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 | 1.9 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.43662 | −0.196073 | −0.0980363 | − | 0.995183i | \(-0.531256\pi\) | ||||
−0.0980363 | + | 0.995183i | \(0.531256\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −492.316 | −0.961556 | ||||||||
\(5\) | 339.476 | 0.242909 | 0.121455 | − | 0.992597i | \(-0.461244\pi\) | ||||
0.121455 | + | 0.992597i | \(0.461244\pi\) | |||||||
\(6\) | 359.366 | 0.113203 | ||||||||
\(7\) | −12342.0 | −1.94287 | −0.971436 | − | 0.237302i | \(-0.923737\pi\) | ||||
−0.971436 | + | 0.237302i | \(0.923737\pi\) | |||||||
\(8\) | 4455.77 | 0.384607 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −1506.13 | −0.0476279 | ||||||||
\(11\) | 52983.7 | 1.09113 | 0.545563 | − | 0.838070i | \(-0.316316\pi\) | ||||
0.545563 | + | 0.838070i | \(0.316316\pi\) | |||||||
\(12\) | 39877.6 | 0.555154 | ||||||||
\(13\) | −128050. | −1.24347 | −0.621733 | − | 0.783229i | \(-0.713571\pi\) | ||||
−0.621733 | + | 0.783229i | \(0.713571\pi\) | |||||||
\(14\) | 54756.7 | 0.380944 | ||||||||
\(15\) | −27497.6 | −0.140244 | ||||||||
\(16\) | 232297. | 0.886145 | ||||||||
\(17\) | −563735. | −1.63702 | −0.818512 | − | 0.574489i | \(-0.805201\pi\) | ||||
−0.818512 | + | 0.574489i | \(0.805201\pi\) | |||||||
\(18\) | −29108.6 | −0.0653576 | ||||||||
\(19\) | 833020. | 1.46644 | 0.733220 | − | 0.679991i | \(-0.238016\pi\) | ||||
0.733220 | + | 0.679991i | \(0.238016\pi\) | |||||||
\(20\) | −167130. | −0.233571 | ||||||||
\(21\) | 999702. | 1.12172 | ||||||||
\(22\) | −235068. | −0.213940 | ||||||||
\(23\) | 2.12601e6 | 1.58413 | 0.792065 | − | 0.610437i | \(-0.209006\pi\) | ||||
0.792065 | + | 0.610437i | \(0.209006\pi\) | |||||||
\(24\) | −360917. | −0.222053 | ||||||||
\(25\) | −1.83788e6 | −0.940995 | ||||||||
\(26\) | 568108. | 0.243810 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 6.07617e6 | 1.86818 | ||||||||
\(29\) | 5.73663e6 | 1.50614 | 0.753071 | − | 0.657939i | \(-0.228572\pi\) | ||||
0.753071 | + | 0.657939i | \(0.228572\pi\) | |||||||
\(30\) | 121996. | 0.0274980 | ||||||||
\(31\) | 1.18319e6 | 0.230106 | 0.115053 | − | 0.993359i | \(-0.463296\pi\) | ||||
0.115053 | + | 0.993359i | \(0.463296\pi\) | |||||||
\(32\) | −3.31197e6 | −0.558356 | ||||||||
\(33\) | −4.29168e6 | −0.629962 | ||||||||
\(34\) | 2.50108e6 | 0.320976 | ||||||||
\(35\) | −4.18981e6 | −0.471942 | ||||||||
\(36\) | −3.23009e6 | −0.320519 | ||||||||
\(37\) | 5.87411e6 | 0.515270 | 0.257635 | − | 0.966242i | \(-0.417057\pi\) | ||||
0.257635 | + | 0.966242i | \(0.417057\pi\) | |||||||
\(38\) | −3.69579e6 | −0.287529 | ||||||||
\(39\) | 1.03720e7 | 0.717916 | ||||||||
\(40\) | 1.51263e6 | 0.0934248 | ||||||||
\(41\) | −2.15771e7 | −1.19252 | −0.596259 | − | 0.802792i | \(-0.703347\pi\) | ||||
−0.596259 | + | 0.802792i | \(0.703347\pi\) | |||||||
\(42\) | −4.43529e6 | −0.219938 | ||||||||
\(43\) | 2.71725e7 | 1.21205 | 0.606025 | − | 0.795445i | \(-0.292763\pi\) | ||||
0.606025 | + | 0.795445i | \(0.292763\pi\) | |||||||
\(44\) | −2.60847e7 | −1.04918 | ||||||||
\(45\) | 2.22730e6 | 0.0809698 | ||||||||
\(46\) | −9.43231e6 | −0.310604 | ||||||||
\(47\) | −2.75285e7 | −0.822889 | −0.411445 | − | 0.911435i | \(-0.634976\pi\) | ||||
−0.411445 | + | 0.911435i | \(0.634976\pi\) | |||||||
\(48\) | −1.88161e7 | −0.511616 | ||||||||
\(49\) | 1.11971e8 | 2.77475 | ||||||||
\(50\) | 8.15398e6 | 0.184503 | ||||||||
\(51\) | 4.56626e7 | 0.945136 | ||||||||
\(52\) | 6.30410e7 | 1.19566 | ||||||||
\(53\) | 2.71958e7 | 0.473435 | 0.236717 | − | 0.971579i | \(-0.423928\pi\) | ||||
0.236717 | + | 0.971579i | \(0.423928\pi\) | |||||||
\(54\) | 2.35780e6 | 0.0377342 | ||||||||
\(55\) | 1.79867e7 | 0.265045 | ||||||||
\(56\) | −5.49931e7 | −0.747243 | ||||||||
\(57\) | −6.74746e7 | −0.846650 | ||||||||
\(58\) | −2.54512e7 | −0.295313 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | 1.35375e7 | 0.134852 | ||||||||
\(61\) | 9.59563e7 | 0.887338 | 0.443669 | − | 0.896191i | \(-0.353677\pi\) | ||||
0.443669 | + | 0.896191i | \(0.353677\pi\) | |||||||
\(62\) | −5.24937e6 | −0.0451175 | ||||||||
\(63\) | −8.09758e7 | −0.647624 | ||||||||
\(64\) | −1.04242e8 | −0.776666 | ||||||||
\(65\) | −4.34699e7 | −0.302050 | ||||||||
\(66\) | 1.90405e7 | 0.123518 | ||||||||
\(67\) | 1.74709e8 | 1.05920 | 0.529602 | − | 0.848246i | \(-0.322341\pi\) | ||||
0.529602 | + | 0.848246i | \(0.322341\pi\) | |||||||
\(68\) | 2.77536e8 | 1.57409 | ||||||||
\(69\) | −1.72207e8 | −0.914597 | ||||||||
\(70\) | 1.85886e7 | 0.0925349 | ||||||||
\(71\) | 1.39282e8 | 0.650480 | 0.325240 | − | 0.945632i | \(-0.394555\pi\) | ||||
0.325240 | + | 0.945632i | \(0.394555\pi\) | |||||||
\(72\) | 2.92343e7 | 0.128202 | ||||||||
\(73\) | −1.56504e8 | −0.645020 | −0.322510 | − | 0.946566i | \(-0.604527\pi\) | ||||
−0.322510 | + | 0.946566i | \(0.604527\pi\) | |||||||
\(74\) | −2.60612e7 | −0.101030 | ||||||||
\(75\) | 1.48868e8 | 0.543284 | ||||||||
\(76\) | −4.10110e8 | −1.41006 | ||||||||
\(77\) | −6.53924e8 | −2.11992 | ||||||||
\(78\) | −4.60168e7 | −0.140764 | ||||||||
\(79\) | −5.55442e8 | −1.60442 | −0.802208 | − | 0.597044i | \(-0.796342\pi\) | ||||
−0.802208 | + | 0.597044i | \(0.796342\pi\) | |||||||
\(80\) | 7.88595e7 | 0.215253 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 9.57292e7 | 0.233820 | ||||||||
\(83\) | −2.03005e8 | −0.469521 | −0.234761 | − | 0.972053i | \(-0.575431\pi\) | ||||
−0.234761 | + | 0.972053i | \(0.575431\pi\) | |||||||
\(84\) | −4.92169e8 | −1.07859 | ||||||||
\(85\) | −1.91375e8 | −0.397649 | ||||||||
\(86\) | −1.20554e8 | −0.237650 | ||||||||
\(87\) | −4.64667e8 | −0.869571 | ||||||||
\(88\) | 2.36083e8 | 0.419655 | ||||||||
\(89\) | 1.86479e7 | 0.0315046 | 0.0157523 | − | 0.999876i | \(-0.494986\pi\) | ||||
0.0157523 | + | 0.999876i | \(0.494986\pi\) | |||||||
\(90\) | −9.88169e6 | −0.0158760 | ||||||||
\(91\) | 1.58039e9 | 2.41590 | ||||||||
\(92\) | −1.04667e9 | −1.52323 | ||||||||
\(93\) | −9.58386e7 | −0.132852 | ||||||||
\(94\) | 1.22133e8 | 0.161346 | ||||||||
\(95\) | 2.82791e8 | 0.356212 | ||||||||
\(96\) | 2.68269e8 | 0.322367 | ||||||||
\(97\) | −6.59088e8 | −0.755911 | −0.377955 | − | 0.925824i | \(-0.623373\pi\) | ||||
−0.377955 | + | 0.925824i | \(0.623373\pi\) | |||||||
\(98\) | −4.96774e8 | −0.544053 | ||||||||
\(99\) | 3.47626e8 | 0.363709 | ||||||||
\(100\) | 9.04819e8 | 0.904819 | ||||||||
\(101\) | −1.82533e8 | −0.174540 | −0.0872699 | − | 0.996185i | \(-0.527814\pi\) | ||||
−0.0872699 | + | 0.996185i | \(0.527814\pi\) | |||||||
\(102\) | −2.02587e8 | −0.185315 | ||||||||
\(103\) | 1.33454e9 | 1.16832 | 0.584162 | − | 0.811637i | \(-0.301423\pi\) | ||||
0.584162 | + | 0.811637i | \(0.301423\pi\) | |||||||
\(104\) | −5.70560e8 | −0.478246 | ||||||||
\(105\) | 3.39375e8 | 0.272476 | ||||||||
\(106\) | −1.20657e8 | −0.0928276 | ||||||||
\(107\) | −1.46868e9 | −1.08318 | −0.541590 | − | 0.840643i | \(-0.682177\pi\) | ||||
−0.541590 | + | 0.840643i | \(0.682177\pi\) | |||||||
\(108\) | 2.61637e8 | 0.185051 | ||||||||
\(109\) | −5.59949e8 | −0.379952 | −0.189976 | − | 0.981789i | \(-0.560841\pi\) | ||||
−0.189976 | + | 0.981789i | \(0.560841\pi\) | |||||||
\(110\) | −7.98001e7 | −0.0519681 | ||||||||
\(111\) | −4.75803e8 | −0.297491 | ||||||||
\(112\) | −2.86701e9 | −1.72167 | ||||||||
\(113\) | 9.22036e8 | 0.531979 | 0.265990 | − | 0.963976i | \(-0.414301\pi\) | ||||
0.265990 | + | 0.963976i | \(0.414301\pi\) | |||||||
\(114\) | 2.99359e8 | 0.166005 | ||||||||
\(115\) | 7.21731e8 | 0.384800 | ||||||||
\(116\) | −2.82424e9 | −1.44824 | ||||||||
\(117\) | −8.40135e8 | −0.414489 | ||||||||
\(118\) | 5.37601e7 | 0.0255265 | ||||||||
\(119\) | 6.95762e9 | 3.18053 | ||||||||
\(120\) | −1.22523e8 | −0.0539388 | ||||||||
\(121\) | 4.49324e8 | 0.190557 | ||||||||
\(122\) | −4.25721e8 | −0.173983 | ||||||||
\(123\) | 1.74774e9 | 0.688501 | ||||||||
\(124\) | −5.82505e8 | −0.221260 | ||||||||
\(125\) | −1.28696e9 | −0.471486 | ||||||||
\(126\) | 3.59259e8 | 0.126981 | ||||||||
\(127\) | −2.91682e9 | −0.994932 | −0.497466 | − | 0.867483i | \(-0.665736\pi\) | ||||
−0.497466 | + | 0.867483i | \(0.665736\pi\) | |||||||
\(128\) | 2.15821e9 | 0.710639 | ||||||||
\(129\) | −2.20097e9 | −0.699778 | ||||||||
\(130\) | 1.92859e8 | 0.0592237 | ||||||||
\(131\) | −4.78537e9 | −1.41969 | −0.709846 | − | 0.704356i | \(-0.751236\pi\) | ||||
−0.709846 | + | 0.704356i | \(0.751236\pi\) | |||||||
\(132\) | 2.11286e9 | 0.605744 | ||||||||
\(133\) | −1.02811e10 | −2.84911 | ||||||||
\(134\) | −7.75119e8 | −0.207681 | ||||||||
\(135\) | −1.80412e8 | −0.0467479 | ||||||||
\(136\) | −2.51187e9 | −0.629612 | ||||||||
\(137\) | 3.90657e9 | 0.947443 | 0.473721 | − | 0.880675i | \(-0.342910\pi\) | ||||
0.473721 | + | 0.880675i | \(0.342910\pi\) | |||||||
\(138\) | 7.64017e8 | 0.179328 | ||||||||
\(139\) | −2.16547e9 | −0.492024 | −0.246012 | − | 0.969267i | \(-0.579120\pi\) | ||||
−0.246012 | + | 0.969267i | \(0.579120\pi\) | |||||||
\(140\) | 2.06271e9 | 0.453798 | ||||||||
\(141\) | 2.22980e9 | 0.475095 | ||||||||
\(142\) | −6.17943e8 | −0.127541 | ||||||||
\(143\) | −6.78455e9 | −1.35678 | ||||||||
\(144\) | 1.52410e9 | 0.295382 | ||||||||
\(145\) | 1.94745e9 | 0.365856 | ||||||||
\(146\) | 6.94349e8 | 0.126471 | ||||||||
\(147\) | −9.06967e9 | −1.60200 | ||||||||
\(148\) | −2.89192e9 | −0.495460 | ||||||||
\(149\) | −9.94536e9 | −1.65304 | −0.826518 | − | 0.562911i | \(-0.809681\pi\) | ||||
−0.826518 | + | 0.562911i | \(0.809681\pi\) | |||||||
\(150\) | −6.60472e8 | −0.106523 | ||||||||
\(151\) | 6.31624e8 | 0.0988695 | 0.0494347 | − | 0.998777i | \(-0.484258\pi\) | ||||
0.0494347 | + | 0.998777i | \(0.484258\pi\) | |||||||
\(152\) | 3.71175e9 | 0.564004 | ||||||||
\(153\) | −3.69867e9 | −0.545675 | ||||||||
\(154\) | 2.90121e9 | 0.415658 | ||||||||
\(155\) | 4.01666e8 | 0.0558949 | ||||||||
\(156\) | −5.10632e9 | −0.690316 | ||||||||
\(157\) | −1.31608e10 | −1.72875 | −0.864375 | − | 0.502847i | \(-0.832286\pi\) | ||||
−0.864375 | + | 0.502847i | \(0.832286\pi\) | |||||||
\(158\) | 2.46429e9 | 0.314582 | ||||||||
\(159\) | −2.20286e9 | −0.273338 | ||||||||
\(160\) | −1.12433e9 | −0.135630 | ||||||||
\(161\) | −2.62392e10 | −3.07776 | ||||||||
\(162\) | −1.90982e8 | −0.0217859 | ||||||||
\(163\) | 1.18425e10 | 1.31402 | 0.657008 | − | 0.753884i | \(-0.271822\pi\) | ||||
0.657008 | + | 0.753884i | \(0.271822\pi\) | |||||||
\(164\) | 1.06227e10 | 1.14667 | ||||||||
\(165\) | −1.45692e9 | −0.153024 | ||||||||
\(166\) | 9.00655e8 | 0.0920603 | ||||||||
\(167\) | −5.43925e9 | −0.541147 | −0.270573 | − | 0.962699i | \(-0.587213\pi\) | ||||
−0.270573 | + | 0.962699i | \(0.587213\pi\) | |||||||
\(168\) | 4.45444e9 | 0.431421 | ||||||||
\(169\) | 5.79226e9 | 0.546208 | ||||||||
\(170\) | 8.49057e8 | 0.0779680 | ||||||||
\(171\) | 5.46545e9 | 0.488813 | ||||||||
\(172\) | −1.33774e10 | −1.16545 | ||||||||
\(173\) | −1.31101e10 | −1.11275 | −0.556376 | − | 0.830930i | \(-0.687809\pi\) | ||||
−0.556376 | + | 0.830930i | \(0.687809\pi\) | |||||||
\(174\) | 2.06155e9 | 0.170499 | ||||||||
\(175\) | 2.26831e10 | 1.82823 | ||||||||
\(176\) | 1.23080e10 | 0.966896 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −8.27335e7 | −0.00617719 | ||||||||
\(179\) | 1.76458e10 | 1.28470 | 0.642351 | − | 0.766411i | \(-0.277959\pi\) | ||||
0.642351 | + | 0.766411i | \(0.277959\pi\) | |||||||
\(180\) | −1.09654e9 | −0.0778570 | ||||||||
\(181\) | 2.64661e10 | 1.83289 | 0.916444 | − | 0.400163i | \(-0.131047\pi\) | ||||
0.916444 | + | 0.400163i | \(0.131047\pi\) | |||||||
\(182\) | −7.01159e9 | −0.473691 | ||||||||
\(183\) | −7.77246e9 | −0.512305 | ||||||||
\(184\) | 9.47302e9 | 0.609268 | ||||||||
\(185\) | 1.99412e9 | 0.125164 | ||||||||
\(186\) | 4.25199e8 | 0.0260486 | ||||||||
\(187\) | −2.98688e10 | −1.78620 | ||||||||
\(188\) | 1.35527e10 | 0.791254 | ||||||||
\(189\) | 6.55904e9 | 0.373906 | ||||||||
\(190\) | −1.25463e9 | −0.0698435 | ||||||||
\(191\) | 2.91012e10 | 1.58220 | 0.791099 | − | 0.611688i | \(-0.209509\pi\) | ||||
0.791099 | + | 0.611688i | \(0.209509\pi\) | |||||||
\(192\) | 8.44363e9 | 0.448408 | ||||||||
\(193\) | 1.79428e10 | 0.930856 | 0.465428 | − | 0.885086i | \(-0.345900\pi\) | ||||
0.465428 | + | 0.885086i | \(0.345900\pi\) | |||||||
\(194\) | 2.92412e9 | 0.148213 | ||||||||
\(195\) | 3.52106e9 | 0.174388 | ||||||||
\(196\) | −5.51253e10 | −2.66808 | ||||||||
\(197\) | −1.30845e10 | −0.618957 | −0.309478 | − | 0.950906i | \(-0.600154\pi\) | ||||
−0.309478 | + | 0.950906i | \(0.600154\pi\) | |||||||
\(198\) | −1.54228e9 | −0.0713134 | ||||||||
\(199\) | −1.01257e10 | −0.457705 | −0.228852 | − | 0.973461i | \(-0.573497\pi\) | ||||
−0.228852 | + | 0.973461i | \(0.573497\pi\) | |||||||
\(200\) | −8.18917e9 | −0.361914 | ||||||||
\(201\) | −1.41515e10 | −0.611532 | ||||||||
\(202\) | 8.09827e8 | 0.0342225 | ||||||||
\(203\) | −7.08015e10 | −2.92624 | ||||||||
\(204\) | −2.24804e10 | −0.908801 | ||||||||
\(205\) | −7.32490e9 | −0.289674 | ||||||||
\(206\) | −5.92083e9 | −0.229076 | ||||||||
\(207\) | 1.39488e10 | 0.528043 | ||||||||
\(208\) | −2.97457e10 | −1.10189 | ||||||||
\(209\) | 4.41365e10 | 1.60007 | ||||||||
\(210\) | −1.50568e9 | −0.0534250 | ||||||||
\(211\) | 1.18601e10 | 0.411923 | 0.205962 | − | 0.978560i | \(-0.433968\pi\) | ||||
0.205962 | + | 0.978560i | \(0.433968\pi\) | |||||||
\(212\) | −1.33889e10 | −0.455234 | ||||||||
\(213\) | −1.12819e10 | −0.375555 | ||||||||
\(214\) | 6.51597e9 | 0.212382 | ||||||||
\(215\) | 9.22440e9 | 0.294419 | ||||||||
\(216\) | −2.36798e9 | −0.0740177 | ||||||||
\(217\) | −1.46030e10 | −0.447066 | ||||||||
\(218\) | 2.48428e9 | 0.0744983 | ||||||||
\(219\) | 1.26768e10 | 0.372402 | ||||||||
\(220\) | −8.85515e9 | −0.254855 | ||||||||
\(221\) | 7.21862e10 | 2.03558 | ||||||||
\(222\) | 2.11096e9 | 0.0583299 | ||||||||
\(223\) | −4.02908e10 | −1.09102 | −0.545512 | − | 0.838103i | \(-0.683665\pi\) | ||||
−0.545512 | + | 0.838103i | \(0.683665\pi\) | |||||||
\(224\) | 4.08763e10 | 1.08481 | ||||||||
\(225\) | −1.20583e10 | −0.313665 | ||||||||
\(226\) | −4.09072e9 | −0.104307 | ||||||||
\(227\) | −6.59239e9 | −0.164788 | −0.0823941 | − | 0.996600i | \(-0.526257\pi\) | ||||
−0.0823941 | + | 0.996600i | \(0.526257\pi\) | |||||||
\(228\) | 3.32189e10 | 0.814101 | ||||||||
\(229\) | 3.98522e10 | 0.957619 | 0.478810 | − | 0.877919i | \(-0.341068\pi\) | ||||
0.478810 | + | 0.877919i | \(0.341068\pi\) | |||||||
\(230\) | −3.20204e9 | −0.0754487 | ||||||||
\(231\) | 5.29679e10 | 1.22394 | ||||||||
\(232\) | 2.55611e10 | 0.579273 | ||||||||
\(233\) | −9.10647e9 | −0.202418 | −0.101209 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101209 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(234\) | 3.72736e9 | 0.0812699 | ||||||||
\(235\) | −9.34526e9 | −0.199888 | ||||||||
\(236\) | 5.96558e9 | 0.125184 | ||||||||
\(237\) | 4.49908e10 | 0.926310 | ||||||||
\(238\) | −3.08683e10 | −0.623615 | ||||||||
\(239\) | 2.75413e10 | 0.546001 | 0.273001 | − | 0.962014i | \(-0.411984\pi\) | ||||
0.273001 | + | 0.962014i | \(0.411984\pi\) | |||||||
\(240\) | −6.38762e9 | −0.124276 | ||||||||
\(241\) | 2.12666e10 | 0.406089 | 0.203045 | − | 0.979169i | \(-0.434916\pi\) | ||||
0.203045 | + | 0.979169i | \(0.434916\pi\) | |||||||
\(242\) | −1.99348e9 | −0.0373631 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −4.72409e10 | −0.853225 | ||||||||
\(245\) | 3.80116e10 | 0.674013 | ||||||||
\(246\) | −7.75407e9 | −0.134996 | ||||||||
\(247\) | −1.06668e11 | −1.82347 | ||||||||
\(248\) | 5.27203e9 | 0.0885005 | ||||||||
\(249\) | 1.64434e10 | 0.271078 | ||||||||
\(250\) | 5.70973e9 | 0.0924455 | ||||||||
\(251\) | −3.66142e10 | −0.582261 | −0.291131 | − | 0.956683i | \(-0.594031\pi\) | ||||
−0.291131 | + | 0.956683i | \(0.594031\pi\) | |||||||
\(252\) | 3.98657e10 | 0.622726 | ||||||||
\(253\) | 1.12644e11 | 1.72849 | ||||||||
\(254\) | 1.29408e10 | 0.195079 | ||||||||
\(255\) | 1.55014e10 | 0.229583 | ||||||||
\(256\) | 4.37969e10 | 0.637329 | ||||||||
\(257\) | 3.46810e10 | 0.495898 | 0.247949 | − | 0.968773i | \(-0.420243\pi\) | ||||
0.247949 | + | 0.968773i | \(0.420243\pi\) | |||||||
\(258\) | 9.76486e9 | 0.137207 | ||||||||
\(259\) | −7.24983e10 | −1.00110 | ||||||||
\(260\) | 2.14009e10 | 0.290437 | ||||||||
\(261\) | 3.76380e10 | 0.502047 | ||||||||
\(262\) | 2.12308e10 | 0.278363 | ||||||||
\(263\) | 1.18027e11 | 1.52119 | 0.760593 | − | 0.649229i | \(-0.224908\pi\) | ||||
0.760593 | + | 0.649229i | \(0.224908\pi\) | |||||||
\(264\) | −1.91227e10 | −0.242288 | ||||||||
\(265\) | 9.23232e9 | 0.115002 | ||||||||
\(266\) | 4.56135e10 | 0.558632 | ||||||||
\(267\) | −1.51048e9 | −0.0181892 | ||||||||
\(268\) | −8.60123e10 | −1.01848 | ||||||||
\(269\) | 1.47003e11 | 1.71175 | 0.855873 | − | 0.517185i | \(-0.173020\pi\) | ||||
0.855873 | + | 0.517185i | \(0.173020\pi\) | |||||||
\(270\) | 8.00417e8 | 0.00916599 | ||||||||
\(271\) | −2.83854e10 | −0.319693 | −0.159846 | − | 0.987142i | \(-0.551100\pi\) | ||||
−0.159846 | + | 0.987142i | \(0.551100\pi\) | |||||||
\(272\) | −1.30954e11 | −1.45064 | ||||||||
\(273\) | −1.28012e11 | −1.39482 | ||||||||
\(274\) | −1.73320e10 | −0.185768 | ||||||||
\(275\) | −9.73777e10 | −1.02674 | ||||||||
\(276\) | 8.47803e10 | 0.879436 | ||||||||
\(277\) | 4.37749e10 | 0.446751 | 0.223376 | − | 0.974732i | \(-0.428292\pi\) | ||||
0.223376 | + | 0.974732i | \(0.428292\pi\) | |||||||
\(278\) | 9.60737e9 | 0.0964724 | ||||||||
\(279\) | 7.76293e9 | 0.0767020 | ||||||||
\(280\) | −1.86688e10 | −0.181512 | ||||||||
\(281\) | 9.03302e10 | 0.864280 | 0.432140 | − | 0.901806i | \(-0.357759\pi\) | ||||
0.432140 | + | 0.901806i | \(0.357759\pi\) | |||||||
\(282\) | −9.89279e9 | −0.0931532 | ||||||||
\(283\) | 1.27299e9 | 0.0117973 | 0.00589867 | − | 0.999983i | \(-0.498122\pi\) | ||||
0.00589867 | + | 0.999983i | \(0.498122\pi\) | |||||||
\(284\) | −6.85711e10 | −0.625473 | ||||||||
\(285\) | −2.29060e10 | −0.205659 | ||||||||
\(286\) | 3.01005e10 | 0.266027 | ||||||||
\(287\) | 2.66304e11 | 2.31691 | ||||||||
\(288\) | −2.17298e10 | −0.186119 | ||||||||
\(289\) | 1.99210e11 | 1.67985 | ||||||||
\(290\) | −8.64009e9 | −0.0717344 | ||||||||
\(291\) | 5.33861e10 | 0.436425 | ||||||||
\(292\) | 7.70496e10 | 0.620222 | ||||||||
\(293\) | −1.74934e11 | −1.38666 | −0.693330 | − | 0.720620i | \(-0.743857\pi\) | ||||
−0.693330 | + | 0.720620i | \(0.743857\pi\) | |||||||
\(294\) | 4.02387e10 | 0.314109 | ||||||||
\(295\) | −4.11356e9 | −0.0316241 | ||||||||
\(296\) | 2.61737e10 | 0.198176 | ||||||||
\(297\) | −2.81577e10 | −0.209987 | ||||||||
\(298\) | 4.41237e10 | 0.324115 | ||||||||
\(299\) | −2.72236e11 | −1.96981 | ||||||||
\(300\) | −7.32903e10 | −0.522397 | ||||||||
\(301\) | −3.35362e11 | −2.35486 | ||||||||
\(302\) | −2.80227e9 | −0.0193856 | ||||||||
\(303\) | 1.47851e10 | 0.100771 | ||||||||
\(304\) | 1.93509e11 | 1.29948 | ||||||||
\(305\) | 3.25749e10 | 0.215543 | ||||||||
\(306\) | 1.64096e10 | 0.106992 | ||||||||
\(307\) | 4.06289e10 | 0.261043 | 0.130522 | − | 0.991445i | \(-0.458335\pi\) | ||||
0.130522 | + | 0.991445i | \(0.458335\pi\) | |||||||
\(308\) | 3.21938e11 | 2.03842 | ||||||||
\(309\) | −1.08097e11 | −0.674532 | ||||||||
\(310\) | −1.78204e9 | −0.0109595 | ||||||||
\(311\) | −4.16431e10 | −0.252419 | −0.126209 | − | 0.992004i | \(-0.540281\pi\) | ||||
−0.126209 | + | 0.992004i | \(0.540281\pi\) | |||||||
\(312\) | 4.62154e10 | 0.276116 | ||||||||
\(313\) | −2.10609e11 | −1.24030 | −0.620152 | − | 0.784482i | \(-0.712929\pi\) | ||||
−0.620152 | + | 0.784482i | \(0.712929\pi\) | |||||||
\(314\) | 5.83892e10 | 0.338961 | ||||||||
\(315\) | −2.74894e10 | −0.157314 | ||||||||
\(316\) | 2.73453e11 | 1.54274 | ||||||||
\(317\) | 6.47864e10 | 0.360344 | 0.180172 | − | 0.983635i | \(-0.442335\pi\) | ||||
0.180172 | + | 0.983635i | \(0.442335\pi\) | |||||||
\(318\) | 9.77324e9 | 0.0535941 | ||||||||
\(319\) | 3.03948e11 | 1.64339 | ||||||||
\(320\) | −3.53878e10 | −0.188660 | ||||||||
\(321\) | 1.18963e11 | 0.625374 | ||||||||
\(322\) | 1.16413e11 | 0.603465 | ||||||||
\(323\) | −4.69603e11 | −2.40060 | ||||||||
\(324\) | −2.11926e10 | −0.106840 | ||||||||
\(325\) | 2.35340e11 | 1.17010 | ||||||||
\(326\) | −5.25408e10 | −0.257643 | ||||||||
\(327\) | 4.53559e10 | 0.219366 | ||||||||
\(328\) | −9.61424e10 | −0.458651 | ||||||||
\(329\) | 3.39756e11 | 1.59877 | ||||||||
\(330\) | 6.46381e9 | 0.0300038 | ||||||||
\(331\) | −2.47766e11 | −1.13453 | −0.567265 | − | 0.823535i | \(-0.691999\pi\) | ||||
−0.567265 | + | 0.823535i | \(0.691999\pi\) | |||||||
\(332\) | 9.99427e10 | 0.451471 | ||||||||
\(333\) | 3.85401e10 | 0.171757 | ||||||||
\(334\) | 2.41319e10 | 0.106104 | ||||||||
\(335\) | 5.93097e10 | 0.257291 | ||||||||
\(336\) | 2.32228e11 | 0.994004 | ||||||||
\(337\) | −2.17120e11 | −0.916991 | −0.458495 | − | 0.888697i | \(-0.651611\pi\) | ||||
−0.458495 | + | 0.888697i | \(0.651611\pi\) | |||||||
\(338\) | −2.56981e10 | −0.107096 | ||||||||
\(339\) | −7.46849e10 | −0.307138 | ||||||||
\(340\) | 9.42169e10 | 0.382361 | ||||||||
\(341\) | 6.26899e10 | 0.251075 | ||||||||
\(342\) | −2.42481e10 | −0.0958430 | ||||||||
\(343\) | −8.83904e11 | −3.44811 | ||||||||
\(344\) | 1.21074e11 | 0.466164 | ||||||||
\(345\) | −5.84602e10 | −0.222164 | ||||||||
\(346\) | 5.81645e10 | 0.218180 | ||||||||
\(347\) | −1.52482e11 | −0.564594 | −0.282297 | − | 0.959327i | \(-0.591096\pi\) | ||||
−0.282297 | + | 0.959327i | \(0.591096\pi\) | |||||||
\(348\) | 2.28763e11 | 0.836141 | ||||||||
\(349\) | 3.33989e11 | 1.20508 | 0.602542 | − | 0.798087i | \(-0.294154\pi\) | ||||
0.602542 | + | 0.798087i | \(0.294154\pi\) | |||||||
\(350\) | −1.00636e11 | −0.358466 | ||||||||
\(351\) | 6.80509e10 | 0.239305 | ||||||||
\(352\) | −1.75480e11 | −0.609237 | ||||||||
\(353\) | 2.18994e11 | 0.750666 | 0.375333 | − | 0.926890i | \(-0.377528\pi\) | ||||
0.375333 | + | 0.926890i | \(0.377528\pi\) | |||||||
\(354\) | −4.35457e9 | −0.0147377 | ||||||||
\(355\) | 4.72831e10 | 0.158008 | ||||||||
\(356\) | −9.18065e9 | −0.0302934 | ||||||||
\(357\) | −5.63567e11 | −1.83628 | ||||||||
\(358\) | −7.82876e10 | −0.251895 | ||||||||
\(359\) | −3.71576e11 | −1.18066 | −0.590328 | − | 0.807164i | \(-0.701001\pi\) | ||||
−0.590328 | + | 0.807164i | \(0.701001\pi\) | |||||||
\(360\) | 9.92435e9 | 0.0311416 | ||||||||
\(361\) | 3.71235e11 | 1.15045 | ||||||||
\(362\) | −1.17420e11 | −0.359379 | ||||||||
\(363\) | −3.63952e10 | −0.110018 | ||||||||
\(364\) | −7.78052e11 | −2.32302 | ||||||||
\(365\) | −5.31295e10 | −0.156681 | ||||||||
\(366\) | 3.44834e10 | 0.100449 | ||||||||
\(367\) | 1.98110e11 | 0.570045 | 0.285022 | − | 0.958521i | \(-0.407999\pi\) | ||||
0.285022 | + | 0.958521i | \(0.407999\pi\) | |||||||
\(368\) | 4.93867e11 | 1.40377 | ||||||||
\(369\) | −1.41567e11 | −0.397506 | ||||||||
\(370\) | −8.84715e9 | −0.0245412 | ||||||||
\(371\) | −3.35650e11 | −0.919823 | ||||||||
\(372\) | 4.71829e10 | 0.127744 | ||||||||
\(373\) | 4.59095e11 | 1.22804 | 0.614021 | − | 0.789290i | \(-0.289551\pi\) | ||||
0.614021 | + | 0.789290i | \(0.289551\pi\) | |||||||
\(374\) | 1.32516e11 | 0.350225 | ||||||||
\(375\) | 1.04243e11 | 0.272213 | ||||||||
\(376\) | −1.22660e11 | −0.316489 | ||||||||
\(377\) | −7.34575e11 | −1.87284 | ||||||||
\(378\) | −2.91000e10 | −0.0733127 | ||||||||
\(379\) | −3.04151e11 | −0.757205 | −0.378602 | − | 0.925559i | \(-0.623595\pi\) | ||||
−0.378602 | + | 0.925559i | \(0.623595\pi\) | |||||||
\(380\) | −1.39222e11 | −0.342518 | ||||||||
\(381\) | 2.36263e11 | 0.574424 | ||||||||
\(382\) | −1.29111e11 | −0.310226 | ||||||||
\(383\) | 1.53059e11 | 0.363465 | 0.181733 | − | 0.983348i | \(-0.441829\pi\) | ||||
0.181733 | + | 0.983348i | \(0.441829\pi\) | |||||||
\(384\) | −1.74815e11 | −0.410288 | ||||||||
\(385\) | −2.21992e11 | −0.514948 | ||||||||
\(386\) | −7.96054e10 | −0.182515 | ||||||||
\(387\) | 1.78278e11 | 0.404017 | ||||||||
\(388\) | 3.24480e11 | 0.726850 | ||||||||
\(389\) | 4.19117e11 | 0.928030 | 0.464015 | − | 0.885827i | \(-0.346408\pi\) | ||||
0.464015 | + | 0.885827i | \(0.346408\pi\) | |||||||
\(390\) | −1.56216e10 | −0.0341928 | ||||||||
\(391\) | −1.19851e12 | −2.59326 | ||||||||
\(392\) | 4.98918e11 | 1.06719 | ||||||||
\(393\) | 3.87615e11 | 0.819660 | ||||||||
\(394\) | 5.80511e10 | 0.121361 | ||||||||
\(395\) | −1.88560e11 | −0.389728 | ||||||||
\(396\) | −1.71142e11 | −0.349726 | ||||||||
\(397\) | −4.01994e11 | −0.812198 | −0.406099 | − | 0.913829i | \(-0.633111\pi\) | ||||
−0.406099 | + | 0.913829i | \(0.633111\pi\) | |||||||
\(398\) | 4.49238e10 | 0.0897434 | ||||||||
\(399\) | 8.32772e11 | 1.64493 | ||||||||
\(400\) | −4.26935e11 | −0.833858 | ||||||||
\(401\) | −5.23348e11 | −1.01074 | −0.505372 | − | 0.862902i | \(-0.668645\pi\) | ||||
−0.505372 | + | 0.862902i | \(0.668645\pi\) | |||||||
\(402\) | 6.27846e10 | 0.119905 | ||||||||
\(403\) | −1.51508e11 | −0.286129 | ||||||||
\(404\) | 8.98638e10 | 0.167830 | ||||||||
\(405\) | 1.46133e10 | 0.0269899 | ||||||||
\(406\) | 3.14119e11 | 0.573756 | ||||||||
\(407\) | 3.11232e11 | 0.562224 | ||||||||
\(408\) | 2.03462e11 | 0.363506 | ||||||||
\(409\) | −5.56139e11 | −0.982716 | −0.491358 | − | 0.870958i | \(-0.663499\pi\) | ||||
−0.491358 | + | 0.870958i | \(0.663499\pi\) | |||||||
\(410\) | 3.24978e10 | 0.0567971 | ||||||||
\(411\) | −3.16432e11 | −0.547006 | ||||||||
\(412\) | −6.57014e11 | −1.12341 | ||||||||
\(413\) | 1.49552e11 | 0.252940 | ||||||||
\(414\) | −6.18854e10 | −0.103535 | ||||||||
\(415\) | −6.89154e10 | −0.114051 | ||||||||
\(416\) | 4.24097e11 | 0.694297 | ||||||||
\(417\) | 1.75403e11 | 0.284070 | ||||||||
\(418\) | −1.95817e11 | −0.313730 | ||||||||
\(419\) | −2.40013e10 | −0.0380427 | −0.0190214 | − | 0.999819i | \(-0.506055\pi\) | ||||
−0.0190214 | + | 0.999819i | \(0.506055\pi\) | |||||||
\(420\) | −1.67080e11 | −0.262001 | ||||||||
\(421\) | −1.44975e11 | −0.224917 | −0.112459 | − | 0.993656i | \(-0.535873\pi\) | ||||
−0.112459 | + | 0.993656i | \(0.535873\pi\) | |||||||
\(422\) | −5.26186e10 | −0.0807669 | ||||||||
\(423\) | −1.80614e11 | −0.274296 | ||||||||
\(424\) | 1.21178e11 | 0.182087 | ||||||||
\(425\) | 1.03608e12 | 1.54043 | ||||||||
\(426\) | 5.00534e10 | 0.0736360 | ||||||||
\(427\) | −1.18429e12 | −1.72398 | ||||||||
\(428\) | 7.23055e11 | 1.04154 | ||||||||
\(429\) | 5.49549e11 | 0.783337 | ||||||||
\(430\) | −4.09251e10 | −0.0577274 | ||||||||
\(431\) | −9.40468e11 | −1.31279 | −0.656397 | − | 0.754416i | \(-0.727920\pi\) | ||||
−0.656397 | + | 0.754416i | \(0.727920\pi\) | |||||||
\(432\) | −1.23452e11 | −0.170539 | ||||||||
\(433\) | −8.32077e11 | −1.13754 | −0.568772 | − | 0.822495i | \(-0.692581\pi\) | ||||
−0.568772 | + | 0.822495i | \(0.692581\pi\) | |||||||
\(434\) | 6.47878e10 | 0.0876575 | ||||||||
\(435\) | −1.57743e11 | −0.211227 | ||||||||
\(436\) | 2.75672e11 | 0.365345 | ||||||||
\(437\) | 1.77101e12 | 2.32303 | ||||||||
\(438\) | −5.62423e10 | −0.0730179 | ||||||||
\(439\) | 9.47325e10 | 0.121733 | 0.0608666 | − | 0.998146i | \(-0.480614\pi\) | ||||
0.0608666 | + | 0.998146i | \(0.480614\pi\) | |||||||
\(440\) | 8.01446e10 | 0.101938 | ||||||||
\(441\) | 7.34643e11 | 0.924917 | ||||||||
\(442\) | −3.20263e11 | −0.399122 | ||||||||
\(443\) | −5.67930e11 | −0.700612 | −0.350306 | − | 0.936635i | \(-0.613922\pi\) | ||||
−0.350306 | + | 0.936635i | \(0.613922\pi\) | |||||||
\(444\) | 2.34246e11 | 0.286054 | ||||||||
\(445\) | 6.33051e9 | 0.00765277 | ||||||||
\(446\) | 1.78755e11 | 0.213920 | ||||||||
\(447\) | 8.05574e11 | 0.954380 | ||||||||
\(448\) | 1.28656e12 | 1.50896 | ||||||||
\(449\) | 6.19806e11 | 0.719693 | 0.359847 | − | 0.933011i | \(-0.382829\pi\) | ||||
0.359847 | + | 0.933011i | \(0.382829\pi\) | |||||||
\(450\) | 5.34982e10 | 0.0615011 | ||||||||
\(451\) | −1.14323e12 | −1.30119 | ||||||||
\(452\) | −4.53933e11 | −0.511528 | ||||||||
\(453\) | −5.11615e10 | −0.0570823 | ||||||||
\(454\) | 2.92479e10 | 0.0323105 | ||||||||
\(455\) | 5.36505e11 | 0.586844 | ||||||||
\(456\) | −3.00651e11 | −0.325628 | ||||||||
\(457\) | −3.07940e11 | −0.330251 | −0.165125 | − | 0.986273i | \(-0.552803\pi\) | ||||
−0.165125 | + | 0.986273i | \(0.552803\pi\) | |||||||
\(458\) | −1.76809e11 | −0.187763 | ||||||||
\(459\) | 2.99592e11 | 0.315045 | ||||||||
\(460\) | −3.55320e11 | −0.370006 | ||||||||
\(461\) | −1.40714e12 | −1.45105 | −0.725526 | − | 0.688195i | \(-0.758403\pi\) | ||||
−0.725526 | + | 0.688195i | \(0.758403\pi\) | |||||||
\(462\) | −2.34998e11 | −0.239980 | ||||||||
\(463\) | 1.36244e12 | 1.37786 | 0.688929 | − | 0.724829i | \(-0.258081\pi\) | ||||
0.688929 | + | 0.724829i | \(0.258081\pi\) | |||||||
\(464\) | 1.33260e12 | 1.33466 | ||||||||
\(465\) | −3.25349e10 | −0.0322709 | ||||||||
\(466\) | 4.04019e10 | 0.0396886 | ||||||||
\(467\) | −9.45768e11 | −0.920150 | −0.460075 | − | 0.887880i | \(-0.652178\pi\) | ||||
−0.460075 | + | 0.887880i | \(0.652178\pi\) | |||||||
\(468\) | 4.13612e11 | 0.398554 | ||||||||
\(469\) | −2.15626e12 | −2.05790 | ||||||||
\(470\) | 4.14613e10 | 0.0391925 | ||||||||
\(471\) | 1.06602e12 | 0.998095 | ||||||||
\(472\) | −5.39922e10 | −0.0500716 | ||||||||
\(473\) | 1.43970e12 | 1.32250 | ||||||||
\(474\) | −1.99607e11 | −0.181624 | ||||||||
\(475\) | −1.53099e12 | −1.37991 | ||||||||
\(476\) | −3.42535e12 | −3.05825 | ||||||||
\(477\) | 1.78432e11 | 0.157812 | ||||||||
\(478\) | −1.22190e11 | −0.107056 | ||||||||
\(479\) | −1.03116e12 | −0.894989 | −0.447495 | − | 0.894287i | \(-0.647684\pi\) | ||||
−0.447495 | + | 0.894287i | \(0.647684\pi\) | |||||||
\(480\) | 9.10711e10 | 0.0783060 | ||||||||
\(481\) | −7.52179e11 | −0.640720 | ||||||||
\(482\) | −9.43518e10 | −0.0796230 | ||||||||
\(483\) | 2.12538e12 | 1.77695 | ||||||||
\(484\) | −2.21210e11 | −0.183231 | ||||||||
\(485\) | −2.23745e11 | −0.183618 | ||||||||
\(486\) | 1.54695e10 | 0.0125781 | ||||||||
\(487\) | −7.67349e11 | −0.618177 | −0.309088 | − | 0.951033i | \(-0.600024\pi\) | ||||
−0.309088 | + | 0.951033i | \(0.600024\pi\) | |||||||
\(488\) | 4.27559e11 | 0.341277 | ||||||||
\(489\) | −9.59245e11 | −0.758647 | ||||||||
\(490\) | −1.68643e11 | −0.132156 | ||||||||
\(491\) | −1.35773e12 | −1.05426 | −0.527129 | − | 0.849785i | \(-0.676731\pi\) | ||||
−0.527129 | + | 0.849785i | \(0.676731\pi\) | |||||||
\(492\) | −8.60442e11 | −0.662032 | ||||||||
\(493\) | −3.23394e12 | −2.46559 | ||||||||
\(494\) | 4.73246e11 | 0.357532 | ||||||||
\(495\) | 1.18011e11 | 0.0883483 | ||||||||
\(496\) | 2.74853e11 | 0.203907 | ||||||||
\(497\) | −1.71902e12 | −1.26380 | ||||||||
\(498\) | −7.29531e10 | −0.0531510 | ||||||||
\(499\) | 6.93814e11 | 0.500945 | 0.250473 | − | 0.968124i | \(-0.419414\pi\) | ||||
0.250473 | + | 0.968124i | \(0.419414\pi\) | |||||||
\(500\) | 6.33590e11 | 0.453360 | ||||||||
\(501\) | 4.40579e11 | 0.312431 | ||||||||
\(502\) | 1.62443e11 | 0.114166 | ||||||||
\(503\) | −2.15196e12 | −1.49892 | −0.749458 | − | 0.662052i | \(-0.769686\pi\) | ||||
−0.749458 | + | 0.662052i | \(0.769686\pi\) | |||||||
\(504\) | −3.60810e11 | −0.249081 | ||||||||
\(505\) | −6.19655e10 | −0.0423973 | ||||||||
\(506\) | −4.99758e11 | −0.338909 | ||||||||
\(507\) | −4.69173e11 | −0.315353 | ||||||||
\(508\) | 1.43600e12 | 0.956683 | ||||||||
\(509\) | −7.20802e11 | −0.475977 | −0.237989 | − | 0.971268i | \(-0.576488\pi\) | ||||
−0.237989 | + | 0.971268i | \(0.576488\pi\) | |||||||
\(510\) | −6.87736e10 | −0.0450149 | ||||||||
\(511\) | 1.93157e12 | 1.25319 | ||||||||
\(512\) | −1.29931e12 | −0.835602 | ||||||||
\(513\) | −4.42701e11 | −0.282217 | ||||||||
\(514\) | −1.53866e11 | −0.0972320 | ||||||||
\(515\) | 4.53044e11 | 0.283797 | ||||||||
\(516\) | 1.08357e12 | 0.672875 | ||||||||
\(517\) | −1.45856e12 | −0.897876 | ||||||||
\(518\) | 3.21647e11 | 0.196289 | ||||||||
\(519\) | 1.06192e12 | 0.642448 | ||||||||
\(520\) | −1.93692e11 | −0.116171 | ||||||||
\(521\) | 1.79148e10 | 0.0106523 | 0.00532615 | − | 0.999986i | \(-0.498305\pi\) | ||||
0.00532615 | + | 0.999986i | \(0.498305\pi\) | |||||||
\(522\) | −1.66986e11 | −0.0984377 | ||||||||
\(523\) | 1.03328e12 | 0.603896 | 0.301948 | − | 0.953324i | \(-0.402363\pi\) | ||||
0.301948 | + | 0.953324i | \(0.402363\pi\) | |||||||
\(524\) | 2.35591e12 | 1.36511 | ||||||||
\(525\) | −1.83733e12 | −1.05553 | ||||||||
\(526\) | −5.23643e11 | −0.298263 | ||||||||
\(527\) | −6.67008e11 | −0.376689 | ||||||||
\(528\) | −9.96946e11 | −0.558238 | ||||||||
\(529\) | 2.71878e12 | 1.50947 | ||||||||
\(530\) | −4.09603e10 | −0.0225487 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | 5.06157e12 | 2.73957 | ||||||||
\(533\) | 2.76294e12 | 1.48286 | ||||||||
\(534\) | 6.70141e9 | 0.00356640 | ||||||||
\(535\) | −4.98582e11 | −0.263114 | ||||||||
\(536\) | 7.78465e11 | 0.407378 | ||||||||
\(537\) | −1.42931e12 | −0.741723 | ||||||||
\(538\) | −6.52194e11 | −0.335627 | ||||||||
\(539\) | 5.93265e12 | 3.02760 | ||||||||
\(540\) | 8.88196e10 | 0.0449507 | ||||||||
\(541\) | −3.38071e12 | −1.69676 | −0.848380 | − | 0.529388i | \(-0.822422\pi\) | ||||
−0.848380 | + | 0.529388i | \(0.822422\pi\) | |||||||
\(542\) | 1.25935e11 | 0.0626830 | ||||||||
\(543\) | −2.14375e12 | −1.05822 | ||||||||
\(544\) | 1.86707e12 | 0.914043 | ||||||||
\(545\) | −1.90089e11 | −0.0922940 | ||||||||
\(546\) | 5.67939e11 | 0.273486 | ||||||||
\(547\) | 2.74815e11 | 0.131249 | 0.0656246 | − | 0.997844i | \(-0.479096\pi\) | ||||
0.0656246 | + | 0.997844i | \(0.479096\pi\) | |||||||
\(548\) | −1.92327e12 | −0.911019 | ||||||||
\(549\) | 6.29569e11 | 0.295779 | ||||||||
\(550\) | 4.32028e11 | 0.201317 | ||||||||
\(551\) | 4.77873e12 | 2.20867 | ||||||||
\(552\) | −7.67315e11 | −0.351761 | ||||||||
\(553\) | 6.85527e12 | 3.11718 | ||||||||
\(554\) | −1.94212e11 | −0.0875957 | ||||||||
\(555\) | −1.61524e11 | −0.0722634 | ||||||||
\(556\) | 1.06610e12 | 0.473108 | ||||||||
\(557\) | 1.71495e11 | 0.0754925 | 0.0377463 | − | 0.999287i | \(-0.487982\pi\) | ||||
0.0377463 | + | 0.999287i | \(0.487982\pi\) | |||||||
\(558\) | −3.44411e10 | −0.0150392 | ||||||||
\(559\) | −3.47943e12 | −1.50714 | ||||||||
\(560\) | −9.73283e11 | −0.418209 | ||||||||
\(561\) | 2.41937e12 | 1.03126 | ||||||||
\(562\) | −4.00761e11 | −0.169462 | ||||||||
\(563\) | 1.49060e12 | 0.625277 | 0.312639 | − | 0.949872i | \(-0.398787\pi\) | ||||
0.312639 | + | 0.949872i | \(0.398787\pi\) | |||||||
\(564\) | −1.09777e12 | −0.456831 | ||||||||
\(565\) | 3.13009e11 | 0.129223 | ||||||||
\(566\) | −5.64775e9 | −0.00231314 | ||||||||
\(567\) | −5.31282e11 | −0.215875 | ||||||||
\(568\) | 6.20610e11 | 0.250179 | ||||||||
\(569\) | 2.46114e12 | 0.984308 | 0.492154 | − | 0.870508i | \(-0.336210\pi\) | ||||
0.492154 | + | 0.870508i | \(0.336210\pi\) | |||||||
\(570\) | 1.01625e11 | 0.0403241 | ||||||||
\(571\) | 5.91742e11 | 0.232954 | 0.116477 | − | 0.993193i | \(-0.462840\pi\) | ||||
0.116477 | + | 0.993193i | \(0.462840\pi\) | |||||||
\(572\) | 3.34015e12 | 1.30462 | ||||||||
\(573\) | −2.35720e12 | −0.913483 | ||||||||
\(574\) | −1.18149e12 | −0.454283 | ||||||||
\(575\) | −3.90736e12 | −1.49066 | ||||||||
\(576\) | −6.83934e11 | −0.258889 | ||||||||
\(577\) | −2.01620e12 | −0.757255 | −0.378627 | − | 0.925549i | \(-0.623604\pi\) | ||||
−0.378627 | + | 0.925549i | \(0.623604\pi\) | |||||||
\(578\) | −8.83817e11 | −0.329372 | ||||||||
\(579\) | −1.45337e12 | −0.537430 | ||||||||
\(580\) | −9.58761e11 | −0.351791 | ||||||||
\(581\) | 2.50549e12 | 0.912220 | ||||||||
\(582\) | −2.36854e11 | −0.0855711 | ||||||||
\(583\) | 1.44093e12 | 0.516577 | ||||||||
\(584\) | −6.97346e11 | −0.248079 | ||||||||
\(585\) | −2.85206e11 | −0.100683 | ||||||||
\(586\) | 7.76116e11 | 0.271886 | ||||||||
\(587\) | −1.31299e12 | −0.456448 | −0.228224 | − | 0.973609i | \(-0.573292\pi\) | ||||
−0.228224 | + | 0.973609i | \(0.573292\pi\) | |||||||
\(588\) | 4.46515e12 | 1.54042 | ||||||||
\(589\) | 9.85624e11 | 0.337437 | ||||||||
\(590\) | 1.82503e10 | 0.00620062 | ||||||||
\(591\) | 1.05985e12 | 0.357355 | ||||||||
\(592\) | 1.36454e12 | 0.456603 | ||||||||
\(593\) | −4.87910e11 | −0.162029 | −0.0810147 | − | 0.996713i | \(-0.525816\pi\) | ||||
−0.0810147 | + | 0.996713i | \(0.525816\pi\) | |||||||
\(594\) | 1.24925e11 | 0.0411728 | ||||||||
\(595\) | 2.36195e12 | 0.772580 | ||||||||
\(596\) | 4.89626e12 | 1.58949 | ||||||||
\(597\) | 8.20180e11 | 0.264256 | ||||||||
\(598\) | 1.20781e12 | 0.386226 | ||||||||
\(599\) | 1.61047e12 | 0.511130 | 0.255565 | − | 0.966792i | \(-0.417739\pi\) | ||||
0.255565 | + | 0.966792i | \(0.417739\pi\) | |||||||
\(600\) | 6.63323e11 | 0.208951 | ||||||||
\(601\) | 2.28175e12 | 0.713399 | 0.356699 | − | 0.934219i | \(-0.383902\pi\) | ||||
0.356699 | + | 0.934219i | \(0.383902\pi\) | |||||||
\(602\) | 1.48787e12 | 0.461724 | ||||||||
\(603\) | 1.14627e12 | 0.353068 | ||||||||
\(604\) | −3.10959e11 | −0.0950685 | ||||||||
\(605\) | 1.52535e11 | 0.0462882 | ||||||||
\(606\) | −6.55960e10 | −0.0197584 | ||||||||
\(607\) | −5.34157e12 | −1.59706 | −0.798528 | − | 0.601958i | \(-0.794387\pi\) | ||||
−0.798528 | + | 0.601958i | \(0.794387\pi\) | |||||||
\(608\) | −2.75894e12 | −0.818796 | ||||||||
\(609\) | 5.73492e12 | 1.68947 | ||||||||
\(610\) | −1.44522e11 | −0.0422620 | ||||||||
\(611\) | 3.52501e12 | 1.02324 | ||||||||
\(612\) | 1.82091e12 | 0.524697 | ||||||||
\(613\) | −1.89520e12 | −0.542103 | −0.271052 | − | 0.962565i | \(-0.587371\pi\) | ||||
−0.271052 | + | 0.962565i | \(0.587371\pi\) | |||||||
\(614\) | −1.80255e11 | −0.0511835 | ||||||||
\(615\) | 5.93317e11 | 0.167243 | ||||||||
\(616\) | −2.91374e12 | −0.815337 | ||||||||
\(617\) | −4.56332e11 | −0.126765 | −0.0633823 | − | 0.997989i | \(-0.520189\pi\) | ||||
−0.0633823 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(618\) | 4.79587e11 | 0.132257 | ||||||||
\(619\) | −3.43083e11 | −0.0939272 | −0.0469636 | − | 0.998897i | \(-0.514954\pi\) | ||||
−0.0469636 | + | 0.998897i | \(0.514954\pi\) | |||||||
\(620\) | −1.97747e11 | −0.0537461 | ||||||||
\(621\) | −1.12985e12 | −0.304866 | ||||||||
\(622\) | 1.84755e11 | 0.0494924 | ||||||||
\(623\) | −2.30152e11 | −0.0612094 | ||||||||
\(624\) | 2.40940e12 | 0.636177 | ||||||||
\(625\) | 3.15272e12 | 0.826467 | ||||||||
\(626\) | 9.34392e11 | 0.243190 | ||||||||
\(627\) | −3.57506e12 | −0.923802 | ||||||||
\(628\) | 6.47926e12 | 1.66229 | ||||||||
\(629\) | −3.31145e12 | −0.843509 | ||||||||
\(630\) | 1.21960e11 | 0.0308450 | ||||||||
\(631\) | −2.43342e12 | −0.611062 | −0.305531 | − | 0.952182i | \(-0.598834\pi\) | ||||
−0.305531 | + | 0.952182i | \(0.598834\pi\) | |||||||
\(632\) | −2.47492e12 | −0.617071 | ||||||||
\(633\) | −9.60666e11 | −0.237824 | ||||||||
\(634\) | −2.87433e11 | −0.0706536 | ||||||||
\(635\) | −9.90193e11 | −0.241678 | ||||||||
\(636\) | 1.08450e12 | 0.262829 | ||||||||
\(637\) | −1.43379e13 | −3.45031 | ||||||||
\(638\) | −1.34850e12 | −0.322224 | ||||||||
\(639\) | 9.13832e11 | 0.216827 | ||||||||
\(640\) | 7.32661e11 | 0.172621 | ||||||||
\(641\) | −6.11253e12 | −1.43008 | −0.715039 | − | 0.699085i | \(-0.753591\pi\) | ||||
−0.715039 | + | 0.699085i | \(0.753591\pi\) | |||||||
\(642\) | −5.27794e11 | −0.122619 | ||||||||
\(643\) | 1.07901e12 | 0.248929 | 0.124465 | − | 0.992224i | \(-0.460279\pi\) | ||||
0.124465 | + | 0.992224i | \(0.460279\pi\) | |||||||
\(644\) | 1.29180e13 | 2.95944 | ||||||||
\(645\) | −7.47177e11 | −0.169983 | ||||||||
\(646\) | 2.08345e12 | 0.470692 | ||||||||
\(647\) | −2.21917e12 | −0.497877 | −0.248939 | − | 0.968519i | \(-0.580082\pi\) | ||||
−0.248939 | + | 0.968519i | \(0.580082\pi\) | |||||||
\(648\) | 1.91806e11 | 0.0427342 | ||||||||
\(649\) | −6.42023e11 | −0.142053 | ||||||||
\(650\) | −1.04412e12 | −0.229424 | ||||||||
\(651\) | 1.18284e12 | 0.258114 | ||||||||
\(652\) | −5.83027e12 | −1.26350 | ||||||||
\(653\) | −4.76854e12 | −1.02630 | −0.513152 | − | 0.858298i | \(-0.671522\pi\) | ||||
−0.513152 | + | 0.858298i | \(0.671522\pi\) | |||||||
\(654\) | −2.01227e11 | −0.0430116 | ||||||||
\(655\) | −1.62452e12 | −0.344857 | ||||||||
\(656\) | −5.01230e12 | −1.05674 | ||||||||
\(657\) | −1.02682e12 | −0.215007 | ||||||||
\(658\) | −1.50737e12 | −0.313475 | ||||||||
\(659\) | 2.36550e12 | 0.488584 | 0.244292 | − | 0.969702i | \(-0.421444\pi\) | ||||
0.244292 | + | 0.969702i | \(0.421444\pi\) | |||||||
\(660\) | 7.17267e11 | 0.147141 | ||||||||
\(661\) | −3.11734e11 | −0.0635152 | −0.0317576 | − | 0.999496i | \(-0.510110\pi\) | ||||
−0.0317576 | + | 0.999496i | \(0.510110\pi\) | |||||||
\(662\) | 1.09924e12 | 0.222451 | ||||||||
\(663\) | −5.84708e12 | −1.17525 | ||||||||
\(664\) | −9.04543e11 | −0.180581 | ||||||||
\(665\) | −3.49020e12 | −0.692075 | ||||||||
\(666\) | −1.70987e11 | −0.0336768 | ||||||||
\(667\) | 1.21961e13 | 2.38592 | ||||||||
\(668\) | 2.67783e12 | 0.520343 | ||||||||
\(669\) | 3.26356e12 | 0.629903 | ||||||||
\(670\) | −2.63134e11 | −0.0504477 | ||||||||
\(671\) | 5.08412e12 | 0.968198 | ||||||||
\(672\) | −3.31098e12 | −0.626318 | ||||||||
\(673\) | 5.18257e12 | 0.973817 | 0.486908 | − | 0.873453i | \(-0.338125\pi\) | ||||
0.486908 | + | 0.873453i | \(0.338125\pi\) | |||||||
\(674\) | 9.63278e11 | 0.179797 | ||||||||
\(675\) | 9.76725e11 | 0.181095 | ||||||||
\(676\) | −2.85163e12 | −0.525209 | ||||||||
\(677\) | 3.26977e12 | 0.598229 | 0.299115 | − | 0.954217i | \(-0.403309\pi\) | ||||
0.299115 | + | 0.954217i | \(0.403309\pi\) | |||||||
\(678\) | 3.31348e11 | 0.0602214 | ||||||||
\(679\) | 8.13446e12 | 1.46864 | ||||||||
\(680\) | −8.52722e11 | −0.152939 | ||||||||
\(681\) | 5.33983e11 | 0.0951406 | ||||||||
\(682\) | −2.78131e11 | −0.0492289 | ||||||||
\(683\) | −4.71601e12 | −0.829242 | −0.414621 | − | 0.909994i | \(-0.636086\pi\) | ||||
−0.414621 | + | 0.909994i | \(0.636086\pi\) | |||||||
\(684\) | −2.69073e12 | −0.470021 | ||||||||
\(685\) | 1.32619e12 | 0.230143 | ||||||||
\(686\) | 3.92155e12 | 0.676081 | ||||||||
\(687\) | −3.22803e12 | −0.552882 | ||||||||
\(688\) | 6.31209e12 | 1.07405 | ||||||||
\(689\) | −3.48242e12 | −0.588700 | ||||||||
\(690\) | 2.59366e11 | 0.0435603 | ||||||||
\(691\) | 8.20731e12 | 1.36946 | 0.684730 | − | 0.728797i | \(-0.259920\pi\) | ||||
0.684730 | + | 0.728797i | \(0.259920\pi\) | |||||||
\(692\) | 6.45432e12 | 1.06997 | ||||||||
\(693\) | −4.29040e12 | −0.706640 | ||||||||
\(694\) | 6.76505e11 | 0.110701 | ||||||||
\(695\) | −7.35126e11 | −0.119517 | ||||||||
\(696\) | −2.07045e12 | −0.334444 | ||||||||
\(697\) | 1.21638e13 | 1.95218 | ||||||||
\(698\) | −1.48178e12 | −0.236284 | ||||||||
\(699\) | 7.37624e11 | 0.116866 | ||||||||
\(700\) | −1.11673e13 | −1.75795 | ||||||||
\(701\) | −4.18348e12 | −0.654345 | −0.327172 | − | 0.944965i | \(-0.606096\pi\) | ||||
−0.327172 | + | 0.944965i | \(0.606096\pi\) | |||||||
\(702\) | −3.01916e11 | −0.0469212 | ||||||||
\(703\) | 4.89326e12 | 0.755612 | ||||||||
\(704\) | −5.52315e12 | −0.847441 | ||||||||
\(705\) | 7.56966e11 | 0.115405 | ||||||||
\(706\) | −9.71594e11 | −0.147185 | ||||||||
\(707\) | 2.25282e12 | 0.339108 | ||||||||
\(708\) | −4.83212e11 | −0.0722749 | ||||||||
\(709\) | −5.97767e12 | −0.888431 | −0.444216 | − | 0.895920i | \(-0.646518\pi\) | ||||
−0.444216 | + | 0.895920i | \(0.646518\pi\) | |||||||
\(710\) | −2.09777e11 | −0.0309810 | ||||||||
\(711\) | −3.64426e12 | −0.534806 | ||||||||
\(712\) | 8.30906e10 | 0.0121169 | ||||||||
\(713\) | 2.51548e12 | 0.364518 | ||||||||
\(714\) | 2.50033e12 | 0.360044 | ||||||||
\(715\) | −2.30319e12 | −0.329574 | ||||||||
\(716\) | −8.68731e12 | −1.23531 | ||||||||
\(717\) | −2.23084e12 | −0.315234 | ||||||||
\(718\) | 1.64854e12 | 0.231494 | ||||||||
\(719\) | 1.85467e11 | 0.0258813 | 0.0129407 | − | 0.999916i | \(-0.495881\pi\) | ||||
0.0129407 | + | 0.999916i | \(0.495881\pi\) | |||||||
\(720\) | 5.17397e11 | 0.0717509 | ||||||||
\(721\) | −1.64708e13 | −2.26990 | ||||||||
\(722\) | −1.64703e12 | −0.225571 | ||||||||
\(723\) | −1.72259e12 | −0.234456 | ||||||||
\(724\) | −1.30297e13 | −1.76242 | ||||||||
\(725\) | −1.05432e13 | −1.41727 | ||||||||
\(726\) | 1.61472e11 | 0.0215716 | ||||||||
\(727\) | −6.25007e12 | −0.829812 | −0.414906 | − | 0.909864i | \(-0.636186\pi\) | ||||
−0.414906 | + | 0.909864i | \(0.636186\pi\) | |||||||
\(728\) | 7.04185e12 | 0.929171 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 2.35715e11 | 0.0307209 | ||||||||
\(731\) | −1.53181e13 | −1.98416 | ||||||||
\(732\) | 3.82651e12 | 0.492610 | ||||||||
\(733\) | −5.09676e12 | −0.652118 | −0.326059 | − | 0.945349i | \(-0.605721\pi\) | ||||
−0.326059 | + | 0.945349i | \(0.605721\pi\) | |||||||
\(734\) | −8.78938e11 | −0.111770 | ||||||||
\(735\) | −3.07894e12 | −0.389142 | ||||||||
\(736\) | −7.04129e12 | −0.884508 | ||||||||
\(737\) | 9.25675e12 | 1.15573 | ||||||||
\(738\) | 6.28079e11 | 0.0779401 | ||||||||
\(739\) | −1.10301e13 | −1.36044 | −0.680220 | − | 0.733008i | \(-0.738116\pi\) | ||||
−0.680220 | + | 0.733008i | \(0.738116\pi\) | |||||||
\(740\) | −9.81739e11 | −0.120352 | ||||||||
\(741\) | 8.64012e12 | 1.05278 | ||||||||
\(742\) | 1.48915e12 | 0.180352 | ||||||||
\(743\) | −4.17587e12 | −0.502687 | −0.251343 | − | 0.967898i | \(-0.580872\pi\) | ||||
−0.251343 | + | 0.967898i | \(0.580872\pi\) | |||||||
\(744\) | −4.27035e11 | −0.0510958 | ||||||||
\(745\) | −3.37621e12 | −0.401538 | ||||||||
\(746\) | −2.03683e12 | −0.240785 | ||||||||
\(747\) | −1.33192e12 | −0.156507 | ||||||||
\(748\) | 1.47049e13 | 1.71753 | ||||||||
\(749\) | 1.81264e13 | 2.10448 | ||||||||
\(750\) | −4.62488e11 | −0.0533734 | ||||||||
\(751\) | 6.90534e12 | 0.792146 | 0.396073 | − | 0.918219i | \(-0.370373\pi\) | ||||
0.396073 | + | 0.918219i | \(0.370373\pi\) | |||||||
\(752\) | −6.39479e12 | −0.729199 | ||||||||
\(753\) | 2.96575e12 | 0.336169 | ||||||||
\(754\) | 3.25903e12 | 0.367212 | ||||||||
\(755\) | 2.14421e11 | 0.0240163 | ||||||||
\(756\) | −3.22912e12 | −0.359531 | ||||||||
\(757\) | 1.53101e13 | 1.69451 | 0.847257 | − | 0.531183i | \(-0.178252\pi\) | ||||
0.847257 | + | 0.531183i | \(0.178252\pi\) | |||||||
\(758\) | 1.34940e12 | 0.148467 | ||||||||
\(759\) | −9.12416e12 | −0.997942 | ||||||||
\(760\) | 1.26005e12 | 0.137002 | ||||||||
\(761\) | −1.27908e12 | −0.138251 | −0.0691253 | − | 0.997608i | \(-0.522021\pi\) | ||||
−0.0691253 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(762\) | −1.04821e12 | −0.112629 | ||||||||
\(763\) | 6.91089e12 | 0.738199 | ||||||||
\(764\) | −1.43270e13 | −1.52137 | ||||||||
\(765\) | −1.25561e12 | −0.132550 | ||||||||
\(766\) | −6.79062e11 | −0.0712656 | ||||||||
\(767\) | 1.55163e12 | 0.161886 | ||||||||
\(768\) | −3.54755e12 | −0.367962 | ||||||||
\(769\) | −3.09767e12 | −0.319423 | −0.159712 | − | 0.987164i | \(-0.551056\pi\) | ||||
−0.159712 | + | 0.987164i | \(0.551056\pi\) | |||||||
\(770\) | 9.84893e11 | 0.100967 | ||||||||
\(771\) | −2.80916e12 | −0.286307 | ||||||||
\(772\) | −8.83354e12 | −0.895070 | ||||||||
\(773\) | −6.48475e12 | −0.653259 | −0.326630 | − | 0.945152i | \(-0.605913\pi\) | ||||
−0.326630 | + | 0.945152i | \(0.605913\pi\) | |||||||
\(774\) | −7.90953e11 | −0.0792167 | ||||||||
\(775\) | −2.17457e12 | −0.216529 | ||||||||
\(776\) | −2.93674e12 | −0.290729 | ||||||||
\(777\) | 5.87236e12 | 0.577987 | ||||||||
\(778\) | −1.85946e12 | −0.181961 | ||||||||
\(779\) | −1.79741e13 | −1.74876 | ||||||||
\(780\) | −1.73348e12 | −0.167684 | ||||||||
\(781\) | 7.37970e12 | 0.709756 | ||||||||
\(782\) | 5.31732e12 | 0.508467 | ||||||||
\(783\) | −3.04868e12 | −0.289857 | ||||||||
\(784\) | 2.60106e13 | 2.45883 | ||||||||
\(785\) | −4.46776e12 | −0.419930 | ||||||||
\(786\) | −1.71970e12 | −0.160713 | ||||||||
\(787\) | 8.41991e12 | 0.782386 | 0.391193 | − | 0.920309i | \(-0.372062\pi\) | ||||
0.391193 | + | 0.920309i | \(0.372062\pi\) | |||||||
\(788\) | 6.44173e12 | 0.595161 | ||||||||
\(789\) | −9.56022e12 | −0.878257 | ||||||||
\(790\) | 8.36567e11 | 0.0764150 | ||||||||
\(791\) | −1.13798e13 | −1.03357 | ||||||||
\(792\) | 1.54894e12 | 0.139885 | ||||||||
\(793\) | −1.22872e13 | −1.10337 | ||||||||
\(794\) | 1.78349e12 | 0.159250 | ||||||||
\(795\) | −7.47818e11 | −0.0663963 | ||||||||
\(796\) | 4.98504e12 | 0.440109 | ||||||||
\(797\) | 2.85116e12 | 0.250299 | 0.125150 | − | 0.992138i | \(-0.460059\pi\) | ||||
0.125150 | + | 0.992138i | \(0.460059\pi\) | |||||||
\(798\) | −3.69469e12 | −0.322526 | ||||||||
\(799\) | 1.55188e13 | 1.34709 | ||||||||
\(800\) | 6.08700e12 | 0.525410 | ||||||||
\(801\) | 1.22349e11 | 0.0105015 | ||||||||
\(802\) | 2.32190e12 | 0.198179 | ||||||||
\(803\) | −8.29217e12 | −0.703798 | ||||||||
\(804\) | 6.96700e12 | 0.588022 | ||||||||
\(805\) | −8.90760e12 | −0.747617 | ||||||||
\(806\) | 6.72182e11 | 0.0561021 | ||||||||
\(807\) | −1.19072e13 | −0.988277 | ||||||||
\(808\) | −8.13323e11 | −0.0671293 | ||||||||
\(809\) | 1.86626e13 | 1.53180 | 0.765902 | − | 0.642958i | \(-0.222293\pi\) | ||||
0.765902 | + | 0.642958i | \(0.222293\pi\) | |||||||
\(810\) | −6.48338e10 | −0.00529199 | ||||||||
\(811\) | 8.25962e12 | 0.670450 | 0.335225 | − | 0.942138i | \(-0.391188\pi\) | ||||
0.335225 | + | 0.942138i | \(0.391188\pi\) | |||||||
\(812\) | 3.48567e13 | 2.81374 | ||||||||
\(813\) | 2.29922e12 | 0.184575 | ||||||||
\(814\) | −1.38082e12 | −0.110237 | ||||||||
\(815\) | 4.02026e12 | 0.319187 | ||||||||
\(816\) | 1.06073e13 | 0.837528 | ||||||||
\(817\) | 2.26352e13 | 1.77740 | ||||||||
\(818\) | 2.46737e12 | 0.192684 | ||||||||
\(819\) | 1.03689e13 | 0.805298 | ||||||||
\(820\) | 3.60617e12 | 0.278538 | ||||||||
\(821\) | 1.10007e13 | 0.845041 | 0.422521 | − | 0.906353i | \(-0.361145\pi\) | ||||
0.422521 | + | 0.906353i | \(0.361145\pi\) | |||||||
\(822\) | 1.40389e12 | 0.107253 | ||||||||
\(823\) | −1.30547e13 | −0.991901 | −0.495950 | − | 0.868351i | \(-0.665180\pi\) | ||||
−0.495950 | + | 0.868351i | \(0.665180\pi\) | |||||||
\(824\) | 5.94639e12 | 0.449346 | ||||||||
\(825\) | 7.88760e12 | 0.592791 | ||||||||
\(826\) | −6.63507e11 | −0.0495947 | ||||||||
\(827\) | −1.98955e13 | −1.47904 | −0.739519 | − | 0.673136i | \(-0.764947\pi\) | ||||
−0.739519 | + | 0.673136i | \(0.764947\pi\) | |||||||
\(828\) | −6.86721e12 | −0.507743 | ||||||||
\(829\) | −2.50037e13 | −1.83869 | −0.919346 | − | 0.393450i | \(-0.871282\pi\) | ||||
−0.919346 | + | 0.393450i | \(0.871282\pi\) | |||||||
\(830\) | 3.05751e11 | 0.0223623 | ||||||||
\(831\) | −3.54576e12 | −0.257932 | ||||||||
\(832\) | 1.33482e13 | 0.965758 | ||||||||
\(833\) | −6.31221e13 | −4.54234 | ||||||||
\(834\) | −7.78197e11 | −0.0556984 | ||||||||
\(835\) | −1.84650e12 | −0.131450 | ||||||||
\(836\) | −2.17291e13 | −1.53856 | ||||||||
\(837\) | −6.28797e11 | −0.0442839 | ||||||||
\(838\) | 1.06485e11 | 0.00745914 | ||||||||
\(839\) | −2.47580e13 | −1.72499 | −0.862494 | − | 0.506067i | \(-0.831099\pi\) | ||||
−0.862494 | + | 0.506067i | \(0.831099\pi\) | |||||||
\(840\) | 1.51218e12 | 0.104796 | ||||||||
\(841\) | 1.84018e13 | 1.26846 | ||||||||
\(842\) | 6.43197e11 | 0.0441001 | ||||||||
\(843\) | −7.31675e12 | −0.498992 | ||||||||
\(844\) | −5.83891e12 | −0.396087 | ||||||||
\(845\) | 1.96634e12 | 0.132679 | ||||||||
\(846\) | 8.01316e11 | 0.0537820 | ||||||||
\(847\) | −5.54556e12 | −0.370228 | ||||||||
\(848\) | 6.31751e12 | 0.419532 | ||||||||
\(849\) | −1.03112e11 | −0.00681120 | ||||||||
\(850\) | −4.59668e12 | −0.302037 | ||||||||
\(851\) | 1.24884e13 | 0.816254 | ||||||||
\(852\) | 5.55426e12 | 0.361117 | ||||||||
\(853\) | −1.01946e13 | −0.659327 | −0.329664 | − | 0.944098i | \(-0.606935\pi\) | ||||
−0.329664 | + | 0.944098i | \(0.606935\pi\) | |||||||
\(854\) | 5.25425e12 | 0.338026 | ||||||||
\(855\) | 1.85539e12 | 0.118737 | ||||||||
\(856\) | −6.54410e12 | −0.416599 | ||||||||
\(857\) | 2.82216e13 | 1.78718 | 0.893589 | − | 0.448885i | \(-0.148179\pi\) | ||||
0.893589 | + | 0.448885i | \(0.148179\pi\) | |||||||
\(858\) | −2.43814e12 | −0.153591 | ||||||||
\(859\) | −2.63641e13 | −1.65213 | −0.826064 | − | 0.563577i | \(-0.809425\pi\) | ||||
−0.826064 | + | 0.563577i | \(0.809425\pi\) | |||||||
\(860\) | −4.54132e12 | −0.283100 | ||||||||
\(861\) | −2.15706e13 | −1.33767 | ||||||||
\(862\) | 4.17250e12 | 0.257403 | ||||||||
\(863\) | 1.78000e13 | 1.09237 | 0.546186 | − | 0.837664i | \(-0.316079\pi\) | ||||
0.546186 | + | 0.837664i | \(0.316079\pi\) | |||||||
\(864\) | 1.76012e12 | 0.107456 | ||||||||
\(865\) | −4.45057e12 | −0.270298 | ||||||||
\(866\) | 3.69161e12 | 0.223041 | ||||||||
\(867\) | −1.61360e13 | −0.969861 | ||||||||
\(868\) | 7.18928e12 | 0.429879 | ||||||||
\(869\) | −2.94294e13 | −1.75062 | ||||||||
\(870\) | 6.99847e11 | 0.0414159 | ||||||||
\(871\) | −2.23715e13 | −1.31708 | ||||||||
\(872\) | −2.49500e12 | −0.146133 | ||||||||
\(873\) | −4.32428e12 | −0.251970 | ||||||||
\(874\) | −7.85730e12 | −0.455483 | ||||||||
\(875\) | 1.58836e13 | 0.916037 | ||||||||
\(876\) | −6.24102e12 | −0.358086 | ||||||||
\(877\) | 2.80232e13 | 1.59963 | 0.799815 | − | 0.600246i | \(-0.204931\pi\) | ||||
0.799815 | + | 0.600246i | \(0.204931\pi\) | |||||||
\(878\) | −4.20292e11 | −0.0238685 | ||||||||
\(879\) | 1.41697e13 | 0.800589 | ||||||||
\(880\) | 4.17827e12 | 0.234868 | ||||||||
\(881\) | 5.48469e12 | 0.306733 | 0.153366 | − | 0.988169i | \(-0.450989\pi\) | ||||
0.153366 | + | 0.988169i | \(0.450989\pi\) | |||||||
\(882\) | −3.25933e12 | −0.181351 | ||||||||
\(883\) | −1.68563e13 | −0.933122 | −0.466561 | − | 0.884489i | \(-0.654507\pi\) | ||||
−0.466561 | + | 0.884489i | \(0.654507\pi\) | |||||||
\(884\) | −3.55385e13 | −1.95733 | ||||||||
\(885\) | 3.33198e11 | 0.0182582 | ||||||||
\(886\) | 2.51969e12 | 0.137371 | ||||||||
\(887\) | −1.17075e13 | −0.635052 | −0.317526 | − | 0.948250i | \(-0.602852\pi\) | ||||
−0.317526 | + | 0.948250i | \(0.602852\pi\) | |||||||
\(888\) | −2.12007e12 | −0.114417 | ||||||||
\(889\) | 3.59994e13 | 1.93303 | ||||||||
\(890\) | −2.80860e10 | −0.00150050 | ||||||||
\(891\) | 2.28077e12 | 0.121236 | ||||||||
\(892\) | 1.98358e13 | 1.04908 | ||||||||
\(893\) | −2.29318e13 | −1.20672 | ||||||||
\(894\) | −3.57402e12 | −0.187128 | ||||||||
\(895\) | 5.99032e12 | 0.312066 | ||||||||
\(896\) | −2.66366e13 | −1.38068 | ||||||||
\(897\) | 2.20511e13 | 1.13727 | ||||||||
\(898\) | −2.74984e12 | −0.141112 | ||||||||
\(899\) | 6.78754e12 | 0.346572 | ||||||||
\(900\) | 5.93652e12 | 0.301606 | ||||||||
\(901\) | −1.53312e13 | −0.775024 | ||||||||
\(902\) | 5.07209e12 | 0.255127 | ||||||||
\(903\) | 2.71643e13 | 1.35958 | ||||||||
\(904\) | 4.10838e12 | 0.204603 | ||||||||
\(905\) | 8.98460e12 | 0.445226 | ||||||||
\(906\) | 2.26984e11 | 0.0111923 | ||||||||
\(907\) | 1.59339e13 | 0.781791 | 0.390895 | − | 0.920435i | \(-0.372165\pi\) | ||||
0.390895 | + | 0.920435i | \(0.372165\pi\) | |||||||
\(908\) | 3.24554e12 | 0.158453 | ||||||||
\(909\) | −1.19760e12 | −0.0581799 | ||||||||
\(910\) | −2.38027e12 | −0.115064 | ||||||||
\(911\) | −1.50810e13 | −0.725433 | −0.362716 | − | 0.931900i | \(-0.618151\pi\) | ||||
−0.362716 | + | 0.931900i | \(0.618151\pi\) | |||||||
\(912\) | −1.56742e13 | −0.750254 | ||||||||
\(913\) | −1.07560e13 | −0.512307 | ||||||||
\(914\) | 1.36621e12 | 0.0647531 | ||||||||
\(915\) | −2.63857e12 | −0.124444 | ||||||||
\(916\) | −1.96199e13 | −0.920804 | ||||||||
\(917\) | 5.90610e13 | 2.75828 | ||||||||
\(918\) | −1.32918e12 | −0.0617718 | ||||||||
\(919\) | 3.13312e13 | 1.44896 | 0.724481 | − | 0.689295i | \(-0.242079\pi\) | ||||
0.724481 | + | 0.689295i | \(0.242079\pi\) | |||||||
\(920\) | 3.21587e12 | 0.147997 | ||||||||
\(921\) | −3.29094e12 | −0.150713 | ||||||||
\(922\) | 6.24294e12 | 0.284512 | ||||||||
\(923\) | −1.78351e13 | −0.808850 | ||||||||
\(924\) | −2.60770e13 | −1.17688 | ||||||||
\(925\) | −1.07959e13 | −0.484866 | ||||||||
\(926\) | −6.04465e12 | −0.270160 | ||||||||
\(927\) | 8.75590e12 | 0.389441 | ||||||||
\(928\) | −1.89995e13 | −0.840964 | ||||||||
\(929\) | 3.82774e13 | 1.68605 | 0.843027 | − | 0.537871i | \(-0.180771\pi\) | ||||
0.843027 | + | 0.537871i | \(0.180771\pi\) | |||||||
\(930\) | 1.44345e11 | 0.00632745 | ||||||||
\(931\) | 9.32743e13 | 4.06901 | ||||||||
\(932\) | 4.48327e12 | 0.194636 | ||||||||
\(933\) | 3.37309e12 | 0.145734 | ||||||||
\(934\) | 4.19601e12 | 0.180416 | ||||||||
\(935\) | −1.01397e13 | −0.433885 | ||||||||
\(936\) | −3.74345e12 | −0.159415 | ||||||||
\(937\) | 2.32522e13 | 0.985454 | 0.492727 | − | 0.870184i | \(-0.336000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(938\) | 9.56651e12 | 0.403498 | ||||||||
\(939\) | 1.70593e13 | 0.716089 | ||||||||
\(940\) | 4.60082e12 | 0.192203 | ||||||||
\(941\) | 3.51809e13 | 1.46270 | 0.731348 | − | 0.682004i | \(-0.238891\pi\) | ||||
0.731348 | + | 0.682004i | \(0.238891\pi\) | |||||||
\(942\) | −4.72953e12 | −0.195699 | ||||||||
\(943\) | −4.58731e13 | −1.88910 | ||||||||
\(944\) | −2.81483e12 | −0.115366 | ||||||||
\(945\) | 2.22664e12 | 0.0908253 | ||||||||
\(946\) | −6.38739e12 | −0.259306 | ||||||||
\(947\) | −3.64229e13 | −1.47163 | −0.735816 | − | 0.677181i | \(-0.763201\pi\) | ||||
−0.735816 | + | 0.677181i | \(0.763201\pi\) | |||||||
\(948\) | −2.21497e13 | −0.890699 | ||||||||
\(949\) | 2.00403e13 | 0.802060 | ||||||||
\(950\) | 6.79243e12 | 0.270563 | ||||||||
\(951\) | −5.24770e12 | −0.208045 | ||||||||
\(952\) | 3.10015e13 | 1.22325 | ||||||||
\(953\) | −2.17649e13 | −0.854750 | −0.427375 | − | 0.904074i | \(-0.640562\pi\) | ||||
−0.427375 | + | 0.904074i | \(0.640562\pi\) | |||||||
\(954\) | −7.91633e11 | −0.0309425 | ||||||||
\(955\) | 9.87917e12 | 0.384331 | ||||||||
\(956\) | −1.35590e13 | −0.525011 | ||||||||
\(957\) | −2.46198e13 | −0.948813 | ||||||||
\(958\) | 4.57488e12 | 0.175483 | ||||||||
\(959\) | −4.82148e13 | −1.84076 | ||||||||
\(960\) | 2.86641e12 | 0.108923 | ||||||||
\(961\) | −2.50397e13 | −0.947051 | ||||||||
\(962\) | 3.33713e12 | 0.125628 | ||||||||
\(963\) | −9.63601e12 | −0.361060 | ||||||||
\(964\) | −1.04699e13 | −0.390477 | ||||||||
\(965\) | 6.09116e12 | 0.226114 | ||||||||
\(966\) | −9.42949e12 | −0.348410 | ||||||||
\(967\) | 2.07696e13 | 0.763851 | 0.381925 | − | 0.924193i | \(-0.375261\pi\) | ||||
0.381925 | + | 0.924193i | \(0.375261\pi\) | |||||||
\(968\) | 2.00208e12 | 0.0732897 | ||||||||
\(969\) | 3.80378e13 | 1.38599 | ||||||||
\(970\) | 9.92670e11 | 0.0360024 | ||||||||
\(971\) | 2.81746e13 | 1.01712 | 0.508559 | − | 0.861027i | \(-0.330179\pi\) | ||||
0.508559 | + | 0.861027i | \(0.330179\pi\) | |||||||
\(972\) | 1.71660e12 | 0.0616838 | ||||||||
\(973\) | 2.67262e13 | 0.955939 | ||||||||
\(974\) | 3.40444e12 | 0.121208 | ||||||||
\(975\) | −1.90626e13 | −0.675555 | ||||||||
\(976\) | 2.22904e13 | 0.786310 | ||||||||
\(977\) | 3.55629e13 | 1.24874 | 0.624369 | − | 0.781130i | \(-0.285356\pi\) | ||||
0.624369 | + | 0.781130i | \(0.285356\pi\) | |||||||
\(978\) | 4.25581e12 | 0.148750 | ||||||||
\(979\) | 9.88033e11 | 0.0343755 | ||||||||
\(980\) | −1.87137e13 | −0.648101 | ||||||||
\(981\) | −3.67382e12 | −0.126651 | ||||||||
\(982\) | 6.02373e12 | 0.206711 | ||||||||
\(983\) | 3.19675e12 | 0.109199 | 0.0545994 | − | 0.998508i | \(-0.482612\pi\) | ||||
0.0545994 | + | 0.998508i | \(0.482612\pi\) | |||||||
\(984\) | 7.78753e12 | 0.264802 | ||||||||
\(985\) | −4.44189e12 | −0.150350 | ||||||||
\(986\) | 1.43478e13 | 0.483435 | ||||||||
\(987\) | −2.75202e13 | −0.923049 | ||||||||
\(988\) | 5.25145e13 | 1.75337 | ||||||||
\(989\) | 5.77690e13 | 1.92005 | ||||||||
\(990\) | −5.23569e11 | −0.0173227 | ||||||||
\(991\) | −2.46648e12 | −0.0812356 | −0.0406178 | − | 0.999175i | \(-0.512933\pi\) | ||||
−0.0406178 | + | 0.999175i | \(0.512933\pi\) | |||||||
\(992\) | −3.91870e12 | −0.128481 | ||||||||
\(993\) | 2.00691e13 | 0.655022 | ||||||||
\(994\) | 7.62665e12 | 0.247796 | ||||||||
\(995\) | −3.43743e12 | −0.111181 | ||||||||
\(996\) | −8.09536e12 | −0.260657 | ||||||||
\(997\) | 5.14255e13 | 1.64835 | 0.824177 | − | 0.566333i | \(-0.191638\pi\) | ||||
0.824177 | + | 0.566333i | \(0.191638\pi\) | |||||||
\(998\) | −3.07819e12 | −0.0982217 | ||||||||
\(999\) | −3.12174e12 | −0.0991637 |
(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.1.9 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.9 | ✓ | 21 | 1.1 | even | 1 | trivial |