Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −24.8760 | −1.09938 | −0.549688 | − | 0.835370i | \(-0.685253\pi\) | ||||
−0.549688 | + | 0.835370i | \(0.685253\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 106.816 | 0.208626 | ||||||||
\(5\) | −222.031 | −0.158872 | −0.0794362 | − | 0.996840i | \(-0.525312\pi\) | ||||
−0.0794362 | + | 0.996840i | \(0.525312\pi\) | |||||||
\(6\) | −2014.96 | −0.634725 | ||||||||
\(7\) | −2494.49 | −0.392681 | −0.196341 | − | 0.980536i | \(-0.562906\pi\) | ||||
−0.196341 | + | 0.980536i | \(0.562906\pi\) | |||||||
\(8\) | 10079.4 | 0.870017 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 5523.25 | 0.174660 | ||||||||
\(11\) | −17730.3 | −0.365131 | −0.182565 | − | 0.983194i | \(-0.558440\pi\) | ||||
−0.182565 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(12\) | 8652.13 | 0.120450 | ||||||||
\(13\) | −12233.5 | −0.118797 | −0.0593987 | − | 0.998234i | \(-0.518918\pi\) | ||||
−0.0593987 | + | 0.998234i | \(0.518918\pi\) | |||||||
\(14\) | 62052.9 | 0.431704 | ||||||||
\(15\) | −17984.5 | −0.0917251 | ||||||||
\(16\) | −305424. | −1.16510 | ||||||||
\(17\) | −170541. | −0.495231 | −0.247616 | − | 0.968858i | \(-0.579647\pi\) | ||||
−0.247616 | + | 0.968858i | \(0.579647\pi\) | |||||||
\(18\) | −163212. | −0.366458 | ||||||||
\(19\) | 800159. | 1.40859 | 0.704296 | − | 0.709906i | \(-0.251263\pi\) | ||||
0.704296 | + | 0.709906i | \(0.251263\pi\) | |||||||
\(20\) | −23716.6 | −0.0331449 | ||||||||
\(21\) | −202053. | −0.226715 | ||||||||
\(22\) | 441059. | 0.401416 | ||||||||
\(23\) | −44122.7 | −0.0328766 | −0.0164383 | − | 0.999865i | \(-0.505233\pi\) | ||||
−0.0164383 | + | 0.999865i | \(0.505233\pi\) | |||||||
\(24\) | 816428. | 0.502305 | ||||||||
\(25\) | −1.90383e6 | −0.974760 | ||||||||
\(26\) | 304322. | 0.130603 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −266452. | −0.0819235 | ||||||||
\(29\) | 2.97244e6 | 0.780409 | 0.390204 | − | 0.920728i | \(-0.372404\pi\) | ||||
0.390204 | + | 0.920728i | \(0.372404\pi\) | |||||||
\(30\) | 447383. | 0.100840 | ||||||||
\(31\) | 3.78495e6 | 0.736093 | 0.368047 | − | 0.929807i | \(-0.380027\pi\) | ||||
0.368047 | + | 0.929807i | \(0.380027\pi\) | |||||||
\(32\) | 2.43711e6 | 0.410866 | ||||||||
\(33\) | −1.43615e6 | −0.210808 | ||||||||
\(34\) | 4.24237e6 | 0.544445 | ||||||||
\(35\) | 553854. | 0.0623862 | ||||||||
\(36\) | 700823. | 0.0695420 | ||||||||
\(37\) | −1.62591e7 | −1.42623 | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||||
−0.713115 | + | 0.701047i | \(0.752716\pi\) | |||||||
\(38\) | −1.99048e7 | −1.54857 | ||||||||
\(39\) | −990917. | −0.0685877 | ||||||||
\(40\) | −2.23793e6 | −0.138222 | ||||||||
\(41\) | 4.70674e6 | 0.260131 | 0.130066 | − | 0.991505i | \(-0.458481\pi\) | ||||
0.130066 | + | 0.991505i | \(0.458481\pi\) | |||||||
\(42\) | 5.02629e6 | 0.249244 | ||||||||
\(43\) | −2.93262e6 | −0.130812 | −0.0654060 | − | 0.997859i | \(-0.520834\pi\) | ||||
−0.0654060 | + | 0.997859i | \(0.520834\pi\) | |||||||
\(44\) | −1.89389e6 | −0.0761758 | ||||||||
\(45\) | −1.45675e6 | −0.0529575 | ||||||||
\(46\) | 1.09760e6 | 0.0361437 | ||||||||
\(47\) | 5.72676e7 | 1.71186 | 0.855931 | − | 0.517089i | \(-0.172985\pi\) | ||||
0.855931 | + | 0.517089i | \(0.172985\pi\) | |||||||
\(48\) | −2.47394e7 | −0.672671 | ||||||||
\(49\) | −3.41311e7 | −0.845801 | ||||||||
\(50\) | 4.73596e7 | 1.07163 | ||||||||
\(51\) | −1.38138e7 | −0.285922 | ||||||||
\(52\) | −1.30674e6 | −0.0247842 | ||||||||
\(53\) | −7.27248e7 | −1.26602 | −0.633011 | − | 0.774143i | \(-0.718181\pi\) | ||||
−0.633011 | + | 0.774143i | \(0.718181\pi\) | |||||||
\(54\) | −1.32201e7 | −0.211575 | ||||||||
\(55\) | 3.93667e6 | 0.0580093 | ||||||||
\(56\) | −2.51428e7 | −0.341639 | ||||||||
\(57\) | 6.48129e7 | 0.813251 | ||||||||
\(58\) | −7.39425e7 | −0.857962 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | −1.92104e6 | −0.0191362 | ||||||||
\(61\) | 1.75038e8 | 1.61863 | 0.809314 | − | 0.587377i | \(-0.199839\pi\) | ||||
0.809314 | + | 0.587377i | \(0.199839\pi\) | |||||||
\(62\) | −9.41546e7 | −0.809243 | ||||||||
\(63\) | −1.63663e7 | −0.130894 | ||||||||
\(64\) | 9.57516e7 | 0.713405 | ||||||||
\(65\) | 2.71623e6 | 0.0188736 | ||||||||
\(66\) | 3.57258e7 | 0.231758 | ||||||||
\(67\) | 2.04648e8 | 1.24071 | 0.620357 | − | 0.784320i | \(-0.286988\pi\) | ||||
0.620357 | + | 0.784320i | \(0.286988\pi\) | |||||||
\(68\) | −1.82166e7 | −0.103318 | ||||||||
\(69\) | −3.57394e6 | −0.0189813 | ||||||||
\(70\) | −1.37777e7 | −0.0685859 | ||||||||
\(71\) | 4.00362e8 | 1.86978 | 0.934890 | − | 0.354938i | \(-0.115498\pi\) | ||||
0.934890 | + | 0.354938i | \(0.115498\pi\) | |||||||
\(72\) | 6.61306e7 | 0.290006 | ||||||||
\(73\) | −2.17223e8 | −0.895269 | −0.447634 | − | 0.894217i | \(-0.647733\pi\) | ||||
−0.447634 | + | 0.894217i | \(0.647733\pi\) | |||||||
\(74\) | 4.04463e8 | 1.56796 | ||||||||
\(75\) | −1.54210e8 | −0.562778 | ||||||||
\(76\) | 8.54702e7 | 0.293869 | ||||||||
\(77\) | 4.42280e7 | 0.143380 | ||||||||
\(78\) | 2.46501e7 | 0.0754036 | ||||||||
\(79\) | 3.33758e8 | 0.964073 | 0.482036 | − | 0.876151i | \(-0.339897\pi\) | ||||
0.482036 | + | 0.876151i | \(0.339897\pi\) | |||||||
\(80\) | 6.78137e7 | 0.185103 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.17085e8 | −0.285982 | ||||||||
\(83\) | −3.31607e8 | −0.766959 | −0.383479 | − | 0.923549i | \(-0.625274\pi\) | ||||
−0.383479 | + | 0.923549i | \(0.625274\pi\) | |||||||
\(84\) | −2.15826e7 | −0.0472985 | ||||||||
\(85\) | 3.78653e7 | 0.0786786 | ||||||||
\(86\) | 7.29519e7 | 0.143811 | ||||||||
\(87\) | 2.40768e8 | 0.450569 | ||||||||
\(88\) | −1.78710e8 | −0.317670 | ||||||||
\(89\) | −9.11608e8 | −1.54011 | −0.770057 | − | 0.637975i | \(-0.779772\pi\) | ||||
−0.770057 | + | 0.637975i | \(0.779772\pi\) | |||||||
\(90\) | 3.62380e7 | 0.0582202 | ||||||||
\(91\) | 3.05164e7 | 0.0466495 | ||||||||
\(92\) | −4.71303e6 | −0.00685890 | ||||||||
\(93\) | 3.06581e8 | 0.424984 | ||||||||
\(94\) | −1.42459e9 | −1.88198 | ||||||||
\(95\) | −1.77660e8 | −0.223786 | ||||||||
\(96\) | 1.97406e8 | 0.237214 | ||||||||
\(97\) | −4.51337e8 | −0.517640 | −0.258820 | − | 0.965926i | \(-0.583334\pi\) | ||||
−0.258820 | + | 0.965926i | \(0.583334\pi\) | |||||||
\(98\) | 8.49047e8 | 0.929853 | ||||||||
\(99\) | −1.16328e8 | −0.121710 | ||||||||
\(100\) | −2.03360e8 | −0.203360 | ||||||||
\(101\) | −9.39227e8 | −0.898099 | −0.449050 | − | 0.893507i | \(-0.648237\pi\) | ||||
−0.449050 | + | 0.893507i | \(0.648237\pi\) | |||||||
\(102\) | 3.43632e8 | 0.314335 | ||||||||
\(103\) | 4.99025e8 | 0.436872 | 0.218436 | − | 0.975851i | \(-0.429904\pi\) | ||||
0.218436 | + | 0.975851i | \(0.429904\pi\) | |||||||
\(104\) | −1.23306e8 | −0.103356 | ||||||||
\(105\) | 4.48621e7 | 0.0360187 | ||||||||
\(106\) | 1.80910e9 | 1.39183 | ||||||||
\(107\) | −1.84221e9 | −1.35866 | −0.679331 | − | 0.733832i | \(-0.737730\pi\) | ||||
−0.679331 | + | 0.733832i | \(0.737730\pi\) | |||||||
\(108\) | 5.67666e7 | 0.0401501 | ||||||||
\(109\) | 1.61168e9 | 1.09360 | 0.546801 | − | 0.837263i | \(-0.315846\pi\) | ||||
0.546801 | + | 0.837263i | \(0.315846\pi\) | |||||||
\(110\) | −9.79288e7 | −0.0637740 | ||||||||
\(111\) | −1.31699e9 | −0.823435 | ||||||||
\(112\) | 7.61877e8 | 0.457513 | ||||||||
\(113\) | −2.32034e9 | −1.33875 | −0.669375 | − | 0.742925i | \(-0.733438\pi\) | ||||
−0.669375 | + | 0.742925i | \(0.733438\pi\) | |||||||
\(114\) | −1.61229e9 | −0.894068 | ||||||||
\(115\) | 9.79660e6 | 0.00522318 | ||||||||
\(116\) | 3.17506e8 | 0.162813 | ||||||||
\(117\) | −8.02642e7 | −0.0395991 | ||||||||
\(118\) | −3.01432e8 | −0.143126 | ||||||||
\(119\) | 4.25412e8 | 0.194468 | ||||||||
\(120\) | −1.81272e8 | −0.0798024 | ||||||||
\(121\) | −2.04358e9 | −0.866679 | ||||||||
\(122\) | −4.35424e9 | −1.77948 | ||||||||
\(123\) | 3.81246e8 | 0.150187 | ||||||||
\(124\) | 4.04295e8 | 0.153568 | ||||||||
\(125\) | 8.56363e8 | 0.313735 | ||||||||
\(126\) | 4.07129e8 | 0.143901 | ||||||||
\(127\) | −6.43612e8 | −0.219537 | −0.109768 | − | 0.993957i | \(-0.535011\pi\) | ||||
−0.109768 | + | 0.993957i | \(0.535011\pi\) | |||||||
\(128\) | −3.62972e9 | −1.19517 | ||||||||
\(129\) | −2.37542e8 | −0.0755243 | ||||||||
\(130\) | −6.75689e7 | −0.0207492 | ||||||||
\(131\) | −1.48253e9 | −0.439827 | −0.219914 | − | 0.975519i | \(-0.570578\pi\) | ||||
−0.219914 | + | 0.975519i | \(0.570578\pi\) | |||||||
\(132\) | −1.53405e8 | −0.0439801 | ||||||||
\(133\) | −1.99599e9 | −0.553128 | ||||||||
\(134\) | −5.09083e9 | −1.36401 | ||||||||
\(135\) | −1.17996e8 | −0.0305750 | ||||||||
\(136\) | −1.71894e9 | −0.430859 | ||||||||
\(137\) | −4.89641e9 | −1.18750 | −0.593752 | − | 0.804648i | \(-0.702354\pi\) | ||||
−0.593752 | + | 0.804648i | \(0.702354\pi\) | |||||||
\(138\) | 8.89053e7 | 0.0208676 | ||||||||
\(139\) | 1.02222e9 | 0.232262 | 0.116131 | − | 0.993234i | \(-0.462951\pi\) | ||||
0.116131 | + | 0.993234i | \(0.462951\pi\) | |||||||
\(140\) | 5.91607e7 | 0.0130154 | ||||||||
\(141\) | 4.63868e9 | 0.988344 | ||||||||
\(142\) | −9.95942e9 | −2.05559 | ||||||||
\(143\) | 2.16904e8 | 0.0433766 | ||||||||
\(144\) | −2.00389e9 | −0.388367 | ||||||||
\(145\) | −6.59974e8 | −0.123986 | ||||||||
\(146\) | 5.40365e9 | 0.984236 | ||||||||
\(147\) | −2.76462e9 | −0.488324 | ||||||||
\(148\) | −1.73674e9 | −0.297549 | ||||||||
\(149\) | −8.58555e9 | −1.42702 | −0.713510 | − | 0.700645i | \(-0.752896\pi\) | ||||
−0.713510 | + | 0.700645i | \(0.752896\pi\) | |||||||
\(150\) | 3.83613e9 | 0.618704 | ||||||||
\(151\) | −7.12323e8 | −0.111501 | −0.0557507 | − | 0.998445i | \(-0.517755\pi\) | ||||
−0.0557507 | + | 0.998445i | \(0.517755\pi\) | |||||||
\(152\) | 8.06509e9 | 1.22550 | ||||||||
\(153\) | −1.11892e9 | −0.165077 | ||||||||
\(154\) | −1.10022e9 | −0.157629 | ||||||||
\(155\) | −8.40377e8 | −0.116945 | ||||||||
\(156\) | −1.05846e8 | −0.0143092 | ||||||||
\(157\) | −1.19629e10 | −1.57141 | −0.785706 | − | 0.618601i | \(-0.787700\pi\) | ||||
−0.785706 | + | 0.618601i | \(0.787700\pi\) | |||||||
\(158\) | −8.30257e9 | −1.05988 | ||||||||
\(159\) | −5.89071e9 | −0.730938 | ||||||||
\(160\) | −5.41114e8 | −0.0652753 | ||||||||
\(161\) | 1.10063e8 | 0.0129100 | ||||||||
\(162\) | −1.07083e9 | −0.122153 | ||||||||
\(163\) | −5.38110e9 | −0.597073 | −0.298536 | − | 0.954398i | \(-0.596498\pi\) | ||||
−0.298536 | + | 0.954398i | \(0.596498\pi\) | |||||||
\(164\) | 5.02757e8 | 0.0542701 | ||||||||
\(165\) | 3.18871e8 | 0.0334917 | ||||||||
\(166\) | 8.24906e9 | 0.843175 | ||||||||
\(167\) | −1.56592e10 | −1.55792 | −0.778960 | − | 0.627074i | \(-0.784253\pi\) | ||||
−0.778960 | + | 0.627074i | \(0.784253\pi\) | |||||||
\(168\) | −2.03657e9 | −0.197246 | ||||||||
\(169\) | −1.04548e10 | −0.985887 | ||||||||
\(170\) | −9.41939e8 | −0.0864973 | ||||||||
\(171\) | 5.24984e9 | 0.469531 | ||||||||
\(172\) | −3.13252e8 | −0.0272908 | ||||||||
\(173\) | −5.95860e9 | −0.505751 | −0.252875 | − | 0.967499i | \(-0.581376\pi\) | ||||
−0.252875 | + | 0.967499i | \(0.581376\pi\) | |||||||
\(174\) | −5.98934e9 | −0.495345 | ||||||||
\(175\) | 4.74907e9 | 0.382770 | ||||||||
\(176\) | 5.41526e9 | 0.425415 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | 2.26772e10 | 1.69316 | ||||||||
\(179\) | 4.50143e9 | 0.327727 | 0.163863 | − | 0.986483i | \(-0.447604\pi\) | ||||
0.163863 | + | 0.986483i | \(0.447604\pi\) | |||||||
\(180\) | −1.55604e8 | −0.0110483 | ||||||||
\(181\) | 1.42253e10 | 0.985163 | 0.492582 | − | 0.870266i | \(-0.336053\pi\) | ||||
0.492582 | + | 0.870266i | \(0.336053\pi\) | |||||||
\(182\) | −7.59127e8 | −0.0512853 | ||||||||
\(183\) | 1.41780e10 | 0.934515 | ||||||||
\(184\) | −4.44728e8 | −0.0286032 | ||||||||
\(185\) | 3.61003e9 | 0.226589 | ||||||||
\(186\) | −7.62652e9 | −0.467217 | ||||||||
\(187\) | 3.02374e9 | 0.180824 | ||||||||
\(188\) | 6.11713e9 | 0.357139 | ||||||||
\(189\) | −1.32567e9 | −0.0755715 | ||||||||
\(190\) | 4.41948e9 | 0.246025 | ||||||||
\(191\) | −3.48150e10 | −1.89285 | −0.946425 | − | 0.322924i | \(-0.895334\pi\) | ||||
−0.946425 | + | 0.322924i | \(0.895334\pi\) | |||||||
\(192\) | 7.75588e9 | 0.411885 | ||||||||
\(193\) | 7.57616e9 | 0.393044 | 0.196522 | − | 0.980499i | \(-0.437035\pi\) | ||||
0.196522 | + | 0.980499i | \(0.437035\pi\) | |||||||
\(194\) | 1.12275e10 | 0.569081 | ||||||||
\(195\) | 2.20014e8 | 0.0108967 | ||||||||
\(196\) | −3.64577e9 | −0.176456 | ||||||||
\(197\) | 3.25173e10 | 1.53821 | 0.769105 | − | 0.639122i | \(-0.220702\pi\) | ||||
0.769105 | + | 0.639122i | \(0.220702\pi\) | |||||||
\(198\) | 2.89379e9 | 0.133805 | ||||||||
\(199\) | −2.52469e10 | −1.14122 | −0.570611 | − | 0.821221i | \(-0.693293\pi\) | ||||
−0.570611 | + | 0.821221i | \(0.693293\pi\) | |||||||
\(200\) | −1.91893e10 | −0.848057 | ||||||||
\(201\) | 1.65765e10 | 0.716326 | ||||||||
\(202\) | 2.33642e10 | 0.987348 | ||||||||
\(203\) | −7.41472e9 | −0.306452 | ||||||||
\(204\) | −1.47554e9 | −0.0596507 | ||||||||
\(205\) | −1.04504e9 | −0.0413277 | ||||||||
\(206\) | −1.24137e10 | −0.480287 | ||||||||
\(207\) | −2.89489e8 | −0.0109589 | ||||||||
\(208\) | 3.73642e9 | 0.138411 | ||||||||
\(209\) | −1.41871e10 | −0.514321 | ||||||||
\(210\) | −1.11599e9 | −0.0395981 | ||||||||
\(211\) | 2.07497e10 | 0.720675 | 0.360338 | − | 0.932822i | \(-0.382661\pi\) | ||||
0.360338 | + | 0.932822i | \(0.382661\pi\) | |||||||
\(212\) | −7.76821e9 | −0.264125 | ||||||||
\(213\) | 3.24293e10 | 1.07952 | ||||||||
\(214\) | 4.58268e10 | 1.49368 | ||||||||
\(215\) | 6.51132e8 | 0.0207824 | ||||||||
\(216\) | 5.35658e9 | 0.167435 | ||||||||
\(217\) | −9.44152e9 | −0.289050 | ||||||||
\(218\) | −4.00921e10 | −1.20228 | ||||||||
\(219\) | −1.75951e10 | −0.516884 | ||||||||
\(220\) | 4.20502e8 | 0.0121022 | ||||||||
\(221\) | 2.08632e9 | 0.0588322 | ||||||||
\(222\) | 3.27615e10 | 0.905264 | ||||||||
\(223\) | 5.08398e10 | 1.37668 | 0.688338 | − | 0.725390i | \(-0.258341\pi\) | ||||
0.688338 | + | 0.725390i | \(0.258341\pi\) | |||||||
\(224\) | −6.07934e9 | −0.161339 | ||||||||
\(225\) | −1.24910e10 | −0.324920 | ||||||||
\(226\) | 5.77209e10 | 1.47179 | ||||||||
\(227\) | −4.19962e10 | −1.04977 | −0.524884 | − | 0.851174i | \(-0.675891\pi\) | ||||
−0.524884 | + | 0.851174i | \(0.675891\pi\) | |||||||
\(228\) | 6.92308e9 | 0.169665 | ||||||||
\(229\) | −5.74889e10 | −1.38142 | −0.690708 | − | 0.723134i | \(-0.742701\pi\) | ||||
−0.690708 | + | 0.723134i | \(0.742701\pi\) | |||||||
\(230\) | −2.43700e8 | −0.00574224 | ||||||||
\(231\) | 3.58247e9 | 0.0827805 | ||||||||
\(232\) | 2.99603e10 | 0.678969 | ||||||||
\(233\) | 8.28802e10 | 1.84225 | 0.921126 | − | 0.389264i | \(-0.127270\pi\) | ||||
0.921126 | + | 0.389264i | \(0.127270\pi\) | |||||||
\(234\) | 1.99666e9 | 0.0435343 | ||||||||
\(235\) | −1.27152e10 | −0.271968 | ||||||||
\(236\) | 1.29433e9 | 0.0271608 | ||||||||
\(237\) | 2.70344e10 | 0.556608 | ||||||||
\(238\) | −1.05825e10 | −0.213793 | ||||||||
\(239\) | −3.92640e10 | −0.778403 | −0.389201 | − | 0.921153i | \(-0.627249\pi\) | ||||
−0.389201 | + | 0.921153i | \(0.627249\pi\) | |||||||
\(240\) | 5.49291e9 | 0.106869 | ||||||||
\(241\) | 4.09839e10 | 0.782595 | 0.391297 | − | 0.920264i | \(-0.372026\pi\) | ||||
0.391297 | + | 0.920264i | \(0.372026\pi\) | |||||||
\(242\) | 5.08363e10 | 0.952806 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 1.86969e10 | 0.337688 | ||||||||
\(245\) | 7.57817e9 | 0.134375 | ||||||||
\(246\) | −9.48388e9 | −0.165112 | ||||||||
\(247\) | −9.78878e9 | −0.167337 | ||||||||
\(248\) | 3.81499e10 | 0.640414 | ||||||||
\(249\) | −2.68601e10 | −0.442804 | ||||||||
\(250\) | −2.13029e10 | −0.344912 | ||||||||
\(251\) | −4.86170e10 | −0.773137 | −0.386569 | − | 0.922261i | \(-0.626340\pi\) | ||||
−0.386569 | + | 0.922261i | \(0.626340\pi\) | |||||||
\(252\) | −1.74819e9 | −0.0273078 | ||||||||
\(253\) | 7.82308e8 | 0.0120043 | ||||||||
\(254\) | 1.60105e10 | 0.241353 | ||||||||
\(255\) | 3.06709e9 | 0.0454251 | ||||||||
\(256\) | 4.12682e10 | 0.600531 | ||||||||
\(257\) | −1.19445e11 | −1.70793 | −0.853965 | − | 0.520331i | \(-0.825809\pi\) | ||||
−0.853965 | + | 0.520331i | \(0.825809\pi\) | |||||||
\(258\) | 5.90910e9 | 0.0830296 | ||||||||
\(259\) | 4.05582e10 | 0.560054 | ||||||||
\(260\) | 2.90138e8 | 0.00393753 | ||||||||
\(261\) | 1.95022e10 | 0.260136 | ||||||||
\(262\) | 3.68794e10 | 0.483535 | ||||||||
\(263\) | −1.23073e11 | −1.58621 | −0.793107 | − | 0.609083i | \(-0.791538\pi\) | ||||
−0.793107 | + | 0.609083i | \(0.791538\pi\) | |||||||
\(264\) | −1.44755e10 | −0.183407 | ||||||||
\(265\) | 1.61472e10 | 0.201136 | ||||||||
\(266\) | 4.96522e10 | 0.608095 | ||||||||
\(267\) | −7.38402e10 | −0.889186 | ||||||||
\(268\) | 2.18598e10 | 0.258845 | ||||||||
\(269\) | −1.84342e10 | −0.214654 | −0.107327 | − | 0.994224i | \(-0.534229\pi\) | ||||
−0.107327 | + | 0.994224i | \(0.534229\pi\) | |||||||
\(270\) | 2.93528e9 | 0.0336134 | ||||||||
\(271\) | 1.45903e11 | 1.64325 | 0.821625 | − | 0.570028i | \(-0.193068\pi\) | ||||
0.821625 | + | 0.570028i | \(0.193068\pi\) | |||||||
\(272\) | 5.20873e10 | 0.576994 | ||||||||
\(273\) | 2.47183e9 | 0.0269331 | ||||||||
\(274\) | 1.21803e11 | 1.30551 | ||||||||
\(275\) | 3.37554e10 | 0.355915 | ||||||||
\(276\) | −3.81755e8 | −0.00395999 | ||||||||
\(277\) | −1.10202e11 | −1.12469 | −0.562345 | − | 0.826903i | \(-0.690101\pi\) | ||||
−0.562345 | + | 0.826903i | \(0.690101\pi\) | |||||||
\(278\) | −2.54288e10 | −0.255344 | ||||||||
\(279\) | 2.48331e10 | 0.245364 | ||||||||
\(280\) | 5.58249e9 | 0.0542771 | ||||||||
\(281\) | 8.05599e10 | 0.770798 | 0.385399 | − | 0.922750i | \(-0.374064\pi\) | ||||
0.385399 | + | 0.922750i | \(0.374064\pi\) | |||||||
\(282\) | −1.15392e11 | −1.08656 | ||||||||
\(283\) | −2.74018e8 | −0.00253945 | −0.00126973 | − | 0.999999i | \(-0.500404\pi\) | ||||
−0.00126973 | + | 0.999999i | \(0.500404\pi\) | |||||||
\(284\) | 4.27653e10 | 0.390084 | ||||||||
\(285\) | −1.43905e10 | −0.129203 | ||||||||
\(286\) | −5.39571e9 | −0.0476872 | ||||||||
\(287\) | −1.17409e10 | −0.102149 | ||||||||
\(288\) | 1.59899e10 | 0.136955 | ||||||||
\(289\) | −8.95037e10 | −0.754746 | ||||||||
\(290\) | 1.64175e10 | 0.136307 | ||||||||
\(291\) | −3.65583e10 | −0.298860 | ||||||||
\(292\) | −2.32030e10 | −0.186776 | ||||||||
\(293\) | −6.56715e10 | −0.520562 | −0.260281 | − | 0.965533i | \(-0.583815\pi\) | ||||
−0.260281 | + | 0.965533i | \(0.583815\pi\) | |||||||
\(294\) | 6.87728e10 | 0.536851 | ||||||||
\(295\) | −2.69043e9 | −0.0206834 | ||||||||
\(296\) | −1.63882e11 | −1.24085 | ||||||||
\(297\) | −9.42260e9 | −0.0702695 | ||||||||
\(298\) | 2.13574e11 | 1.56883 | ||||||||
\(299\) | 5.39776e8 | 0.00390565 | ||||||||
\(300\) | −1.64722e10 | −0.117410 | ||||||||
\(301\) | 7.31538e9 | 0.0513674 | ||||||||
\(302\) | 1.77198e10 | 0.122582 | ||||||||
\(303\) | −7.60774e10 | −0.518518 | ||||||||
\(304\) | −2.44388e11 | −1.64115 | ||||||||
\(305\) | −3.88638e10 | −0.257155 | ||||||||
\(306\) | 2.78342e10 | 0.181482 | ||||||||
\(307\) | 2.68465e10 | 0.172490 | 0.0862452 | − | 0.996274i | \(-0.472513\pi\) | ||||
0.0862452 | + | 0.996274i | \(0.472513\pi\) | |||||||
\(308\) | 4.72428e9 | 0.0299128 | ||||||||
\(309\) | 4.04210e10 | 0.252228 | ||||||||
\(310\) | 2.09052e10 | 0.128566 | ||||||||
\(311\) | −2.14410e11 | −1.29964 | −0.649821 | − | 0.760088i | \(-0.725156\pi\) | ||||
−0.649821 | + | 0.760088i | \(0.725156\pi\) | |||||||
\(312\) | −9.98780e9 | −0.0596725 | ||||||||
\(313\) | 2.76816e11 | 1.63020 | 0.815102 | − | 0.579318i | \(-0.196681\pi\) | ||||
0.815102 | + | 0.579318i | \(0.196681\pi\) | |||||||
\(314\) | 2.97591e11 | 1.72757 | ||||||||
\(315\) | 3.63383e9 | 0.0207954 | ||||||||
\(316\) | 3.56508e10 | 0.201130 | ||||||||
\(317\) | 9.32046e10 | 0.518407 | 0.259203 | − | 0.965823i | \(-0.416540\pi\) | ||||
0.259203 | + | 0.965823i | \(0.416540\pi\) | |||||||
\(318\) | 1.46537e11 | 0.803575 | ||||||||
\(319\) | −5.27022e10 | −0.284951 | ||||||||
\(320\) | −2.12598e10 | −0.113340 | ||||||||
\(321\) | −1.49219e11 | −0.784424 | ||||||||
\(322\) | −2.73794e9 | −0.0141929 | ||||||||
\(323\) | −1.36460e11 | −0.697578 | ||||||||
\(324\) | 4.59810e9 | 0.0231807 | ||||||||
\(325\) | 2.32905e10 | 0.115799 | ||||||||
\(326\) | 1.33860e11 | 0.656407 | ||||||||
\(327\) | 1.30546e11 | 0.631391 | ||||||||
\(328\) | 4.74409e10 | 0.226319 | ||||||||
\(329\) | −1.42853e11 | −0.672216 | ||||||||
\(330\) | −7.93223e9 | −0.0368199 | ||||||||
\(331\) | −2.31416e11 | −1.05966 | −0.529831 | − | 0.848103i | \(-0.677745\pi\) | ||||
−0.529831 | + | 0.848103i | \(0.677745\pi\) | |||||||
\(332\) | −3.54211e10 | −0.160007 | ||||||||
\(333\) | −1.06676e11 | −0.475410 | ||||||||
\(334\) | 3.89538e11 | 1.71274 | ||||||||
\(335\) | −4.54383e10 | −0.197115 | ||||||||
\(336\) | 6.17120e10 | 0.264145 | ||||||||
\(337\) | −3.10705e11 | −1.31224 | −0.656121 | − | 0.754655i | \(-0.727804\pi\) | ||||
−0.656121 | + | 0.754655i | \(0.727804\pi\) | |||||||
\(338\) | 2.60075e11 | 1.08386 | ||||||||
\(339\) | −1.87948e11 | −0.772927 | ||||||||
\(340\) | 4.04464e9 | 0.0164144 | ||||||||
\(341\) | −6.71083e10 | −0.268770 | ||||||||
\(342\) | −1.30595e11 | −0.516190 | ||||||||
\(343\) | 1.85801e11 | 0.724812 | ||||||||
\(344\) | −2.95589e10 | −0.113809 | ||||||||
\(345\) | 7.93525e8 | 0.00301561 | ||||||||
\(346\) | 1.48226e11 | 0.556010 | ||||||||
\(347\) | 4.06988e11 | 1.50695 | 0.753475 | − | 0.657476i | \(-0.228376\pi\) | ||||
0.753475 | + | 0.657476i | \(0.228376\pi\) | |||||||
\(348\) | 2.57180e10 | 0.0940004 | ||||||||
\(349\) | 3.09331e11 | 1.11612 | 0.558058 | − | 0.829802i | \(-0.311547\pi\) | ||||
0.558058 | + | 0.829802i | \(0.311547\pi\) | |||||||
\(350\) | −1.18138e11 | −0.420808 | ||||||||
\(351\) | −6.50140e9 | −0.0228626 | ||||||||
\(352\) | −4.32107e10 | −0.150020 | ||||||||
\(353\) | 1.60790e11 | 0.551154 | 0.275577 | − | 0.961279i | \(-0.411131\pi\) | ||||
0.275577 | + | 0.961279i | \(0.411131\pi\) | |||||||
\(354\) | −2.44160e10 | −0.0826341 | ||||||||
\(355\) | −8.88928e10 | −0.297057 | ||||||||
\(356\) | −9.73747e10 | −0.321308 | ||||||||
\(357\) | 3.44583e10 | 0.112276 | ||||||||
\(358\) | −1.11978e11 | −0.360294 | ||||||||
\(359\) | 4.04099e10 | 0.128399 | 0.0641996 | − | 0.997937i | \(-0.479551\pi\) | ||||
0.0641996 | + | 0.997937i | \(0.479551\pi\) | |||||||
\(360\) | −1.46831e10 | −0.0460739 | ||||||||
\(361\) | 3.17567e11 | 0.984131 | ||||||||
\(362\) | −3.53869e11 | −1.08306 | ||||||||
\(363\) | −1.65530e11 | −0.500378 | ||||||||
\(364\) | 3.25965e9 | 0.00973230 | ||||||||
\(365\) | 4.82303e10 | 0.142234 | ||||||||
\(366\) | −3.52693e11 | −1.02738 | ||||||||
\(367\) | 4.75777e11 | 1.36901 | 0.684505 | − | 0.729009i | \(-0.260019\pi\) | ||||
0.684505 | + | 0.729009i | \(0.260019\pi\) | |||||||
\(368\) | 1.34761e10 | 0.0383045 | ||||||||
\(369\) | 3.08809e10 | 0.0867104 | ||||||||
\(370\) | −8.98033e10 | −0.249106 | ||||||||
\(371\) | 1.81411e11 | 0.497143 | ||||||||
\(372\) | 3.27479e10 | 0.0886626 | ||||||||
\(373\) | −6.63497e11 | −1.77480 | −0.887400 | − | 0.461001i | \(-0.847490\pi\) | ||||
−0.887400 | + | 0.461001i | \(0.847490\pi\) | |||||||
\(374\) | −7.52185e10 | −0.198794 | ||||||||
\(375\) | 6.93654e10 | 0.181135 | ||||||||
\(376\) | 5.77221e11 | 1.48935 | ||||||||
\(377\) | −3.63635e10 | −0.0927106 | ||||||||
\(378\) | 3.29775e10 | 0.0830815 | ||||||||
\(379\) | −1.62805e11 | −0.405313 | −0.202657 | − | 0.979250i | \(-0.564957\pi\) | ||||
−0.202657 | + | 0.979250i | \(0.564957\pi\) | |||||||
\(380\) | −1.89770e10 | −0.0466877 | ||||||||
\(381\) | −5.21326e10 | −0.126750 | ||||||||
\(382\) | 8.66058e11 | 2.08095 | ||||||||
\(383\) | 3.31529e11 | 0.787276 | 0.393638 | − | 0.919266i | \(-0.371216\pi\) | ||||
0.393638 | + | 0.919266i | \(0.371216\pi\) | |||||||
\(384\) | −2.94007e11 | −0.690029 | ||||||||
\(385\) | −9.81998e9 | −0.0227792 | ||||||||
\(386\) | −1.88465e11 | −0.432103 | ||||||||
\(387\) | −1.92409e10 | −0.0436040 | ||||||||
\(388\) | −4.82102e10 | −0.107993 | ||||||||
\(389\) | −6.01100e11 | −1.33099 | −0.665494 | − | 0.746404i | \(-0.731779\pi\) | ||||
−0.665494 | + | 0.746404i | \(0.731779\pi\) | |||||||
\(390\) | −5.47308e9 | −0.0119796 | ||||||||
\(391\) | 7.52471e9 | 0.0162815 | ||||||||
\(392\) | −3.44020e11 | −0.735862 | ||||||||
\(393\) | −1.20085e11 | −0.253934 | ||||||||
\(394\) | −8.08900e11 | −1.69107 | ||||||||
\(395\) | −7.41046e10 | −0.153165 | ||||||||
\(396\) | −1.24258e10 | −0.0253919 | ||||||||
\(397\) | −2.47379e11 | −0.499811 | −0.249905 | − | 0.968270i | \(-0.580399\pi\) | ||||
−0.249905 | + | 0.968270i | \(0.580399\pi\) | |||||||
\(398\) | 6.28043e11 | 1.25463 | ||||||||
\(399\) | −1.61675e11 | −0.319348 | ||||||||
\(400\) | 5.81475e11 | 1.13569 | ||||||||
\(401\) | −5.01181e11 | −0.967931 | −0.483966 | − | 0.875087i | \(-0.660804\pi\) | ||||
−0.483966 | + | 0.875087i | \(0.660804\pi\) | |||||||
\(402\) | −4.12358e11 | −0.787511 | ||||||||
\(403\) | −4.63034e10 | −0.0874460 | ||||||||
\(404\) | −1.00325e11 | −0.187367 | ||||||||
\(405\) | −9.55771e9 | −0.0176525 | ||||||||
\(406\) | 1.84449e11 | 0.336906 | ||||||||
\(407\) | 2.88279e11 | 0.520761 | ||||||||
\(408\) | −1.39234e11 | −0.248757 | ||||||||
\(409\) | 3.05359e11 | 0.539580 | 0.269790 | − | 0.962919i | \(-0.413046\pi\) | ||||
0.269790 | + | 0.962919i | \(0.413046\pi\) | |||||||
\(410\) | 2.59965e10 | 0.0454347 | ||||||||
\(411\) | −3.96609e11 | −0.685606 | ||||||||
\(412\) | 5.33040e10 | 0.0911429 | ||||||||
\(413\) | −3.02266e10 | −0.0511227 | ||||||||
\(414\) | 7.20133e9 | 0.0120479 | ||||||||
\(415\) | 7.36270e10 | 0.121849 | ||||||||
\(416\) | −2.98145e10 | −0.0488098 | ||||||||
\(417\) | 8.28000e10 | 0.134097 | ||||||||
\(418\) | 3.52917e11 | 0.565431 | ||||||||
\(419\) | 8.08727e11 | 1.28186 | 0.640928 | − | 0.767601i | \(-0.278550\pi\) | ||||
0.640928 | + | 0.767601i | \(0.278550\pi\) | |||||||
\(420\) | 4.79202e9 | 0.00751444 | ||||||||
\(421\) | −1.20078e12 | −1.86292 | −0.931459 | − | 0.363846i | \(-0.881463\pi\) | ||||
−0.931459 | + | 0.363846i | \(0.881463\pi\) | |||||||
\(422\) | −5.16169e11 | −0.792293 | ||||||||
\(423\) | 3.75733e11 | 0.570621 | ||||||||
\(424\) | −7.33019e11 | −1.10146 | ||||||||
\(425\) | 3.24680e11 | 0.482731 | ||||||||
\(426\) | −8.06713e11 | −1.18680 | ||||||||
\(427\) | −4.36629e11 | −0.635605 | ||||||||
\(428\) | −1.96778e11 | −0.283452 | ||||||||
\(429\) | 1.75692e10 | 0.0250435 | ||||||||
\(430\) | −1.61976e10 | −0.0228477 | ||||||||
\(431\) | 8.17289e11 | 1.14085 | 0.570424 | − | 0.821350i | \(-0.306779\pi\) | ||||
0.570424 | + | 0.821350i | \(0.306779\pi\) | |||||||
\(432\) | −1.62315e11 | −0.224224 | ||||||||
\(433\) | 4.47154e11 | 0.611310 | 0.305655 | − | 0.952142i | \(-0.401125\pi\) | ||||
0.305655 | + | 0.952142i | \(0.401125\pi\) | |||||||
\(434\) | 2.34867e11 | 0.317774 | ||||||||
\(435\) | −5.34579e10 | −0.0715831 | ||||||||
\(436\) | 1.72154e11 | 0.228154 | ||||||||
\(437\) | −3.53052e10 | −0.0463097 | ||||||||
\(438\) | 4.37696e11 | 0.568249 | ||||||||
\(439\) | 4.14846e11 | 0.533086 | 0.266543 | − | 0.963823i | \(-0.414119\pi\) | ||||
0.266543 | + | 0.963823i | \(0.414119\pi\) | |||||||
\(440\) | 3.96791e10 | 0.0504691 | ||||||||
\(441\) | −2.23934e11 | −0.281934 | ||||||||
\(442\) | −5.18992e10 | −0.0646786 | ||||||||
\(443\) | −1.52484e12 | −1.88108 | −0.940540 | − | 0.339684i | \(-0.889680\pi\) | ||||
−0.940540 | + | 0.339684i | \(0.889680\pi\) | |||||||
\(444\) | −1.40676e11 | −0.171790 | ||||||||
\(445\) | 2.02405e11 | 0.244682 | ||||||||
\(446\) | −1.26469e12 | −1.51348 | ||||||||
\(447\) | −6.95429e11 | −0.823890 | ||||||||
\(448\) | −2.38851e11 | −0.280141 | ||||||||
\(449\) | 2.41329e10 | 0.0280221 | 0.0140111 | − | 0.999902i | \(-0.495540\pi\) | ||||
0.0140111 | + | 0.999902i | \(0.495540\pi\) | |||||||
\(450\) | 3.10727e11 | 0.357209 | ||||||||
\(451\) | −8.34518e10 | −0.0949820 | ||||||||
\(452\) | −2.47851e11 | −0.279298 | ||||||||
\(453\) | −5.76982e10 | −0.0643754 | ||||||||
\(454\) | 1.04470e12 | 1.15409 | ||||||||
\(455\) | −6.77559e9 | −0.00741132 | ||||||||
\(456\) | 6.53272e11 | 0.707542 | ||||||||
\(457\) | 1.37101e12 | 1.47034 | 0.735170 | − | 0.677883i | \(-0.237102\pi\) | ||||
0.735170 | + | 0.677883i | \(0.237102\pi\) | |||||||
\(458\) | 1.43010e12 | 1.51869 | ||||||||
\(459\) | −9.06323e10 | −0.0953073 | ||||||||
\(460\) | 1.04644e9 | 0.00108969 | ||||||||
\(461\) | 8.56735e11 | 0.883471 | 0.441735 | − | 0.897145i | \(-0.354363\pi\) | ||||
0.441735 | + | 0.897145i | \(0.354363\pi\) | |||||||
\(462\) | −8.91175e10 | −0.0910069 | ||||||||
\(463\) | −1.77854e12 | −1.79866 | −0.899328 | − | 0.437274i | \(-0.855944\pi\) | ||||
−0.899328 | + | 0.437274i | \(0.855944\pi\) | |||||||
\(464\) | −9.07856e11 | −0.909255 | ||||||||
\(465\) | −6.80705e10 | −0.0675182 | ||||||||
\(466\) | −2.06173e12 | −2.02533 | ||||||||
\(467\) | −1.26353e12 | −1.22931 | −0.614654 | − | 0.788797i | \(-0.710704\pi\) | ||||
−0.614654 | + | 0.788797i | \(0.710704\pi\) | |||||||
\(468\) | −8.57354e9 | −0.00826141 | ||||||||
\(469\) | −5.10492e11 | −0.487205 | ||||||||
\(470\) | 3.16303e11 | 0.298995 | ||||||||
\(471\) | −9.68999e11 | −0.907255 | ||||||||
\(472\) | 1.22135e11 | 0.113267 | ||||||||
\(473\) | 5.19962e10 | 0.0477635 | ||||||||
\(474\) | −6.72508e11 | −0.611921 | ||||||||
\(475\) | −1.52336e12 | −1.37304 | ||||||||
\(476\) | 4.54410e10 | 0.0405710 | ||||||||
\(477\) | −4.77147e11 | −0.422007 | ||||||||
\(478\) | 9.76733e11 | 0.855757 | ||||||||
\(479\) | −1.36613e12 | −1.18572 | −0.592862 | − | 0.805304i | \(-0.702002\pi\) | ||||
−0.592862 | + | 0.805304i | \(0.702002\pi\) | |||||||
\(480\) | −4.38303e10 | −0.0376867 | ||||||||
\(481\) | 1.98907e11 | 0.169433 | ||||||||
\(482\) | −1.01952e12 | −0.860365 | ||||||||
\(483\) | 8.91514e9 | 0.00745360 | ||||||||
\(484\) | −2.18288e11 | −0.180812 | ||||||||
\(485\) | 1.00211e11 | 0.0822388 | ||||||||
\(486\) | −8.67373e10 | −0.0705250 | ||||||||
\(487\) | 1.70385e12 | 1.37263 | 0.686313 | − | 0.727306i | \(-0.259228\pi\) | ||||
0.686313 | + | 0.727306i | \(0.259228\pi\) | |||||||
\(488\) | 1.76427e12 | 1.40823 | ||||||||
\(489\) | −4.35869e11 | −0.344720 | ||||||||
\(490\) | −1.88515e11 | −0.147728 | ||||||||
\(491\) | 1.97165e12 | 1.53096 | 0.765478 | − | 0.643462i | \(-0.222503\pi\) | ||||
0.765478 | + | 0.643462i | \(0.222503\pi\) | |||||||
\(492\) | 4.07233e10 | 0.0313329 | ||||||||
\(493\) | −5.06922e11 | −0.386483 | ||||||||
\(494\) | 2.43506e11 | 0.183966 | ||||||||
\(495\) | 2.58285e10 | 0.0193364 | ||||||||
\(496\) | −1.15602e12 | −0.857623 | ||||||||
\(497\) | −9.98698e11 | −0.734227 | ||||||||
\(498\) | 6.68174e11 | 0.486808 | ||||||||
\(499\) | 2.47891e12 | 1.78981 | 0.894907 | − | 0.446253i | \(-0.147242\pi\) | ||||
0.894907 | + | 0.446253i | \(0.147242\pi\) | |||||||
\(500\) | 9.14737e10 | 0.0654532 | ||||||||
\(501\) | −1.26839e12 | −0.899466 | ||||||||
\(502\) | 1.20940e12 | 0.849968 | ||||||||
\(503\) | −1.22607e12 | −0.854006 | −0.427003 | − | 0.904250i | \(-0.640431\pi\) | ||||
−0.427003 | + | 0.904250i | \(0.640431\pi\) | |||||||
\(504\) | −1.64962e11 | −0.113880 | ||||||||
\(505\) | 2.08537e11 | 0.142683 | ||||||||
\(506\) | −1.94607e10 | −0.0131972 | ||||||||
\(507\) | −8.46842e11 | −0.569202 | ||||||||
\(508\) | −6.87484e10 | −0.0458011 | ||||||||
\(509\) | −1.41506e12 | −0.934427 | −0.467213 | − | 0.884145i | \(-0.654742\pi\) | ||||
−0.467213 | + | 0.884145i | \(0.654742\pi\) | |||||||
\(510\) | −7.62970e10 | −0.0499392 | ||||||||
\(511\) | 5.41861e11 | 0.351555 | ||||||||
\(512\) | 8.31829e11 | 0.534957 | ||||||||
\(513\) | 4.25237e11 | 0.271084 | ||||||||
\(514\) | 2.97132e12 | 1.87766 | ||||||||
\(515\) | −1.10799e11 | −0.0694070 | ||||||||
\(516\) | −2.53734e10 | −0.0157563 | ||||||||
\(517\) | −1.01537e12 | −0.625054 | ||||||||
\(518\) | −1.00893e12 | −0.615710 | ||||||||
\(519\) | −4.82647e11 | −0.291995 | ||||||||
\(520\) | 2.73778e10 | 0.0164204 | ||||||||
\(521\) | 2.78794e11 | 0.165773 | 0.0828865 | − | 0.996559i | \(-0.473586\pi\) | ||||
0.0828865 | + | 0.996559i | \(0.473586\pi\) | |||||||
\(522\) | −4.85137e11 | −0.285987 | ||||||||
\(523\) | 2.29079e12 | 1.33884 | 0.669418 | − | 0.742886i | \(-0.266544\pi\) | ||||
0.669418 | + | 0.742886i | \(0.266544\pi\) | |||||||
\(524\) | −1.58358e11 | −0.0917593 | ||||||||
\(525\) | 3.84675e11 | 0.220992 | ||||||||
\(526\) | 3.06156e12 | 1.74384 | ||||||||
\(527\) | −6.45489e11 | −0.364536 | ||||||||
\(528\) | 4.38636e11 | 0.245613 | ||||||||
\(529\) | −1.79921e12 | −0.998919 | ||||||||
\(530\) | −4.01677e11 | −0.221124 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | −2.13204e11 | −0.115397 | ||||||||
\(533\) | −5.75801e10 | −0.0309029 | ||||||||
\(534\) | 1.83685e12 | 0.977549 | ||||||||
\(535\) | 4.09027e11 | 0.215854 | ||||||||
\(536\) | 2.06272e12 | 1.07944 | ||||||||
\(537\) | 3.64616e11 | 0.189213 | ||||||||
\(538\) | 4.58570e11 | 0.235986 | ||||||||
\(539\) | 6.05155e11 | 0.308828 | ||||||||
\(540\) | −1.26040e10 | −0.00637874 | ||||||||
\(541\) | 4.25469e11 | 0.213541 | 0.106770 | − | 0.994284i | \(-0.465949\pi\) | ||||
0.106770 | + | 0.994284i | \(0.465949\pi\) | |||||||
\(542\) | −3.62950e12 | −1.80655 | ||||||||
\(543\) | 1.15225e12 | 0.568784 | ||||||||
\(544\) | −4.15627e11 | −0.203474 | ||||||||
\(545\) | −3.57843e11 | −0.173743 | ||||||||
\(546\) | −6.14893e10 | −0.0296096 | ||||||||
\(547\) | −1.78323e12 | −0.851657 | −0.425829 | − | 0.904804i | \(-0.640017\pi\) | ||||
−0.425829 | + | 0.904804i | \(0.640017\pi\) | |||||||
\(548\) | −5.23017e11 | −0.247744 | ||||||||
\(549\) | 1.14842e12 | 0.539542 | ||||||||
\(550\) | −8.39700e11 | −0.391284 | ||||||||
\(551\) | 2.37843e12 | 1.09928 | ||||||||
\(552\) | −3.60230e10 | −0.0165141 | ||||||||
\(553\) | −8.32555e11 | −0.378573 | ||||||||
\(554\) | 2.74140e12 | 1.23646 | ||||||||
\(555\) | 2.92413e11 | 0.130821 | ||||||||
\(556\) | 1.09190e11 | 0.0484560 | ||||||||
\(557\) | −8.32903e11 | −0.366645 | −0.183323 | − | 0.983053i | \(-0.558685\pi\) | ||||
−0.183323 | + | 0.983053i | \(0.558685\pi\) | |||||||
\(558\) | −6.17748e11 | −0.269748 | ||||||||
\(559\) | 3.58763e10 | 0.0155401 | ||||||||
\(560\) | −1.69160e11 | −0.0726863 | ||||||||
\(561\) | 2.44923e11 | 0.104399 | ||||||||
\(562\) | −2.00401e12 | −0.847396 | ||||||||
\(563\) | 8.32713e10 | 0.0349307 | 0.0174654 | − | 0.999847i | \(-0.494440\pi\) | ||||
0.0174654 | + | 0.999847i | \(0.494440\pi\) | |||||||
\(564\) | 4.95487e11 | 0.206194 | ||||||||
\(565\) | 5.15188e11 | 0.212690 | ||||||||
\(566\) | 6.81647e9 | 0.00279181 | ||||||||
\(567\) | −1.07380e11 | −0.0436312 | ||||||||
\(568\) | 4.03539e12 | 1.62674 | ||||||||
\(569\) | −3.63936e12 | −1.45553 | −0.727763 | − | 0.685829i | \(-0.759440\pi\) | ||||
−0.727763 | + | 0.685829i | \(0.759440\pi\) | |||||||
\(570\) | 3.57978e11 | 0.142043 | ||||||||
\(571\) | −1.64875e12 | −0.649073 | −0.324536 | − | 0.945873i | \(-0.605208\pi\) | ||||
−0.324536 | + | 0.945873i | \(0.605208\pi\) | |||||||
\(572\) | 2.31689e10 | 0.00904949 | ||||||||
\(573\) | −2.82001e12 | −1.09284 | ||||||||
\(574\) | 2.92067e11 | 0.112300 | ||||||||
\(575\) | 8.40019e10 | 0.0320468 | ||||||||
\(576\) | 6.28226e11 | 0.237802 | ||||||||
\(577\) | −3.55485e11 | −0.133515 | −0.0667574 | − | 0.997769i | \(-0.521265\pi\) | ||||
−0.0667574 | + | 0.997769i | \(0.521265\pi\) | |||||||
\(578\) | 2.22650e12 | 0.829749 | ||||||||
\(579\) | 6.13669e11 | 0.226924 | ||||||||
\(580\) | −7.04961e10 | −0.0258666 | ||||||||
\(581\) | 8.27189e11 | 0.301170 | ||||||||
\(582\) | 9.09424e11 | 0.328559 | ||||||||
\(583\) | 1.28943e12 | 0.462264 | ||||||||
\(584\) | −2.18947e12 | −0.778899 | ||||||||
\(585\) | 1.78212e10 | 0.00629121 | ||||||||
\(586\) | 1.63365e12 | 0.572293 | ||||||||
\(587\) | 2.57122e12 | 0.893856 | 0.446928 | − | 0.894570i | \(-0.352518\pi\) | ||||
0.446928 | + | 0.894570i | \(0.352518\pi\) | |||||||
\(588\) | −2.95307e11 | −0.101877 | ||||||||
\(589\) | 3.02856e12 | 1.03686 | ||||||||
\(590\) | 6.69272e10 | 0.0227389 | ||||||||
\(591\) | 2.63390e12 | 0.888086 | ||||||||
\(592\) | 4.96594e12 | 1.66170 | ||||||||
\(593\) | 2.41018e12 | 0.800392 | 0.400196 | − | 0.916430i | \(-0.368942\pi\) | ||||
0.400196 | + | 0.916430i | \(0.368942\pi\) | |||||||
\(594\) | 2.34397e11 | 0.0772525 | ||||||||
\(595\) | −9.44546e10 | −0.0308956 | ||||||||
\(596\) | −9.17078e11 | −0.297713 | ||||||||
\(597\) | −2.04500e12 | −0.658884 | ||||||||
\(598\) | −1.34275e10 | −0.00429378 | ||||||||
\(599\) | −4.24751e12 | −1.34807 | −0.674036 | − | 0.738698i | \(-0.735441\pi\) | ||||
−0.674036 | + | 0.738698i | \(0.735441\pi\) | |||||||
\(600\) | −1.55434e12 | −0.489626 | ||||||||
\(601\) | 2.12128e12 | 0.663227 | 0.331613 | − | 0.943415i | \(-0.392407\pi\) | ||||
0.331613 | + | 0.943415i | \(0.392407\pi\) | |||||||
\(602\) | −1.81978e11 | −0.0564721 | ||||||||
\(603\) | 1.34270e12 | 0.413571 | ||||||||
\(604\) | −7.60878e10 | −0.0232621 | ||||||||
\(605\) | 4.53739e11 | 0.137691 | ||||||||
\(606\) | 1.89250e12 | 0.570046 | ||||||||
\(607\) | −7.37312e11 | −0.220446 | −0.110223 | − | 0.993907i | \(-0.535156\pi\) | ||||
−0.110223 | + | 0.993907i | \(0.535156\pi\) | |||||||
\(608\) | 1.95008e12 | 0.578743 | ||||||||
\(609\) | −6.00592e11 | −0.176930 | ||||||||
\(610\) | 9.66776e11 | 0.282710 | ||||||||
\(611\) | −7.00586e11 | −0.203365 | ||||||||
\(612\) | −1.19519e11 | −0.0344393 | ||||||||
\(613\) | −1.75322e12 | −0.501494 | −0.250747 | − | 0.968053i | \(-0.580676\pi\) | ||||
−0.250747 | + | 0.968053i | \(0.580676\pi\) | |||||||
\(614\) | −6.67834e11 | −0.189632 | ||||||||
\(615\) | −8.46484e10 | −0.0238606 | ||||||||
\(616\) | 4.45790e11 | 0.124743 | ||||||||
\(617\) | −3.50243e11 | −0.0972940 | −0.0486470 | − | 0.998816i | \(-0.515491\pi\) | ||||
−0.0486470 | + | 0.998816i | \(0.515491\pi\) | |||||||
\(618\) | −1.00551e12 | −0.277294 | ||||||||
\(619\) | 3.58750e11 | 0.0982163 | 0.0491082 | − | 0.998793i | \(-0.484362\pi\) | ||||
0.0491082 | + | 0.998793i | \(0.484362\pi\) | |||||||
\(620\) | −8.97661e10 | −0.0243977 | ||||||||
\(621\) | −2.34486e10 | −0.00632710 | ||||||||
\(622\) | 5.33367e12 | 1.42879 | ||||||||
\(623\) | 2.27399e12 | 0.604774 | ||||||||
\(624\) | 3.02650e11 | 0.0799116 | ||||||||
\(625\) | 3.52827e12 | 0.924916 | ||||||||
\(626\) | −6.88608e12 | −1.79221 | ||||||||
\(627\) | −1.14915e12 | −0.296943 | ||||||||
\(628\) | −1.27784e12 | −0.327837 | ||||||||
\(629\) | 2.77284e12 | 0.706314 | ||||||||
\(630\) | −9.03953e10 | −0.0228620 | ||||||||
\(631\) | −1.63671e12 | −0.410998 | −0.205499 | − | 0.978657i | \(-0.565882\pi\) | ||||
−0.205499 | + | 0.978657i | \(0.565882\pi\) | |||||||
\(632\) | 3.36406e12 | 0.838760 | ||||||||
\(633\) | 1.68072e12 | 0.416082 | ||||||||
\(634\) | −2.31856e12 | −0.569924 | ||||||||
\(635\) | 1.42902e11 | 0.0348784 | ||||||||
\(636\) | −6.29225e11 | −0.152493 | ||||||||
\(637\) | 4.17545e11 | 0.100479 | ||||||||
\(638\) | 1.31102e12 | 0.313269 | ||||||||
\(639\) | 2.62678e12 | 0.623260 | ||||||||
\(640\) | 8.05910e11 | 0.189879 | ||||||||
\(641\) | 1.03690e11 | 0.0242592 | 0.0121296 | − | 0.999926i | \(-0.496139\pi\) | ||||
0.0121296 | + | 0.999926i | \(0.496139\pi\) | |||||||
\(642\) | 3.71197e12 | 0.862376 | ||||||||
\(643\) | 5.90450e12 | 1.36218 | 0.681089 | − | 0.732201i | \(-0.261507\pi\) | ||||
0.681089 | + | 0.732201i | \(0.261507\pi\) | |||||||
\(644\) | 1.17566e10 | 0.00269336 | ||||||||
\(645\) | 5.27417e10 | 0.0119987 | ||||||||
\(646\) | 3.39457e12 | 0.766900 | ||||||||
\(647\) | −1.37816e12 | −0.309194 | −0.154597 | − | 0.987978i | \(-0.549408\pi\) | ||||
−0.154597 | + | 0.987978i | \(0.549408\pi\) | |||||||
\(648\) | 4.33883e11 | 0.0966686 | ||||||||
\(649\) | −2.14844e11 | −0.0475360 | ||||||||
\(650\) | −5.79376e11 | −0.127306 | ||||||||
\(651\) | −7.64763e11 | −0.166883 | ||||||||
\(652\) | −5.74790e11 | −0.124565 | ||||||||
\(653\) | 3.68278e12 | 0.792624 | 0.396312 | − | 0.918116i | \(-0.370290\pi\) | ||||
0.396312 | + | 0.918116i | \(0.370290\pi\) | |||||||
\(654\) | −3.24746e12 | −0.694136 | ||||||||
\(655\) | 3.29167e11 | 0.0698764 | ||||||||
\(656\) | −1.43755e12 | −0.303079 | ||||||||
\(657\) | −1.42520e12 | −0.298423 | ||||||||
\(658\) | 3.55362e12 | 0.739018 | ||||||||
\(659\) | 2.25561e11 | 0.0465887 | 0.0232943 | − | 0.999729i | \(-0.492585\pi\) | ||||
0.0232943 | + | 0.999729i | \(0.492585\pi\) | |||||||
\(660\) | 3.40606e10 | 0.00698723 | ||||||||
\(661\) | 4.85476e12 | 0.989148 | 0.494574 | − | 0.869135i | \(-0.335324\pi\) | ||||
0.494574 | + | 0.869135i | \(0.335324\pi\) | |||||||
\(662\) | 5.75671e12 | 1.16497 | ||||||||
\(663\) | 1.68992e11 | 0.0339668 | ||||||||
\(664\) | −3.34238e12 | −0.667267 | ||||||||
\(665\) | 4.43171e11 | 0.0878768 | ||||||||
\(666\) | 2.65368e12 | 0.522654 | ||||||||
\(667\) | −1.31152e11 | −0.0256572 | ||||||||
\(668\) | −1.67266e12 | −0.325022 | ||||||||
\(669\) | 4.11802e12 | 0.794825 | ||||||||
\(670\) | 1.13032e12 | 0.216704 | ||||||||
\(671\) | −3.10347e12 | −0.591011 | ||||||||
\(672\) | −4.92427e11 | −0.0931494 | ||||||||
\(673\) | −8.95636e12 | −1.68292 | −0.841460 | − | 0.540319i | \(-0.818304\pi\) | ||||
−0.841460 | + | 0.540319i | \(0.818304\pi\) | |||||||
\(674\) | 7.72911e12 | 1.44265 | ||||||||
\(675\) | −1.01177e12 | −0.187593 | ||||||||
\(676\) | −1.11675e12 | −0.205682 | ||||||||
\(677\) | −4.88016e12 | −0.892863 | −0.446432 | − | 0.894818i | \(-0.647305\pi\) | ||||
−0.446432 | + | 0.894818i | \(0.647305\pi\) | |||||||
\(678\) | 4.67539e12 | 0.849737 | ||||||||
\(679\) | 1.12585e12 | 0.203268 | ||||||||
\(680\) | 3.81658e11 | 0.0684517 | ||||||||
\(681\) | −3.40169e12 | −0.606084 | ||||||||
\(682\) | 1.66939e12 | 0.295480 | ||||||||
\(683\) | 4.85322e12 | 0.853369 | 0.426685 | − | 0.904400i | \(-0.359681\pi\) | ||||
0.426685 | + | 0.904400i | \(0.359681\pi\) | |||||||
\(684\) | 5.60770e11 | 0.0979562 | ||||||||
\(685\) | 1.08716e12 | 0.188662 | ||||||||
\(686\) | −4.62200e12 | −0.796840 | ||||||||
\(687\) | −4.65660e12 | −0.797561 | ||||||||
\(688\) | 8.95693e11 | 0.152409 | ||||||||
\(689\) | 8.89682e11 | 0.150400 | ||||||||
\(690\) | −1.97397e10 | −0.00331528 | ||||||||
\(691\) | −2.42661e12 | −0.404901 | −0.202450 | − | 0.979293i | \(-0.564890\pi\) | ||||
−0.202450 | + | 0.979293i | \(0.564890\pi\) | |||||||
\(692\) | −6.36476e11 | −0.105513 | ||||||||
\(693\) | 2.90180e11 | 0.0477934 | ||||||||
\(694\) | −1.01242e13 | −1.65670 | ||||||||
\(695\) | −2.26965e11 | −0.0369001 | ||||||||
\(696\) | 2.42678e12 | 0.392003 | ||||||||
\(697\) | −8.02690e11 | −0.128825 | ||||||||
\(698\) | −7.69493e12 | −1.22703 | ||||||||
\(699\) | 6.71330e12 | 1.06363 | ||||||||
\(700\) | 5.07279e11 | 0.0798557 | ||||||||
\(701\) | −2.58871e12 | −0.404904 | −0.202452 | − | 0.979292i | \(-0.564891\pi\) | ||||
−0.202452 | + | 0.979292i | \(0.564891\pi\) | |||||||
\(702\) | 1.61729e11 | 0.0251345 | ||||||||
\(703\) | −1.30099e13 | −2.00898 | ||||||||
\(704\) | −1.69770e12 | −0.260486 | ||||||||
\(705\) | −1.02993e12 | −0.157021 | ||||||||
\(706\) | −3.99982e12 | −0.605926 | ||||||||
\(707\) | 2.34289e12 | 0.352667 | ||||||||
\(708\) | 1.04841e11 | 0.0156813 | ||||||||
\(709\) | −7.50290e12 | −1.11512 | −0.557559 | − | 0.830137i | \(-0.688262\pi\) | ||||
−0.557559 | + | 0.830137i | \(0.688262\pi\) | |||||||
\(710\) | 2.21130e12 | 0.326577 | ||||||||
\(711\) | 2.18979e12 | 0.321358 | ||||||||
\(712\) | −9.18842e12 | −1.33993 | ||||||||
\(713\) | −1.67002e11 | −0.0242002 | ||||||||
\(714\) | −8.57186e11 | −0.123434 | ||||||||
\(715\) | −4.81595e10 | −0.00689135 | ||||||||
\(716\) | 4.80827e11 | 0.0683722 | ||||||||
\(717\) | −3.18039e12 | −0.449411 | ||||||||
\(718\) | −1.00524e12 | −0.141159 | ||||||||
\(719\) | −2.42649e12 | −0.338609 | −0.169304 | − | 0.985564i | \(-0.554152\pi\) | ||||
−0.169304 | + | 0.985564i | \(0.554152\pi\) | |||||||
\(720\) | 4.44925e11 | 0.0617008 | ||||||||
\(721\) | −1.24481e12 | −0.171552 | ||||||||
\(722\) | −7.89980e12 | −1.08193 | ||||||||
\(723\) | 3.31970e12 | 0.451831 | ||||||||
\(724\) | 1.51950e12 | 0.205531 | ||||||||
\(725\) | −5.65901e12 | −0.760711 | ||||||||
\(726\) | 4.11774e12 | 0.550103 | ||||||||
\(727\) | 1.31300e13 | 1.74325 | 0.871627 | − | 0.490169i | \(-0.163065\pi\) | ||||
0.871627 | + | 0.490169i | \(0.163065\pi\) | |||||||
\(728\) | 3.07586e11 | 0.0405859 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −1.19978e12 | −0.156368 | ||||||||
\(731\) | 5.00131e11 | 0.0647822 | ||||||||
\(732\) | 1.51445e12 | 0.194964 | ||||||||
\(733\) | −3.38940e11 | −0.0433666 | −0.0216833 | − | 0.999765i | \(-0.506903\pi\) | ||||
−0.0216833 | + | 0.999765i | \(0.506903\pi\) | |||||||
\(734\) | −1.18354e13 | −1.50505 | ||||||||
\(735\) | 6.13832e11 | 0.0775812 | ||||||||
\(736\) | −1.07532e11 | −0.0135079 | ||||||||
\(737\) | −3.62847e12 | −0.453023 | ||||||||
\(738\) | −7.68194e11 | −0.0953273 | ||||||||
\(739\) | −7.80178e12 | −0.962262 | −0.481131 | − | 0.876649i | \(-0.659774\pi\) | ||||
−0.481131 | + | 0.876649i | \(0.659774\pi\) | |||||||
\(740\) | 3.85611e11 | 0.0472723 | ||||||||
\(741\) | −7.92891e11 | −0.0966121 | ||||||||
\(742\) | −4.51279e12 | −0.546547 | ||||||||
\(743\) | −5.12727e11 | −0.0617215 | −0.0308607 | − | 0.999524i | \(-0.509825\pi\) | ||||
−0.0308607 | + | 0.999524i | \(0.509825\pi\) | |||||||
\(744\) | 3.09014e12 | 0.369743 | ||||||||
\(745\) | 1.90626e12 | 0.226714 | ||||||||
\(746\) | 1.65052e13 | 1.95117 | ||||||||
\(747\) | −2.17567e12 | −0.255653 | ||||||||
\(748\) | 3.22985e11 | 0.0377246 | ||||||||
\(749\) | 4.59536e12 | 0.533521 | ||||||||
\(750\) | −1.72554e12 | −0.199135 | ||||||||
\(751\) | −9.33550e12 | −1.07092 | −0.535461 | − | 0.844560i | \(-0.679862\pi\) | ||||
−0.535461 | + | 0.844560i | \(0.679862\pi\) | |||||||
\(752\) | −1.74909e13 | −1.99449 | ||||||||
\(753\) | −3.93798e12 | −0.446371 | ||||||||
\(754\) | 9.04578e11 | 0.101924 | ||||||||
\(755\) | 1.58158e11 | 0.0177145 | ||||||||
\(756\) | −1.41604e11 | −0.0157662 | ||||||||
\(757\) | −8.67301e12 | −0.959928 | −0.479964 | − | 0.877288i | \(-0.659350\pi\) | ||||
−0.479964 | + | 0.877288i | \(0.659350\pi\) | |||||||
\(758\) | 4.04993e12 | 0.445591 | ||||||||
\(759\) | 6.33669e10 | 0.00693066 | ||||||||
\(760\) | −1.79070e12 | −0.194698 | ||||||||
\(761\) | 2.14892e12 | 0.232268 | 0.116134 | − | 0.993234i | \(-0.462950\pi\) | ||||
0.116134 | + | 0.993234i | \(0.462950\pi\) | |||||||
\(762\) | 1.29685e12 | 0.139345 | ||||||||
\(763\) | −4.02031e12 | −0.429437 | ||||||||
\(764\) | −3.71881e12 | −0.394897 | ||||||||
\(765\) | 2.48434e11 | 0.0262262 | ||||||||
\(766\) | −8.24712e12 | −0.865511 | ||||||||
\(767\) | −1.48238e11 | −0.0154661 | ||||||||
\(768\) | 3.34272e12 | 0.346717 | ||||||||
\(769\) | −1.38294e13 | −1.42605 | −0.713023 | − | 0.701140i | \(-0.752675\pi\) | ||||
−0.713023 | + | 0.701140i | \(0.752675\pi\) | |||||||
\(770\) | 2.44282e11 | 0.0250428 | ||||||||
\(771\) | −9.67507e12 | −0.986074 | ||||||||
\(772\) | 8.09259e11 | 0.0819992 | ||||||||
\(773\) | −1.73146e13 | −1.74424 | −0.872118 | − | 0.489295i | \(-0.837254\pi\) | ||||
−0.872118 | + | 0.489295i | \(0.837254\pi\) | |||||||
\(774\) | 4.78637e11 | 0.0479372 | ||||||||
\(775\) | −7.20590e12 | −0.717514 | ||||||||
\(776\) | −4.54918e12 | −0.450356 | ||||||||
\(777\) | 3.28522e12 | 0.323347 | ||||||||
\(778\) | 1.49530e13 | 1.46325 | ||||||||
\(779\) | 3.76614e12 | 0.366419 | ||||||||
\(780\) | 2.35011e10 | 0.00227333 | ||||||||
\(781\) | −7.09854e12 | −0.682714 | ||||||||
\(782\) | −1.87185e11 | −0.0178995 | ||||||||
\(783\) | 1.57968e12 | 0.150190 | ||||||||
\(784\) | 1.04245e13 | 0.985444 | ||||||||
\(785\) | 2.65615e12 | 0.249654 | ||||||||
\(786\) | 2.98723e12 | 0.279169 | ||||||||
\(787\) | −1.42737e13 | −1.32633 | −0.663165 | − | 0.748474i | \(-0.730787\pi\) | ||||
−0.663165 | + | 0.748474i | \(0.730787\pi\) | |||||||
\(788\) | 3.47338e12 | 0.320911 | ||||||||
\(789\) | −9.96891e12 | −0.915801 | ||||||||
\(790\) | 1.84343e12 | 0.168385 | ||||||||
\(791\) | 5.78807e12 | 0.525702 | ||||||||
\(792\) | −1.17252e12 | −0.105890 | ||||||||
\(793\) | −2.14133e12 | −0.192289 | ||||||||
\(794\) | 6.15380e12 | 0.549479 | ||||||||
\(795\) | 1.30792e12 | 0.116126 | ||||||||
\(796\) | −2.69679e12 | −0.238088 | ||||||||
\(797\) | 3.64156e12 | 0.319687 | 0.159843 | − | 0.987142i | \(-0.448901\pi\) | ||||
0.159843 | + | 0.987142i | \(0.448901\pi\) | |||||||
\(798\) | 4.02183e12 | 0.351084 | ||||||||
\(799\) | −9.76646e12 | −0.847768 | ||||||||
\(800\) | −4.63984e12 | −0.400496 | ||||||||
\(801\) | −5.98106e12 | −0.513372 | ||||||||
\(802\) | 1.24674e13 | 1.06412 | ||||||||
\(803\) | 3.85143e12 | 0.326890 | ||||||||
\(804\) | 1.77064e12 | 0.149444 | ||||||||
\(805\) | −2.44375e10 | −0.00205105 | ||||||||
\(806\) | 1.15184e12 | 0.0961360 | ||||||||
\(807\) | −1.49317e12 | −0.123931 | ||||||||
\(808\) | −9.46680e12 | −0.781362 | ||||||||
\(809\) | 1.26684e13 | 1.03981 | 0.519903 | − | 0.854225i | \(-0.325968\pi\) | ||||
0.519903 | + | 0.854225i | \(0.325968\pi\) | |||||||
\(810\) | 2.37758e11 | 0.0194067 | ||||||||
\(811\) | 2.26177e13 | 1.83592 | 0.917961 | − | 0.396670i | \(-0.129834\pi\) | ||||
0.917961 | + | 0.396670i | \(0.129834\pi\) | |||||||
\(812\) | −7.92014e11 | −0.0639338 | ||||||||
\(813\) | 1.18182e13 | 0.948731 | ||||||||
\(814\) | −7.17124e12 | −0.572512 | ||||||||
\(815\) | 1.19477e12 | 0.0948584 | ||||||||
\(816\) | 4.21907e12 | 0.333128 | ||||||||
\(817\) | −2.34656e12 | −0.184261 | ||||||||
\(818\) | −7.59611e12 | −0.593200 | ||||||||
\(819\) | 2.00218e11 | 0.0155498 | ||||||||
\(820\) | −1.11628e11 | −0.00862203 | ||||||||
\(821\) | −1.76896e12 | −0.135886 | −0.0679428 | − | 0.997689i | \(-0.521644\pi\) | ||||
−0.0679428 | + | 0.997689i | \(0.521644\pi\) | |||||||
\(822\) | 9.86606e12 | 0.753739 | ||||||||
\(823\) | −2.02207e13 | −1.53638 | −0.768189 | − | 0.640224i | \(-0.778842\pi\) | ||||
−0.768189 | + | 0.640224i | \(0.778842\pi\) | |||||||
\(824\) | 5.02985e12 | 0.380086 | ||||||||
\(825\) | 2.73419e12 | 0.205488 | ||||||||
\(826\) | 7.51918e11 | 0.0562031 | ||||||||
\(827\) | −1.25520e13 | −0.933120 | −0.466560 | − | 0.884489i | \(-0.654507\pi\) | ||||
−0.466560 | + | 0.884489i | \(0.654507\pi\) | |||||||
\(828\) | −3.09222e10 | −0.00228630 | ||||||||
\(829\) | 4.15017e12 | 0.305190 | 0.152595 | − | 0.988289i | \(-0.451237\pi\) | ||||
0.152595 | + | 0.988289i | \(0.451237\pi\) | |||||||
\(830\) | −1.83155e12 | −0.133957 | ||||||||
\(831\) | −8.92640e12 | −0.649340 | ||||||||
\(832\) | −1.17138e12 | −0.0847507 | ||||||||
\(833\) | 5.82075e12 | 0.418867 | ||||||||
\(834\) | −2.05974e12 | −0.147423 | ||||||||
\(835\) | 3.47683e12 | 0.247511 | ||||||||
\(836\) | −1.51541e12 | −0.107301 | ||||||||
\(837\) | 2.01148e12 | 0.141661 | ||||||||
\(838\) | −2.01179e13 | −1.40924 | ||||||||
\(839\) | 1.24366e13 | 0.866506 | 0.433253 | − | 0.901272i | \(-0.357366\pi\) | ||||
0.433253 | + | 0.901272i | \(0.357366\pi\) | |||||||
\(840\) | 4.52181e11 | 0.0313369 | ||||||||
\(841\) | −5.67174e12 | −0.390962 | ||||||||
\(842\) | 2.98706e13 | 2.04805 | ||||||||
\(843\) | 6.52535e12 | 0.445021 | ||||||||
\(844\) | 2.21640e12 | 0.150352 | ||||||||
\(845\) | 2.32130e12 | 0.156630 | ||||||||
\(846\) | −9.34674e12 | −0.627326 | ||||||||
\(847\) | 5.09770e12 | 0.340329 | ||||||||
\(848\) | 2.22119e13 | 1.47504 | ||||||||
\(849\) | −2.21954e10 | −0.00146615 | ||||||||
\(850\) | −8.07675e12 | −0.530703 | ||||||||
\(851\) | 7.17397e11 | 0.0468896 | ||||||||
\(852\) | 3.46399e12 | 0.225215 | ||||||||
\(853\) | −1.12775e13 | −0.729358 | −0.364679 | − | 0.931133i | \(-0.618821\pi\) | ||||
−0.364679 | + | 0.931133i | \(0.618821\pi\) | |||||||
\(854\) | 1.08616e13 | 0.698768 | ||||||||
\(855\) | −1.16563e12 | −0.0745955 | ||||||||
\(856\) | −1.85683e13 | −1.18206 | ||||||||
\(857\) | 6.20340e12 | 0.392840 | 0.196420 | − | 0.980520i | \(-0.437068\pi\) | ||||
0.196420 | + | 0.980520i | \(0.437068\pi\) | |||||||
\(858\) | −4.37053e11 | −0.0275322 | ||||||||
\(859\) | −2.33530e12 | −0.146343 | −0.0731716 | − | 0.997319i | \(-0.523312\pi\) | ||||
−0.0731716 | + | 0.997319i | \(0.523312\pi\) | |||||||
\(860\) | 6.95517e10 | 0.00433575 | ||||||||
\(861\) | −9.51013e11 | −0.0589756 | ||||||||
\(862\) | −2.03309e13 | −1.25422 | ||||||||
\(863\) | −8.44146e12 | −0.518047 | −0.259023 | − | 0.965871i | \(-0.583401\pi\) | ||||
−0.259023 | + | 0.965871i | \(0.583401\pi\) | |||||||
\(864\) | 1.29518e12 | 0.0790712 | ||||||||
\(865\) | 1.32299e12 | 0.0803499 | ||||||||
\(866\) | −1.11234e13 | −0.672059 | ||||||||
\(867\) | −7.24980e12 | −0.435753 | ||||||||
\(868\) | −1.00851e12 | −0.0603033 | ||||||||
\(869\) | −5.91762e12 | −0.352013 | ||||||||
\(870\) | 1.32982e12 | 0.0786966 | ||||||||
\(871\) | −2.50357e12 | −0.147394 | ||||||||
\(872\) | 1.62447e13 | 0.951452 | ||||||||
\(873\) | −2.96122e12 | −0.172547 | ||||||||
\(874\) | 8.78252e11 | 0.0509117 | ||||||||
\(875\) | −2.13619e12 | −0.123198 | ||||||||
\(876\) | −1.87944e12 | −0.107835 | ||||||||
\(877\) | 1.55888e13 | 0.889846 | 0.444923 | − | 0.895569i | \(-0.353231\pi\) | ||||
0.444923 | + | 0.895569i | \(0.353231\pi\) | |||||||
\(878\) | −1.03197e13 | −0.586061 | ||||||||
\(879\) | −5.31939e12 | −0.300547 | ||||||||
\(880\) | −1.20236e12 | −0.0675867 | ||||||||
\(881\) | 5.38270e11 | 0.0301029 | 0.0150515 | − | 0.999887i | \(-0.495209\pi\) | ||||
0.0150515 | + | 0.999887i | \(0.495209\pi\) | |||||||
\(882\) | 5.57060e12 | 0.309951 | ||||||||
\(883\) | 5.19066e12 | 0.287342 | 0.143671 | − | 0.989625i | \(-0.454109\pi\) | ||||
0.143671 | + | 0.989625i | \(0.454109\pi\) | |||||||
\(884\) | 2.22853e11 | 0.0122739 | ||||||||
\(885\) | −2.17925e11 | −0.0119416 | ||||||||
\(886\) | 3.79319e13 | 2.06801 | ||||||||
\(887\) | 1.69013e13 | 0.916776 | 0.458388 | − | 0.888752i | \(-0.348427\pi\) | ||||
0.458388 | + | 0.888752i | \(0.348427\pi\) | |||||||
\(888\) | −1.32744e13 | −0.716402 | ||||||||
\(889\) | 1.60548e12 | 0.0862080 | ||||||||
\(890\) | −5.03504e12 | −0.268997 | ||||||||
\(891\) | −7.63231e11 | −0.0405701 | ||||||||
\(892\) | 5.43053e12 | 0.287210 | ||||||||
\(893\) | 4.58232e13 | 2.41132 | ||||||||
\(894\) | 1.72995e13 | 0.905764 | ||||||||
\(895\) | −9.99457e11 | −0.0520667 | ||||||||
\(896\) | 9.05429e12 | 0.469319 | ||||||||
\(897\) | 4.37219e10 | 0.00225493 | ||||||||
\(898\) | −6.00331e11 | −0.0308068 | ||||||||
\(899\) | 1.12505e13 | 0.574454 | ||||||||
\(900\) | −1.33425e12 | −0.0677867 | ||||||||
\(901\) | 1.24025e13 | 0.626973 | ||||||||
\(902\) | 2.07595e12 | 0.104421 | ||||||||
\(903\) | 5.92546e11 | 0.0296570 | ||||||||
\(904\) | −2.33876e13 | −1.16473 | ||||||||
\(905\) | −3.15846e12 | −0.156515 | ||||||||
\(906\) | 1.43530e12 | 0.0707727 | ||||||||
\(907\) | 3.37968e12 | 0.165822 | 0.0829112 | − | 0.996557i | \(-0.473578\pi\) | ||||
0.0829112 | + | 0.996557i | \(0.473578\pi\) | |||||||
\(908\) | −4.48588e12 | −0.219009 | ||||||||
\(909\) | −6.16227e12 | −0.299366 | ||||||||
\(910\) | 1.68550e11 | 0.00814783 | ||||||||
\(911\) | 3.39086e13 | 1.63109 | 0.815544 | − | 0.578696i | \(-0.196438\pi\) | ||||
0.815544 | + | 0.578696i | \(0.196438\pi\) | |||||||
\(912\) | −1.97954e13 | −0.947520 | ||||||||
\(913\) | 5.87948e12 | 0.280040 | ||||||||
\(914\) | −3.41053e13 | −1.61645 | ||||||||
\(915\) | −3.14796e12 | −0.148469 | ||||||||
\(916\) | −6.14076e12 | −0.288199 | ||||||||
\(917\) | 3.69815e12 | 0.172712 | ||||||||
\(918\) | 2.25457e12 | 0.104778 | ||||||||
\(919\) | 1.99191e13 | 0.921191 | 0.460596 | − | 0.887610i | \(-0.347636\pi\) | ||||
0.460596 | + | 0.887610i | \(0.347636\pi\) | |||||||
\(920\) | 9.87434e10 | 0.00454426 | ||||||||
\(921\) | 2.17457e12 | 0.0995874 | ||||||||
\(922\) | −2.13121e13 | −0.971266 | ||||||||
\(923\) | −4.89785e12 | −0.222125 | ||||||||
\(924\) | 3.82666e11 | 0.0172702 | ||||||||
\(925\) | 3.09546e13 | 1.39023 | ||||||||
\(926\) | 4.42429e13 | 1.97740 | ||||||||
\(927\) | 3.27410e12 | 0.145624 | ||||||||
\(928\) | 7.24417e12 | 0.320644 | ||||||||
\(929\) | −9.51657e12 | −0.419189 | −0.209594 | − | 0.977788i | \(-0.567214\pi\) | ||||
−0.209594 | + | 0.977788i | \(0.567214\pi\) | |||||||
\(930\) | 1.69332e12 | 0.0742278 | ||||||||
\(931\) | −2.73103e13 | −1.19139 | ||||||||
\(932\) | 8.85297e12 | 0.384342 | ||||||||
\(933\) | −1.73672e13 | −0.750348 | ||||||||
\(934\) | 3.14317e13 | 1.35147 | ||||||||
\(935\) | −6.71363e11 | −0.0287280 | ||||||||
\(936\) | −8.09012e11 | −0.0344519 | ||||||||
\(937\) | −1.61966e13 | −0.686431 | −0.343216 | − | 0.939257i | \(-0.611516\pi\) | ||||
−0.343216 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(938\) | 1.26990e13 | 0.535621 | ||||||||
\(939\) | 2.24221e13 | 0.941198 | ||||||||
\(940\) | −1.35819e12 | −0.0567395 | ||||||||
\(941\) | 1.72664e12 | 0.0717874 | 0.0358937 | − | 0.999356i | \(-0.488572\pi\) | ||||
0.0358937 | + | 0.999356i | \(0.488572\pi\) | |||||||
\(942\) | 2.41048e13 | 0.997413 | ||||||||
\(943\) | −2.07674e11 | −0.00855222 | ||||||||
\(944\) | −3.70094e12 | −0.151683 | ||||||||
\(945\) | 2.94341e11 | 0.0120062 | ||||||||
\(946\) | −1.29346e12 | −0.0525100 | ||||||||
\(947\) | 1.75876e13 | 0.710610 | 0.355305 | − | 0.934750i | \(-0.384377\pi\) | ||||
0.355305 | + | 0.934750i | \(0.384377\pi\) | |||||||
\(948\) | 2.88772e12 | 0.116123 | ||||||||
\(949\) | 2.65741e12 | 0.106356 | ||||||||
\(950\) | 3.78953e13 | 1.50948 | ||||||||
\(951\) | 7.54958e12 | 0.299302 | ||||||||
\(952\) | 4.28787e12 | 0.169190 | ||||||||
\(953\) | 3.21974e13 | 1.26445 | 0.632226 | − | 0.774784i | \(-0.282141\pi\) | ||||
0.632226 | + | 0.774784i | \(0.282141\pi\) | |||||||
\(954\) | 1.18695e13 | 0.463944 | ||||||||
\(955\) | 7.73001e12 | 0.300722 | ||||||||
\(956\) | −4.19405e12 | −0.162395 | ||||||||
\(957\) | −4.26888e12 | −0.164517 | ||||||||
\(958\) | 3.39840e13 | 1.30355 | ||||||||
\(959\) | 1.22140e13 | 0.466311 | ||||||||
\(960\) | −1.72205e12 | −0.0654371 | ||||||||
\(961\) | −1.21138e13 | −0.458167 | ||||||||
\(962\) | −4.94801e12 | −0.186270 | ||||||||
\(963\) | −1.20867e13 | −0.452887 | ||||||||
\(964\) | 4.37776e12 | 0.163270 | ||||||||
\(965\) | −1.68214e12 | −0.0624439 | ||||||||
\(966\) | −2.21773e11 | −0.00819430 | ||||||||
\(967\) | −4.18164e13 | −1.53790 | −0.768950 | − | 0.639309i | \(-0.779220\pi\) | ||||
−0.768950 | + | 0.639309i | \(0.779220\pi\) | |||||||
\(968\) | −2.05980e13 | −0.754026 | ||||||||
\(969\) | −1.10532e13 | −0.402747 | ||||||||
\(970\) | −2.49284e12 | −0.0904112 | ||||||||
\(971\) | −3.40994e13 | −1.23101 | −0.615503 | − | 0.788135i | \(-0.711047\pi\) | ||||
−0.615503 | + | 0.788135i | \(0.711047\pi\) | |||||||
\(972\) | 3.72446e11 | 0.0133834 | ||||||||
\(973\) | −2.54992e12 | −0.0912051 | ||||||||
\(974\) | −4.23851e13 | −1.50903 | ||||||||
\(975\) | 1.88653e12 | 0.0668565 | ||||||||
\(976\) | −5.34607e13 | −1.88586 | ||||||||
\(977\) | 4.01527e13 | 1.40990 | 0.704952 | − | 0.709255i | \(-0.250969\pi\) | ||||
0.704952 | + | 0.709255i | \(0.250969\pi\) | |||||||
\(978\) | 1.08427e13 | 0.378977 | ||||||||
\(979\) | 1.61631e13 | 0.562344 | ||||||||
\(980\) | 8.09473e11 | 0.0280340 | ||||||||
\(981\) | 1.05742e13 | 0.364534 | ||||||||
\(982\) | −4.90468e13 | −1.68309 | ||||||||
\(983\) | 1.78216e13 | 0.608775 | 0.304387 | − | 0.952548i | \(-0.401548\pi\) | ||||
0.304387 | + | 0.952548i | \(0.401548\pi\) | |||||||
\(984\) | 3.84271e12 | 0.130665 | ||||||||
\(985\) | −7.21984e12 | −0.244379 | ||||||||
\(986\) | 1.26102e13 | 0.424890 | ||||||||
\(987\) | −1.15711e13 | −0.388104 | ||||||||
\(988\) | −1.04560e12 | −0.0349108 | ||||||||
\(989\) | 1.29395e11 | 0.00430065 | ||||||||
\(990\) | −6.42511e11 | −0.0212580 | ||||||||
\(991\) | −8.05274e12 | −0.265223 | −0.132612 | − | 0.991168i | \(-0.542336\pi\) | ||||
−0.132612 | + | 0.991168i | \(0.542336\pi\) | |||||||
\(992\) | 9.22435e12 | 0.302436 | ||||||||
\(993\) | −1.87447e13 | −0.611796 | ||||||||
\(994\) | 2.48436e13 | 0.807191 | ||||||||
\(995\) | 5.60560e12 | 0.181309 | ||||||||
\(996\) | −2.86911e12 | −0.0923803 | ||||||||
\(997\) | 7.38050e12 | 0.236569 | 0.118285 | − | 0.992980i | \(-0.462261\pi\) | ||||
0.118285 | + | 0.992980i | \(0.462261\pi\) | |||||||
\(998\) | −6.16653e13 | −1.96768 | ||||||||
\(999\) | −8.64077e12 | −0.274478 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.a.1.7 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.7 | ✓ | 21 | 1.1 | even | 1 | trivial |