Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −39.7571 | −1.75703 | −0.878516 | − | 0.477712i | \(-0.841466\pi\) | ||||
−0.878516 | + | 0.477712i | \(0.841466\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 1068.63 | 2.08716 | ||||||||
\(5\) | −1871.54 | −1.33917 | −0.669584 | − | 0.742736i | \(-0.733528\pi\) | ||||
−0.669584 | + | 0.742736i | \(0.733528\pi\) | |||||||
\(6\) | −3220.33 | −1.01442 | ||||||||
\(7\) | −43.1074 | −0.00678595 | −0.00339298 | − | 0.999994i | \(-0.501080\pi\) | ||||
−0.00339298 | + | 0.999994i | \(0.501080\pi\) | |||||||
\(8\) | −22129.9 | −1.91018 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 74407.2 | 2.35296 | ||||||||
\(11\) | 76107.0 | 1.56732 | 0.783659 | − | 0.621191i | \(-0.213351\pi\) | ||||
0.783659 | + | 0.621191i | \(0.213351\pi\) | |||||||
\(12\) | 86558.9 | 1.20503 | ||||||||
\(13\) | −43732.0 | −0.424673 | −0.212336 | − | 0.977197i | \(-0.568107\pi\) | ||||
−0.212336 | + | 0.977197i | \(0.568107\pi\) | |||||||
\(14\) | 1713.83 | 0.0119231 | ||||||||
\(15\) | −151595. | −0.773169 | ||||||||
\(16\) | 332685. | 1.26909 | ||||||||
\(17\) | 420385. | 1.22075 | 0.610375 | − | 0.792113i | \(-0.291019\pi\) | ||||
0.610375 | + | 0.792113i | \(0.291019\pi\) | |||||||
\(18\) | −260846. | −0.585678 | ||||||||
\(19\) | −333780. | −0.587583 | −0.293791 | − | 0.955870i | \(-0.594917\pi\) | ||||
−0.293791 | + | 0.955870i | \(0.594917\pi\) | |||||||
\(20\) | −1.99999e6 | −2.79507 | ||||||||
\(21\) | −3491.70 | −0.00391787 | ||||||||
\(22\) | −3.02579e6 | −2.75383 | ||||||||
\(23\) | −114536. | −0.0853424 | −0.0426712 | − | 0.999089i | \(-0.513587\pi\) | ||||
−0.0426712 | + | 0.999089i | \(0.513587\pi\) | |||||||
\(24\) | −1.79253e6 | −1.10285 | ||||||||
\(25\) | 1.54955e6 | 0.793372 | ||||||||
\(26\) | 1.73866e6 | 0.746164 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −46065.8 | −0.0141634 | ||||||||
\(29\) | 2.58705e6 | 0.679226 | 0.339613 | − | 0.940565i | \(-0.389704\pi\) | ||||
0.339613 | + | 0.940565i | \(0.389704\pi\) | |||||||
\(30\) | 6.02699e6 | 1.35848 | ||||||||
\(31\) | −1.72886e6 | −0.336226 | −0.168113 | − | 0.985768i | \(-0.553767\pi\) | ||||
−0.168113 | + | 0.985768i | \(0.553767\pi\) | |||||||
\(32\) | −1.89606e6 | −0.319652 | ||||||||
\(33\) | 6.16467e6 | 0.904892 | ||||||||
\(34\) | −1.67133e7 | −2.14490 | ||||||||
\(35\) | 80677.4 | 0.00908753 | ||||||||
\(36\) | 7.01127e6 | 0.695722 | ||||||||
\(37\) | 4.90694e6 | 0.430430 | 0.215215 | − | 0.976567i | \(-0.430955\pi\) | ||||
0.215215 | + | 0.976567i | \(0.430955\pi\) | |||||||
\(38\) | 1.32701e7 | 1.03240 | ||||||||
\(39\) | −3.54229e6 | −0.245185 | ||||||||
\(40\) | 4.14172e7 | 2.55806 | ||||||||
\(41\) | 7.23989e6 | 0.400133 | 0.200067 | − | 0.979782i | \(-0.435884\pi\) | ||||
0.200067 | + | 0.979782i | \(0.435884\pi\) | |||||||
\(42\) | 138820. | 0.00688383 | ||||||||
\(43\) | −8.98509e6 | −0.400788 | −0.200394 | − | 0.979715i | \(-0.564222\pi\) | ||||
−0.200394 | + | 0.979715i | \(0.564222\pi\) | |||||||
\(44\) | 8.13301e7 | 3.27125 | ||||||||
\(45\) | −1.22792e7 | −0.446389 | ||||||||
\(46\) | 4.55360e6 | 0.149949 | ||||||||
\(47\) | 5.61464e7 | 1.67835 | 0.839174 | − | 0.543864i | \(-0.183039\pi\) | ||||
0.839174 | + | 0.543864i | \(0.183039\pi\) | |||||||
\(48\) | 2.69475e7 | 0.732711 | ||||||||
\(49\) | −4.03517e7 | −0.999954 | ||||||||
\(50\) | −6.16058e7 | −1.39398 | ||||||||
\(51\) | 3.40512e7 | 0.704800 | ||||||||
\(52\) | −4.67333e7 | −0.886362 | ||||||||
\(53\) | −9.20424e7 | −1.60231 | −0.801155 | − | 0.598457i | \(-0.795781\pi\) | ||||
−0.801155 | + | 0.598457i | \(0.795781\pi\) | |||||||
\(54\) | −2.11286e7 | −0.338141 | ||||||||
\(55\) | −1.42438e8 | −2.09890 | ||||||||
\(56\) | 953964. | 0.0129624 | ||||||||
\(57\) | −2.70362e7 | −0.339241 | ||||||||
\(58\) | −1.02854e8 | −1.19342 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −1.61999e8 | −1.61373 | ||||||||
\(61\) | −8.95394e7 | −0.827999 | −0.413999 | − | 0.910277i | \(-0.635868\pi\) | ||||
−0.413999 | + | 0.910277i | \(0.635868\pi\) | |||||||
\(62\) | 6.87344e7 | 0.590761 | ||||||||
\(63\) | −282828. | −0.00226198 | ||||||||
\(64\) | −9.49527e7 | −0.707453 | ||||||||
\(65\) | 8.18464e7 | 0.568708 | ||||||||
\(66\) | −2.45089e8 | −1.58993 | ||||||||
\(67\) | −1.59831e8 | −0.969004 | −0.484502 | − | 0.874790i | \(-0.660999\pi\) | ||||
−0.484502 | + | 0.874790i | \(0.660999\pi\) | |||||||
\(68\) | 4.49235e8 | 2.54791 | ||||||||
\(69\) | −9.27738e6 | −0.0492725 | ||||||||
\(70\) | −3.20750e6 | −0.0159671 | ||||||||
\(71\) | 1.68944e8 | 0.789007 | 0.394504 | − | 0.918894i | \(-0.370917\pi\) | ||||
0.394504 | + | 0.918894i | \(0.370917\pi\) | |||||||
\(72\) | −1.45195e8 | −0.636728 | ||||||||
\(73\) | −1.57076e8 | −0.647378 | −0.323689 | − | 0.946163i | \(-0.604923\pi\) | ||||
−0.323689 | + | 0.946163i | \(0.604923\pi\) | |||||||
\(74\) | −1.95086e8 | −0.756281 | ||||||||
\(75\) | 1.25514e8 | 0.458054 | ||||||||
\(76\) | −3.56687e8 | −1.22638 | ||||||||
\(77\) | −3.28077e6 | −0.0106357 | ||||||||
\(78\) | 1.40831e8 | 0.430798 | ||||||||
\(79\) | 5.77979e8 | 1.66951 | 0.834757 | − | 0.550619i | \(-0.185608\pi\) | ||||
0.834757 | + | 0.550619i | \(0.185608\pi\) | |||||||
\(80\) | −6.22635e8 | −1.69953 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −2.87837e8 | −0.703047 | ||||||||
\(83\) | −4.29141e8 | −0.992541 | −0.496270 | − | 0.868168i | \(-0.665297\pi\) | ||||
−0.496270 | + | 0.868168i | \(0.665297\pi\) | |||||||
\(84\) | −3.73133e6 | −0.00817724 | ||||||||
\(85\) | −7.86769e8 | −1.63479 | ||||||||
\(86\) | 3.57221e8 | 0.704197 | ||||||||
\(87\) | 2.09551e8 | 0.392151 | ||||||||
\(88\) | −1.68424e9 | −2.99387 | ||||||||
\(89\) | −6.09435e8 | −1.02961 | −0.514805 | − | 0.857308i | \(-0.672135\pi\) | ||||
−0.514805 | + | 0.857308i | \(0.672135\pi\) | |||||||
\(90\) | 4.88186e8 | 0.784321 | ||||||||
\(91\) | 1.88517e6 | 0.00288181 | ||||||||
\(92\) | −1.22396e8 | −0.178124 | ||||||||
\(93\) | −1.40037e8 | −0.194120 | ||||||||
\(94\) | −2.23222e9 | −2.94891 | ||||||||
\(95\) | 6.24684e8 | 0.786872 | ||||||||
\(96\) | −1.53581e8 | −0.184551 | ||||||||
\(97\) | 1.42423e9 | 1.63345 | 0.816727 | − | 0.577025i | \(-0.195786\pi\) | ||||
0.816727 | + | 0.577025i | \(0.195786\pi\) | |||||||
\(98\) | 1.60427e9 | 1.75695 | ||||||||
\(99\) | 4.99338e8 | 0.522440 | ||||||||
\(100\) | 1.65590e9 | 1.65590 | ||||||||
\(101\) | −2.28375e8 | −0.218374 | −0.109187 | − | 0.994021i | \(-0.534825\pi\) | ||||
−0.109187 | + | 0.994021i | \(0.534825\pi\) | |||||||
\(102\) | −1.35378e9 | −1.23836 | ||||||||
\(103\) | 1.56336e9 | 1.36864 | 0.684321 | − | 0.729180i | \(-0.260099\pi\) | ||||
0.684321 | + | 0.729180i | \(0.260099\pi\) | |||||||
\(104\) | 9.67787e8 | 0.811203 | ||||||||
\(105\) | 6.53487e6 | 0.00524669 | ||||||||
\(106\) | 3.65934e9 | 2.81531 | ||||||||
\(107\) | −1.24104e9 | −0.915288 | −0.457644 | − | 0.889136i | \(-0.651307\pi\) | ||||
−0.457644 | + | 0.889136i | \(0.651307\pi\) | |||||||
\(108\) | 5.67913e8 | 0.401675 | ||||||||
\(109\) | −2.59764e9 | −1.76263 | −0.881314 | − | 0.472532i | \(-0.843340\pi\) | ||||
−0.881314 | + | 0.472532i | \(0.843340\pi\) | |||||||
\(110\) | 5.66291e9 | 3.68784 | ||||||||
\(111\) | 3.97462e8 | 0.248509 | ||||||||
\(112\) | −1.43412e7 | −0.00861200 | ||||||||
\(113\) | 6.59340e7 | 0.0380414 | 0.0190207 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190207 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(114\) | 1.07488e9 | 0.596058 | ||||||||
\(115\) | 2.14358e8 | 0.114288 | ||||||||
\(116\) | 2.76460e9 | 1.41766 | ||||||||
\(117\) | −2.86926e8 | −0.141558 | ||||||||
\(118\) | 4.81751e8 | 0.228746 | ||||||||
\(119\) | −1.81217e7 | −0.00828395 | ||||||||
\(120\) | 3.35479e9 | 1.47690 | ||||||||
\(121\) | 3.43432e9 | 1.45649 | ||||||||
\(122\) | 3.55983e9 | 1.45482 | ||||||||
\(123\) | 5.86431e8 | 0.231017 | ||||||||
\(124\) | −1.84751e9 | −0.701760 | ||||||||
\(125\) | 7.55300e8 | 0.276710 | ||||||||
\(126\) | 1.12444e7 | 0.00397438 | ||||||||
\(127\) | 9.03648e8 | 0.308235 | 0.154118 | − | 0.988052i | \(-0.450747\pi\) | ||||
0.154118 | + | 0.988052i | \(0.450747\pi\) | |||||||
\(128\) | 4.74583e9 | 1.56267 | ||||||||
\(129\) | −7.27792e8 | −0.231395 | ||||||||
\(130\) | −3.25398e9 | −0.999239 | ||||||||
\(131\) | −1.48993e9 | −0.442024 | −0.221012 | − | 0.975271i | \(-0.570936\pi\) | ||||
−0.221012 | + | 0.975271i | \(0.570936\pi\) | |||||||
\(132\) | 6.58774e9 | 1.88866 | ||||||||
\(133\) | 1.43884e7 | 0.00398731 | ||||||||
\(134\) | 6.35444e9 | 1.70257 | ||||||||
\(135\) | −9.94616e8 | −0.257723 | ||||||||
\(136\) | −9.30309e9 | −2.33186 | ||||||||
\(137\) | 3.80197e9 | 0.922074 | 0.461037 | − | 0.887381i | \(-0.347478\pi\) | ||||
0.461037 | + | 0.887381i | \(0.347478\pi\) | |||||||
\(138\) | 3.68842e8 | 0.0865734 | ||||||||
\(139\) | −3.94690e8 | −0.0896788 | −0.0448394 | − | 0.998994i | \(-0.514278\pi\) | ||||
−0.0448394 | + | 0.998994i | \(0.514278\pi\) | |||||||
\(140\) | 8.62142e7 | 0.0189672 | ||||||||
\(141\) | 4.54786e9 | 0.968994 | ||||||||
\(142\) | −6.71674e9 | −1.38631 | ||||||||
\(143\) | −3.32831e9 | −0.665598 | ||||||||
\(144\) | 2.18275e9 | 0.423031 | ||||||||
\(145\) | −4.84178e9 | −0.909598 | ||||||||
\(146\) | 6.24491e9 | 1.13746 | ||||||||
\(147\) | −3.26849e9 | −0.577324 | ||||||||
\(148\) | 5.24370e9 | 0.898379 | ||||||||
\(149\) | 2.09979e9 | 0.349009 | 0.174505 | − | 0.984656i | \(-0.444168\pi\) | ||||
0.174505 | + | 0.984656i | \(0.444168\pi\) | |||||||
\(150\) | −4.99007e9 | −0.804815 | ||||||||
\(151\) | 5.15317e9 | 0.806638 | 0.403319 | − | 0.915060i | \(-0.367857\pi\) | ||||
0.403319 | + | 0.915060i | \(0.367857\pi\) | |||||||
\(152\) | 7.38653e9 | 1.12239 | ||||||||
\(153\) | 2.75814e9 | 0.406917 | ||||||||
\(154\) | 1.30434e8 | 0.0186874 | ||||||||
\(155\) | 3.23563e9 | 0.450264 | ||||||||
\(156\) | −3.78540e9 | −0.511741 | ||||||||
\(157\) | 6.27151e9 | 0.823804 | 0.411902 | − | 0.911228i | \(-0.364865\pi\) | ||||
0.411902 | + | 0.911228i | \(0.364865\pi\) | |||||||
\(158\) | −2.29788e10 | −2.93339 | ||||||||
\(159\) | −7.45544e9 | −0.925094 | ||||||||
\(160\) | 3.54856e9 | 0.428068 | ||||||||
\(161\) | 4.93733e6 | 0.000579129 0 | ||||||||
\(162\) | −1.71141e9 | −0.195226 | ||||||||
\(163\) | 2.97767e9 | 0.330394 | 0.165197 | − | 0.986261i | \(-0.447174\pi\) | ||||
0.165197 | + | 0.986261i | \(0.447174\pi\) | |||||||
\(164\) | 7.73675e9 | 0.835144 | ||||||||
\(165\) | −1.15374e10 | −1.21180 | ||||||||
\(166\) | 1.70614e10 | 1.74393 | ||||||||
\(167\) | −1.67149e9 | −0.166295 | −0.0831474 | − | 0.996537i | \(-0.526497\pi\) | ||||
−0.0831474 | + | 0.996537i | \(0.526497\pi\) | |||||||
\(168\) | 7.72711e7 | 0.00748385 | ||||||||
\(169\) | −8.69201e9 | −0.819653 | ||||||||
\(170\) | 3.12797e10 | 2.87238 | ||||||||
\(171\) | −2.18993e9 | −0.195861 | ||||||||
\(172\) | −9.60172e9 | −0.836510 | ||||||||
\(173\) | 1.34059e10 | 1.13786 | 0.568929 | − | 0.822387i | \(-0.307358\pi\) | ||||
0.568929 | + | 0.822387i | \(0.307358\pi\) | |||||||
\(174\) | −8.33115e9 | −0.689023 | ||||||||
\(175\) | −6.67973e7 | −0.00538378 | ||||||||
\(176\) | 2.53196e10 | 1.98907 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | 2.42294e10 | 1.80906 | ||||||||
\(179\) | −1.19814e10 | −0.872307 | −0.436154 | − | 0.899872i | \(-0.643660\pi\) | ||||
−0.436154 | + | 0.899872i | \(0.643660\pi\) | |||||||
\(180\) | −1.31219e10 | −0.931688 | ||||||||
\(181\) | 1.22163e10 | 0.846027 | 0.423014 | − | 0.906123i | \(-0.360972\pi\) | ||||
0.423014 | + | 0.906123i | \(0.360972\pi\) | |||||||
\(182\) | −7.49491e7 | −0.00506343 | ||||||||
\(183\) | −7.25269e9 | −0.478045 | ||||||||
\(184\) | 2.53466e9 | 0.163020 | ||||||||
\(185\) | −9.18356e9 | −0.576419 | ||||||||
\(186\) | 5.56749e9 | 0.341076 | ||||||||
\(187\) | 3.19942e10 | 1.91330 | ||||||||
\(188\) | 5.99997e10 | 3.50299 | ||||||||
\(189\) | −2.29090e7 | −0.00130596 | ||||||||
\(190\) | −2.48356e10 | −1.38256 | ||||||||
\(191\) | 1.63472e10 | 0.888779 | 0.444390 | − | 0.895834i | \(-0.353421\pi\) | ||||
0.444390 | + | 0.895834i | \(0.353421\pi\) | |||||||
\(192\) | −7.69117e9 | −0.408448 | ||||||||
\(193\) | 3.04342e10 | 1.57890 | 0.789448 | − | 0.613817i | \(-0.210367\pi\) | ||||
0.789448 | + | 0.613817i | \(0.210367\pi\) | |||||||
\(194\) | −5.66232e10 | −2.87003 | ||||||||
\(195\) | 6.62956e9 | 0.328344 | ||||||||
\(196\) | −4.31210e10 | −2.08707 | ||||||||
\(197\) | 1.94201e10 | 0.918656 | 0.459328 | − | 0.888267i | \(-0.348090\pi\) | ||||
0.459328 | + | 0.888267i | \(0.348090\pi\) | |||||||
\(198\) | −1.98522e10 | −0.917944 | ||||||||
\(199\) | 1.94633e10 | 0.879786 | 0.439893 | − | 0.898050i | \(-0.355016\pi\) | ||||
0.439893 | + | 0.898050i | \(0.355016\pi\) | |||||||
\(200\) | −3.42916e10 | −1.51549 | ||||||||
\(201\) | −1.29463e10 | −0.559455 | ||||||||
\(202\) | 9.07952e9 | 0.383691 | ||||||||
\(203\) | −1.11521e8 | −0.00460919 | ||||||||
\(204\) | 3.63880e10 | 1.47103 | ||||||||
\(205\) | −1.35498e10 | −0.535846 | ||||||||
\(206\) | −6.21545e10 | −2.40475 | ||||||||
\(207\) | −7.51468e8 | −0.0284475 | ||||||||
\(208\) | −1.45490e10 | −0.538949 | ||||||||
\(209\) | −2.54030e10 | −0.920929 | ||||||||
\(210\) | −2.59808e8 | −0.00921860 | ||||||||
\(211\) | −9.77363e9 | −0.339457 | −0.169728 | − | 0.985491i | \(-0.554289\pi\) | ||||
−0.169728 | + | 0.985491i | \(0.554289\pi\) | |||||||
\(212\) | −9.83591e10 | −3.34429 | ||||||||
\(213\) | 1.36845e10 | 0.455534 | ||||||||
\(214\) | 4.93400e10 | 1.60819 | ||||||||
\(215\) | 1.68160e10 | 0.536722 | ||||||||
\(216\) | −1.17608e10 | −0.367615 | ||||||||
\(217\) | 7.45266e7 | 0.00228161 | ||||||||
\(218\) | 1.03275e11 | 3.09699 | ||||||||
\(219\) | −1.27232e10 | −0.373764 | ||||||||
\(220\) | −1.52213e11 | −4.38076 | ||||||||
\(221\) | −1.83843e10 | −0.518419 | ||||||||
\(222\) | −1.58020e10 | −0.436639 | ||||||||
\(223\) | −1.07041e10 | −0.289853 | −0.144926 | − | 0.989442i | \(-0.546295\pi\) | ||||
−0.144926 | + | 0.989442i | \(0.546295\pi\) | |||||||
\(224\) | 8.17343e7 | 0.00216914 | ||||||||
\(225\) | 1.01666e10 | 0.264457 | ||||||||
\(226\) | −2.62134e9 | −0.0668399 | ||||||||
\(227\) | −7.59741e9 | −0.189911 | −0.0949553 | − | 0.995482i | \(-0.530271\pi\) | ||||
−0.0949553 | + | 0.995482i | \(0.530271\pi\) | |||||||
\(228\) | −2.88916e10 | −0.708052 | ||||||||
\(229\) | 3.95453e10 | 0.950244 | 0.475122 | − | 0.879920i | \(-0.342404\pi\) | ||||
0.475122 | + | 0.879920i | \(0.342404\pi\) | |||||||
\(230\) | −8.52227e9 | −0.200808 | ||||||||
\(231\) | −2.65743e8 | −0.00614055 | ||||||||
\(232\) | −5.72513e10 | −1.29745 | ||||||||
\(233\) | 8.75737e10 | 1.94658 | 0.973290 | − | 0.229581i | \(-0.0737355\pi\) | ||||
0.973290 | + | 0.229581i | \(0.0737355\pi\) | |||||||
\(234\) | 1.14073e10 | 0.248721 | ||||||||
\(235\) | −1.05081e11 | −2.24759 | ||||||||
\(236\) | −1.29490e10 | −0.271726 | ||||||||
\(237\) | 4.68163e10 | 0.963894 | ||||||||
\(238\) | 7.20466e8 | 0.0145552 | ||||||||
\(239\) | 3.19699e10 | 0.633797 | 0.316899 | − | 0.948459i | \(-0.397358\pi\) | ||||
0.316899 | + | 0.948459i | \(0.397358\pi\) | |||||||
\(240\) | −5.04334e10 | −0.981223 | ||||||||
\(241\) | 3.52544e10 | 0.673188 | 0.336594 | − | 0.941650i | \(-0.390725\pi\) | ||||
0.336594 | + | 0.941650i | \(0.390725\pi\) | |||||||
\(242\) | −1.36539e11 | −2.55910 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | −9.56843e10 | −1.72817 | ||||||||
\(245\) | 7.55201e10 | 1.33911 | ||||||||
\(246\) | −2.33148e10 | −0.405905 | ||||||||
\(247\) | 1.45969e10 | 0.249530 | ||||||||
\(248\) | 3.82595e10 | 0.642254 | ||||||||
\(249\) | −3.47604e10 | −0.573044 | ||||||||
\(250\) | −3.00285e10 | −0.486188 | ||||||||
\(251\) | 1.19741e10 | 0.190419 | 0.0952093 | − | 0.995457i | \(-0.469648\pi\) | ||||
0.0952093 | + | 0.995457i | \(0.469648\pi\) | |||||||
\(252\) | −3.02238e8 | −0.00472113 | ||||||||
\(253\) | −8.71695e9 | −0.133759 | ||||||||
\(254\) | −3.59264e10 | −0.541580 | ||||||||
\(255\) | −6.37283e10 | −0.943846 | ||||||||
\(256\) | −1.40065e11 | −2.03821 | ||||||||
\(257\) | 6.96218e10 | 0.995511 | 0.497755 | − | 0.867318i | \(-0.334158\pi\) | ||||
0.497755 | + | 0.867318i | \(0.334158\pi\) | |||||||
\(258\) | 2.89349e10 | 0.406568 | ||||||||
\(259\) | −2.11525e8 | −0.00292088 | ||||||||
\(260\) | 8.74634e10 | 1.18699 | ||||||||
\(261\) | 1.69736e10 | 0.226409 | ||||||||
\(262\) | 5.92354e10 | 0.776650 | ||||||||
\(263\) | 8.95325e10 | 1.15393 | 0.576965 | − | 0.816769i | \(-0.304237\pi\) | ||||
0.576965 | + | 0.816769i | \(0.304237\pi\) | |||||||
\(264\) | −1.36424e11 | −1.72851 | ||||||||
\(265\) | 1.72261e11 | 2.14576 | ||||||||
\(266\) | −5.72041e8 | −0.00700583 | ||||||||
\(267\) | −4.93642e10 | −0.594445 | ||||||||
\(268\) | −1.70800e11 | −2.02247 | ||||||||
\(269\) | 1.11073e11 | 1.29337 | 0.646685 | − | 0.762758i | \(-0.276155\pi\) | ||||
0.646685 | + | 0.762758i | \(0.276155\pi\) | |||||||
\(270\) | 3.95431e10 | 0.452828 | ||||||||
\(271\) | −2.70781e10 | −0.304970 | −0.152485 | − | 0.988306i | \(-0.548728\pi\) | ||||
−0.152485 | + | 0.988306i | \(0.548728\pi\) | |||||||
\(272\) | 1.39856e11 | 1.54924 | ||||||||
\(273\) | 1.52699e8 | 0.00166381 | ||||||||
\(274\) | −1.51155e11 | −1.62011 | ||||||||
\(275\) | 1.17932e11 | 1.24347 | ||||||||
\(276\) | −9.91407e9 | −0.102840 | ||||||||
\(277\) | −4.80043e10 | −0.489916 | −0.244958 | − | 0.969534i | \(-0.578774\pi\) | ||||
−0.244958 | + | 0.969534i | \(0.578774\pi\) | |||||||
\(278\) | 1.56917e10 | 0.157569 | ||||||||
\(279\) | −1.13430e10 | −0.112075 | ||||||||
\(280\) | −1.78539e9 | −0.0173589 | ||||||||
\(281\) | −1.13338e11 | −1.08442 | −0.542208 | − | 0.840244i | \(-0.682412\pi\) | ||||
−0.542208 | + | 0.840244i | \(0.682412\pi\) | |||||||
\(282\) | −1.80810e11 | −1.70255 | ||||||||
\(283\) | −6.41100e10 | −0.594138 | −0.297069 | − | 0.954856i | \(-0.596009\pi\) | ||||
−0.297069 | + | 0.954856i | \(0.596009\pi\) | |||||||
\(284\) | 1.80539e11 | 1.64679 | ||||||||
\(285\) | 5.05994e10 | 0.454301 | ||||||||
\(286\) | 1.32324e11 | 1.16948 | ||||||||
\(287\) | −3.12093e8 | −0.00271528 | ||||||||
\(288\) | −1.24401e10 | −0.106551 | ||||||||
\(289\) | 5.81354e10 | 0.490231 | ||||||||
\(290\) | 1.92495e11 | 1.59819 | ||||||||
\(291\) | 1.15362e11 | 0.943075 | ||||||||
\(292\) | −1.67856e11 | −1.35119 | ||||||||
\(293\) | 1.30027e11 | 1.03069 | 0.515345 | − | 0.856983i | \(-0.327664\pi\) | ||||
0.515345 | + | 0.856983i | \(0.327664\pi\) | |||||||
\(294\) | 1.29946e11 | 1.01438 | ||||||||
\(295\) | 2.26782e10 | 0.174345 | ||||||||
\(296\) | −1.08590e11 | −0.822202 | ||||||||
\(297\) | 4.04464e10 | 0.301631 | ||||||||
\(298\) | −8.34814e10 | −0.613221 | ||||||||
\(299\) | 5.00887e9 | 0.0362426 | ||||||||
\(300\) | 1.34128e11 | 0.956033 | ||||||||
\(301\) | 3.87324e8 | 0.00271972 | ||||||||
\(302\) | −2.04875e11 | −1.41729 | ||||||||
\(303\) | −1.84983e10 | −0.126079 | ||||||||
\(304\) | −1.11044e11 | −0.745696 | ||||||||
\(305\) | 1.67577e11 | 1.10883 | ||||||||
\(306\) | −1.09656e11 | −0.714966 | ||||||||
\(307\) | 9.33203e10 | 0.599589 | 0.299794 | − | 0.954004i | \(-0.403082\pi\) | ||||
0.299794 | + | 0.954004i | \(0.403082\pi\) | |||||||
\(308\) | −3.50593e9 | −0.0221986 | ||||||||
\(309\) | 1.26632e11 | 0.790186 | ||||||||
\(310\) | −1.28639e11 | −0.791128 | ||||||||
\(311\) | 1.57941e11 | 0.957352 | 0.478676 | − | 0.877992i | \(-0.341117\pi\) | ||||
0.478676 | + | 0.877992i | \(0.341117\pi\) | |||||||
\(312\) | 7.83907e10 | 0.468348 | ||||||||
\(313\) | −8.35400e10 | −0.491977 | −0.245989 | − | 0.969273i | \(-0.579113\pi\) | ||||
−0.245989 | + | 0.969273i | \(0.579113\pi\) | |||||||
\(314\) | −2.49337e11 | −1.44745 | ||||||||
\(315\) | 5.29325e8 | 0.00302918 | ||||||||
\(316\) | 6.17645e11 | 3.48455 | ||||||||
\(317\) | −1.98225e11 | −1.10253 | −0.551265 | − | 0.834330i | \(-0.685855\pi\) | ||||
−0.551265 | + | 0.834330i | \(0.685855\pi\) | |||||||
\(318\) | 2.96407e11 | 1.62542 | ||||||||
\(319\) | 1.96893e11 | 1.06456 | ||||||||
\(320\) | 1.77708e11 | 0.947398 | ||||||||
\(321\) | −1.00524e11 | −0.528442 | ||||||||
\(322\) | −1.96294e8 | −0.00101755 | ||||||||
\(323\) | −1.40316e11 | −0.717291 | ||||||||
\(324\) | 4.60009e10 | 0.231907 | ||||||||
\(325\) | −6.77652e10 | −0.336924 | ||||||||
\(326\) | −1.18383e11 | −0.580513 | ||||||||
\(327\) | −2.10409e11 | −1.01765 | ||||||||
\(328\) | −1.60218e11 | −0.764328 | ||||||||
\(329\) | −2.42033e9 | −0.0113892 | ||||||||
\(330\) | 4.58696e11 | 2.12918 | ||||||||
\(331\) | −2.61910e10 | −0.119930 | −0.0599648 | − | 0.998200i | \(-0.519099\pi\) | ||||
−0.0599648 | + | 0.998200i | \(0.519099\pi\) | |||||||
\(332\) | −4.58592e11 | −2.07160 | ||||||||
\(333\) | 3.21944e10 | 0.143477 | ||||||||
\(334\) | 6.64535e10 | 0.292185 | ||||||||
\(335\) | 2.99132e11 | 1.29766 | ||||||||
\(336\) | −1.16164e9 | −0.00497214 | ||||||||
\(337\) | 1.09795e11 | 0.463714 | 0.231857 | − | 0.972750i | \(-0.425520\pi\) | ||||
0.231857 | + | 0.972750i | \(0.425520\pi\) | |||||||
\(338\) | 3.45569e11 | 1.44016 | ||||||||
\(339\) | 5.34065e9 | 0.0219632 | ||||||||
\(340\) | −8.40763e11 | −3.41208 | ||||||||
\(341\) | −1.31578e11 | −0.526974 | ||||||||
\(342\) | 8.70653e10 | 0.344134 | ||||||||
\(343\) | 3.47900e9 | 0.0135716 | ||||||||
\(344\) | 1.98839e11 | 0.765578 | ||||||||
\(345\) | 1.73630e10 | 0.0659841 | ||||||||
\(346\) | −5.32980e11 | −1.99925 | ||||||||
\(347\) | 4.82368e10 | 0.178606 | 0.0893029 | − | 0.996005i | \(-0.471536\pi\) | ||||
0.0893029 | + | 0.996005i | \(0.471536\pi\) | |||||||
\(348\) | 2.23932e11 | 0.818484 | ||||||||
\(349\) | −3.17295e11 | −1.14485 | −0.572425 | − | 0.819957i | \(-0.693997\pi\) | ||||
−0.572425 | + | 0.819957i | \(0.693997\pi\) | |||||||
\(350\) | 2.65567e9 | 0.00945949 | ||||||||
\(351\) | −2.32410e10 | −0.0817283 | ||||||||
\(352\) | −1.44304e11 | −0.500997 | ||||||||
\(353\) | 2.17995e11 | 0.747239 | 0.373620 | − | 0.927582i | \(-0.378117\pi\) | ||||
0.373620 | + | 0.927582i | \(0.378117\pi\) | |||||||
\(354\) | 3.90219e10 | 0.132067 | ||||||||
\(355\) | −3.16187e11 | −1.05661 | ||||||||
\(356\) | −6.51259e11 | −2.14896 | ||||||||
\(357\) | −1.46786e9 | −0.00478274 | ||||||||
\(358\) | 4.76346e11 | 1.53267 | ||||||||
\(359\) | −4.21124e11 | −1.33809 | −0.669044 | − | 0.743222i | \(-0.733296\pi\) | ||||
−0.669044 | + | 0.743222i | \(0.733296\pi\) | |||||||
\(360\) | 2.71738e11 | 0.852686 | ||||||||
\(361\) | −2.11279e11 | −0.654747 | ||||||||
\(362\) | −4.85683e11 | −1.48650 | ||||||||
\(363\) | 2.78180e11 | 0.840904 | ||||||||
\(364\) | 2.01455e9 | 0.00601481 | ||||||||
\(365\) | 2.93976e11 | 0.866949 | ||||||||
\(366\) | 2.88346e11 | 0.839942 | ||||||||
\(367\) | −4.66968e11 | −1.34366 | −0.671831 | − | 0.740705i | \(-0.734492\pi\) | ||||
−0.671831 | + | 0.740705i | \(0.734492\pi\) | |||||||
\(368\) | −3.81042e10 | −0.108307 | ||||||||
\(369\) | 4.75009e10 | 0.133378 | ||||||||
\(370\) | 3.65112e11 | 1.01279 | ||||||||
\(371\) | 3.96771e9 | 0.0108732 | ||||||||
\(372\) | −1.49648e11 | −0.405161 | ||||||||
\(373\) | −7.06913e11 | −1.89093 | −0.945467 | − | 0.325719i | \(-0.894394\pi\) | ||||
−0.945467 | + | 0.325719i | \(0.894394\pi\) | |||||||
\(374\) | −1.27200e12 | −3.36174 | ||||||||
\(375\) | 6.11793e10 | 0.159758 | ||||||||
\(376\) | −1.24252e12 | −3.20595 | ||||||||
\(377\) | −1.13137e11 | −0.288449 | ||||||||
\(378\) | 9.10797e8 | 0.00229461 | ||||||||
\(379\) | 4.89494e11 | 1.21863 | 0.609313 | − | 0.792930i | \(-0.291445\pi\) | ||||
0.609313 | + | 0.792930i | \(0.291445\pi\) | |||||||
\(380\) | 6.67555e11 | 1.64233 | ||||||||
\(381\) | 7.31955e10 | 0.177960 | ||||||||
\(382\) | −6.49918e11 | −1.56161 | ||||||||
\(383\) | 1.59864e11 | 0.379627 | 0.189814 | − | 0.981820i | \(-0.439212\pi\) | ||||
0.189814 | + | 0.981820i | \(0.439212\pi\) | |||||||
\(384\) | 3.84412e11 | 0.902208 | ||||||||
\(385\) | 6.14012e9 | 0.0142431 | ||||||||
\(386\) | −1.20997e12 | −2.77417 | ||||||||
\(387\) | −5.89512e10 | −0.133596 | ||||||||
\(388\) | 1.52197e12 | 3.40929 | ||||||||
\(389\) | 3.92974e11 | 0.870143 | 0.435072 | − | 0.900396i | \(-0.356723\pi\) | ||||
0.435072 | + | 0.900396i | \(0.356723\pi\) | |||||||
\(390\) | −2.63572e11 | −0.576911 | ||||||||
\(391\) | −4.81490e10 | −0.104182 | ||||||||
\(392\) | 8.92982e11 | 1.91010 | ||||||||
\(393\) | −1.20684e11 | −0.255202 | ||||||||
\(394\) | −7.72087e11 | −1.61411 | ||||||||
\(395\) | −1.08171e12 | −2.23576 | ||||||||
\(396\) | 5.33607e11 | 1.09042 | ||||||||
\(397\) | 8.13926e11 | 1.64448 | 0.822238 | − | 0.569144i | \(-0.192725\pi\) | ||||
0.822238 | + | 0.569144i | \(0.192725\pi\) | |||||||
\(398\) | −7.73804e11 | −1.54581 | ||||||||
\(399\) | 1.16546e9 | 0.00230207 | ||||||||
\(400\) | 5.15513e11 | 1.00686 | ||||||||
\(401\) | −4.34991e11 | −0.840099 | −0.420050 | − | 0.907501i | \(-0.637987\pi\) | ||||
−0.420050 | + | 0.907501i | \(0.637987\pi\) | |||||||
\(402\) | 5.14709e11 | 0.982980 | ||||||||
\(403\) | 7.56064e10 | 0.142786 | ||||||||
\(404\) | −2.44048e11 | −0.455783 | ||||||||
\(405\) | −8.05639e10 | −0.148796 | ||||||||
\(406\) | 4.43376e9 | 0.00809850 | ||||||||
\(407\) | 3.73452e11 | 0.674622 | ||||||||
\(408\) | −7.53550e11 | −1.34630 | ||||||||
\(409\) | −3.30766e11 | −0.584475 | −0.292237 | − | 0.956346i | \(-0.594400\pi\) | ||||
−0.292237 | + | 0.956346i | \(0.594400\pi\) | |||||||
\(410\) | 5.38700e11 | 0.941499 | ||||||||
\(411\) | 3.07959e11 | 0.532360 | ||||||||
\(412\) | 1.67065e12 | 2.85658 | ||||||||
\(413\) | 5.22348e8 | 0.000883456 0 | ||||||||
\(414\) | 2.98762e10 | 0.0499832 | ||||||||
\(415\) | 8.03156e11 | 1.32918 | ||||||||
\(416\) | 8.29186e10 | 0.135748 | ||||||||
\(417\) | −3.19699e10 | −0.0517761 | ||||||||
\(418\) | 1.00995e12 | 1.61810 | ||||||||
\(419\) | 7.85962e10 | 0.124577 | 0.0622886 | − | 0.998058i | \(-0.480160\pi\) | ||||
0.0622886 | + | 0.998058i | \(0.480160\pi\) | |||||||
\(420\) | 6.98335e9 | 0.0109507 | ||||||||
\(421\) | 1.15531e12 | 1.79238 | 0.896190 | − | 0.443671i | \(-0.146324\pi\) | ||||
0.896190 | + | 0.443671i | \(0.146324\pi\) | |||||||
\(422\) | 3.88571e11 | 0.596437 | ||||||||
\(423\) | 3.68377e11 | 0.559449 | ||||||||
\(424\) | 2.03689e12 | 3.06071 | ||||||||
\(425\) | 6.51409e11 | 0.968509 | ||||||||
\(426\) | −5.44056e11 | −0.800388 | ||||||||
\(427\) | 3.85981e9 | 0.00561876 | ||||||||
\(428\) | −1.32621e12 | −1.91036 | ||||||||
\(429\) | −2.69593e11 | −0.384283 | ||||||||
\(430\) | −6.68555e11 | −0.943038 | ||||||||
\(431\) | 9.27162e11 | 1.29422 | 0.647109 | − | 0.762397i | \(-0.275978\pi\) | ||||
0.647109 | + | 0.762397i | \(0.275978\pi\) | |||||||
\(432\) | 1.76802e11 | 0.244237 | ||||||||
\(433\) | −5.34982e11 | −0.731381 | −0.365690 | − | 0.930737i | \(-0.619167\pi\) | ||||
−0.365690 | + | 0.930737i | \(0.619167\pi\) | |||||||
\(434\) | −2.96296e9 | −0.00400887 | ||||||||
\(435\) | −3.92184e11 | −0.525157 | ||||||||
\(436\) | −2.77592e12 | −3.67889 | ||||||||
\(437\) | 3.82297e10 | 0.0501457 | ||||||||
\(438\) | 5.05837e11 | 0.656716 | ||||||||
\(439\) | −3.68635e11 | −0.473703 | −0.236852 | − | 0.971546i | \(-0.576116\pi\) | ||||
−0.236852 | + | 0.971546i | \(0.576116\pi\) | |||||||
\(440\) | 3.15214e12 | 4.00929 | ||||||||
\(441\) | −2.64748e11 | −0.333318 | ||||||||
\(442\) | 7.30906e11 | 0.910880 | ||||||||
\(443\) | −1.14608e12 | −1.41384 | −0.706919 | − | 0.707294i | \(-0.749916\pi\) | ||||
−0.706919 | + | 0.707294i | \(0.749916\pi\) | |||||||
\(444\) | 4.24739e11 | 0.518680 | ||||||||
\(445\) | 1.14058e12 | 1.37882 | ||||||||
\(446\) | 4.25563e11 | 0.509281 | ||||||||
\(447\) | 1.70083e11 | 0.201501 | ||||||||
\(448\) | 4.09316e9 | 0.00480074 | ||||||||
\(449\) | 7.33272e11 | 0.851445 | 0.425722 | − | 0.904854i | \(-0.360020\pi\) | ||||
0.425722 | + | 0.904854i | \(0.360020\pi\) | |||||||
\(450\) | −4.04196e11 | −0.464660 | ||||||||
\(451\) | 5.51006e11 | 0.627137 | ||||||||
\(452\) | 7.04589e10 | 0.0793986 | ||||||||
\(453\) | 4.17407e11 | 0.465712 | ||||||||
\(454\) | 3.02051e11 | 0.333679 | ||||||||
\(455\) | −3.52819e9 | −0.00385923 | ||||||||
\(456\) | 5.98309e11 | 0.648013 | ||||||||
\(457\) | 6.95065e11 | 0.745422 | 0.372711 | − | 0.927947i | \(-0.378428\pi\) | ||||
0.372711 | + | 0.927947i | \(0.378428\pi\) | |||||||
\(458\) | −1.57221e12 | −1.66961 | ||||||||
\(459\) | 2.23410e11 | 0.234933 | ||||||||
\(460\) | 2.29069e11 | 0.238538 | ||||||||
\(461\) | 5.56679e11 | 0.574052 | 0.287026 | − | 0.957923i | \(-0.407333\pi\) | ||||
0.287026 | + | 0.957923i | \(0.407333\pi\) | |||||||
\(462\) | 1.05652e10 | 0.0107892 | ||||||||
\(463\) | 1.58767e12 | 1.60563 | 0.802815 | − | 0.596228i | \(-0.203334\pi\) | ||||
0.802815 | + | 0.596228i | \(0.203334\pi\) | |||||||
\(464\) | 8.60673e11 | 0.862000 | ||||||||
\(465\) | 2.62086e11 | 0.259960 | ||||||||
\(466\) | −3.48168e12 | −3.42020 | ||||||||
\(467\) | −9.73788e10 | −0.0947411 | −0.0473706 | − | 0.998877i | \(-0.515084\pi\) | ||||
−0.0473706 | + | 0.998877i | \(0.515084\pi\) | |||||||
\(468\) | −3.06617e11 | −0.295454 | ||||||||
\(469\) | 6.88992e9 | 0.00657561 | ||||||||
\(470\) | 4.17770e12 | 3.94909 | ||||||||
\(471\) | 5.07993e11 | 0.475623 | ||||||||
\(472\) | 2.68156e11 | 0.248685 | ||||||||
\(473\) | −6.83828e11 | −0.628162 | ||||||||
\(474\) | −1.86128e12 | −1.69359 | ||||||||
\(475\) | −5.17210e11 | −0.466172 | ||||||||
\(476\) | −1.93654e10 | −0.0172900 | ||||||||
\(477\) | −6.03890e11 | −0.534103 | ||||||||
\(478\) | −1.27103e12 | −1.11360 | ||||||||
\(479\) | −4.31480e11 | −0.374499 | −0.187249 | − | 0.982312i | \(-0.559957\pi\) | ||||
−0.187249 | + | 0.982312i | \(0.559957\pi\) | |||||||
\(480\) | 2.87434e11 | 0.247145 | ||||||||
\(481\) | −2.14590e11 | −0.182792 | ||||||||
\(482\) | −1.40161e12 | −1.18281 | ||||||||
\(483\) | 3.99924e8 | 0.000334361 0 | ||||||||
\(484\) | 3.67002e12 | 3.03993 | ||||||||
\(485\) | −2.66551e12 | −2.18747 | ||||||||
\(486\) | −1.38624e11 | −0.112714 | ||||||||
\(487\) | −2.09753e12 | −1.68977 | −0.844886 | − | 0.534946i | \(-0.820332\pi\) | ||||
−0.844886 | + | 0.534946i | \(0.820332\pi\) | |||||||
\(488\) | 1.98150e12 | 1.58163 | ||||||||
\(489\) | 2.41191e11 | 0.190753 | ||||||||
\(490\) | −3.00246e12 | −2.35285 | ||||||||
\(491\) | −1.32643e11 | −0.102995 | −0.0514976 | − | 0.998673i | \(-0.516399\pi\) | ||||
−0.0514976 | + | 0.998673i | \(0.516399\pi\) | |||||||
\(492\) | 6.26677e11 | 0.482171 | ||||||||
\(493\) | 1.08756e12 | 0.829165 | ||||||||
\(494\) | −5.80329e11 | −0.438433 | ||||||||
\(495\) | −9.34533e11 | −0.699635 | ||||||||
\(496\) | −5.75165e11 | −0.426702 | ||||||||
\(497\) | −7.28275e9 | −0.00535416 | ||||||||
\(498\) | 1.38197e12 | 1.00686 | ||||||||
\(499\) | −3.85614e11 | −0.278420 | −0.139210 | − | 0.990263i | \(-0.544456\pi\) | ||||
−0.139210 | + | 0.990263i | \(0.544456\pi\) | |||||||
\(500\) | 8.07135e11 | 0.577538 | ||||||||
\(501\) | −1.35390e11 | −0.0960103 | ||||||||
\(502\) | −4.76054e11 | −0.334572 | ||||||||
\(503\) | −1.68499e11 | −0.117366 | −0.0586829 | − | 0.998277i | \(-0.518690\pi\) | ||||
−0.0586829 | + | 0.998277i | \(0.518690\pi\) | |||||||
\(504\) | 6.25896e9 | 0.00432081 | ||||||||
\(505\) | 4.27413e11 | 0.292440 | ||||||||
\(506\) | 3.46561e11 | 0.235019 | ||||||||
\(507\) | −7.04053e11 | −0.473227 | ||||||||
\(508\) | 9.65664e11 | 0.643338 | ||||||||
\(509\) | 4.71940e11 | 0.311642 | 0.155821 | − | 0.987785i | \(-0.450198\pi\) | ||||
0.155821 | + | 0.987785i | \(0.450198\pi\) | |||||||
\(510\) | 2.53365e12 | 1.65837 | ||||||||
\(511\) | 6.77116e9 | 0.00439308 | ||||||||
\(512\) | 3.13870e12 | 2.01853 | ||||||||
\(513\) | −1.77384e11 | −0.113080 | ||||||||
\(514\) | −2.76796e12 | −1.74914 | ||||||||
\(515\) | −2.92589e12 | −1.83284 | ||||||||
\(516\) | −7.77739e11 | −0.482959 | ||||||||
\(517\) | 4.27314e12 | 2.63051 | ||||||||
\(518\) | 8.40964e9 | 0.00513208 | ||||||||
\(519\) | 1.08588e12 | 0.656943 | ||||||||
\(520\) | −1.81126e12 | −1.08634 | ||||||||
\(521\) | −2.64327e12 | −1.57171 | −0.785853 | − | 0.618414i | \(-0.787776\pi\) | ||||
−0.785853 | + | 0.618414i | \(0.787776\pi\) | |||||||
\(522\) | −6.74823e11 | −0.397807 | ||||||||
\(523\) | −3.72234e11 | −0.217549 | −0.108775 | − | 0.994066i | \(-0.534693\pi\) | ||||
−0.108775 | + | 0.994066i | \(0.534693\pi\) | |||||||
\(524\) | −1.59218e12 | −0.922576 | ||||||||
\(525\) | −5.41058e9 | −0.00310833 | ||||||||
\(526\) | −3.55955e12 | −2.02749 | ||||||||
\(527\) | −7.26785e11 | −0.410448 | ||||||||
\(528\) | 2.05089e12 | 1.14839 | ||||||||
\(529\) | −1.78803e12 | −0.992717 | ||||||||
\(530\) | −6.84862e12 | −3.77018 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | 1.53758e10 | 0.00832217 | ||||||||
\(533\) | −3.16615e11 | −0.169926 | ||||||||
\(534\) | 1.96258e12 | 1.04446 | ||||||||
\(535\) | 2.32266e12 | 1.22572 | ||||||||
\(536\) | 3.53706e12 | 1.85098 | ||||||||
\(537\) | −9.70494e11 | −0.503627 | ||||||||
\(538\) | −4.41593e12 | −2.27249 | ||||||||
\(539\) | −3.07105e12 | −1.56725 | ||||||||
\(540\) | −1.06287e12 | −0.537911 | ||||||||
\(541\) | 3.80779e12 | 1.91111 | 0.955554 | − | 0.294815i | \(-0.0952579\pi\) | ||||
0.955554 | + | 0.294815i | \(0.0952579\pi\) | |||||||
\(542\) | 1.07655e12 | 0.535842 | ||||||||
\(543\) | 9.89516e11 | 0.488454 | ||||||||
\(544\) | −7.97075e11 | −0.390215 | ||||||||
\(545\) | 4.86161e12 | 2.36045 | ||||||||
\(546\) | −6.07088e9 | −0.00292337 | ||||||||
\(547\) | 2.49470e12 | 1.19145 | 0.595725 | − | 0.803189i | \(-0.296865\pi\) | ||||
0.595725 | + | 0.803189i | \(0.296865\pi\) | |||||||
\(548\) | 4.06289e12 | 1.92452 | ||||||||
\(549\) | −5.87468e11 | −0.276000 | ||||||||
\(550\) | −4.68863e12 | −2.18481 | ||||||||
\(551\) | −8.63506e11 | −0.399101 | ||||||||
\(552\) | 2.05308e11 | 0.0941195 | ||||||||
\(553\) | −2.49152e10 | −0.0113292 | ||||||||
\(554\) | 1.90851e12 | 0.860798 | ||||||||
\(555\) | −7.43868e11 | −0.332796 | ||||||||
\(556\) | −4.21777e11 | −0.187174 | ||||||||
\(557\) | 3.97099e12 | 1.74804 | 0.874019 | − | 0.485892i | \(-0.161505\pi\) | ||||
0.874019 | + | 0.485892i | \(0.161505\pi\) | |||||||
\(558\) | 4.50966e11 | 0.196920 | ||||||||
\(559\) | 3.92936e11 | 0.170204 | ||||||||
\(560\) | 2.68402e10 | 0.0115329 | ||||||||
\(561\) | 2.59153e12 | 1.10465 | ||||||||
\(562\) | 4.50598e12 | 1.90535 | ||||||||
\(563\) | 3.54645e12 | 1.48767 | 0.743833 | − | 0.668365i | \(-0.233006\pi\) | ||||
0.743833 | + | 0.668365i | \(0.233006\pi\) | |||||||
\(564\) | 4.85997e12 | 2.02245 | ||||||||
\(565\) | −1.23398e11 | −0.0509438 | ||||||||
\(566\) | 2.54883e12 | 1.04392 | ||||||||
\(567\) | −1.85563e9 | −0.000753995 0 | ||||||||
\(568\) | −3.73873e12 | −1.50715 | ||||||||
\(569\) | 3.10044e12 | 1.23999 | 0.619994 | − | 0.784606i | \(-0.287135\pi\) | ||||
0.619994 | + | 0.784606i | \(0.287135\pi\) | |||||||
\(570\) | −2.01169e12 | −0.798221 | ||||||||
\(571\) | −4.49759e12 | −1.77059 | −0.885294 | − | 0.465032i | \(-0.846043\pi\) | ||||
−0.885294 | + | 0.465032i | \(0.846043\pi\) | |||||||
\(572\) | −3.55673e12 | −1.38921 | ||||||||
\(573\) | 1.32413e12 | 0.513137 | ||||||||
\(574\) | 1.24079e10 | 0.00477084 | ||||||||
\(575\) | −1.77479e11 | −0.0677083 | ||||||||
\(576\) | −6.22985e11 | −0.235818 | ||||||||
\(577\) | 3.67193e12 | 1.37912 | 0.689562 | − | 0.724227i | \(-0.257803\pi\) | ||||
0.689562 | + | 0.724227i | \(0.257803\pi\) | |||||||
\(578\) | −2.31130e12 | −0.861351 | ||||||||
\(579\) | 2.46517e12 | 0.911576 | ||||||||
\(580\) | −5.17407e12 | −1.89848 | ||||||||
\(581\) | 1.84991e10 | 0.00673533 | ||||||||
\(582\) | −4.58648e12 | −1.65701 | ||||||||
\(583\) | −7.00507e12 | −2.51133 | ||||||||
\(584\) | 3.47609e12 | 1.23661 | ||||||||
\(585\) | 5.36994e11 | 0.189569 | ||||||||
\(586\) | −5.16948e12 | −1.81095 | ||||||||
\(587\) | −3.14786e12 | −1.09432 | −0.547159 | − | 0.837029i | \(-0.684291\pi\) | ||||
−0.547159 | + | 0.837029i | \(0.684291\pi\) | |||||||
\(588\) | −3.49280e12 | −1.20497 | ||||||||
\(589\) | 5.77058e11 | 0.197561 | ||||||||
\(590\) | −9.01619e11 | −0.306330 | ||||||||
\(591\) | 1.57303e12 | 0.530387 | ||||||||
\(592\) | 1.63246e12 | 0.546256 | ||||||||
\(593\) | 1.66698e12 | 0.553584 | 0.276792 | − | 0.960930i | \(-0.410729\pi\) | ||||
0.276792 | + | 0.960930i | \(0.410729\pi\) | |||||||
\(594\) | −1.60803e12 | −0.529975 | ||||||||
\(595\) | 3.39156e10 | 0.0110936 | ||||||||
\(596\) | 2.24389e12 | 0.728440 | ||||||||
\(597\) | 1.57652e12 | 0.507945 | ||||||||
\(598\) | −1.99138e11 | −0.0636795 | ||||||||
\(599\) | −1.17016e12 | −0.371387 | −0.185693 | − | 0.982608i | \(-0.559453\pi\) | ||||
−0.185693 | + | 0.982608i | \(0.559453\pi\) | |||||||
\(600\) | −2.77762e12 | −0.874967 | ||||||||
\(601\) | −4.19866e12 | −1.31273 | −0.656366 | − | 0.754443i | \(-0.727907\pi\) | ||||
−0.656366 | + | 0.754443i | \(0.727907\pi\) | |||||||
\(602\) | −1.53989e10 | −0.00477865 | ||||||||
\(603\) | −1.04865e12 | −0.323001 | ||||||||
\(604\) | 5.50683e12 | 1.68359 | ||||||||
\(605\) | −6.42749e12 | −1.95048 | ||||||||
\(606\) | 7.35441e11 | 0.221524 | ||||||||
\(607\) | −3.46965e12 | −1.03738 | −0.518689 | − | 0.854963i | \(-0.673580\pi\) | ||||
−0.518689 | + | 0.854963i | \(0.673580\pi\) | |||||||
\(608\) | 6.32867e11 | 0.187822 | ||||||||
\(609\) | −9.03321e9 | −0.00266112 | ||||||||
\(610\) | −6.66238e12 | −1.94825 | ||||||||
\(611\) | −2.45540e12 | −0.712748 | ||||||||
\(612\) | 2.94743e12 | 0.849302 | ||||||||
\(613\) | −1.07824e12 | −0.308420 | −0.154210 | − | 0.988038i | \(-0.549283\pi\) | ||||
−0.154210 | + | 0.988038i | \(0.549283\pi\) | |||||||
\(614\) | −3.71015e12 | −1.05350 | ||||||||
\(615\) | −1.09753e12 | −0.309371 | ||||||||
\(616\) | 7.26033e10 | 0.0203162 | ||||||||
\(617\) | 3.25905e11 | 0.0905331 | 0.0452666 | − | 0.998975i | \(-0.485586\pi\) | ||||
0.0452666 | + | 0.998975i | \(0.485586\pi\) | |||||||
\(618\) | −5.03451e12 | −1.38838 | ||||||||
\(619\) | −3.86487e12 | −1.05810 | −0.529051 | − | 0.848590i | \(-0.677452\pi\) | ||||
−0.529051 | + | 0.848590i | \(0.677452\pi\) | |||||||
\(620\) | 3.45769e12 | 0.939774 | ||||||||
\(621\) | −6.08689e10 | −0.0164242 | ||||||||
\(622\) | −6.27926e12 | −1.68210 | ||||||||
\(623\) | 2.62712e10 | 0.00698688 | ||||||||
\(624\) | −1.17847e12 | −0.311162 | ||||||||
\(625\) | −4.44005e12 | −1.16393 | ||||||||
\(626\) | 3.32131e12 | 0.864420 | ||||||||
\(627\) | −2.05764e12 | −0.531699 | ||||||||
\(628\) | 6.70192e12 | 1.71941 | ||||||||
\(629\) | 2.06280e12 | 0.525448 | ||||||||
\(630\) | −2.10444e10 | −0.00532236 | ||||||||
\(631\) | 5.72504e12 | 1.43763 | 0.718813 | − | 0.695203i | \(-0.244686\pi\) | ||||
0.718813 | + | 0.695203i | \(0.244686\pi\) | |||||||
\(632\) | −1.27906e13 | −3.18908 | ||||||||
\(633\) | −7.91664e11 | −0.195986 | ||||||||
\(634\) | 7.88084e12 | 1.93718 | ||||||||
\(635\) | −1.69122e12 | −0.412779 | ||||||||
\(636\) | −7.96709e12 | −1.93082 | ||||||||
\(637\) | 1.76466e12 | 0.424653 | ||||||||
\(638\) | −7.82789e12 | −1.87047 | ||||||||
\(639\) | 1.10844e12 | 0.263002 | ||||||||
\(640\) | −8.88203e12 | −2.09268 | ||||||||
\(641\) | 2.78162e12 | 0.650785 | 0.325392 | − | 0.945579i | \(-0.394504\pi\) | ||||
0.325392 | + | 0.945579i | \(0.394504\pi\) | |||||||
\(642\) | 3.99654e12 | 0.928489 | ||||||||
\(643\) | 5.67681e12 | 1.30965 | 0.654824 | − | 0.755781i | \(-0.272743\pi\) | ||||
0.654824 | + | 0.755781i | \(0.272743\pi\) | |||||||
\(644\) | 5.27617e9 | 0.00120874 | ||||||||
\(645\) | 1.36210e12 | 0.309877 | ||||||||
\(646\) | 5.57856e12 | 1.26030 | ||||||||
\(647\) | 6.36165e10 | 0.0142725 | 0.00713626 | − | 0.999975i | \(-0.497728\pi\) | ||||
0.00713626 | + | 0.999975i | \(0.497728\pi\) | |||||||
\(648\) | −9.52621e11 | −0.212243 | ||||||||
\(649\) | −9.22216e11 | −0.204048 | ||||||||
\(650\) | 2.69415e12 | 0.591986 | ||||||||
\(651\) | 6.03665e9 | 0.00131729 | ||||||||
\(652\) | 3.18202e12 | 0.689586 | ||||||||
\(653\) | 3.08169e12 | 0.663255 | 0.331627 | − | 0.943410i | \(-0.392402\pi\) | ||||
0.331627 | + | 0.943410i | \(0.392402\pi\) | |||||||
\(654\) | 8.36526e12 | 1.78805 | ||||||||
\(655\) | 2.78847e12 | 0.591944 | ||||||||
\(656\) | 2.40860e12 | 0.507806 | ||||||||
\(657\) | −1.03058e12 | −0.215793 | ||||||||
\(658\) | 9.62252e10 | 0.0200112 | ||||||||
\(659\) | −7.50754e11 | −0.155065 | −0.0775324 | − | 0.996990i | \(-0.524704\pi\) | ||||
−0.0775324 | + | 0.996990i | \(0.524704\pi\) | |||||||
\(660\) | −1.23292e13 | −2.52923 | ||||||||
\(661\) | −5.89525e12 | −1.20115 | −0.600573 | − | 0.799570i | \(-0.705061\pi\) | ||||
−0.600573 | + | 0.799570i | \(0.705061\pi\) | |||||||
\(662\) | 1.04128e12 | 0.210720 | ||||||||
\(663\) | −1.48913e12 | −0.299310 | ||||||||
\(664\) | 9.49686e12 | 1.89594 | ||||||||
\(665\) | −2.69285e10 | −0.00533967 | ||||||||
\(666\) | −1.27996e12 | −0.252094 | ||||||||
\(667\) | −2.96309e11 | −0.0579668 | ||||||||
\(668\) | −1.78620e12 | −0.347085 | ||||||||
\(669\) | −8.67031e11 | −0.167347 | ||||||||
\(670\) | −1.18926e13 | −2.28003 | ||||||||
\(671\) | −6.81457e12 | −1.29774 | ||||||||
\(672\) | 6.62048e9 | 0.00125236 | ||||||||
\(673\) | −1.26722e11 | −0.0238113 | −0.0119057 | − | 0.999929i | \(-0.503790\pi\) | ||||
−0.0119057 | + | 0.999929i | \(0.503790\pi\) | |||||||
\(674\) | −4.36515e12 | −0.814760 | ||||||||
\(675\) | 8.23497e11 | 0.152685 | ||||||||
\(676\) | −9.28853e12 | −1.71075 | ||||||||
\(677\) | 5.40759e12 | 0.989361 | 0.494681 | − | 0.869075i | \(-0.335285\pi\) | ||||
0.494681 | + | 0.869075i | \(0.335285\pi\) | |||||||
\(678\) | −2.12329e11 | −0.0385901 | ||||||||
\(679\) | −6.13948e10 | −0.0110845 | ||||||||
\(680\) | 1.74111e13 | 3.12275 | ||||||||
\(681\) | −6.15390e11 | −0.109645 | ||||||||
\(682\) | 5.23117e12 | 0.925910 | ||||||||
\(683\) | −3.34048e12 | −0.587376 | −0.293688 | − | 0.955901i | \(-0.594883\pi\) | ||||
−0.293688 | + | 0.955901i | \(0.594883\pi\) | |||||||
\(684\) | −2.34022e12 | −0.408794 | ||||||||
\(685\) | −7.11555e12 | −1.23481 | ||||||||
\(686\) | −1.38315e11 | −0.0238457 | ||||||||
\(687\) | 3.20317e12 | 0.548623 | ||||||||
\(688\) | −2.98920e12 | −0.508636 | ||||||||
\(689\) | 4.02520e12 | 0.680458 | ||||||||
\(690\) | −6.90304e11 | −0.115936 | ||||||||
\(691\) | −5.76394e12 | −0.961764 | −0.480882 | − | 0.876785i | \(-0.659683\pi\) | ||||
−0.480882 | + | 0.876785i | \(0.659683\pi\) | |||||||
\(692\) | 1.43259e13 | 2.37490 | ||||||||
\(693\) | −2.15252e10 | −0.00354525 | ||||||||
\(694\) | −1.91776e12 | −0.313816 | ||||||||
\(695\) | 7.38680e11 | 0.120095 | ||||||||
\(696\) | −4.63736e12 | −0.749081 | ||||||||
\(697\) | 3.04354e12 | 0.488463 | ||||||||
\(698\) | 1.26147e13 | 2.01154 | ||||||||
\(699\) | 7.09347e12 | 1.12386 | ||||||||
\(700\) | −7.13815e10 | −0.0112368 | ||||||||
\(701\) | −5.48007e12 | −0.857147 | −0.428573 | − | 0.903507i | \(-0.640984\pi\) | ||||
−0.428573 | + | 0.903507i | \(0.640984\pi\) | |||||||
\(702\) | 9.23995e11 | 0.143599 | ||||||||
\(703\) | −1.63784e12 | −0.252913 | ||||||||
\(704\) | −7.22656e12 | −1.10880 | ||||||||
\(705\) | −8.51153e12 | −1.29765 | ||||||||
\(706\) | −8.66684e12 | −1.31292 | ||||||||
\(707\) | 9.84464e9 | 0.00148188 | ||||||||
\(708\) | −1.04887e12 | −0.156881 | ||||||||
\(709\) | 8.14487e12 | 1.21053 | 0.605265 | − | 0.796024i | \(-0.293067\pi\) | ||||
0.605265 | + | 0.796024i | \(0.293067\pi\) | |||||||
\(710\) | 1.25707e13 | 1.85651 | ||||||||
\(711\) | 3.79212e12 | 0.556505 | ||||||||
\(712\) | 1.34868e13 | 1.96674 | ||||||||
\(713\) | 1.98016e11 | 0.0286944 | ||||||||
\(714\) | 5.83578e10 | 0.00840343 | ||||||||
\(715\) | 6.22909e12 | 0.891348 | ||||||||
\(716\) | −1.28037e13 | −1.82065 | ||||||||
\(717\) | 2.58956e12 | 0.365923 | ||||||||
\(718\) | 1.67427e13 | 2.35107 | ||||||||
\(719\) | 9.83293e12 | 1.37215 | 0.686077 | − | 0.727529i | \(-0.259331\pi\) | ||||
0.686077 | + | 0.727529i | \(0.259331\pi\) | |||||||
\(720\) | −4.08511e12 | −0.566509 | ||||||||
\(721\) | −6.73922e10 | −0.00928754 | ||||||||
\(722\) | 8.39983e12 | 1.15041 | ||||||||
\(723\) | 2.85560e12 | 0.388665 | ||||||||
\(724\) | 1.30546e13 | 1.76580 | ||||||||
\(725\) | 4.00878e12 | 0.538879 | ||||||||
\(726\) | −1.10596e13 | −1.47750 | ||||||||
\(727\) | −3.89292e12 | −0.516857 | −0.258428 | − | 0.966030i | \(-0.583205\pi\) | ||||
−0.258428 | + | 0.966030i | \(0.583205\pi\) | |||||||
\(728\) | −4.17188e10 | −0.00550479 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −1.16876e13 | −1.52326 | ||||||||
\(731\) | −3.77719e12 | −0.489261 | ||||||||
\(732\) | −7.75043e12 | −0.997760 | ||||||||
\(733\) | −8.99834e12 | −1.15132 | −0.575658 | − | 0.817691i | \(-0.695254\pi\) | ||||
−0.575658 | + | 0.817691i | \(0.695254\pi\) | |||||||
\(734\) | 1.85653e13 | 2.36086 | ||||||||
\(735\) | 6.11713e12 | 0.773134 | ||||||||
\(736\) | 2.17166e11 | 0.0272799 | ||||||||
\(737\) | −1.21643e13 | −1.51874 | ||||||||
\(738\) | −1.88850e12 | −0.234349 | ||||||||
\(739\) | 5.20306e12 | 0.641739 | 0.320870 | − | 0.947123i | \(-0.396025\pi\) | ||||
0.320870 | + | 0.947123i | \(0.396025\pi\) | |||||||
\(740\) | −9.81381e12 | −1.20308 | ||||||||
\(741\) | 1.18235e12 | 0.144066 | ||||||||
\(742\) | −1.57745e11 | −0.0191046 | ||||||||
\(743\) | −1.31280e12 | −0.158033 | −0.0790165 | − | 0.996873i | \(-0.525178\pi\) | ||||
−0.0790165 | + | 0.996873i | \(0.525178\pi\) | |||||||
\(744\) | 3.09902e12 | 0.370806 | ||||||||
\(745\) | −3.92984e12 | −0.467382 | ||||||||
\(746\) | 2.81048e13 | 3.32243 | ||||||||
\(747\) | −2.81559e12 | −0.330847 | ||||||||
\(748\) | 3.41899e13 | 3.99338 | ||||||||
\(749\) | 5.34979e10 | 0.00621110 | ||||||||
\(750\) | −2.43231e12 | −0.280701 | ||||||||
\(751\) | 1.71718e13 | 1.96987 | 0.984933 | − | 0.172939i | \(-0.0553262\pi\) | ||||
0.984933 | + | 0.172939i | \(0.0553262\pi\) | |||||||
\(752\) | 1.86791e13 | 2.12998 | ||||||||
\(753\) | 9.69898e11 | 0.109938 | ||||||||
\(754\) | 4.49800e12 | 0.506814 | ||||||||
\(755\) | −9.64439e12 | −1.08022 | ||||||||
\(756\) | −2.44813e10 | −0.00272575 | ||||||||
\(757\) | 1.66475e13 | 1.84255 | 0.921273 | − | 0.388916i | \(-0.127150\pi\) | ||||
0.921273 | + | 0.388916i | \(0.127150\pi\) | |||||||
\(758\) | −1.94609e13 | −2.14117 | ||||||||
\(759\) | −7.06073e11 | −0.0772257 | ||||||||
\(760\) | −1.38242e13 | −1.50307 | ||||||||
\(761\) | 6.16014e12 | 0.665825 | 0.332912 | − | 0.942958i | \(-0.391969\pi\) | ||||
0.332912 | + | 0.942958i | \(0.391969\pi\) | |||||||
\(762\) | −2.91004e12 | −0.312681 | ||||||||
\(763\) | 1.11978e11 | 0.0119611 | ||||||||
\(764\) | 1.74691e13 | 1.85503 | ||||||||
\(765\) | −5.16199e12 | −0.544930 | ||||||||
\(766\) | −6.35575e12 | −0.667017 | ||||||||
\(767\) | 5.29917e11 | 0.0552877 | ||||||||
\(768\) | −1.13452e13 | −1.17676 | ||||||||
\(769\) | 1.33568e13 | 1.37731 | 0.688657 | − | 0.725087i | \(-0.258200\pi\) | ||||
0.688657 | + | 0.725087i | \(0.258200\pi\) | |||||||
\(770\) | −2.44113e11 | −0.0250255 | ||||||||
\(771\) | 5.63936e12 | 0.574758 | ||||||||
\(772\) | 3.25228e13 | 3.29542 | ||||||||
\(773\) | −3.22073e12 | −0.324449 | −0.162225 | − | 0.986754i | \(-0.551867\pi\) | ||||
−0.162225 | + | 0.986754i | \(0.551867\pi\) | |||||||
\(774\) | 2.34373e12 | 0.234732 | ||||||||
\(775\) | −2.67896e12 | −0.266753 | ||||||||
\(776\) | −3.15181e13 | −3.12020 | ||||||||
\(777\) | −1.71336e10 | −0.00168637 | ||||||||
\(778\) | −1.56235e13 | −1.52887 | ||||||||
\(779\) | −2.41653e12 | −0.235111 | ||||||||
\(780\) | 7.08454e12 | 0.685308 | ||||||||
\(781\) | 1.28578e13 | 1.23663 | ||||||||
\(782\) | 1.91426e12 | 0.183051 | ||||||||
\(783\) | 1.37487e12 | 0.130717 | ||||||||
\(784\) | −1.34244e13 | −1.26903 | ||||||||
\(785\) | −1.17374e13 | −1.10321 | ||||||||
\(786\) | 4.79807e12 | 0.448399 | ||||||||
\(787\) | 1.14501e13 | 1.06395 | 0.531977 | − | 0.846759i | \(-0.321449\pi\) | ||||
0.531977 | + | 0.846759i | \(0.321449\pi\) | |||||||
\(788\) | 2.07529e13 | 1.91739 | ||||||||
\(789\) | 7.25213e12 | 0.666222 | ||||||||
\(790\) | 4.30058e13 | 3.92830 | ||||||||
\(791\) | −2.84224e9 | −0.000258147 0 | ||||||||
\(792\) | −1.10503e13 | −0.997956 | ||||||||
\(793\) | 3.91574e12 | 0.351629 | ||||||||
\(794\) | −3.23593e13 | −2.88940 | ||||||||
\(795\) | 1.39532e13 | 1.23886 | ||||||||
\(796\) | 2.07990e13 | 1.83626 | ||||||||
\(797\) | 7.25906e12 | 0.637262 | 0.318631 | − | 0.947879i | \(-0.396777\pi\) | ||||
0.318631 | + | 0.947879i | \(0.396777\pi\) | |||||||
\(798\) | −4.63353e10 | −0.00404482 | ||||||||
\(799\) | 2.36031e13 | 2.04884 | ||||||||
\(800\) | −2.93805e12 | −0.253603 | ||||||||
\(801\) | −3.99850e12 | −0.343203 | ||||||||
\(802\) | 1.72940e13 | 1.47608 | ||||||||
\(803\) | −1.19546e13 | −1.01465 | ||||||||
\(804\) | −1.38348e13 | −1.16767 | ||||||||
\(805\) | −9.24043e9 | −0.000775552 0 | ||||||||
\(806\) | −3.00589e12 | −0.250880 | ||||||||
\(807\) | 8.99690e12 | 0.746727 | ||||||||
\(808\) | 5.05392e12 | 0.417135 | ||||||||
\(809\) | −1.85851e13 | −1.52544 | −0.762722 | − | 0.646726i | \(-0.776138\pi\) | ||||
−0.762722 | + | 0.646726i | \(0.776138\pi\) | |||||||
\(810\) | 3.20299e12 | 0.261440 | ||||||||
\(811\) | 2.15522e13 | 1.74944 | 0.874719 | − | 0.484630i | \(-0.161046\pi\) | ||||
0.874719 | + | 0.484630i | \(0.161046\pi\) | |||||||
\(812\) | −1.19175e11 | −0.00962014 | ||||||||
\(813\) | −2.19333e12 | −0.176074 | ||||||||
\(814\) | −1.48474e13 | −1.18533 | ||||||||
\(815\) | −5.57284e12 | −0.442453 | ||||||||
\(816\) | 1.13283e13 | 0.894457 | ||||||||
\(817\) | 2.99904e12 | 0.235496 | ||||||||
\(818\) | 1.31503e13 | 1.02694 | ||||||||
\(819\) | 1.23686e10 | 0.000960603 0 | ||||||||
\(820\) | −1.44797e13 | −1.11840 | ||||||||
\(821\) | 2.08276e13 | 1.59991 | 0.799954 | − | 0.600062i | \(-0.204857\pi\) | ||||
0.799954 | + | 0.600062i | \(0.204857\pi\) | |||||||
\(822\) | −1.22436e13 | −0.935373 | ||||||||
\(823\) | −9.47540e12 | −0.719943 | −0.359972 | − | 0.932963i | \(-0.617214\pi\) | ||||
−0.359972 | + | 0.932963i | \(0.617214\pi\) | |||||||
\(824\) | −3.45970e13 | −2.61436 | ||||||||
\(825\) | 9.55249e12 | 0.717916 | ||||||||
\(826\) | −2.07670e10 | −0.00155226 | ||||||||
\(827\) | 3.45208e12 | 0.256629 | 0.128315 | − | 0.991734i | \(-0.459043\pi\) | ||||
0.128315 | + | 0.991734i | \(0.459043\pi\) | |||||||
\(828\) | −8.03040e11 | −0.0593746 | ||||||||
\(829\) | −1.59708e13 | −1.17444 | −0.587222 | − | 0.809426i | \(-0.699779\pi\) | ||||
−0.587222 | + | 0.809426i | \(0.699779\pi\) | |||||||
\(830\) | −3.19312e13 | −2.33541 | ||||||||
\(831\) | −3.88835e12 | −0.282853 | ||||||||
\(832\) | 4.15247e12 | 0.300436 | ||||||||
\(833\) | −1.69633e13 | −1.22069 | ||||||||
\(834\) | 1.27103e12 | 0.0909723 | ||||||||
\(835\) | 3.12826e12 | 0.222697 | ||||||||
\(836\) | −2.71463e13 | −1.92213 | ||||||||
\(837\) | −9.18786e11 | −0.0647068 | ||||||||
\(838\) | −3.12476e12 | −0.218886 | ||||||||
\(839\) | 5.84124e12 | 0.406983 | 0.203491 | − | 0.979077i | \(-0.434771\pi\) | ||||
0.203491 | + | 0.979077i | \(0.434771\pi\) | |||||||
\(840\) | −1.44616e11 | −0.0100221 | ||||||||
\(841\) | −7.81431e12 | −0.538652 | ||||||||
\(842\) | −4.59319e13 | −3.14927 | ||||||||
\(843\) | −9.18035e12 | −0.626088 | ||||||||
\(844\) | −1.04444e13 | −0.708503 | ||||||||
\(845\) | 1.62675e13 | 1.09765 | ||||||||
\(846\) | −1.46456e13 | −0.982971 | ||||||||
\(847\) | −1.48045e11 | −0.00988366 | ||||||||
\(848\) | −3.06211e13 | −2.03348 | ||||||||
\(849\) | −5.19291e12 | −0.343025 | ||||||||
\(850\) | −2.58982e13 | −1.70170 | ||||||||
\(851\) | −5.62019e11 | −0.0367340 | ||||||||
\(852\) | 1.46236e13 | 0.950774 | ||||||||
\(853\) | 2.01733e10 | 0.00130468 | 0.000652342 | − | 1.00000i | \(-0.499792\pi\) | ||||
0.000652342 | 1.00000i | \(0.499792\pi\) | ||||||||
\(854\) | −1.53455e11 | −0.00987235 | ||||||||
\(855\) | 4.09855e12 | 0.262291 | ||||||||
\(856\) | 2.74641e13 | 1.74837 | ||||||||
\(857\) | 2.71965e12 | 0.172226 | 0.0861130 | − | 0.996285i | \(-0.472555\pi\) | ||||
0.0861130 | + | 0.996285i | \(0.472555\pi\) | |||||||
\(858\) | 1.07183e13 | 0.675198 | ||||||||
\(859\) | −1.34952e13 | −0.845688 | −0.422844 | − | 0.906203i | \(-0.638968\pi\) | ||||
−0.422844 | + | 0.906203i | \(0.638968\pi\) | |||||||
\(860\) | 1.79700e13 | 1.12023 | ||||||||
\(861\) | −2.52795e10 | −0.00156767 | ||||||||
\(862\) | −3.68613e13 | −2.27399 | ||||||||
\(863\) | −1.46281e13 | −0.897717 | −0.448859 | − | 0.893603i | \(-0.648169\pi\) | ||||
−0.448859 | + | 0.893603i | \(0.648169\pi\) | |||||||
\(864\) | −1.00765e12 | −0.0615171 | ||||||||
\(865\) | −2.50897e13 | −1.52378 | ||||||||
\(866\) | 2.12693e13 | 1.28506 | ||||||||
\(867\) | 4.70897e12 | 0.283035 | ||||||||
\(868\) | 7.96412e10 | 0.00476211 | ||||||||
\(869\) | 4.39882e13 | 2.61666 | ||||||||
\(870\) | 1.55921e13 | 0.922717 | ||||||||
\(871\) | 6.98975e12 | 0.411510 | ||||||||
\(872\) | 5.74857e13 | 3.36694 | ||||||||
\(873\) | 9.34436e12 | 0.544484 | ||||||||
\(874\) | −1.51990e12 | −0.0881077 | ||||||||
\(875\) | −3.25590e10 | −0.00187774 | ||||||||
\(876\) | −1.35964e13 | −0.780107 | ||||||||
\(877\) | 1.06900e13 | 0.610209 | 0.305105 | − | 0.952319i | \(-0.401309\pi\) | ||||
0.305105 | + | 0.952319i | \(0.401309\pi\) | |||||||
\(878\) | 1.46559e13 | 0.832312 | ||||||||
\(879\) | 1.05321e13 | 0.595069 | ||||||||
\(880\) | −4.73868e13 | −2.66370 | ||||||||
\(881\) | −2.64579e13 | −1.47967 | −0.739833 | − | 0.672790i | \(-0.765096\pi\) | ||||
−0.739833 | + | 0.672790i | \(0.765096\pi\) | |||||||
\(882\) | 1.05256e13 | 0.585651 | ||||||||
\(883\) | −1.05016e13 | −0.581342 | −0.290671 | − | 0.956823i | \(-0.593879\pi\) | ||||
−0.290671 | + | 0.956823i | \(0.593879\pi\) | |||||||
\(884\) | −1.96460e13 | −1.08203 | ||||||||
\(885\) | 1.83693e12 | 0.100658 | ||||||||
\(886\) | 4.55650e13 | 2.48416 | ||||||||
\(887\) | 1.51558e13 | 0.822098 | 0.411049 | − | 0.911613i | \(-0.365162\pi\) | ||||
0.411049 | + | 0.911613i | \(0.365162\pi\) | |||||||
\(888\) | −8.79581e12 | −0.474698 | ||||||||
\(889\) | −3.89539e10 | −0.00209167 | ||||||||
\(890\) | −4.53464e13 | −2.42263 | ||||||||
\(891\) | 3.27616e12 | 0.174147 | ||||||||
\(892\) | −1.14387e13 | −0.604971 | ||||||||
\(893\) | −1.87405e13 | −0.986168 | ||||||||
\(894\) | −6.76200e12 | −0.354043 | ||||||||
\(895\) | 2.24237e13 | 1.16817 | ||||||||
\(896\) | −2.04580e11 | −0.0106042 | ||||||||
\(897\) | 4.05719e11 | 0.0209247 | ||||||||
\(898\) | −2.91528e13 | −1.49602 | ||||||||
\(899\) | −4.47264e12 | −0.228374 | ||||||||
\(900\) | 1.08643e13 | 0.551966 | ||||||||
\(901\) | −3.86932e13 | −1.95602 | ||||||||
\(902\) | −2.19064e13 | −1.10190 | ||||||||
\(903\) | 3.13732e10 | 0.00157023 | ||||||||
\(904\) | −1.45911e12 | −0.0726660 | ||||||||
\(905\) | −2.28633e13 | −1.13297 | ||||||||
\(906\) | −1.65949e13 | −0.818272 | ||||||||
\(907\) | 1.91598e13 | 0.940067 | 0.470034 | − | 0.882649i | \(-0.344242\pi\) | ||||
0.470034 | + | 0.882649i | \(0.344242\pi\) | |||||||
\(908\) | −8.11881e12 | −0.396375 | ||||||||
\(909\) | −1.49837e12 | −0.0727915 | ||||||||
\(910\) | 1.40271e11 | 0.00678079 | ||||||||
\(911\) | 9.06518e12 | 0.436058 | 0.218029 | − | 0.975942i | \(-0.430037\pi\) | ||||
0.218029 | + | 0.975942i | \(0.430037\pi\) | |||||||
\(912\) | −8.99452e12 | −0.430528 | ||||||||
\(913\) | −3.26606e13 | −1.55563 | ||||||||
\(914\) | −2.76338e13 | −1.30973 | ||||||||
\(915\) | 1.35737e13 | 0.640183 | ||||||||
\(916\) | 4.22592e13 | 1.98332 | ||||||||
\(917\) | 6.42271e10 | 0.00299955 | ||||||||
\(918\) | −8.88212e12 | −0.412786 | ||||||||
\(919\) | 3.18663e13 | 1.47371 | 0.736854 | − | 0.676052i | \(-0.236310\pi\) | ||||
0.736854 | + | 0.676052i | \(0.236310\pi\) | |||||||
\(920\) | −4.74374e12 | −0.218311 | ||||||||
\(921\) | 7.55894e12 | 0.346173 | ||||||||
\(922\) | −2.21320e13 | −1.00863 | ||||||||
\(923\) | −7.38828e12 | −0.335070 | ||||||||
\(924\) | −2.83980e11 | −0.0128163 | ||||||||
\(925\) | 7.60357e12 | 0.341492 | ||||||||
\(926\) | −6.31212e13 | −2.82115 | ||||||||
\(927\) | 1.02572e13 | 0.456214 | ||||||||
\(928\) | −4.90521e12 | −0.217116 | ||||||||
\(929\) | −1.82057e13 | −0.801930 | −0.400965 | − | 0.916093i | \(-0.631325\pi\) | ||||
−0.400965 | + | 0.916093i | \(0.631325\pi\) | |||||||
\(930\) | −1.04198e13 | −0.456758 | ||||||||
\(931\) | 1.34686e13 | 0.587556 | ||||||||
\(932\) | 9.35837e13 | 4.06283 | ||||||||
\(933\) | 1.27932e13 | 0.552728 | ||||||||
\(934\) | 3.87150e12 | 0.166463 | ||||||||
\(935\) | −5.98786e13 | −2.56224 | ||||||||
\(936\) | 6.34965e12 | 0.270401 | ||||||||
\(937\) | 2.86463e13 | 1.21406 | 0.607029 | − | 0.794679i | \(-0.292361\pi\) | ||||
0.607029 | + | 0.794679i | \(0.292361\pi\) | |||||||
\(938\) | −2.73923e11 | −0.0115536 | ||||||||
\(939\) | −6.76674e12 | −0.284043 | ||||||||
\(940\) | −1.12292e14 | −4.69109 | ||||||||
\(941\) | 2.02281e13 | 0.841012 | 0.420506 | − | 0.907290i | \(-0.361853\pi\) | ||||
0.420506 | + | 0.907290i | \(0.361853\pi\) | |||||||
\(942\) | −2.01963e13 | −0.835686 | ||||||||
\(943\) | −8.29225e11 | −0.0341483 | ||||||||
\(944\) | −4.03126e12 | −0.165222 | ||||||||
\(945\) | 4.28753e10 | 0.00174890 | ||||||||
\(946\) | 2.71870e13 | 1.10370 | ||||||||
\(947\) | 4.65361e13 | 1.88025 | 0.940124 | − | 0.340833i | \(-0.110709\pi\) | ||||
0.940124 | + | 0.340833i | \(0.110709\pi\) | |||||||
\(948\) | 5.00292e13 | 2.01181 | ||||||||
\(949\) | 6.86927e12 | 0.274924 | ||||||||
\(950\) | 2.05628e13 | 0.819079 | ||||||||
\(951\) | −1.60562e13 | −0.636546 | ||||||||
\(952\) | 4.01032e11 | 0.0158239 | ||||||||
\(953\) | −7.93310e11 | −0.0311548 | −0.0155774 | − | 0.999879i | \(-0.504959\pi\) | ||||
−0.0155774 | + | 0.999879i | \(0.504959\pi\) | |||||||
\(954\) | 2.40089e13 | 0.938437 | ||||||||
\(955\) | −3.05946e13 | −1.19022 | ||||||||
\(956\) | 3.41639e13 | 1.32284 | ||||||||
\(957\) | 1.59483e13 | 0.614626 | ||||||||
\(958\) | 1.71544e13 | 0.658007 | ||||||||
\(959\) | −1.63893e11 | −0.00625715 | ||||||||
\(960\) | 1.43944e13 | 0.546981 | ||||||||
\(961\) | −2.34507e13 | −0.886952 | ||||||||
\(962\) | 8.53150e12 | 0.321172 | ||||||||
\(963\) | −8.14244e12 | −0.305096 | ||||||||
\(964\) | 3.76738e13 | 1.40505 | ||||||||
\(965\) | −5.69589e13 | −2.11441 | ||||||||
\(966\) | −1.58998e10 | −0.000587483 0 | ||||||||
\(967\) | 2.13665e13 | 0.785805 | 0.392903 | − | 0.919580i | \(-0.371471\pi\) | ||||
0.392903 | + | 0.919580i | \(0.371471\pi\) | |||||||
\(968\) | −7.60014e13 | −2.78216 | ||||||||
\(969\) | −1.13656e13 | −0.414128 | ||||||||
\(970\) | 1.05973e14 | 3.84346 | ||||||||
\(971\) | −3.68918e13 | −1.33181 | −0.665906 | − | 0.746036i | \(-0.731955\pi\) | ||||
−0.665906 | + | 0.746036i | \(0.731955\pi\) | |||||||
\(972\) | 3.72608e12 | 0.133892 | ||||||||
\(973\) | 1.70141e10 | 0.000608556 0 | ||||||||
\(974\) | 8.33918e13 | 2.96899 | ||||||||
\(975\) | −5.48898e12 | −0.194523 | ||||||||
\(976\) | −2.97884e13 | −1.05081 | ||||||||
\(977\) | 2.31976e13 | 0.814550 | 0.407275 | − | 0.913306i | \(-0.366479\pi\) | ||||
0.407275 | + | 0.913306i | \(0.366479\pi\) | |||||||
\(978\) | −9.58906e12 | −0.335159 | ||||||||
\(979\) | −4.63823e13 | −1.61373 | ||||||||
\(980\) | 8.07029e13 | 2.79494 | ||||||||
\(981\) | −1.70431e13 | −0.587542 | ||||||||
\(982\) | 5.27350e12 | 0.180966 | ||||||||
\(983\) | −3.48605e13 | −1.19081 | −0.595405 | − | 0.803425i | \(-0.703009\pi\) | ||||
−0.595405 | + | 0.803425i | \(0.703009\pi\) | |||||||
\(984\) | −1.29777e13 | −0.441285 | ||||||||
\(985\) | −3.63456e13 | −1.23024 | ||||||||
\(986\) | −4.32381e13 | −1.45687 | ||||||||
\(987\) | −1.96046e11 | −0.00657555 | ||||||||
\(988\) | 1.55986e13 | 0.520811 | ||||||||
\(989\) | 1.02911e12 | 0.0342042 | ||||||||
\(990\) | 3.71543e13 | 1.22928 | ||||||||
\(991\) | −5.67925e13 | −1.87051 | −0.935254 | − | 0.353977i | \(-0.884829\pi\) | ||||
−0.935254 | + | 0.353977i | \(0.884829\pi\) | |||||||
\(992\) | 3.27802e12 | 0.107475 | ||||||||
\(993\) | −2.12147e12 | −0.0692413 | ||||||||
\(994\) | 2.89541e11 | 0.00940744 | ||||||||
\(995\) | −3.64264e13 | −1.17818 | ||||||||
\(996\) | −3.71459e13 | −1.19604 | ||||||||
\(997\) | −2.65675e13 | −0.851575 | −0.425787 | − | 0.904823i | \(-0.640003\pi\) | ||||
−0.425787 | + | 0.904823i | \(0.640003\pi\) | |||||||
\(998\) | 1.53309e13 | 0.489192 | ||||||||
\(999\) | 2.60775e12 | 0.0828364 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.d.1.1 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.d.1.1 | ✓ | 22 | 1.1 | even | 1 | trivial |