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 | 1.14 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.7099 | 0.694287 | 0.347143 | − | 0.937812i | \(-0.387152\pi\) | ||||
0.347143 | + | 0.937812i | \(0.387152\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −265.198 | −0.517966 | ||||||||
\(5\) | −2481.38 | −1.77553 | −0.887767 | − | 0.460293i | \(-0.847744\pi\) | ||||
−0.887767 | + | 0.460293i | \(0.847744\pi\) | |||||||
\(6\) | −1272.50 | −0.400847 | ||||||||
\(7\) | 1632.53 | 0.256992 | 0.128496 | − | 0.991710i | \(-0.458985\pi\) | ||||
0.128496 | + | 0.991710i | \(0.458985\pi\) | |||||||
\(8\) | −12209.7 | −1.05390 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −38982.3 | −1.23273 | ||||||||
\(11\) | 71994.6 | 1.48263 | 0.741315 | − | 0.671158i | \(-0.234203\pi\) | ||||
0.741315 | + | 0.671158i | \(0.234203\pi\) | |||||||
\(12\) | 21481.1 | 0.299048 | ||||||||
\(13\) | 20979.3 | 0.203726 | 0.101863 | − | 0.994798i | \(-0.467520\pi\) | ||||
0.101863 | + | 0.994798i | \(0.467520\pi\) | |||||||
\(14\) | 25646.9 | 0.178426 | ||||||||
\(15\) | 200992. | 1.02511 | ||||||||
\(16\) | −56032.2 | −0.213746 | ||||||||
\(17\) | −100423. | −0.291618 | −0.145809 | − | 0.989313i | \(-0.546579\pi\) | ||||
−0.145809 | + | 0.989313i | \(0.546579\pi\) | |||||||
\(18\) | 103073. | 0.231429 | ||||||||
\(19\) | 125554. | 0.221024 | 0.110512 | − | 0.993875i | \(-0.464751\pi\) | ||||
0.110512 | + | 0.993875i | \(0.464751\pi\) | |||||||
\(20\) | 658059. | 0.919666 | ||||||||
\(21\) | −132235. | −0.148374 | ||||||||
\(22\) | 1.13103e6 | 1.02937 | ||||||||
\(23\) | 759888. | 0.566206 | 0.283103 | − | 0.959090i | \(-0.408636\pi\) | ||||
0.283103 | + | 0.959090i | \(0.408636\pi\) | |||||||
\(24\) | 988988. | 0.608472 | ||||||||
\(25\) | 4.20414e6 | 2.15252 | ||||||||
\(26\) | 329583. | 0.141444 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −432944. | −0.133113 | ||||||||
\(29\) | −1.44179e6 | −0.378539 | −0.189269 | − | 0.981925i | \(-0.560612\pi\) | ||||
−0.189269 | + | 0.981925i | \(0.560612\pi\) | |||||||
\(30\) | 3.15757e6 | 0.711717 | ||||||||
\(31\) | −973200. | −0.189267 | −0.0946334 | − | 0.995512i | \(-0.530168\pi\) | ||||
−0.0946334 | + | 0.995512i | \(0.530168\pi\) | |||||||
\(32\) | 5.37112e6 | 0.905503 | ||||||||
\(33\) | −5.83156e6 | −0.855997 | ||||||||
\(34\) | −1.57764e6 | −0.202467 | ||||||||
\(35\) | −4.05093e6 | −0.456298 | ||||||||
\(36\) | −1.73997e6 | −0.172655 | ||||||||
\(37\) | 6.01928e6 | 0.528004 | 0.264002 | − | 0.964522i | \(-0.414957\pi\) | ||||
0.264002 | + | 0.964522i | \(0.414957\pi\) | |||||||
\(38\) | 1.97245e6 | 0.153454 | ||||||||
\(39\) | −1.69932e6 | −0.117621 | ||||||||
\(40\) | 3.02970e7 | 1.87124 | ||||||||
\(41\) | 6.93821e6 | 0.383460 | 0.191730 | − | 0.981448i | \(-0.438590\pi\) | ||||
0.191730 | + | 0.981448i | \(0.438590\pi\) | |||||||
\(42\) | −2.07740e6 | −0.103014 | ||||||||
\(43\) | 5.22977e6 | 0.233278 | 0.116639 | − | 0.993174i | \(-0.462788\pi\) | ||||
0.116639 | + | 0.993174i | \(0.462788\pi\) | |||||||
\(44\) | −1.90928e7 | −0.767951 | ||||||||
\(45\) | −1.62804e7 | −0.591845 | ||||||||
\(46\) | 1.19378e7 | 0.393109 | ||||||||
\(47\) | −3.13303e7 | −0.936535 | −0.468267 | − | 0.883587i | \(-0.655122\pi\) | ||||
−0.468267 | + | 0.883587i | \(0.655122\pi\) | |||||||
\(48\) | 4.53861e6 | 0.123406 | ||||||||
\(49\) | −3.76885e7 | −0.933955 | ||||||||
\(50\) | 6.60467e7 | 1.49447 | ||||||||
\(51\) | 8.13429e6 | 0.168366 | ||||||||
\(52\) | −5.56368e6 | −0.105523 | ||||||||
\(53\) | 5.51922e7 | 0.960807 | 0.480403 | − | 0.877048i | \(-0.340490\pi\) | ||||
0.480403 | + | 0.877048i | \(0.340490\pi\) | |||||||
\(54\) | −8.34890e6 | −0.133616 | ||||||||
\(55\) | −1.78646e8 | −2.63246 | ||||||||
\(56\) | −1.99327e7 | −0.270845 | ||||||||
\(57\) | −1.01699e7 | −0.127608 | ||||||||
\(58\) | −2.26504e7 | −0.262815 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −5.33028e7 | −0.530969 | ||||||||
\(61\) | −1.66783e8 | −1.54229 | −0.771147 | − | 0.636658i | \(-0.780317\pi\) | ||||
−0.771147 | + | 0.636658i | \(0.780317\pi\) | |||||||
\(62\) | −1.52889e7 | −0.131406 | ||||||||
\(63\) | 1.07110e7 | 0.0856639 | ||||||||
\(64\) | 1.13068e8 | 0.842425 | ||||||||
\(65\) | −5.20577e7 | −0.361722 | ||||||||
\(66\) | −9.16133e7 | −0.594307 | ||||||||
\(67\) | 9.31844e7 | 0.564945 | 0.282473 | − | 0.959275i | \(-0.408845\pi\) | ||||
0.282473 | + | 0.959275i | \(0.408845\pi\) | |||||||
\(68\) | 2.66321e7 | 0.151048 | ||||||||
\(69\) | −6.15509e7 | −0.326899 | ||||||||
\(70\) | −6.36397e7 | −0.316801 | ||||||||
\(71\) | −4.01312e7 | −0.187422 | −0.0937108 | − | 0.995599i | \(-0.529873\pi\) | ||||
−0.0937108 | + | 0.995599i | \(0.529873\pi\) | |||||||
\(72\) | −8.01080e7 | −0.351301 | ||||||||
\(73\) | −2.58311e8 | −1.06461 | −0.532305 | − | 0.846553i | \(-0.678674\pi\) | ||||
−0.532305 | + | 0.846553i | \(0.678674\pi\) | |||||||
\(74\) | 9.45624e7 | 0.366586 | ||||||||
\(75\) | −3.40536e8 | −1.24276 | ||||||||
\(76\) | −3.32968e7 | −0.114483 | ||||||||
\(77\) | 1.17533e8 | 0.381024 | ||||||||
\(78\) | −2.66962e7 | −0.0816628 | ||||||||
\(79\) | −3.62808e8 | −1.04798 | −0.523992 | − | 0.851723i | \(-0.675558\pi\) | ||||
−0.523992 | + | 0.851723i | \(0.675558\pi\) | |||||||
\(80\) | 1.39037e8 | 0.379513 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 1.08999e8 | 0.266231 | ||||||||
\(83\) | 5.97676e8 | 1.38234 | 0.691169 | − | 0.722693i | \(-0.257096\pi\) | ||||
0.691169 | + | 0.722693i | \(0.257096\pi\) | |||||||
\(84\) | 3.50684e7 | 0.0768528 | ||||||||
\(85\) | 2.49189e8 | 0.517778 | ||||||||
\(86\) | 8.21592e7 | 0.161962 | ||||||||
\(87\) | 1.16785e8 | 0.218549 | ||||||||
\(88\) | −8.79034e8 | −1.56255 | ||||||||
\(89\) | 6.86238e8 | 1.15936 | 0.579682 | − | 0.814843i | \(-0.303177\pi\) | ||||
0.579682 | + | 0.814843i | \(0.303177\pi\) | |||||||
\(90\) | −2.55763e8 | −0.410910 | ||||||||
\(91\) | 3.42493e7 | 0.0523559 | ||||||||
\(92\) | −2.01521e8 | −0.293275 | ||||||||
\(93\) | 7.88292e7 | 0.109273 | ||||||||
\(94\) | −4.92196e8 | −0.650224 | ||||||||
\(95\) | −3.11548e8 | −0.392436 | ||||||||
\(96\) | −4.35061e8 | −0.522792 | ||||||||
\(97\) | 2.73324e7 | 0.0313476 | 0.0156738 | − | 0.999877i | \(-0.495011\pi\) | ||||
0.0156738 | + | 0.999877i | \(0.495011\pi\) | |||||||
\(98\) | −5.92083e8 | −0.648433 | ||||||||
\(99\) | 4.72356e8 | 0.494210 | ||||||||
\(100\) | −1.11493e9 | −1.11493 | ||||||||
\(101\) | −1.63234e9 | −1.56087 | −0.780433 | − | 0.625240i | \(-0.785001\pi\) | ||||
−0.780433 | + | 0.625240i | \(0.785001\pi\) | |||||||
\(102\) | 1.27789e8 | 0.116894 | ||||||||
\(103\) | 1.28691e9 | 1.12663 | 0.563315 | − | 0.826242i | \(-0.309526\pi\) | ||||
0.563315 | + | 0.826242i | \(0.309526\pi\) | |||||||
\(104\) | −2.56152e8 | −0.214707 | ||||||||
\(105\) | 3.28125e8 | 0.263444 | ||||||||
\(106\) | 8.67064e8 | 0.667075 | ||||||||
\(107\) | 8.46105e8 | 0.624018 | 0.312009 | − | 0.950079i | \(-0.398998\pi\) | ||||
0.312009 | + | 0.950079i | \(0.398998\pi\) | |||||||
\(108\) | 1.40937e8 | 0.0996825 | ||||||||
\(109\) | −6.07335e8 | −0.412106 | −0.206053 | − | 0.978541i | \(-0.566062\pi\) | ||||
−0.206053 | + | 0.978541i | \(0.566062\pi\) | |||||||
\(110\) | −2.80652e9 | −1.82768 | ||||||||
\(111\) | −4.87562e8 | −0.304843 | ||||||||
\(112\) | −9.14741e7 | −0.0549309 | ||||||||
\(113\) | −1.20739e9 | −0.696620 | −0.348310 | − | 0.937379i | \(-0.613244\pi\) | ||||
−0.348310 | + | 0.937379i | \(0.613244\pi\) | |||||||
\(114\) | −1.59768e8 | −0.0885969 | ||||||||
\(115\) | −1.88557e9 | −1.00532 | ||||||||
\(116\) | 3.82360e8 | 0.196070 | ||||||||
\(117\) | 1.37645e8 | 0.0679086 | ||||||||
\(118\) | −1.90363e8 | −0.0903885 | ||||||||
\(119\) | −1.63944e8 | −0.0749435 | ||||||||
\(120\) | −2.45406e9 | −1.08036 | ||||||||
\(121\) | 2.82527e9 | 1.19819 | ||||||||
\(122\) | −2.62014e9 | −1.07079 | ||||||||
\(123\) | −5.61995e8 | −0.221391 | ||||||||
\(124\) | 2.58091e8 | 0.0980338 | ||||||||
\(125\) | −5.58564e9 | −2.04634 | ||||||||
\(126\) | 1.68269e8 | 0.0594753 | ||||||||
\(127\) | 4.29748e9 | 1.46587 | 0.732937 | − | 0.680296i | \(-0.238149\pi\) | ||||
0.732937 | + | 0.680296i | \(0.238149\pi\) | |||||||
\(128\) | −9.73718e8 | −0.320618 | ||||||||
\(129\) | −4.23611e8 | −0.134683 | ||||||||
\(130\) | −8.17823e8 | −0.251139 | ||||||||
\(131\) | 6.42427e8 | 0.190591 | 0.0952956 | − | 0.995449i | \(-0.469620\pi\) | ||||
0.0952956 | + | 0.995449i | \(0.469620\pi\) | |||||||
\(132\) | 1.54652e9 | 0.443377 | ||||||||
\(133\) | 2.04971e8 | 0.0568015 | ||||||||
\(134\) | 1.46392e9 | 0.392234 | ||||||||
\(135\) | 1.31871e9 | 0.341702 | ||||||||
\(136\) | 1.22614e9 | 0.307337 | ||||||||
\(137\) | 4.33548e9 | 1.05146 | 0.525732 | − | 0.850650i | \(-0.323792\pi\) | ||||
0.525732 | + | 0.850650i | \(0.323792\pi\) | |||||||
\(138\) | −9.66960e8 | −0.226962 | ||||||||
\(139\) | −3.46178e9 | −0.786563 | −0.393281 | − | 0.919418i | \(-0.628660\pi\) | ||||
−0.393281 | + | 0.919418i | \(0.628660\pi\) | |||||||
\(140\) | 1.07430e9 | 0.236347 | ||||||||
\(141\) | 2.53775e9 | 0.540709 | ||||||||
\(142\) | −6.30458e8 | −0.130124 | ||||||||
\(143\) | 1.51040e9 | 0.302050 | ||||||||
\(144\) | −3.67627e8 | −0.0712486 | ||||||||
\(145\) | 3.57763e9 | 0.672108 | ||||||||
\(146\) | −4.05805e9 | −0.739145 | ||||||||
\(147\) | 3.05277e9 | 0.539219 | ||||||||
\(148\) | −1.59630e9 | −0.273488 | ||||||||
\(149\) | −1.39148e9 | −0.231280 | −0.115640 | − | 0.993291i | \(-0.536892\pi\) | ||||
−0.115640 | + | 0.993291i | \(0.536892\pi\) | |||||||
\(150\) | −5.34979e9 | −0.862831 | ||||||||
\(151\) | 4.41234e9 | 0.690673 | 0.345336 | − | 0.938479i | \(-0.387765\pi\) | ||||
0.345336 | + | 0.938479i | \(0.387765\pi\) | |||||||
\(152\) | −1.53298e9 | −0.232938 | ||||||||
\(153\) | −6.58878e8 | −0.0972061 | ||||||||
\(154\) | 1.84644e9 | 0.264540 | ||||||||
\(155\) | 2.41488e9 | 0.336050 | ||||||||
\(156\) | 4.50658e8 | 0.0609237 | ||||||||
\(157\) | −1.34294e10 | −1.76404 | −0.882021 | − | 0.471211i | \(-0.843817\pi\) | ||||
−0.882021 | + | 0.471211i | \(0.843817\pi\) | |||||||
\(158\) | −5.69968e9 | −0.727602 | ||||||||
\(159\) | −4.47056e9 | −0.554722 | ||||||||
\(160\) | −1.33278e10 | −1.60775 | ||||||||
\(161\) | 1.24054e9 | 0.145510 | ||||||||
\(162\) | 6.76261e8 | 0.0771430 | ||||||||
\(163\) | 1.05500e10 | 1.17060 | 0.585298 | − | 0.810818i | \(-0.300978\pi\) | ||||
0.585298 | + | 0.810818i | \(0.300978\pi\) | |||||||
\(164\) | −1.84000e9 | −0.198619 | ||||||||
\(165\) | 1.44703e10 | 1.51985 | ||||||||
\(166\) | 9.38943e9 | 0.959739 | ||||||||
\(167\) | 1.91306e9 | 0.190328 | 0.0951642 | − | 0.995462i | \(-0.469662\pi\) | ||||
0.0951642 | + | 0.995462i | \(0.469662\pi\) | |||||||
\(168\) | 1.61455e9 | 0.156372 | ||||||||
\(169\) | −1.01644e10 | −0.958496 | ||||||||
\(170\) | 3.91474e9 | 0.359486 | ||||||||
\(171\) | 8.23761e8 | 0.0736748 | ||||||||
\(172\) | −1.38693e9 | −0.120830 | ||||||||
\(173\) | −1.79045e10 | −1.51969 | −0.759846 | − | 0.650103i | \(-0.774726\pi\) | ||||
−0.759846 | + | 0.650103i | \(0.774726\pi\) | |||||||
\(174\) | 1.83468e9 | 0.151736 | ||||||||
\(175\) | 6.86338e9 | 0.553180 | ||||||||
\(176\) | −4.03401e9 | −0.316906 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | 1.07807e10 | 0.804931 | ||||||||
\(179\) | −7.61767e9 | −0.554605 | −0.277302 | − | 0.960783i | \(-0.589440\pi\) | ||||
−0.277302 | + | 0.960783i | \(0.589440\pi\) | |||||||
\(180\) | 4.31753e9 | 0.306555 | ||||||||
\(181\) | −2.33571e10 | −1.61758 | −0.808788 | − | 0.588101i | \(-0.799876\pi\) | ||||
−0.808788 | + | 0.588101i | \(0.799876\pi\) | |||||||
\(182\) | 5.38054e8 | 0.0363500 | ||||||||
\(183\) | 1.35094e10 | 0.890443 | ||||||||
\(184\) | −9.27803e9 | −0.596727 | ||||||||
\(185\) | −1.49362e10 | −0.937489 | ||||||||
\(186\) | 1.23840e9 | 0.0758670 | ||||||||
\(187\) | −7.22994e9 | −0.432362 | ||||||||
\(188\) | 8.30874e9 | 0.485093 | ||||||||
\(189\) | −8.67592e8 | −0.0494581 | ||||||||
\(190\) | −4.89440e9 | −0.272463 | ||||||||
\(191\) | −1.50832e10 | −0.820057 | −0.410029 | − | 0.912073i | \(-0.634481\pi\) | ||||
−0.410029 | + | 0.912073i | \(0.634481\pi\) | |||||||
\(192\) | −9.15853e9 | −0.486374 | ||||||||
\(193\) | −1.68362e10 | −0.873446 | −0.436723 | − | 0.899596i | \(-0.643861\pi\) | ||||
−0.436723 | + | 0.899596i | \(0.643861\pi\) | |||||||
\(194\) | 4.29389e8 | 0.0217642 | ||||||||
\(195\) | 4.21667e9 | 0.208840 | ||||||||
\(196\) | 9.99492e9 | 0.483757 | ||||||||
\(197\) | −1.40072e10 | −0.662601 | −0.331301 | − | 0.943525i | \(-0.607487\pi\) | ||||
−0.331301 | + | 0.943525i | \(0.607487\pi\) | |||||||
\(198\) | 7.42068e9 | 0.343123 | ||||||||
\(199\) | 7.08429e9 | 0.320227 | 0.160113 | − | 0.987099i | \(-0.448814\pi\) | ||||
0.160113 | + | 0.987099i | \(0.448814\pi\) | |||||||
\(200\) | −5.13314e10 | −2.26855 | ||||||||
\(201\) | −7.54794e9 | −0.326171 | ||||||||
\(202\) | −2.56440e10 | −1.08369 | ||||||||
\(203\) | −2.35376e9 | −0.0972814 | ||||||||
\(204\) | −2.15720e9 | −0.0872077 | ||||||||
\(205\) | −1.72164e10 | −0.680847 | ||||||||
\(206\) | 2.02173e10 | 0.782205 | ||||||||
\(207\) | 4.98563e9 | 0.188735 | ||||||||
\(208\) | −1.17552e9 | −0.0435455 | ||||||||
\(209\) | 9.03922e9 | 0.327697 | ||||||||
\(210\) | 5.15482e9 | 0.182905 | ||||||||
\(211\) | −1.28875e10 | −0.447609 | −0.223804 | − | 0.974634i | \(-0.571848\pi\) | ||||
−0.223804 | + | 0.974634i | \(0.571848\pi\) | |||||||
\(212\) | −1.46369e10 | −0.497665 | ||||||||
\(213\) | 3.25063e9 | 0.108208 | ||||||||
\(214\) | 1.32922e10 | 0.433248 | ||||||||
\(215\) | −1.29771e10 | −0.414194 | ||||||||
\(216\) | 6.48875e9 | 0.202824 | ||||||||
\(217\) | −1.58878e9 | −0.0486400 | ||||||||
\(218\) | −9.54119e9 | −0.286120 | ||||||||
\(219\) | 2.09232e10 | 0.614653 | ||||||||
\(220\) | 4.73767e10 | 1.36352 | ||||||||
\(221\) | −2.10681e9 | −0.0594101 | ||||||||
\(222\) | −7.65956e9 | −0.211649 | ||||||||
\(223\) | −1.54290e10 | −0.417799 | −0.208899 | − | 0.977937i | \(-0.566988\pi\) | ||||
−0.208899 | + | 0.977937i | \(0.566988\pi\) | |||||||
\(224\) | 8.76850e9 | 0.232707 | ||||||||
\(225\) | 2.75834e10 | 0.717507 | ||||||||
\(226\) | −1.89681e10 | −0.483654 | ||||||||
\(227\) | 7.87485e9 | 0.196846 | 0.0984229 | − | 0.995145i | \(-0.468620\pi\) | ||||
0.0984229 | + | 0.995145i | \(0.468620\pi\) | |||||||
\(228\) | 2.69704e9 | 0.0660968 | ||||||||
\(229\) | 2.02461e10 | 0.486499 | 0.243250 | − | 0.969964i | \(-0.421787\pi\) | ||||
0.243250 | + | 0.969964i | \(0.421787\pi\) | |||||||
\(230\) | −2.96222e10 | −0.697979 | ||||||||
\(231\) | −9.52018e9 | −0.219984 | ||||||||
\(232\) | 1.76038e10 | 0.398943 | ||||||||
\(233\) | 1.16127e10 | 0.258126 | 0.129063 | − | 0.991636i | \(-0.458803\pi\) | ||||
0.129063 | + | 0.991636i | \(0.458803\pi\) | |||||||
\(234\) | 2.16240e9 | 0.0471481 | ||||||||
\(235\) | 7.77425e10 | 1.66285 | ||||||||
\(236\) | 3.21351e9 | 0.0674334 | ||||||||
\(237\) | 2.93874e10 | 0.605054 | ||||||||
\(238\) | −2.57554e9 | −0.0520323 | ||||||||
\(239\) | 3.57480e10 | 0.708697 | 0.354349 | − | 0.935113i | \(-0.384703\pi\) | ||||
0.354349 | + | 0.935113i | \(0.384703\pi\) | |||||||
\(240\) | −1.12620e10 | −0.219112 | ||||||||
\(241\) | 3.30065e10 | 0.630264 | 0.315132 | − | 0.949048i | \(-0.397951\pi\) | ||||
0.315132 | + | 0.949048i | \(0.397951\pi\) | |||||||
\(242\) | 4.43848e10 | 0.831888 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 4.42305e10 | 0.798855 | ||||||||
\(245\) | 9.35196e10 | 1.65827 | ||||||||
\(246\) | −8.82890e9 | −0.153709 | ||||||||
\(247\) | 2.63404e9 | 0.0450284 | ||||||||
\(248\) | 1.18825e10 | 0.199469 | ||||||||
\(249\) | −4.84117e10 | −0.798093 | ||||||||
\(250\) | −8.77499e10 | −1.42075 | ||||||||
\(251\) | −1.11796e10 | −0.177785 | −0.0888926 | − | 0.996041i | \(-0.528333\pi\) | ||||
−0.0888926 | + | 0.996041i | \(0.528333\pi\) | |||||||
\(252\) | −2.84054e9 | −0.0443710 | ||||||||
\(253\) | 5.47078e10 | 0.839474 | ||||||||
\(254\) | 6.75130e10 | 1.01774 | ||||||||
\(255\) | −2.01843e10 | −0.298939 | ||||||||
\(256\) | −7.31880e10 | −1.06503 | ||||||||
\(257\) | 6.82071e10 | 0.975283 | 0.487642 | − | 0.873044i | \(-0.337857\pi\) | ||||
0.487642 | + | 0.873044i | \(0.337857\pi\) | |||||||
\(258\) | −6.65490e9 | −0.0935089 | ||||||||
\(259\) | 9.82664e9 | 0.135693 | ||||||||
\(260\) | 1.38056e10 | 0.187360 | ||||||||
\(261\) | −9.45957e9 | −0.126180 | ||||||||
\(262\) | 1.00925e10 | 0.132325 | ||||||||
\(263\) | −1.28524e11 | −1.65647 | −0.828236 | − | 0.560379i | \(-0.810655\pi\) | ||||
−0.828236 | + | 0.560379i | \(0.810655\pi\) | |||||||
\(264\) | 7.12017e10 | 0.902138 | ||||||||
\(265\) | −1.36953e11 | −1.70594 | ||||||||
\(266\) | 3.22007e9 | 0.0394365 | ||||||||
\(267\) | −5.55853e10 | −0.669359 | ||||||||
\(268\) | −2.47124e10 | −0.292622 | ||||||||
\(269\) | −1.82550e9 | −0.0212567 | −0.0106283 | − | 0.999944i | \(-0.503383\pi\) | ||||
−0.0106283 | + | 0.999944i | \(0.503383\pi\) | |||||||
\(270\) | 2.07168e10 | 0.237239 | ||||||||
\(271\) | 1.42806e11 | 1.60836 | 0.804182 | − | 0.594383i | \(-0.202604\pi\) | ||||
0.804182 | + | 0.594383i | \(0.202604\pi\) | |||||||
\(272\) | 5.62694e9 | 0.0623322 | ||||||||
\(273\) | −2.77419e9 | −0.0302277 | ||||||||
\(274\) | 6.81100e10 | 0.730017 | ||||||||
\(275\) | 3.02675e11 | 3.19139 | ||||||||
\(276\) | 1.63232e10 | 0.169323 | ||||||||
\(277\) | −1.25742e11 | −1.28328 | −0.641640 | − | 0.767006i | \(-0.721745\pi\) | ||||
−0.641640 | + | 0.767006i | \(0.721745\pi\) | |||||||
\(278\) | −5.43843e10 | −0.546100 | ||||||||
\(279\) | −6.38517e9 | −0.0630890 | ||||||||
\(280\) | 4.94607e10 | 0.480894 | ||||||||
\(281\) | 6.80928e10 | 0.651513 | 0.325756 | − | 0.945454i | \(-0.394381\pi\) | ||||
0.325756 | + | 0.945454i | \(0.394381\pi\) | |||||||
\(282\) | 3.98679e10 | 0.375407 | ||||||||
\(283\) | −1.28817e11 | −1.19381 | −0.596904 | − | 0.802313i | \(-0.703603\pi\) | ||||
−0.596904 | + | 0.802313i | \(0.703603\pi\) | |||||||
\(284\) | 1.06427e10 | 0.0970780 | ||||||||
\(285\) | 2.52354e10 | 0.226573 | ||||||||
\(286\) | 2.37282e10 | 0.209709 | ||||||||
\(287\) | 1.13268e10 | 0.0985461 | ||||||||
\(288\) | 3.52399e10 | 0.301834 | ||||||||
\(289\) | −1.08503e11 | −0.914959 | ||||||||
\(290\) | 5.62043e10 | 0.466636 | ||||||||
\(291\) | −2.21392e9 | −0.0180986 | ||||||||
\(292\) | 6.85038e10 | 0.551432 | ||||||||
\(293\) | 1.18257e11 | 0.937394 | 0.468697 | − | 0.883359i | \(-0.344724\pi\) | ||||
0.468697 | + | 0.883359i | \(0.344724\pi\) | |||||||
\(294\) | 4.79587e10 | 0.374373 | ||||||||
\(295\) | 3.00678e10 | 0.231155 | ||||||||
\(296\) | −7.34938e10 | −0.556465 | ||||||||
\(297\) | −3.82609e10 | −0.285332 | ||||||||
\(298\) | −2.18600e10 | −0.160575 | ||||||||
\(299\) | 1.59419e10 | 0.115351 | ||||||||
\(300\) | 9.03095e10 | 0.643706 | ||||||||
\(301\) | 8.53774e9 | 0.0599506 | ||||||||
\(302\) | 6.93174e10 | 0.479525 | ||||||||
\(303\) | 1.32220e11 | 0.901166 | ||||||||
\(304\) | −7.03508e9 | −0.0472430 | ||||||||
\(305\) | 4.13852e11 | 2.73839 | ||||||||
\(306\) | −1.03509e10 | −0.0674889 | ||||||||
\(307\) | 1.20165e11 | 0.772070 | 0.386035 | − | 0.922484i | \(-0.373844\pi\) | ||||
0.386035 | + | 0.922484i | \(0.373844\pi\) | |||||||
\(308\) | −3.11696e10 | −0.197357 | ||||||||
\(309\) | −1.04240e11 | −0.650461 | ||||||||
\(310\) | 3.79376e10 | 0.233315 | ||||||||
\(311\) | 1.52314e11 | 0.923246 | 0.461623 | − | 0.887076i | \(-0.347267\pi\) | ||||
0.461623 | + | 0.887076i | \(0.347267\pi\) | |||||||
\(312\) | 2.07483e10 | 0.123961 | ||||||||
\(313\) | −1.43895e11 | −0.847416 | −0.423708 | − | 0.905799i | \(-0.639272\pi\) | ||||
−0.423708 | + | 0.905799i | \(0.639272\pi\) | |||||||
\(314\) | −2.10975e11 | −1.22475 | ||||||||
\(315\) | −2.65781e10 | −0.152099 | ||||||||
\(316\) | 9.62161e10 | 0.542820 | ||||||||
\(317\) | 4.34701e10 | 0.241782 | 0.120891 | − | 0.992666i | \(-0.461425\pi\) | ||||
0.120891 | + | 0.992666i | \(0.461425\pi\) | |||||||
\(318\) | −7.02322e10 | −0.385136 | ||||||||
\(319\) | −1.03801e11 | −0.561233 | ||||||||
\(320\) | −2.80566e11 | −1.49575 | ||||||||
\(321\) | −6.85345e10 | −0.360277 | ||||||||
\(322\) | 1.94888e10 | 0.101026 | ||||||||
\(323\) | −1.26086e10 | −0.0644547 | ||||||||
\(324\) | −1.14159e10 | −0.0575517 | ||||||||
\(325\) | 8.82000e10 | 0.438524 | ||||||||
\(326\) | 1.65739e11 | 0.812729 | ||||||||
\(327\) | 4.91941e10 | 0.237930 | ||||||||
\(328\) | −8.47137e10 | −0.404130 | ||||||||
\(329\) | −5.11475e10 | −0.240682 | ||||||||
\(330\) | 2.27328e11 | 1.05521 | ||||||||
\(331\) | 1.33209e11 | 0.609968 | 0.304984 | − | 0.952358i | \(-0.401349\pi\) | ||||
0.304984 | + | 0.952358i | \(0.401349\pi\) | |||||||
\(332\) | −1.58503e11 | −0.716003 | ||||||||
\(333\) | 3.94925e10 | 0.176001 | ||||||||
\(334\) | 3.00539e10 | 0.132142 | ||||||||
\(335\) | −2.31226e11 | −1.00308 | ||||||||
\(336\) | 7.40940e9 | 0.0317144 | ||||||||
\(337\) | 4.38081e10 | 0.185020 | 0.0925102 | − | 0.995712i | \(-0.470511\pi\) | ||||
0.0925102 | + | 0.995712i | \(0.470511\pi\) | |||||||
\(338\) | −1.59681e11 | −0.665471 | ||||||||
\(339\) | 9.77989e10 | 0.402194 | ||||||||
\(340\) | −6.60845e10 | −0.268191 | ||||||||
\(341\) | −7.00651e10 | −0.280613 | ||||||||
\(342\) | 1.29412e10 | 0.0511514 | ||||||||
\(343\) | −1.27406e11 | −0.497011 | ||||||||
\(344\) | −6.38540e10 | −0.245853 | ||||||||
\(345\) | 1.52732e11 | 0.580421 | ||||||||
\(346\) | −2.81279e11 | −1.05510 | ||||||||
\(347\) | −2.17392e11 | −0.804935 | −0.402467 | − | 0.915434i | \(-0.631847\pi\) | ||||
−0.402467 | + | 0.915434i | \(0.631847\pi\) | |||||||
\(348\) | −3.09711e10 | −0.113201 | ||||||||
\(349\) | 9.21736e10 | 0.332577 | 0.166288 | − | 0.986077i | \(-0.446822\pi\) | ||||
0.166288 | + | 0.986077i | \(0.446822\pi\) | |||||||
\(350\) | 1.07823e11 | 0.384066 | ||||||||
\(351\) | −1.11493e10 | −0.0392070 | ||||||||
\(352\) | 3.86691e11 | 1.34253 | ||||||||
\(353\) | −4.92901e11 | −1.68956 | −0.844781 | − | 0.535113i | \(-0.820269\pi\) | ||||
−0.844781 | + | 0.535113i | \(0.820269\pi\) | |||||||
\(354\) | 1.54194e10 | 0.0521858 | ||||||||
\(355\) | 9.95810e10 | 0.332773 | ||||||||
\(356\) | −1.81989e11 | −0.600511 | ||||||||
\(357\) | 1.32795e10 | 0.0432686 | ||||||||
\(358\) | −1.19673e11 | −0.385055 | ||||||||
\(359\) | 1.26242e11 | 0.401123 | 0.200562 | − | 0.979681i | \(-0.435723\pi\) | ||||
0.200562 | + | 0.979681i | \(0.435723\pi\) | |||||||
\(360\) | 1.98779e11 | 0.623747 | ||||||||
\(361\) | −3.06924e11 | −0.951148 | ||||||||
\(362\) | −3.66937e11 | −1.12306 | ||||||||
\(363\) | −2.28847e11 | −0.691775 | ||||||||
\(364\) | −9.08286e9 | −0.0271185 | ||||||||
\(365\) | 6.40970e11 | 1.89025 | ||||||||
\(366\) | 2.12232e11 | 0.618223 | ||||||||
\(367\) | −4.99871e11 | −1.43834 | −0.719169 | − | 0.694835i | \(-0.755477\pi\) | ||||
−0.719169 | + | 0.694835i | \(0.755477\pi\) | |||||||
\(368\) | −4.25782e10 | −0.121024 | ||||||||
\(369\) | 4.55216e10 | 0.127820 | ||||||||
\(370\) | −2.34646e11 | −0.650886 | ||||||||
\(371\) | 9.01027e10 | 0.246919 | ||||||||
\(372\) | −2.09054e10 | −0.0565998 | ||||||||
\(373\) | −3.99849e11 | −1.06956 | −0.534781 | − | 0.844991i | \(-0.679606\pi\) | ||||
−0.534781 | + | 0.844991i | \(0.679606\pi\) | |||||||
\(374\) | −1.13582e11 | −0.300183 | ||||||||
\(375\) | 4.52437e11 | 1.18145 | ||||||||
\(376\) | 3.82534e11 | 0.987018 | ||||||||
\(377\) | −3.02477e10 | −0.0771181 | ||||||||
\(378\) | −1.36298e10 | −0.0343381 | ||||||||
\(379\) | 6.91858e11 | 1.72243 | 0.861213 | − | 0.508245i | \(-0.169705\pi\) | ||||
0.861213 | + | 0.508245i | \(0.169705\pi\) | |||||||
\(380\) | 8.26221e10 | 0.203269 | ||||||||
\(381\) | −3.48096e11 | −0.846323 | ||||||||
\(382\) | −2.36956e11 | −0.569355 | ||||||||
\(383\) | −2.13034e11 | −0.505888 | −0.252944 | − | 0.967481i | \(-0.581399\pi\) | ||||
−0.252944 | + | 0.967481i | \(0.581399\pi\) | |||||||
\(384\) | 7.88712e10 | 0.185109 | ||||||||
\(385\) | −2.91645e11 | −0.676520 | ||||||||
\(386\) | −2.64495e11 | −0.606422 | ||||||||
\(387\) | 3.43125e10 | 0.0777594 | ||||||||
\(388\) | −7.24850e9 | −0.0162370 | ||||||||
\(389\) | 2.17993e11 | 0.482692 | 0.241346 | − | 0.970439i | \(-0.422411\pi\) | ||||
0.241346 | + | 0.970439i | \(0.422411\pi\) | |||||||
\(390\) | 6.62436e10 | 0.144995 | ||||||||
\(391\) | −7.63105e10 | −0.165116 | ||||||||
\(392\) | 4.60166e11 | 0.984299 | ||||||||
\(393\) | −5.20366e10 | −0.110038 | ||||||||
\(394\) | −2.20052e11 | −0.460035 | ||||||||
\(395\) | 9.00266e11 | 1.86073 | ||||||||
\(396\) | −1.25268e11 | −0.255984 | ||||||||
\(397\) | −1.38887e11 | −0.280612 | −0.140306 | − | 0.990108i | \(-0.544809\pi\) | ||||
−0.140306 | + | 0.990108i | \(0.544809\pi\) | |||||||
\(398\) | 1.11294e11 | 0.222329 | ||||||||
\(399\) | −1.66026e10 | −0.0327943 | ||||||||
\(400\) | −2.35567e11 | −0.460092 | ||||||||
\(401\) | −7.87148e11 | −1.52022 | −0.760111 | − | 0.649794i | \(-0.774855\pi\) | ||||
−0.760111 | + | 0.649794i | \(0.774855\pi\) | |||||||
\(402\) | −1.18577e11 | −0.226457 | ||||||||
\(403\) | −2.04171e10 | −0.0385585 | ||||||||
\(404\) | 4.32895e11 | 0.808475 | ||||||||
\(405\) | −1.06815e11 | −0.197282 | ||||||||
\(406\) | −3.69773e10 | −0.0675412 | ||||||||
\(407\) | 4.33356e11 | 0.782834 | ||||||||
\(408\) | −9.93175e10 | −0.177441 | ||||||||
\(409\) | −1.03924e12 | −1.83637 | −0.918187 | − | 0.396148i | \(-0.870347\pi\) | ||||
−0.918187 | + | 0.396148i | \(0.870347\pi\) | |||||||
\(410\) | −2.70468e11 | −0.472703 | ||||||||
\(411\) | −3.51174e11 | −0.607063 | ||||||||
\(412\) | −3.41287e11 | −0.583556 | ||||||||
\(413\) | −1.97819e10 | −0.0334575 | ||||||||
\(414\) | 7.83238e10 | 0.131036 | ||||||||
\(415\) | −1.48306e12 | −2.45439 | ||||||||
\(416\) | 1.12682e11 | 0.184474 | ||||||||
\(417\) | 2.80404e11 | 0.454122 | ||||||||
\(418\) | 1.42005e11 | 0.227516 | ||||||||
\(419\) | −1.85571e11 | −0.294136 | −0.147068 | − | 0.989126i | \(-0.546984\pi\) | ||||
−0.147068 | + | 0.989126i | \(0.546984\pi\) | |||||||
\(420\) | −8.70183e10 | −0.136455 | ||||||||
\(421\) | −5.98397e11 | −0.928368 | −0.464184 | − | 0.885739i | \(-0.653652\pi\) | ||||
−0.464184 | + | 0.885739i | \(0.653652\pi\) | |||||||
\(422\) | −2.02462e11 | −0.310769 | ||||||||
\(423\) | −2.05558e11 | −0.312178 | ||||||||
\(424\) | −6.73881e11 | −1.01260 | ||||||||
\(425\) | −4.22194e11 | −0.627714 | ||||||||
\(426\) | 5.10671e10 | 0.0751274 | ||||||||
\(427\) | −2.72277e11 | −0.396357 | ||||||||
\(428\) | −2.24386e11 | −0.323220 | ||||||||
\(429\) | −1.22342e11 | −0.174389 | ||||||||
\(430\) | −2.03869e11 | −0.287569 | ||||||||
\(431\) | 1.23001e12 | 1.71696 | 0.858478 | − | 0.512850i | \(-0.171410\pi\) | ||||
0.858478 | + | 0.512850i | \(0.171410\pi\) | |||||||
\(432\) | 2.97778e10 | 0.0411354 | ||||||||
\(433\) | −5.20413e11 | −0.711463 | −0.355732 | − | 0.934588i | \(-0.615768\pi\) | ||||
−0.355732 | + | 0.934588i | \(0.615768\pi\) | |||||||
\(434\) | −2.49595e10 | −0.0337701 | ||||||||
\(435\) | −2.89788e11 | −0.388042 | ||||||||
\(436\) | 1.61064e11 | 0.213457 | ||||||||
\(437\) | 9.54072e10 | 0.125145 | ||||||||
\(438\) | 3.28702e11 | 0.426746 | ||||||||
\(439\) | −7.79982e11 | −1.00229 | −0.501146 | − | 0.865363i | \(-0.667088\pi\) | ||||
−0.501146 | + | 0.865363i | \(0.667088\pi\) | |||||||
\(440\) | 2.18122e12 | 2.77436 | ||||||||
\(441\) | −2.47274e11 | −0.311318 | ||||||||
\(442\) | −3.30978e10 | −0.0412477 | ||||||||
\(443\) | −1.51957e12 | −1.87458 | −0.937291 | − | 0.348548i | \(-0.886675\pi\) | ||||
−0.937291 | + | 0.348548i | \(0.886675\pi\) | |||||||
\(444\) | 1.29301e11 | 0.157898 | ||||||||
\(445\) | −1.70282e12 | −2.05849 | ||||||||
\(446\) | −2.42389e11 | −0.290072 | ||||||||
\(447\) | 1.12710e11 | 0.133530 | ||||||||
\(448\) | 1.84587e11 | 0.216496 | ||||||||
\(449\) | 9.46589e11 | 1.09914 | 0.549570 | − | 0.835448i | \(-0.314792\pi\) | ||||
0.549570 | + | 0.835448i | \(0.314792\pi\) | |||||||
\(450\) | 4.33333e11 | 0.498156 | ||||||||
\(451\) | 4.99514e11 | 0.568530 | ||||||||
\(452\) | 3.20199e11 | 0.360825 | ||||||||
\(453\) | −3.57399e11 | −0.398760 | ||||||||
\(454\) | 1.23713e11 | 0.136667 | ||||||||
\(455\) | −8.49856e10 | −0.0929596 | ||||||||
\(456\) | 1.24172e11 | 0.134487 | ||||||||
\(457\) | −1.31278e12 | −1.40789 | −0.703943 | − | 0.710256i | \(-0.748579\pi\) | ||||
−0.703943 | + | 0.710256i | \(0.748579\pi\) | |||||||
\(458\) | 3.18065e11 | 0.337770 | ||||||||
\(459\) | 5.33691e10 | 0.0561219 | ||||||||
\(460\) | 5.00051e11 | 0.520720 | ||||||||
\(461\) | −9.37640e10 | −0.0966901 | −0.0483450 | − | 0.998831i | \(-0.515395\pi\) | ||||
−0.0483450 | + | 0.998831i | \(0.515395\pi\) | |||||||
\(462\) | −1.49561e11 | −0.152732 | ||||||||
\(463\) | −4.76737e11 | −0.482131 | −0.241065 | − | 0.970509i | \(-0.577497\pi\) | ||||
−0.241065 | + | 0.970509i | \(0.577497\pi\) | |||||||
\(464\) | 8.07865e10 | 0.0809111 | ||||||||
\(465\) | −1.95606e11 | −0.194018 | ||||||||
\(466\) | 1.82435e11 | 0.179214 | ||||||||
\(467\) | 1.50733e12 | 1.46650 | 0.733249 | − | 0.679960i | \(-0.238003\pi\) | ||||
0.733249 | + | 0.679960i | \(0.238003\pi\) | |||||||
\(468\) | −3.65033e10 | −0.0351743 | ||||||||
\(469\) | 1.52126e11 | 0.145186 | ||||||||
\(470\) | 1.22133e12 | 1.15449 | ||||||||
\(471\) | 1.08778e12 | 1.01847 | ||||||||
\(472\) | 1.47950e11 | 0.137207 | ||||||||
\(473\) | 3.76515e11 | 0.345865 | ||||||||
\(474\) | 4.61674e11 | 0.420081 | ||||||||
\(475\) | 5.27848e11 | 0.475760 | ||||||||
\(476\) | 4.34777e10 | 0.0388181 | ||||||||
\(477\) | 3.62116e11 | 0.320269 | ||||||||
\(478\) | 5.61598e11 | 0.492039 | ||||||||
\(479\) | −4.82675e11 | −0.418933 | −0.209467 | − | 0.977816i | \(-0.567173\pi\) | ||||
−0.209467 | + | 0.977816i | \(0.567173\pi\) | |||||||
\(480\) | 1.07955e12 | 0.928235 | ||||||||
\(481\) | 1.26280e11 | 0.107568 | ||||||||
\(482\) | 5.18529e11 | 0.437584 | ||||||||
\(483\) | −1.00484e11 | −0.0840104 | ||||||||
\(484\) | −7.49257e11 | −0.620621 | ||||||||
\(485\) | −6.78221e10 | −0.0556588 | ||||||||
\(486\) | −5.47771e10 | −0.0445385 | ||||||||
\(487\) | −1.54778e12 | −1.24690 | −0.623448 | − | 0.781865i | \(-0.714269\pi\) | ||||
−0.623448 | + | 0.781865i | \(0.714269\pi\) | |||||||
\(488\) | 2.03637e12 | 1.62543 | ||||||||
\(489\) | −8.54547e11 | −0.675844 | ||||||||
\(490\) | 1.46918e12 | 1.15131 | ||||||||
\(491\) | 1.47468e12 | 1.14507 | 0.572534 | − | 0.819881i | \(-0.305961\pi\) | ||||
0.572534 | + | 0.819881i | \(0.305961\pi\) | |||||||
\(492\) | 1.49040e11 | 0.114673 | ||||||||
\(493\) | 1.44789e11 | 0.110389 | ||||||||
\(494\) | 4.13806e10 | 0.0312626 | ||||||||
\(495\) | −1.17210e12 | −0.877486 | ||||||||
\(496\) | 5.45306e10 | 0.0404550 | ||||||||
\(497\) | −6.55153e10 | −0.0481658 | ||||||||
\(498\) | −7.60544e11 | −0.554105 | ||||||||
\(499\) | −8.77017e11 | −0.633222 | −0.316611 | − | 0.948556i | \(-0.602545\pi\) | ||||
−0.316611 | + | 0.948556i | \(0.602545\pi\) | |||||||
\(500\) | 1.48130e12 | 1.05993 | ||||||||
\(501\) | −1.54957e11 | −0.109886 | ||||||||
\(502\) | −1.75631e11 | −0.123434 | ||||||||
\(503\) | −1.48585e12 | −1.03495 | −0.517474 | − | 0.855699i | \(-0.673128\pi\) | ||||
−0.517474 | + | 0.855699i | \(0.673128\pi\) | |||||||
\(504\) | −1.30778e11 | −0.0902815 | ||||||||
\(505\) | 4.05047e12 | 2.77137 | ||||||||
\(506\) | 8.59455e11 | 0.582836 | ||||||||
\(507\) | 8.23314e11 | 0.553388 | ||||||||
\(508\) | −1.13968e12 | −0.759273 | ||||||||
\(509\) | −1.72731e12 | −1.14062 | −0.570308 | − | 0.821431i | \(-0.693176\pi\) | ||||
−0.570308 | + | 0.821431i | \(0.693176\pi\) | |||||||
\(510\) | −3.17094e11 | −0.207550 | ||||||||
\(511\) | −4.21700e11 | −0.273596 | ||||||||
\(512\) | −6.51234e11 | −0.418815 | ||||||||
\(513\) | −6.67247e10 | −0.0425362 | ||||||||
\(514\) | 1.07153e12 | 0.677126 | ||||||||
\(515\) | −3.19333e12 | −2.00037 | ||||||||
\(516\) | 1.12341e11 | 0.0697613 | ||||||||
\(517\) | −2.25561e12 | −1.38853 | ||||||||
\(518\) | 1.54376e11 | 0.0942096 | ||||||||
\(519\) | 1.45027e12 | 0.877395 | ||||||||
\(520\) | 6.35610e11 | 0.381220 | ||||||||
\(521\) | 7.82017e11 | 0.464993 | 0.232496 | − | 0.972597i | \(-0.425311\pi\) | ||||
0.232496 | + | 0.972597i | \(0.425311\pi\) | |||||||
\(522\) | −1.48609e11 | −0.0876048 | ||||||||
\(523\) | −2.13367e12 | −1.24701 | −0.623504 | − | 0.781820i | \(-0.714291\pi\) | ||||
−0.623504 | + | 0.781820i | \(0.714291\pi\) | |||||||
\(524\) | −1.70371e11 | −0.0987197 | ||||||||
\(525\) | −5.55934e11 | −0.319379 | ||||||||
\(526\) | −2.01911e12 | −1.15007 | ||||||||
\(527\) | 9.77320e10 | 0.0551937 | ||||||||
\(528\) | 3.26755e11 | 0.182966 | ||||||||
\(529\) | −1.22372e12 | −0.679411 | ||||||||
\(530\) | −2.15152e12 | −1.18442 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −5.43579e10 | −0.0294212 | ||||||||
\(533\) | 1.45559e11 | 0.0781207 | ||||||||
\(534\) | −8.73240e11 | −0.464727 | ||||||||
\(535\) | −2.09951e12 | −1.10797 | ||||||||
\(536\) | −1.13776e12 | −0.595398 | ||||||||
\(537\) | 6.17031e11 | 0.320201 | ||||||||
\(538\) | −2.86784e10 | −0.0147582 | ||||||||
\(539\) | −2.71336e12 | −1.38471 | ||||||||
\(540\) | −3.49720e11 | −0.176990 | ||||||||
\(541\) | −8.84532e11 | −0.443941 | −0.221971 | − | 0.975053i | \(-0.571249\pi\) | ||||
−0.221971 | + | 0.975053i | \(0.571249\pi\) | |||||||
\(542\) | 2.24347e12 | 1.11667 | ||||||||
\(543\) | 1.89192e12 | 0.933907 | ||||||||
\(544\) | −5.39386e11 | −0.264061 | ||||||||
\(545\) | 1.50703e12 | 0.731709 | ||||||||
\(546\) | −4.35823e10 | −0.0209867 | ||||||||
\(547\) | 1.54270e12 | 0.736783 | 0.368391 | − | 0.929671i | \(-0.379909\pi\) | ||||
0.368391 | + | 0.929671i | \(0.379909\pi\) | |||||||
\(548\) | −1.14976e12 | −0.544622 | ||||||||
\(549\) | −1.09426e12 | −0.514098 | ||||||||
\(550\) | 4.75501e12 | 2.21574 | ||||||||
\(551\) | −1.81023e11 | −0.0836663 | ||||||||
\(552\) | 7.51520e11 | 0.344520 | ||||||||
\(553\) | −5.92294e11 | −0.269323 | ||||||||
\(554\) | −1.97540e12 | −0.890964 | ||||||||
\(555\) | 1.20983e12 | 0.541259 | ||||||||
\(556\) | 9.18060e11 | 0.407412 | ||||||||
\(557\) | 2.50149e12 | 1.10116 | 0.550580 | − | 0.834782i | \(-0.314406\pi\) | ||||
0.550580 | + | 0.834782i | \(0.314406\pi\) | |||||||
\(558\) | −1.00310e11 | −0.0438018 | ||||||||
\(559\) | 1.09717e11 | 0.0475248 | ||||||||
\(560\) | 2.26982e11 | 0.0975317 | ||||||||
\(561\) | 5.85625e11 | 0.249624 | ||||||||
\(562\) | 1.06973e12 | 0.452337 | ||||||||
\(563\) | 4.12189e12 | 1.72906 | 0.864528 | − | 0.502584i | \(-0.167617\pi\) | ||||
0.864528 | + | 0.502584i | \(0.167617\pi\) | |||||||
\(564\) | −6.73008e11 | −0.280069 | ||||||||
\(565\) | 2.99601e12 | 1.23687 | ||||||||
\(566\) | −2.02371e12 | −0.828845 | ||||||||
\(567\) | 7.02749e10 | 0.0285546 | ||||||||
\(568\) | 4.89991e11 | 0.197524 | ||||||||
\(569\) | −1.93214e12 | −0.772738 | −0.386369 | − | 0.922344i | \(-0.626271\pi\) | ||||
−0.386369 | + | 0.922344i | \(0.626271\pi\) | |||||||
\(570\) | 3.96446e11 | 0.157307 | ||||||||
\(571\) | 1.99421e12 | 0.785071 | 0.392536 | − | 0.919737i | \(-0.371598\pi\) | ||||
0.392536 | + | 0.919737i | \(0.371598\pi\) | |||||||
\(572\) | −4.00555e11 | −0.156451 | ||||||||
\(573\) | 1.22174e12 | 0.473460 | ||||||||
\(574\) | 1.77944e11 | 0.0684193 | ||||||||
\(575\) | 3.19468e12 | 1.21877 | ||||||||
\(576\) | 7.41841e11 | 0.280808 | ||||||||
\(577\) | 1.57088e12 | 0.590001 | 0.295000 | − | 0.955497i | \(-0.404680\pi\) | ||||
0.295000 | + | 0.955497i | \(0.404680\pi\) | |||||||
\(578\) | −1.70457e12 | −0.635244 | ||||||||
\(579\) | 1.36373e12 | 0.504284 | ||||||||
\(580\) | −9.48782e11 | −0.348129 | ||||||||
\(581\) | 9.75722e11 | 0.355249 | ||||||||
\(582\) | −3.47805e10 | −0.0125656 | ||||||||
\(583\) | 3.97354e12 | 1.42452 | ||||||||
\(584\) | 3.15391e12 | 1.12200 | ||||||||
\(585\) | −3.41551e11 | −0.120574 | ||||||||
\(586\) | 1.85781e12 | 0.650820 | ||||||||
\(587\) | 1.24412e12 | 0.432504 | 0.216252 | − | 0.976338i | \(-0.430617\pi\) | ||||
0.216252 | + | 0.976338i | \(0.430617\pi\) | |||||||
\(588\) | −8.09589e11 | −0.279297 | ||||||||
\(589\) | −1.22189e11 | −0.0418326 | ||||||||
\(590\) | 4.72363e11 | 0.160488 | ||||||||
\(591\) | 1.13458e12 | 0.382553 | ||||||||
\(592\) | −3.37274e11 | −0.112859 | ||||||||
\(593\) | −2.93383e12 | −0.974292 | −0.487146 | − | 0.873321i | \(-0.661962\pi\) | ||||
−0.487146 | + | 0.873321i | \(0.661962\pi\) | |||||||
\(594\) | −6.01075e11 | −0.198102 | ||||||||
\(595\) | 4.06808e11 | 0.133065 | ||||||||
\(596\) | 3.69018e11 | 0.119795 | ||||||||
\(597\) | −5.73828e11 | −0.184883 | ||||||||
\(598\) | 2.50446e11 | 0.0800865 | ||||||||
\(599\) | 2.07249e12 | 0.657767 | 0.328884 | − | 0.944370i | \(-0.393328\pi\) | ||||
0.328884 | + | 0.944370i | \(0.393328\pi\) | |||||||
\(600\) | 4.15785e12 | 1.30975 | ||||||||
\(601\) | −4.76700e12 | −1.49043 | −0.745213 | − | 0.666827i | \(-0.767652\pi\) | ||||
−0.745213 | + | 0.666827i | \(0.767652\pi\) | |||||||
\(602\) | 1.34127e11 | 0.0416229 | ||||||||
\(603\) | 6.11383e11 | 0.188315 | ||||||||
\(604\) | −1.17014e12 | −0.357745 | ||||||||
\(605\) | −7.01058e12 | −2.12743 | ||||||||
\(606\) | 2.07716e12 | 0.625668 | ||||||||
\(607\) | 3.17116e11 | 0.0948133 | 0.0474066 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474066 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(608\) | 6.74367e11 | 0.200138 | ||||||||
\(609\) | 1.90654e11 | 0.0561654 | ||||||||
\(610\) | 6.50158e12 | 1.90123 | ||||||||
\(611\) | −6.57288e11 | −0.190796 | ||||||||
\(612\) | 1.74733e11 | 0.0503494 | ||||||||
\(613\) | −5.57634e12 | −1.59506 | −0.797530 | − | 0.603279i | \(-0.793860\pi\) | ||||
−0.797530 | + | 0.603279i | \(0.793860\pi\) | |||||||
\(614\) | 1.88779e12 | 0.536038 | ||||||||
\(615\) | 1.39453e12 | 0.393087 | ||||||||
\(616\) | −1.43505e12 | −0.401562 | ||||||||
\(617\) | −4.78857e12 | −1.33022 | −0.665108 | − | 0.746747i | \(-0.731615\pi\) | ||||
−0.665108 | + | 0.746747i | \(0.731615\pi\) | |||||||
\(618\) | −1.63760e12 | −0.451606 | ||||||||
\(619\) | 1.27618e12 | 0.349384 | 0.174692 | − | 0.984623i | \(-0.444107\pi\) | ||||
0.174692 | + | 0.984623i | \(0.444107\pi\) | |||||||
\(620\) | −6.40423e11 | −0.174062 | ||||||||
\(621\) | −4.03836e11 | −0.108966 | ||||||||
\(622\) | 2.39284e12 | 0.640998 | ||||||||
\(623\) | 1.12030e12 | 0.297947 | ||||||||
\(624\) | 9.52168e10 | 0.0251410 | ||||||||
\(625\) | 5.64890e12 | 1.48083 | ||||||||
\(626\) | −2.26058e12 | −0.588350 | ||||||||
\(627\) | −7.32177e11 | −0.189196 | ||||||||
\(628\) | 3.56146e12 | 0.913713 | ||||||||
\(629\) | −6.04477e11 | −0.153975 | ||||||||
\(630\) | −4.17540e11 | −0.105600 | ||||||||
\(631\) | 4.94728e12 | 1.24232 | 0.621161 | − | 0.783683i | \(-0.286661\pi\) | ||||
0.621161 | + | 0.783683i | \(0.286661\pi\) | |||||||
\(632\) | 4.42978e12 | 1.10447 | ||||||||
\(633\) | 1.04389e12 | 0.258427 | ||||||||
\(634\) | 6.82911e11 | 0.167866 | ||||||||
\(635\) | −1.06637e13 | −2.60271 | ||||||||
\(636\) | 1.18559e12 | 0.287327 | ||||||||
\(637\) | −7.90678e11 | −0.190271 | ||||||||
\(638\) | −1.63070e12 | −0.389657 | ||||||||
\(639\) | −2.63301e11 | −0.0624739 | ||||||||
\(640\) | 2.41617e12 | 0.569269 | ||||||||
\(641\) | 5.38898e12 | 1.26080 | 0.630399 | − | 0.776271i | \(-0.282891\pi\) | ||||
0.630399 | + | 0.776271i | \(0.282891\pi\) | |||||||
\(642\) | −1.07667e12 | −0.250136 | ||||||||
\(643\) | −1.02124e12 | −0.235602 | −0.117801 | − | 0.993037i | \(-0.537585\pi\) | ||||
−0.117801 | + | 0.993037i | \(0.537585\pi\) | |||||||
\(644\) | −3.28989e11 | −0.0753693 | ||||||||
\(645\) | 1.05114e12 | 0.239135 | ||||||||
\(646\) | −1.98080e11 | −0.0447501 | ||||||||
\(647\) | −3.44500e12 | −0.772895 | −0.386447 | − | 0.922311i | \(-0.626298\pi\) | ||||
−0.386447 | + | 0.922311i | \(0.626298\pi\) | |||||||
\(648\) | −5.25589e11 | −0.117100 | ||||||||
\(649\) | −8.72384e11 | −0.193022 | ||||||||
\(650\) | 1.38561e12 | 0.304461 | ||||||||
\(651\) | 1.28691e11 | 0.0280823 | ||||||||
\(652\) | −2.79783e12 | −0.606328 | ||||||||
\(653\) | 6.88490e12 | 1.48180 | 0.740898 | − | 0.671617i | \(-0.234400\pi\) | ||||
0.740898 | + | 0.671617i | \(0.234400\pi\) | |||||||
\(654\) | 7.72836e11 | 0.165191 | ||||||||
\(655\) | −1.59411e12 | −0.338401 | ||||||||
\(656\) | −3.88763e11 | −0.0819630 | ||||||||
\(657\) | −1.69478e12 | −0.354870 | ||||||||
\(658\) | −8.03524e11 | −0.167102 | ||||||||
\(659\) | −4.67100e12 | −0.964773 | −0.482386 | − | 0.875958i | \(-0.660230\pi\) | ||||
−0.482386 | + | 0.875958i | \(0.660230\pi\) | |||||||
\(660\) | −3.83751e12 | −0.787231 | ||||||||
\(661\) | 3.71454e12 | 0.756830 | 0.378415 | − | 0.925636i | \(-0.376469\pi\) | ||||
0.378415 | + | 0.925636i | \(0.376469\pi\) | |||||||
\(662\) | 2.09270e12 | 0.423492 | ||||||||
\(663\) | 1.70652e11 | 0.0343005 | ||||||||
\(664\) | −7.29745e12 | −1.45685 | ||||||||
\(665\) | −5.08611e11 | −0.100853 | ||||||||
\(666\) | 6.20424e11 | 0.122195 | ||||||||
\(667\) | −1.09560e12 | −0.214331 | ||||||||
\(668\) | −5.07339e11 | −0.0985835 | ||||||||
\(669\) | 1.24975e12 | 0.241216 | ||||||||
\(670\) | −3.63255e12 | −0.696425 | ||||||||
\(671\) | −1.20075e13 | −2.28665 | ||||||||
\(672\) | −7.10248e11 | −0.134353 | ||||||||
\(673\) | 1.00851e12 | 0.189502 | 0.0947511 | − | 0.995501i | \(-0.469794\pi\) | ||||
0.0947511 | + | 0.995501i | \(0.469794\pi\) | |||||||
\(674\) | 6.88221e11 | 0.128457 | ||||||||
\(675\) | −2.23425e12 | −0.414253 | ||||||||
\(676\) | 2.69557e12 | 0.496468 | ||||||||
\(677\) | 9.99402e12 | 1.82848 | 0.914242 | − | 0.405168i | \(-0.132787\pi\) | ||||
0.914242 | + | 0.405168i | \(0.132787\pi\) | |||||||
\(678\) | 1.53641e12 | 0.279238 | ||||||||
\(679\) | 4.46208e10 | 0.00805608 | ||||||||
\(680\) | −3.04253e12 | −0.545688 | ||||||||
\(681\) | −6.37863e11 | −0.113649 | ||||||||
\(682\) | −1.10072e12 | −0.194826 | ||||||||
\(683\) | −2.94151e12 | −0.517222 | −0.258611 | − | 0.965981i | \(-0.583265\pi\) | ||||
−0.258611 | + | 0.965981i | \(0.583265\pi\) | |||||||
\(684\) | −2.18460e11 | −0.0381610 | ||||||||
\(685\) | −1.07580e13 | −1.86691 | ||||||||
\(686\) | −2.00153e12 | −0.345068 | ||||||||
\(687\) | −1.63994e12 | −0.280881 | ||||||||
\(688\) | −2.93035e11 | −0.0498623 | ||||||||
\(689\) | 1.15789e12 | 0.195741 | ||||||||
\(690\) | 2.39940e12 | 0.402978 | ||||||||
\(691\) | 5.36780e12 | 0.895664 | 0.447832 | − | 0.894118i | \(-0.352196\pi\) | ||||
0.447832 | + | 0.894118i | \(0.352196\pi\) | |||||||
\(692\) | 4.74826e12 | 0.787149 | ||||||||
\(693\) | 7.71135e11 | 0.127008 | ||||||||
\(694\) | −3.41521e12 | −0.558856 | ||||||||
\(695\) | 8.59001e12 | 1.39657 | ||||||||
\(696\) | −1.42591e12 | −0.230330 | ||||||||
\(697\) | −6.96759e11 | −0.111824 | ||||||||
\(698\) | 1.44804e12 | 0.230904 | ||||||||
\(699\) | −9.40631e11 | −0.149029 | ||||||||
\(700\) | −1.82016e12 | −0.286528 | ||||||||
\(701\) | −6.20303e12 | −0.970226 | −0.485113 | − | 0.874451i | \(-0.661222\pi\) | ||||
−0.485113 | + | 0.874451i | \(0.661222\pi\) | |||||||
\(702\) | −1.75154e11 | −0.0272209 | ||||||||
\(703\) | 7.55746e11 | 0.116702 | ||||||||
\(704\) | 8.14030e12 | 1.24900 | ||||||||
\(705\) | −6.29714e12 | −0.960047 | ||||||||
\(706\) | −7.74344e12 | −1.17304 | ||||||||
\(707\) | −2.66485e12 | −0.401130 | ||||||||
\(708\) | −2.60294e11 | −0.0389327 | ||||||||
\(709\) | 1.11494e13 | 1.65708 | 0.828541 | − | 0.559928i | \(-0.189171\pi\) | ||||
0.828541 | + | 0.559928i | \(0.189171\pi\) | |||||||
\(710\) | 1.56441e12 | 0.231040 | ||||||||
\(711\) | −2.38038e12 | −0.349328 | ||||||||
\(712\) | −8.37878e12 | −1.22186 | ||||||||
\(713\) | −7.39523e11 | −0.107164 | ||||||||
\(714\) | 2.08619e11 | 0.0300408 | ||||||||
\(715\) | −3.74787e12 | −0.536300 | ||||||||
\(716\) | 2.02019e12 | 0.287266 | ||||||||
\(717\) | −2.89558e12 | −0.409166 | ||||||||
\(718\) | 1.98325e12 | 0.278495 | ||||||||
\(719\) | −1.13389e13 | −1.58231 | −0.791154 | − | 0.611616i | \(-0.790520\pi\) | ||||
−0.791154 | + | 0.611616i | \(0.790520\pi\) | |||||||
\(720\) | 9.12224e11 | 0.126504 | ||||||||
\(721\) | 2.10092e12 | 0.289535 | ||||||||
\(722\) | −4.82175e12 | −0.660370 | ||||||||
\(723\) | −2.67352e12 | −0.363883 | ||||||||
\(724\) | 6.19425e12 | 0.837848 | ||||||||
\(725\) | −6.06148e12 | −0.814813 | ||||||||
\(726\) | −3.59517e12 | −0.480291 | ||||||||
\(727\) | 9.02273e12 | 1.19793 | 0.598967 | − | 0.800773i | \(-0.295578\pi\) | ||||
0.598967 | + | 0.800773i | \(0.295578\pi\) | |||||||
\(728\) | −4.18174e11 | −0.0551780 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 1.00696e13 | 1.31238 | ||||||||
\(731\) | −5.25191e11 | −0.0680282 | ||||||||
\(732\) | −3.58267e12 | −0.461219 | ||||||||
\(733\) | −1.56301e12 | −0.199984 | −0.0999920 | − | 0.994988i | \(-0.531882\pi\) | ||||
−0.0999920 | + | 0.994988i | \(0.531882\pi\) | |||||||
\(734\) | −7.85294e12 | −0.998619 | ||||||||
\(735\) | −7.57508e12 | −0.957402 | ||||||||
\(736\) | 4.08145e12 | 0.512701 | ||||||||
\(737\) | 6.70877e12 | 0.837605 | ||||||||
\(738\) | 7.15141e11 | 0.0887438 | ||||||||
\(739\) | −5.73629e12 | −0.707507 | −0.353754 | − | 0.935339i | \(-0.615095\pi\) | ||||
−0.353754 | + | 0.935339i | \(0.615095\pi\) | |||||||
\(740\) | 3.96104e12 | 0.485587 | ||||||||
\(741\) | −2.13357e11 | −0.0259971 | ||||||||
\(742\) | 1.41551e12 | 0.171433 | ||||||||
\(743\) | 5.90927e12 | 0.711352 | 0.355676 | − | 0.934609i | \(-0.384251\pi\) | ||||
0.355676 | + | 0.934609i | \(0.384251\pi\) | |||||||
\(744\) | −9.62483e11 | −0.115164 | ||||||||
\(745\) | 3.45279e12 | 0.410645 | ||||||||
\(746\) | −6.28159e12 | −0.742583 | ||||||||
\(747\) | 3.92135e12 | 0.460779 | ||||||||
\(748\) | 1.91737e12 | 0.223949 | ||||||||
\(749\) | 1.38129e12 | 0.160368 | ||||||||
\(750\) | 7.10774e12 | 0.820269 | ||||||||
\(751\) | 6.05076e11 | 0.0694113 | 0.0347056 | − | 0.999398i | \(-0.488951\pi\) | ||||
0.0347056 | + | 0.999398i | \(0.488951\pi\) | |||||||
\(752\) | 1.75550e12 | 0.200180 | ||||||||
\(753\) | 9.05550e11 | 0.102644 | ||||||||
\(754\) | −4.75189e11 | −0.0535421 | ||||||||
\(755\) | −1.09487e13 | −1.22631 | ||||||||
\(756\) | 2.30084e11 | 0.0256176 | ||||||||
\(757\) | 1.87357e12 | 0.207366 | 0.103683 | − | 0.994610i | \(-0.466937\pi\) | ||||
0.103683 | + | 0.994610i | \(0.466937\pi\) | |||||||
\(758\) | 1.08690e13 | 1.19586 | ||||||||
\(759\) | −4.43133e12 | −0.484670 | ||||||||
\(760\) | 3.80392e12 | 0.413590 | ||||||||
\(761\) | 9.68739e12 | 1.04707 | 0.523535 | − | 0.852004i | \(-0.324613\pi\) | ||||
0.523535 | + | 0.852004i | \(0.324613\pi\) | |||||||
\(762\) | −5.46856e12 | −0.587591 | ||||||||
\(763\) | −9.91491e11 | −0.105908 | ||||||||
\(764\) | 4.00005e12 | 0.424762 | ||||||||
\(765\) | 1.63493e12 | 0.172593 | ||||||||
\(766\) | −3.34675e12 | −0.351232 | ||||||||
\(767\) | −2.54214e11 | −0.0265228 | ||||||||
\(768\) | 5.92823e12 | 0.614893 | ||||||||
\(769\) | −1.11147e13 | −1.14611 | −0.573057 | − | 0.819516i | \(-0.694243\pi\) | ||||
−0.573057 | + | 0.819516i | \(0.694243\pi\) | |||||||
\(770\) | −4.58172e12 | −0.469699 | ||||||||
\(771\) | −5.52478e12 | −0.563080 | ||||||||
\(772\) | 4.46493e12 | 0.452415 | ||||||||
\(773\) | 5.13307e12 | 0.517094 | 0.258547 | − | 0.965999i | \(-0.416756\pi\) | ||||
0.258547 | + | 0.965999i | \(0.416756\pi\) | |||||||
\(774\) | 5.39047e11 | 0.0539874 | ||||||||
\(775\) | −4.09147e12 | −0.407401 | ||||||||
\(776\) | −3.33721e11 | −0.0330374 | ||||||||
\(777\) | −7.95958e11 | −0.0783422 | ||||||||
\(778\) | 3.42466e12 | 0.335127 | ||||||||
\(779\) | 8.71122e11 | 0.0847541 | ||||||||
\(780\) | −1.11826e12 | −0.108172 | ||||||||
\(781\) | −2.88923e12 | −0.277877 | ||||||||
\(782\) | −1.19883e12 | −0.114638 | ||||||||
\(783\) | 7.66225e11 | 0.0728498 | ||||||||
\(784\) | 2.11177e12 | 0.199629 | ||||||||
\(785\) | 3.33235e13 | 3.13212 | ||||||||
\(786\) | −8.17491e11 | −0.0763979 | ||||||||
\(787\) | −6.86470e12 | −0.637875 | −0.318937 | − | 0.947776i | \(-0.603326\pi\) | ||||
−0.318937 | + | 0.947776i | \(0.603326\pi\) | |||||||
\(788\) | 3.71468e12 | 0.343205 | ||||||||
\(789\) | 1.04105e13 | 0.956365 | ||||||||
\(790\) | 1.41431e13 | 1.29188 | ||||||||
\(791\) | −1.97110e12 | −0.179026 | ||||||||
\(792\) | −5.76734e12 | −0.520850 | ||||||||
\(793\) | −3.49899e12 | −0.314205 | ||||||||
\(794\) | −2.18191e12 | −0.194825 | ||||||||
\(795\) | 1.10932e13 | 0.984928 | ||||||||
\(796\) | −1.87874e12 | −0.165866 | ||||||||
\(797\) | 9.50994e12 | 0.834863 | 0.417432 | − | 0.908708i | \(-0.362930\pi\) | ||||
0.417432 | + | 0.908708i | \(0.362930\pi\) | |||||||
\(798\) | −2.60826e11 | −0.0227687 | ||||||||
\(799\) | 3.14629e12 | 0.273111 | ||||||||
\(800\) | 2.25809e13 | 1.94911 | ||||||||
\(801\) | 4.50241e12 | 0.386455 | ||||||||
\(802\) | −1.23660e13 | −1.05547 | ||||||||
\(803\) | −1.85970e13 | −1.57842 | ||||||||
\(804\) | 2.00170e12 | 0.168946 | ||||||||
\(805\) | −3.07825e12 | −0.258358 | ||||||||
\(806\) | −3.20750e11 | −0.0267707 | ||||||||
\(807\) | 1.47865e11 | 0.0122726 | ||||||||
\(808\) | 1.99305e13 | 1.64500 | ||||||||
\(809\) | −1.84582e13 | −1.51503 | −0.757516 | − | 0.652816i | \(-0.773587\pi\) | ||||
−0.757516 | + | 0.652816i | \(0.773587\pi\) | |||||||
\(810\) | −1.67806e12 | −0.136970 | ||||||||
\(811\) | −7.97245e12 | −0.647139 | −0.323570 | − | 0.946204i | \(-0.604883\pi\) | ||||
−0.323570 | + | 0.946204i | \(0.604883\pi\) | |||||||
\(812\) | 6.24213e11 | 0.0503884 | ||||||||
\(813\) | −1.15673e13 | −0.928589 | ||||||||
\(814\) | 6.80798e12 | 0.543511 | ||||||||
\(815\) | −2.61785e13 | −2.07843 | ||||||||
\(816\) | −4.55782e11 | −0.0359875 | ||||||||
\(817\) | 6.56620e11 | 0.0515602 | ||||||||
\(818\) | −1.63264e13 | −1.27497 | ||||||||
\(819\) | 2.24710e11 | 0.0174520 | ||||||||
\(820\) | 4.56576e12 | 0.352655 | ||||||||
\(821\) | −1.51036e13 | −1.16021 | −0.580103 | − | 0.814543i | \(-0.696988\pi\) | ||||
−0.580103 | + | 0.814543i | \(0.696988\pi\) | |||||||
\(822\) | −5.51691e12 | −0.421476 | ||||||||
\(823\) | −2.55362e13 | −1.94025 | −0.970125 | − | 0.242607i | \(-0.921997\pi\) | ||||
−0.970125 | + | 0.242607i | \(0.921997\pi\) | |||||||
\(824\) | −1.57129e13 | −1.18736 | ||||||||
\(825\) | −2.45167e13 | −1.84255 | ||||||||
\(826\) | −3.10772e11 | −0.0232291 | ||||||||
\(827\) | 2.06767e13 | 1.53712 | 0.768558 | − | 0.639780i | \(-0.220974\pi\) | ||||
0.768558 | + | 0.639780i | \(0.220974\pi\) | |||||||
\(828\) | −1.32218e12 | −0.0977584 | ||||||||
\(829\) | 2.61708e13 | 1.92452 | 0.962258 | − | 0.272137i | \(-0.0877304\pi\) | ||||
0.962258 | + | 0.272137i | \(0.0877304\pi\) | |||||||
\(830\) | −2.32988e13 | −1.70405 | ||||||||
\(831\) | 1.01851e13 | 0.740902 | ||||||||
\(832\) | 2.37209e12 | 0.171624 | ||||||||
\(833\) | 3.78480e12 | 0.272358 | ||||||||
\(834\) | 4.40513e12 | 0.315291 | ||||||||
\(835\) | −4.74703e12 | −0.337934 | ||||||||
\(836\) | −2.39719e12 | −0.169736 | ||||||||
\(837\) | 5.17199e11 | 0.0364244 | ||||||||
\(838\) | −2.91531e12 | −0.204214 | ||||||||
\(839\) | −1.97813e13 | −1.37824 | −0.689122 | − | 0.724645i | \(-0.742004\pi\) | ||||
−0.689122 | + | 0.724645i | \(0.742004\pi\) | |||||||
\(840\) | −4.00632e12 | −0.277644 | ||||||||
\(841\) | −1.24284e13 | −0.856708 | ||||||||
\(842\) | −9.40078e12 | −0.644554 | ||||||||
\(843\) | −5.51552e12 | −0.376151 | ||||||||
\(844\) | 3.41775e12 | 0.231846 | ||||||||
\(845\) | 2.52217e13 | 1.70184 | ||||||||
\(846\) | −3.22930e12 | −0.216741 | ||||||||
\(847\) | 4.61233e12 | 0.307925 | ||||||||
\(848\) | −3.09254e12 | −0.205368 | ||||||||
\(849\) | 1.04342e13 | 0.689246 | ||||||||
\(850\) | −6.63263e12 | −0.435814 | ||||||||
\(851\) | 4.57398e12 | 0.298959 | ||||||||
\(852\) | −8.62062e11 | −0.0560480 | ||||||||
\(853\) | −9.83550e12 | −0.636101 | −0.318050 | − | 0.948074i | \(-0.603028\pi\) | ||||
−0.318050 | + | 0.948074i | \(0.603028\pi\) | |||||||
\(854\) | −4.27746e12 | −0.275185 | ||||||||
\(855\) | −2.04407e12 | −0.130812 | ||||||||
\(856\) | −1.03307e13 | −0.657655 | ||||||||
\(857\) | −2.31797e13 | −1.46789 | −0.733947 | − | 0.679207i | \(-0.762324\pi\) | ||||
−0.733947 | + | 0.679207i | \(0.762324\pi\) | |||||||
\(858\) | −1.92198e12 | −0.121076 | ||||||||
\(859\) | −4.78226e12 | −0.299684 | −0.149842 | − | 0.988710i | \(-0.547877\pi\) | ||||
−0.149842 | + | 0.988710i | \(0.547877\pi\) | |||||||
\(860\) | 3.44150e12 | 0.214538 | ||||||||
\(861\) | −9.17473e11 | −0.0568956 | ||||||||
\(862\) | 1.93233e13 | 1.19206 | ||||||||
\(863\) | −7.08844e11 | −0.0435013 | −0.0217506 | − | 0.999763i | \(-0.506924\pi\) | ||||
−0.0217506 | + | 0.999763i | \(0.506924\pi\) | |||||||
\(864\) | −2.85443e12 | −0.174264 | ||||||||
\(865\) | 4.44281e13 | 2.69827 | ||||||||
\(866\) | −8.17564e12 | −0.493960 | ||||||||
\(867\) | 8.78875e12 | 0.528252 | ||||||||
\(868\) | 4.21341e11 | 0.0251939 | ||||||||
\(869\) | −2.61202e13 | −1.55377 | ||||||||
\(870\) | −4.55255e12 | −0.269412 | ||||||||
\(871\) | 1.95494e12 | 0.115094 | ||||||||
\(872\) | 7.41540e12 | 0.434320 | ||||||||
\(873\) | 1.79328e11 | 0.0104492 | ||||||||
\(874\) | 1.49884e12 | 0.0868868 | ||||||||
\(875\) | −9.11871e12 | −0.525893 | ||||||||
\(876\) | −5.54880e12 | −0.318369 | ||||||||
\(877\) | −1.86698e13 | −1.06572 | −0.532859 | − | 0.846204i | \(-0.678883\pi\) | ||||
−0.532859 | + | 0.846204i | \(0.678883\pi\) | |||||||
\(878\) | −1.22535e13 | −0.695878 | ||||||||
\(879\) | −9.57880e12 | −0.541204 | ||||||||
\(880\) | 1.00099e13 | 0.562677 | ||||||||
\(881\) | −1.11188e12 | −0.0621825 | −0.0310912 | − | 0.999517i | \(-0.509898\pi\) | ||||
−0.0310912 | + | 0.999517i | \(0.509898\pi\) | |||||||
\(882\) | −3.88465e12 | −0.216144 | ||||||||
\(883\) | −2.83915e13 | −1.57169 | −0.785843 | − | 0.618426i | \(-0.787771\pi\) | ||||
−0.785843 | + | 0.618426i | \(0.787771\pi\) | |||||||
\(884\) | 5.58723e11 | 0.0307724 | ||||||||
\(885\) | −2.43549e12 | −0.133457 | ||||||||
\(886\) | −2.38723e13 | −1.30150 | ||||||||
\(887\) | −2.15452e13 | −1.16868 | −0.584339 | − | 0.811510i | \(-0.698646\pi\) | ||||
−0.584339 | + | 0.811510i | \(0.698646\pi\) | |||||||
\(888\) | 5.95300e12 | 0.321275 | ||||||||
\(889\) | 7.01575e12 | 0.376718 | ||||||||
\(890\) | −2.67512e13 | −1.42918 | ||||||||
\(891\) | 3.09913e12 | 0.164737 | ||||||||
\(892\) | 4.09176e12 | 0.216405 | ||||||||
\(893\) | −3.93365e12 | −0.206997 | ||||||||
\(894\) | 1.77066e12 | 0.0927078 | ||||||||
\(895\) | 1.89024e13 | 0.984719 | ||||||||
\(896\) | −1.58962e12 | −0.0823963 | ||||||||
\(897\) | −1.29130e12 | −0.0665978 | ||||||||
\(898\) | 1.48708e13 | 0.763118 | ||||||||
\(899\) | 1.40315e12 | 0.0716449 | ||||||||
\(900\) | −7.31507e12 | −0.371644 | ||||||||
\(901\) | −5.54258e12 | −0.280189 | ||||||||
\(902\) | 7.84732e12 | 0.394723 | ||||||||
\(903\) | −6.91557e11 | −0.0346125 | ||||||||
\(904\) | 1.47419e13 | 0.734170 | ||||||||
\(905\) | 5.79578e13 | 2.87206 | ||||||||
\(906\) | −5.61471e12 | −0.276854 | ||||||||
\(907\) | 2.80098e13 | 1.37429 | 0.687143 | − | 0.726522i | \(-0.258865\pi\) | ||||
0.687143 | + | 0.726522i | \(0.258865\pi\) | |||||||
\(908\) | −2.08840e12 | −0.101959 | ||||||||
\(909\) | −1.07098e13 | −0.520288 | ||||||||
\(910\) | −1.33512e12 | −0.0645406 | ||||||||
\(911\) | 1.11071e13 | 0.534281 | 0.267141 | − | 0.963658i | \(-0.413921\pi\) | ||||
0.267141 | + | 0.963658i | \(0.413921\pi\) | |||||||
\(912\) | 5.69841e11 | 0.0272758 | ||||||||
\(913\) | 4.30294e13 | 2.04949 | ||||||||
\(914\) | −2.06236e13 | −0.977477 | ||||||||
\(915\) | −3.35220e13 | −1.58101 | ||||||||
\(916\) | −5.36924e12 | −0.251990 | ||||||||
\(917\) | 1.04878e12 | 0.0489804 | ||||||||
\(918\) | 8.38424e11 | 0.0389647 | ||||||||
\(919\) | −1.57365e13 | −0.727758 | −0.363879 | − | 0.931446i | \(-0.618548\pi\) | ||||
−0.363879 | + | 0.931446i | \(0.618548\pi\) | |||||||
\(920\) | 2.30223e13 | 1.05951 | ||||||||
\(921\) | −9.73339e12 | −0.445755 | ||||||||
\(922\) | −1.47302e12 | −0.0671307 | ||||||||
\(923\) | −8.41925e11 | −0.0381826 | ||||||||
\(924\) | 2.52474e12 | 0.113944 | ||||||||
\(925\) | 2.53059e13 | 1.13654 | ||||||||
\(926\) | −7.48951e12 | −0.334737 | ||||||||
\(927\) | 8.44344e12 | 0.375544 | ||||||||
\(928\) | −7.74401e12 | −0.342768 | ||||||||
\(929\) | 2.12139e13 | 0.934435 | 0.467217 | − | 0.884142i | \(-0.345257\pi\) | ||||
0.467217 | + | 0.884142i | \(0.345257\pi\) | |||||||
\(930\) | −3.07295e12 | −0.134704 | ||||||||
\(931\) | −4.73195e12 | −0.206427 | ||||||||
\(932\) | −3.07968e12 | −0.133701 | ||||||||
\(933\) | −1.23374e13 | −0.533036 | ||||||||
\(934\) | 2.36800e13 | 1.01817 | ||||||||
\(935\) | 1.79402e13 | 0.767673 | ||||||||
\(936\) | −1.68061e12 | −0.0715691 | ||||||||
\(937\) | 4.96097e12 | 0.210251 | 0.105126 | − | 0.994459i | \(-0.466476\pi\) | ||||
0.105126 | + | 0.994459i | \(0.466476\pi\) | |||||||
\(938\) | 2.38989e12 | 0.100801 | ||||||||
\(939\) | 1.16555e13 | 0.489256 | ||||||||
\(940\) | −2.06172e13 | −0.861299 | ||||||||
\(941\) | 2.81479e13 | 1.17029 | 0.585143 | − | 0.810930i | \(-0.301038\pi\) | ||||
0.585143 | + | 0.810930i | \(0.301038\pi\) | |||||||
\(942\) | 1.70890e13 | 0.707110 | ||||||||
\(943\) | 5.27227e12 | 0.217117 | ||||||||
\(944\) | 6.78962e11 | 0.0278273 | ||||||||
\(945\) | 2.15283e12 | 0.0878145 | ||||||||
\(946\) | 5.91502e12 | 0.240130 | ||||||||
\(947\) | 3.56313e13 | 1.43965 | 0.719824 | − | 0.694156i | \(-0.244222\pi\) | ||||
0.719824 | + | 0.694156i | \(0.244222\pi\) | |||||||
\(948\) | −7.79350e12 | −0.313397 | ||||||||
\(949\) | −5.41919e12 | −0.216889 | ||||||||
\(950\) | 8.29245e12 | 0.330314 | ||||||||
\(951\) | −3.52108e12 | −0.139593 | ||||||||
\(952\) | 2.00171e12 | 0.0789832 | ||||||||
\(953\) | 2.49292e13 | 0.979018 | 0.489509 | − | 0.871998i | \(-0.337176\pi\) | ||||
0.489509 | + | 0.871998i | \(0.337176\pi\) | |||||||
\(954\) | 5.68881e12 | 0.222358 | ||||||||
\(955\) | 3.74273e13 | 1.45604 | ||||||||
\(956\) | −9.48030e12 | −0.367081 | ||||||||
\(957\) | 8.40787e12 | 0.324028 | ||||||||
\(958\) | −7.58278e12 | −0.290860 | ||||||||
\(959\) | 7.07778e12 | 0.270218 | ||||||||
\(960\) | 2.27258e13 | 0.863574 | ||||||||
\(961\) | −2.54925e13 | −0.964178 | ||||||||
\(962\) | 1.98385e12 | 0.0746830 | ||||||||
\(963\) | 5.55129e12 | 0.208006 | ||||||||
\(964\) | −8.75326e12 | −0.326455 | ||||||||
\(965\) | 4.17771e13 | 1.55083 | ||||||||
\(966\) | −1.57859e12 | −0.0583273 | ||||||||
\(967\) | −4.82176e13 | −1.77332 | −0.886659 | − | 0.462424i | \(-0.846980\pi\) | ||||
−0.886659 | + | 0.462424i | \(0.846980\pi\) | |||||||
\(968\) | −3.44958e13 | −1.26278 | ||||||||
\(969\) | 1.02129e12 | 0.0372130 | ||||||||
\(970\) | −1.06548e12 | −0.0386432 | ||||||||
\(971\) | 2.25803e12 | 0.0815161 | 0.0407580 | − | 0.999169i | \(-0.487023\pi\) | ||||
0.0407580 | + | 0.999169i | \(0.487023\pi\) | |||||||
\(972\) | 9.24690e11 | 0.0332275 | ||||||||
\(973\) | −5.65146e12 | −0.202140 | ||||||||
\(974\) | −2.43156e13 | −0.865703 | ||||||||
\(975\) | −7.14420e12 | −0.253182 | ||||||||
\(976\) | 9.34521e12 | 0.329659 | ||||||||
\(977\) | 4.23005e13 | 1.48532 | 0.742660 | − | 0.669669i | \(-0.233564\pi\) | ||||
0.742660 | + | 0.669669i | \(0.233564\pi\) | |||||||
\(978\) | −1.34249e13 | −0.469229 | ||||||||
\(979\) | 4.94054e13 | 1.71891 | ||||||||
\(980\) | −2.48012e13 | −0.858927 | ||||||||
\(981\) | −3.98473e12 | −0.137369 | ||||||||
\(982\) | 2.31671e13 | 0.795005 | ||||||||
\(983\) | 3.49372e13 | 1.19343 | 0.596716 | − | 0.802453i | \(-0.296472\pi\) | ||||
0.596716 | + | 0.802453i | \(0.296472\pi\) | |||||||
\(984\) | 6.86181e12 | 0.233325 | ||||||||
\(985\) | 3.47572e13 | 1.17647 | ||||||||
\(986\) | 2.27463e12 | 0.0766415 | ||||||||
\(987\) | 4.14295e12 | 0.138958 | ||||||||
\(988\) | −6.98543e11 | −0.0233231 | ||||||||
\(989\) | 3.97404e12 | 0.132084 | ||||||||
\(990\) | −1.84136e13 | −0.609227 | ||||||||
\(991\) | 4.83227e13 | 1.59155 | 0.795774 | − | 0.605594i | \(-0.207064\pi\) | ||||
0.795774 | + | 0.605594i | \(0.207064\pi\) | |||||||
\(992\) | −5.22717e12 | −0.171382 | ||||||||
\(993\) | −1.07899e13 | −0.352165 | ||||||||
\(994\) | −1.02924e12 | −0.0334409 | ||||||||
\(995\) | −1.75788e13 | −0.568573 | ||||||||
\(996\) | 1.28387e13 | 0.413385 | ||||||||
\(997\) | −1.14216e13 | −0.366098 | −0.183049 | − | 0.983104i | \(-0.558597\pi\) | ||||
−0.183049 | + | 0.983104i | \(0.558597\pi\) | |||||||
\(998\) | −1.37779e13 | −0.439637 | ||||||||
\(999\) | −3.19889e12 | −0.101614 |
(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.b.1.14 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.14 | ✓ | 21 | 1.1 | even | 1 | trivial |