ||||
−0.648161 | + | 0.761503i | \(0.724462\pi\) | |||||||
\(440\) | −9.77566e8 | −0.547094 | ||||||||
\(441\) | 4.45311e8 | 0.247246 | ||||||||
\(442\) | −1.98507e9 | −1.09345 | ||||||||
\(443\) | −5.72726e8 | −0.312992 | −0.156496 | − | 0.987679i | \(-0.550020\pi\) | ||||
−0.156496 | + | 0.987679i | \(0.550020\pi\) | |||||||
\(444\) | −1.28341e8 | −0.0695867 | ||||||||
\(445\) | 1.70704e8 | 0.0918300 | ||||||||
\(446\) | 1.72347e9 | 0.919884 | ||||||||
\(447\) | 1.30872e8 | 0.0693058 | ||||||||
\(448\) | 5.17315e8 | 0.271820 | ||||||||
\(449\) | −2.51611e9 | −1.31180 | −0.655899 | − | 0.754848i | \(-0.727710\pi\) | ||||
−0.655899 | + | 0.754848i | \(0.727710\pi\) | |||||||
\(450\) | 2.65266e8 | 0.137226 | ||||||||
\(451\) | −7.37880e8 | −0.378763 | ||||||||
\(452\) | −4.76952e8 | −0.242935 | ||||||||
\(453\) | −2.07074e9 | −1.04660 | ||||||||
\(454\) | −8.75521e8 | −0.439108 | ||||||||
\(455\) | 1.68259e9 | 0.837409 | ||||||||
\(456\) | −1.18416e8 | −0.0584836 | ||||||||
\(457\) | −9.31683e8 | −0.456627 | −0.228314 | − | 0.973588i | \(-0.573321\pi\) | ||||
−0.228314 | + | 0.973588i | \(0.573321\pi\) | |||||||
\(458\) | −6.68708e8 | −0.325242 | ||||||||
\(459\) | −5.78727e8 | −0.279338 | ||||||||
\(460\) | 4.26500e8 | 0.204299 | ||||||||
\(461\) | −2.12369e8 | −0.100957 | −0.0504786 | − | 0.998725i | \(-0.516075\pi\) | ||||
−0.0504786 | + | 0.998725i | \(0.516075\pi\) | |||||||
\(462\) | −1.19755e9 | −0.565000 | ||||||||
\(463\) | 3.14522e9 | 1.47271 | 0.736355 | − | 0.676596i | \(-0.236545\pi\) | ||||
0.736355 | + | 0.676596i | \(0.236545\pi\) | |||||||
\(464\) | −1.05713e9 | −0.491264 | ||||||||
\(465\) | −3.54881e8 | −0.163681 | ||||||||
\(466\) | 3.86409e8 | 0.176887 | ||||||||
\(467\) | 3.87688e9 | 1.76146 | 0.880732 | − | 0.473615i | \(-0.157051\pi\) | ||||
0.880732 | + | 0.473615i | \(0.157051\pi\) | |||||||
\(468\) | −8.33111e8 | −0.375701 | ||||||||
\(469\) | −3.88006e9 | −1.73673 | ||||||||
\(470\) | −8.17341e8 | −0.363129 | ||||||||
\(471\) | 1.34239e8 | 0.0591978 | ||||||||
\(472\) | −2.60529e8 | −0.114040 | ||||||||
\(473\) | 2.54900e8 | 0.110753 | ||||||||
\(474\) | 1.07296e9 | 0.462763 | ||||||||
\(475\) | −2.22054e8 | −0.0950671 | ||||||||
\(476\) | −3.37709e9 | −1.43522 | ||||||||
\(477\) | −3.46471e8 | −0.146168 | ||||||||
\(478\) | 4.53825e8 | 0.190060 | ||||||||
\(479\) | −3.88318e9 | −1.61441 | −0.807205 | − | 0.590272i | \(-0.799021\pi\) | ||||
−0.807205 | + | 0.590272i | \(0.799021\pi\) | |||||||
\(480\) | 6.08619e8 | 0.251189 | ||||||||
\(481\) | −5.90648e8 | −0.242003 | ||||||||
\(482\) | −5.35342e8 | −0.217754 | ||||||||
\(483\) | 1.21983e9 | 0.492589 | ||||||||
\(484\) | −2.22878e9 | −0.893528 | ||||||||
\(485\) | −1.40541e9 | −0.559378 | ||||||||
\(486\) | 8.12947e7 | 0.0321244 | ||||||||
\(487\) | −1.79849e9 | −0.705597 | −0.352799 | − | 0.935699i | \(-0.614770\pi\) | ||||
−0.352799 | + | 0.935699i | \(0.614770\pi\) | |||||||
\(488\) | 8.87224e8 | 0.345592 | ||||||||
\(489\) | −4.87535e8 | −0.188549 | ||||||||
\(490\) | −4.08011e8 | −0.156670 | ||||||||
\(491\) | −1.24531e9 | −0.474780 | −0.237390 | − | 0.971414i | \(-0.576292\pi\) | ||||
−0.237390 | + | 0.971414i | \(0.576292\pi\) | |||||||
\(492\) | 2.92294e8 | 0.110648 | ||||||||
\(493\) | −6.10837e9 | −2.29594 | ||||||||
\(494\) | −2.33421e8 | −0.0871157 | ||||||||
\(495\) | −5.61790e8 | −0.208188 | ||||||||
\(496\) | 5.67299e8 | 0.208750 | ||||||||
\(497\) | 6.15051e9 | 2.24731 | ||||||||
\(498\) | 9.49761e8 | 0.344597 | ||||||||
\(499\) | 3.02782e9 | 1.09088 | 0.545442 | − | 0.838148i | \(-0.316362\pi\) | ||||
0.545442 | + | 0.838148i | \(0.316362\pi\) | |||||||
\(500\) | 1.60945e9 | 0.575815 | ||||||||
\(501\) | 1.05108e9 | 0.373424 | ||||||||
\(502\) | 1.34727e9 | 0.475326 | ||||||||
\(503\) | −3.67205e9 | −1.28653 | −0.643267 | − | 0.765642i | \(-0.722421\pi\) | ||||
−0.643267 | + | 0.765642i | \(0.722421\pi\) | |||||||
\(504\) | 1.10755e9 | 0.385350 | ||||||||
\(505\) | −1.57523e9 | −0.544284 | ||||||||
\(506\) | −1.39701e9 | −0.479371 | ||||||||
\(507\) | −2.13990e9 | −0.729232 | ||||||||
\(508\) | −4.16521e9 | −1.40966 | ||||||||
\(509\) | −7.51140e8 | −0.252469 | −0.126235 | − | 0.992000i | \(-0.540289\pi\) | ||||
−0.126235 | + | 0.992000i | \(0.540289\pi\) | |||||||
\(510\) | 5.30252e8 | 0.177005 | ||||||||
\(511\) | 6.08767e9 | 2.01826 | ||||||||
\(512\) | −1.79913e9 | −0.592405 | ||||||||
\(513\) | −6.80516e7 | −0.0222550 | ||||||||
\(514\) | −3.81680e6 | −0.00123973 | ||||||||
\(515\) | 3.04540e8 | 0.0982469 | ||||||||
\(516\) | −1.00973e8 | −0.0323542 | ||||||||
\(517\) | −7.99873e9 | −2.54568 | ||||||||
\(518\) | 3.36322e8 | 0.106317 | ||||||||
\(519\) | −2.44161e9 | −0.766638 | ||||||||
\(520\) | 1.78214e9 | 0.555816 | ||||||||
\(521\) | 2.30813e9 | 0.715036 | 0.357518 | − | 0.933906i | \(-0.383623\pi\) | ||||
0.357518 | + | 0.933906i | \(0.383623\pi\) | |||||||
\(522\) | 8.58051e8 | 0.264038 | ||||||||
\(523\) | −9.93626e8 | −0.303716 | −0.151858 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151858 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(524\) | 3.29371e9 | 1.00006 | ||||||||
\(525\) | 2.07687e9 | 0.626399 | ||||||||
\(526\) | 1.83316e8 | 0.0549224 | ||||||||
\(527\) | 3.27800e9 | 0.975601 | ||||||||
\(528\) | 8.98055e8 | 0.265512 | ||||||||
\(529\) | −1.98183e9 | −0.582065 | ||||||||
\(530\) | 3.17450e8 | 0.0926210 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | −3.97106e8 | −0.114345 | ||||||||
\(533\) | 1.34519e9 | 0.384802 | ||||||||
\(534\) | 2.21492e8 | 0.0629455 | ||||||||
\(535\) | −5.33427e8 | −0.150604 | ||||||||
\(536\) | −4.10964e9 | −1.15273 | ||||||||
\(537\) | −3.09131e8 | −0.0861456 | ||||||||
\(538\) | −1.48298e9 | −0.410579 | ||||||||
\(539\) | −3.99291e9 | −1.09832 | ||||||||
\(540\) | 2.22540e8 | 0.0608178 | ||||||||
\(541\) | −7.57542e8 | −0.205691 | −0.102846 | − | 0.994697i | \(-0.532795\pi\) | ||||
−0.102846 | + | 0.994697i | \(0.532795\pi\) | |||||||
\(542\) | −3.52320e9 | −0.950472 | ||||||||
\(543\) | 2.49780e9 | 0.669512 | ||||||||
\(544\) | −5.62175e9 | −1.49719 | ||||||||
\(545\) | −3.68552e7 | −0.00975240 | ||||||||
\(546\) | 2.18319e9 | 0.574007 | ||||||||
\(547\) | −7.20248e9 | −1.88160 | −0.940798 | − | 0.338969i | \(-0.889922\pi\) | ||||
−0.940798 | + | 0.338969i | \(0.889922\pi\) | |||||||
\(548\) | 4.94567e9 | 1.28379 | ||||||||
\(549\) | 5.09872e8 | 0.131510 | ||||||||
\(550\) | −2.37852e9 | −0.609590 | ||||||||
\(551\) | −7.18273e8 | −0.182919 | ||||||||
\(552\) | 1.29201e9 | 0.326948 | ||||||||
\(553\) | 8.40060e9 | 2.11238 | ||||||||
\(554\) | −1.59636e9 | −0.398884 | ||||||||
\(555\) | 1.57774e8 | 0.0391750 | ||||||||
\(556\) | −6.00300e9 | −1.48118 | ||||||||
\(557\) | −2.72425e9 | −0.667966 | −0.333983 | − | 0.942579i | \(-0.608393\pi\) | ||||
−0.333983 | + | 0.942579i | \(0.608393\pi\) | |||||||
\(558\) | −4.60466e8 | −0.112196 | ||||||||
\(559\) | −4.64693e8 | −0.112519 | ||||||||
\(560\) | 7.18477e8 | 0.172884 | ||||||||
\(561\) | 5.18920e9 | 1.24088 | ||||||||
\(562\) | −1.32585e9 | −0.315077 | ||||||||
\(563\) | 4.08861e9 | 0.965599 | 0.482799 | − | 0.875731i | \(-0.339620\pi\) | ||||
0.482799 | + | 0.875731i | \(0.339620\pi\) | |||||||
\(564\) | 3.16852e9 | 0.743668 | ||||||||
\(565\) | 5.86330e8 | 0.136764 | ||||||||
\(566\) | 2.03440e9 | 0.471604 | ||||||||
\(567\) | 6.36487e8 | 0.146639 | ||||||||
\(568\) | 6.51443e9 | 1.49162 | ||||||||
\(569\) | −6.62224e9 | −1.50699 | −0.753497 | − | 0.657451i | \(-0.771635\pi\) | ||||
−0.753497 | + | 0.657451i | \(0.771635\pi\) | |||||||
\(570\) | 6.23515e7 | 0.0141021 | ||||||||
\(571\) | 1.73743e9 | 0.390555 | 0.195277 | − | 0.980748i | \(-0.437439\pi\) | ||||
0.195277 | + | 0.980748i | \(0.437439\pi\) | |||||||
\(572\) | 7.47014e9 | 1.66895 | ||||||||
\(573\) | −7.51472e8 | −0.166867 | ||||||||
\(574\) | −7.65966e8 | −0.169051 | ||||||||
\(575\) | 2.42277e9 | 0.531465 | ||||||||
\(576\) | 3.14882e8 | 0.0686545 | ||||||||
\(577\) | 3.85948e9 | 0.836399 | 0.418200 | − | 0.908355i | \(-0.362661\pi\) | ||||
0.418200 | + | 0.908355i | \(0.362661\pi\) | |||||||
\(578\) | −2.57309e9 | −0.554252 | ||||||||
\(579\) | 9.52223e8 | 0.203875 | ||||||||
\(580\) | 2.34887e9 | 0.499875 | ||||||||
\(581\) | 7.43604e9 | 1.57299 | ||||||||
\(582\) | −1.82354e9 | −0.383430 | ||||||||
\(583\) | 3.10665e9 | 0.649311 | ||||||||
\(584\) | 6.44787e9 | 1.33959 | ||||||||
\(585\) | 1.02417e9 | 0.211507 | ||||||||
\(586\) | −1.40682e9 | −0.288799 | ||||||||
\(587\) | −2.98276e9 | −0.608674 | −0.304337 | − | 0.952564i | \(-0.598435\pi\) | ||||
−0.304337 | + | 0.952564i | \(0.598435\pi\) | |||||||
\(588\) | 1.58170e9 | 0.320852 | ||||||||
\(589\) | 3.85455e8 | 0.0777267 | ||||||||
\(590\) | 1.37180e8 | 0.0274985 | ||||||||
\(591\) | −4.75470e9 | −0.947473 | ||||||||
\(592\) | −2.52211e8 | −0.0499618 | ||||||||
\(593\) | 2.61405e9 | 0.514781 | 0.257390 | − | 0.966308i | \(-0.417137\pi\) | ||||
0.257390 | + | 0.966308i | \(0.417137\pi\) | |||||||
\(594\) | −7.28934e8 | −0.142704 | ||||||||
\(595\) | 4.15155e9 | 0.807980 | ||||||||
\(596\) | 4.64844e8 | 0.0899384 | ||||||||
\(597\) | −5.25994e9 | −1.01174 | ||||||||
\(598\) | 2.54680e9 | 0.487014 | ||||||||
\(599\) | −2.42519e8 | −0.0461054 | −0.0230527 | − | 0.999734i | \(-0.507339\pi\) | ||||
−0.0230527 | + | 0.999734i | \(0.507339\pi\) | |||||||
\(600\) | 2.19975e9 | 0.415762 | ||||||||
\(601\) | 6.57764e9 | 1.23597 | 0.617987 | − | 0.786188i | \(-0.287948\pi\) | ||||
0.617987 | + | 0.786188i | \(0.287948\pi\) | |||||||
\(602\) | 2.64602e8 | 0.0494317 | ||||||||
\(603\) | −2.36174e9 | −0.438653 | ||||||||
\(604\) | −7.35507e9 | −1.35818 | ||||||||
\(605\) | 2.73990e9 | 0.503027 | ||||||||
\(606\) | −2.04390e9 | −0.373083 | ||||||||
\(607\) | 3.79055e9 | 0.687927 | 0.343963 | − | 0.938983i | \(-0.388230\pi\) | ||||
0.343963 | + | 0.938983i | \(0.388230\pi\) | |||||||
\(608\) | −6.61053e8 | −0.119282 | ||||||||
\(609\) | 6.71801e9 | 1.20526 | ||||||||
\(610\) | −4.67164e8 | −0.0833326 | ||||||||
\(611\) | 1.45820e10 | 2.58627 | ||||||||
\(612\) | −2.05558e9 | −0.362498 | ||||||||
\(613\) | −5.87144e9 | −1.02952 | −0.514758 | − | 0.857336i | \(-0.672118\pi\) | ||||
−0.514758 | + | 0.857336i | \(0.672118\pi\) | |||||||
\(614\) | −1.09022e9 | −0.190075 | ||||||||
\(615\) | −3.59326e8 | −0.0622910 | ||||||||
\(616\) | −9.93089e9 | −1.71181 | ||||||||
\(617\) | −4.89410e9 | −0.838832 | −0.419416 | − | 0.907794i | \(-0.637765\pi\) | ||||
−0.419416 | + | 0.907794i | \(0.637765\pi\) | |||||||
\(618\) | 3.95147e8 | 0.0673440 | ||||||||
\(619\) | 9.45629e9 | 1.60252 | 0.801260 | − | 0.598316i | \(-0.204163\pi\) | ||||
0.801260 | + | 0.598316i | \(0.204163\pi\) | |||||||
\(620\) | −1.26050e9 | −0.212409 | ||||||||
\(621\) | 7.42494e8 | 0.124415 | ||||||||
\(622\) | 2.72362e9 | 0.453817 | ||||||||
\(623\) | 1.73415e9 | 0.287328 | ||||||||
\(624\) | −1.63719e9 | −0.269745 | ||||||||
\(625\) | 3.03911e9 | 0.497928 | ||||||||
\(626\) | −4.45278e9 | −0.725473 | ||||||||
\(627\) | 6.10189e8 | 0.0988617 | ||||||||
\(628\) | 4.76804e8 | 0.0768212 | ||||||||
\(629\) | −1.45734e9 | −0.233498 | ||||||||
\(630\) | −5.83173e8 | −0.0929193 | ||||||||
\(631\) | 2.37404e9 | 0.376171 | 0.188086 | − | 0.982153i | \(-0.439772\pi\) | ||||
0.188086 | + | 0.982153i | \(0.439772\pi\) | |||||||
\(632\) | 8.89766e9 | 1.40206 | ||||||||
\(633\) | −2.54670e9 | −0.399085 | ||||||||
\(634\) | 1.18432e9 | 0.184569 | ||||||||
\(635\) | 5.12041e9 | 0.793590 | ||||||||
\(636\) | −1.23063e9 | −0.189683 | ||||||||
\(637\) | 7.27925e9 | 1.11583 | ||||||||
\(638\) | −7.69377e9 | −1.17292 | ||||||||
\(639\) | 3.74372e9 | 0.567611 | ||||||||
\(640\) | 2.59680e9 | 0.391569 | ||||||||
\(641\) | 1.19471e10 | 1.79168 | 0.895841 | − | 0.444375i | \(-0.146574\pi\) | ||||
0.895841 | + | 0.444375i | \(0.146574\pi\) | |||||||
\(642\) | −6.92133e8 | −0.103233 | ||||||||
\(643\) | 3.95645e9 | 0.586904 | 0.293452 | − | 0.955974i | \(-0.405196\pi\) | ||||
0.293452 | + | 0.955974i | \(0.405196\pi\) | |||||||
\(644\) | 4.33272e9 | 0.639235 | ||||||||
\(645\) | 1.24129e8 | 0.0182143 | ||||||||
\(646\) | −5.75935e8 | −0.0840542 | ||||||||
\(647\) | 8.69167e9 | 1.26165 | 0.630824 | − | 0.775926i | \(-0.282717\pi\) | ||||
0.630824 | + | 0.775926i | \(0.282717\pi\) | |||||||
\(648\) | 6.74148e8 | 0.0973290 | ||||||||
\(649\) | 1.34249e9 | 0.192776 | ||||||||
\(650\) | 4.33615e9 | 0.619309 | ||||||||
\(651\) | −3.60516e9 | −0.512143 | ||||||||
\(652\) | −1.73168e9 | −0.244681 | ||||||||
\(653\) | 2.95452e9 | 0.415231 | 0.207616 | − | 0.978210i | \(-0.433430\pi\) | ||||
0.207616 | + | 0.978210i | \(0.433430\pi\) | |||||||
\(654\) | −4.78204e7 | −0.00668485 | ||||||||
\(655\) | −4.04904e9 | −0.562999 | ||||||||
\(656\) | 5.74404e8 | 0.0794427 | ||||||||
\(657\) | 3.70548e9 | 0.509759 | ||||||||
\(658\) | −8.30319e9 | −1.13620 | ||||||||
\(659\) | −6.81330e9 | −0.927382 | −0.463691 | − | 0.885997i | \(-0.653475\pi\) | ||||
−0.463691 | + | 0.885997i | \(0.653475\pi\) | |||||||
\(660\) | −1.99542e9 | −0.270166 | ||||||||
\(661\) | −9.65769e9 | −1.30067 | −0.650336 | − | 0.759646i | \(-0.725372\pi\) | ||||
−0.650336 | + | 0.759646i | \(0.725372\pi\) | |||||||
\(662\) | −4.50860e9 | −0.604003 | ||||||||
\(663\) | −9.46013e9 | −1.26066 | ||||||||
\(664\) | 7.87603e9 | 1.04404 | ||||||||
\(665\) | 4.88173e8 | 0.0643722 | ||||||||
\(666\) | 2.04715e8 | 0.0268528 | ||||||||
\(667\) | 7.83690e9 | 1.02259 | ||||||||
\(668\) | 3.73332e9 | 0.484594 | ||||||||
\(669\) | 8.21345e9 | 1.06056 | ||||||||
\(670\) | 2.16391e9 | 0.277957 | ||||||||
\(671\) | −4.57180e9 | −0.584196 | ||||||||
\(672\) | 6.18283e9 | 0.785950 | ||||||||
\(673\) | −5.74382e9 | −0.726354 | −0.363177 | − | 0.931720i | \(-0.618308\pi\) | ||||
−0.363177 | + | 0.931720i | \(0.618308\pi\) | |||||||
\(674\) | −1.56275e9 | −0.196599 | ||||||||
\(675\) | 1.26416e9 | 0.158212 | ||||||||
\(676\) | −7.60072e9 | −0.946327 | ||||||||
\(677\) | −6.39314e9 | −0.791870 | −0.395935 | − | 0.918279i | \(-0.629579\pi\) | ||||
−0.395935 | + | 0.918279i | \(0.629579\pi\) | |||||||
\(678\) | 7.60776e8 | 0.0937460 | ||||||||
\(679\) | −1.42772e10 | −1.75025 | ||||||||
\(680\) | 4.39719e9 | 0.536283 | ||||||||
\(681\) | −4.17241e9 | −0.506259 | ||||||||
\(682\) | 4.12880e9 | 0.498400 | ||||||||
\(683\) | −1.10711e10 | −1.32959 | −0.664794 | − | 0.747027i | \(-0.731481\pi\) | ||||
−0.664794 | + | 0.747027i | \(0.731481\pi\) | |||||||
\(684\) | −2.41713e8 | −0.0288804 | ||||||||
\(685\) | −6.07985e9 | −0.722729 | ||||||||
\(686\) | 1.44320e9 | 0.170684 | ||||||||
\(687\) | −3.18681e9 | −0.374980 | ||||||||
\(688\) | −1.98427e8 | −0.0232296 | ||||||||
\(689\) | −5.66356e9 | −0.659663 | ||||||||
\(690\) | −6.80301e8 | −0.0788369 | ||||||||
\(691\) | 1.01541e10 | 1.17077 | 0.585383 | − | 0.810757i | \(-0.300944\pi\) | ||||
0.585383 | + | 0.810757i | \(0.300944\pi\) | |||||||
\(692\) | −8.67236e9 | −0.994869 | ||||||||
\(693\) | −5.70710e9 | −0.651402 | ||||||||
\(694\) | −2.72871e9 | −0.309884 | ||||||||
\(695\) | 7.37965e9 | 0.833852 | ||||||||
\(696\) | 7.11551e9 | 0.799970 | ||||||||
\(697\) | 3.31906e9 | 0.371279 | ||||||||
\(698\) | 1.82246e9 | 0.202845 | ||||||||
\(699\) | 1.84149e9 | 0.203938 | ||||||||
\(700\) | 7.37683e9 | 0.812880 | ||||||||
\(701\) | 6.42013e9 | 0.703933 | 0.351966 | − | 0.936013i | \(-0.385513\pi\) | ||||
0.351966 | + | 0.936013i | \(0.385513\pi\) | |||||||
\(702\) | 1.32888e9 | 0.144979 | ||||||||
\(703\) | −1.71366e8 | −0.0186029 | ||||||||
\(704\) | −2.82341e9 | −0.304979 | ||||||||
\(705\) | −3.89515e9 | −0.418660 | ||||||||
\(706\) | −6.65794e9 | −0.712071 | ||||||||
\(707\) | −1.60025e10 | −1.70302 | ||||||||
\(708\) | −5.31796e8 | −0.0563155 | ||||||||
\(709\) | −1.49237e10 | −1.57259 | −0.786293 | − | 0.617854i | \(-0.788002\pi\) | ||||
−0.786293 | + | 0.617854i | \(0.788002\pi\) | |||||||
\(710\) | −3.43014e9 | −0.359673 | ||||||||
\(711\) | 5.11332e9 | 0.533531 | ||||||||
\(712\) | 1.83676e9 | 0.190709 | ||||||||
\(713\) | −4.20560e9 | −0.434525 | ||||||||
\(714\) | 5.38672e9 | 0.553835 | ||||||||
\(715\) | −9.18326e9 | −0.939562 | ||||||||
\(716\) | −1.09800e9 | −0.111791 | ||||||||
\(717\) | 2.16276e9 | 0.219125 | ||||||||
\(718\) | −1.86293e9 | −0.187828 | ||||||||
\(719\) | −3.46295e9 | −0.347452 | −0.173726 | − | 0.984794i | \(-0.555581\pi\) | ||||
−0.173726 | + | 0.984794i | \(0.555581\pi\) | |||||||
\(720\) | 4.37326e8 | 0.0436659 | ||||||||
\(721\) | 3.09376e9 | 0.307406 | ||||||||
\(722\) | 4.99656e9 | 0.494073 | ||||||||
\(723\) | −2.55124e9 | −0.251054 | ||||||||
\(724\) | 8.87195e9 | 0.868828 | ||||||||
\(725\) | 1.33430e10 | 1.30038 | ||||||||
\(726\) | 3.55508e9 | 0.344803 | ||||||||
\(727\) | −1.19482e10 | −1.15327 | −0.576637 | − | 0.817000i | \(-0.695635\pi\) | ||||
−0.576637 | + | 0.817000i | \(0.695635\pi\) | |||||||
\(728\) | 1.81044e10 | 1.73910 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −3.39510e9 | −0.323015 | ||||||||
\(731\) | −1.14656e9 | −0.108564 | ||||||||
\(732\) | 1.81102e9 | 0.170661 | ||||||||
\(733\) | −4.90087e9 | −0.459631 | −0.229815 | − | 0.973234i | \(-0.573812\pi\) | ||||
−0.229815 | + | 0.973234i | \(0.573812\pi\) | |||||||
\(734\) | 3.94071e9 | 0.367823 | ||||||||
\(735\) | −1.94443e9 | −0.180629 | ||||||||
\(736\) | 7.21258e9 | 0.666835 | ||||||||
\(737\) | 2.11767e10 | 1.94859 | ||||||||
\(738\) | −4.66233e8 | −0.0426978 | ||||||||
\(739\) | −1.16073e10 | −1.05797 | −0.528986 | − | 0.848631i | \(-0.677428\pi\) | ||||
−0.528986 | + | 0.848631i | \(0.677428\pi\) | |||||||
\(740\) | 5.60397e8 | 0.0508375 | ||||||||
\(741\) | −1.11240e9 | −0.100438 | ||||||||
\(742\) | 3.22490e9 | 0.289803 | ||||||||
\(743\) | −1.83926e10 | −1.64506 | −0.822531 | − | 0.568720i | \(-0.807439\pi\) | ||||
−0.822531 | + | 0.568720i | \(0.807439\pi\) | |||||||
\(744\) | −3.81848e9 | −0.339926 | ||||||||
\(745\) | −5.71445e8 | −0.0506323 | ||||||||
\(746\) | −5.93617e9 | −0.523504 | ||||||||
\(747\) | 4.52621e9 | 0.397295 | ||||||||
\(748\) | 1.84315e10 | 1.61030 | ||||||||
\(749\) | −5.41897e9 | −0.471227 | ||||||||
\(750\) | −2.56720e9 | −0.222201 | ||||||||
\(751\) | −1.54442e10 | −1.33054 | −0.665268 | − | 0.746604i | \(-0.731683\pi\) | ||||
−0.665268 | + | 0.746604i | \(0.731683\pi\) | |||||||
\(752\) | 6.22663e9 | 0.533938 | ||||||||
\(753\) | 6.42060e9 | 0.548016 | ||||||||
\(754\) | 1.40261e10 | 1.19162 | ||||||||
\(755\) | 9.04180e9 | 0.764611 | ||||||||
\(756\) | 2.26074e9 | 0.190294 | ||||||||
\(757\) | −1.95008e10 | −1.63387 | −0.816933 | − | 0.576732i | \(-0.804328\pi\) | ||||
−0.816933 | + | 0.576732i | \(0.804328\pi\) | |||||||
\(758\) | −5.13111e9 | −0.427926 | ||||||||
\(759\) | −6.65762e9 | −0.552679 | ||||||||
\(760\) | 5.17059e8 | 0.0427260 | ||||||||
\(761\) | −9.37201e9 | −0.770880 | −0.385440 | − | 0.922733i | \(-0.625950\pi\) | ||||
−0.385440 | + | 0.922733i | \(0.625950\pi\) | |||||||
\(762\) | 6.64383e9 | 0.543972 | ||||||||
\(763\) | −3.74405e8 | −0.0305144 | ||||||||
\(764\) | −2.66916e9 | −0.216544 | ||||||||
\(765\) | 2.52699e9 | 0.204074 | ||||||||
\(766\) | −6.40231e9 | −0.514679 | ||||||||
\(767\) | −2.44741e9 | −0.195850 | ||||||||
\(768\) | 4.86217e9 | 0.387317 | ||||||||
\(769\) | −1.02340e10 | −0.811528 | −0.405764 | − | 0.913978i | \(-0.632994\pi\) | ||||
−0.405764 | + | 0.913978i | \(0.632994\pi\) | |||||||
\(770\) | 5.22906e9 | 0.412768 | ||||||||
\(771\) | −1.81895e7 | −0.00142932 | ||||||||
\(772\) | 3.38220e9 | 0.264569 | ||||||||
\(773\) | 2.44487e10 | 1.90383 | 0.951913 | − | 0.306367i | \(-0.0991135\pi\) | ||||
0.951913 | + | 0.306367i | \(0.0991135\pi\) | |||||||
\(774\) | 1.61060e8 | 0.0124851 | ||||||||
\(775\) | −7.16040e9 | −0.552562 | ||||||||
\(776\) | −1.51220e10 | −1.16170 | ||||||||
\(777\) | 1.60279e9 | 0.122575 | ||||||||
\(778\) | 5.49546e9 | 0.418384 | ||||||||
\(779\) | 3.90283e8 | 0.0295800 | ||||||||
\(780\) | 3.63774e9 | 0.274474 | ||||||||
\(781\) | −3.35684e10 | −2.52146 | ||||||||
\(782\) | 6.28388e9 | 0.469899 | ||||||||
\(783\) | 4.08915e9 | 0.304416 | ||||||||
\(784\) | 3.10829e9 | 0.230364 | ||||||||
\(785\) | −5.86148e8 | −0.0432478 | ||||||||
\(786\) | −5.25372e9 | −0.385912 | ||||||||
\(787\) | −3.61895e8 | −0.0264649 | −0.0132325 | − | 0.999912i | \(-0.504212\pi\) | ||||
−0.0132325 | + | 0.999912i | \(0.504212\pi\) | |||||||
\(788\) | −1.68882e10 | −1.22954 | ||||||||
\(789\) | 8.73615e8 | 0.0633214 | ||||||||
\(790\) | −4.68502e9 | −0.338078 | ||||||||
\(791\) | 5.95640e9 | 0.427924 | ||||||||
\(792\) | −6.04479e9 | −0.432358 | ||||||||
\(793\) | 8.33458e9 | 0.593510 | ||||||||
\(794\) | 7.78325e9 | 0.551810 | ||||||||
\(795\) | 1.51285e9 | 0.106785 | ||||||||
\(796\) | −1.86828e10 | −1.31294 | ||||||||
\(797\) | −5.22352e9 | −0.365476 | −0.182738 | − | 0.983162i | \(-0.558496\pi\) | ||||
−0.182738 | + | 0.983162i | \(0.558496\pi\) | |||||||
\(798\) | 6.33415e8 | 0.0441244 | ||||||||
\(799\) | 3.59791e10 | 2.49538 | ||||||||
\(800\) | 1.22800e10 | 0.847978 | ||||||||
\(801\) | 1.05555e9 | 0.0725714 | ||||||||
\(802\) | −3.24262e9 | −0.221966 | ||||||||
\(803\) | −3.32254e10 | −2.26447 | ||||||||
\(804\) | −8.38866e9 | −0.569241 | ||||||||
\(805\) | −5.32634e9 | −0.359868 | ||||||||
\(806\) | −7.52697e9 | −0.506346 | ||||||||
\(807\) | −7.06733e9 | −0.473367 | ||||||||
\(808\) | −1.69493e10 | −1.13035 | ||||||||
\(809\) | −2.37703e10 | −1.57839 | −0.789194 | − | 0.614144i | \(-0.789502\pi\) | ||||
−0.789194 | + | 0.614144i | \(0.789502\pi\) | |||||||
\(810\) | −3.54969e8 | −0.0234689 | ||||||||
\(811\) | 1.74347e10 | 1.14774 | 0.573868 | − | 0.818948i | \(-0.305442\pi\) | ||||
0.573868 | + | 0.818948i | \(0.305442\pi\) | |||||||
\(812\) | 2.38617e10 | 1.56407 | ||||||||
\(813\) | −1.67903e10 | −1.09582 | ||||||||
\(814\) | −1.83559e9 | −0.119286 | ||||||||
\(815\) | 2.12880e9 | 0.137747 | ||||||||
\(816\) | −4.03954e9 | −0.260266 | ||||||||
\(817\) | −1.34823e8 | −0.00864940 | ||||||||
\(818\) | −6.08550e8 | −0.0388741 | ||||||||
\(819\) | 1.04043e10 | 0.661788 | ||||||||
\(820\) | −1.27629e9 | −0.0808353 | ||||||||
\(821\) | −2.87309e9 | −0.181196 | −0.0905978 | − | 0.995888i | \(-0.528878\pi\) | ||||
−0.0905978 | + | 0.995888i | \(0.528878\pi\) | |||||||
\(822\) | −7.88873e9 | −0.495400 | ||||||||
\(823\) | 6.48563e9 | 0.405558 | 0.202779 | − | 0.979225i | \(-0.435003\pi\) | ||||
0.202779 | + | 0.979225i | \(0.435003\pi\) | |||||||
\(824\) | 3.27681e9 | 0.204036 | ||||||||
\(825\) | −1.13352e10 | −0.702812 | ||||||||
\(826\) | 1.39359e9 | 0.0860406 | ||||||||
\(827\) | −1.45803e10 | −0.896388 | −0.448194 | − | 0.893936i | \(-0.647933\pi\) | ||||
−0.448194 | + | 0.893936i | \(0.647933\pi\) | |||||||
\(828\) | 2.63727e9 | 0.161454 | ||||||||
\(829\) | 2.97207e9 | 0.181183 | 0.0905916 | − | 0.995888i | \(-0.471124\pi\) | ||||
0.0905916 | + | 0.995888i | \(0.471124\pi\) | |||||||
\(830\) | −4.14709e9 | −0.251750 | ||||||||
\(831\) | −7.60766e9 | −0.459883 | ||||||||
\(832\) | 5.14720e9 | 0.309841 | ||||||||
\(833\) | 1.79605e10 | 1.07662 | ||||||||
\(834\) | 9.57526e9 | 0.571570 | ||||||||
\(835\) | −4.58948e9 | −0.272810 | ||||||||
\(836\) | 2.16733e9 | 0.128293 | ||||||||
\(837\) | −2.19441e9 | −0.129354 | ||||||||
\(838\) | −2.81307e9 | −0.165130 | ||||||||
\(839\) | −1.23558e10 | −0.722276 | −0.361138 | − | 0.932512i | \(-0.617612\pi\) | ||||
−0.361138 | + | 0.932512i | \(0.617612\pi\) | |||||||
\(840\) | −4.83605e9 | −0.281523 | ||||||||
\(841\) | 2.59104e10 | 1.50206 | ||||||||
\(842\) | −1.20830e10 | −0.697562 | ||||||||
\(843\) | −6.31851e9 | −0.363261 | ||||||||
\(844\) | −9.04564e9 | −0.517894 | ||||||||
\(845\) | 9.34377e9 | 0.532750 | ||||||||
\(846\) | −5.05403e9 | −0.286974 | ||||||||
\(847\) | 2.78341e10 | 1.57393 | ||||||||
\(848\) | −2.41838e9 | −0.136188 | ||||||||
\(849\) | 9.69518e9 | 0.543725 | ||||||||
\(850\) | 1.06988e10 | 0.597545 | ||||||||
\(851\) | 1.86973e9 | 0.103998 | ||||||||
\(852\) | 1.32973e10 | 0.736591 | ||||||||
\(853\) | −3.00088e9 | −0.165549 | −0.0827746 | − | 0.996568i | \(-0.526378\pi\) | ||||
−0.0827746 | + | 0.996568i | \(0.526378\pi\) | |||||||
\(854\) | −4.74582e9 | −0.260741 | ||||||||
\(855\) | 2.97144e8 | 0.0162587 | ||||||||
\(856\) | −5.73961e9 | −0.312769 | ||||||||
\(857\) | 6.68872e9 | 0.363003 | 0.181502 | − | 0.983391i | \(-0.441904\pi\) | ||||
0.181502 | + | 0.983391i | \(0.441904\pi\) | |||||||
\(858\) | −1.19155e10 | −0.644029 | ||||||||
\(859\) | 9.56843e9 | 0.515068 | 0.257534 | − | 0.966269i | \(-0.417090\pi\) | ||||
0.257534 | + | 0.966269i | \(0.417090\pi\) | |||||||
\(860\) | 4.40893e8 | 0.0236368 | ||||||||
\(861\) | −3.65031e9 | −0.194903 | ||||||||
\(862\) | 1.56113e9 | 0.0830161 | ||||||||
\(863\) | 3.10651e10 | 1.64526 | 0.822632 | − | 0.568575i | \(-0.192505\pi\) | ||||
0.822632 | + | 0.568575i | \(0.192505\pi\) | |||||||
\(864\) | 3.76340e9 | 0.198510 | ||||||||
\(865\) | 1.06612e10 | 0.560078 | ||||||||
\(866\) | −8.09971e9 | −0.423796 | ||||||||
\(867\) | −1.22624e10 | −0.639011 | ||||||||
\(868\) | −1.28052e10 | −0.664610 | ||||||||
\(869\) | −4.58490e10 | −2.37006 | ||||||||
\(870\) | −3.74664e9 | −0.192897 | ||||||||
\(871\) | −3.86060e10 | −1.97966 | ||||||||
\(872\) | −3.96558e8 | −0.0202534 | ||||||||
\(873\) | −8.69034e9 | −0.442066 | ||||||||
\(874\) | 7.38911e8 | 0.0374371 | ||||||||
\(875\) | −2.00996e10 | −1.01428 | ||||||||
\(876\) | 1.31615e10 | 0.661516 | ||||||||
\(877\) | −3.23289e10 | −1.61843 | −0.809213 | − | 0.587515i | \(-0.800106\pi\) | ||||
−0.809213 | + | 0.587515i | \(0.800106\pi\) | |||||||
\(878\) | 1.30191e10 | 0.649159 | ||||||||
\(879\) | −6.70438e9 | −0.332964 | ||||||||
\(880\) | −3.92132e9 | −0.193974 | ||||||||
\(881\) | 1.05719e10 | 0.520881 | 0.260440 | − | 0.965490i | \(-0.416132\pi\) | ||||
0.260440 | + | 0.965490i | \(0.416132\pi\) | |||||||
\(882\) | −2.52294e9 | −0.123813 | ||||||||
\(883\) | 1.62742e10 | 0.795493 | 0.397746 | − | 0.917495i | \(-0.369792\pi\) | ||||
0.397746 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(884\) | −3.36015e10 | −1.63597 | ||||||||
\(885\) | 6.53751e8 | 0.0317038 | ||||||||
\(886\) | 3.24481e9 | 0.156737 | ||||||||
\(887\) | −5.54686e9 | −0.266879 | −0.133440 | − | 0.991057i | \(-0.542602\pi\) | ||||
−0.133440 | + | 0.991057i | \(0.542602\pi\) | |||||||
\(888\) | 1.69763e9 | 0.0813573 | ||||||||
\(889\) | 5.20171e10 | 2.48308 | ||||||||
\(890\) | −9.67136e8 | −0.0459857 | ||||||||
\(891\) | −3.47383e9 | −0.164527 | ||||||||
\(892\) | 2.91734e10 | 1.37629 | ||||||||
\(893\) | 4.23072e9 | 0.198808 | ||||||||
\(894\) | −7.41462e8 | −0.0347062 | ||||||||
\(895\) | 1.34981e9 | 0.0629348 | ||||||||
\(896\) | 2.63803e10 | 1.22519 | ||||||||
\(897\) | 1.21371e10 | 0.561490 | ||||||||
\(898\) | 1.42552e10 | 0.656909 | ||||||||
\(899\) | −2.31616e10 | −1.06319 | ||||||||
\(900\) | 4.49017e9 | 0.205312 | ||||||||
\(901\) | −1.39740e10 | −0.636481 | ||||||||
\(902\) | 4.18051e9 | 0.189673 | ||||||||
\(903\) | 1.26100e9 | 0.0569911 | ||||||||
\(904\) | 6.30884e9 | 0.284027 | ||||||||
\(905\) | −1.09065e10 | −0.489121 | ||||||||
\(906\) | 1.17319e10 | 0.524107 | ||||||||
\(907\) | 2.33401e10 | 1.03867 | 0.519335 | − | 0.854571i | \(-0.326180\pi\) | ||||
0.519335 | + | 0.854571i | \(0.326180\pi\) | |||||||
\(908\) | −1.48200e10 | −0.656974 | ||||||||
\(909\) | −9.74047e9 | −0.430137 | ||||||||
\(910\) | −9.53280e9 | −0.419349 | ||||||||
\(911\) | 1.77936e10 | 0.779740 | 0.389870 | − | 0.920870i | \(-0.372520\pi\) | ||||
0.389870 | + | 0.920870i | \(0.372520\pi\) | |||||||
\(912\) | −4.75003e8 | −0.0207355 | ||||||||
\(913\) | −4.05846e10 | −1.76487 | ||||||||
\(914\) | 5.27851e9 | 0.228665 | ||||||||
\(915\) | −2.22633e9 | −0.0960762 | ||||||||
\(916\) | −1.13193e10 | −0.486613 | ||||||||
\(917\) | −4.11334e10 | −1.76158 | ||||||||
\(918\) | 3.27882e9 | 0.139884 | ||||||||
\(919\) | 2.41659e10 | 1.02706 | 0.513532 | − | 0.858070i | \(-0.328337\pi\) | ||||
0.513532 | + | 0.858070i | \(0.328337\pi\) | |||||||
\(920\) | −5.64150e9 | −0.238856 | ||||||||
\(921\) | −5.19559e9 | −0.219142 | ||||||||
\(922\) | 1.20319e9 | 0.0505563 | ||||||||
\(923\) | 6.11965e10 | 2.56166 | ||||||||
\(924\) | −2.02711e10 | −0.845327 | ||||||||
\(925\) | 3.18338e9 | 0.132249 | ||||||||
\(926\) | −1.78194e10 | −0.737489 | ||||||||
\(927\) | 1.88313e9 | 0.0776426 | ||||||||
\(928\) | 3.97220e10 | 1.63160 | ||||||||
\(929\) | −2.78712e10 | −1.14052 | −0.570258 | − | 0.821466i | \(-0.693157\pi\) | ||||
−0.570258 | + | 0.821466i | \(0.693157\pi\) | |||||||
\(930\) | 2.01060e9 | 0.0819664 | ||||||||
\(931\) | 2.11195e9 | 0.0857747 | ||||||||
\(932\) | 6.54078e9 | 0.264651 | ||||||||
\(933\) | 1.29798e10 | 0.523217 | ||||||||
\(934\) | −2.19647e10 | −0.882088 | ||||||||
\(935\) | −2.26584e10 | −0.906543 | ||||||||
\(936\) | 1.10199e10 | 0.439251 | ||||||||
\(937\) | 1.83113e10 | 0.727162 | 0.363581 | − | 0.931563i | \(-0.381554\pi\) | ||||
0.363581 | + | 0.931563i | \(0.381554\pi\) | |||||||
\(938\) | 2.19827e10 | 0.869704 | ||||||||
\(939\) | −2.12203e10 | −0.836416 | ||||||||
\(940\) | −1.38352e10 | −0.543297 | ||||||||
\(941\) | 3.20558e9 | 0.125413 | 0.0627066 | − | 0.998032i | \(-0.480027\pi\) | ||||
0.0627066 | + | 0.998032i | \(0.480027\pi\) | |||||||
\(942\) | −7.60540e8 | −0.0296445 | ||||||||
\(943\) | −4.25828e9 | −0.165365 | ||||||||
\(944\) | −1.04506e9 | −0.0404333 | ||||||||
\(945\) | −2.77919e9 | −0.107129 | ||||||||
\(946\) | −1.44415e9 | −0.0554618 | ||||||||
\(947\) | 1.13660e10 | 0.434895 | 0.217448 | − | 0.976072i | \(-0.430227\pi\) | ||||
0.217448 | + | 0.976072i | \(0.430227\pi\) | |||||||
\(948\) | 1.81620e10 | 0.692365 | ||||||||
\(949\) | 6.05713e10 | 2.30057 | ||||||||
\(950\) | 1.25806e9 | 0.0476067 | ||||||||
\(951\) | 5.64405e9 | 0.212794 | ||||||||
\(952\) | 4.46701e10 | 1.67798 | ||||||||
\(953\) | −2.26241e10 | −0.846732 | −0.423366 | − | 0.905959i | \(-0.639152\pi\) | ||||
−0.423366 | + | 0.905959i | \(0.639152\pi\) | |||||||
\(954\) | 1.96295e9 | 0.0731965 | ||||||||
\(955\) | 3.28127e9 | 0.121907 | ||||||||
\(956\) | 7.68193e9 | 0.284359 | ||||||||
\(957\) | −3.66657e10 | −1.35228 | ||||||||
\(958\) | 2.20004e10 | 0.808447 | ||||||||
\(959\) | −6.17639e10 | −2.26136 | ||||||||
\(960\) | −1.37492e9 | −0.0501565 | ||||||||
\(961\) | −1.50831e10 | −0.548226 | ||||||||
\(962\) | 3.34635e9 | 0.121188 | ||||||||
\(963\) | −3.29845e9 | −0.119019 | ||||||||
\(964\) | −9.06176e9 | −0.325794 | ||||||||
\(965\) | −4.15784e9 | −0.148944 | ||||||||
\(966\) | −6.91104e9 | −0.246674 | ||||||||
\(967\) | 4.77814e10 | 1.69928 | 0.849642 | − | 0.527359i | \(-0.176818\pi\) | ||||
0.849642 | + | 0.527359i | \(0.176818\pi\) | |||||||
\(968\) | 2.94810e10 | 1.04467 | ||||||||
\(969\) | −2.74469e9 | −0.0969082 | ||||||||
\(970\) | 7.96242e9 | 0.280120 | ||||||||
\(971\) | 2.36126e9 | 0.0827707 | 0.0413854 | − | 0.999143i | \(-0.486823\pi\) | ||||
0.0413854 | + | 0.999143i | \(0.486823\pi\) | |||||||
\(972\) | 1.37608e9 | 0.0480631 | ||||||||
\(973\) | 7.49683e10 | 2.60905 | ||||||||
\(974\) | 1.01895e10 | 0.353342 | ||||||||
\(975\) | 2.06645e10 | 0.714017 | ||||||||
\(976\) | 3.55893e9 | 0.122531 | ||||||||
\(977\) | −2.09178e10 | −0.717604 | −0.358802 | − | 0.933414i | \(-0.616815\pi\) | ||||
−0.358802 | + | 0.933414i | \(0.616815\pi\) | |||||||
\(978\) | 2.76216e9 | 0.0944197 | ||||||||
\(979\) | −9.46467e9 | −0.322379 | ||||||||
\(980\) | −6.90643e9 | −0.234403 | ||||||||
\(981\) | −2.27895e8 | −0.00770713 | ||||||||
\(982\) | 7.05538e9 | 0.237755 | ||||||||
\(983\) | −5.00358e9 | −0.168013 | −0.0840066 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840066 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(984\) | −3.86630e9 | −0.129364 | ||||||||
\(985\) | 2.07612e10 | 0.692190 | ||||||||
\(986\) | 3.46073e10 | 1.14974 | ||||||||
\(987\) | −3.95700e10 | −1.30995 | ||||||||
\(988\) | −3.95114e9 | −0.130339 | ||||||||
\(989\) | 1.47102e9 | 0.0483538 | ||||||||
\(990\) | 3.18286e9 | 0.104254 | ||||||||
\(991\) | 2.88517e10 | 0.941702 | 0.470851 | − | 0.882213i | \(-0.343947\pi\) | ||||
0.470851 | + | 0.882213i | \(0.343947\pi\) | |||||||
\(992\) | −2.13165e10 | −0.693306 | ||||||||
\(993\) | −2.14863e10 | −0.696370 | ||||||||
\(994\) | −3.48461e10 | −1.12539 | ||||||||
\(995\) | 2.29673e10 | 0.739144 | ||||||||
\(996\) | 1.60767e10 | 0.515571 | ||||||||
\(997\) | −4.64145e10 | −1.48327 | −0.741636 | − | 0.670802i | \(-0.765950\pi\) | ||||
−0.741636 | + | 0.670802i | \(0.765950\pi\) | |||||||
\(998\) | −1.71543e10 | −0.546282 | ||||||||
\(999\) | 9.75595e8 | 0.0309592 |
(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 | 177.8.a.c.1.7 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.c.1.11 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.7 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.c.1.11 | 17 | 3.2 | odd | 2 |