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 | 1.3 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −35.8479 | −1.58427 | −0.792135 | − | 0.610346i | \(-0.791030\pi\) | ||||
−0.792135 | + | 0.610346i | \(0.791030\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 773.074 | 1.50991 | ||||||||
\(5\) | 1881.24 | 1.34610 | 0.673051 | − | 0.739596i | \(-0.264983\pi\) | ||||
0.673051 | + | 0.739596i | \(0.264983\pi\) | |||||||
\(6\) | −2903.68 | −0.914679 | ||||||||
\(7\) | −9737.47 | −1.53287 | −0.766435 | − | 0.642322i | \(-0.777971\pi\) | ||||
−0.766435 | + | 0.642322i | \(0.777971\pi\) | |||||||
\(8\) | −9358.98 | −0.807836 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −67438.4 | −2.13259 | ||||||||
\(11\) | −61627.4 | −1.26913 | −0.634566 | − | 0.772868i | \(-0.718821\pi\) | ||||
−0.634566 | + | 0.772868i | \(0.718821\pi\) | |||||||
\(12\) | 62619.0 | 0.871747 | ||||||||
\(13\) | 169936. | 1.65021 | 0.825107 | − | 0.564977i | \(-0.191115\pi\) | ||||
0.825107 | + | 0.564977i | \(0.191115\pi\) | |||||||
\(14\) | 349068. | 2.42848 | ||||||||
\(15\) | 152380. | 0.777173 | ||||||||
\(16\) | −60314.1 | −0.230080 | ||||||||
\(17\) | 560769. | 1.62841 | 0.814205 | − | 0.580578i | \(-0.197173\pi\) | ||||
0.814205 | + | 0.580578i | \(0.197173\pi\) | |||||||
\(18\) | −235198. | −0.528090 | ||||||||
\(19\) | −659805. | −1.16151 | −0.580757 | − | 0.814077i | \(-0.697243\pi\) | ||||
−0.580757 | + | 0.814077i | \(0.697243\pi\) | |||||||
\(20\) | 1.45434e6 | 2.03250 | ||||||||
\(21\) | −788735. | −0.885002 | ||||||||
\(22\) | 2.20922e6 | 2.01065 | ||||||||
\(23\) | −535600. | −0.399085 | −0.199543 | − | 0.979889i | \(-0.563946\pi\) | ||||
−0.199543 | + | 0.979889i | \(0.563946\pi\) | |||||||
\(24\) | −758077. | −0.466405 | ||||||||
\(25\) | 1.58592e6 | 0.811992 | ||||||||
\(26\) | −6.09185e6 | −2.61438 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | −7.52779e6 | −2.31450 | ||||||||
\(29\) | 1.76519e6 | 0.463446 | 0.231723 | − | 0.972782i | \(-0.425564\pi\) | ||||
0.231723 | + | 0.972782i | \(0.425564\pi\) | |||||||
\(30\) | −5.46251e6 | −1.23125 | ||||||||
\(31\) | −7.35837e6 | −1.43105 | −0.715523 | − | 0.698589i | \(-0.753812\pi\) | ||||
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(32\) | 6.95393e6 | 1.17235 | ||||||||
\(33\) | −4.99182e6 | −0.732734 | ||||||||
\(34\) | −2.01024e7 | −2.57984 | ||||||||
\(35\) | −1.83185e7 | −2.06340 | ||||||||
\(36\) | 5.07214e6 | 0.503304 | ||||||||
\(37\) | −1.11914e7 | −0.981699 | −0.490849 | − | 0.871245i | \(-0.663313\pi\) | ||||
−0.490849 | + | 0.871245i | \(0.663313\pi\) | |||||||
\(38\) | 2.36527e7 | 1.84015 | ||||||||
\(39\) | 1.37648e7 | 0.952751 | ||||||||
\(40\) | −1.76064e7 | −1.08743 | ||||||||
\(41\) | 9.17749e6 | 0.507220 | 0.253610 | − | 0.967307i | \(-0.418382\pi\) | ||||
0.253610 | + | 0.967307i | \(0.418382\pi\) | |||||||
\(42\) | 2.82745e7 | 1.40208 | ||||||||
\(43\) | 1.27647e7 | 0.569379 | 0.284689 | − | 0.958620i | \(-0.408110\pi\) | ||||
0.284689 | + | 0.958620i | \(0.408110\pi\) | |||||||
\(44\) | −4.76426e7 | −1.91628 | ||||||||
\(45\) | 1.23428e7 | 0.448701 | ||||||||
\(46\) | 1.92002e7 | 0.632258 | ||||||||
\(47\) | 7.13479e6 | 0.213275 | 0.106638 | − | 0.994298i | \(-0.465991\pi\) | ||||
0.106638 | + | 0.994298i | \(0.465991\pi\) | |||||||
\(48\) | −4.88544e6 | −0.132837 | ||||||||
\(49\) | 5.44648e7 | 1.34969 | ||||||||
\(50\) | −5.68520e7 | −1.28641 | ||||||||
\(51\) | 4.54223e7 | 0.940163 | ||||||||
\(52\) | 1.31373e8 | 2.49168 | ||||||||
\(53\) | −1.07603e8 | −1.87320 | −0.936602 | − | 0.350396i | \(-0.886047\pi\) | ||||
−0.936602 | + | 0.350396i | \(0.886047\pi\) | |||||||
\(54\) | −1.90511e7 | −0.304893 | ||||||||
\(55\) | −1.15936e8 | −1.70838 | ||||||||
\(56\) | 9.11328e7 | 1.23831 | ||||||||
\(57\) | −5.34442e7 | −0.670601 | ||||||||
\(58\) | −6.32783e7 | −0.734224 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 1.17801e8 | 1.17346 | ||||||||
\(61\) | −2.18590e7 | −0.202138 | −0.101069 | − | 0.994879i | \(-0.532226\pi\) | ||||
−0.101069 | + | 0.994879i | \(0.532226\pi\) | |||||||
\(62\) | 2.63782e8 | 2.26716 | ||||||||
\(63\) | −6.38876e7 | −0.510956 | ||||||||
\(64\) | −2.18403e8 | −1.62723 | ||||||||
\(65\) | 3.19690e8 | 2.22136 | ||||||||
\(66\) | 1.78947e8 | 1.16085 | ||||||||
\(67\) | 3.04061e8 | 1.84342 | 0.921709 | − | 0.387883i | \(-0.126794\pi\) | ||||
0.921709 | + | 0.387883i | \(0.126794\pi\) | |||||||
\(68\) | 4.33516e8 | 2.45875 | ||||||||
\(69\) | −4.33836e7 | −0.230412 | ||||||||
\(70\) | 6.56680e8 | 3.26898 | ||||||||
\(71\) | −2.46812e8 | −1.15267 | −0.576334 | − | 0.817214i | \(-0.695517\pi\) | ||||
−0.576334 | + | 0.817214i | \(0.695517\pi\) | |||||||
\(72\) | −6.14042e7 | −0.269279 | ||||||||
\(73\) | −9.89167e7 | −0.407678 | −0.203839 | − | 0.979004i | \(-0.565342\pi\) | ||||
−0.203839 | + | 0.979004i | \(0.565342\pi\) | |||||||
\(74\) | 4.01190e8 | 1.55528 | ||||||||
\(75\) | 1.28460e8 | 0.468804 | ||||||||
\(76\) | −5.10079e8 | −1.75378 | ||||||||
\(77\) | 6.00096e8 | 1.94541 | ||||||||
\(78\) | −4.93440e8 | −1.50941 | ||||||||
\(79\) | −1.89951e7 | −0.0548679 | −0.0274340 | − | 0.999624i | \(-0.508734\pi\) | ||||
−0.0274340 | + | 0.999624i | \(0.508734\pi\) | |||||||
\(80\) | −1.13465e8 | −0.309711 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −3.28994e8 | −0.803574 | ||||||||
\(83\) | −3.82819e8 | −0.885405 | −0.442703 | − | 0.896668i | \(-0.645980\pi\) | ||||
−0.442703 | + | 0.896668i | \(0.645980\pi\) | |||||||
\(84\) | −6.09751e8 | −1.33627 | ||||||||
\(85\) | 1.05494e9 | 2.19201 | ||||||||
\(86\) | −4.57587e8 | −0.902049 | ||||||||
\(87\) | 1.42980e8 | 0.267571 | ||||||||
\(88\) | 5.76770e8 | 1.02525 | ||||||||
\(89\) | 8.54743e8 | 1.44405 | 0.722023 | − | 0.691869i | \(-0.243213\pi\) | ||||
0.722023 | + | 0.691869i | \(0.243213\pi\) | |||||||
\(90\) | −4.42463e8 | −0.710863 | ||||||||
\(91\) | −1.65475e9 | −2.52956 | ||||||||
\(92\) | −4.14059e8 | −0.602583 | ||||||||
\(93\) | −5.96028e8 | −0.826215 | ||||||||
\(94\) | −2.55767e8 | −0.337886 | ||||||||
\(95\) | −1.24125e9 | −1.56352 | ||||||||
\(96\) | 5.63268e8 | 0.676854 | ||||||||
\(97\) | 1.05008e9 | 1.20434 | 0.602169 | − | 0.798369i | \(-0.294303\pi\) | ||||
0.602169 | + | 0.798369i | \(0.294303\pi\) | |||||||
\(98\) | −1.95245e9 | −2.13827 | ||||||||
\(99\) | −4.04338e8 | −0.423044 | ||||||||
\(100\) | 1.22604e9 | 1.22604 | ||||||||
\(101\) | −1.45452e9 | −1.39083 | −0.695415 | − | 0.718608i | \(-0.744779\pi\) | ||||
−0.695415 | + | 0.718608i | \(0.744779\pi\) | |||||||
\(102\) | −1.62829e9 | −1.48947 | ||||||||
\(103\) | 1.64504e9 | 1.44015 | 0.720076 | − | 0.693895i | \(-0.244107\pi\) | ||||
0.720076 | + | 0.693895i | \(0.244107\pi\) | |||||||
\(104\) | −1.59043e9 | −1.33310 | ||||||||
\(105\) | −1.48380e9 | −1.19130 | ||||||||
\(106\) | 3.85736e9 | 2.96766 | ||||||||
\(107\) | 4.75094e8 | 0.350391 | 0.175195 | − | 0.984534i | \(-0.443944\pi\) | ||||
0.175195 | + | 0.984534i | \(0.443944\pi\) | |||||||
\(108\) | 4.10843e8 | 0.290582 | ||||||||
\(109\) | −2.37857e9 | −1.61398 | −0.806988 | − | 0.590568i | \(-0.798904\pi\) | ||||
−0.806988 | + | 0.590568i | \(0.798904\pi\) | |||||||
\(110\) | 4.15606e9 | 2.70654 | ||||||||
\(111\) | −9.06506e8 | −0.566784 | ||||||||
\(112\) | 5.87307e8 | 0.352682 | ||||||||
\(113\) | −1.39288e9 | −0.803636 | −0.401818 | − | 0.915720i | \(-0.631622\pi\) | ||||
−0.401818 | + | 0.915720i | \(0.631622\pi\) | |||||||
\(114\) | 1.91587e9 | 1.06241 | ||||||||
\(115\) | −1.00759e9 | −0.537209 | ||||||||
\(116\) | 1.36462e9 | 0.699763 | ||||||||
\(117\) | 1.11495e9 | 0.550071 | ||||||||
\(118\) | −4.34382e8 | −0.206254 | ||||||||
\(119\) | −5.46047e9 | −2.49614 | ||||||||
\(120\) | −1.42612e9 | −0.627828 | ||||||||
\(121\) | 1.43999e9 | 0.610698 | ||||||||
\(122\) | 7.83602e8 | 0.320240 | ||||||||
\(123\) | 7.43377e8 | 0.292844 | ||||||||
\(124\) | −5.68856e9 | −2.16075 | ||||||||
\(125\) | −6.90795e8 | −0.253078 | ||||||||
\(126\) | 2.29024e9 | 0.809493 | ||||||||
\(127\) | 4.26841e8 | 0.145596 | 0.0727980 | − | 0.997347i | \(-0.476807\pi\) | ||||
0.0727980 | + | 0.997347i | \(0.476807\pi\) | |||||||
\(128\) | 4.26889e9 | 1.40563 | ||||||||
\(129\) | 1.03394e9 | 0.328731 | ||||||||
\(130\) | −1.14602e10 | −3.51923 | ||||||||
\(131\) | −2.55369e9 | −0.757614 | −0.378807 | − | 0.925476i | \(-0.623666\pi\) | ||||
−0.378807 | + | 0.925476i | \(0.623666\pi\) | |||||||
\(132\) | −3.85905e9 | −1.10636 | ||||||||
\(133\) | 6.42484e9 | 1.78045 | ||||||||
\(134\) | −1.08999e10 | −2.92047 | ||||||||
\(135\) | 9.99766e8 | 0.259058 | ||||||||
\(136\) | −5.24822e9 | −1.31549 | ||||||||
\(137\) | −1.89733e9 | −0.460150 | −0.230075 | − | 0.973173i | \(-0.573897\pi\) | ||||
−0.230075 | + | 0.973173i | \(0.573897\pi\) | |||||||
\(138\) | 1.55521e9 | 0.365035 | ||||||||
\(139\) | 1.42180e9 | 0.323052 | 0.161526 | − | 0.986868i | \(-0.448358\pi\) | ||||
0.161526 | + | 0.986868i | \(0.448358\pi\) | |||||||
\(140\) | −1.41615e10 | −3.11555 | ||||||||
\(141\) | 5.77918e8 | 0.123135 | ||||||||
\(142\) | 8.84771e9 | 1.82614 | ||||||||
\(143\) | −1.04727e10 | −2.09434 | ||||||||
\(144\) | −3.95721e8 | −0.0766933 | ||||||||
\(145\) | 3.32073e9 | 0.623846 | ||||||||
\(146\) | 3.54596e9 | 0.645871 | ||||||||
\(147\) | 4.41165e9 | 0.779243 | ||||||||
\(148\) | −8.65181e9 | −1.48228 | ||||||||
\(149\) | −9.87928e9 | −1.64205 | −0.821027 | − | 0.570890i | \(-0.806598\pi\) | ||||
−0.821027 | + | 0.570890i | \(0.806598\pi\) | |||||||
\(150\) | −4.60502e9 | −0.742712 | ||||||||
\(151\) | −6.67305e9 | −1.04455 | −0.522274 | − | 0.852778i | \(-0.674916\pi\) | ||||
−0.522274 | + | 0.852778i | \(0.674916\pi\) | |||||||
\(152\) | 6.17510e9 | 0.938314 | ||||||||
\(153\) | 3.67920e9 | 0.542803 | ||||||||
\(154\) | −2.15122e10 | −3.08206 | ||||||||
\(155\) | −1.38428e10 | −1.92634 | ||||||||
\(156\) | 1.06412e10 | 1.43857 | ||||||||
\(157\) | 6.15305e9 | 0.808243 | 0.404122 | − | 0.914705i | \(-0.367577\pi\) | ||||
0.404122 | + | 0.914705i | \(0.367577\pi\) | |||||||
\(158\) | 6.80934e8 | 0.0869256 | ||||||||
\(159\) | −8.71588e9 | −1.08149 | ||||||||
\(160\) | 1.30820e10 | 1.57810 | ||||||||
\(161\) | 5.21539e9 | 0.611745 | ||||||||
\(162\) | −1.54314e9 | −0.176030 | ||||||||
\(163\) | 1.59815e10 | 1.77326 | 0.886630 | − | 0.462480i | \(-0.153040\pi\) | ||||
0.886630 | + | 0.462480i | \(0.153040\pi\) | |||||||
\(164\) | 7.09488e9 | 0.765857 | ||||||||
\(165\) | −9.39080e9 | −0.986335 | ||||||||
\(166\) | 1.37233e10 | 1.40272 | ||||||||
\(167\) | −3.33847e9 | −0.332141 | −0.166071 | − | 0.986114i | \(-0.553108\pi\) | ||||
−0.166071 | + | 0.986114i | \(0.553108\pi\) | |||||||
\(168\) | 7.38176e9 | 0.714937 | ||||||||
\(169\) | 1.82737e10 | 1.72320 | ||||||||
\(170\) | −3.78174e10 | −3.47273 | ||||||||
\(171\) | −4.32898e9 | −0.387171 | ||||||||
\(172\) | 9.86803e9 | 0.859711 | ||||||||
\(173\) | −6.91460e9 | −0.586894 | −0.293447 | − | 0.955975i | \(-0.594802\pi\) | ||||
−0.293447 | + | 0.955975i | \(0.594802\pi\) | |||||||
\(174\) | −5.12554e9 | −0.423904 | ||||||||
\(175\) | −1.54429e10 | −1.24468 | ||||||||
\(176\) | 3.71700e9 | 0.292002 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −3.06408e10 | −2.28776 | ||||||||
\(179\) | −3.30267e9 | −0.240451 | −0.120226 | − | 0.992747i | \(-0.538362\pi\) | ||||
−0.120226 | + | 0.992747i | \(0.538362\pi\) | |||||||
\(180\) | 9.54189e9 | 0.677498 | ||||||||
\(181\) | −2.48966e10 | −1.72419 | −0.862096 | − | 0.506744i | \(-0.830849\pi\) | ||||
−0.862096 | + | 0.506744i | \(0.830849\pi\) | |||||||
\(182\) | 5.93192e10 | 4.00751 | ||||||||
\(183\) | −1.77058e9 | −0.116704 | ||||||||
\(184\) | 5.01267e9 | 0.322395 | ||||||||
\(185\) | −2.10537e10 | −1.32147 | ||||||||
\(186\) | 2.13664e10 | 1.30895 | ||||||||
\(187\) | −3.45587e10 | −2.06667 | ||||||||
\(188\) | 5.51572e9 | 0.322027 | ||||||||
\(189\) | −5.17489e9 | −0.295001 | ||||||||
\(190\) | 4.44962e10 | 2.47703 | ||||||||
\(191\) | −1.74235e9 | −0.0947295 | −0.0473648 | − | 0.998878i | \(-0.515082\pi\) | ||||
−0.0473648 | + | 0.998878i | \(0.515082\pi\) | |||||||
\(192\) | −1.76907e10 | −0.939482 | ||||||||
\(193\) | −1.25460e10 | −0.650875 | −0.325438 | − | 0.945563i | \(-0.605512\pi\) | ||||
−0.325438 | + | 0.945563i | \(0.605512\pi\) | |||||||
\(194\) | −3.76431e10 | −1.90800 | ||||||||
\(195\) | 2.58949e10 | 1.28250 | ||||||||
\(196\) | 4.21053e10 | 2.03791 | ||||||||
\(197\) | 5.37321e9 | 0.254177 | 0.127088 | − | 0.991891i | \(-0.459437\pi\) | ||||
0.127088 | + | 0.991891i | \(0.459437\pi\) | |||||||
\(198\) | 1.44947e10 | 0.670216 | ||||||||
\(199\) | −2.42720e10 | −1.09715 | −0.548576 | − | 0.836101i | \(-0.684830\pi\) | ||||
−0.548576 | + | 0.836101i | \(0.684830\pi\) | |||||||
\(200\) | −1.48426e10 | −0.655957 | ||||||||
\(201\) | 2.46289e10 | 1.06430 | ||||||||
\(202\) | 5.21416e10 | 2.20345 | ||||||||
\(203\) | −1.71884e10 | −0.710403 | ||||||||
\(204\) | 3.51148e10 | 1.41956 | ||||||||
\(205\) | 1.72650e10 | 0.682770 | ||||||||
\(206\) | −5.89712e10 | −2.28159 | ||||||||
\(207\) | −3.51407e9 | −0.133028 | ||||||||
\(208\) | −1.02495e10 | −0.379681 | ||||||||
\(209\) | 4.06621e10 | 1.47412 | ||||||||
\(210\) | 5.31911e10 | 1.88735 | ||||||||
\(211\) | 8.97002e9 | 0.311546 | 0.155773 | − | 0.987793i | \(-0.450213\pi\) | ||||
0.155773 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(212\) | −8.31855e10 | −2.82837 | ||||||||
\(213\) | −1.99918e10 | −0.665493 | ||||||||
\(214\) | −1.70311e10 | −0.555113 | ||||||||
\(215\) | 2.40133e10 | 0.766442 | ||||||||
\(216\) | −4.97374e9 | −0.155468 | ||||||||
\(217\) | 7.16519e10 | 2.19361 | ||||||||
\(218\) | 8.52669e10 | 2.55697 | ||||||||
\(219\) | −8.01226e9 | −0.235373 | ||||||||
\(220\) | −8.96270e10 | −2.57951 | ||||||||
\(221\) | 9.52948e10 | 2.68722 | ||||||||
\(222\) | 3.24964e10 | 0.897939 | ||||||||
\(223\) | −5.14153e10 | −1.39226 | −0.696130 | − | 0.717916i | \(-0.745096\pi\) | ||||
−0.696130 | + | 0.717916i | \(0.745096\pi\) | |||||||
\(224\) | −6.77137e10 | −1.79705 | ||||||||
\(225\) | 1.04052e10 | 0.270664 | ||||||||
\(226\) | 4.99317e10 | 1.27318 | ||||||||
\(227\) | −2.13816e10 | −0.534470 | −0.267235 | − | 0.963631i | \(-0.586110\pi\) | ||||
−0.267235 | + | 0.963631i | \(0.586110\pi\) | |||||||
\(228\) | −4.13164e10 | −1.01255 | ||||||||
\(229\) | 4.05363e10 | 0.974057 | 0.487028 | − | 0.873386i | \(-0.338081\pi\) | ||||
0.487028 | + | 0.873386i | \(0.338081\pi\) | |||||||
\(230\) | 3.61200e10 | 0.851085 | ||||||||
\(231\) | 4.86077e10 | 1.12319 | ||||||||
\(232\) | −1.65203e10 | −0.374389 | ||||||||
\(233\) | 3.97623e10 | 0.883833 | 0.441916 | − | 0.897056i | \(-0.354299\pi\) | ||||
0.441916 | + | 0.897056i | \(0.354299\pi\) | |||||||
\(234\) | −3.99686e10 | −0.871461 | ||||||||
\(235\) | 1.34222e10 | 0.287091 | ||||||||
\(236\) | 9.36762e9 | 0.196574 | ||||||||
\(237\) | −1.53860e9 | −0.0316780 | ||||||||
\(238\) | 1.95747e11 | 3.95456 | ||||||||
\(239\) | −3.15480e10 | −0.625434 | −0.312717 | − | 0.949846i | \(-0.601239\pi\) | ||||
−0.312717 | + | 0.949846i | \(0.601239\pi\) | |||||||
\(240\) | −9.19067e9 | −0.178812 | ||||||||
\(241\) | −8.14750e10 | −1.55578 | −0.777889 | − | 0.628402i | \(-0.783709\pi\) | ||||
−0.777889 | + | 0.628402i | \(0.783709\pi\) | |||||||
\(242\) | −5.16208e10 | −0.967511 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | −1.68987e10 | −0.305210 | ||||||||
\(245\) | 1.02461e11 | 1.81682 | ||||||||
\(246\) | −2.66485e10 | −0.463943 | ||||||||
\(247\) | −1.12125e11 | −1.91675 | ||||||||
\(248\) | 6.88668e10 | 1.15605 | ||||||||
\(249\) | −3.10083e10 | −0.511189 | ||||||||
\(250\) | 2.47636e10 | 0.400943 | ||||||||
\(251\) | −3.36364e9 | −0.0534907 | −0.0267453 | − | 0.999642i | \(-0.508514\pi\) | ||||
−0.0267453 | + | 0.999642i | \(0.508514\pi\) | |||||||
\(252\) | −4.93898e10 | −0.771499 | ||||||||
\(253\) | 3.30077e10 | 0.506492 | ||||||||
\(254\) | −1.53014e10 | −0.230663 | ||||||||
\(255\) | 8.54500e10 | 1.26556 | ||||||||
\(256\) | −4.12085e10 | −0.599663 | ||||||||
\(257\) | −6.90974e10 | −0.988013 | −0.494007 | − | 0.869458i | \(-0.664468\pi\) | ||||
−0.494007 | + | 0.869458i | \(0.664468\pi\) | |||||||
\(258\) | −3.70645e10 | −0.520798 | ||||||||
\(259\) | 1.08976e11 | 1.50482 | ||||||||
\(260\) | 2.47144e11 | 3.35405 | ||||||||
\(261\) | 1.15814e10 | 0.154482 | ||||||||
\(262\) | 9.15447e10 | 1.20027 | ||||||||
\(263\) | −8.29232e10 | −1.06875 | −0.534374 | − | 0.845248i | \(-0.679453\pi\) | ||||
−0.534374 | + | 0.845248i | \(0.679453\pi\) | |||||||
\(264\) | 4.67184e10 | 0.591929 | ||||||||
\(265\) | −2.02427e11 | −2.52152 | ||||||||
\(266\) | −2.30317e11 | −2.82071 | ||||||||
\(267\) | 6.92342e10 | 0.833720 | ||||||||
\(268\) | 2.35062e11 | 2.78340 | ||||||||
\(269\) | 4.87849e10 | 0.568068 | 0.284034 | − | 0.958814i | \(-0.408327\pi\) | ||||
0.284034 | + | 0.958814i | \(0.408327\pi\) | |||||||
\(270\) | −3.58395e10 | −0.410417 | ||||||||
\(271\) | −1.15620e11 | −1.30218 | −0.651088 | − | 0.759002i | \(-0.725687\pi\) | ||||
−0.651088 | + | 0.759002i | \(0.725687\pi\) | |||||||
\(272\) | −3.38223e10 | −0.374664 | ||||||||
\(273\) | −1.34034e11 | −1.46044 | ||||||||
\(274\) | 6.80152e10 | 0.729002 | ||||||||
\(275\) | −9.77363e10 | −1.03053 | ||||||||
\(276\) | −3.35388e10 | −0.347901 | ||||||||
\(277\) | −7.34803e10 | −0.749914 | −0.374957 | − | 0.927042i | \(-0.622343\pi\) | ||||
−0.374957 | + | 0.927042i | \(0.622343\pi\) | |||||||
\(278\) | −5.09686e10 | −0.511801 | ||||||||
\(279\) | −4.82782e10 | −0.477016 | ||||||||
\(280\) | 1.71442e11 | 1.66689 | ||||||||
\(281\) | −4.09307e10 | −0.391626 | −0.195813 | − | 0.980641i | \(-0.562735\pi\) | ||||
−0.195813 | + | 0.980641i | \(0.562735\pi\) | |||||||
\(282\) | −2.07172e10 | −0.195078 | ||||||||
\(283\) | −1.88250e11 | −1.74460 | −0.872300 | − | 0.488970i | \(-0.837373\pi\) | ||||
−0.872300 | + | 0.488970i | \(0.837373\pi\) | |||||||
\(284\) | −1.90804e11 | −1.74043 | ||||||||
\(285\) | −1.00541e11 | −0.902697 | ||||||||
\(286\) | 3.75425e11 | 3.31800 | ||||||||
\(287\) | −8.93655e10 | −0.777502 | ||||||||
\(288\) | 4.56247e10 | 0.390782 | ||||||||
\(289\) | 1.95874e11 | 1.65172 | ||||||||
\(290\) | −1.19041e11 | −0.988341 | ||||||||
\(291\) | 8.50563e10 | 0.695325 | ||||||||
\(292\) | −7.64700e10 | −0.615557 | ||||||||
\(293\) | 9.87036e10 | 0.782400 | 0.391200 | − | 0.920306i | \(-0.372060\pi\) | ||||
0.391200 | + | 0.920306i | \(0.372060\pi\) | |||||||
\(294\) | −1.58148e11 | −1.23453 | ||||||||
\(295\) | 2.27956e10 | 0.175248 | ||||||||
\(296\) | 1.04740e11 | 0.793052 | ||||||||
\(297\) | −3.27514e10 | −0.244245 | ||||||||
\(298\) | 3.54152e11 | 2.60146 | ||||||||
\(299\) | −9.10177e10 | −0.658575 | ||||||||
\(300\) | 9.93089e10 | 0.707852 | ||||||||
\(301\) | −1.24295e11 | −0.872783 | ||||||||
\(302\) | 2.39215e11 | 1.65484 | ||||||||
\(303\) | −1.17816e11 | −0.802996 | ||||||||
\(304\) | 3.97956e10 | 0.267241 | ||||||||
\(305\) | −4.11220e10 | −0.272098 | ||||||||
\(306\) | −1.31892e11 | −0.859947 | ||||||||
\(307\) | −1.14378e11 | −0.734885 | −0.367442 | − | 0.930046i | \(-0.619766\pi\) | ||||
−0.367442 | + | 0.930046i | \(0.619766\pi\) | |||||||
\(308\) | 4.63919e11 | 2.93740 | ||||||||
\(309\) | 1.33248e11 | 0.831472 | ||||||||
\(310\) | 4.96236e11 | 3.05184 | ||||||||
\(311\) | −2.11753e10 | −0.128354 | −0.0641768 | − | 0.997939i | \(-0.520442\pi\) | ||||
−0.0641768 | + | 0.997939i | \(0.520442\pi\) | |||||||
\(312\) | −1.28825e11 | −0.769667 | ||||||||
\(313\) | −9.81324e10 | −0.577914 | −0.288957 | − | 0.957342i | \(-0.593308\pi\) | ||||
−0.288957 | + | 0.957342i | \(0.593308\pi\) | |||||||
\(314\) | −2.20574e11 | −1.28048 | ||||||||
\(315\) | −1.20188e11 | −0.687800 | ||||||||
\(316\) | −1.46846e10 | −0.0828457 | ||||||||
\(317\) | −4.64728e10 | −0.258483 | −0.129242 | − | 0.991613i | \(-0.541254\pi\) | ||||
−0.129242 | + | 0.991613i | \(0.541254\pi\) | |||||||
\(318\) | 3.12446e11 | 1.71338 | ||||||||
\(319\) | −1.08784e11 | −0.588175 | ||||||||
\(320\) | −4.10868e11 | −2.19042 | ||||||||
\(321\) | 3.84826e10 | 0.202298 | ||||||||
\(322\) | −1.86961e11 | −0.969169 | ||||||||
\(323\) | −3.69998e11 | −1.89142 | ||||||||
\(324\) | 3.32783e10 | 0.167768 | ||||||||
\(325\) | 2.69505e11 | 1.33996 | ||||||||
\(326\) | −5.72902e11 | −2.80932 | ||||||||
\(327\) | −1.92664e11 | −0.931829 | ||||||||
\(328\) | −8.58919e10 | −0.409751 | ||||||||
\(329\) | −6.94748e10 | −0.326923 | ||||||||
\(330\) | 3.36641e11 | 1.56262 | ||||||||
\(331\) | 5.07093e10 | 0.232200 | 0.116100 | − | 0.993238i | \(-0.462961\pi\) | ||||
0.116100 | + | 0.993238i | \(0.462961\pi\) | |||||||
\(332\) | −2.95948e11 | −1.33688 | ||||||||
\(333\) | −7.34270e10 | −0.327233 | ||||||||
\(334\) | 1.19677e11 | 0.526201 | ||||||||
\(335\) | 5.72010e11 | 2.48143 | ||||||||
\(336\) | 4.75718e10 | 0.203621 | ||||||||
\(337\) | −3.44025e11 | −1.45297 | −0.726484 | − | 0.687184i | \(-0.758847\pi\) | ||||
−0.726484 | + | 0.687184i | \(0.758847\pi\) | |||||||
\(338\) | −6.55075e11 | −2.73002 | ||||||||
\(339\) | −1.12823e11 | −0.463980 | ||||||||
\(340\) | 8.15546e11 | 3.30973 | ||||||||
\(341\) | 4.53477e11 | 1.81619 | ||||||||
\(342\) | 1.55185e11 | 0.613384 | ||||||||
\(343\) | −1.37407e11 | −0.536026 | ||||||||
\(344\) | −1.19464e11 | −0.459965 | ||||||||
\(345\) | −8.16148e10 | −0.310158 | ||||||||
\(346\) | 2.47874e11 | 0.929799 | ||||||||
\(347\) | −1.06614e11 | −0.394758 | −0.197379 | − | 0.980327i | \(-0.563243\pi\) | ||||
−0.197379 | + | 0.980327i | \(0.563243\pi\) | |||||||
\(348\) | 1.10534e11 | 0.404008 | ||||||||
\(349\) | −3.09166e11 | −1.11552 | −0.557761 | − | 0.830002i | \(-0.688339\pi\) | ||||
−0.557761 | + | 0.830002i | \(0.688339\pi\) | |||||||
\(350\) | 5.53595e11 | 1.97191 | ||||||||
\(351\) | 9.03109e10 | 0.317584 | ||||||||
\(352\) | −4.28553e11 | −1.48786 | ||||||||
\(353\) | −3.60113e11 | −1.23439 | −0.617195 | − | 0.786810i | \(-0.711731\pi\) | ||||
−0.617195 | + | 0.786810i | \(0.711731\pi\) | |||||||
\(354\) | −3.51850e10 | −0.119081 | ||||||||
\(355\) | −4.64312e11 | −1.55161 | ||||||||
\(356\) | 6.60780e11 | 2.18038 | ||||||||
\(357\) | −4.42298e11 | −1.44115 | ||||||||
\(358\) | 1.18394e11 | 0.380940 | ||||||||
\(359\) | 7.09609e10 | 0.225473 | 0.112736 | − | 0.993625i | \(-0.464038\pi\) | ||||
0.112736 | + | 0.993625i | \(0.464038\pi\) | |||||||
\(360\) | −1.15516e11 | −0.362477 | ||||||||
\(361\) | 1.12655e11 | 0.349116 | ||||||||
\(362\) | 8.92490e11 | 2.73159 | ||||||||
\(363\) | 1.16640e11 | 0.352587 | ||||||||
\(364\) | −1.27924e12 | −3.81941 | ||||||||
\(365\) | −1.86086e11 | −0.548776 | ||||||||
\(366\) | 6.34717e10 | 0.184891 | ||||||||
\(367\) | 3.13142e10 | 0.0901041 | 0.0450520 | − | 0.998985i | \(-0.485655\pi\) | ||||
0.0450520 | + | 0.998985i | \(0.485655\pi\) | |||||||
\(368\) | 3.23042e10 | 0.0918215 | ||||||||
\(369\) | 6.02135e10 | 0.169073 | ||||||||
\(370\) | 7.54733e11 | 2.09356 | ||||||||
\(371\) | 1.04779e12 | 2.87138 | ||||||||
\(372\) | −4.60774e11 | −1.24751 | ||||||||
\(373\) | 6.03351e11 | 1.61391 | 0.806957 | − | 0.590610i | \(-0.201113\pi\) | ||||
0.806957 | + | 0.590610i | \(0.201113\pi\) | |||||||
\(374\) | 1.23886e12 | 3.27416 | ||||||||
\(375\) | −5.59544e10 | −0.146114 | ||||||||
\(376\) | −6.67743e10 | −0.172292 | ||||||||
\(377\) | 2.99968e11 | 0.764785 | ||||||||
\(378\) | 1.85509e11 | 0.467361 | ||||||||
\(379\) | −1.57900e11 | −0.393101 | −0.196551 | − | 0.980494i | \(-0.562974\pi\) | ||||
−0.196551 | + | 0.980494i | \(0.562974\pi\) | |||||||
\(380\) | −9.59578e11 | −2.36077 | ||||||||
\(381\) | 3.45741e10 | 0.0840599 | ||||||||
\(382\) | 6.24597e10 | 0.150077 | ||||||||
\(383\) | −7.59563e11 | −1.80372 | −0.901861 | − | 0.432027i | \(-0.857799\pi\) | ||||
−0.901861 | + | 0.432027i | \(0.857799\pi\) | |||||||
\(384\) | 3.45780e11 | 0.811540 | ||||||||
\(385\) | 1.12892e12 | 2.61873 | ||||||||
\(386\) | 4.49749e11 | 1.03116 | ||||||||
\(387\) | 8.37489e10 | 0.189793 | ||||||||
\(388\) | 8.11788e11 | 1.81844 | ||||||||
\(389\) | −1.69262e11 | −0.374788 | −0.187394 | − | 0.982285i | \(-0.560004\pi\) | ||||
−0.187394 | + | 0.982285i | \(0.560004\pi\) | |||||||
\(390\) | −9.28277e11 | −2.03183 | ||||||||
\(391\) | −3.00348e11 | −0.649874 | ||||||||
\(392\) | −5.09735e11 | −1.09033 | ||||||||
\(393\) | −2.06849e11 | −0.437409 | ||||||||
\(394\) | −1.92619e11 | −0.402685 | ||||||||
\(395\) | −3.57342e10 | −0.0738579 | ||||||||
\(396\) | −3.12583e11 | −0.638759 | ||||||||
\(397\) | 2.11292e10 | 0.0426899 | 0.0213450 | − | 0.999772i | \(-0.493205\pi\) | ||||
0.0213450 | + | 0.999772i | \(0.493205\pi\) | |||||||
\(398\) | 8.70101e11 | 1.73818 | ||||||||
\(399\) | 5.20412e11 | 1.02794 | ||||||||
\(400\) | −9.56535e10 | −0.186823 | ||||||||
\(401\) | −1.24151e11 | −0.239774 | −0.119887 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119887 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(402\) | −8.82896e11 | −1.68613 | ||||||||
\(403\) | −1.25045e12 | −2.36153 | ||||||||
\(404\) | −1.12445e12 | −2.10003 | ||||||||
\(405\) | 8.09810e10 | 0.149567 | ||||||||
\(406\) | 6.16170e11 | 1.12547 | ||||||||
\(407\) | 6.89700e11 | 1.24591 | ||||||||
\(408\) | −4.25106e11 | −0.759498 | ||||||||
\(409\) | 5.91126e11 | 1.04454 | 0.522270 | − | 0.852780i | \(-0.325085\pi\) | ||||
0.522270 | + | 0.852780i | \(0.325085\pi\) | |||||||
\(410\) | −6.18915e11 | −1.08169 | ||||||||
\(411\) | −1.53683e11 | −0.265668 | ||||||||
\(412\) | 1.27174e12 | 2.17450 | ||||||||
\(413\) | −1.17992e11 | −0.199563 | ||||||||
\(414\) | 1.25972e11 | 0.210753 | ||||||||
\(415\) | −7.20173e11 | −1.19185 | ||||||||
\(416\) | 1.18172e12 | 1.93462 | ||||||||
\(417\) | 1.15166e11 | 0.186514 | ||||||||
\(418\) | −1.45765e12 | −2.33540 | ||||||||
\(419\) | −5.16849e11 | −0.819221 | −0.409610 | − | 0.912261i | \(-0.634335\pi\) | ||||
−0.409610 | + | 0.912261i | \(0.634335\pi\) | |||||||
\(420\) | −1.14709e12 | −1.79876 | ||||||||
\(421\) | 4.07079e11 | 0.631552 | 0.315776 | − | 0.948834i | \(-0.397735\pi\) | ||||
0.315776 | + | 0.948834i | \(0.397735\pi\) | |||||||
\(422\) | −3.21557e11 | −0.493573 | ||||||||
\(423\) | 4.68114e10 | 0.0710918 | ||||||||
\(424\) | 1.00706e12 | 1.51324 | ||||||||
\(425\) | 8.89336e11 | 1.32226 | ||||||||
\(426\) | 7.16665e11 | 1.05432 | ||||||||
\(427\) | 2.12852e11 | 0.309850 | ||||||||
\(428\) | 3.67283e11 | 0.529059 | ||||||||
\(429\) | −8.48290e11 | −1.20917 | ||||||||
\(430\) | −8.60828e11 | −1.21425 | ||||||||
\(431\) | −8.85168e11 | −1.23560 | −0.617800 | − | 0.786335i | \(-0.711976\pi\) | ||||
−0.617800 | + | 0.786335i | \(0.711976\pi\) | |||||||
\(432\) | −3.20534e10 | −0.0442789 | ||||||||
\(433\) | 6.74952e11 | 0.922735 | 0.461368 | − | 0.887209i | \(-0.347359\pi\) | ||||
0.461368 | + | 0.887209i | \(0.347359\pi\) | |||||||
\(434\) | −2.56857e12 | −3.47527 | ||||||||
\(435\) | 2.68979e11 | 0.360178 | ||||||||
\(436\) | −1.83881e12 | −2.43696 | ||||||||
\(437\) | 3.53392e11 | 0.463543 | ||||||||
\(438\) | 2.87223e11 | 0.372894 | ||||||||
\(439\) | 1.28318e12 | 1.64892 | 0.824458 | − | 0.565922i | \(-0.191480\pi\) | ||||
0.824458 | + | 0.565922i | \(0.191480\pi\) | |||||||
\(440\) | 1.08504e12 | 1.38009 | ||||||||
\(441\) | 3.57343e11 | 0.449896 | ||||||||
\(442\) | −3.41612e12 | −4.25729 | ||||||||
\(443\) | 1.44560e12 | 1.78332 | 0.891662 | − | 0.452701i | \(-0.149539\pi\) | ||||
0.891662 | + | 0.452701i | \(0.149539\pi\) | |||||||
\(444\) | −7.00797e11 | −0.855793 | ||||||||
\(445\) | 1.60797e12 | 1.94383 | ||||||||
\(446\) | 1.84313e12 | 2.20572 | ||||||||
\(447\) | −8.00222e11 | −0.948040 | ||||||||
\(448\) | 2.12670e12 | 2.49433 | ||||||||
\(449\) | −7.76770e11 | −0.901953 | −0.450977 | − | 0.892536i | \(-0.648924\pi\) | ||||
−0.450977 | + | 0.892536i | \(0.648924\pi\) | |||||||
\(450\) | −3.73006e11 | −0.428805 | ||||||||
\(451\) | −5.65585e11 | −0.643730 | ||||||||
\(452\) | −1.07680e12 | −1.21342 | ||||||||
\(453\) | −5.40517e11 | −0.603070 | ||||||||
\(454\) | 7.66486e11 | 0.846745 | ||||||||
\(455\) | −3.11297e12 | −3.40505 | ||||||||
\(456\) | 5.00183e11 | 0.541736 | ||||||||
\(457\) | 7.01907e11 | 0.752760 | 0.376380 | − | 0.926465i | \(-0.377169\pi\) | ||||
0.376380 | + | 0.926465i | \(0.377169\pi\) | |||||||
\(458\) | −1.45314e12 | −1.54317 | ||||||||
\(459\) | 2.98016e11 | 0.313388 | ||||||||
\(460\) | −7.78942e11 | −0.811138 | ||||||||
\(461\) | −4.87181e11 | −0.502385 | −0.251192 | − | 0.967937i | \(-0.580823\pi\) | ||||
−0.251192 | + | 0.967937i | \(0.580823\pi\) | |||||||
\(462\) | −1.74249e12 | −1.77943 | ||||||||
\(463\) | 1.22256e12 | 1.23639 | 0.618194 | − | 0.786025i | \(-0.287864\pi\) | ||||
0.618194 | + | 0.786025i | \(0.287864\pi\) | |||||||
\(464\) | −1.06466e11 | −0.106630 | ||||||||
\(465\) | −1.12127e12 | −1.11217 | ||||||||
\(466\) | −1.42540e12 | −1.40023 | ||||||||
\(467\) | 1.39487e12 | 1.35709 | 0.678543 | − | 0.734561i | \(-0.262612\pi\) | ||||
0.678543 | + | 0.734561i | \(0.262612\pi\) | |||||||
\(468\) | 8.61939e11 | 0.830558 | ||||||||
\(469\) | −2.96078e12 | −2.82572 | ||||||||
\(470\) | −4.81159e11 | −0.454829 | ||||||||
\(471\) | 4.98397e11 | 0.466639 | ||||||||
\(472\) | −1.13406e11 | −0.105171 | ||||||||
\(473\) | −7.86653e11 | −0.722617 | ||||||||
\(474\) | 5.51556e10 | 0.0501865 | ||||||||
\(475\) | −1.04640e12 | −0.943141 | ||||||||
\(476\) | −4.22135e12 | −3.76895 | ||||||||
\(477\) | −7.05986e11 | −0.624401 | ||||||||
\(478\) | 1.13093e12 | 0.990856 | ||||||||
\(479\) | 7.97510e11 | 0.692192 | 0.346096 | − | 0.938199i | \(-0.387507\pi\) | ||||
0.346096 | + | 0.938199i | \(0.387507\pi\) | |||||||
\(480\) | 1.05964e12 | 0.911115 | ||||||||
\(481\) | −1.90183e12 | −1.62001 | ||||||||
\(482\) | 2.92071e12 | 2.46477 | ||||||||
\(483\) | 4.22447e11 | 0.353191 | ||||||||
\(484\) | 1.11322e12 | 0.922100 | ||||||||
\(485\) | 1.97544e12 | 1.62116 | ||||||||
\(486\) | −1.24994e11 | −0.101631 | ||||||||
\(487\) | −1.76341e12 | −1.42060 | −0.710302 | − | 0.703897i | \(-0.751442\pi\) | ||||
−0.710302 | + | 0.703897i | \(0.751442\pi\) | |||||||
\(488\) | 2.04578e11 | 0.163294 | ||||||||
\(489\) | 1.29450e12 | 1.02379 | ||||||||
\(490\) | −3.67302e12 | −2.87833 | ||||||||
\(491\) | 9.35179e11 | 0.726153 | 0.363077 | − | 0.931759i | \(-0.381726\pi\) | ||||
0.363077 | + | 0.931759i | \(0.381726\pi\) | |||||||
\(492\) | 5.74685e11 | 0.442168 | ||||||||
\(493\) | 9.89861e11 | 0.754680 | ||||||||
\(494\) | 4.01944e12 | 3.03664 | ||||||||
\(495\) | −7.60654e11 | −0.569461 | ||||||||
\(496\) | 4.43813e11 | 0.329255 | ||||||||
\(497\) | 2.40333e12 | 1.76689 | ||||||||
\(498\) | 1.11158e12 | 0.809861 | ||||||||
\(499\) | 2.32592e12 | 1.67935 | 0.839676 | − | 0.543088i | \(-0.182745\pi\) | ||||
0.839676 | + | 0.543088i | \(0.182745\pi\) | |||||||
\(500\) | −5.34036e11 | −0.382125 | ||||||||
\(501\) | −2.70416e11 | −0.191762 | ||||||||
\(502\) | 1.20580e11 | 0.0847436 | ||||||||
\(503\) | −2.02638e12 | −1.41145 | −0.705723 | − | 0.708488i | \(-0.749378\pi\) | ||||
−0.705723 | + | 0.708488i | \(0.749378\pi\) | |||||||
\(504\) | 5.97922e11 | 0.412769 | ||||||||
\(505\) | −2.73630e12 | −1.87220 | ||||||||
\(506\) | −1.18326e12 | −0.802420 | ||||||||
\(507\) | 1.48017e12 | 0.994893 | ||||||||
\(508\) | 3.29980e11 | 0.219837 | ||||||||
\(509\) | 2.28341e12 | 1.50784 | 0.753919 | − | 0.656968i | \(-0.228161\pi\) | ||||
0.753919 | + | 0.656968i | \(0.228161\pi\) | |||||||
\(510\) | −3.06321e12 | −2.00498 | ||||||||
\(511\) | 9.63199e11 | 0.624917 | ||||||||
\(512\) | −7.08433e11 | −0.455600 | ||||||||
\(513\) | −3.50648e11 | −0.223534 | ||||||||
\(514\) | 2.47700e12 | 1.56528 | ||||||||
\(515\) | 3.09470e12 | 1.93859 | ||||||||
\(516\) | 7.99310e11 | 0.496354 | ||||||||
\(517\) | −4.39699e11 | −0.270675 | ||||||||
\(518\) | −3.90658e12 | −2.38403 | ||||||||
\(519\) | −5.60083e11 | −0.338844 | ||||||||
\(520\) | −2.99197e12 | −1.79449 | ||||||||
\(521\) | 1.64372e12 | 0.977367 | 0.488683 | − | 0.872461i | \(-0.337477\pi\) | ||||
0.488683 | + | 0.872461i | \(0.337477\pi\) | |||||||
\(522\) | −4.15169e11 | −0.244741 | ||||||||
\(523\) | −3.11181e11 | −0.181868 | −0.0909339 | − | 0.995857i | \(-0.528985\pi\) | ||||
−0.0909339 | + | 0.995857i | \(0.528985\pi\) | |||||||
\(524\) | −1.97420e12 | −1.14393 | ||||||||
\(525\) | −1.25087e12 | −0.718615 | ||||||||
\(526\) | 2.97263e12 | 1.69319 | ||||||||
\(527\) | −4.12634e12 | −2.33033 | ||||||||
\(528\) | 3.01077e11 | 0.168587 | ||||||||
\(529\) | −1.51429e12 | −0.840731 | ||||||||
\(530\) | 7.25661e12 | 3.99477 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | 4.96688e12 | 2.68832 | ||||||||
\(533\) | 1.55958e12 | 0.837021 | ||||||||
\(534\) | −2.48190e12 | −1.32084 | ||||||||
\(535\) | 8.93764e11 | 0.471662 | ||||||||
\(536\) | −2.84570e12 | −1.48918 | ||||||||
\(537\) | −2.67517e11 | −0.138825 | ||||||||
\(538\) | −1.74884e12 | −0.899973 | ||||||||
\(539\) | −3.35652e12 | −1.71293 | ||||||||
\(540\) | 7.72893e11 | 0.391154 | ||||||||
\(541\) | −8.12242e11 | −0.407659 | −0.203830 | − | 0.979006i | \(-0.565339\pi\) | ||||
−0.203830 | + | 0.979006i | \(0.565339\pi\) | |||||||
\(542\) | 4.14473e12 | 2.06300 | ||||||||
\(543\) | −2.01662e12 | −0.995463 | ||||||||
\(544\) | 3.89955e12 | 1.90906 | ||||||||
\(545\) | −4.47465e12 | −2.17258 | ||||||||
\(546\) | 4.80486e12 | 2.31374 | ||||||||
\(547\) | −5.36570e11 | −0.256261 | −0.128131 | − | 0.991757i | \(-0.540898\pi\) | ||||
−0.128131 | + | 0.991757i | \(0.540898\pi\) | |||||||
\(548\) | −1.46677e12 | −0.694786 | ||||||||
\(549\) | −1.43417e11 | −0.0673792 | ||||||||
\(550\) | 3.50365e12 | 1.63263 | ||||||||
\(551\) | −1.16468e12 | −0.538299 | ||||||||
\(552\) | 4.06026e11 | 0.186135 | ||||||||
\(553\) | 1.84964e11 | 0.0841054 | ||||||||
\(554\) | 2.63412e12 | 1.18807 | ||||||||
\(555\) | −1.70535e12 | −0.762949 | ||||||||
\(556\) | 1.09916e12 | 0.487779 | ||||||||
\(557\) | 6.35994e11 | 0.279965 | 0.139983 | − | 0.990154i | \(-0.455295\pi\) | ||||
0.139983 | + | 0.990154i | \(0.455295\pi\) | |||||||
\(558\) | 1.73068e12 | 0.755721 | ||||||||
\(559\) | 2.16917e12 | 0.939596 | ||||||||
\(560\) | 1.10486e12 | 0.474747 | ||||||||
\(561\) | −2.79926e12 | −1.19319 | ||||||||
\(562\) | 1.46728e12 | 0.620441 | ||||||||
\(563\) | 5.11920e11 | 0.214741 | 0.107370 | − | 0.994219i | \(-0.465757\pi\) | ||||
0.107370 | + | 0.994219i | \(0.465757\pi\) | |||||||
\(564\) | 4.46774e11 | 0.185922 | ||||||||
\(565\) | −2.62033e12 | −1.08178 | ||||||||
\(566\) | 6.74837e12 | 2.76392 | ||||||||
\(567\) | −4.19166e11 | −0.170319 | ||||||||
\(568\) | 2.30991e12 | 0.931167 | ||||||||
\(569\) | 4.59360e11 | 0.183716 | 0.0918581 | − | 0.995772i | \(-0.470719\pi\) | ||||
0.0918581 | + | 0.995772i | \(0.470719\pi\) | |||||||
\(570\) | 3.60419e12 | 1.43012 | ||||||||
\(571\) | 3.99628e12 | 1.57323 | 0.786616 | − | 0.617442i | \(-0.211831\pi\) | ||||
0.786616 | + | 0.617442i | \(0.211831\pi\) | |||||||
\(572\) | −8.09619e12 | −3.16227 | ||||||||
\(573\) | −1.41130e11 | −0.0546921 | ||||||||
\(574\) | 3.20357e12 | 1.23177 | ||||||||
\(575\) | −8.49420e11 | −0.324054 | ||||||||
\(576\) | −1.43294e12 | −0.542410 | ||||||||
\(577\) | −1.20235e12 | −0.451584 | −0.225792 | − | 0.974176i | \(-0.572497\pi\) | ||||
−0.225792 | + | 0.974176i | \(0.572497\pi\) | |||||||
\(578\) | −7.02167e12 | −2.61677 | ||||||||
\(579\) | −1.01623e12 | −0.375783 | ||||||||
\(580\) | 2.56717e12 | 0.941952 | ||||||||
\(581\) | 3.72769e12 | 1.35721 | ||||||||
\(582\) | −3.04909e12 | −1.10158 | ||||||||
\(583\) | 6.63133e12 | 2.37734 | ||||||||
\(584\) | 9.25760e11 | 0.329337 | ||||||||
\(585\) | 2.09748e12 | 0.740452 | ||||||||
\(586\) | −3.53832e12 | −1.23953 | ||||||||
\(587\) | −4.83604e12 | −1.68120 | −0.840598 | − | 0.541660i | \(-0.817796\pi\) | ||||
−0.840598 | + | 0.541660i | \(0.817796\pi\) | |||||||
\(588\) | 3.41053e12 | 1.17659 | ||||||||
\(589\) | 4.85509e12 | 1.66218 | ||||||||
\(590\) | −8.17176e11 | −0.277640 | ||||||||
\(591\) | 4.35230e11 | 0.146749 | ||||||||
\(592\) | 6.75001e11 | 0.225869 | ||||||||
\(593\) | −3.57818e12 | −1.18827 | −0.594136 | − | 0.804365i | \(-0.702506\pi\) | ||||
−0.594136 | + | 0.804365i | \(0.702506\pi\) | |||||||
\(594\) | 1.17407e12 | 0.386950 | ||||||||
\(595\) | −1.02724e13 | −3.36006 | ||||||||
\(596\) | −7.63742e12 | −2.47935 | ||||||||
\(597\) | −1.96603e12 | −0.633441 | ||||||||
\(598\) | 3.26280e12 | 1.04336 | ||||||||
\(599\) | 5.28387e12 | 1.67699 | 0.838496 | − | 0.544907i | \(-0.183435\pi\) | ||||
0.838496 | + | 0.544907i | \(0.183435\pi\) | |||||||
\(600\) | −1.20225e12 | −0.378717 | ||||||||
\(601\) | 2.67502e12 | 0.836359 | 0.418179 | − | 0.908365i | \(-0.362668\pi\) | ||||
0.418179 | + | 0.908365i | \(0.362668\pi\) | |||||||
\(602\) | 4.45574e12 | 1.38272 | ||||||||
\(603\) | 1.99494e12 | 0.614472 | ||||||||
\(604\) | −5.15876e12 | −1.57717 | ||||||||
\(605\) | 2.70897e12 | 0.822062 | ||||||||
\(606\) | 4.22347e12 | 1.27216 | ||||||||
\(607\) | 3.70644e12 | 1.10818 | 0.554088 | − | 0.832458i | \(-0.313067\pi\) | ||||
0.554088 | + | 0.832458i | \(0.313067\pi\) | |||||||
\(608\) | −4.58824e12 | −1.36170 | ||||||||
\(609\) | −1.39226e12 | −0.410151 | ||||||||
\(610\) | 1.47414e12 | 0.431076 | ||||||||
\(611\) | 1.21246e12 | 0.351950 | ||||||||
\(612\) | 2.84430e12 | 0.819584 | ||||||||
\(613\) | 6.45333e12 | 1.84592 | 0.922958 | − | 0.384900i | \(-0.125764\pi\) | ||||
0.922958 | + | 0.384900i | \(0.125764\pi\) | |||||||
\(614\) | 4.10021e12 | 1.16426 | ||||||||
\(615\) | 1.39847e12 | 0.394198 | ||||||||
\(616\) | −5.61628e12 | −1.57158 | ||||||||
\(617\) | −6.71687e12 | −1.86588 | −0.932941 | − | 0.360031i | \(-0.882766\pi\) | ||||
−0.932941 | + | 0.360031i | \(0.882766\pi\) | |||||||
\(618\) | −4.77667e12 | −1.31728 | ||||||||
\(619\) | −4.48065e12 | −1.22669 | −0.613343 | − | 0.789817i | \(-0.710176\pi\) | ||||
−0.613343 | + | 0.789817i | \(0.710176\pi\) | |||||||
\(620\) | −1.07015e13 | −2.90859 | ||||||||
\(621\) | −2.84640e11 | −0.0768039 | ||||||||
\(622\) | 7.59092e11 | 0.203347 | ||||||||
\(623\) | −8.32304e12 | −2.21353 | ||||||||
\(624\) | −8.30212e11 | −0.219209 | ||||||||
\(625\) | −4.39705e12 | −1.15266 | ||||||||
\(626\) | 3.51784e12 | 0.915571 | ||||||||
\(627\) | 3.29363e12 | 0.851081 | ||||||||
\(628\) | 4.75676e12 | 1.22037 | ||||||||
\(629\) | −6.27581e12 | −1.59861 | ||||||||
\(630\) | 4.30848e12 | 1.08966 | ||||||||
\(631\) | 3.31200e12 | 0.831683 | 0.415842 | − | 0.909437i | \(-0.363487\pi\) | ||||
0.415842 | + | 0.909437i | \(0.363487\pi\) | |||||||
\(632\) | 1.77774e11 | 0.0443243 | ||||||||
\(633\) | 7.26571e11 | 0.179871 | ||||||||
\(634\) | 1.66595e12 | 0.409507 | ||||||||
\(635\) | 8.02988e11 | 0.195987 | ||||||||
\(636\) | −6.73803e12 | −1.63296 | ||||||||
\(637\) | 9.25552e12 | 2.22727 | ||||||||
\(638\) | 3.89968e12 | 0.931828 | ||||||||
\(639\) | −1.61934e12 | −0.384223 | ||||||||
\(640\) | 8.03079e12 | 1.89212 | ||||||||
\(641\) | 3.34924e12 | 0.783584 | 0.391792 | − | 0.920054i | \(-0.371855\pi\) | ||||
0.391792 | + | 0.920054i | \(0.371855\pi\) | |||||||
\(642\) | −1.37952e12 | −0.320495 | ||||||||
\(643\) | −3.43017e12 | −0.791345 | −0.395673 | − | 0.918392i | \(-0.629489\pi\) | ||||
−0.395673 | + | 0.918392i | \(0.629489\pi\) | |||||||
\(644\) | 4.03189e12 | 0.923681 | ||||||||
\(645\) | 1.94508e12 | 0.442505 | ||||||||
\(646\) | 1.32637e13 | 2.99652 | ||||||||
\(647\) | 5.54972e12 | 1.24509 | 0.622546 | − | 0.782583i | \(-0.286098\pi\) | ||||
0.622546 | + | 0.782583i | \(0.286098\pi\) | |||||||
\(648\) | −4.02873e11 | −0.0897596 | ||||||||
\(649\) | −7.46762e11 | −0.165227 | ||||||||
\(650\) | −9.66120e12 | −2.12286 | ||||||||
\(651\) | 5.80380e12 | 1.26648 | ||||||||
\(652\) | 1.23549e13 | 2.67746 | ||||||||
\(653\) | −2.85530e11 | −0.0614529 | −0.0307265 | − | 0.999528i | \(-0.509782\pi\) | ||||
−0.0307265 | + | 0.999528i | \(0.509782\pi\) | |||||||
\(654\) | 6.90662e12 | 1.47627 | ||||||||
\(655\) | −4.80410e12 | −1.01983 | ||||||||
\(656\) | −5.53532e11 | −0.116701 | ||||||||
\(657\) | −6.48993e11 | −0.135893 | ||||||||
\(658\) | 2.49053e12 | 0.517935 | ||||||||
\(659\) | 7.57432e11 | 0.156444 | 0.0782221 | − | 0.996936i | \(-0.475076\pi\) | ||||
0.0782221 | + | 0.996936i | \(0.475076\pi\) | |||||||
\(660\) | −7.25978e12 | −1.48928 | ||||||||
\(661\) | 5.28983e12 | 1.07779 | 0.538896 | − | 0.842372i | \(-0.318841\pi\) | ||||
0.538896 | + | 0.842372i | \(0.318841\pi\) | |||||||
\(662\) | −1.81782e12 | −0.367867 | ||||||||
\(663\) | 7.71888e12 | 1.55147 | ||||||||
\(664\) | 3.58279e12 | 0.715263 | ||||||||
\(665\) | 1.20866e13 | 2.39667 | ||||||||
\(666\) | 2.63221e12 | 0.518425 | ||||||||
\(667\) | −9.45434e11 | −0.184954 | ||||||||
\(668\) | −2.58088e12 | −0.501504 | ||||||||
\(669\) | −4.16464e12 | −0.803822 | ||||||||
\(670\) | −2.05054e13 | −3.93125 | ||||||||
\(671\) | 1.34712e12 | 0.256539 | ||||||||
\(672\) | −5.48481e12 | −1.03753 | ||||||||
\(673\) | 3.50601e12 | 0.658788 | 0.329394 | − | 0.944193i | \(-0.393156\pi\) | ||||
0.329394 | + | 0.944193i | \(0.393156\pi\) | |||||||
\(674\) | 1.23326e13 | 2.30189 | ||||||||
\(675\) | 8.42824e11 | 0.156268 | ||||||||
\(676\) | 1.41269e13 | 2.60189 | ||||||||
\(677\) | −3.61379e12 | −0.661171 | −0.330585 | − | 0.943776i | \(-0.607246\pi\) | ||||
−0.330585 | + | 0.943776i | \(0.607246\pi\) | |||||||
\(678\) | 4.04447e12 | 0.735069 | ||||||||
\(679\) | −1.02251e13 | −1.84609 | ||||||||
\(680\) | −9.87314e12 | −1.77078 | ||||||||
\(681\) | −1.73191e12 | −0.308577 | ||||||||
\(682\) | −1.62562e13 | −2.87733 | ||||||||
\(683\) | −1.51664e12 | −0.266680 | −0.133340 | − | 0.991070i | \(-0.542570\pi\) | ||||
−0.133340 | + | 0.991070i | \(0.542570\pi\) | |||||||
\(684\) | −3.34663e12 | −0.584594 | ||||||||
\(685\) | −3.56932e12 | −0.619409 | ||||||||
\(686\) | 4.92576e12 | 0.849209 | ||||||||
\(687\) | 3.28344e12 | 0.562372 | ||||||||
\(688\) | −7.69889e11 | −0.131003 | ||||||||
\(689\) | −1.82857e13 | −3.09119 | ||||||||
\(690\) | 2.92572e12 | 0.491374 | ||||||||
\(691\) | 7.69784e12 | 1.28445 | 0.642226 | − | 0.766515i | \(-0.278011\pi\) | ||||
0.642226 | + | 0.766515i | \(0.278011\pi\) | |||||||
\(692\) | −5.34550e12 | −0.886158 | ||||||||
\(693\) | 3.93723e12 | 0.648472 | ||||||||
\(694\) | 3.82189e12 | 0.625404 | ||||||||
\(695\) | 2.67474e12 | 0.434861 | ||||||||
\(696\) | −1.33815e12 | −0.216153 | ||||||||
\(697\) | 5.14645e12 | 0.825962 | ||||||||
\(698\) | 1.10830e13 | 1.76729 | ||||||||
\(699\) | 3.22075e12 | 0.510281 | ||||||||
\(700\) | −1.19385e13 | −1.87935 | ||||||||
\(701\) | −6.31846e11 | −0.0988280 | −0.0494140 | − | 0.998778i | \(-0.515735\pi\) | ||||
−0.0494140 | + | 0.998778i | \(0.515735\pi\) | |||||||
\(702\) | −3.23746e12 | −0.503138 | ||||||||
\(703\) | 7.38417e12 | 1.14026 | ||||||||
\(704\) | 1.34596e13 | 2.06517 | ||||||||
\(705\) | 1.08720e12 | 0.165752 | ||||||||
\(706\) | 1.29093e13 | 1.95561 | ||||||||
\(707\) | 1.41634e13 | 2.13196 | ||||||||
\(708\) | 7.58777e11 | 0.113492 | ||||||||
\(709\) | −7.86914e12 | −1.16955 | −0.584775 | − | 0.811195i | \(-0.698817\pi\) | ||||
−0.584775 | + | 0.811195i | \(0.698817\pi\) | |||||||
\(710\) | 1.66446e13 | 2.45817 | ||||||||
\(711\) | −1.24627e11 | −0.0182893 | ||||||||
\(712\) | −7.99952e12 | −1.16655 | ||||||||
\(713\) | 3.94114e12 | 0.571109 | ||||||||
\(714\) | 1.58555e13 | 2.28316 | ||||||||
\(715\) | −1.97016e13 | −2.81920 | ||||||||
\(716\) | −2.55321e12 | −0.363060 | ||||||||
\(717\) | −2.55539e12 | −0.361094 | ||||||||
\(718\) | −2.54380e12 | −0.357210 | ||||||||
\(719\) | 1.18994e13 | 1.66052 | 0.830259 | − | 0.557378i | \(-0.188193\pi\) | ||||
0.830259 | + | 0.557378i | \(0.188193\pi\) | |||||||
\(720\) | −7.44444e11 | −0.103237 | ||||||||
\(721\) | −1.60185e13 | −2.20756 | ||||||||
\(722\) | −4.03846e12 | −0.553093 | ||||||||
\(723\) | −6.59947e12 | −0.898229 | ||||||||
\(724\) | −1.92469e13 | −2.60338 | ||||||||
\(725\) | 2.79945e12 | 0.376315 | ||||||||
\(726\) | −4.18129e12 | −0.558593 | ||||||||
\(727\) | −9.95970e12 | −1.32233 | −0.661167 | − | 0.750238i | \(-0.729939\pi\) | ||||
−0.661167 | + | 0.750238i | \(0.729939\pi\) | |||||||
\(728\) | 1.54867e13 | 2.04347 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 6.67079e12 | 0.869409 | ||||||||
\(731\) | 7.15802e12 | 0.927181 | ||||||||
\(732\) | −1.36879e12 | −0.176213 | ||||||||
\(733\) | −2.10318e12 | −0.269097 | −0.134549 | − | 0.990907i | \(-0.542958\pi\) | ||||
−0.134549 | + | 0.990907i | \(0.542958\pi\) | |||||||
\(734\) | −1.12255e12 | −0.142749 | ||||||||
\(735\) | 8.29935e12 | 1.04894 | ||||||||
\(736\) | −3.72453e12 | −0.467865 | ||||||||
\(737\) | −1.87385e13 | −2.33954 | ||||||||
\(738\) | −2.15853e12 | −0.267858 | ||||||||
\(739\) | −1.19388e13 | −1.47251 | −0.736256 | − | 0.676703i | \(-0.763408\pi\) | ||||
−0.736256 | + | 0.676703i | \(0.763408\pi\) | |||||||
\(740\) | −1.62761e13 | −1.99530 | ||||||||
\(741\) | −9.08209e12 | −1.10663 | ||||||||
\(742\) | −3.75610e13 | −4.54903 | ||||||||
\(743\) | −9.79773e12 | −1.17944 | −0.589720 | − | 0.807608i | \(-0.700762\pi\) | ||||
−0.589720 | + | 0.807608i | \(0.700762\pi\) | |||||||
\(744\) | 5.57821e12 | 0.667447 | ||||||||
\(745\) | −1.85853e13 | −2.21037 | ||||||||
\(746\) | −2.16289e13 | −2.55687 | ||||||||
\(747\) | −2.51168e12 | −0.295135 | ||||||||
\(748\) | −2.67165e13 | −3.12048 | ||||||||
\(749\) | −4.62621e12 | −0.537103 | ||||||||
\(750\) | 2.00585e12 | 0.231485 | ||||||||
\(751\) | −1.06936e13 | −1.22672 | −0.613359 | − | 0.789804i | \(-0.710182\pi\) | ||||
−0.613359 | + | 0.789804i | \(0.710182\pi\) | |||||||
\(752\) | −4.30328e11 | −0.0490704 | ||||||||
\(753\) | −2.72455e11 | −0.0308828 | ||||||||
\(754\) | −1.07532e13 | −1.21163 | ||||||||
\(755\) | −1.25536e13 | −1.40607 | ||||||||
\(756\) | −4.00058e12 | −0.445425 | ||||||||
\(757\) | −5.82516e12 | −0.644728 | −0.322364 | − | 0.946616i | \(-0.604477\pi\) | ||||
−0.322364 | + | 0.946616i | \(0.604477\pi\) | |||||||
\(758\) | 5.66037e12 | 0.622778 | ||||||||
\(759\) | 2.67362e12 | 0.292423 | ||||||||
\(760\) | 1.16168e13 | 1.26307 | ||||||||
\(761\) | 6.06747e12 | 0.655808 | 0.327904 | − | 0.944711i | \(-0.393658\pi\) | ||||
0.327904 | + | 0.944711i | \(0.393658\pi\) | |||||||
\(762\) | −1.23941e12 | −0.133174 | ||||||||
\(763\) | 2.31613e13 | 2.47401 | ||||||||
\(764\) | −1.34697e12 | −0.143033 | ||||||||
\(765\) | 6.92145e12 | 0.730669 | ||||||||
\(766\) | 2.72288e13 | 2.85758 | ||||||||
\(767\) | 2.05918e12 | 0.214839 | ||||||||
\(768\) | −3.33789e12 | −0.346216 | ||||||||
\(769\) | −8.69120e12 | −0.896213 | −0.448107 | − | 0.893980i | \(-0.647902\pi\) | ||||
−0.448107 | + | 0.893980i | \(0.647902\pi\) | |||||||
\(770\) | −4.04695e13 | −4.14877 | ||||||||
\(771\) | −5.59689e12 | −0.570430 | ||||||||
\(772\) | −9.69900e12 | −0.982764 | ||||||||
\(773\) | −6.91962e12 | −0.697067 | −0.348534 | − | 0.937296i | \(-0.613320\pi\) | ||||
−0.348534 | + | 0.937296i | \(0.613320\pi\) | |||||||
\(774\) | −3.00223e12 | −0.300683 | ||||||||
\(775\) | −1.16698e13 | −1.16200 | ||||||||
\(776\) | −9.82765e12 | −0.972908 | ||||||||
\(777\) | 8.82708e12 | 0.868806 | ||||||||
\(778\) | 6.06769e12 | 0.593766 | ||||||||
\(779\) | −6.05535e12 | −0.589143 | ||||||||
\(780\) | 2.00186e13 | 1.93646 | ||||||||
\(781\) | 1.52104e13 | 1.46289 | ||||||||
\(782\) | 1.07668e13 | 1.02958 | ||||||||
\(783\) | 9.38092e11 | 0.0891903 | ||||||||
\(784\) | −3.28499e12 | −0.310536 | ||||||||
\(785\) | 1.15753e13 | 1.08798 | ||||||||
\(786\) | 7.41512e12 | 0.692973 | ||||||||
\(787\) | −1.52860e13 | −1.42039 | −0.710195 | − | 0.704005i | \(-0.751393\pi\) | ||||
−0.710195 | + | 0.704005i | \(0.751393\pi\) | |||||||
\(788\) | 4.15389e12 | 0.383784 | ||||||||
\(789\) | −6.71678e12 | −0.617042 | ||||||||
\(790\) | 1.28100e12 | 0.117011 | ||||||||
\(791\) | 1.35631e13 | 1.23187 | ||||||||
\(792\) | 3.78419e12 | 0.341751 | ||||||||
\(793\) | −3.71464e12 | −0.333570 | ||||||||
\(794\) | −7.57438e11 | −0.0676324 | ||||||||
\(795\) | −1.63966e13 | −1.45580 | ||||||||
\(796\) | −1.87641e13 | −1.65660 | ||||||||
\(797\) | −1.37425e13 | −1.20644 | −0.603219 | − | 0.797576i | \(-0.706115\pi\) | ||||
−0.603219 | + | 0.797576i | \(0.706115\pi\) | |||||||
\(798\) | −1.86557e13 | −1.62854 | ||||||||
\(799\) | 4.00097e12 | 0.347300 | ||||||||
\(800\) | 1.10284e13 | 0.951935 | ||||||||
\(801\) | 5.60797e12 | 0.481348 | ||||||||
\(802\) | 4.45056e12 | 0.379866 | ||||||||
\(803\) | 6.09599e12 | 0.517397 | ||||||||
\(804\) | 1.90400e13 | 1.60699 | ||||||||
\(805\) | 9.81138e12 | 0.823472 | ||||||||
\(806\) | 4.48261e13 | 3.74130 | ||||||||
\(807\) | 3.95158e12 | 0.327974 | ||||||||
\(808\) | 1.36128e13 | 1.12356 | ||||||||
\(809\) | −3.57292e12 | −0.293262 | −0.146631 | − | 0.989191i | \(-0.546843\pi\) | ||||
−0.146631 | + | 0.989191i | \(0.546843\pi\) | |||||||
\(810\) | −2.90300e12 | −0.236954 | ||||||||
\(811\) | 1.71499e13 | 1.39209 | 0.696046 | − | 0.717998i | \(-0.254941\pi\) | ||||
0.696046 | + | 0.717998i | \(0.254941\pi\) | |||||||
\(812\) | −1.32879e13 | −1.07264 | ||||||||
\(813\) | −9.36519e12 | −0.751812 | ||||||||
\(814\) | −2.47243e13 | −1.97385 | ||||||||
\(815\) | 3.00649e13 | 2.38699 | ||||||||
\(816\) | −2.73960e12 | −0.216313 | ||||||||
\(817\) | −8.42219e12 | −0.661341 | ||||||||
\(818\) | −2.11906e13 | −1.65483 | ||||||||
\(819\) | −1.08568e13 | −0.843187 | ||||||||
\(820\) | 1.33471e13 | 1.03092 | ||||||||
\(821\) | −6.68653e12 | −0.513637 | −0.256819 | − | 0.966460i | \(-0.582674\pi\) | ||||
−0.256819 | + | 0.966460i | \(0.582674\pi\) | |||||||
\(822\) | 5.50924e12 | 0.420890 | ||||||||
\(823\) | 1.36851e13 | 1.03979 | 0.519897 | − | 0.854229i | \(-0.325970\pi\) | ||||
0.519897 | + | 0.854229i | \(0.325970\pi\) | |||||||
\(824\) | −1.53959e13 | −1.16341 | ||||||||
\(825\) | −7.91664e12 | −0.594974 | ||||||||
\(826\) | 4.22979e12 | 0.316161 | ||||||||
\(827\) | 1.79247e13 | 1.33253 | 0.666265 | − | 0.745715i | \(-0.267892\pi\) | ||||
0.666265 | + | 0.745715i | \(0.267892\pi\) | |||||||
\(828\) | −2.71664e12 | −0.200861 | ||||||||
\(829\) | 6.90632e12 | 0.507869 | 0.253934 | − | 0.967221i | \(-0.418275\pi\) | ||||
0.253934 | + | 0.967221i | \(0.418275\pi\) | |||||||
\(830\) | 2.58167e13 | 1.88821 | ||||||||
\(831\) | −5.95190e12 | −0.432963 | ||||||||
\(832\) | −3.71146e13 | −2.68528 | ||||||||
\(833\) | 3.05421e13 | 2.19784 | ||||||||
\(834\) | −4.12846e12 | −0.295488 | ||||||||
\(835\) | −6.28044e12 | −0.447096 | ||||||||
\(836\) | 3.14348e13 | 2.22578 | ||||||||
\(837\) | −3.91054e12 | −0.275405 | ||||||||
\(838\) | 1.85280e13 | 1.29787 | ||||||||
\(839\) | −2.60104e13 | −1.81225 | −0.906124 | − | 0.423011i | \(-0.860973\pi\) | ||||
−0.906124 | + | 0.423011i | \(0.860973\pi\) | |||||||
\(840\) | 1.38868e13 | 0.962379 | ||||||||
\(841\) | −1.13913e13 | −0.785218 | ||||||||
\(842\) | −1.45929e13 | −1.00055 | ||||||||
\(843\) | −3.31539e12 | −0.226105 | ||||||||
\(844\) | 6.93449e12 | 0.470407 | ||||||||
\(845\) | 3.43772e13 | 2.31961 | ||||||||
\(846\) | −1.67809e12 | −0.112629 | ||||||||
\(847\) | −1.40219e13 | −0.936120 | ||||||||
\(848\) | 6.49001e12 | 0.430987 | ||||||||
\(849\) | −1.52483e13 | −1.00725 | ||||||||
\(850\) | −3.18808e13 | −2.09481 | ||||||||
\(851\) | 5.99414e12 | 0.391781 | ||||||||
\(852\) | −1.54551e13 | −1.00484 | ||||||||
\(853\) | 1.41771e13 | 0.916888 | 0.458444 | − | 0.888723i | \(-0.348407\pi\) | ||||
0.458444 | + | 0.888723i | \(0.348407\pi\) | |||||||
\(854\) | −7.63030e12 | −0.490887 | ||||||||
\(855\) | −8.14384e12 | −0.521172 | ||||||||
\(856\) | −4.44639e12 | −0.283058 | ||||||||
\(857\) | 1.12350e13 | 0.711476 | 0.355738 | − | 0.934586i | \(-0.384230\pi\) | ||||
0.355738 | + | 0.934586i | \(0.384230\pi\) | |||||||
\(858\) | 3.04094e13 | 1.91565 | ||||||||
\(859\) | 2.44792e13 | 1.53401 | 0.767003 | − | 0.641643i | \(-0.221747\pi\) | ||||
0.767003 | + | 0.641643i | \(0.221747\pi\) | |||||||
\(860\) | 1.85641e13 | 1.15726 | ||||||||
\(861\) | −7.23861e12 | −0.448891 | ||||||||
\(862\) | 3.17315e13 | 1.95752 | ||||||||
\(863\) | 2.35658e13 | 1.44622 | 0.723110 | − | 0.690733i | \(-0.242712\pi\) | ||||
0.723110 | + | 0.690733i | \(0.242712\pi\) | |||||||
\(864\) | 3.69560e12 | 0.225618 | ||||||||
\(865\) | −1.30080e13 | −0.790020 | ||||||||
\(866\) | −2.41956e13 | −1.46186 | ||||||||
\(867\) | 1.58658e13 | 0.953620 | ||||||||
\(868\) | 5.53922e13 | 3.31215 | ||||||||
\(869\) | 1.17062e12 | 0.0696347 | ||||||||
\(870\) | −9.64235e12 | −0.570619 | ||||||||
\(871\) | 5.16708e13 | 3.04203 | ||||||||
\(872\) | 2.22610e13 | 1.30383 | ||||||||
\(873\) | 6.88956e12 | 0.401446 | ||||||||
\(874\) | −1.26684e13 | −0.734377 | ||||||||
\(875\) | 6.72659e12 | 0.387935 | ||||||||
\(876\) | −6.19407e12 | −0.355392 | ||||||||
\(877\) | −2.44619e12 | −0.139634 | −0.0698170 | − | 0.997560i | \(-0.522242\pi\) | ||||
−0.0698170 | + | 0.997560i | \(0.522242\pi\) | |||||||
\(878\) | −4.59995e13 | −2.61233 | ||||||||
\(879\) | 7.99499e12 | 0.451719 | ||||||||
\(880\) | 6.99256e12 | 0.393065 | ||||||||
\(881\) | −9.21734e12 | −0.515483 | −0.257741 | − | 0.966214i | \(-0.582978\pi\) | ||||
−0.257741 | + | 0.966214i | \(0.582978\pi\) | |||||||
\(882\) | −1.28100e13 | −0.712757 | ||||||||
\(883\) | 2.92106e12 | 0.161703 | 0.0808515 | − | 0.996726i | \(-0.474236\pi\) | ||||
0.0808515 | + | 0.996726i | \(0.474236\pi\) | |||||||
\(884\) | 7.36699e13 | 4.05747 | ||||||||
\(885\) | 1.84644e12 | 0.101179 | ||||||||
\(886\) | −5.18217e13 | −2.82527 | ||||||||
\(887\) | 1.35029e13 | 0.732436 | 0.366218 | − | 0.930529i | \(-0.380652\pi\) | ||||
0.366218 | + | 0.930529i | \(0.380652\pi\) | |||||||
\(888\) | 8.48397e12 | 0.457869 | ||||||||
\(889\) | −4.15635e12 | −0.223180 | ||||||||
\(890\) | −5.76425e13 | −3.07956 | ||||||||
\(891\) | −2.65286e12 | −0.141015 | ||||||||
\(892\) | −3.97478e13 | −2.10219 | ||||||||
\(893\) | −4.70757e12 | −0.247722 | ||||||||
\(894\) | 2.86863e13 | 1.50195 | ||||||||
\(895\) | −6.21311e12 | −0.323672 | ||||||||
\(896\) | −4.15682e13 | −2.15464 | ||||||||
\(897\) | −7.37243e12 | −0.380229 | ||||||||
\(898\) | 2.78456e13 | 1.42894 | ||||||||
\(899\) | −1.29889e13 | −0.663213 | ||||||||
\(900\) | 8.04402e12 | 0.408679 | ||||||||
\(901\) | −6.03407e13 | −3.05034 | ||||||||
\(902\) | 2.02751e13 | 1.01984 | ||||||||
\(903\) | −1.00679e13 | −0.503901 | ||||||||
\(904\) | 1.30359e13 | 0.649207 | ||||||||
\(905\) | −4.68363e13 | −2.32094 | ||||||||
\(906\) | 1.93764e13 | 0.955425 | ||||||||
\(907\) | −8.48404e12 | −0.416265 | −0.208133 | − | 0.978101i | \(-0.566739\pi\) | ||||
−0.208133 | + | 0.978101i | \(0.566739\pi\) | |||||||
\(908\) | −1.65296e13 | −0.807002 | ||||||||
\(909\) | −9.54312e12 | −0.463610 | ||||||||
\(910\) | 1.11593e14 | 5.39452 | ||||||||
\(911\) | 2.66713e13 | 1.28295 | 0.641477 | − | 0.767142i | \(-0.278322\pi\) | ||||
0.641477 | + | 0.767142i | \(0.278322\pi\) | |||||||
\(912\) | 3.22344e12 | 0.154292 | ||||||||
\(913\) | 2.35922e13 | 1.12370 | ||||||||
\(914\) | −2.51619e13 | −1.19257 | ||||||||
\(915\) | −3.33088e12 | −0.157096 | ||||||||
\(916\) | 3.13376e13 | 1.47074 | ||||||||
\(917\) | 2.48665e13 | 1.16132 | ||||||||
\(918\) | −1.06832e13 | −0.496490 | ||||||||
\(919\) | 2.08506e13 | 0.964270 | 0.482135 | − | 0.876097i | \(-0.339861\pi\) | ||||
0.482135 | + | 0.876097i | \(0.339861\pi\) | |||||||
\(920\) | 9.43001e12 | 0.433977 | ||||||||
\(921\) | −9.26461e12 | −0.424286 | ||||||||
\(922\) | 1.74644e13 | 0.795913 | ||||||||
\(923\) | −4.19423e13 | −1.90215 | ||||||||
\(924\) | 3.75774e13 | 1.69591 | ||||||||
\(925\) | −1.77488e13 | −0.797132 | ||||||||
\(926\) | −4.38262e13 | −1.95877 | ||||||||
\(927\) | 1.07931e13 | 0.480051 | ||||||||
\(928\) | 1.22750e13 | 0.543319 | ||||||||
\(929\) | 1.22073e13 | 0.537712 | 0.268856 | − | 0.963180i | \(-0.413355\pi\) | ||||
0.268856 | + | 0.963180i | \(0.413355\pi\) | |||||||
\(930\) | 4.01952e13 | 1.76198 | ||||||||
\(931\) | −3.59361e13 | −1.56768 | ||||||||
\(932\) | 3.07392e13 | 1.33451 | ||||||||
\(933\) | −1.71520e12 | −0.0741050 | ||||||||
\(934\) | −5.00031e13 | −2.14999 | ||||||||
\(935\) | −6.50131e13 | −2.78195 | ||||||||
\(936\) | −1.04348e13 | −0.444368 | ||||||||
\(937\) | 3.42377e13 | 1.45103 | 0.725514 | − | 0.688207i | \(-0.241602\pi\) | ||||
0.725514 | + | 0.688207i | \(0.241602\pi\) | |||||||
\(938\) | 1.06138e14 | 4.47670 | ||||||||
\(939\) | −7.94873e12 | −0.333659 | ||||||||
\(940\) | 1.03764e13 | 0.433481 | ||||||||
\(941\) | −7.47857e12 | −0.310932 | −0.155466 | − | 0.987841i | \(-0.549688\pi\) | ||||
−0.155466 | + | 0.987841i | \(0.549688\pi\) | |||||||
\(942\) | −1.78665e13 | −0.739283 | ||||||||
\(943\) | −4.91546e12 | −0.202424 | ||||||||
\(944\) | −7.30848e11 | −0.0299539 | ||||||||
\(945\) | −9.73519e12 | −0.397101 | ||||||||
\(946\) | 2.81999e13 | 1.14482 | ||||||||
\(947\) | −2.42514e13 | −0.979857 | −0.489928 | − | 0.871763i | \(-0.662977\pi\) | ||||
−0.489928 | + | 0.871763i | \(0.662977\pi\) | |||||||
\(948\) | −1.18945e12 | −0.0478310 | ||||||||
\(949\) | −1.68095e13 | −0.672755 | ||||||||
\(950\) | 3.75113e13 | 1.49419 | ||||||||
\(951\) | −3.76430e12 | −0.149235 | ||||||||
\(952\) | 5.11044e13 | 2.01647 | ||||||||
\(953\) | 2.59499e13 | 1.01910 | 0.509551 | − | 0.860440i | \(-0.329811\pi\) | ||||
0.509551 | + | 0.860440i | \(0.329811\pi\) | |||||||
\(954\) | 2.53082e13 | 0.989220 | ||||||||
\(955\) | −3.27777e12 | −0.127516 | ||||||||
\(956\) | −2.43890e13 | −0.944350 | ||||||||
\(957\) | −8.81149e12 | −0.339583 | ||||||||
\(958\) | −2.85891e13 | −1.09662 | ||||||||
\(959\) | 1.84752e13 | 0.705350 | ||||||||
\(960\) | −3.32803e13 | −1.26464 | ||||||||
\(961\) | 2.77059e13 | 1.04789 | ||||||||
\(962\) | 6.81766e13 | 2.56654 | ||||||||
\(963\) | 3.11709e12 | 0.116797 | ||||||||
\(964\) | −6.29862e13 | −2.34909 | ||||||||
\(965\) | −2.36020e13 | −0.876145 | ||||||||
\(966\) | −1.51438e13 | −0.559550 | ||||||||
\(967\) | 1.84647e13 | 0.679085 | 0.339542 | − | 0.940591i | \(-0.389728\pi\) | ||||
0.339542 | + | 0.940591i | \(0.389728\pi\) | |||||||
\(968\) | −1.34769e13 | −0.493344 | ||||||||
\(969\) | −2.99699e13 | −1.09201 | ||||||||
\(970\) | −7.08155e13 | −2.56836 | ||||||||
\(971\) | 5.23071e13 | 1.88831 | 0.944157 | − | 0.329495i | \(-0.106878\pi\) | ||||
0.944157 | + | 0.329495i | \(0.106878\pi\) | |||||||
\(972\) | 2.69554e12 | 0.0968608 | ||||||||
\(973\) | −1.38447e13 | −0.495196 | ||||||||
\(974\) | 6.32146e13 | 2.25062 | ||||||||
\(975\) | 2.18299e13 | 0.773627 | ||||||||
\(976\) | 1.31841e12 | 0.0465078 | ||||||||
\(977\) | 2.96462e13 | 1.04098 | 0.520491 | − | 0.853867i | \(-0.325749\pi\) | ||||
0.520491 | + | 0.853867i | \(0.325749\pi\) | |||||||
\(978\) | −4.64051e13 | −1.62196 | ||||||||
\(979\) | −5.26757e13 | −1.83269 | ||||||||
\(980\) | 7.92100e13 | 2.74323 | ||||||||
\(981\) | −1.56058e13 | −0.537992 | ||||||||
\(982\) | −3.35242e13 | −1.15042 | ||||||||
\(983\) | −1.15962e13 | −0.396117 | −0.198059 | − | 0.980190i | \(-0.563464\pi\) | ||||
−0.198059 | + | 0.980190i | \(0.563464\pi\) | |||||||
\(984\) | −6.95724e12 | −0.236570 | ||||||||
\(985\) | 1.01083e13 | 0.342148 | ||||||||
\(986\) | −3.54845e13 | −1.19562 | ||||||||
\(987\) | −5.62746e12 | −0.188749 | ||||||||
\(988\) | −8.66807e13 | −2.89412 | ||||||||
\(989\) | −6.83675e12 | −0.227230 | ||||||||
\(990\) | 2.72679e13 | 0.902180 | ||||||||
\(991\) | 2.04116e13 | 0.672273 | 0.336137 | − | 0.941813i | \(-0.390880\pi\) | ||||
0.336137 | + | 0.941813i | \(0.390880\pi\) | |||||||
\(992\) | −5.11696e13 | −1.67768 | ||||||||
\(993\) | 4.10745e12 | 0.134060 | ||||||||
\(994\) | −8.61543e13 | −2.79923 | ||||||||
\(995\) | −4.56614e13 | −1.47688 | ||||||||
\(996\) | −2.39718e13 | −0.771850 | ||||||||
\(997\) | −5.11008e13 | −1.63794 | −0.818972 | − | 0.573833i | \(-0.805456\pi\) | ||||
−0.818972 | + | 0.573833i | \(0.805456\pi\) | |||||||
\(998\) | −8.33793e13 | −2.66055 | ||||||||
\(999\) | −5.94759e12 | −0.188928 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.a.1.3 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.3 | ✓ | 21 | 1.1 | even | 1 | trivial |