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: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
Defining polynomial: | \(x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} - 226132003872 x^{7} - 3353576629440 x^{6} + 16796366777600 x^{5} + 99470801612800 x^{4} - 494039551757568 x^{3} - 493048066650624 x^{2} + 3193975642099712 x - 2385018853548032\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(19.0314\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −19.0314 | −1.68216 | −0.841078 | − | 0.540914i | \(-0.818079\pi\) | ||||
−0.841078 | + | 0.540914i | \(0.818079\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 234.195 | 1.82965 | ||||||||
\(5\) | 37.6075 | 0.134549 | 0.0672743 | − | 0.997735i | \(-0.478570\pi\) | ||||
0.0672743 | + | 0.997735i | \(0.478570\pi\) | |||||||
\(6\) | 513.848 | 0.971193 | ||||||||
\(7\) | 1158.54 | 1.27664 | 0.638318 | − | 0.769773i | \(-0.279630\pi\) | ||||
0.638318 | + | 0.769773i | \(0.279630\pi\) | |||||||
\(8\) | −2021.05 | −1.39560 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −715.724 | −0.226332 | ||||||||
\(11\) | 1618.00 | 0.366526 | 0.183263 | − | 0.983064i | \(-0.441334\pi\) | ||||
0.183263 | + | 0.983064i | \(0.441334\pi\) | |||||||
\(12\) | −6323.27 | −1.05635 | ||||||||
\(13\) | −7200.81 | −0.909033 | −0.454516 | − | 0.890738i | \(-0.650188\pi\) | ||||
−0.454516 | + | 0.890738i | \(0.650188\pi\) | |||||||
\(14\) | −22048.6 | −2.14750 | ||||||||
\(15\) | −1015.40 | −0.0776817 | ||||||||
\(16\) | 8486.39 | 0.517968 | ||||||||
\(17\) | 25827.4 | 1.27500 | 0.637499 | − | 0.770451i | \(-0.279969\pi\) | ||||
0.637499 | + | 0.770451i | \(0.279969\pi\) | |||||||
\(18\) | −13873.9 | −0.560719 | ||||||||
\(19\) | −45988.2 | −1.53819 | −0.769093 | − | 0.639137i | \(-0.779292\pi\) | ||||
−0.769093 | + | 0.639137i | \(0.779292\pi\) | |||||||
\(20\) | 8807.49 | 0.246177 | ||||||||
\(21\) | −31280.5 | −0.737067 | ||||||||
\(22\) | −30792.9 | −0.616554 | ||||||||
\(23\) | −53080.0 | −0.909670 | −0.454835 | − | 0.890576i | \(-0.650302\pi\) | ||||
−0.454835 | + | 0.890576i | \(0.650302\pi\) | |||||||
\(24\) | 54568.2 | 0.805750 | ||||||||
\(25\) | −76710.7 | −0.981897 | ||||||||
\(26\) | 137042. | 1.52913 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 271324. | 2.33580 | ||||||||
\(29\) | 164417. | 1.25185 | 0.625926 | − | 0.779882i | \(-0.284721\pi\) | ||||
0.625926 | + | 0.779882i | \(0.284721\pi\) | |||||||
\(30\) | 19324.6 | 0.130673 | ||||||||
\(31\) | 69217.7 | 0.417303 | 0.208651 | − | 0.977990i | \(-0.433093\pi\) | ||||
0.208651 | + | 0.977990i | \(0.433093\pi\) | |||||||
\(32\) | 97185.7 | 0.524297 | ||||||||
\(33\) | −43686.1 | −0.211614 | ||||||||
\(34\) | −491532. | −2.14475 | ||||||||
\(35\) | 43569.7 | 0.171770 | ||||||||
\(36\) | 170728. | 0.609883 | ||||||||
\(37\) | −382449. | −1.24127 | −0.620637 | − | 0.784098i | \(-0.713126\pi\) | ||||
−0.620637 | + | 0.784098i | \(0.713126\pi\) | |||||||
\(38\) | 875221. | 2.58747 | ||||||||
\(39\) | 194422. | 0.524830 | ||||||||
\(40\) | −76006.5 | −0.187776 | ||||||||
\(41\) | −531606. | −1.20461 | −0.602305 | − | 0.798266i | \(-0.705751\pi\) | ||||
−0.602305 | + | 0.798266i | \(0.705751\pi\) | |||||||
\(42\) | 595313. | 1.23986 | ||||||||
\(43\) | 562745. | 1.07937 | 0.539687 | − | 0.841866i | \(-0.318543\pi\) | ||||
0.539687 | + | 0.841866i | \(0.318543\pi\) | |||||||
\(44\) | 378929. | 0.670615 | ||||||||
\(45\) | 27415.9 | 0.0448496 | ||||||||
\(46\) | 1.01019e6 | 1.53021 | ||||||||
\(47\) | 1.23094e6 | 1.72939 | 0.864695 | − | 0.502298i | \(-0.167512\pi\) | ||||
0.864695 | + | 0.502298i | \(0.167512\pi\) | |||||||
\(48\) | −229133. | −0.299049 | ||||||||
\(49\) | 518668. | 0.629801 | ||||||||
\(50\) | 1.45991e6 | 1.65170 | ||||||||
\(51\) | −697340. | −0.736120 | ||||||||
\(52\) | −1.68639e6 | −1.66321 | ||||||||
\(53\) | 273502. | 0.252345 | 0.126173 | − | 0.992008i | \(-0.459731\pi\) | ||||
0.126173 | + | 0.992008i | \(0.459731\pi\) | |||||||
\(54\) | 374596. | 0.323731 | ||||||||
\(55\) | 60849.1 | 0.0493156 | ||||||||
\(56\) | −2.34146e6 | −1.78167 | ||||||||
\(57\) | 1.24168e6 | 0.888072 | ||||||||
\(58\) | −3.12909e6 | −2.10581 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −237802. | −0.142130 | ||||||||
\(61\) | 2.63599e6 | 1.48693 | 0.743464 | − | 0.668776i | \(-0.233182\pi\) | ||||
0.743464 | + | 0.668776i | \(0.233182\pi\) | |||||||
\(62\) | −1.31731e6 | −0.701968 | ||||||||
\(63\) | 844575. | 0.425546 | ||||||||
\(64\) | −2.93584e6 | −1.39992 | ||||||||
\(65\) | −270804. | −0.122309 | ||||||||
\(66\) | 831409. | 0.355968 | ||||||||
\(67\) | −4.66343e6 | −1.89428 | −0.947138 | − | 0.320825i | \(-0.896040\pi\) | ||||
−0.947138 | + | 0.320825i | \(0.896040\pi\) | |||||||
\(68\) | 6.04865e6 | 2.33280 | ||||||||
\(69\) | 1.43316e6 | 0.525198 | ||||||||
\(70\) | −829194. | −0.288944 | ||||||||
\(71\) | −5.88720e6 | −1.95211 | −0.976056 | − | 0.217521i | \(-0.930203\pi\) | ||||
−0.976056 | + | 0.217521i | \(0.930203\pi\) | |||||||
\(72\) | −1.47334e6 | −0.465200 | ||||||||
\(73\) | −3.00177e6 | −0.903124 | −0.451562 | − | 0.892240i | \(-0.649133\pi\) | ||||
−0.451562 | + | 0.892240i | \(0.649133\pi\) | |||||||
\(74\) | 7.27855e6 | 2.08802 | ||||||||
\(75\) | 2.07119e6 | 0.566898 | ||||||||
\(76\) | −1.07702e7 | −2.81434 | ||||||||
\(77\) | 1.87452e6 | 0.467921 | ||||||||
\(78\) | −3.70012e6 | −0.882846 | ||||||||
\(79\) | 5.62846e6 | 1.28438 | 0.642192 | − | 0.766544i | \(-0.278025\pi\) | ||||
0.642192 | + | 0.766544i | \(0.278025\pi\) | |||||||
\(80\) | 319152. | 0.0696919 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.01172e7 | 2.02634 | ||||||||
\(83\) | −5.80414e6 | −1.11420 | −0.557102 | − | 0.830444i | \(-0.688087\pi\) | ||||
−0.557102 | + | 0.830444i | \(0.688087\pi\) | |||||||
\(84\) | −7.32575e6 | −1.34857 | ||||||||
\(85\) | 971304. | 0.171549 | ||||||||
\(86\) | −1.07098e7 | −1.81568 | ||||||||
\(87\) | −4.43925e6 | −0.722757 | ||||||||
\(88\) | −3.27006e6 | −0.511524 | ||||||||
\(89\) | −5.58369e6 | −0.839569 | −0.419784 | − | 0.907624i | \(-0.637894\pi\) | ||||
−0.419784 | + | 0.907624i | \(0.637894\pi\) | |||||||
\(90\) | −521763. | −0.0754440 | ||||||||
\(91\) | −8.34241e6 | −1.16050 | ||||||||
\(92\) | −1.24311e7 | −1.66438 | ||||||||
\(93\) | −1.86888e6 | −0.240930 | ||||||||
\(94\) | −2.34265e7 | −2.90910 | ||||||||
\(95\) | −1.72950e6 | −0.206961 | ||||||||
\(96\) | −2.62401e6 | −0.302703 | ||||||||
\(97\) | 3.69012e6 | 0.410525 | 0.205262 | − | 0.978707i | \(-0.434195\pi\) | ||||
0.205262 | + | 0.978707i | \(0.434195\pi\) | |||||||
\(98\) | −9.87100e6 | −1.05942 | ||||||||
\(99\) | 1.17952e6 | 0.122175 | ||||||||
\(100\) | −1.79653e7 | −1.79653 | ||||||||
\(101\) | 1.00192e7 | 0.967632 | 0.483816 | − | 0.875170i | \(-0.339250\pi\) | ||||
0.483816 | + | 0.875170i | \(0.339250\pi\) | |||||||
\(102\) | 1.32714e7 | 1.23827 | ||||||||
\(103\) | −8.73833e6 | −0.787949 | −0.393974 | − | 0.919121i | \(-0.628900\pi\) | ||||
−0.393974 | + | 0.919121i | \(0.628900\pi\) | |||||||
\(104\) | 1.45532e7 | 1.26865 | ||||||||
\(105\) | −1.17638e6 | −0.0991713 | ||||||||
\(106\) | −5.20513e6 | −0.424484 | ||||||||
\(107\) | 3.46301e6 | 0.273282 | 0.136641 | − | 0.990621i | \(-0.456369\pi\) | ||||
0.136641 | + | 0.990621i | \(0.456369\pi\) | |||||||
\(108\) | −4.60966e6 | −0.352116 | ||||||||
\(109\) | 108153. | 0.00799916 | 0.00399958 | − | 0.999992i | \(-0.498727\pi\) | ||||
0.00399958 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(110\) | −1.15804e6 | −0.0829566 | ||||||||
\(111\) | 1.03261e7 | 0.716649 | ||||||||
\(112\) | 9.83181e6 | 0.661257 | ||||||||
\(113\) | 1.27204e6 | 0.0829328 | 0.0414664 | − | 0.999140i | \(-0.486797\pi\) | ||||
0.0414664 | + | 0.999140i | \(0.486797\pi\) | |||||||
\(114\) | −2.36310e7 | −1.49388 | ||||||||
\(115\) | −1.99621e6 | −0.122395 | ||||||||
\(116\) | 3.85056e7 | 2.29045 | ||||||||
\(117\) | −5.24939e6 | −0.303011 | ||||||||
\(118\) | −3.90866e6 | −0.218998 | ||||||||
\(119\) | 2.99220e7 | 1.62771 | ||||||||
\(120\) | 2.05217e6 | 0.108413 | ||||||||
\(121\) | −1.68692e7 | −0.865658 | ||||||||
\(122\) | −5.01667e7 | −2.50124 | ||||||||
\(123\) | 1.43534e7 | 0.695482 | ||||||||
\(124\) | 1.62104e7 | 0.763518 | ||||||||
\(125\) | −5.82298e6 | −0.266662 | ||||||||
\(126\) | −1.60735e7 | −0.715834 | ||||||||
\(127\) | 1.46482e7 | 0.634560 | 0.317280 | − | 0.948332i | \(-0.397230\pi\) | ||||
0.317280 | + | 0.948332i | \(0.397230\pi\) | |||||||
\(128\) | 4.34335e7 | 1.83058 | ||||||||
\(129\) | −1.51941e7 | −0.623177 | ||||||||
\(130\) | 5.15379e6 | 0.205743 | ||||||||
\(131\) | 3.44414e7 | 1.33854 | 0.669270 | − | 0.743019i | \(-0.266607\pi\) | ||||
0.669270 | + | 0.743019i | \(0.266607\pi\) | |||||||
\(132\) | −1.02311e7 | −0.387180 | ||||||||
\(133\) | −5.32791e7 | −1.96370 | ||||||||
\(134\) | 8.87517e7 | 3.18647 | ||||||||
\(135\) | −740228. | −0.0258939 | ||||||||
\(136\) | −5.21983e7 | −1.77939 | ||||||||
\(137\) | −4.41452e7 | −1.46677 | −0.733385 | − | 0.679814i | \(-0.762060\pi\) | ||||
−0.733385 | + | 0.679814i | \(0.762060\pi\) | |||||||
\(138\) | −2.72751e7 | −0.883465 | ||||||||
\(139\) | −1.22144e7 | −0.385762 | −0.192881 | − | 0.981222i | \(-0.561783\pi\) | ||||
−0.192881 | + | 0.981222i | \(0.561783\pi\) | |||||||
\(140\) | 1.02038e7 | 0.314279 | ||||||||
\(141\) | −3.32353e7 | −0.998463 | ||||||||
\(142\) | 1.12042e8 | 3.28376 | ||||||||
\(143\) | −1.16509e7 | −0.333184 | ||||||||
\(144\) | 6.18658e6 | 0.172656 | ||||||||
\(145\) | 6.18330e6 | 0.168435 | ||||||||
\(146\) | 5.71279e7 | 1.51920 | ||||||||
\(147\) | −1.40040e7 | −0.363616 | ||||||||
\(148\) | −8.95677e7 | −2.27109 | ||||||||
\(149\) | 4.50817e7 | 1.11647 | 0.558237 | − | 0.829682i | \(-0.311478\pi\) | ||||
0.558237 | + | 0.829682i | \(0.311478\pi\) | |||||||
\(150\) | −3.94177e7 | −0.953612 | ||||||||
\(151\) | −2.91236e7 | −0.688376 | −0.344188 | − | 0.938901i | \(-0.611846\pi\) | ||||
−0.344188 | + | 0.938901i | \(0.611846\pi\) | |||||||
\(152\) | 9.29443e7 | 2.14669 | ||||||||
\(153\) | 1.88282e7 | 0.424999 | ||||||||
\(154\) | −3.56748e7 | −0.787116 | ||||||||
\(155\) | 2.60310e6 | 0.0561475 | ||||||||
\(156\) | 4.55326e7 | 0.960255 | ||||||||
\(157\) | 7.43102e7 | 1.53250 | 0.766249 | − | 0.642544i | \(-0.222121\pi\) | ||||
0.766249 | + | 0.642544i | \(0.222121\pi\) | |||||||
\(158\) | −1.07118e8 | −2.16053 | ||||||||
\(159\) | −7.38455e6 | −0.145692 | ||||||||
\(160\) | 3.65491e6 | 0.0705434 | ||||||||
\(161\) | −6.14952e7 | −1.16132 | ||||||||
\(162\) | −1.01141e7 | −0.186906 | ||||||||
\(163\) | −5.15149e7 | −0.931700 | −0.465850 | − | 0.884864i | \(-0.654251\pi\) | ||||
−0.465850 | + | 0.884864i | \(0.654251\pi\) | |||||||
\(164\) | −1.24500e8 | −2.20401 | ||||||||
\(165\) | −1.64292e6 | −0.0284724 | ||||||||
\(166\) | 1.10461e8 | 1.87426 | ||||||||
\(167\) | 3.03652e7 | 0.504508 | 0.252254 | − | 0.967661i | \(-0.418828\pi\) | ||||
0.252254 | + | 0.967661i | \(0.418828\pi\) | |||||||
\(168\) | 6.32194e7 | 1.02865 | ||||||||
\(169\) | −1.08969e7 | −0.173660 | ||||||||
\(170\) | −1.84853e7 | −0.288573 | ||||||||
\(171\) | −3.35254e7 | −0.512729 | ||||||||
\(172\) | 1.31792e8 | 1.97488 | ||||||||
\(173\) | −9.23593e7 | −1.35619 | −0.678093 | − | 0.734976i | \(-0.737193\pi\) | ||||
−0.678093 | + | 0.734976i | \(0.737193\pi\) | |||||||
\(174\) | 8.44853e7 | 1.21579 | ||||||||
\(175\) | −8.88723e7 | −1.25353 | ||||||||
\(176\) | 1.37310e7 | 0.189849 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 1.06266e8 | 1.41229 | ||||||||
\(179\) | 6.85422e7 | 0.893249 | 0.446624 | − | 0.894722i | \(-0.352626\pi\) | ||||
0.446624 | + | 0.894722i | \(0.352626\pi\) | |||||||
\(180\) | 6.42066e6 | 0.0820590 | ||||||||
\(181\) | −3.27553e7 | −0.410588 | −0.205294 | − | 0.978700i | \(-0.565815\pi\) | ||||
−0.205294 | + | 0.978700i | \(0.565815\pi\) | |||||||
\(182\) | 1.58768e8 | 1.95215 | ||||||||
\(183\) | −7.11718e7 | −0.858478 | ||||||||
\(184\) | 1.07277e8 | 1.26954 | ||||||||
\(185\) | −1.43829e7 | −0.167012 | ||||||||
\(186\) | 3.55674e7 | 0.405282 | ||||||||
\(187\) | 4.17888e7 | 0.467320 | ||||||||
\(188\) | 2.88279e8 | 3.16418 | ||||||||
\(189\) | −2.28035e7 | −0.245689 | ||||||||
\(190\) | 3.29149e7 | 0.348141 | ||||||||
\(191\) | 2.83438e7 | 0.294335 | 0.147167 | − | 0.989112i | \(-0.452984\pi\) | ||||
0.147167 | + | 0.989112i | \(0.452984\pi\) | |||||||
\(192\) | 7.92677e7 | 0.808243 | ||||||||
\(193\) | −1.12860e8 | −1.13003 | −0.565013 | − | 0.825082i | \(-0.691129\pi\) | ||||
−0.565013 | + | 0.825082i | \(0.691129\pi\) | |||||||
\(194\) | −7.02282e7 | −0.690567 | ||||||||
\(195\) | 7.31172e6 | 0.0706152 | ||||||||
\(196\) | 1.21470e8 | 1.15232 | ||||||||
\(197\) | −1.98897e7 | −0.185352 | −0.0926760 | − | 0.995696i | \(-0.529542\pi\) | ||||
−0.0926760 | + | 0.995696i | \(0.529542\pi\) | |||||||
\(198\) | −2.24480e7 | −0.205518 | ||||||||
\(199\) | 1.48348e8 | 1.33443 | 0.667217 | − | 0.744863i | \(-0.267485\pi\) | ||||
0.667217 | + | 0.744863i | \(0.267485\pi\) | |||||||
\(200\) | 1.55036e8 | 1.37034 | ||||||||
\(201\) | 1.25913e8 | 1.09366 | ||||||||
\(202\) | −1.90680e8 | −1.62771 | ||||||||
\(203\) | 1.90483e8 | 1.59816 | ||||||||
\(204\) | −1.63314e8 | −1.34684 | ||||||||
\(205\) | −1.99924e7 | −0.162079 | ||||||||
\(206\) | 1.66303e8 | 1.32545 | ||||||||
\(207\) | −3.86953e7 | −0.303223 | ||||||||
\(208\) | −6.11089e7 | −0.470850 | ||||||||
\(209\) | −7.44091e7 | −0.563786 | ||||||||
\(210\) | 2.23882e7 | 0.166822 | ||||||||
\(211\) | −2.67425e8 | −1.95981 | −0.979905 | − | 0.199465i | \(-0.936079\pi\) | ||||
−0.979905 | + | 0.199465i | \(0.936079\pi\) | |||||||
\(212\) | 6.40528e7 | 0.461703 | ||||||||
\(213\) | 1.58954e8 | 1.12705 | ||||||||
\(214\) | −6.59061e7 | −0.459703 | ||||||||
\(215\) | 2.11634e7 | 0.145228 | ||||||||
\(216\) | 3.97802e7 | 0.268583 | ||||||||
\(217\) | 8.01913e7 | 0.532744 | ||||||||
\(218\) | −2.05830e6 | −0.0134558 | ||||||||
\(219\) | 8.10478e7 | 0.521419 | ||||||||
\(220\) | 1.42506e7 | 0.0902303 | ||||||||
\(221\) | −1.85978e8 | −1.15901 | ||||||||
\(222\) | −1.96521e8 | −1.20552 | ||||||||
\(223\) | −2.62238e8 | −1.58354 | −0.791768 | − | 0.610822i | \(-0.790839\pi\) | ||||
−0.791768 | + | 0.610822i | \(0.790839\pi\) | |||||||
\(224\) | 1.12593e8 | 0.669337 | ||||||||
\(225\) | −5.59221e7 | −0.327299 | ||||||||
\(226\) | −2.42087e7 | −0.139506 | ||||||||
\(227\) | −3.00342e7 | −0.170422 | −0.0852109 | − | 0.996363i | \(-0.527156\pi\) | ||||
−0.0852109 | + | 0.996363i | \(0.527156\pi\) | |||||||
\(228\) | 2.90796e8 | 1.62486 | ||||||||
\(229\) | −1.22290e8 | −0.672925 | −0.336463 | − | 0.941697i | \(-0.609231\pi\) | ||||
−0.336463 | + | 0.941697i | \(0.609231\pi\) | |||||||
\(230\) | 3.79907e7 | 0.205887 | ||||||||
\(231\) | −5.06120e7 | −0.270154 | ||||||||
\(232\) | −3.32294e8 | −1.74709 | ||||||||
\(233\) | −1.17471e8 | −0.608396 | −0.304198 | − | 0.952609i | \(-0.598388\pi\) | ||||
−0.304198 | + | 0.952609i | \(0.598388\pi\) | |||||||
\(234\) | 9.99033e7 | 0.509712 | ||||||||
\(235\) | 4.62924e7 | 0.232687 | ||||||||
\(236\) | 4.80988e7 | 0.238200 | ||||||||
\(237\) | −1.51968e8 | −0.741539 | ||||||||
\(238\) | −5.69459e8 | −2.73806 | ||||||||
\(239\) | 1.02120e8 | 0.483859 | 0.241930 | − | 0.970294i | \(-0.422220\pi\) | ||||
0.241930 | + | 0.970294i | \(0.422220\pi\) | |||||||
\(240\) | −8.61710e6 | −0.0402367 | ||||||||
\(241\) | −1.01574e8 | −0.467439 | −0.233719 | − | 0.972304i | \(-0.575090\pi\) | ||||
−0.233719 | + | 0.972304i | \(0.575090\pi\) | |||||||
\(242\) | 3.21046e8 | 1.45617 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 6.17337e8 | 2.72056 | ||||||||
\(245\) | 1.95058e7 | 0.0847389 | ||||||||
\(246\) | −2.73165e8 | −1.16991 | ||||||||
\(247\) | 3.31152e8 | 1.39826 | ||||||||
\(248\) | −1.39892e8 | −0.582388 | ||||||||
\(249\) | 1.56712e8 | 0.643286 | ||||||||
\(250\) | 1.10820e8 | 0.448566 | ||||||||
\(251\) | −4.09066e8 | −1.63281 | −0.816405 | − | 0.577480i | \(-0.804036\pi\) | ||||
−0.816405 | + | 0.577480i | \(0.804036\pi\) | |||||||
\(252\) | 1.97795e8 | 0.778599 | ||||||||
\(253\) | −8.58837e7 | −0.333418 | ||||||||
\(254\) | −2.78777e8 | −1.06743 | ||||||||
\(255\) | −2.62252e7 | −0.0990440 | ||||||||
\(256\) | −4.50813e8 | −1.67941 | ||||||||
\(257\) | −5.16514e8 | −1.89809 | −0.949043 | − | 0.315147i | \(-0.897946\pi\) | ||||
−0.949043 | + | 0.315147i | \(0.897946\pi\) | |||||||
\(258\) | 2.89166e8 | 1.04828 | ||||||||
\(259\) | −4.43082e8 | −1.58465 | ||||||||
\(260\) | −6.34211e7 | −0.223783 | ||||||||
\(261\) | 1.19860e8 | 0.417284 | ||||||||
\(262\) | −6.55469e8 | −2.25163 | ||||||||
\(263\) | −5.42714e8 | −1.83961 | −0.919805 | − | 0.392377i | \(-0.871653\pi\) | ||||
−0.919805 | + | 0.392377i | \(0.871653\pi\) | |||||||
\(264\) | 8.82916e7 | 0.295329 | ||||||||
\(265\) | 1.02857e7 | 0.0339527 | ||||||||
\(266\) | 1.01398e9 | 3.30326 | ||||||||
\(267\) | 1.50760e8 | 0.484725 | ||||||||
\(268\) | −1.09215e9 | −3.46586 | ||||||||
\(269\) | 1.04494e8 | 0.327309 | 0.163655 | − | 0.986518i | \(-0.447672\pi\) | ||||
0.163655 | + | 0.986518i | \(0.447672\pi\) | |||||||
\(270\) | 1.40876e7 | 0.0435576 | ||||||||
\(271\) | 6.80419e7 | 0.207675 | 0.103837 | − | 0.994594i | \(-0.466888\pi\) | ||||
0.103837 | + | 0.994594i | \(0.466888\pi\) | |||||||
\(272\) | 2.19181e8 | 0.660408 | ||||||||
\(273\) | 2.25245e8 | 0.670017 | ||||||||
\(274\) | 8.40147e8 | 2.46733 | ||||||||
\(275\) | −1.24118e8 | −0.359891 | ||||||||
\(276\) | 3.35639e8 | 0.960928 | ||||||||
\(277\) | −2.90966e8 | −0.822553 | −0.411276 | − | 0.911511i | \(-0.634917\pi\) | ||||
−0.411276 | + | 0.911511i | \(0.634917\pi\) | |||||||
\(278\) | 2.32457e8 | 0.648913 | ||||||||
\(279\) | 5.04597e7 | 0.139101 | ||||||||
\(280\) | −8.80564e7 | −0.239722 | ||||||||
\(281\) | −6.50736e7 | −0.174958 | −0.0874788 | − | 0.996166i | \(-0.527881\pi\) | ||||
−0.0874788 | + | 0.996166i | \(0.527881\pi\) | |||||||
\(282\) | 6.32514e8 | 1.67957 | ||||||||
\(283\) | 5.18818e8 | 1.36070 | 0.680350 | − | 0.732887i | \(-0.261828\pi\) | ||||
0.680350 | + | 0.732887i | \(0.261828\pi\) | |||||||
\(284\) | −1.37875e9 | −3.57168 | ||||||||
\(285\) | 4.66965e7 | 0.119489 | ||||||||
\(286\) | 2.21734e8 | 0.560468 | ||||||||
\(287\) | −6.15886e8 | −1.53785 | ||||||||
\(288\) | 7.08483e7 | 0.174766 | ||||||||
\(289\) | 2.56716e8 | 0.625620 | ||||||||
\(290\) | −1.17677e8 | −0.283334 | ||||||||
\(291\) | −9.96332e7 | −0.237017 | ||||||||
\(292\) | −7.03000e8 | −1.65240 | ||||||||
\(293\) | 2.50544e7 | 0.0581900 | 0.0290950 | − | 0.999577i | \(-0.490737\pi\) | ||||
0.0290950 | + | 0.999577i | \(0.490737\pi\) | |||||||
\(294\) | 2.66517e8 | 0.611659 | ||||||||
\(295\) | 7.72379e6 | 0.0175167 | ||||||||
\(296\) | 7.72946e8 | 1.73232 | ||||||||
\(297\) | −3.18472e7 | −0.0705380 | ||||||||
\(298\) | −8.57969e8 | −1.87808 | ||||||||
\(299\) | 3.82219e8 | 0.826919 | ||||||||
\(300\) | 4.85062e8 | 1.03723 | ||||||||
\(301\) | 6.51961e8 | 1.37797 | ||||||||
\(302\) | 5.54264e8 | 1.15796 | ||||||||
\(303\) | −2.70520e8 | −0.558662 | ||||||||
\(304\) | −3.90274e8 | −0.796732 | ||||||||
\(305\) | 9.91331e7 | 0.200064 | ||||||||
\(306\) | −3.58327e8 | −0.714915 | ||||||||
\(307\) | −3.47020e8 | −0.684496 | −0.342248 | − | 0.939610i | \(-0.611188\pi\) | ||||
−0.342248 | + | 0.939610i | \(0.611188\pi\) | |||||||
\(308\) | 4.39003e8 | 0.856131 | ||||||||
\(309\) | 2.35935e8 | 0.454922 | ||||||||
\(310\) | −4.95408e7 | −0.0944489 | ||||||||
\(311\) | −1.38483e8 | −0.261058 | −0.130529 | − | 0.991445i | \(-0.541668\pi\) | ||||
−0.130529 | + | 0.991445i | \(0.541668\pi\) | |||||||
\(312\) | −3.92935e8 | −0.732453 | ||||||||
\(313\) | −3.52364e8 | −0.649511 | −0.324756 | − | 0.945798i | \(-0.605282\pi\) | ||||
−0.324756 | + | 0.945798i | \(0.605282\pi\) | |||||||
\(314\) | −1.41423e9 | −2.57790 | ||||||||
\(315\) | 3.17623e7 | 0.0572566 | ||||||||
\(316\) | 1.31816e9 | 2.34997 | ||||||||
\(317\) | −31157.4 | −5.49355e−5 0 | −2.74678e−5 | − | 1.00000i | \(-0.500009\pi\) | ||||
−2.74678e−5 | 1.00000i | \(0.500009\pi\) | ||||||||
\(318\) | 1.40539e8 | 0.245076 | ||||||||
\(319\) | 2.66027e8 | 0.458837 | ||||||||
\(320\) | −1.10410e8 | −0.188357 | ||||||||
\(321\) | −9.35014e7 | −0.157779 | ||||||||
\(322\) | 1.17034e9 | 1.95352 | ||||||||
\(323\) | −1.18776e9 | −1.96118 | ||||||||
\(324\) | 1.24461e8 | 0.203294 | ||||||||
\(325\) | 5.52379e8 | 0.892576 | ||||||||
\(326\) | 9.80402e8 | 1.56727 | ||||||||
\(327\) | −2.92012e6 | −0.00461832 | ||||||||
\(328\) | 1.07440e9 | 1.68115 | ||||||||
\(329\) | 1.42609e9 | 2.20780 | ||||||||
\(330\) | 3.12672e7 | 0.0478950 | ||||||||
\(331\) | 1.16652e9 | 1.76805 | 0.884026 | − | 0.467438i | \(-0.154823\pi\) | ||||
0.884026 | + | 0.467438i | \(0.154823\pi\) | |||||||
\(332\) | −1.35930e9 | −2.03860 | ||||||||
\(333\) | −2.78805e8 | −0.413758 | ||||||||
\(334\) | −5.77893e8 | −0.848662 | ||||||||
\(335\) | −1.75380e8 | −0.254872 | ||||||||
\(336\) | −2.65459e8 | −0.381777 | ||||||||
\(337\) | −4.15334e8 | −0.591143 | −0.295572 | − | 0.955321i | \(-0.595510\pi\) | ||||
−0.295572 | + | 0.955321i | \(0.595510\pi\) | |||||||
\(338\) | 2.07383e8 | 0.292123 | ||||||||
\(339\) | −3.43451e7 | −0.0478813 | ||||||||
\(340\) | 2.27475e8 | 0.313875 | ||||||||
\(341\) | 1.11994e8 | 0.152952 | ||||||||
\(342\) | 6.38036e8 | 0.862490 | ||||||||
\(343\) | −3.53209e8 | −0.472609 | ||||||||
\(344\) | −1.13733e9 | −1.50637 | ||||||||
\(345\) | 5.38976e7 | 0.0706647 | ||||||||
\(346\) | 1.75773e9 | 2.28132 | ||||||||
\(347\) | 7.92787e8 | 1.01860 | 0.509300 | − | 0.860589i | \(-0.329904\pi\) | ||||
0.509300 | + | 0.860589i | \(0.329904\pi\) | |||||||
\(348\) | −1.03965e9 | −1.32239 | ||||||||
\(349\) | 3.35615e7 | 0.0422622 | 0.0211311 | − | 0.999777i | \(-0.493273\pi\) | ||||
0.0211311 | + | 0.999777i | \(0.493273\pi\) | |||||||
\(350\) | 1.69137e9 | 2.10863 | ||||||||
\(351\) | 1.41733e8 | 0.174943 | ||||||||
\(352\) | 1.57247e8 | 0.192169 | ||||||||
\(353\) | −8.45067e8 | −1.02254 | −0.511269 | − | 0.859421i | \(-0.670825\pi\) | ||||
−0.511269 | + | 0.859421i | \(0.670825\pi\) | |||||||
\(354\) | 1.05534e8 | 0.126439 | ||||||||
\(355\) | −2.21403e8 | −0.262654 | ||||||||
\(356\) | −1.30767e9 | −1.53612 | ||||||||
\(357\) | −8.07895e8 | −0.939758 | ||||||||
\(358\) | −1.30446e9 | −1.50258 | ||||||||
\(359\) | −9.14770e8 | −1.04347 | −0.521736 | − | 0.853107i | \(-0.674716\pi\) | ||||
−0.521736 | + | 0.853107i | \(0.674716\pi\) | |||||||
\(360\) | −5.54087e7 | −0.0625921 | ||||||||
\(361\) | 1.22104e9 | 1.36602 | ||||||||
\(362\) | 6.23380e8 | 0.690673 | ||||||||
\(363\) | 4.55469e8 | 0.499788 | ||||||||
\(364\) | −1.95375e9 | −2.12332 | ||||||||
\(365\) | −1.12889e8 | −0.121514 | ||||||||
\(366\) | 1.35450e9 | 1.44409 | ||||||||
\(367\) | −1.55832e9 | −1.64561 | −0.822805 | − | 0.568324i | \(-0.807592\pi\) | ||||
−0.822805 | + | 0.568324i | \(0.807592\pi\) | |||||||
\(368\) | −4.50458e8 | −0.471180 | ||||||||
\(369\) | −3.87541e8 | −0.401537 | ||||||||
\(370\) | 2.73728e8 | 0.280940 | ||||||||
\(371\) | 3.16863e8 | 0.322153 | ||||||||
\(372\) | −4.37682e8 | −0.440817 | ||||||||
\(373\) | 1.33970e9 | 1.33667 | 0.668337 | − | 0.743858i | \(-0.267006\pi\) | ||||
0.668337 | + | 0.743858i | \(0.267006\pi\) | |||||||
\(374\) | −7.95301e8 | −0.786106 | ||||||||
\(375\) | 1.57221e8 | 0.153957 | ||||||||
\(376\) | −2.48778e9 | −2.41354 | ||||||||
\(377\) | −1.18393e9 | −1.13797 | ||||||||
\(378\) | 4.33983e8 | 0.413287 | ||||||||
\(379\) | −3.03138e8 | −0.286024 | −0.143012 | − | 0.989721i | \(-0.545679\pi\) | ||||
−0.143012 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(380\) | −4.05041e8 | −0.378666 | ||||||||
\(381\) | −3.95503e8 | −0.366363 | ||||||||
\(382\) | −5.39423e8 | −0.495117 | ||||||||
\(383\) | −7.20550e8 | −0.655342 | −0.327671 | − | 0.944792i | \(-0.606264\pi\) | ||||
−0.327671 | + | 0.944792i | \(0.606264\pi\) | |||||||
\(384\) | −1.17270e9 | −1.05689 | ||||||||
\(385\) | 7.04960e7 | 0.0629581 | ||||||||
\(386\) | 2.14788e9 | 1.90088 | ||||||||
\(387\) | 4.10241e8 | 0.359791 | ||||||||
\(388\) | 8.64208e8 | 0.751117 | ||||||||
\(389\) | −5.84956e8 | −0.503848 | −0.251924 | − | 0.967747i | \(-0.581063\pi\) | ||||
−0.251924 | + | 0.967747i | \(0.581063\pi\) | |||||||
\(390\) | −1.39152e8 | −0.118786 | ||||||||
\(391\) | −1.37092e9 | −1.15983 | ||||||||
\(392\) | −1.04825e9 | −0.878951 | ||||||||
\(393\) | −9.29918e8 | −0.772807 | ||||||||
\(394\) | 3.78530e8 | 0.311791 | ||||||||
\(395\) | 2.11672e8 | 0.172812 | ||||||||
\(396\) | 2.76239e8 | 0.223538 | ||||||||
\(397\) | 7.98494e8 | 0.640479 | 0.320240 | − | 0.947337i | \(-0.396237\pi\) | ||||
0.320240 | + | 0.947337i | \(0.396237\pi\) | |||||||
\(398\) | −2.82328e9 | −2.24473 | ||||||||
\(399\) | 1.43854e9 | 1.13375 | ||||||||
\(400\) | −6.50997e8 | −0.508591 | ||||||||
\(401\) | −1.07381e9 | −0.831618 | −0.415809 | − | 0.909452i | \(-0.636501\pi\) | ||||
−0.415809 | + | 0.909452i | \(0.636501\pi\) | |||||||
\(402\) | −2.39630e9 | −1.83971 | ||||||||
\(403\) | −4.98423e8 | −0.379342 | ||||||||
\(404\) | 2.34646e9 | 1.77043 | ||||||||
\(405\) | 1.99862e7 | 0.0149499 | ||||||||
\(406\) | −3.62517e9 | −2.68836 | ||||||||
\(407\) | −6.18804e8 | −0.454959 | ||||||||
\(408\) | 1.40936e9 | 1.02733 | ||||||||
\(409\) | −6.01255e8 | −0.434537 | −0.217269 | − | 0.976112i | \(-0.569715\pi\) | ||||
−0.217269 | + | 0.976112i | \(0.569715\pi\) | |||||||
\(410\) | 3.80483e8 | 0.272642 | ||||||||
\(411\) | 1.19192e9 | 0.846840 | ||||||||
\(412\) | −2.04647e9 | −1.44167 | ||||||||
\(413\) | 2.37939e8 | 0.166204 | ||||||||
\(414\) | 7.36427e8 | 0.510069 | ||||||||
\(415\) | −2.18279e8 | −0.149915 | ||||||||
\(416\) | −6.99815e8 | −0.476603 | ||||||||
\(417\) | 3.29788e8 | 0.222720 | ||||||||
\(418\) | 1.41611e9 | 0.948376 | ||||||||
\(419\) | 1.42631e9 | 0.947251 | 0.473626 | − | 0.880726i | \(-0.342945\pi\) | ||||
0.473626 | + | 0.880726i | \(0.342945\pi\) | |||||||
\(420\) | −2.75503e8 | −0.181449 | ||||||||
\(421\) | −6.51184e8 | −0.425320 | −0.212660 | − | 0.977126i | \(-0.568213\pi\) | ||||
−0.212660 | + | 0.977126i | \(0.568213\pi\) | |||||||
\(422\) | 5.08948e9 | 3.29671 | ||||||||
\(423\) | 8.97352e8 | 0.576463 | ||||||||
\(424\) | −5.52760e8 | −0.352173 | ||||||||
\(425\) | −1.98124e9 | −1.25192 | ||||||||
\(426\) | −3.02513e9 | −1.89588 | ||||||||
\(427\) | 3.05390e9 | 1.89827 | ||||||||
\(428\) | 8.11021e8 | 0.500010 | ||||||||
\(429\) | 3.14575e8 | 0.192364 | ||||||||
\(430\) | −4.02770e8 | −0.244297 | ||||||||
\(431\) | 1.75470e9 | 1.05568 | 0.527841 | − | 0.849343i | \(-0.323002\pi\) | ||||
0.527841 | + | 0.849343i | \(0.323002\pi\) | |||||||
\(432\) | −1.67038e8 | −0.0996830 | ||||||||
\(433\) | 9.35278e8 | 0.553647 | 0.276824 | − | 0.960921i | \(-0.410718\pi\) | ||||
0.276824 | + | 0.960921i | \(0.410718\pi\) | |||||||
\(434\) | −1.52616e9 | −0.896158 | ||||||||
\(435\) | −1.66949e8 | −0.0972461 | ||||||||
\(436\) | 2.53288e7 | 0.0146357 | ||||||||
\(437\) | 2.44106e9 | 1.39924 | ||||||||
\(438\) | −1.54245e9 | −0.877108 | ||||||||
\(439\) | 8.68080e8 | 0.489704 | 0.244852 | − | 0.969560i | \(-0.421261\pi\) | ||||
0.244852 | + | 0.969560i | \(0.421261\pi\) | |||||||
\(440\) | −1.22979e8 | −0.0688249 | ||||||||
\(441\) | 3.78109e8 | 0.209934 | ||||||||
\(442\) | 3.53943e9 | 1.94964 | ||||||||
\(443\) | 8.22011e8 | 0.449226 | 0.224613 | − | 0.974448i | \(-0.427888\pi\) | ||||
0.224613 | + | 0.974448i | \(0.427888\pi\) | |||||||
\(444\) | 2.41833e9 | 1.31122 | ||||||||
\(445\) | −2.09989e8 | −0.112963 | ||||||||
\(446\) | 4.99076e9 | 2.66376 | ||||||||
\(447\) | −1.21721e9 | −0.644596 | ||||||||
\(448\) | −3.40128e9 | −1.78719 | ||||||||
\(449\) | 1.57362e9 | 0.820422 | 0.410211 | − | 0.911991i | \(-0.365455\pi\) | ||||
0.410211 | + | 0.911991i | \(0.365455\pi\) | |||||||
\(450\) | 1.06428e9 | 0.550568 | ||||||||
\(451\) | −8.60140e8 | −0.441521 | ||||||||
\(452\) | 2.97906e8 | 0.151738 | ||||||||
\(453\) | 7.86338e8 | 0.397434 | ||||||||
\(454\) | 5.71593e8 | 0.286676 | ||||||||
\(455\) | −3.13737e8 | −0.156144 | ||||||||
\(456\) | −2.50950e9 | −1.23939 | ||||||||
\(457\) | 2.23657e9 | 1.09616 | 0.548081 | − | 0.836425i | \(-0.315358\pi\) | ||||
0.548081 | + | 0.836425i | \(0.315358\pi\) | |||||||
\(458\) | 2.32735e9 | 1.13197 | ||||||||
\(459\) | −5.08361e8 | −0.245373 | ||||||||
\(460\) | −4.67502e8 | −0.223940 | ||||||||
\(461\) | 3.55618e9 | 1.69056 | 0.845280 | − | 0.534324i | \(-0.179434\pi\) | ||||
0.845280 | + | 0.534324i | \(0.179434\pi\) | |||||||
\(462\) | 9.63219e8 | 0.454442 | ||||||||
\(463\) | −3.48898e9 | −1.63367 | −0.816836 | − | 0.576870i | \(-0.804274\pi\) | ||||
−0.816836 | + | 0.576870i | \(0.804274\pi\) | |||||||
\(464\) | 1.39531e9 | 0.648420 | ||||||||
\(465\) | −7.02838e7 | −0.0324168 | ||||||||
\(466\) | 2.23565e9 | 1.02342 | ||||||||
\(467\) | −9.44654e8 | −0.429204 | −0.214602 | − | 0.976702i | \(-0.568845\pi\) | ||||
−0.214602 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(468\) | −1.22938e9 | −0.554404 | ||||||||
\(469\) | −5.40276e9 | −2.41830 | ||||||||
\(470\) | −8.81010e8 | −0.391416 | ||||||||
\(471\) | −2.00638e9 | −0.884788 | ||||||||
\(472\) | −4.15080e8 | −0.181692 | ||||||||
\(473\) | 9.10523e8 | 0.395619 | ||||||||
\(474\) | 2.89217e9 | 1.24738 | ||||||||
\(475\) | 3.52779e9 | 1.51034 | ||||||||
\(476\) | 7.00760e9 | 2.97814 | ||||||||
\(477\) | 1.99383e8 | 0.0841150 | ||||||||
\(478\) | −1.94349e9 | −0.813927 | ||||||||
\(479\) | 3.10871e8 | 0.129243 | 0.0646213 | − | 0.997910i | \(-0.479416\pi\) | ||||
0.0646213 | + | 0.997910i | \(0.479416\pi\) | |||||||
\(480\) | −9.86825e7 | −0.0407283 | ||||||||
\(481\) | 2.75394e9 | 1.12836 | ||||||||
\(482\) | 1.93311e9 | 0.786305 | ||||||||
\(483\) | 1.66037e9 | 0.670487 | ||||||||
\(484\) | −3.95069e9 | −1.58385 | ||||||||
\(485\) | 1.38776e8 | 0.0552356 | ||||||||
\(486\) | 2.73080e8 | 0.107910 | ||||||||
\(487\) | −2.73852e9 | −1.07440 | −0.537198 | − | 0.843456i | \(-0.680517\pi\) | ||||
−0.537198 | + | 0.843456i | \(0.680517\pi\) | |||||||
\(488\) | −5.32746e9 | −2.07516 | ||||||||
\(489\) | 1.39090e9 | 0.537917 | ||||||||
\(490\) | −3.71224e8 | −0.142544 | ||||||||
\(491\) | −3.51022e8 | −0.133829 | −0.0669143 | − | 0.997759i | \(-0.521315\pi\) | ||||
−0.0669143 | + | 0.997759i | \(0.521315\pi\) | |||||||
\(492\) | 3.36149e9 | 1.27249 | ||||||||
\(493\) | 4.24646e9 | 1.59611 | ||||||||
\(494\) | −6.30230e9 | −2.35209 | ||||||||
\(495\) | 4.43590e7 | 0.0164385 | ||||||||
\(496\) | 5.87408e8 | 0.216150 | ||||||||
\(497\) | −6.82055e9 | −2.49214 | ||||||||
\(498\) | −2.98245e9 | −1.08211 | ||||||||
\(499\) | −4.09829e9 | −1.47656 | −0.738280 | − | 0.674495i | \(-0.764362\pi\) | ||||
−0.738280 | + | 0.674495i | \(0.764362\pi\) | |||||||
\(500\) | −1.36371e9 | −0.487897 | ||||||||
\(501\) | −8.19860e8 | −0.291278 | ||||||||
\(502\) | 7.78511e9 | 2.74664 | ||||||||
\(503\) | −3.66315e9 | −1.28341 | −0.641707 | − | 0.766950i | \(-0.721774\pi\) | ||||
−0.641707 | + | 0.766950i | \(0.721774\pi\) | |||||||
\(504\) | −1.70692e9 | −0.593892 | ||||||||
\(505\) | 3.76799e8 | 0.130194 | ||||||||
\(506\) | 1.63449e9 | 0.560861 | ||||||||
\(507\) | 2.94216e8 | 0.100263 | ||||||||
\(508\) | 3.43055e9 | 1.16102 | ||||||||
\(509\) | −2.18735e9 | −0.735202 | −0.367601 | − | 0.929984i | \(-0.619821\pi\) | ||||
−0.367601 | + | 0.929984i | \(0.619821\pi\) | |||||||
\(510\) | 4.99103e8 | 0.166608 | ||||||||
\(511\) | −3.47767e9 | −1.15296 | ||||||||
\(512\) | 3.02013e9 | 0.994446 | ||||||||
\(513\) | 9.05186e8 | 0.296024 | ||||||||
\(514\) | 9.82999e9 | 3.19288 | ||||||||
\(515\) | −3.28627e8 | −0.106017 | ||||||||
\(516\) | −3.55839e9 | −1.14019 | ||||||||
\(517\) | 1.99166e9 | 0.633867 | ||||||||
\(518\) | 8.43248e9 | 2.66564 | ||||||||
\(519\) | 2.49370e9 | 0.782994 | ||||||||
\(520\) | 5.47308e8 | 0.170695 | ||||||||
\(521\) | 2.54763e9 | 0.789231 | 0.394615 | − | 0.918846i | \(-0.370878\pi\) | ||||
0.394615 | + | 0.918846i | \(0.370878\pi\) | |||||||
\(522\) | −2.28110e9 | −0.701937 | ||||||||
\(523\) | 1.00934e9 | 0.308519 | 0.154259 | − | 0.988030i | \(-0.450701\pi\) | ||||
0.154259 | + | 0.988030i | \(0.450701\pi\) | |||||||
\(524\) | 8.06601e9 | 2.44906 | ||||||||
\(525\) | 2.39955e9 | 0.723723 | ||||||||
\(526\) | 1.03286e10 | 3.09451 | ||||||||
\(527\) | 1.78771e9 | 0.532060 | ||||||||
\(528\) | −3.70737e8 | −0.109609 | ||||||||
\(529\) | −5.87336e8 | −0.172501 | ||||||||
\(530\) | −1.95752e8 | −0.0571138 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | −1.24777e10 | −3.59289 | ||||||||
\(533\) | 3.82799e9 | 1.09503 | ||||||||
\(534\) | −2.86917e9 | −0.815384 | ||||||||
\(535\) | 1.30235e8 | 0.0367697 | ||||||||
\(536\) | 9.42500e9 | 2.64365 | ||||||||
\(537\) | −1.85064e9 | −0.515717 | ||||||||
\(538\) | −1.98867e9 | −0.550585 | ||||||||
\(539\) | 8.39207e8 | 0.230839 | ||||||||
\(540\) | −1.73358e8 | −0.0473768 | ||||||||
\(541\) | −9.25297e8 | −0.251241 | −0.125621 | − | 0.992078i | \(-0.540092\pi\) | ||||
−0.125621 | + | 0.992078i | \(0.540092\pi\) | |||||||
\(542\) | −1.29493e9 | −0.349341 | ||||||||
\(543\) | 8.84393e8 | 0.237053 | ||||||||
\(544\) | 2.51005e9 | 0.668477 | ||||||||
\(545\) | 4.06735e6 | 0.00107628 | ||||||||
\(546\) | −4.28674e9 | −1.12707 | ||||||||
\(547\) | −5.27884e9 | −1.37906 | −0.689530 | − | 0.724257i | \(-0.742183\pi\) | ||||
−0.689530 | + | 0.724257i | \(0.742183\pi\) | |||||||
\(548\) | −1.03386e10 | −2.68367 | ||||||||
\(549\) | 1.92164e9 | 0.495642 | ||||||||
\(550\) | 2.36215e9 | 0.605393 | ||||||||
\(551\) | −7.56123e9 | −1.92558 | ||||||||
\(552\) | −2.89648e9 | −0.732967 | ||||||||
\(553\) | 6.52079e9 | 1.63969 | ||||||||
\(554\) | 5.53751e9 | 1.38366 | ||||||||
\(555\) | 3.88339e8 | 0.0964242 | ||||||||
\(556\) | −2.86055e9 | −0.705810 | ||||||||
\(557\) | 3.38179e9 | 0.829190 | 0.414595 | − | 0.910006i | \(-0.363923\pi\) | ||||
0.414595 | + | 0.910006i | \(0.363923\pi\) | |||||||
\(558\) | −9.60320e8 | −0.233989 | ||||||||
\(559\) | −4.05222e9 | −0.981186 | ||||||||
\(560\) | 3.69750e8 | 0.0889713 | ||||||||
\(561\) | −1.12830e9 | −0.269807 | ||||||||
\(562\) | 1.23844e9 | 0.294306 | ||||||||
\(563\) | −8.68855e7 | −0.0205196 | −0.0102598 | − | 0.999947i | \(-0.503266\pi\) | ||||
−0.0102598 | + | 0.999947i | \(0.503266\pi\) | |||||||
\(564\) | −7.78354e9 | −1.82684 | ||||||||
\(565\) | 4.78383e7 | 0.0111585 | ||||||||
\(566\) | −9.87385e9 | −2.28891 | ||||||||
\(567\) | 6.15695e8 | 0.141849 | ||||||||
\(568\) | 1.18983e10 | 2.72437 | ||||||||
\(569\) | 3.35876e9 | 0.764338 | 0.382169 | − | 0.924092i | \(-0.375177\pi\) | ||||
0.382169 | + | 0.924092i | \(0.375177\pi\) | |||||||
\(570\) | −8.88702e8 | −0.200999 | ||||||||
\(571\) | −4.94562e9 | −1.11172 | −0.555859 | − | 0.831277i | \(-0.687610\pi\) | ||||
−0.555859 | + | 0.831277i | \(0.687610\pi\) | |||||||
\(572\) | −2.72859e9 | −0.609611 | ||||||||
\(573\) | −7.65283e8 | −0.169934 | ||||||||
\(574\) | 1.17212e10 | 2.58690 | ||||||||
\(575\) | 4.07180e9 | 0.893202 | ||||||||
\(576\) | −2.14023e9 | −0.466639 | ||||||||
\(577\) | −6.72074e9 | −1.45647 | −0.728235 | − | 0.685327i | \(-0.759659\pi\) | ||||
−0.728235 | + | 0.685327i | \(0.759659\pi\) | |||||||
\(578\) | −4.88567e9 | −1.05239 | ||||||||
\(579\) | 3.04721e9 | 0.652421 | ||||||||
\(580\) | 1.44810e9 | 0.308177 | ||||||||
\(581\) | −6.72432e9 | −1.42243 | ||||||||
\(582\) | 1.89616e9 | 0.398699 | ||||||||
\(583\) | 4.42527e8 | 0.0924911 | ||||||||
\(584\) | 6.06671e9 | 1.26040 | ||||||||
\(585\) | −1.97416e8 | −0.0407697 | ||||||||
\(586\) | −4.76822e8 | −0.0978846 | ||||||||
\(587\) | −9.21166e9 | −1.87977 | −0.939885 | − | 0.341491i | \(-0.889068\pi\) | ||||
−0.939885 | + | 0.341491i | \(0.889068\pi\) | |||||||
\(588\) | −3.27968e9 | −0.665290 | ||||||||
\(589\) | −3.18320e9 | −0.641889 | ||||||||
\(590\) | −1.46995e8 | −0.0294659 | ||||||||
\(591\) | 5.37023e8 | 0.107013 | ||||||||
\(592\) | −3.24561e9 | −0.642940 | ||||||||
\(593\) | −5.16913e9 | −1.01795 | −0.508974 | − | 0.860782i | \(-0.669975\pi\) | ||||
−0.508974 | + | 0.860782i | \(0.669975\pi\) | |||||||
\(594\) | 6.06097e8 | 0.118656 | ||||||||
\(595\) | 1.12529e9 | 0.219006 | ||||||||
\(596\) | 1.05579e10 | 2.04275 | ||||||||
\(597\) | −4.00541e9 | −0.770436 | ||||||||
\(598\) | −7.27417e9 | −1.39101 | ||||||||
\(599\) | −2.29633e9 | −0.436557 | −0.218278 | − | 0.975887i | \(-0.570044\pi\) | ||||
−0.218278 | + | 0.975887i | \(0.570044\pi\) | |||||||
\(600\) | −4.18597e9 | −0.791163 | ||||||||
\(601\) | 4.46476e9 | 0.838952 | 0.419476 | − | 0.907766i | \(-0.362214\pi\) | ||||
0.419476 | + | 0.907766i | \(0.362214\pi\) | |||||||
\(602\) | −1.24078e10 | −2.31796 | ||||||||
\(603\) | −3.39964e9 | −0.631426 | ||||||||
\(604\) | −6.82061e9 | −1.25949 | ||||||||
\(605\) | −6.34410e8 | −0.116473 | ||||||||
\(606\) | 5.14837e9 | 0.939757 | ||||||||
\(607\) | −2.99837e9 | −0.544158 | −0.272079 | − | 0.962275i | \(-0.587711\pi\) | ||||
−0.272079 | + | 0.962275i | \(0.587711\pi\) | |||||||
\(608\) | −4.46939e9 | −0.806466 | ||||||||
\(609\) | −5.14305e9 | −0.922699 | ||||||||
\(610\) | −1.88664e9 | −0.336539 | ||||||||
\(611\) | −8.86373e9 | −1.57207 | ||||||||
\(612\) | 4.40947e9 | 0.777600 | ||||||||
\(613\) | 8.71253e9 | 1.52768 | 0.763840 | − | 0.645405i | \(-0.223312\pi\) | ||||
0.763840 | + | 0.645405i | \(0.223312\pi\) | |||||||
\(614\) | 6.60429e9 | 1.15143 | ||||||||
\(615\) | 5.39794e8 | 0.0935761 | ||||||||
\(616\) | −3.78849e9 | −0.653031 | ||||||||
\(617\) | 3.68960e9 | 0.632385 | 0.316192 | − | 0.948695i | \(-0.397595\pi\) | ||||
0.316192 | + | 0.948695i | \(0.397595\pi\) | |||||||
\(618\) | −4.49018e9 | −0.765251 | ||||||||
\(619\) | 2.78943e9 | 0.472713 | 0.236357 | − | 0.971666i | \(-0.424047\pi\) | ||||
0.236357 | + | 0.971666i | \(0.424047\pi\) | |||||||
\(620\) | 6.09634e8 | 0.102730 | ||||||||
\(621\) | 1.04477e9 | 0.175066 | ||||||||
\(622\) | 2.63554e9 | 0.439140 | ||||||||
\(623\) | −6.46892e9 | −1.07182 | ||||||||
\(624\) | 1.64994e9 | 0.271845 | ||||||||
\(625\) | 5.77403e9 | 0.946018 | ||||||||
\(626\) | 6.70599e9 | 1.09258 | ||||||||
\(627\) | 2.00905e9 | 0.325502 | ||||||||
\(628\) | 1.74031e10 | 2.80393 | ||||||||
\(629\) | −9.87766e9 | −1.58262 | ||||||||
\(630\) | −6.04483e8 | −0.0963145 | ||||||||
\(631\) | 1.40846e9 | 0.223173 | 0.111587 | − | 0.993755i | \(-0.464407\pi\) | ||||
0.111587 | + | 0.993755i | \(0.464407\pi\) | |||||||
\(632\) | −1.13754e10 | −1.79249 | ||||||||
\(633\) | 7.22048e9 | 1.13150 | ||||||||
\(634\) | 592969. | 9.24101e−5 0 | ||||||||
\(635\) | 5.50884e8 | 0.0853792 | ||||||||
\(636\) | −1.72943e9 | −0.266564 | ||||||||
\(637\) | −3.73483e9 | −0.572510 | ||||||||
\(638\) | −5.06287e9 | −0.771835 | ||||||||
\(639\) | −4.29177e9 | −0.650704 | ||||||||
\(640\) | 1.63342e9 | 0.246303 | ||||||||
\(641\) | −8.08641e9 | −1.21270 | −0.606349 | − | 0.795199i | \(-0.707367\pi\) | ||||
−0.606349 | + | 0.795199i | \(0.707367\pi\) | |||||||
\(642\) | 1.77946e9 | 0.265410 | ||||||||
\(643\) | −5.86883e9 | −0.870590 | −0.435295 | − | 0.900288i | \(-0.643356\pi\) | ||||
−0.435295 | + | 0.900288i | \(0.643356\pi\) | |||||||
\(644\) | −1.44019e10 | −2.12480 | ||||||||
\(645\) | −5.71412e8 | −0.0838476 | ||||||||
\(646\) | 2.26047e10 | 3.29902 | ||||||||
\(647\) | 3.25260e9 | 0.472135 | 0.236067 | − | 0.971737i | \(-0.424141\pi\) | ||||
0.236067 | + | 0.971737i | \(0.424141\pi\) | |||||||
\(648\) | −1.07407e9 | −0.155067 | ||||||||
\(649\) | 3.32304e8 | 0.0477177 | ||||||||
\(650\) | −1.05126e10 | −1.50145 | ||||||||
\(651\) | −2.16517e9 | −0.307580 | ||||||||
\(652\) | −1.20645e10 | −1.70469 | ||||||||
\(653\) | −1.64182e9 | −0.230744 | −0.115372 | − | 0.993322i | \(-0.536806\pi\) | ||||
−0.115372 | + | 0.993322i | \(0.536806\pi\) | |||||||
\(654\) | 5.55741e7 | 0.00776874 | ||||||||
\(655\) | 1.29526e9 | 0.180099 | ||||||||
\(656\) | −4.51142e9 | −0.623950 | ||||||||
\(657\) | −2.18829e9 | −0.301041 | ||||||||
\(658\) | −2.71404e10 | −3.71387 | ||||||||
\(659\) | 4.63845e9 | 0.631355 | 0.315678 | − | 0.948866i | \(-0.397768\pi\) | ||||
0.315678 | + | 0.948866i | \(0.397768\pi\) | |||||||
\(660\) | −3.84765e8 | −0.0520945 | ||||||||
\(661\) | 9.44802e9 | 1.27244 | 0.636218 | − | 0.771510i | \(-0.280498\pi\) | ||||
0.636218 | + | 0.771510i | \(0.280498\pi\) | |||||||
\(662\) | −2.22006e10 | −2.97414 | ||||||||
\(663\) | 5.02141e9 | 0.669157 | ||||||||
\(664\) | 1.17304e10 | 1.55498 | ||||||||
\(665\) | −2.00369e9 | −0.264214 | ||||||||
\(666\) | 5.30606e9 | 0.696005 | ||||||||
\(667\) | −8.72725e9 | −1.13877 | ||||||||
\(668\) | 7.11138e9 | 0.923073 | ||||||||
\(669\) | 7.08042e9 | 0.914255 | ||||||||
\(670\) | 3.33773e9 | 0.428735 | ||||||||
\(671\) | 4.26505e9 | 0.544998 | ||||||||
\(672\) | −3.04002e9 | −0.386442 | ||||||||
\(673\) | 8.85543e9 | 1.11984 | 0.559921 | − | 0.828546i | \(-0.310831\pi\) | ||||
0.559921 | + | 0.828546i | \(0.310831\pi\) | |||||||
\(674\) | 7.90440e9 | 0.994395 | ||||||||
\(675\) | 1.50990e9 | 0.188966 | ||||||||
\(676\) | −2.55200e9 | −0.317737 | ||||||||
\(677\) | 1.90990e8 | 0.0236565 | 0.0118283 | − | 0.999930i | \(-0.496235\pi\) | ||||
0.0118283 | + | 0.999930i | \(0.496235\pi\) | |||||||
\(678\) | 6.53636e8 | 0.0805438 | ||||||||
\(679\) | 4.27515e9 | 0.524091 | ||||||||
\(680\) | −1.96305e9 | −0.239414 | ||||||||
\(681\) | 8.10922e8 | 0.0983930 | ||||||||
\(682\) | −2.13141e9 | −0.257290 | ||||||||
\(683\) | −3.13279e9 | −0.376235 | −0.188117 | − | 0.982147i | \(-0.560239\pi\) | ||||
−0.188117 | + | 0.982147i | \(0.560239\pi\) | |||||||
\(684\) | −7.85149e9 | −0.938114 | ||||||||
\(685\) | −1.66019e9 | −0.197352 | ||||||||
\(686\) | 6.72207e9 | 0.795003 | ||||||||
\(687\) | 3.30183e9 | 0.388513 | ||||||||
\(688\) | 4.77567e9 | 0.559081 | ||||||||
\(689\) | −1.96944e9 | −0.229390 | ||||||||
\(690\) | −1.02575e9 | −0.118869 | ||||||||
\(691\) | 1.83456e9 | 0.211524 | 0.105762 | − | 0.994391i | \(-0.466272\pi\) | ||||
0.105762 | + | 0.994391i | \(0.466272\pi\) | |||||||
\(692\) | −2.16301e10 | −2.48135 | ||||||||
\(693\) | 1.36652e9 | 0.155974 | ||||||||
\(694\) | −1.50879e10 | −1.71344 | ||||||||
\(695\) | −4.59352e8 | −0.0519038 | ||||||||
\(696\) | 8.97193e9 | 1.00868 | ||||||||
\(697\) | −1.37300e10 | −1.53587 | ||||||||
\(698\) | −6.38723e8 | −0.0710917 | ||||||||
\(699\) | 3.17173e9 | 0.351258 | ||||||||
\(700\) | −2.08135e10 | −2.29351 | ||||||||
\(701\) | 5.98660e9 | 0.656398 | 0.328199 | − | 0.944609i | \(-0.393558\pi\) | ||||
0.328199 | + | 0.944609i | \(0.393558\pi\) | |||||||
\(702\) | −2.69739e9 | −0.294282 | ||||||||
\(703\) | 1.75881e10 | 1.90931 | ||||||||
\(704\) | −4.75020e9 | −0.513107 | ||||||||
\(705\) | −1.24989e9 | −0.134342 | ||||||||
\(706\) | 1.60828e10 | 1.72007 | ||||||||
\(707\) | 1.16077e10 | 1.23531 | ||||||||
\(708\) | −1.29867e9 | −0.137525 | ||||||||
\(709\) | 6.41985e9 | 0.676493 | 0.338246 | − | 0.941058i | \(-0.390166\pi\) | ||||
0.338246 | + | 0.941058i | \(0.390166\pi\) | |||||||
\(710\) | 4.21361e9 | 0.441825 | ||||||||
\(711\) | 4.10315e9 | 0.428128 | ||||||||
\(712\) | 1.12849e10 | 1.17170 | ||||||||
\(713\) | −3.67408e9 | −0.379608 | ||||||||
\(714\) | 1.53754e10 | 1.58082 | ||||||||
\(715\) | −4.38162e8 | −0.0448295 | ||||||||
\(716\) | 1.60523e10 | 1.63433 | ||||||||
\(717\) | −2.75725e9 | −0.279356 | ||||||||
\(718\) | 1.74094e10 | 1.75528 | ||||||||
\(719\) | −1.53454e10 | −1.53967 | −0.769836 | − | 0.638242i | \(-0.779662\pi\) | ||||
−0.769836 | + | 0.638242i | \(0.779662\pi\) | |||||||
\(720\) | 2.32662e8 | 0.0232306 | ||||||||
\(721\) | −1.01237e10 | −1.00592 | ||||||||
\(722\) | −2.32382e10 | −2.29785 | ||||||||
\(723\) | 2.74251e9 | 0.269876 | ||||||||
\(724\) | −7.67113e9 | −0.751232 | ||||||||
\(725\) | −1.26125e10 | −1.22919 | ||||||||
\(726\) | −8.66823e9 | −0.840722 | ||||||||
\(727\) | 5.06244e8 | 0.0488640 | 0.0244320 | − | 0.999701i | \(-0.492222\pi\) | ||||
0.0244320 | + | 0.999701i | \(0.492222\pi\) | |||||||
\(728\) | 1.68604e10 | 1.61960 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 2.14844e9 | 0.204406 | ||||||||
\(731\) | 1.45342e10 | 1.37620 | ||||||||
\(732\) | −1.66681e10 | −1.57071 | ||||||||
\(733\) | −1.29579e10 | −1.21527 | −0.607633 | − | 0.794218i | \(-0.707881\pi\) | ||||
−0.607633 | + | 0.794218i | \(0.707881\pi\) | |||||||
\(734\) | 2.96571e10 | 2.76817 | ||||||||
\(735\) | −5.26657e8 | −0.0489240 | ||||||||
\(736\) | −5.15862e9 | −0.476937 | ||||||||
\(737\) | −7.54544e9 | −0.694302 | ||||||||
\(738\) | 7.37545e9 | 0.675447 | ||||||||
\(739\) | −3.46591e9 | −0.315909 | −0.157955 | − | 0.987446i | \(-0.550490\pi\) | ||||
−0.157955 | + | 0.987446i | \(0.550490\pi\) | |||||||
\(740\) | −3.36842e9 | −0.305573 | ||||||||
\(741\) | −8.94111e9 | −0.807287 | ||||||||
\(742\) | −6.03035e9 | −0.541912 | ||||||||
\(743\) | 4.65023e9 | 0.415924 | 0.207962 | − | 0.978137i | \(-0.433317\pi\) | ||||
0.207962 | + | 0.978137i | \(0.433317\pi\) | |||||||
\(744\) | 3.77709e9 | 0.336242 | ||||||||
\(745\) | 1.69541e9 | 0.150220 | ||||||||
\(746\) | −2.54963e10 | −2.24850 | ||||||||
\(747\) | −4.23122e9 | −0.371401 | ||||||||
\(748\) | 9.78674e9 | 0.855032 | ||||||||
\(749\) | 4.01204e9 | 0.348882 | ||||||||
\(750\) | −2.99213e9 | −0.258980 | ||||||||
\(751\) | 2.20118e10 | 1.89634 | 0.948169 | − | 0.317766i | \(-0.102933\pi\) | ||||
0.948169 | + | 0.317766i | \(0.102933\pi\) | |||||||
\(752\) | 1.04462e10 | 0.895769 | ||||||||
\(753\) | 1.10448e10 | 0.942703 | ||||||||
\(754\) | 2.25319e10 | 1.91425 | ||||||||
\(755\) | −1.09527e9 | −0.0926201 | ||||||||
\(756\) | −5.34047e9 | −0.449525 | ||||||||
\(757\) | 5.77225e9 | 0.483626 | 0.241813 | − | 0.970323i | \(-0.422258\pi\) | ||||
0.241813 | + | 0.970323i | \(0.422258\pi\) | |||||||
\(758\) | 5.76914e9 | 0.481137 | ||||||||
\(759\) | 2.31886e9 | 0.192499 | ||||||||
\(760\) | 3.49540e9 | 0.288835 | ||||||||
\(761\) | 5.11102e9 | 0.420398 | 0.210199 | − | 0.977659i | \(-0.432589\pi\) | ||||
0.210199 | + | 0.977659i | \(0.432589\pi\) | |||||||
\(762\) | 7.52698e9 | 0.616280 | ||||||||
\(763\) | 1.25299e8 | 0.0102120 | ||||||||
\(764\) | 6.63798e9 | 0.538529 | ||||||||
\(765\) | 7.08081e8 | 0.0571831 | ||||||||
\(766\) | 1.37131e10 | 1.10239 | ||||||||
\(767\) | −1.47889e9 | −0.118346 | ||||||||
\(768\) | 1.21720e10 | 0.969607 | ||||||||
\(769\) | 2.04941e9 | 0.162512 | 0.0812560 | − | 0.996693i | \(-0.474107\pi\) | ||||
0.0812560 | + | 0.996693i | \(0.474107\pi\) | |||||||
\(770\) | −1.34164e9 | −0.105905 | ||||||||
\(771\) | 1.39459e10 | 1.09586 | ||||||||
\(772\) | −2.64312e10 | −2.06755 | ||||||||
\(773\) | 2.05915e10 | 1.60346 | 0.801732 | − | 0.597683i | \(-0.203912\pi\) | ||||
0.801732 | + | 0.597683i | \(0.203912\pi\) | |||||||
\(774\) | −7.80747e9 | −0.605225 | ||||||||
\(775\) | −5.30974e9 | −0.409748 | ||||||||
\(776\) | −7.45790e9 | −0.572929 | ||||||||
\(777\) | 1.19632e10 | 0.914901 | ||||||||
\(778\) | 1.11326e10 | 0.847552 | ||||||||
\(779\) | 2.44476e10 | 1.85291 | ||||||||
\(780\) | 1.71237e9 | 0.129201 | ||||||||
\(781\) | −9.52551e9 | −0.715500 | ||||||||
\(782\) | 2.60905e10 | 1.95101 | ||||||||
\(783\) | −3.23622e9 | −0.240919 | ||||||||
\(784\) | 4.40162e9 | 0.326217 | ||||||||
\(785\) | 2.79462e9 | 0.206196 | ||||||||
\(786\) | 1.76977e10 | 1.29998 | ||||||||
\(787\) | −1.82710e10 | −1.33613 | −0.668067 | − | 0.744101i | \(-0.732878\pi\) | ||||
−0.668067 | + | 0.744101i | \(0.732878\pi\) | |||||||
\(788\) | −4.65808e9 | −0.339129 | ||||||||
\(789\) | 1.46533e10 | 1.06210 | ||||||||
\(790\) | −4.02842e9 | −0.290697 | ||||||||
\(791\) | 1.47371e9 | 0.105875 | ||||||||
\(792\) | −2.38387e9 | −0.170508 | ||||||||
\(793\) | −1.89813e10 | −1.35167 | ||||||||
\(794\) | −1.51965e10 | −1.07739 | ||||||||
\(795\) | −2.77715e8 | −0.0196026 | ||||||||
\(796\) | 3.47425e10 | 2.44155 | ||||||||
\(797\) | 2.36801e10 | 1.65684 | 0.828418 | − | 0.560110i | \(-0.189241\pi\) | ||||
0.828418 | + | 0.560110i | \(0.189241\pi\) | |||||||
\(798\) | −2.73774e10 | −1.90714 | ||||||||
\(799\) | 3.17919e10 | 2.20497 | ||||||||
\(800\) | −7.45518e9 | −0.514805 | ||||||||
\(801\) | −4.07051e9 | −0.279856 | ||||||||
\(802\) | 2.04362e10 | 1.39891 | ||||||||
\(803\) | −4.85687e9 | −0.331019 | ||||||||
\(804\) | 2.94881e10 | 2.00102 | ||||||||
\(805\) | −2.31268e9 | −0.156254 | ||||||||
\(806\) | 9.48570e9 | 0.638112 | ||||||||
\(807\) | −2.82134e9 | −0.188972 | ||||||||
\(808\) | −2.02493e10 | −1.35043 | ||||||||
\(809\) | 1.22571e10 | 0.813897 | 0.406949 | − | 0.913451i | \(-0.366593\pi\) | ||||
0.406949 | + | 0.913451i | \(0.366593\pi\) | |||||||
\(810\) | −3.80365e8 | −0.0251480 | ||||||||
\(811\) | −7.84590e9 | −0.516499 | −0.258250 | − | 0.966078i | \(-0.583146\pi\) | ||||
−0.258250 | + | 0.966078i | \(0.583146\pi\) | |||||||
\(812\) | 4.46102e10 | 2.92407 | ||||||||
\(813\) | −1.83713e9 | −0.119901 | ||||||||
\(814\) | 1.17767e10 | 0.765312 | ||||||||
\(815\) | −1.93735e9 | −0.125359 | ||||||||
\(816\) | −5.91790e9 | −0.381287 | ||||||||
\(817\) | −2.58796e10 | −1.66028 | ||||||||
\(818\) | 1.14427e10 | 0.730960 | ||||||||
\(819\) | −6.08162e9 | −0.386835 | ||||||||
\(820\) | −4.68212e9 | −0.296547 | ||||||||
\(821\) | −8.10180e9 | −0.510952 | −0.255476 | − | 0.966815i | \(-0.582232\pi\) | ||||
−0.255476 | + | 0.966815i | \(0.582232\pi\) | |||||||
\(822\) | −2.26840e10 | −1.42452 | ||||||||
\(823\) | 1.64265e9 | 0.102718 | 0.0513588 | − | 0.998680i | \(-0.483645\pi\) | ||||
0.0513588 | + | 0.998680i | \(0.483645\pi\) | |||||||
\(824\) | 1.76606e10 | 1.09966 | ||||||||
\(825\) | 3.35119e9 | 0.207783 | ||||||||
\(826\) | −4.52833e9 | −0.279581 | ||||||||
\(827\) | −2.72238e10 | −1.67371 | −0.836854 | − | 0.547427i | \(-0.815607\pi\) | ||||
−0.836854 | + | 0.547427i | \(0.815607\pi\) | |||||||
\(828\) | −9.06226e9 | −0.554792 | ||||||||
\(829\) | 1.28481e10 | 0.783245 | 0.391623 | − | 0.920126i | \(-0.371914\pi\) | ||||
0.391623 | + | 0.920126i | \(0.371914\pi\) | |||||||
\(830\) | 4.15416e9 | 0.252180 | ||||||||
\(831\) | 7.85609e9 | 0.474901 | ||||||||
\(832\) | 2.11404e10 | 1.27257 | ||||||||
\(833\) | 1.33959e10 | 0.802995 | ||||||||
\(834\) | −6.27634e9 | −0.374650 | ||||||||
\(835\) | 1.14196e9 | 0.0678809 | ||||||||
\(836\) | −1.74263e10 | −1.03153 | ||||||||
\(837\) | −1.36241e9 | −0.0803099 | ||||||||
\(838\) | −2.71447e10 | −1.59342 | ||||||||
\(839\) | −2.14886e10 | −1.25615 | −0.628073 | − | 0.778154i | \(-0.716156\pi\) | ||||
−0.628073 | + | 0.778154i | \(0.716156\pi\) | |||||||
\(840\) | 2.37752e9 | 0.138404 | ||||||||
\(841\) | 9.78301e9 | 0.567135 | ||||||||
\(842\) | 1.23930e10 | 0.715455 | ||||||||
\(843\) | 1.75699e9 | 0.101012 | ||||||||
\(844\) | −6.26297e10 | −3.58577 | ||||||||
\(845\) | −4.09805e8 | −0.0233657 | ||||||||
\(846\) | −1.70779e10 | −0.969701 | ||||||||
\(847\) | −1.95437e10 | −1.10513 | ||||||||
\(848\) | 2.32105e9 | 0.130707 | ||||||||
\(849\) | −1.40081e10 | −0.785601 | ||||||||
\(850\) | 3.77058e10 | 2.10592 | ||||||||
\(851\) | 2.03004e10 | 1.12915 | ||||||||
\(852\) | 3.72264e10 | 2.06211 | ||||||||
\(853\) | 7.06458e9 | 0.389731 | 0.194865 | − | 0.980830i | \(-0.437573\pi\) | ||||
0.194865 | + | 0.980830i | \(0.437573\pi\) | |||||||
\(854\) | −5.81200e10 | −3.19318 | ||||||||
\(855\) | −1.26081e9 | −0.0689870 | ||||||||
\(856\) | −6.99891e9 | −0.381393 | ||||||||
\(857\) | −1.97164e10 | −1.07003 | −0.535015 | − | 0.844843i | \(-0.679694\pi\) | ||||
−0.535015 | + | 0.844843i | \(0.679694\pi\) | |||||||
\(858\) | −5.98681e9 | −0.323586 | ||||||||
\(859\) | −1.48500e10 | −0.799376 | −0.399688 | − | 0.916651i | \(-0.630882\pi\) | ||||
−0.399688 | + | 0.916651i | \(0.630882\pi\) | |||||||
\(860\) | 4.95637e9 | 0.265717 | ||||||||
\(861\) | 1.66289e10 | 0.887877 | ||||||||
\(862\) | −3.33945e10 | −1.77582 | ||||||||
\(863\) | 1.20569e10 | 0.638552 | 0.319276 | − | 0.947662i | \(-0.396560\pi\) | ||||
0.319276 | + | 0.947662i | \(0.396560\pi\) | |||||||
\(864\) | −1.91291e9 | −0.100901 | ||||||||
\(865\) | −3.47340e9 | −0.182473 | ||||||||
\(866\) | −1.77997e10 | −0.931321 | ||||||||
\(867\) | −6.93133e9 | −0.361202 | ||||||||
\(868\) | 1.87804e10 | 0.974735 | ||||||||
\(869\) | 9.10687e9 | 0.470760 | ||||||||
\(870\) | 3.17728e9 | 0.163583 | ||||||||
\(871\) | 3.35804e10 | 1.72196 | ||||||||
\(872\) | −2.18581e8 | −0.0111636 | ||||||||
\(873\) | 2.69010e9 | 0.136842 | ||||||||
\(874\) | −4.64568e10 | −2.35374 | ||||||||
\(875\) | −6.74615e9 | −0.340430 | ||||||||
\(876\) | 1.89810e10 | 0.954014 | ||||||||
\(877\) | 3.18390e10 | 1.59390 | 0.796949 | − | 0.604046i | \(-0.206446\pi\) | ||||
0.796949 | + | 0.604046i | \(0.206446\pi\) | |||||||
\(878\) | −1.65208e10 | −0.823759 | ||||||||
\(879\) | −6.76470e8 | −0.0335960 | ||||||||
\(880\) | 5.16389e8 | 0.0255439 | ||||||||
\(881\) | −2.68011e10 | −1.32050 | −0.660248 | − | 0.751048i | \(-0.729549\pi\) | ||||
−0.660248 | + | 0.751048i | \(0.729549\pi\) | |||||||
\(882\) | −7.19596e9 | −0.353141 | ||||||||
\(883\) | −3.21062e10 | −1.56937 | −0.784686 | − | 0.619893i | \(-0.787176\pi\) | ||||
−0.784686 | + | 0.619893i | \(0.787176\pi\) | |||||||
\(884\) | −4.35552e10 | −2.12059 | ||||||||
\(885\) | −2.08542e8 | −0.0101133 | ||||||||
\(886\) | −1.56440e10 | −0.755667 | ||||||||
\(887\) | 1.26881e10 | 0.610468 | 0.305234 | − | 0.952277i | \(-0.401265\pi\) | ||||
0.305234 | + | 0.952277i | \(0.401265\pi\) | |||||||
\(888\) | −2.08696e10 | −1.00016 | ||||||||
\(889\) | 1.69706e10 | 0.810103 | ||||||||
\(890\) | 3.99638e9 | 0.190021 | ||||||||
\(891\) | 8.59874e8 | 0.0407251 | ||||||||
\(892\) | −6.14148e10 | −2.89732 | ||||||||
\(893\) | −5.66085e10 | −2.66012 | ||||||||
\(894\) | 2.31652e10 | 1.08431 | ||||||||
\(895\) | 2.57770e9 | 0.120185 | ||||||||
\(896\) | 5.03193e10 | 2.33699 | ||||||||
\(897\) | −1.03199e10 | −0.477422 | ||||||||
\(898\) | −2.99482e10 | −1.38008 | ||||||||
\(899\) | 1.13805e10 | 0.522401 | ||||||||
\(900\) | −1.30967e10 | −0.598842 | ||||||||
\(901\) | 7.06385e9 | 0.321740 | ||||||||
\(902\) | 1.63697e10 | 0.742708 | ||||||||
\(903\) | −1.76030e10 | −0.795570 | ||||||||
\(904\) | −2.57085e9 | −0.115741 | ||||||||
\(905\) | −1.23184e9 | −0.0552441 | ||||||||
\(906\) | −1.49651e10 | −0.668546 | ||||||||
\(907\) | −1.35224e10 | −0.601767 | −0.300884 | − | 0.953661i | \(-0.597282\pi\) | ||||
−0.300884 | + | 0.953661i | \(0.597282\pi\) | |||||||
\(908\) | −7.03385e9 | −0.311812 | ||||||||
\(909\) | 7.30403e9 | 0.322544 | ||||||||
\(910\) | 5.97087e9 | 0.262659 | ||||||||
\(911\) | 2.02421e10 | 0.887035 | 0.443517 | − | 0.896266i | \(-0.353730\pi\) | ||||
0.443517 | + | 0.896266i | \(0.353730\pi\) | |||||||
\(912\) | 1.05374e10 | 0.459993 | ||||||||
\(913\) | −9.39112e9 | −0.408385 | ||||||||
\(914\) | −4.25650e10 | −1.84392 | ||||||||
\(915\) | −2.67659e9 | −0.115507 | ||||||||
\(916\) | −2.86397e10 | −1.23122 | ||||||||
\(917\) | 3.99017e10 | 1.70883 | ||||||||
\(918\) | 9.67483e9 | 0.412756 | ||||||||
\(919\) | 3.59827e10 | 1.52929 | 0.764644 | − | 0.644453i | \(-0.222915\pi\) | ||||
0.764644 | + | 0.644453i | \(0.222915\pi\) | |||||||
\(920\) | 4.03442e9 | 0.170814 | ||||||||
\(921\) | 9.36955e9 | 0.395194 | ||||||||
\(922\) | −6.76791e10 | −2.84378 | ||||||||
\(923\) | 4.23926e10 | 1.77453 | ||||||||
\(924\) | −1.18531e10 | −0.494288 | ||||||||
\(925\) | 2.93379e10 | 1.21880 | ||||||||
\(926\) | 6.64002e10 | 2.74809 | ||||||||
\(927\) | −6.37024e9 | −0.262650 | ||||||||
\(928\) | 1.59790e10 | 0.656342 | ||||||||
\(929\) | 3.99605e10 | 1.63522 | 0.817609 | − | 0.575774i | \(-0.195299\pi\) | ||||
0.817609 | + | 0.575774i | \(0.195299\pi\) | |||||||
\(930\) | 1.33760e9 | 0.0545301 | ||||||||
\(931\) | −2.38526e10 | −0.968751 | ||||||||
\(932\) | −2.75112e10 | −1.11315 | ||||||||
\(933\) | 3.73905e9 | 0.150722 | ||||||||
\(934\) | 1.79781e10 | 0.721988 | ||||||||
\(935\) | 1.57157e9 | 0.0628773 | ||||||||
\(936\) | 1.06093e10 | 0.422882 | ||||||||
\(937\) | 2.19504e10 | 0.871674 | 0.435837 | − | 0.900026i | \(-0.356452\pi\) | ||||
0.435837 | + | 0.900026i | \(0.356452\pi\) | |||||||
\(938\) | 1.02822e11 | 4.06796 | ||||||||
\(939\) | 9.51384e9 | 0.374996 | ||||||||
\(940\) | 1.08415e10 | 0.425736 | ||||||||
\(941\) | −2.26436e10 | −0.885896 | −0.442948 | − | 0.896547i | \(-0.646067\pi\) | ||||
−0.442948 | + | 0.896547i | \(0.646067\pi\) | |||||||
\(942\) | 3.81842e10 | 1.48835 | ||||||||
\(943\) | 2.82177e10 | 1.09580 | ||||||||
\(944\) | 1.74293e9 | 0.0674337 | ||||||||
\(945\) | −8.57583e8 | −0.0330571 | ||||||||
\(946\) | −1.73286e10 | −0.665493 | ||||||||
\(947\) | 7.27658e9 | 0.278421 | 0.139211 | − | 0.990263i | \(-0.455543\pi\) | ||||
0.139211 | + | 0.990263i | \(0.455543\pi\) | |||||||
\(948\) | −3.55903e10 | −1.35676 | ||||||||
\(949\) | 2.16152e10 | 0.820969 | ||||||||
\(950\) | −6.71388e10 | −2.54063 | ||||||||
\(951\) | 841249. | 3.17170e−5 0 | ||||||||
\(952\) | −6.04738e10 | −2.27163 | ||||||||
\(953\) | 4.70442e10 | 1.76068 | 0.880340 | − | 0.474343i | \(-0.157314\pi\) | ||||
0.880340 | + | 0.474343i | \(0.157314\pi\) | |||||||
\(954\) | −3.79454e9 | −0.141495 | ||||||||
\(955\) | 1.06594e9 | 0.0396023 | ||||||||
\(956\) | 2.39161e10 | 0.885293 | ||||||||
\(957\) | −7.18273e9 | −0.264910 | ||||||||
\(958\) | −5.91631e9 | −0.217406 | ||||||||
\(959\) | −5.11439e10 | −1.87253 | ||||||||
\(960\) | 2.98106e9 | 0.108748 | ||||||||
\(961\) | −2.27215e10 | −0.825859 | ||||||||
\(962\) | −5.24114e10 | −1.89807 | ||||||||
\(963\) | 2.52454e9 | 0.0910940 | ||||||||
\(964\) | −2.37882e10 | −0.855249 | ||||||||
\(965\) | −4.24437e9 | −0.152043 | ||||||||
\(966\) | −3.15992e10 | −1.12786 | ||||||||
\(967\) | −2.01441e8 | −0.00716400 | −0.00358200 | − | 0.999994i | \(-0.501140\pi\) | ||||
−0.00358200 | + | 0.999994i | \(0.501140\pi\) | |||||||
\(968\) | 3.40935e10 | 1.20811 | ||||||||
\(969\) | 3.20694e10 | 1.13229 | ||||||||
\(970\) | −2.64111e9 | −0.0929149 | ||||||||
\(971\) | 4.43321e10 | 1.55400 | 0.777001 | − | 0.629500i | \(-0.216740\pi\) | ||||
0.777001 | + | 0.629500i | \(0.216740\pi\) | |||||||
\(972\) | −3.36044e9 | −0.117372 | ||||||||
\(973\) | −1.41508e10 | −0.492478 | ||||||||
\(974\) | 5.21179e10 | 1.80730 | ||||||||
\(975\) | −1.49142e10 | −0.515329 | ||||||||
\(976\) | 2.23701e10 | 0.770181 | ||||||||
\(977\) | 4.78091e10 | 1.64013 | 0.820067 | − | 0.572268i | \(-0.193936\pi\) | ||||
0.820067 | + | 0.572268i | \(0.193936\pi\) | |||||||
\(978\) | −2.64709e10 | −0.904861 | ||||||||
\(979\) | −9.03443e9 | −0.307724 | ||||||||
\(980\) | 4.56817e9 | 0.155043 | ||||||||
\(981\) | 7.88433e7 | 0.00266639 | ||||||||
\(982\) | 6.68045e9 | 0.225121 | ||||||||
\(983\) | −3.22996e10 | −1.08458 | −0.542288 | − | 0.840193i | \(-0.682442\pi\) | ||||
−0.542288 | + | 0.840193i | \(0.682442\pi\) | |||||||
\(984\) | −2.90088e10 | −0.970615 | ||||||||
\(985\) | −7.48003e8 | −0.0249389 | ||||||||
\(986\) | −8.08162e10 | −2.68491 | ||||||||
\(987\) | −3.85043e10 | −1.27467 | ||||||||
\(988\) | 7.75543e10 | 2.55833 | ||||||||
\(989\) | −2.98705e10 | −0.981873 | ||||||||
\(990\) | −8.44215e8 | −0.0276522 | ||||||||
\(991\) | −5.62073e10 | −1.83457 | −0.917286 | − | 0.398230i | \(-0.869625\pi\) | ||||
−0.917286 | + | 0.398230i | \(0.869625\pi\) | |||||||
\(992\) | 6.72697e9 | 0.218790 | ||||||||
\(993\) | −3.14961e10 | −1.02079 | ||||||||
\(994\) | 1.29805e11 | 4.19216 | ||||||||
\(995\) | 5.57901e9 | 0.179546 | ||||||||
\(996\) | 3.67011e10 | 1.17699 | ||||||||
\(997\) | −6.21852e9 | −0.198726 | −0.0993629 | − | 0.995051i | \(-0.531680\pi\) | ||||
−0.0993629 | + | 0.995051i | \(0.531680\pi\) | |||||||
\(998\) | 7.79963e10 | 2.48380 | ||||||||
\(999\) | 7.52774e9 | 0.238883 |
(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.a.1.2 | ✓ | 16 | |
3.2 | odd | 2 | 531.8.a.b.1.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
531.8.a.b.1.15 | 16 | 3.2 | odd | 2 |