Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
Defining polynomial: | \(x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} - 89298188 x^{10} + 64650816672 x^{9} + 33122051904 x^{8} - 6210397064704 x^{7} - 2735256748800 x^{6} + 288860762071040 x^{5} - 34502173230080 x^{4} - 5633463408885760 x^{3} + 4719471961341952 x^{2} + 37636623107620864 x - 58321181718347776\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-15.9892\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −17.9892 | −1.59004 | −0.795018 | − | 0.606585i | \(-0.792539\pi\) | ||||
−0.795018 | + | 0.606585i | \(0.792539\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 195.612 | 1.52822 | ||||||||
\(5\) | −98.9095 | −0.353869 | −0.176935 | − | 0.984223i | \(-0.556618\pi\) | ||||
−0.176935 | + | 0.984223i | \(0.556618\pi\) | |||||||
\(6\) | −485.709 | −0.918008 | ||||||||
\(7\) | 159.201 | 0.175429 | 0.0877147 | − | 0.996146i | \(-0.472044\pi\) | ||||
0.0877147 | + | 0.996146i | \(0.472044\pi\) | |||||||
\(8\) | −1216.28 | −0.839884 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 1779.30 | 0.562665 | ||||||||
\(11\) | −4884.97 | −1.10659 | −0.553296 | − | 0.832985i | \(-0.686630\pi\) | ||||
−0.553296 | + | 0.832985i | \(0.686630\pi\) | |||||||
\(12\) | 5281.52 | 0.882316 | ||||||||
\(13\) | 11664.5 | 1.47253 | 0.736265 | − | 0.676694i | \(-0.236588\pi\) | ||||
0.736265 | + | 0.676694i | \(0.236588\pi\) | |||||||
\(14\) | −2863.90 | −0.278939 | ||||||||
\(15\) | −2670.56 | −0.204307 | ||||||||
\(16\) | −3158.35 | −0.192770 | ||||||||
\(17\) | −10463.7 | −0.516550 | −0.258275 | − | 0.966071i | \(-0.583154\pi\) | ||||
−0.258275 | + | 0.966071i | \(0.583154\pi\) | |||||||
\(18\) | −13114.1 | −0.530012 | ||||||||
\(19\) | 14966.8 | 0.500599 | 0.250300 | − | 0.968168i | \(-0.419471\pi\) | ||||
0.250300 | + | 0.968168i | \(0.419471\pi\) | |||||||
\(20\) | −19347.9 | −0.540789 | ||||||||
\(21\) | 4298.42 | 0.101284 | ||||||||
\(22\) | 87876.7 | 1.75952 | ||||||||
\(23\) | −88.0105 | −0.00150830 | −0.000754148 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000754148 | 1.00000i | \(0.500240\pi\) | ||||||||
\(24\) | −32839.6 | −0.484907 | ||||||||
\(25\) | −68341.9 | −0.874776 | ||||||||
\(26\) | −209835. | −2.34138 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 31141.6 | 0.268094 | ||||||||
\(29\) | −102600. | −0.781185 | −0.390592 | − | 0.920564i | \(-0.627730\pi\) | ||||
−0.390592 | + | 0.920564i | \(0.627730\pi\) | |||||||
\(30\) | 48041.2 | 0.324855 | ||||||||
\(31\) | −287624. | −1.73404 | −0.867019 | − | 0.498275i | \(-0.833967\pi\) | ||||
−0.867019 | + | 0.498275i | \(0.833967\pi\) | |||||||
\(32\) | 212500. | 1.14640 | ||||||||
\(33\) | −131894. | −0.638891 | ||||||||
\(34\) | 188233. | 0.821333 | ||||||||
\(35\) | −15746.5 | −0.0620791 | ||||||||
\(36\) | 142601. | 0.509406 | ||||||||
\(37\) | 566144. | 1.83747 | 0.918737 | − | 0.394870i | \(-0.129210\pi\) | ||||
0.918737 | + | 0.394870i | \(0.129210\pi\) | |||||||
\(38\) | −269240. | −0.795971 | ||||||||
\(39\) | 314941. | 0.850165 | ||||||||
\(40\) | 120302. | 0.297209 | ||||||||
\(41\) | 296117. | 0.670995 | 0.335497 | − | 0.942041i | \(-0.391096\pi\) | ||||
0.335497 | + | 0.942041i | \(0.391096\pi\) | |||||||
\(42\) | −77325.3 | −0.161046 | ||||||||
\(43\) | 740471. | 1.42026 | 0.710131 | − | 0.704070i | \(-0.248636\pi\) | ||||
0.710131 | + | 0.704070i | \(0.248636\pi\) | |||||||
\(44\) | −955557. | −1.69111 | ||||||||
\(45\) | −72105.0 | −0.117956 | ||||||||
\(46\) | 1583.24 | 0.00239825 | ||||||||
\(47\) | 958168. | 1.34617 | 0.673084 | − | 0.739566i | \(-0.264969\pi\) | ||||
0.673084 | + | 0.739566i | \(0.264969\pi\) | |||||||
\(48\) | −85275.4 | −0.111296 | ||||||||
\(49\) | −798198. | −0.969225 | ||||||||
\(50\) | 1.22942e6 | 1.39093 | ||||||||
\(51\) | −282519. | −0.298230 | ||||||||
\(52\) | 2.28171e6 | 2.25034 | ||||||||
\(53\) | −732872. | −0.676181 | −0.338090 | − | 0.941114i | \(-0.609781\pi\) | ||||
−0.338090 | + | 0.941114i | \(0.609781\pi\) | |||||||
\(54\) | −354082. | −0.306003 | ||||||||
\(55\) | 483170. | 0.391589 | ||||||||
\(56\) | −193633. | −0.147340 | ||||||||
\(57\) | 404103. | 0.289021 | ||||||||
\(58\) | 1.84569e6 | 1.24211 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −522392. | −0.312225 | ||||||||
\(61\) | 2.28293e6 | 1.28777 | 0.643884 | − | 0.765123i | \(-0.277322\pi\) | ||||
0.643884 | + | 0.765123i | \(0.277322\pi\) | |||||||
\(62\) | 5.17412e6 | 2.75718 | ||||||||
\(63\) | 116057. | 0.0584765 | ||||||||
\(64\) | −3.41844e6 | −1.63004 | ||||||||
\(65\) | −1.15373e6 | −0.521083 | ||||||||
\(66\) | 2.37267e6 | 1.01586 | ||||||||
\(67\) | −4.29840e6 | −1.74600 | −0.873001 | − | 0.487719i | \(-0.837829\pi\) | ||||
−0.873001 | + | 0.487719i | \(0.837829\pi\) | |||||||
\(68\) | −2.04681e6 | −0.789400 | ||||||||
\(69\) | −2376.28 | −0.000870816 0 | ||||||||
\(70\) | 283267. | 0.0987080 | ||||||||
\(71\) | −4.99901e6 | −1.65760 | −0.828800 | − | 0.559545i | \(-0.810976\pi\) | ||||
−0.828800 | + | 0.559545i | \(0.810976\pi\) | |||||||
\(72\) | −886670. | −0.279961 | ||||||||
\(73\) | 3.66974e6 | 1.10409 | 0.552046 | − | 0.833814i | \(-0.313847\pi\) | ||||
0.552046 | + | 0.833814i | \(0.313847\pi\) | |||||||
\(74\) | −1.01845e7 | −2.92165 | ||||||||
\(75\) | −1.84523e6 | −0.505052 | ||||||||
\(76\) | 2.92768e6 | 0.765024 | ||||||||
\(77\) | −777691. | −0.194129 | ||||||||
\(78\) | −5.66554e6 | −1.35179 | ||||||||
\(79\) | 3.18719e6 | 0.727300 | 0.363650 | − | 0.931536i | \(-0.381530\pi\) | ||||
0.363650 | + | 0.931536i | \(0.381530\pi\) | |||||||
\(80\) | 312391. | 0.0682155 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −5.32690e6 | −1.06691 | ||||||||
\(83\) | −4.43945e6 | −0.852228 | −0.426114 | − | 0.904670i | \(-0.640118\pi\) | ||||
−0.426114 | + | 0.904670i | \(0.640118\pi\) | |||||||
\(84\) | 840822. | 0.154784 | ||||||||
\(85\) | 1.03496e6 | 0.182791 | ||||||||
\(86\) | −1.33205e7 | −2.25827 | ||||||||
\(87\) | −2.77020e6 | −0.451017 | ||||||||
\(88\) | 5.94150e6 | 0.929409 | ||||||||
\(89\) | −1.07216e7 | −1.61211 | −0.806056 | − | 0.591839i | \(-0.798402\pi\) | ||||
−0.806056 | + | 0.591839i | \(0.798402\pi\) | |||||||
\(90\) | 1.29711e6 | 0.187555 | ||||||||
\(91\) | 1.85700e6 | 0.258325 | ||||||||
\(92\) | −17215.9 | −0.00230500 | ||||||||
\(93\) | −7.76584e6 | −1.00115 | ||||||||
\(94\) | −1.72367e7 | −2.14046 | ||||||||
\(95\) | −1.48036e6 | −0.177147 | ||||||||
\(96\) | 5.73751e6 | 0.661872 | ||||||||
\(97\) | −4.05589e6 | −0.451216 | −0.225608 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225608 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(98\) | 1.43590e7 | 1.54110 | ||||||||
\(99\) | −3.56114e6 | −0.368864 | ||||||||
\(100\) | −1.33685e7 | −1.33685 | ||||||||
\(101\) | −1.05360e7 | −1.01754 | −0.508768 | − | 0.860904i | \(-0.669899\pi\) | ||||
−0.508768 | + | 0.860904i | \(0.669899\pi\) | |||||||
\(102\) | 5.08229e6 | 0.474197 | ||||||||
\(103\) | −9.49129e6 | −0.855845 | −0.427922 | − | 0.903816i | \(-0.640754\pi\) | ||||
−0.427922 | + | 0.903816i | \(0.640754\pi\) | |||||||
\(104\) | −1.41873e7 | −1.23675 | ||||||||
\(105\) | −425155. | −0.0358414 | ||||||||
\(106\) | 1.31838e7 | 1.07515 | ||||||||
\(107\) | −7.68612e6 | −0.606547 | −0.303273 | − | 0.952904i | \(-0.598079\pi\) | ||||
−0.303273 | + | 0.952904i | \(0.598079\pi\) | |||||||
\(108\) | 3.85023e6 | 0.294105 | ||||||||
\(109\) | 1.46696e7 | 1.08499 | 0.542494 | − | 0.840059i | \(-0.317480\pi\) | ||||
0.542494 | + | 0.840059i | \(0.317480\pi\) | |||||||
\(110\) | −8.69185e6 | −0.622641 | ||||||||
\(111\) | 1.52859e7 | 1.06087 | ||||||||
\(112\) | −502812. | −0.0338176 | ||||||||
\(113\) | −1.52191e7 | −0.992234 | −0.496117 | − | 0.868256i | \(-0.665241\pi\) | ||||
−0.496117 | + | 0.868256i | \(0.665241\pi\) | |||||||
\(114\) | −7.26949e6 | −0.459554 | ||||||||
\(115\) | 8705.07 | 0.000533740 0 | ||||||||
\(116\) | −2.00697e7 | −1.19382 | ||||||||
\(117\) | 8.50341e6 | 0.490843 | ||||||||
\(118\) | 3.69461e6 | 0.207005 | ||||||||
\(119\) | −1.66582e6 | −0.0906180 | ||||||||
\(120\) | 3.24815e6 | 0.171594 | ||||||||
\(121\) | 4.37575e6 | 0.224545 | ||||||||
\(122\) | −4.10680e7 | −2.04760 | ||||||||
\(123\) | 7.99515e6 | 0.387399 | ||||||||
\(124\) | −5.62626e7 | −2.64999 | ||||||||
\(125\) | 1.44870e7 | 0.663426 | ||||||||
\(126\) | −2.08778e6 | −0.0929797 | ||||||||
\(127\) | 1.49590e7 | 0.648021 | 0.324011 | − | 0.946053i | \(-0.394969\pi\) | ||||
0.324011 | + | 0.946053i | \(0.394969\pi\) | |||||||
\(128\) | 3.42951e7 | 1.44543 | ||||||||
\(129\) | 1.99927e7 | 0.819988 | ||||||||
\(130\) | 2.07547e7 | 0.828541 | ||||||||
\(131\) | −2.82534e7 | −1.09805 | −0.549024 | − | 0.835807i | \(-0.685000\pi\) | ||||
−0.549024 | + | 0.835807i | \(0.685000\pi\) | |||||||
\(132\) | −2.58000e7 | −0.976364 | ||||||||
\(133\) | 2.38272e6 | 0.0878198 | ||||||||
\(134\) | 7.73248e7 | 2.77621 | ||||||||
\(135\) | −1.94684e6 | −0.0681022 | ||||||||
\(136\) | 1.27268e7 | 0.433842 | ||||||||
\(137\) | 4.47666e7 | 1.48741 | 0.743707 | − | 0.668506i | \(-0.233066\pi\) | ||||
0.743707 | + | 0.668506i | \(0.233066\pi\) | |||||||
\(138\) | 42747.4 | 0.00138463 | ||||||||
\(139\) | −4.23885e7 | −1.33874 | −0.669370 | − | 0.742929i | \(-0.733436\pi\) | ||||
−0.669370 | + | 0.742929i | \(0.733436\pi\) | |||||||
\(140\) | −3.08020e6 | −0.0948703 | ||||||||
\(141\) | 2.58705e7 | 0.777210 | ||||||||
\(142\) | 8.99283e7 | 2.63565 | ||||||||
\(143\) | −5.69807e7 | −1.62949 | ||||||||
\(144\) | −2.30244e6 | −0.0642567 | ||||||||
\(145\) | 1.01481e7 | 0.276437 | ||||||||
\(146\) | −6.60157e7 | −1.75555 | ||||||||
\(147\) | −2.15513e7 | −0.559582 | ||||||||
\(148\) | 1.10744e8 | 2.80806 | ||||||||
\(149\) | −3.46535e7 | −0.858214 | −0.429107 | − | 0.903254i | \(-0.641172\pi\) | ||||
−0.429107 | + | 0.903254i | \(0.641172\pi\) | |||||||
\(150\) | 3.31943e7 | 0.803052 | ||||||||
\(151\) | −7.67555e7 | −1.81422 | −0.907110 | − | 0.420893i | \(-0.861717\pi\) | ||||
−0.907110 | + | 0.420893i | \(0.861717\pi\) | |||||||
\(152\) | −1.82038e7 | −0.420445 | ||||||||
\(153\) | −7.62801e6 | −0.172183 | ||||||||
\(154\) | 1.39901e7 | 0.308672 | ||||||||
\(155\) | 2.84487e7 | 0.613623 | ||||||||
\(156\) | 6.16062e7 | 1.29924 | ||||||||
\(157\) | −6.08764e7 | −1.25545 | −0.627726 | − | 0.778434i | \(-0.716014\pi\) | ||||
−0.627726 | + | 0.778434i | \(0.716014\pi\) | |||||||
\(158\) | −5.73351e7 | −1.15643 | ||||||||
\(159\) | −1.97875e7 | −0.390393 | ||||||||
\(160\) | −2.10183e7 | −0.405675 | ||||||||
\(161\) | −14011.3 | −0.000264600 0 | ||||||||
\(162\) | −9.56020e6 | −0.176671 | ||||||||
\(163\) | −9.26090e7 | −1.67493 | −0.837465 | − | 0.546491i | \(-0.815963\pi\) | ||||
−0.837465 | + | 0.546491i | \(0.815963\pi\) | |||||||
\(164\) | 5.79239e7 | 1.02543 | ||||||||
\(165\) | 1.30456e7 | 0.226084 | ||||||||
\(166\) | 7.98622e7 | 1.35507 | ||||||||
\(167\) | 6.05390e7 | 1.00584 | 0.502918 | − | 0.864334i | \(-0.332260\pi\) | ||||
0.502918 | + | 0.864334i | \(0.332260\pi\) | |||||||
\(168\) | −5.22810e6 | −0.0850670 | ||||||||
\(169\) | 7.33117e7 | 1.16834 | ||||||||
\(170\) | −1.86180e7 | −0.290645 | ||||||||
\(171\) | 1.09108e7 | 0.166866 | ||||||||
\(172\) | 1.44845e8 | 2.17047 | ||||||||
\(173\) | 6.39593e6 | 0.0939166 | 0.0469583 | − | 0.998897i | \(-0.485047\pi\) | ||||
0.0469583 | + | 0.998897i | \(0.485047\pi\) | |||||||
\(174\) | 4.98336e7 | 0.717134 | ||||||||
\(175\) | −1.08801e7 | −0.153461 | ||||||||
\(176\) | 1.54284e7 | 0.213318 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 1.92873e8 | 2.56332 | ||||||||
\(179\) | −1.31141e8 | −1.70904 | −0.854519 | − | 0.519421i | \(-0.826148\pi\) | ||||
−0.854519 | + | 0.519421i | \(0.826148\pi\) | |||||||
\(180\) | −1.41046e7 | −0.180263 | ||||||||
\(181\) | −3.39901e7 | −0.426066 | −0.213033 | − | 0.977045i | \(-0.568334\pi\) | ||||
−0.213033 | + | 0.977045i | \(0.568334\pi\) | |||||||
\(182\) | −3.34059e7 | −0.410746 | ||||||||
\(183\) | 6.16390e7 | 0.743493 | ||||||||
\(184\) | 107046. | 0.00126679 | ||||||||
\(185\) | −5.59971e7 | −0.650226 | ||||||||
\(186\) | 1.39701e8 | 1.59186 | ||||||||
\(187\) | 5.11147e7 | 0.571610 | ||||||||
\(188\) | 1.87429e8 | 2.05724 | ||||||||
\(189\) | 3.13355e6 | 0.0337614 | ||||||||
\(190\) | 2.66304e7 | 0.281670 | ||||||||
\(191\) | 1.52054e8 | 1.57899 | 0.789497 | − | 0.613755i | \(-0.210342\pi\) | ||||
0.789497 | + | 0.613755i | \(0.210342\pi\) | |||||||
\(192\) | −9.22980e7 | −0.941105 | ||||||||
\(193\) | 5.77384e6 | 0.0578115 | 0.0289057 | − | 0.999582i | \(-0.490798\pi\) | ||||
0.0289057 | + | 0.999582i | \(0.490798\pi\) | |||||||
\(194\) | 7.29622e7 | 0.717450 | ||||||||
\(195\) | −3.11507e7 | −0.300847 | ||||||||
\(196\) | −1.56137e8 | −1.48119 | ||||||||
\(197\) | −1.02503e8 | −0.955221 | −0.477611 | − | 0.878572i | \(-0.658497\pi\) | ||||
−0.477611 | + | 0.878572i | \(0.658497\pi\) | |||||||
\(198\) | 6.40622e7 | 0.586507 | ||||||||
\(199\) | 8.62017e7 | 0.775408 | 0.387704 | − | 0.921784i | \(-0.373268\pi\) | ||||
0.387704 | + | 0.921784i | \(0.373268\pi\) | |||||||
\(200\) | 8.31230e7 | 0.734711 | ||||||||
\(201\) | −1.16057e8 | −1.00805 | ||||||||
\(202\) | 1.89534e8 | 1.61792 | ||||||||
\(203\) | −1.63340e7 | −0.137043 | ||||||||
\(204\) | −5.52640e7 | −0.455761 | ||||||||
\(205\) | −2.92887e7 | −0.237445 | ||||||||
\(206\) | 1.70741e8 | 1.36082 | ||||||||
\(207\) | −64159.6 | −0.000502766 0 | ||||||||
\(208\) | −3.68405e7 | −0.283860 | ||||||||
\(209\) | −7.31122e7 | −0.553959 | ||||||||
\(210\) | 7.64820e6 | 0.0569891 | ||||||||
\(211\) | 2.46914e7 | 0.180949 | 0.0904746 | − | 0.995899i | \(-0.471162\pi\) | ||||
0.0904746 | + | 0.995899i | \(0.471162\pi\) | |||||||
\(212\) | −1.43358e8 | −1.03335 | ||||||||
\(213\) | −1.34973e8 | −0.957016 | ||||||||
\(214\) | 1.38267e8 | 0.964431 | ||||||||
\(215\) | −7.32396e7 | −0.502587 | ||||||||
\(216\) | −2.39401e7 | −0.161636 | ||||||||
\(217\) | −4.57899e7 | −0.304201 | ||||||||
\(218\) | −2.63894e8 | −1.72517 | ||||||||
\(219\) | 9.90830e7 | 0.637448 | ||||||||
\(220\) | 9.45137e7 | 0.598433 | ||||||||
\(221\) | −1.22053e8 | −0.760635 | ||||||||
\(222\) | −2.74981e8 | −1.68682 | ||||||||
\(223\) | 4.55302e7 | 0.274936 | 0.137468 | − | 0.990506i | \(-0.456104\pi\) | ||||
0.137468 | + | 0.990506i | \(0.456104\pi\) | |||||||
\(224\) | 3.38302e7 | 0.201111 | ||||||||
\(225\) | −4.98212e7 | −0.291592 | ||||||||
\(226\) | 2.73780e8 | 1.57769 | ||||||||
\(227\) | −2.56384e8 | −1.45479 | −0.727395 | − | 0.686219i | \(-0.759269\pi\) | ||||
−0.727395 | + | 0.686219i | \(0.759269\pi\) | |||||||
\(228\) | 7.90472e7 | 0.441687 | ||||||||
\(229\) | −3.44709e8 | −1.89683 | −0.948415 | − | 0.317033i | \(-0.897314\pi\) | ||||
−0.948415 | + | 0.317033i | \(0.897314\pi\) | |||||||
\(230\) | −156597. | −0.000848667 0 | ||||||||
\(231\) | −2.09977e7 | −0.112080 | ||||||||
\(232\) | 1.24790e8 | 0.656104 | ||||||||
\(233\) | −1.44767e8 | −0.749762 | −0.374881 | − | 0.927073i | \(-0.622316\pi\) | ||||
−0.374881 | + | 0.927073i | \(0.622316\pi\) | |||||||
\(234\) | −1.52970e8 | −0.780458 | ||||||||
\(235\) | −9.47720e7 | −0.476368 | ||||||||
\(236\) | −4.01745e7 | −0.198957 | ||||||||
\(237\) | 8.60542e7 | 0.419907 | ||||||||
\(238\) | 2.99669e7 | 0.144086 | ||||||||
\(239\) | −2.45941e8 | −1.16530 | −0.582650 | − | 0.812723i | \(-0.697984\pi\) | ||||
−0.582650 | + | 0.812723i | \(0.697984\pi\) | |||||||
\(240\) | 8.43455e6 | 0.0393842 | ||||||||
\(241\) | 2.54396e8 | 1.17071 | 0.585357 | − | 0.810775i | \(-0.300954\pi\) | ||||
0.585357 | + | 0.810775i | \(0.300954\pi\) | |||||||
\(242\) | −7.87164e7 | −0.357035 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 4.46567e8 | 1.96799 | ||||||||
\(245\) | 7.89494e7 | 0.342979 | ||||||||
\(246\) | −1.43826e8 | −0.615979 | ||||||||
\(247\) | 1.74580e8 | 0.737147 | ||||||||
\(248\) | 3.49831e8 | 1.45639 | ||||||||
\(249\) | −1.19865e8 | −0.492034 | ||||||||
\(250\) | −2.60609e8 | −1.05487 | ||||||||
\(251\) | 3.25172e8 | 1.29794 | 0.648971 | − | 0.760813i | \(-0.275200\pi\) | ||||
0.648971 | + | 0.760813i | \(0.275200\pi\) | |||||||
\(252\) | 2.27022e7 | 0.0893647 | ||||||||
\(253\) | 429928. | 0.00166907 | ||||||||
\(254\) | −2.69100e8 | −1.03038 | ||||||||
\(255\) | 2.79438e7 | 0.105535 | ||||||||
\(256\) | −1.79381e8 | −0.668245 | ||||||||
\(257\) | 2.54981e8 | 0.937003 | 0.468502 | − | 0.883463i | \(-0.344794\pi\) | ||||
0.468502 | + | 0.883463i | \(0.344794\pi\) | |||||||
\(258\) | −3.59653e8 | −1.30381 | ||||||||
\(259\) | 9.01307e7 | 0.322347 | ||||||||
\(260\) | −2.25683e8 | −0.796328 | ||||||||
\(261\) | −7.47953e7 | −0.260395 | ||||||||
\(262\) | 5.08256e8 | 1.74594 | ||||||||
\(263\) | 4.19400e8 | 1.42162 | 0.710809 | − | 0.703385i | \(-0.248329\pi\) | ||||
0.710809 | + | 0.703385i | \(0.248329\pi\) | |||||||
\(264\) | 1.60421e8 | 0.536594 | ||||||||
\(265\) | 7.24880e7 | 0.239280 | ||||||||
\(266\) | −4.28633e7 | −0.139637 | ||||||||
\(267\) | −2.89484e8 | −0.930754 | ||||||||
\(268\) | −8.40817e8 | −2.66827 | ||||||||
\(269\) | −4.15320e8 | −1.30092 | −0.650459 | − | 0.759541i | \(-0.725424\pi\) | ||||
−0.650459 | + | 0.759541i | \(0.725424\pi\) | |||||||
\(270\) | 3.50220e7 | 0.108285 | ||||||||
\(271\) | −5.50963e7 | −0.168163 | −0.0840814 | − | 0.996459i | \(-0.526796\pi\) | ||||
−0.0840814 | + | 0.996459i | \(0.526796\pi\) | |||||||
\(272\) | 3.30479e7 | 0.0995755 | ||||||||
\(273\) | 5.01389e7 | 0.149144 | ||||||||
\(274\) | −8.05315e8 | −2.36504 | ||||||||
\(275\) | 3.33848e8 | 0.968020 | ||||||||
\(276\) | −464829. | −0.00133080 | ||||||||
\(277\) | −2.16584e8 | −0.612275 | −0.306138 | − | 0.951987i | \(-0.599037\pi\) | ||||
−0.306138 | + | 0.951987i | \(0.599037\pi\) | |||||||
\(278\) | 7.62536e8 | 2.12865 | ||||||||
\(279\) | −2.09678e8 | −0.578013 | ||||||||
\(280\) | 1.91522e7 | 0.0521392 | ||||||||
\(281\) | −1.30596e8 | −0.351123 | −0.175561 | − | 0.984468i | \(-0.556174\pi\) | ||||
−0.175561 | + | 0.984468i | \(0.556174\pi\) | |||||||
\(282\) | −4.65391e8 | −1.23579 | ||||||||
\(283\) | 4.03750e8 | 1.05891 | 0.529457 | − | 0.848337i | \(-0.322396\pi\) | ||||
0.529457 | + | 0.848337i | \(0.322396\pi\) | |||||||
\(284\) | −9.77865e8 | −2.53317 | ||||||||
\(285\) | −3.99696e7 | −0.102276 | ||||||||
\(286\) | 1.02504e9 | 2.59095 | ||||||||
\(287\) | 4.71420e7 | 0.117712 | ||||||||
\(288\) | 1.54913e8 | 0.382132 | ||||||||
\(289\) | −3.00851e8 | −0.733176 | ||||||||
\(290\) | −1.82556e8 | −0.439546 | ||||||||
\(291\) | −1.09509e8 | −0.260510 | ||||||||
\(292\) | 7.17844e8 | 1.68729 | ||||||||
\(293\) | 1.61200e8 | 0.374394 | 0.187197 | − | 0.982322i | \(-0.440060\pi\) | ||||
0.187197 | + | 0.982322i | \(0.440060\pi\) | |||||||
\(294\) | 3.87692e8 | 0.889756 | ||||||||
\(295\) | 2.03139e7 | 0.0460699 | ||||||||
\(296\) | −6.88591e8 | −1.54327 | ||||||||
\(297\) | −9.61509e7 | −0.212964 | ||||||||
\(298\) | 6.23390e8 | 1.36459 | ||||||||
\(299\) | −1.02660e6 | −0.00222101 | ||||||||
\(300\) | −3.60949e8 | −0.771830 | ||||||||
\(301\) | 1.17884e8 | 0.249156 | ||||||||
\(302\) | 1.38077e9 | 2.88468 | ||||||||
\(303\) | −2.84471e8 | −0.587474 | ||||||||
\(304\) | −4.72702e7 | −0.0965007 | ||||||||
\(305\) | −2.25803e8 | −0.455701 | ||||||||
\(306\) | 1.37222e8 | 0.273778 | ||||||||
\(307\) | −7.32355e8 | −1.44457 | −0.722283 | − | 0.691597i | \(-0.756907\pi\) | ||||
−0.722283 | + | 0.691597i | \(0.756907\pi\) | |||||||
\(308\) | −1.52126e8 | −0.296671 | ||||||||
\(309\) | −2.56265e8 | −0.494122 | ||||||||
\(310\) | −5.11770e8 | −0.975683 | ||||||||
\(311\) | 1.98727e8 | 0.374624 | 0.187312 | − | 0.982300i | \(-0.440022\pi\) | ||||
0.187312 | + | 0.982300i | \(0.440022\pi\) | |||||||
\(312\) | −3.83057e8 | −0.714040 | ||||||||
\(313\) | 2.25644e8 | 0.415929 | 0.207964 | − | 0.978136i | \(-0.433316\pi\) | ||||
0.207964 | + | 0.978136i | \(0.433316\pi\) | |||||||
\(314\) | 1.09512e9 | 1.99622 | ||||||||
\(315\) | −1.14792e7 | −0.0206930 | ||||||||
\(316\) | 6.23453e8 | 1.11147 | ||||||||
\(317\) | 5.60321e8 | 0.987937 | 0.493968 | − | 0.869480i | \(-0.335546\pi\) | ||||
0.493968 | + | 0.869480i | \(0.335546\pi\) | |||||||
\(318\) | 3.55962e8 | 0.620739 | ||||||||
\(319\) | 5.01197e8 | 0.864452 | ||||||||
\(320\) | 3.38117e8 | 0.576822 | ||||||||
\(321\) | −2.07525e8 | −0.350190 | ||||||||
\(322\) | 252053. | 0.000420723 0 | ||||||||
\(323\) | −1.56607e8 | −0.258585 | ||||||||
\(324\) | 1.03956e8 | 0.169802 | ||||||||
\(325\) | −7.97173e8 | −1.28813 | ||||||||
\(326\) | 1.66596e9 | 2.66320 | ||||||||
\(327\) | 3.96079e8 | 0.626419 | ||||||||
\(328\) | −3.60161e8 | −0.563558 | ||||||||
\(329\) | 1.52541e8 | 0.236157 | ||||||||
\(330\) | −2.34680e8 | −0.359482 | ||||||||
\(331\) | 4.88144e7 | 0.0739861 | 0.0369930 | − | 0.999316i | \(-0.488222\pi\) | ||||
0.0369930 | + | 0.999316i | \(0.488222\pi\) | |||||||
\(332\) | −8.68408e8 | −1.30239 | ||||||||
\(333\) | 4.12719e8 | 0.612491 | ||||||||
\(334\) | −1.08905e9 | −1.59932 | ||||||||
\(335\) | 4.25152e8 | 0.617857 | ||||||||
\(336\) | −1.35759e7 | −0.0195246 | ||||||||
\(337\) | −4.98448e8 | −0.709439 | −0.354720 | − | 0.934973i | \(-0.615424\pi\) | ||||
−0.354720 | + | 0.934973i | \(0.615424\pi\) | |||||||
\(338\) | −1.31882e9 | −1.85771 | ||||||||
\(339\) | −4.10916e8 | −0.572867 | ||||||||
\(340\) | 2.02449e8 | 0.279345 | ||||||||
\(341\) | 1.40503e9 | 1.91887 | ||||||||
\(342\) | −1.96276e8 | −0.265324 | ||||||||
\(343\) | −2.58183e8 | −0.345460 | ||||||||
\(344\) | −9.00621e8 | −1.19286 | ||||||||
\(345\) | 235037. | 0.000308155 0 | ||||||||
\(346\) | −1.15058e8 | −0.149331 | ||||||||
\(347\) | 4.64305e8 | 0.596554 | 0.298277 | − | 0.954479i | \(-0.403588\pi\) | ||||
0.298277 | + | 0.954479i | \(0.403588\pi\) | |||||||
\(348\) | −5.41883e8 | −0.689252 | ||||||||
\(349\) | −3.75860e8 | −0.473301 | −0.236651 | − | 0.971595i | \(-0.576050\pi\) | ||||
−0.236651 | + | 0.971595i | \(0.576050\pi\) | |||||||
\(350\) | 1.95724e8 | 0.244009 | ||||||||
\(351\) | 2.29592e8 | 0.283388 | ||||||||
\(352\) | −1.03806e9 | −1.26859 | ||||||||
\(353\) | −6.79230e8 | −0.821874 | −0.410937 | − | 0.911664i | \(-0.634798\pi\) | ||||
−0.410937 | + | 0.911664i | \(0.634798\pi\) | |||||||
\(354\) | 9.97544e7 | 0.119514 | ||||||||
\(355\) | 4.94450e8 | 0.586574 | ||||||||
\(356\) | −2.09727e9 | −2.46366 | ||||||||
\(357\) | −4.49772e7 | −0.0523184 | ||||||||
\(358\) | 2.35912e9 | 2.71743 | ||||||||
\(359\) | 4.73258e8 | 0.539843 | 0.269922 | − | 0.962882i | \(-0.413002\pi\) | ||||
0.269922 | + | 0.962882i | \(0.413002\pi\) | |||||||
\(360\) | 8.77001e7 | 0.0990698 | ||||||||
\(361\) | −6.69868e8 | −0.749400 | ||||||||
\(362\) | 6.11455e8 | 0.677461 | ||||||||
\(363\) | 1.18145e8 | 0.129641 | ||||||||
\(364\) | 3.63250e8 | 0.394776 | ||||||||
\(365\) | −3.62972e8 | −0.390704 | ||||||||
\(366\) | −1.10884e9 | −1.18218 | ||||||||
\(367\) | 1.29401e9 | 1.36649 | 0.683245 | − | 0.730189i | \(-0.260568\pi\) | ||||
0.683245 | + | 0.730189i | \(0.260568\pi\) | |||||||
\(368\) | 277968. | 0.000290755 0 | ||||||||
\(369\) | 2.15869e8 | 0.223665 | ||||||||
\(370\) | 1.00734e9 | 1.03388 | ||||||||
\(371\) | −1.16674e8 | −0.118622 | ||||||||
\(372\) | −1.51909e9 | −1.52997 | ||||||||
\(373\) | −6.91706e8 | −0.690146 | −0.345073 | − | 0.938576i | \(-0.612146\pi\) | ||||
−0.345073 | + | 0.938576i | \(0.612146\pi\) | |||||||
\(374\) | −9.19512e8 | −0.908881 | ||||||||
\(375\) | 3.91148e8 | 0.383029 | ||||||||
\(376\) | −1.16540e9 | −1.13062 | ||||||||
\(377\) | −1.19677e9 | −1.15032 | ||||||||
\(378\) | −5.63701e7 | −0.0536819 | ||||||||
\(379\) | −9.69203e8 | −0.914487 | −0.457243 | − | 0.889342i | \(-0.651163\pi\) | ||||
−0.457243 | + | 0.889342i | \(0.651163\pi\) | |||||||
\(380\) | −2.89575e8 | −0.270719 | ||||||||
\(381\) | 4.03893e8 | 0.374135 | ||||||||
\(382\) | −2.73533e9 | −2.51066 | ||||||||
\(383\) | −1.28084e9 | −1.16493 | −0.582465 | − | 0.812856i | \(-0.697912\pi\) | ||||
−0.582465 | + | 0.812856i | \(0.697912\pi\) | |||||||
\(384\) | 9.25967e8 | 0.834519 | ||||||||
\(385\) | 7.69211e7 | 0.0686962 | ||||||||
\(386\) | −1.03867e8 | −0.0919224 | ||||||||
\(387\) | 5.39803e8 | 0.473421 | ||||||||
\(388\) | −7.93379e8 | −0.689556 | ||||||||
\(389\) | 1.19302e9 | 1.02760 | 0.513802 | − | 0.857909i | \(-0.328237\pi\) | ||||
0.513802 | + | 0.857909i | \(0.328237\pi\) | |||||||
\(390\) | 5.60376e8 | 0.478359 | ||||||||
\(391\) | 920911. | 0.000779111 0 | ||||||||
\(392\) | 9.70834e8 | 0.814036 | ||||||||
\(393\) | −7.62842e8 | −0.633958 | ||||||||
\(394\) | 1.84394e9 | 1.51884 | ||||||||
\(395\) | −3.15244e8 | −0.257369 | ||||||||
\(396\) | −6.96601e8 | −0.563704 | ||||||||
\(397\) | −4.46557e7 | −0.0358187 | −0.0179094 | − | 0.999840i | \(-0.505701\pi\) | ||||
−0.0179094 | + | 0.999840i | \(0.505701\pi\) | |||||||
\(398\) | −1.55070e9 | −1.23293 | ||||||||
\(399\) | 6.43335e7 | 0.0507028 | ||||||||
\(400\) | 2.15847e8 | 0.168631 | ||||||||
\(401\) | 5.52185e8 | 0.427641 | 0.213821 | − | 0.976873i | \(-0.431409\pi\) | ||||
0.213821 | + | 0.976873i | \(0.431409\pi\) | |||||||
\(402\) | 2.08777e9 | 1.60284 | ||||||||
\(403\) | −3.35498e9 | −2.55342 | ||||||||
\(404\) | −2.06096e9 | −1.55501 | ||||||||
\(405\) | −5.25646e7 | −0.0393188 | ||||||||
\(406\) | 2.93835e8 | 0.217903 | ||||||||
\(407\) | −2.76560e9 | −2.03333 | ||||||||
\(408\) | 3.43623e8 | 0.250479 | ||||||||
\(409\) | 8.01492e8 | 0.579252 | 0.289626 | − | 0.957140i | \(-0.406469\pi\) | ||||
0.289626 | + | 0.957140i | \(0.406469\pi\) | |||||||
\(410\) | 5.26881e8 | 0.377546 | ||||||||
\(411\) | 1.20870e9 | 0.858759 | ||||||||
\(412\) | −1.85661e9 | −1.30792 | ||||||||
\(413\) | −3.26965e7 | −0.0228390 | ||||||||
\(414\) | 1.15418e6 | 0.000799416 0 | ||||||||
\(415\) | 4.39104e8 | 0.301577 | ||||||||
\(416\) | 2.47871e9 | 1.68810 | ||||||||
\(417\) | −1.14449e9 | −0.772922 | ||||||||
\(418\) | 1.31523e9 | 0.880815 | ||||||||
\(419\) | −3.06611e8 | −0.203629 | −0.101814 | − | 0.994803i | \(-0.532465\pi\) | ||||
−0.101814 | + | 0.994803i | \(0.532465\pi\) | |||||||
\(420\) | −8.31653e7 | −0.0547734 | ||||||||
\(421\) | 1.08219e9 | 0.706832 | 0.353416 | − | 0.935466i | \(-0.385020\pi\) | ||||
0.353416 | + | 0.935466i | \(0.385020\pi\) | |||||||
\(422\) | −4.44178e8 | −0.287716 | ||||||||
\(423\) | 6.98505e8 | 0.448723 | ||||||||
\(424\) | 8.91379e8 | 0.567913 | ||||||||
\(425\) | 7.15106e8 | 0.451866 | ||||||||
\(426\) | 2.42806e9 | 1.52169 | ||||||||
\(427\) | 3.63444e8 | 0.225912 | ||||||||
\(428\) | −1.50350e9 | −0.926935 | ||||||||
\(429\) | −1.53848e9 | −0.940786 | ||||||||
\(430\) | 1.31752e9 | 0.799132 | ||||||||
\(431\) | 1.67605e9 | 1.00836 | 0.504182 | − | 0.863597i | \(-0.331794\pi\) | ||||
0.504182 | + | 0.863597i | \(0.331794\pi\) | |||||||
\(432\) | −6.21658e7 | −0.0370986 | ||||||||
\(433\) | 2.51807e9 | 1.49060 | 0.745300 | − | 0.666730i | \(-0.232306\pi\) | ||||
0.745300 | + | 0.666730i | \(0.232306\pi\) | |||||||
\(434\) | 8.23725e8 | 0.483691 | ||||||||
\(435\) | 2.73999e8 | 0.159601 | ||||||||
\(436\) | 2.86954e9 | 1.65810 | ||||||||
\(437\) | −1.31723e6 | −0.000755053 0 | ||||||||
\(438\) | −1.78242e9 | −1.01357 | ||||||||
\(439\) | −1.36932e9 | −0.772465 | −0.386232 | − | 0.922402i | \(-0.626224\pi\) | ||||
−0.386232 | + | 0.922402i | \(0.626224\pi\) | |||||||
\(440\) | −5.87671e8 | −0.328889 | ||||||||
\(441\) | −5.81886e8 | −0.323075 | ||||||||
\(442\) | 2.19564e9 | 1.20944 | ||||||||
\(443\) | −3.62914e7 | −0.0198331 | −0.00991656 | − | 0.999951i | \(-0.503157\pi\) | ||||
−0.00991656 | + | 0.999951i | \(0.503157\pi\) | |||||||
\(444\) | 2.99010e9 | 1.62123 | ||||||||
\(445\) | 1.06047e9 | 0.570477 | ||||||||
\(446\) | −8.19052e8 | −0.437159 | ||||||||
\(447\) | −9.35646e8 | −0.495490 | ||||||||
\(448\) | −5.44219e8 | −0.285957 | ||||||||
\(449\) | −2.01372e9 | −1.04987 | −0.524937 | − | 0.851141i | \(-0.675911\pi\) | ||||
−0.524937 | + | 0.851141i | \(0.675911\pi\) | |||||||
\(450\) | 8.96245e8 | 0.463642 | ||||||||
\(451\) | −1.44652e9 | −0.742517 | ||||||||
\(452\) | −2.97703e9 | −1.51635 | ||||||||
\(453\) | −2.07240e9 | −1.04744 | ||||||||
\(454\) | 4.61214e9 | 2.31317 | ||||||||
\(455\) | −1.83675e8 | −0.0914133 | ||||||||
\(456\) | −4.91503e8 | −0.242744 | ||||||||
\(457\) | −1.10905e8 | −0.0543554 | −0.0271777 | − | 0.999631i | \(-0.508652\pi\) | ||||
−0.0271777 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(458\) | 6.20104e9 | 3.01603 | ||||||||
\(459\) | −2.05956e8 | −0.0994101 | ||||||||
\(460\) | 1.70281e6 | 0.000815671 0 | ||||||||
\(461\) | 3.59226e9 | 1.70771 | 0.853856 | − | 0.520510i | \(-0.174258\pi\) | ||||
0.853856 | + | 0.520510i | \(0.174258\pi\) | |||||||
\(462\) | 3.77731e8 | 0.178212 | ||||||||
\(463\) | −2.38603e9 | −1.11723 | −0.558614 | − | 0.829427i | \(-0.688667\pi\) | ||||
−0.558614 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(464\) | 3.24046e8 | 0.150589 | ||||||||
\(465\) | 7.68115e8 | 0.354275 | ||||||||
\(466\) | 2.60424e9 | 1.19215 | ||||||||
\(467\) | 1.97044e9 | 0.895271 | 0.447636 | − | 0.894216i | \(-0.352266\pi\) | ||||
0.447636 | + | 0.894216i | \(0.352266\pi\) | |||||||
\(468\) | 1.66337e9 | 0.750115 | ||||||||
\(469\) | −6.84308e8 | −0.306300 | ||||||||
\(470\) | 1.70487e9 | 0.757442 | ||||||||
\(471\) | −1.64366e9 | −0.724836 | ||||||||
\(472\) | 2.49799e8 | 0.109344 | ||||||||
\(473\) | −3.61718e9 | −1.57165 | ||||||||
\(474\) | −1.54805e9 | −0.667667 | ||||||||
\(475\) | −1.02286e9 | −0.437913 | ||||||||
\(476\) | −3.25855e8 | −0.138484 | ||||||||
\(477\) | −5.34264e8 | −0.225394 | ||||||||
\(478\) | 4.42428e9 | 1.85287 | ||||||||
\(479\) | 4.56276e9 | 1.89694 | 0.948469 | − | 0.316869i | \(-0.102632\pi\) | ||||
0.948469 | + | 0.316869i | \(0.102632\pi\) | |||||||
\(480\) | −5.67494e8 | −0.234216 | ||||||||
\(481\) | 6.60378e9 | 2.70573 | ||||||||
\(482\) | −4.57639e9 | −1.86148 | ||||||||
\(483\) | −378306. | −0.000152767 0 | ||||||||
\(484\) | 8.55949e8 | 0.343154 | ||||||||
\(485\) | 4.01166e8 | 0.159672 | ||||||||
\(486\) | −2.58126e8 | −0.102001 | ||||||||
\(487\) | 2.91958e9 | 1.14543 | 0.572715 | − | 0.819754i | \(-0.305890\pi\) | ||||
0.572715 | + | 0.819754i | \(0.305890\pi\) | |||||||
\(488\) | −2.77668e9 | −1.08158 | ||||||||
\(489\) | −2.50044e9 | −0.967021 | ||||||||
\(490\) | −1.42024e9 | −0.545349 | ||||||||
\(491\) | −8.15321e8 | −0.310845 | −0.155422 | − | 0.987848i | \(-0.549674\pi\) | ||||
−0.155422 | + | 0.987848i | \(0.549674\pi\) | |||||||
\(492\) | 1.56394e9 | 0.592030 | ||||||||
\(493\) | 1.07357e9 | 0.403521 | ||||||||
\(494\) | −3.14055e9 | −1.17209 | ||||||||
\(495\) | 3.52231e8 | 0.130530 | ||||||||
\(496\) | 9.08415e8 | 0.334271 | ||||||||
\(497\) | −7.95847e8 | −0.290792 | ||||||||
\(498\) | 2.15628e9 | 0.782352 | ||||||||
\(499\) | −3.24554e9 | −1.16932 | −0.584662 | − | 0.811277i | \(-0.698773\pi\) | ||||
−0.584662 | + | 0.811277i | \(0.698773\pi\) | |||||||
\(500\) | 2.83382e9 | 1.01386 | ||||||||
\(501\) | 1.63455e9 | 0.580720 | ||||||||
\(502\) | −5.84959e9 | −2.06378 | ||||||||
\(503\) | −4.45372e9 | −1.56040 | −0.780198 | − | 0.625532i | \(-0.784882\pi\) | ||||
−0.780198 | + | 0.625532i | \(0.784882\pi\) | |||||||
\(504\) | −1.41159e8 | −0.0491134 | ||||||||
\(505\) | 1.04211e9 | 0.360075 | ||||||||
\(506\) | −7.73407e6 | −0.00265388 | ||||||||
\(507\) | 1.97942e9 | 0.674542 | ||||||||
\(508\) | 2.92615e9 | 0.990317 | ||||||||
\(509\) | 4.82014e9 | 1.62012 | 0.810060 | − | 0.586347i | \(-0.199435\pi\) | ||||
0.810060 | + | 0.586347i | \(0.199435\pi\) | |||||||
\(510\) | −5.02687e8 | −0.167804 | ||||||||
\(511\) | 5.84226e8 | 0.193690 | ||||||||
\(512\) | −1.16285e9 | −0.382896 | ||||||||
\(513\) | 2.94591e8 | 0.0963404 | ||||||||
\(514\) | −4.58690e9 | −1.48987 | ||||||||
\(515\) | 9.38779e8 | 0.302857 | ||||||||
\(516\) | 3.91081e9 | 1.25312 | ||||||||
\(517\) | −4.68062e9 | −1.48966 | ||||||||
\(518\) | −1.62138e9 | −0.512543 | ||||||||
\(519\) | 1.72690e8 | 0.0542228 | ||||||||
\(520\) | 1.40326e9 | 0.437649 | ||||||||
\(521\) | −3.16646e9 | −0.980939 | −0.490469 | − | 0.871458i | \(-0.663175\pi\) | ||||
−0.490469 | + | 0.871458i | \(0.663175\pi\) | |||||||
\(522\) | 1.34551e9 | 0.414037 | ||||||||
\(523\) | −1.33084e9 | −0.406790 | −0.203395 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203395 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(524\) | −5.52670e9 | −1.67806 | ||||||||
\(525\) | −2.93762e8 | −0.0886010 | ||||||||
\(526\) | −7.54467e9 | −2.26042 | ||||||||
\(527\) | 3.00960e9 | 0.895717 | ||||||||
\(528\) | 4.16568e8 | 0.123159 | ||||||||
\(529\) | −3.40482e9 | −0.999998 | ||||||||
\(530\) | −1.30400e9 | −0.380463 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | 4.66088e8 | 0.134208 | ||||||||
\(533\) | 3.45405e9 | 0.988059 | ||||||||
\(534\) | 5.20758e9 | 1.47993 | ||||||||
\(535\) | 7.60231e8 | 0.214638 | ||||||||
\(536\) | 5.22806e9 | 1.46644 | ||||||||
\(537\) | −3.54080e9 | −0.986713 | ||||||||
\(538\) | 7.47128e9 | 2.06851 | ||||||||
\(539\) | 3.89917e9 | 1.07254 | ||||||||
\(540\) | −3.80824e8 | −0.104075 | ||||||||
\(541\) | 2.45311e8 | 0.0666081 | 0.0333040 | − | 0.999445i | \(-0.489397\pi\) | ||||
0.0333040 | + | 0.999445i | \(0.489397\pi\) | |||||||
\(542\) | 9.91139e8 | 0.267385 | ||||||||
\(543\) | −9.17732e8 | −0.245990 | ||||||||
\(544\) | −2.22353e9 | −0.592171 | ||||||||
\(545\) | −1.45096e9 | −0.383944 | ||||||||
\(546\) | −9.01959e8 | −0.237144 | ||||||||
\(547\) | 1.35454e9 | 0.353865 | 0.176933 | − | 0.984223i | \(-0.443383\pi\) | ||||
0.176933 | + | 0.984223i | \(0.443383\pi\) | |||||||
\(548\) | 8.75687e9 | 2.27309 | ||||||||
\(549\) | 1.66425e9 | 0.429256 | ||||||||
\(550\) | −6.00566e9 | −1.53919 | ||||||||
\(551\) | −1.53559e9 | −0.391061 | ||||||||
\(552\) | 2.89023e6 | 0.000731384 0 | ||||||||
\(553\) | 5.07404e8 | 0.127590 | ||||||||
\(554\) | 3.89617e9 | 0.973540 | ||||||||
\(555\) | −1.51192e9 | −0.375408 | ||||||||
\(556\) | −8.29169e9 | −2.04589 | ||||||||
\(557\) | −2.79389e9 | −0.685041 | −0.342520 | − | 0.939510i | \(-0.611281\pi\) | ||||
−0.342520 | + | 0.939510i | \(0.611281\pi\) | |||||||
\(558\) | 3.77194e9 | 0.919061 | ||||||||
\(559\) | 8.63721e9 | 2.09138 | ||||||||
\(560\) | 4.97329e7 | 0.0119670 | ||||||||
\(561\) | 1.38010e9 | 0.330019 | ||||||||
\(562\) | 2.34933e9 | 0.558298 | ||||||||
\(563\) | 1.29186e9 | 0.305095 | 0.152548 | − | 0.988296i | \(-0.451252\pi\) | ||||
0.152548 | + | 0.988296i | \(0.451252\pi\) | |||||||
\(564\) | 5.06058e9 | 1.18775 | ||||||||
\(565\) | 1.50531e9 | 0.351121 | ||||||||
\(566\) | −7.26315e9 | −1.68371 | ||||||||
\(567\) | 8.46059e7 | 0.0194922 | ||||||||
\(568\) | 6.08021e9 | 1.39219 | ||||||||
\(569\) | 2.83891e9 | 0.646040 | 0.323020 | − | 0.946392i | \(-0.395302\pi\) | ||||
0.323020 | + | 0.946392i | \(0.395302\pi\) | |||||||
\(570\) | 7.19022e8 | 0.162622 | ||||||||
\(571\) | −2.52009e9 | −0.566487 | −0.283243 | − | 0.959048i | \(-0.591410\pi\) | ||||
−0.283243 | + | 0.959048i | \(0.591410\pi\) | |||||||
\(572\) | −1.11461e10 | −2.49021 | ||||||||
\(573\) | 4.10545e9 | 0.911632 | ||||||||
\(574\) | −8.48048e8 | −0.187167 | ||||||||
\(575\) | 6.01480e6 | 0.00131942 | ||||||||
\(576\) | −2.49205e9 | −0.543347 | ||||||||
\(577\) | −7.41099e9 | −1.60606 | −0.803028 | − | 0.595941i | \(-0.796779\pi\) | ||||
−0.803028 | + | 0.595941i | \(0.796779\pi\) | |||||||
\(578\) | 5.41206e9 | 1.16578 | ||||||||
\(579\) | 1.55894e8 | 0.0333775 | ||||||||
\(580\) | 1.98509e9 | 0.422456 | ||||||||
\(581\) | −7.06764e8 | −0.149506 | ||||||||
\(582\) | 1.96998e9 | 0.414220 | ||||||||
\(583\) | 3.58006e9 | 0.748256 | ||||||||
\(584\) | −4.46344e9 | −0.927309 | ||||||||
\(585\) | −8.41068e8 | −0.173694 | ||||||||
\(586\) | −2.89987e9 | −0.595301 | ||||||||
\(587\) | −2.54336e9 | −0.519008 | −0.259504 | − | 0.965742i | \(-0.583559\pi\) | ||||
−0.259504 | + | 0.965742i | \(0.583559\pi\) | |||||||
\(588\) | −4.21570e9 | −0.855163 | ||||||||
\(589\) | −4.30480e9 | −0.868058 | ||||||||
\(590\) | −3.65432e8 | −0.0732528 | ||||||||
\(591\) | −2.76758e9 | −0.551497 | ||||||||
\(592\) | −1.78808e9 | −0.354210 | ||||||||
\(593\) | 9.16399e9 | 1.80465 | 0.902326 | − | 0.431055i | \(-0.141858\pi\) | ||||
0.902326 | + | 0.431055i | \(0.141858\pi\) | |||||||
\(594\) | 1.72968e9 | 0.338620 | ||||||||
\(595\) | 1.64766e8 | 0.0320670 | ||||||||
\(596\) | −6.77864e9 | −1.31154 | ||||||||
\(597\) | 2.32745e9 | 0.447682 | ||||||||
\(598\) | 1.84677e7 | 0.00353149 | ||||||||
\(599\) | −5.47291e9 | −1.04046 | −0.520229 | − | 0.854027i | \(-0.674153\pi\) | ||||
−0.520229 | + | 0.854027i | \(0.674153\pi\) | |||||||
\(600\) | 2.24432e9 | 0.424185 | ||||||||
\(601\) | −4.19336e9 | −0.787955 | −0.393977 | − | 0.919120i | \(-0.628901\pi\) | ||||
−0.393977 | + | 0.919120i | \(0.628901\pi\) | |||||||
\(602\) | −2.12063e9 | −0.396167 | ||||||||
\(603\) | −3.13353e9 | −0.582001 | ||||||||
\(604\) | −1.50143e10 | −2.77252 | ||||||||
\(605\) | −4.32804e8 | −0.0794598 | ||||||||
\(606\) | 5.11741e9 | 0.934106 | ||||||||
\(607\) | 6.57768e9 | 1.19375 | 0.596874 | − | 0.802335i | \(-0.296409\pi\) | ||||
0.596874 | + | 0.802335i | \(0.296409\pi\) | |||||||
\(608\) | 3.18044e9 | 0.573885 | ||||||||
\(609\) | −4.41018e8 | −0.0791216 | ||||||||
\(610\) | 4.06202e9 | 0.724582 | ||||||||
\(611\) | 1.11765e10 | 1.98227 | ||||||||
\(612\) | −1.49213e9 | −0.263133 | ||||||||
\(613\) | −7.04485e9 | −1.23527 | −0.617633 | − | 0.786467i | \(-0.711908\pi\) | ||||
−0.617633 | + | 0.786467i | \(0.711908\pi\) | |||||||
\(614\) | 1.31745e10 | 2.29691 | ||||||||
\(615\) | −7.90796e8 | −0.137089 | ||||||||
\(616\) | 9.45892e8 | 0.163046 | ||||||||
\(617\) | −4.68870e9 | −0.803627 | −0.401813 | − | 0.915722i | \(-0.631620\pi\) | ||||
−0.401813 | + | 0.915722i | \(0.631620\pi\) | |||||||
\(618\) | 4.61000e9 | 0.785672 | ||||||||
\(619\) | −6.66470e9 | −1.12944 | −0.564720 | − | 0.825282i | \(-0.691016\pi\) | ||||
−0.564720 | + | 0.825282i | \(0.691016\pi\) | |||||||
\(620\) | 5.56490e9 | 0.937749 | ||||||||
\(621\) | −1.73231e6 | −0.000290272 0 | ||||||||
\(622\) | −3.57495e9 | −0.595667 | ||||||||
\(623\) | −1.70689e9 | −0.282812 | ||||||||
\(624\) | −9.94693e8 | −0.163887 | ||||||||
\(625\) | 3.90631e9 | 0.640010 | ||||||||
\(626\) | −4.05916e9 | −0.661342 | ||||||||
\(627\) | −1.97403e9 | −0.319828 | ||||||||
\(628\) | −1.19081e10 | −1.91860 | ||||||||
\(629\) | −5.92394e9 | −0.949147 | ||||||||
\(630\) | 2.06502e8 | 0.0329027 | ||||||||
\(631\) | 6.09161e8 | 0.0965227 | 0.0482614 | − | 0.998835i | \(-0.484632\pi\) | ||||
0.0482614 | + | 0.998835i | \(0.484632\pi\) | |||||||
\(632\) | −3.87653e9 | −0.610848 | ||||||||
\(633\) | 6.66667e8 | 0.104471 | ||||||||
\(634\) | −1.00797e10 | −1.57086 | ||||||||
\(635\) | −1.47959e9 | −0.229315 | ||||||||
\(636\) | −3.87068e9 | −0.596605 | ||||||||
\(637\) | −9.31057e9 | −1.42721 | ||||||||
\(638\) | −9.01614e9 | −1.37451 | ||||||||
\(639\) | −3.64428e9 | −0.552534 | ||||||||
\(640\) | −3.39211e9 | −0.511493 | ||||||||
\(641\) | −3.31465e7 | −0.00497089 | −0.00248545 | − | 0.999997i | \(-0.500791\pi\) | ||||
−0.00248545 | + | 0.999997i | \(0.500791\pi\) | |||||||
\(642\) | 3.73322e9 | 0.556815 | ||||||||
\(643\) | −4.47226e9 | −0.663421 | −0.331710 | − | 0.943381i | \(-0.607626\pi\) | ||||
−0.331710 | + | 0.943381i | \(0.607626\pi\) | |||||||
\(644\) | −2.74078e6 | −0.000404366 0 | ||||||||
\(645\) | −1.97747e9 | −0.290169 | ||||||||
\(646\) | 2.81724e9 | 0.411159 | ||||||||
\(647\) | −4.33561e9 | −0.629340 | −0.314670 | − | 0.949201i | \(-0.601894\pi\) | ||||
−0.314670 | + | 0.949201i | \(0.601894\pi\) | |||||||
\(648\) | −6.46382e8 | −0.0933205 | ||||||||
\(649\) | 1.00327e9 | 0.144066 | ||||||||
\(650\) | 1.43405e10 | 2.04818 | ||||||||
\(651\) | −1.23633e9 | −0.175631 | ||||||||
\(652\) | −1.81154e10 | −2.55966 | ||||||||
\(653\) | −5.43227e9 | −0.763458 | −0.381729 | − | 0.924274i | \(-0.624671\pi\) | ||||
−0.381729 | + | 0.924274i | \(0.624671\pi\) | |||||||
\(654\) | −7.12515e9 | −0.996029 | ||||||||
\(655\) | 2.79453e9 | 0.388566 | ||||||||
\(656\) | −9.35239e8 | −0.129348 | ||||||||
\(657\) | 2.67524e9 | 0.368031 | ||||||||
\(658\) | −2.74410e9 | −0.375499 | ||||||||
\(659\) | 5.26358e9 | 0.716444 | 0.358222 | − | 0.933636i | \(-0.383383\pi\) | ||||
0.358222 | + | 0.933636i | \(0.383383\pi\) | |||||||
\(660\) | 2.55187e9 | 0.345505 | ||||||||
\(661\) | 1.51100e9 | 0.203497 | 0.101749 | − | 0.994810i | \(-0.467556\pi\) | ||||
0.101749 | + | 0.994810i | \(0.467556\pi\) | |||||||
\(662\) | −8.78133e8 | −0.117641 | ||||||||
\(663\) | −3.29544e9 | −0.439153 | ||||||||
\(664\) | 5.39962e9 | 0.715772 | ||||||||
\(665\) | −2.35674e8 | −0.0310768 | ||||||||
\(666\) | −7.42449e9 | −0.973884 | ||||||||
\(667\) | 9.02986e6 | 0.00117826 | ||||||||
\(668\) | 1.18421e10 | 1.53714 | ||||||||
\(669\) | 1.22931e9 | 0.158735 | ||||||||
\(670\) | −7.64816e9 | −0.982415 | ||||||||
\(671\) | −1.11520e10 | −1.42503 | ||||||||
\(672\) | 9.13416e8 | 0.116112 | ||||||||
\(673\) | 4.92429e8 | 0.0622717 | 0.0311359 | − | 0.999515i | \(-0.490088\pi\) | ||||
0.0311359 | + | 0.999515i | \(0.490088\pi\) | |||||||
\(674\) | 8.96668e9 | 1.12803 | ||||||||
\(675\) | −1.34517e9 | −0.168351 | ||||||||
\(676\) | 1.43406e10 | 1.78548 | ||||||||
\(677\) | 1.38348e10 | 1.71361 | 0.856805 | − | 0.515640i | \(-0.172446\pi\) | ||||
0.856805 | + | 0.515640i | \(0.172446\pi\) | |||||||
\(678\) | 7.39205e9 | 0.910879 | ||||||||
\(679\) | −6.45701e8 | −0.0791566 | ||||||||
\(680\) | −1.25880e9 | −0.153523 | ||||||||
\(681\) | −6.92236e9 | −0.839923 | ||||||||
\(682\) | −2.52754e10 | −3.05108 | ||||||||
\(683\) | 8.01482e8 | 0.0962545 | 0.0481273 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481273 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(684\) | 2.13428e9 | 0.255008 | ||||||||
\(685\) | −4.42784e9 | −0.526350 | ||||||||
\(686\) | 4.64450e9 | 0.549294 | ||||||||
\(687\) | −9.30714e9 | −1.09513 | ||||||||
\(688\) | −2.33866e9 | −0.273784 | ||||||||
\(689\) | −8.54858e9 | −0.995696 | ||||||||
\(690\) | −4.22813e6 | −0.000489978 0 | ||||||||
\(691\) | −2.59241e9 | −0.298903 | −0.149452 | − | 0.988769i | \(-0.547751\pi\) | ||||
−0.149452 | + | 0.988769i | \(0.547751\pi\) | |||||||
\(692\) | 1.25112e9 | 0.143525 | ||||||||
\(693\) | −5.66937e8 | −0.0647096 | ||||||||
\(694\) | −8.35247e9 | −0.948543 | ||||||||
\(695\) | 4.19263e9 | 0.473739 | ||||||||
\(696\) | 3.36934e9 | 0.378802 | ||||||||
\(697\) | −3.09846e9 | −0.346602 | ||||||||
\(698\) | 6.76143e9 | 0.752566 | ||||||||
\(699\) | −3.90871e9 | −0.432876 | ||||||||
\(700\) | −2.12827e9 | −0.234522 | ||||||||
\(701\) | 1.40491e10 | 1.54040 | 0.770201 | − | 0.637801i | \(-0.220156\pi\) | ||||
0.770201 | + | 0.637801i | \(0.220156\pi\) | |||||||
\(702\) | −4.13018e9 | −0.450598 | ||||||||
\(703\) | 8.47335e9 | 0.919838 | ||||||||
\(704\) | 1.66990e10 | 1.80379 | ||||||||
\(705\) | −2.55884e9 | −0.275031 | ||||||||
\(706\) | 1.22188e10 | 1.30681 | ||||||||
\(707\) | −1.67733e9 | −0.178506 | ||||||||
\(708\) | −1.08471e9 | −0.114868 | ||||||||
\(709\) | −9.39937e9 | −0.990460 | −0.495230 | − | 0.868762i | \(-0.664916\pi\) | ||||
−0.495230 | + | 0.868762i | \(0.664916\pi\) | |||||||
\(710\) | −8.89476e9 | −0.932675 | ||||||||
\(711\) | 2.32346e9 | 0.242433 | ||||||||
\(712\) | 1.30405e10 | 1.35399 | ||||||||
\(713\) | 2.53139e7 | 0.00261544 | ||||||||
\(714\) | 8.09105e8 | 0.0831881 | ||||||||
\(715\) | 5.63593e9 | 0.576626 | ||||||||
\(716\) | −2.56526e10 | −2.61178 | ||||||||
\(717\) | −6.64040e9 | −0.672786 | ||||||||
\(718\) | −8.51354e9 | −0.858371 | ||||||||
\(719\) | 1.11397e10 | 1.11769 | 0.558846 | − | 0.829272i | \(-0.311244\pi\) | ||||
0.558846 | + | 0.829272i | \(0.311244\pi\) | |||||||
\(720\) | 2.27733e8 | 0.0227385 | ||||||||
\(721\) | −1.51102e9 | −0.150140 | ||||||||
\(722\) | 1.20504e10 | 1.19157 | ||||||||
\(723\) | 6.86870e9 | 0.675912 | ||||||||
\(724\) | −6.64886e9 | −0.651122 | ||||||||
\(725\) | 7.01187e9 | 0.683362 | ||||||||
\(726\) | −2.12534e9 | −0.206134 | ||||||||
\(727\) | −9.70625e9 | −0.936874 | −0.468437 | − | 0.883497i | \(-0.655183\pi\) | ||||
−0.468437 | + | 0.883497i | \(0.655183\pi\) | |||||||
\(728\) | −2.25863e9 | −0.216963 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 6.52958e9 | 0.621234 | ||||||||
\(731\) | −7.74803e9 | −0.733636 | ||||||||
\(732\) | 1.20573e10 | 1.13622 | ||||||||
\(733\) | 4.02746e9 | 0.377718 | 0.188859 | − | 0.982004i | \(-0.439521\pi\) | ||||
0.188859 | + | 0.982004i | \(0.439521\pi\) | |||||||
\(734\) | −2.32782e10 | −2.17277 | ||||||||
\(735\) | 2.13163e9 | 0.198019 | ||||||||
\(736\) | −1.87022e7 | −0.00172911 | ||||||||
\(737\) | 2.09975e10 | 1.93211 | ||||||||
\(738\) | −3.88331e9 | −0.355635 | ||||||||
\(739\) | 1.14088e10 | 1.03989 | 0.519943 | − | 0.854201i | \(-0.325953\pi\) | ||||
0.519943 | + | 0.854201i | \(0.325953\pi\) | |||||||
\(740\) | −1.09537e10 | −0.993686 | ||||||||
\(741\) | 4.71365e9 | 0.425592 | ||||||||
\(742\) | 2.09887e9 | 0.188613 | ||||||||
\(743\) | −3.48068e9 | −0.311317 | −0.155659 | − | 0.987811i | \(-0.549750\pi\) | ||||
−0.155659 | + | 0.987811i | \(0.549750\pi\) | |||||||
\(744\) | 9.44545e9 | 0.840848 | ||||||||
\(745\) | 3.42757e9 | 0.303696 | ||||||||
\(746\) | 1.24432e10 | 1.09736 | ||||||||
\(747\) | −3.23636e9 | −0.284076 | ||||||||
\(748\) | 9.99863e9 | 0.873544 | ||||||||
\(749\) | −1.22364e9 | −0.106406 | ||||||||
\(750\) | −7.03645e9 | −0.609031 | ||||||||
\(751\) | −1.06375e10 | −0.916433 | −0.458217 | − | 0.888841i | \(-0.651512\pi\) | ||||
−0.458217 | + | 0.888841i | \(0.651512\pi\) | |||||||
\(752\) | −3.02623e9 | −0.259501 | ||||||||
\(753\) | 8.77965e9 | 0.749367 | ||||||||
\(754\) | 2.15290e10 | 1.82905 | ||||||||
\(755\) | 7.59185e9 | 0.641997 | ||||||||
\(756\) | 6.12959e8 | 0.0515947 | ||||||||
\(757\) | 2.08009e10 | 1.74279 | 0.871397 | − | 0.490578i | \(-0.163214\pi\) | ||||
0.871397 | + | 0.490578i | \(0.163214\pi\) | |||||||
\(758\) | 1.74352e10 | 1.45407 | ||||||||
\(759\) | 1.16081e7 | 0.000963637 0 | ||||||||
\(760\) | 1.80053e9 | 0.148783 | ||||||||
\(761\) | 1.33150e9 | 0.109521 | 0.0547604 | − | 0.998500i | \(-0.482561\pi\) | ||||
0.0547604 | + | 0.998500i | \(0.482561\pi\) | |||||||
\(762\) | −7.26571e9 | −0.594889 | ||||||||
\(763\) | 2.33541e9 | 0.190339 | ||||||||
\(764\) | 2.97435e10 | 2.41304 | ||||||||
\(765\) | 7.54483e8 | 0.0609304 | ||||||||
\(766\) | 2.30413e10 | 1.85228 | ||||||||
\(767\) | −2.39564e9 | −0.191707 | ||||||||
\(768\) | −4.84328e9 | −0.385811 | ||||||||
\(769\) | −2.19213e10 | −1.73830 | −0.869148 | − | 0.494553i | \(-0.835332\pi\) | ||||
−0.869148 | + | 0.494553i | \(0.835332\pi\) | |||||||
\(770\) | −1.38375e9 | −0.109230 | ||||||||
\(771\) | 6.88448e9 | 0.540979 | ||||||||
\(772\) | 1.12943e9 | 0.0883485 | ||||||||
\(773\) | 3.83517e9 | 0.298646 | 0.149323 | − | 0.988788i | \(-0.452291\pi\) | ||||
0.149323 | + | 0.988788i | \(0.452291\pi\) | |||||||
\(774\) | −9.71064e9 | −0.752756 | ||||||||
\(775\) | 1.96567e10 | 1.51690 | ||||||||
\(776\) | 4.93310e9 | 0.378969 | ||||||||
\(777\) | 2.43353e9 | 0.186107 | ||||||||
\(778\) | −2.14616e10 | −1.63393 | ||||||||
\(779\) | 4.43191e9 | 0.335900 | ||||||||
\(780\) | −6.09344e9 | −0.459760 | ||||||||
\(781\) | 2.44200e10 | 1.83429 | ||||||||
\(782\) | −1.65665e7 | −0.00123881 | ||||||||
\(783\) | −2.01947e9 | −0.150339 | ||||||||
\(784\) | 2.52099e9 | 0.186838 | ||||||||
\(785\) | 6.02126e9 | 0.444266 | ||||||||
\(786\) | 1.37229e10 | 1.00802 | ||||||||
\(787\) | 1.79274e10 | 1.31101 | 0.655504 | − | 0.755192i | \(-0.272456\pi\) | ||||
0.655504 | + | 0.755192i | \(0.272456\pi\) | |||||||
\(788\) | −2.00508e10 | −1.45979 | ||||||||
\(789\) | 1.13238e10 | 0.820771 | ||||||||
\(790\) | 5.67099e9 | 0.409227 | ||||||||
\(791\) | −2.42289e9 | −0.174067 | ||||||||
\(792\) | 4.33135e9 | 0.309803 | ||||||||
\(793\) | 2.66292e10 | 1.89627 | ||||||||
\(794\) | 8.03321e8 | 0.0569531 | ||||||||
\(795\) | 1.95718e9 | 0.138148 | ||||||||
\(796\) | 1.68621e10 | 1.18499 | ||||||||
\(797\) | −5.47185e9 | −0.382851 | −0.191426 | − | 0.981507i | \(-0.561311\pi\) | ||||
−0.191426 | + | 0.981507i | \(0.561311\pi\) | |||||||
\(798\) | −1.15731e9 | −0.0806193 | ||||||||
\(799\) | −1.00259e10 | −0.695363 | ||||||||
\(800\) | −1.45227e10 | −1.00284 | ||||||||
\(801\) | −7.81606e9 | −0.537371 | ||||||||
\(802\) | −9.93338e9 | −0.679965 | ||||||||
\(803\) | −1.79266e10 | −1.22178 | ||||||||
\(804\) | −2.27021e10 | −1.54053 | ||||||||
\(805\) | 1.38586e6 | 9.36337e−5 0 | ||||||||
\(806\) | 6.03535e10 | 4.06003 | ||||||||
\(807\) | −1.12136e10 | −0.751086 | ||||||||
\(808\) | 1.28147e10 | 0.854612 | ||||||||
\(809\) | 2.20226e9 | 0.146234 | 0.0731171 | − | 0.997323i | \(-0.476705\pi\) | ||||
0.0731171 | + | 0.997323i | \(0.476705\pi\) | |||||||
\(810\) | 9.45595e8 | 0.0625184 | ||||||||
\(811\) | −5.11433e9 | −0.336679 | −0.168339 | − | 0.985729i | \(-0.553840\pi\) | ||||
−0.168339 | + | 0.985729i | \(0.553840\pi\) | |||||||
\(812\) | −3.19512e9 | −0.209431 | ||||||||
\(813\) | −1.48760e9 | −0.0970889 | ||||||||
\(814\) | 4.97509e10 | 3.23307 | ||||||||
\(815\) | 9.15991e9 | 0.592707 | ||||||||
\(816\) | 8.92293e8 | 0.0574899 | ||||||||
\(817\) | 1.10825e10 | 0.710982 | ||||||||
\(818\) | −1.44182e10 | −0.921032 | ||||||||
\(819\) | 1.35375e9 | 0.0861083 | ||||||||
\(820\) | −5.72922e9 | −0.362867 | ||||||||
\(821\) | −4.81471e9 | −0.303647 | −0.151824 | − | 0.988408i | \(-0.548515\pi\) | ||||
−0.151824 | + | 0.988408i | \(0.548515\pi\) | |||||||
\(822\) | −2.17435e10 | −1.36546 | ||||||||
\(823\) | −2.90096e10 | −1.81402 | −0.907011 | − | 0.421107i | \(-0.861642\pi\) | ||||
−0.907011 | + | 0.421107i | \(0.861642\pi\) | |||||||
\(824\) | 1.15441e10 | 0.718810 | ||||||||
\(825\) | 9.01390e9 | 0.558887 | ||||||||
\(826\) | 5.88185e8 | 0.0363148 | ||||||||
\(827\) | 5.95215e9 | 0.365936 | 0.182968 | − | 0.983119i | \(-0.441430\pi\) | ||||
0.182968 | + | 0.983119i | \(0.441430\pi\) | |||||||
\(828\) | −1.25504e7 | −0.000768335 0 | ||||||||
\(829\) | 1.00332e10 | 0.611643 | 0.305821 | − | 0.952089i | \(-0.401069\pi\) | ||||
0.305821 | + | 0.952089i | \(0.401069\pi\) | |||||||
\(830\) | −7.89913e9 | −0.479519 | ||||||||
\(831\) | −5.84776e9 | −0.353497 | ||||||||
\(832\) | −3.98744e10 | −2.40028 | ||||||||
\(833\) | 8.35207e9 | 0.500653 | ||||||||
\(834\) | 2.05885e10 | 1.22897 | ||||||||
\(835\) | −5.98788e9 | −0.355935 | ||||||||
\(836\) | −1.43016e10 | −0.846570 | ||||||||
\(837\) | −5.66130e9 | −0.333716 | ||||||||
\(838\) | 5.51569e9 | 0.323777 | ||||||||
\(839\) | 7.75973e9 | 0.453607 | 0.226803 | − | 0.973941i | \(-0.427173\pi\) | ||||
0.226803 | + | 0.973941i | \(0.427173\pi\) | |||||||
\(840\) | 5.17108e8 | 0.0301026 | ||||||||
\(841\) | −6.72315e9 | −0.389751 | ||||||||
\(842\) | −1.94677e10 | −1.12389 | ||||||||
\(843\) | −3.52610e9 | −0.202721 | ||||||||
\(844\) | 4.82992e9 | 0.276529 | ||||||||
\(845\) | −7.25123e9 | −0.413441 | ||||||||
\(846\) | −1.25655e10 | −0.713485 | ||||||||
\(847\) | 6.96624e8 | 0.0393919 | ||||||||
\(848\) | 2.31466e9 | 0.130347 | ||||||||
\(849\) | 1.09013e10 | 0.611364 | ||||||||
\(850\) | −1.28642e10 | −0.718483 | ||||||||
\(851\) | −4.98266e7 | −0.00277146 | ||||||||
\(852\) | −2.64024e10 | −1.46253 | ||||||||
\(853\) | 3.15852e10 | 1.74246 | 0.871229 | − | 0.490877i | \(-0.163324\pi\) | ||||
0.871229 | + | 0.490877i | \(0.163324\pi\) | |||||||
\(854\) | −6.53807e9 | −0.359209 | ||||||||
\(855\) | −1.07918e9 | −0.0590490 | ||||||||
\(856\) | 9.34849e9 | 0.509429 | ||||||||
\(857\) | −1.81369e10 | −0.984304 | −0.492152 | − | 0.870509i | \(-0.663790\pi\) | ||||
−0.492152 | + | 0.870509i | \(0.663790\pi\) | |||||||
\(858\) | 2.76760e10 | 1.49588 | ||||||||
\(859\) | 2.80979e10 | 1.51251 | 0.756253 | − | 0.654279i | \(-0.227028\pi\) | ||||
0.756253 | + | 0.654279i | \(0.227028\pi\) | |||||||
\(860\) | −1.43265e10 | −0.768062 | ||||||||
\(861\) | 1.27283e9 | 0.0679612 | ||||||||
\(862\) | −3.01509e10 | −1.60334 | ||||||||
\(863\) | −1.12434e10 | −0.595467 | −0.297734 | − | 0.954649i | \(-0.596231\pi\) | ||||
−0.297734 | + | 0.954649i | \(0.596231\pi\) | |||||||
\(864\) | 4.18264e9 | 0.220624 | ||||||||
\(865\) | −6.32618e8 | −0.0332342 | ||||||||
\(866\) | −4.52982e10 | −2.37011 | ||||||||
\(867\) | −8.12296e9 | −0.423299 | ||||||||
\(868\) | −8.95705e9 | −0.464885 | ||||||||
\(869\) | −1.55693e10 | −0.804824 | ||||||||
\(870\) | −4.92902e9 | −0.253772 | ||||||||
\(871\) | −5.01386e10 | −2.57104 | ||||||||
\(872\) | −1.78424e10 | −0.911265 | ||||||||
\(873\) | −2.95674e9 | −0.150405 | ||||||||
\(874\) | 2.36960e7 | 0.00120056 | ||||||||
\(875\) | 2.30634e9 | 0.116384 | ||||||||
\(876\) | 1.93818e10 | 0.974158 | ||||||||
\(877\) | −1.39725e10 | −0.699481 | −0.349740 | − | 0.936847i | \(-0.613730\pi\) | ||||
−0.349740 | + | 0.936847i | \(0.613730\pi\) | |||||||
\(878\) | 2.46330e10 | 1.22825 | ||||||||
\(879\) | 4.35241e9 | 0.216157 | ||||||||
\(880\) | −1.52602e9 | −0.0754867 | ||||||||
\(881\) | −1.05370e10 | −0.519158 | −0.259579 | − | 0.965722i | \(-0.583584\pi\) | ||||
−0.259579 | + | 0.965722i | \(0.583584\pi\) | |||||||
\(882\) | 1.04677e10 | 0.513701 | ||||||||
\(883\) | 2.48119e10 | 1.21282 | 0.606412 | − | 0.795151i | \(-0.292608\pi\) | ||||
0.606412 | + | 0.795151i | \(0.292608\pi\) | |||||||
\(884\) | −2.38750e10 | −1.16242 | ||||||||
\(885\) | 5.48476e8 | 0.0265985 | ||||||||
\(886\) | 6.52854e8 | 0.0315354 | ||||||||
\(887\) | 3.02069e10 | 1.45336 | 0.726680 | − | 0.686976i | \(-0.241062\pi\) | ||||
0.726680 | + | 0.686976i | \(0.241062\pi\) | |||||||
\(888\) | −1.85920e10 | −0.891005 | ||||||||
\(889\) | 2.38148e9 | 0.113682 | ||||||||
\(890\) | −1.90770e10 | −0.907080 | ||||||||
\(891\) | −2.59607e9 | −0.122955 | ||||||||
\(892\) | 8.90624e9 | 0.420162 | ||||||||
\(893\) | 1.43407e10 | 0.673891 | ||||||||
\(894\) | 1.68315e10 | 0.787848 | ||||||||
\(895\) | 1.29711e10 | 0.604776 | ||||||||
\(896\) | 5.45981e9 | 0.253571 | ||||||||
\(897\) | −2.77181e7 | −0.00128230 | ||||||||
\(898\) | 3.62253e10 | 1.66934 | ||||||||
\(899\) | 2.95101e10 | 1.35460 | ||||||||
\(900\) | −9.74562e9 | −0.445616 | ||||||||
\(901\) | 7.66853e9 | 0.349281 | ||||||||
\(902\) | 2.60218e10 | 1.18063 | ||||||||
\(903\) | 3.18286e9 | 0.143850 | ||||||||
\(904\) | 1.85107e10 | 0.833362 | ||||||||
\(905\) | 3.36194e9 | 0.150772 | ||||||||
\(906\) | 3.72808e10 | 1.66547 | ||||||||
\(907\) | 1.15712e10 | 0.514937 | 0.257468 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257468 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(908\) | −5.01517e10 | −2.22323 | ||||||||
\(909\) | −7.68072e9 | −0.339178 | ||||||||
\(910\) | 3.30416e9 | 0.145350 | ||||||||
\(911\) | −1.60273e10 | −0.702338 | −0.351169 | − | 0.936312i | \(-0.614216\pi\) | ||||
−0.351169 | + | 0.936312i | \(0.614216\pi\) | |||||||
\(912\) | −1.27630e9 | −0.0557147 | ||||||||
\(913\) | 2.16866e10 | 0.943068 | ||||||||
\(914\) | 1.99509e9 | 0.0864271 | ||||||||
\(915\) | −6.09668e9 | −0.263099 | ||||||||
\(916\) | −6.74291e10 | −2.89877 | ||||||||
\(917\) | −4.49797e9 | −0.192630 | ||||||||
\(918\) | 3.70499e9 | 0.158066 | ||||||||
\(919\) | 9.52685e9 | 0.404897 | 0.202449 | − | 0.979293i | \(-0.435110\pi\) | ||||
0.202449 | + | 0.979293i | \(0.435110\pi\) | |||||||
\(920\) | −1.05878e7 | −0.000448280 0 | ||||||||
\(921\) | −1.97736e10 | −0.834021 | ||||||||
\(922\) | −6.46219e10 | −2.71532 | ||||||||
\(923\) | −5.83109e10 | −2.44086 | ||||||||
\(924\) | −4.10739e9 | −0.171283 | ||||||||
\(925\) | −3.86914e10 | −1.60738 | ||||||||
\(926\) | 4.29228e10 | 1.77643 | ||||||||
\(927\) | −6.91915e9 | −0.285282 | ||||||||
\(928\) | −2.18025e10 | −0.895547 | ||||||||
\(929\) | 7.62148e9 | 0.311878 | 0.155939 | − | 0.987767i | \(-0.450160\pi\) | ||||
0.155939 | + | 0.987767i | \(0.450160\pi\) | |||||||
\(930\) | −1.38178e10 | −0.563311 | ||||||||
\(931\) | −1.19464e10 | −0.485193 | ||||||||
\(932\) | −2.83181e10 | −1.14580 | ||||||||
\(933\) | 5.36564e9 | 0.216290 | ||||||||
\(934\) | −3.54467e10 | −1.42351 | ||||||||
\(935\) | −5.05573e9 | −0.202275 | ||||||||
\(936\) | −1.03425e10 | −0.412251 | ||||||||
\(937\) | 2.55429e9 | 0.101434 | 0.0507168 | − | 0.998713i | \(-0.483849\pi\) | ||||
0.0507168 | + | 0.998713i | \(0.483849\pi\) | |||||||
\(938\) | 1.23102e10 | 0.487028 | ||||||||
\(939\) | 6.09239e9 | 0.240137 | ||||||||
\(940\) | −1.85385e10 | −0.727993 | ||||||||
\(941\) | −1.11902e10 | −0.437797 | −0.218898 | − | 0.975748i | \(-0.570246\pi\) | ||||
−0.218898 | + | 0.975748i | \(0.570246\pi\) | |||||||
\(942\) | 2.95682e10 | 1.15252 | ||||||||
\(943\) | −2.60613e7 | −0.00101206 | ||||||||
\(944\) | 6.48658e8 | 0.0250965 | ||||||||
\(945\) | −3.09938e8 | −0.0119471 | ||||||||
\(946\) | 6.50702e10 | 2.49898 | ||||||||
\(947\) | 2.91042e10 | 1.11361 | 0.556803 | − | 0.830645i | \(-0.312028\pi\) | ||||
0.556803 | + | 0.830645i | \(0.312028\pi\) | |||||||
\(948\) | 1.68332e10 | 0.641709 | ||||||||
\(949\) | 4.28056e10 | 1.62581 | ||||||||
\(950\) | 1.84004e10 | 0.696297 | ||||||||
\(951\) | 1.51287e10 | 0.570386 | ||||||||
\(952\) | 2.02611e9 | 0.0761087 | ||||||||
\(953\) | 1.18538e10 | 0.443643 | 0.221821 | − | 0.975087i | \(-0.428800\pi\) | ||||
0.221821 | + | 0.975087i | \(0.428800\pi\) | |||||||
\(954\) | 9.61099e9 | 0.358384 | ||||||||
\(955\) | −1.50396e10 | −0.558758 | ||||||||
\(956\) | −4.81089e10 | −1.78083 | ||||||||
\(957\) | 1.35323e10 | 0.499092 | ||||||||
\(958\) | −8.20804e10 | −3.01620 | ||||||||
\(959\) | 7.12688e9 | 0.260936 | ||||||||
\(960\) | 9.12915e9 | 0.333028 | ||||||||
\(961\) | 5.52147e10 | 2.00689 | ||||||||
\(962\) | −1.18797e11 | −4.30222 | ||||||||
\(963\) | −5.60318e9 | −0.202182 | ||||||||
\(964\) | 4.97629e10 | 1.78911 | ||||||||
\(965\) | −5.71088e8 | −0.0204577 | ||||||||
\(966\) | 6.80543e6 | 0.000242905 0 | ||||||||
\(967\) | −3.91605e10 | −1.39269 | −0.696347 | − | 0.717705i | \(-0.745193\pi\) | ||||
−0.696347 | + | 0.717705i | \(0.745193\pi\) | |||||||
\(968\) | −5.32215e9 | −0.188592 | ||||||||
\(969\) | −4.22839e9 | −0.149294 | ||||||||
\(970\) | −7.21666e9 | −0.253884 | ||||||||
\(971\) | 4.49711e10 | 1.57640 | 0.788200 | − | 0.615419i | \(-0.211013\pi\) | ||||
0.788200 | + | 0.615419i | \(0.211013\pi\) | |||||||
\(972\) | 2.80681e9 | 0.0980352 | ||||||||
\(973\) | −6.74829e9 | −0.234854 | ||||||||
\(974\) | −5.25209e10 | −1.82128 | ||||||||
\(975\) | −2.15237e10 | −0.743704 | ||||||||
\(976\) | −7.21027e9 | −0.248243 | ||||||||
\(977\) | −3.26239e10 | −1.11919 | −0.559597 | − | 0.828765i | \(-0.689044\pi\) | ||||
−0.559597 | + | 0.828765i | \(0.689044\pi\) | |||||||
\(978\) | 4.49810e10 | 1.53760 | ||||||||
\(979\) | 5.23748e10 | 1.78395 | ||||||||
\(980\) | 1.54434e10 | 0.524146 | ||||||||
\(981\) | 1.06941e10 | 0.361663 | ||||||||
\(982\) | 1.46670e10 | 0.494254 | ||||||||
\(983\) | −4.19068e10 | −1.40717 | −0.703585 | − | 0.710611i | \(-0.748419\pi\) | ||||
−0.703585 | + | 0.710611i | \(0.748419\pi\) | |||||||
\(984\) | −9.72435e9 | −0.325370 | ||||||||
\(985\) | 1.01385e10 | 0.338024 | ||||||||
\(986\) | −1.93127e10 | −0.641613 | ||||||||
\(987\) | 4.11861e9 | 0.136346 | ||||||||
\(988\) | 3.41498e10 | 1.12652 | ||||||||
\(989\) | −6.51692e7 | −0.00214218 | ||||||||
\(990\) | −6.33636e9 | −0.207547 | ||||||||
\(991\) | 1.39919e10 | 0.456687 | 0.228343 | − | 0.973581i | \(-0.426669\pi\) | ||||
0.228343 | + | 0.973581i | \(0.426669\pi\) | |||||||
\(992\) | −6.11201e10 | −1.98789 | ||||||||
\(993\) | 1.31799e9 | 0.0427159 | ||||||||
\(994\) | 1.43167e10 | 0.462370 | ||||||||
\(995\) | −8.52617e9 | −0.274393 | ||||||||
\(996\) | −2.34470e10 | −0.751934 | ||||||||
\(997\) | 5.75080e10 | 1.83779 | 0.918893 | − | 0.394506i | \(-0.129084\pi\) | ||||
0.918893 | + | 0.394506i | \(0.129084\pi\) | |||||||
\(998\) | 5.83846e10 | 1.85927 | ||||||||
\(999\) | 1.11434e10 | 0.353622 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.8.a.b.1.3 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.d.1.15 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.3 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.d.1.15 | 17 | 3.2 | odd | 2 |