Newspace parameters
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 23.7768 | 0.525398 | 0.262699 | − | 0.964878i | \(-0.415387\pi\) | ||||
0.262699 | + | 0.964878i | \(0.415387\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −1482.66 | −0.723957 | ||||||||
\(5\) | 6921.85 | 0.990575 | 0.495287 | − | 0.868729i | \(-0.335063\pi\) | ||||
0.495287 | + | 0.868729i | \(0.335063\pi\) | |||||||
\(6\) | 5777.76 | 0.303338 | ||||||||
\(7\) | 24486.4 | 0.550664 | 0.275332 | − | 0.961349i | \(-0.411212\pi\) | ||||
0.275332 | + | 0.961349i | \(0.411212\pi\) | |||||||
\(8\) | −83947.8 | −0.905763 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 164579. | 0.520446 | ||||||||
\(11\) | −888355. | −1.66313 | −0.831567 | − | 0.555425i | \(-0.812556\pi\) | ||||
−0.831567 | + | 0.555425i | \(0.812556\pi\) | |||||||
\(12\) | −360287. | −0.417977 | ||||||||
\(13\) | −914574. | −0.683172 | −0.341586 | − | 0.939850i | \(-0.610964\pi\) | ||||
−0.341586 | + | 0.939850i | \(0.610964\pi\) | |||||||
\(14\) | 582209. | 0.289317 | ||||||||
\(15\) | 1.68201e6 | 0.571909 | ||||||||
\(16\) | 1.04049e6 | 0.248072 | ||||||||
\(17\) | −3.69383e6 | −0.630968 | −0.315484 | − | 0.948931i | \(-0.602167\pi\) | ||||
−0.315484 | + | 0.948931i | \(0.602167\pi\) | |||||||
\(18\) | 1.40400e6 | 0.175133 | ||||||||
\(19\) | 4.55382e6 | 0.421921 | 0.210961 | − | 0.977495i | \(-0.432341\pi\) | ||||
0.210961 | + | 0.977495i | \(0.432341\pi\) | |||||||
\(20\) | −1.02628e7 | −0.717134 | ||||||||
\(21\) | 5.95021e6 | 0.317926 | ||||||||
\(22\) | −2.11222e7 | −0.873806 | ||||||||
\(23\) | 7.76606e6 | 0.251593 | 0.125796 | − | 0.992056i | \(-0.459851\pi\) | ||||
0.125796 | + | 0.992056i | \(0.459851\pi\) | |||||||
\(24\) | −2.03993e7 | −0.522943 | ||||||||
\(25\) | −916085. | −0.0187614 | ||||||||
\(26\) | −2.17456e7 | −0.358937 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −3.63052e7 | −0.398657 | ||||||||
\(29\) | 2.05865e8 | 1.86377 | 0.931886 | − | 0.362750i | \(-0.118162\pi\) | ||||
0.931886 | + | 0.362750i | \(0.118162\pi\) | |||||||
\(30\) | 3.99928e7 | 0.300479 | ||||||||
\(31\) | 3.06950e8 | 1.92566 | 0.962828 | − | 0.270114i | \(-0.0870615\pi\) | ||||
0.962828 | + | 0.270114i | \(0.0870615\pi\) | |||||||
\(32\) | 1.96665e8 | 1.03610 | ||||||||
\(33\) | −2.15870e8 | −0.960210 | ||||||||
\(34\) | −8.78273e7 | −0.331509 | ||||||||
\(35\) | 1.69492e8 | 0.545474 | ||||||||
\(36\) | −8.75499e7 | −0.241319 | ||||||||
\(37\) | 2.90102e8 | 0.687767 | 0.343884 | − | 0.939012i | \(-0.388257\pi\) | ||||
0.343884 | + | 0.939012i | \(0.388257\pi\) | |||||||
\(38\) | 1.08275e8 | 0.221676 | ||||||||
\(39\) | −2.22241e8 | −0.394430 | ||||||||
\(40\) | −5.81075e8 | −0.897226 | ||||||||
\(41\) | −7.24652e7 | −0.0976828 | −0.0488414 | − | 0.998807i | \(-0.515553\pi\) | ||||
−0.0488414 | + | 0.998807i | \(0.515553\pi\) | |||||||
\(42\) | 1.41477e8 | 0.167037 | ||||||||
\(43\) | −5.44136e8 | −0.564457 | −0.282229 | − | 0.959347i | \(-0.591074\pi\) | ||||
−0.282229 | + | 0.959347i | \(0.591074\pi\) | |||||||
\(44\) | 1.31713e9 | 1.20404 | ||||||||
\(45\) | 4.08728e8 | 0.330192 | ||||||||
\(46\) | 1.84652e8 | 0.132186 | ||||||||
\(47\) | −4.59684e8 | −0.292362 | −0.146181 | − | 0.989258i | \(-0.546698\pi\) | ||||
−0.146181 | + | 0.989258i | \(0.546698\pi\) | |||||||
\(48\) | 2.52838e8 | 0.143224 | ||||||||
\(49\) | −1.37774e9 | −0.696769 | ||||||||
\(50\) | −2.17816e7 | −0.00985721 | ||||||||
\(51\) | −8.97600e8 | −0.364290 | ||||||||
\(52\) | 1.35601e9 | 0.494588 | ||||||||
\(53\) | 2.43404e9 | 0.799485 | 0.399743 | − | 0.916627i | \(-0.369100\pi\) | ||||
0.399743 | + | 0.916627i | \(0.369100\pi\) | |||||||
\(54\) | 3.41171e8 | 0.101113 | ||||||||
\(55\) | −6.14907e9 | −1.64746 | ||||||||
\(56\) | −2.05558e9 | −0.498771 | ||||||||
\(57\) | 1.10658e9 | 0.243596 | ||||||||
\(58\) | 4.89480e9 | 0.979222 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | −2.49386e9 | −0.414037 | ||||||||
\(61\) | 1.80781e9 | 0.274055 | 0.137028 | − | 0.990567i | \(-0.456245\pi\) | ||||
0.137028 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(62\) | 7.29829e9 | 1.01174 | ||||||||
\(63\) | 1.44590e9 | 0.183555 | ||||||||
\(64\) | 2.54513e9 | 0.296293 | ||||||||
\(65\) | −6.33055e9 | −0.676734 | ||||||||
\(66\) | −5.13270e9 | −0.504492 | ||||||||
\(67\) | 1.65711e9 | 0.149948 | 0.0749738 | − | 0.997186i | \(-0.476113\pi\) | ||||
0.0749738 | + | 0.997186i | \(0.476113\pi\) | |||||||
\(68\) | 5.47671e9 | 0.456794 | ||||||||
\(69\) | 1.88715e9 | 0.145257 | ||||||||
\(70\) | 4.02996e9 | 0.286591 | ||||||||
\(71\) | 2.44530e10 | 1.60846 | 0.804231 | − | 0.594317i | \(-0.202578\pi\) | ||||
0.804231 | + | 0.594317i | \(0.202578\pi\) | |||||||
\(72\) | −4.95704e9 | −0.301921 | ||||||||
\(73\) | −3.35655e10 | −1.89503 | −0.947517 | − | 0.319705i | \(-0.896416\pi\) | ||||
−0.947517 | + | 0.319705i | \(0.896416\pi\) | |||||||
\(74\) | 6.89770e9 | 0.361351 | ||||||||
\(75\) | −2.22609e8 | −0.0108319 | ||||||||
\(76\) | −6.75179e9 | −0.305453 | ||||||||
\(77\) | −2.17527e10 | −0.915827 | ||||||||
\(78\) | −5.28419e9 | −0.207233 | ||||||||
\(79\) | 2.48737e10 | 0.909477 | 0.454739 | − | 0.890625i | \(-0.349733\pi\) | ||||
0.454739 | + | 0.890625i | \(0.349733\pi\) | |||||||
\(80\) | 7.20210e9 | 0.245733 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −1.72299e9 | −0.0513223 | ||||||||
\(83\) | 6.34936e9 | 0.176930 | 0.0884648 | − | 0.996079i | \(-0.471804\pi\) | ||||
0.0884648 | + | 0.996079i | \(0.471804\pi\) | |||||||
\(84\) | −8.82216e9 | −0.230165 | ||||||||
\(85\) | −2.55681e10 | −0.625021 | ||||||||
\(86\) | −1.29378e10 | −0.296565 | ||||||||
\(87\) | 5.00251e10 | 1.07605 | ||||||||
\(88\) | 7.45755e10 | 1.50640 | ||||||||
\(89\) | 8.37878e10 | 1.59051 | 0.795254 | − | 0.606276i | \(-0.207337\pi\) | ||||
0.795254 | + | 0.606276i | \(0.207337\pi\) | |||||||
\(90\) | 9.71825e9 | 0.173482 | ||||||||
\(91\) | −2.23947e10 | −0.376198 | ||||||||
\(92\) | −1.15145e10 | −0.182142 | ||||||||
\(93\) | 7.45889e10 | 1.11178 | ||||||||
\(94\) | −1.09298e10 | −0.153606 | ||||||||
\(95\) | 3.15209e10 | 0.417944 | ||||||||
\(96\) | 4.77895e10 | 0.598192 | ||||||||
\(97\) | 1.27019e11 | 1.50184 | 0.750921 | − | 0.660392i | \(-0.229610\pi\) | ||||
0.750921 | + | 0.660392i | \(0.229610\pi\) | |||||||
\(98\) | −3.27582e10 | −0.366081 | ||||||||
\(99\) | −5.24565e10 | −0.554378 | ||||||||
\(100\) | 1.35825e9 | 0.0135825 | ||||||||
\(101\) | 3.15002e10 | 0.298227 | 0.149113 | − | 0.988820i | \(-0.452358\pi\) | ||||
0.149113 | + | 0.988820i | \(0.452358\pi\) | |||||||
\(102\) | −2.13420e10 | −0.191397 | ||||||||
\(103\) | 1.13132e11 | 0.961568 | 0.480784 | − | 0.876839i | \(-0.340352\pi\) | ||||
0.480784 | + | 0.876839i | \(0.340352\pi\) | |||||||
\(104\) | 7.67765e10 | 0.618792 | ||||||||
\(105\) | 4.11864e10 | 0.314929 | ||||||||
\(106\) | 5.78736e10 | 0.420048 | ||||||||
\(107\) | −2.48504e11 | −1.71286 | −0.856431 | − | 0.516262i | \(-0.827323\pi\) | ||||
−0.856431 | + | 0.516262i | \(0.827323\pi\) | |||||||
\(108\) | −2.12746e10 | −0.139326 | ||||||||
\(109\) | 2.02030e11 | 1.25768 | 0.628840 | − | 0.777535i | \(-0.283530\pi\) | ||||
0.628840 | + | 0.777535i | \(0.283530\pi\) | |||||||
\(110\) | −1.46205e11 | −0.865570 | ||||||||
\(111\) | 7.04948e10 | 0.397083 | ||||||||
\(112\) | 2.54778e10 | 0.136604 | ||||||||
\(113\) | 1.51738e11 | 0.774755 | 0.387377 | − | 0.921921i | \(-0.373381\pi\) | ||||
0.387377 | + | 0.921921i | \(0.373381\pi\) | |||||||
\(114\) | 2.63109e10 | 0.127985 | ||||||||
\(115\) | 5.37555e10 | 0.249221 | ||||||||
\(116\) | −3.05228e11 | −1.34929 | ||||||||
\(117\) | −5.40047e10 | −0.227724 | ||||||||
\(118\) | 1.69986e10 | 0.0684009 | ||||||||
\(119\) | −9.04487e10 | −0.347451 | ||||||||
\(120\) | −1.41201e11 | −0.518014 | ||||||||
\(121\) | 5.03864e11 | 1.76601 | ||||||||
\(122\) | 4.29839e10 | 0.143988 | ||||||||
\(123\) | −1.76090e10 | −0.0563972 | ||||||||
\(124\) | −4.55104e11 | −1.39409 | ||||||||
\(125\) | −3.44322e11 | −1.00916 | ||||||||
\(126\) | 3.43788e10 | 0.0964391 | ||||||||
\(127\) | −2.49462e11 | −0.670014 | −0.335007 | − | 0.942216i | \(-0.608739\pi\) | ||||
−0.335007 | + | 0.942216i | \(0.608739\pi\) | |||||||
\(128\) | −3.42254e11 | −0.880428 | ||||||||
\(129\) | −1.32225e11 | −0.325890 | ||||||||
\(130\) | −1.50520e11 | −0.355554 | ||||||||
\(131\) | −3.18121e11 | −0.720444 | −0.360222 | − | 0.932867i | \(-0.617299\pi\) | ||||
−0.360222 | + | 0.932867i | \(0.617299\pi\) | |||||||
\(132\) | 3.20063e11 | 0.695151 | ||||||||
\(133\) | 1.11507e11 | 0.232337 | ||||||||
\(134\) | 3.94007e10 | 0.0787821 | ||||||||
\(135\) | 9.93210e10 | 0.190636 | ||||||||
\(136\) | 3.10089e11 | 0.571508 | ||||||||
\(137\) | 6.28463e11 | 1.11254 | 0.556271 | − | 0.831001i | \(-0.312232\pi\) | ||||
0.556271 | + | 0.831001i | \(0.312232\pi\) | |||||||
\(138\) | 4.48704e10 | 0.0763177 | ||||||||
\(139\) | 1.09931e12 | 1.79696 | 0.898480 | − | 0.439015i | \(-0.144673\pi\) | ||||
0.898480 | + | 0.439015i | \(0.144673\pi\) | |||||||
\(140\) | −2.51299e11 | −0.394900 | ||||||||
\(141\) | −1.11703e11 | −0.168795 | ||||||||
\(142\) | 5.81413e11 | 0.845082 | ||||||||
\(143\) | 8.12467e11 | 1.13621 | ||||||||
\(144\) | 6.14397e10 | 0.0826905 | ||||||||
\(145\) | 1.42497e12 | 1.84621 | ||||||||
\(146\) | −7.98079e11 | −0.995646 | ||||||||
\(147\) | −3.34791e11 | −0.402280 | ||||||||
\(148\) | −4.30124e11 | −0.497914 | ||||||||
\(149\) | −6.56389e11 | −0.732212 | −0.366106 | − | 0.930573i | \(-0.619309\pi\) | ||||
−0.366106 | + | 0.930573i | \(0.619309\pi\) | |||||||
\(150\) | −5.29292e9 | −0.00569106 | ||||||||
\(151\) | −1.51015e12 | −1.56548 | −0.782741 | − | 0.622348i | \(-0.786179\pi\) | ||||
−0.782741 | + | 0.622348i | \(0.786179\pi\) | |||||||
\(152\) | −3.82284e11 | −0.382161 | ||||||||
\(153\) | −2.18117e11 | −0.210323 | ||||||||
\(154\) | −5.17208e11 | −0.481173 | ||||||||
\(155\) | 2.12466e12 | 1.90751 | ||||||||
\(156\) | 3.29510e11 | 0.285550 | ||||||||
\(157\) | −1.32963e12 | −1.11246 | −0.556229 | − | 0.831029i | \(-0.687752\pi\) | ||||
−0.556229 | + | 0.831029i | \(0.687752\pi\) | |||||||
\(158\) | 5.91417e11 | 0.477837 | ||||||||
\(159\) | 5.91472e11 | 0.461583 | ||||||||
\(160\) | 1.36128e12 | 1.02633 | ||||||||
\(161\) | 1.90163e11 | 0.138543 | ||||||||
\(162\) | 8.29045e10 | 0.0583775 | ||||||||
\(163\) | 2.23220e12 | 1.51950 | 0.759752 | − | 0.650213i | \(-0.225320\pi\) | ||||
0.759752 | + | 0.650213i | \(0.225320\pi\) | |||||||
\(164\) | 1.07442e11 | 0.0707182 | ||||||||
\(165\) | −1.49422e12 | −0.951160 | ||||||||
\(166\) | 1.50967e11 | 0.0929584 | ||||||||
\(167\) | 6.78703e11 | 0.404333 | 0.202167 | − | 0.979351i | \(-0.435202\pi\) | ||||
0.202167 | + | 0.979351i | \(0.435202\pi\) | |||||||
\(168\) | −4.99507e11 | −0.287966 | ||||||||
\(169\) | −9.55715e11 | −0.533275 | ||||||||
\(170\) | −6.07928e11 | −0.328385 | ||||||||
\(171\) | 2.68899e11 | 0.140640 | ||||||||
\(172\) | 8.06772e11 | 0.408643 | ||||||||
\(173\) | 3.16596e12 | 1.55329 | 0.776645 | − | 0.629939i | \(-0.216920\pi\) | ||||
0.776645 | + | 0.629939i | \(0.216920\pi\) | |||||||
\(174\) | 1.18944e12 | 0.565354 | ||||||||
\(175\) | −2.24317e10 | −0.0103312 | ||||||||
\(176\) | −9.24323e11 | −0.412576 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 1.99220e12 | 0.835649 | ||||||||
\(179\) | −1.83525e12 | −0.746454 | −0.373227 | − | 0.927740i | \(-0.621749\pi\) | ||||
−0.373227 | + | 0.927740i | \(0.621749\pi\) | |||||||
\(180\) | −6.06007e11 | −0.239045 | ||||||||
\(181\) | 4.33122e11 | 0.165721 | 0.0828606 | − | 0.996561i | \(-0.473594\pi\) | ||||
0.0828606 | + | 0.996561i | \(0.473594\pi\) | |||||||
\(182\) | −5.32473e11 | −0.197654 | ||||||||
\(183\) | 4.39297e11 | 0.158226 | ||||||||
\(184\) | −6.51944e11 | −0.227883 | ||||||||
\(185\) | 2.00804e12 | 0.681285 | ||||||||
\(186\) | 1.77348e12 | 0.584126 | ||||||||
\(187\) | 3.28143e12 | 1.04938 | ||||||||
\(188\) | 6.81557e11 | 0.211658 | ||||||||
\(189\) | 3.51354e11 | 0.105975 | ||||||||
\(190\) | 7.49465e11 | 0.219587 | ||||||||
\(191\) | −6.20522e12 | −1.76634 | −0.883169 | − | 0.469054i | \(-0.844595\pi\) | ||||
−0.883169 | + | 0.469054i | \(0.844595\pi\) | |||||||
\(192\) | 6.18468e11 | 0.171065 | ||||||||
\(193\) | 2.56884e12 | 0.690513 | 0.345256 | − | 0.938508i | \(-0.387792\pi\) | ||||
0.345256 | + | 0.938508i | \(0.387792\pi\) | |||||||
\(194\) | 3.02010e12 | 0.789064 | ||||||||
\(195\) | −1.53832e12 | −0.390712 | ||||||||
\(196\) | 2.04273e12 | 0.504431 | ||||||||
\(197\) | 6.44753e12 | 1.54821 | 0.774103 | − | 0.633060i | \(-0.218201\pi\) | ||||
0.774103 | + | 0.633060i | \(0.218201\pi\) | |||||||
\(198\) | −1.24725e12 | −0.291269 | ||||||||
\(199\) | 2.26246e12 | 0.513912 | 0.256956 | − | 0.966423i | \(-0.417280\pi\) | ||||
0.256956 | + | 0.966423i | \(0.417280\pi\) | |||||||
\(200\) | 7.69034e10 | 0.0169934 | ||||||||
\(201\) | 4.02677e11 | 0.0865723 | ||||||||
\(202\) | 7.48974e11 | 0.156688 | ||||||||
\(203\) | 5.04089e12 | 1.02631 | ||||||||
\(204\) | 1.33084e12 | 0.263730 | ||||||||
\(205\) | −5.01593e11 | −0.0967622 | ||||||||
\(206\) | 2.68991e12 | 0.505206 | ||||||||
\(207\) | 4.58578e11 | 0.0838642 | ||||||||
\(208\) | −9.51603e11 | −0.169476 | ||||||||
\(209\) | −4.04541e12 | −0.701711 | ||||||||
\(210\) | 9.79281e11 | 0.165463 | ||||||||
\(211\) | 6.14974e12 | 1.01229 | 0.506143 | − | 0.862450i | \(-0.331071\pi\) | ||||
0.506143 | + | 0.862450i | \(0.331071\pi\) | |||||||
\(212\) | −3.60886e12 | −0.578793 | ||||||||
\(213\) | 5.94207e12 | 0.928646 | ||||||||
\(214\) | −5.90862e12 | −0.899933 | ||||||||
\(215\) | −3.76643e12 | −0.559137 | ||||||||
\(216\) | −1.20456e12 | −0.174314 | ||||||||
\(217\) | 7.51612e12 | 1.06039 | ||||||||
\(218\) | 4.80362e12 | 0.660782 | ||||||||
\(219\) | −8.15641e12 | −1.09410 | ||||||||
\(220\) | 9.11700e12 | 1.19269 | ||||||||
\(221\) | 3.37828e12 | 0.431060 | ||||||||
\(222\) | 1.67614e12 | 0.208626 | ||||||||
\(223\) | −1.23110e13 | −1.49491 | −0.747457 | − | 0.664310i | \(-0.768726\pi\) | ||||
−0.747457 | + | 0.664310i | \(0.768726\pi\) | |||||||
\(224\) | 4.81562e12 | 0.570542 | ||||||||
\(225\) | −5.40939e10 | −0.00625381 | ||||||||
\(226\) | 3.60785e12 | 0.407054 | ||||||||
\(227\) | 1.40310e13 | 1.54507 | 0.772534 | − | 0.634974i | \(-0.218989\pi\) | ||||
0.772534 | + | 0.634974i | \(0.218989\pi\) | |||||||
\(228\) | −1.64069e12 | −0.176353 | ||||||||
\(229\) | −1.64351e12 | −0.172455 | −0.0862277 | − | 0.996275i | \(-0.527481\pi\) | ||||
−0.0862277 | + | 0.996275i | \(0.527481\pi\) | |||||||
\(230\) | 1.27813e12 | 0.130940 | ||||||||
\(231\) | −5.28590e12 | −0.528753 | ||||||||
\(232\) | −1.72819e13 | −1.68814 | ||||||||
\(233\) | −1.93499e13 | −1.84596 | −0.922978 | − | 0.384853i | \(-0.874252\pi\) | ||||
−0.922978 | + | 0.384853i | \(0.874252\pi\) | |||||||
\(234\) | −1.28406e12 | −0.119646 | ||||||||
\(235\) | −3.18187e12 | −0.289607 | ||||||||
\(236\) | −1.05999e12 | −0.0942512 | ||||||||
\(237\) | 6.04432e12 | 0.525087 | ||||||||
\(238\) | −2.15058e12 | −0.182550 | ||||||||
\(239\) | 1.91104e13 | 1.58519 | 0.792594 | − | 0.609750i | \(-0.208730\pi\) | ||||
0.792594 | + | 0.609750i | \(0.208730\pi\) | |||||||
\(240\) | 1.75011e12 | 0.141874 | ||||||||
\(241\) | −1.44086e12 | −0.114164 | −0.0570820 | − | 0.998369i | \(-0.518180\pi\) | ||||
−0.0570820 | + | 0.998369i | \(0.518180\pi\) | |||||||
\(242\) | 1.19803e13 | 0.927858 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −2.68037e12 | −0.198404 | ||||||||
\(245\) | −9.53652e12 | −0.690202 | ||||||||
\(246\) | −4.18686e11 | −0.0296310 | ||||||||
\(247\) | −4.16481e12 | −0.288245 | ||||||||
\(248\) | −2.57678e13 | −1.74419 | ||||||||
\(249\) | 1.54289e12 | 0.102150 | ||||||||
\(250\) | −8.18687e12 | −0.530210 | ||||||||
\(251\) | 6.54826e12 | 0.414878 | 0.207439 | − | 0.978248i | \(-0.433487\pi\) | ||||
0.207439 | + | 0.978248i | \(0.433487\pi\) | |||||||
\(252\) | −2.14378e12 | −0.132886 | ||||||||
\(253\) | −6.89902e12 | −0.418432 | ||||||||
\(254\) | −5.93140e12 | −0.352024 | ||||||||
\(255\) | −6.21305e12 | −0.360856 | ||||||||
\(256\) | −1.33501e13 | −0.758867 | ||||||||
\(257\) | −1.75348e12 | −0.0975594 | −0.0487797 | − | 0.998810i | \(-0.515533\pi\) | ||||
−0.0487797 | + | 0.998810i | \(0.515533\pi\) | |||||||
\(258\) | −3.14389e12 | −0.171222 | ||||||||
\(259\) | 7.10357e12 | 0.378728 | ||||||||
\(260\) | 9.38608e12 | 0.489926 | ||||||||
\(261\) | 1.21561e13 | 0.621258 | ||||||||
\(262\) | −7.56389e12 | −0.378520 | ||||||||
\(263\) | 1.49939e13 | 0.734780 | 0.367390 | − | 0.930067i | \(-0.380251\pi\) | ||||
0.367390 | + | 0.930067i | \(0.380251\pi\) | |||||||
\(264\) | 1.81219e13 | 0.869723 | ||||||||
\(265\) | 1.68481e13 | 0.791950 | ||||||||
\(266\) | 2.65128e12 | 0.122069 | ||||||||
\(267\) | 2.03604e13 | 0.918280 | ||||||||
\(268\) | −2.45694e12 | −0.108556 | ||||||||
\(269\) | 2.22020e13 | 0.961069 | 0.480534 | − | 0.876976i | \(-0.340443\pi\) | ||||
0.480534 | + | 0.876976i | \(0.340443\pi\) | |||||||
\(270\) | 2.36153e12 | 0.100160 | ||||||||
\(271\) | −8.63351e12 | −0.358803 | −0.179402 | − | 0.983776i | \(-0.557416\pi\) | ||||
−0.179402 | + | 0.983776i | \(0.557416\pi\) | |||||||
\(272\) | −3.84338e12 | −0.156525 | ||||||||
\(273\) | −5.44190e12 | −0.217198 | ||||||||
\(274\) | 1.49428e13 | 0.584527 | ||||||||
\(275\) | 8.13809e11 | 0.0312028 | ||||||||
\(276\) | −2.79802e12 | −0.105160 | ||||||||
\(277\) | 5.13042e13 | 1.89023 | 0.945114 | − | 0.326740i | \(-0.105950\pi\) | ||||
0.945114 | + | 0.326740i | \(0.105950\pi\) | |||||||
\(278\) | 2.61380e13 | 0.944118 | ||||||||
\(279\) | 1.81251e13 | 0.641885 | ||||||||
\(280\) | −1.42284e13 | −0.494070 | ||||||||
\(281\) | 2.26330e13 | 0.770651 | 0.385325 | − | 0.922781i | \(-0.374089\pi\) | ||||
0.385325 | + | 0.922781i | \(0.374089\pi\) | |||||||
\(282\) | −2.65594e12 | −0.0886847 | ||||||||
\(283\) | 2.57270e13 | 0.842486 | 0.421243 | − | 0.906948i | \(-0.361594\pi\) | ||||
0.421243 | + | 0.906948i | \(0.361594\pi\) | |||||||
\(284\) | −3.62556e13 | −1.16446 | ||||||||
\(285\) | 7.65957e12 | 0.241300 | ||||||||
\(286\) | 1.93178e13 | 0.596960 | ||||||||
\(287\) | −1.77441e12 | −0.0537904 | ||||||||
\(288\) | 1.16128e13 | 0.345366 | ||||||||
\(289\) | −2.06275e13 | −0.601879 | ||||||||
\(290\) | 3.38811e13 | 0.969993 | ||||||||
\(291\) | 3.08656e13 | 0.867089 | ||||||||
\(292\) | 4.97663e13 | 1.37192 | ||||||||
\(293\) | −5.35154e13 | −1.44779 | −0.723896 | − | 0.689909i | \(-0.757651\pi\) | ||||
−0.723896 | + | 0.689909i | \(0.757651\pi\) | |||||||
\(294\) | −7.96025e12 | −0.211357 | ||||||||
\(295\) | 4.94860e12 | 0.128962 | ||||||||
\(296\) | −2.43535e13 | −0.622954 | ||||||||
\(297\) | −1.27469e13 | −0.320070 | ||||||||
\(298\) | −1.56068e13 | −0.384702 | ||||||||
\(299\) | −7.10264e12 | −0.171881 | ||||||||
\(300\) | 3.30054e11 | 0.00784185 | ||||||||
\(301\) | −1.33240e13 | −0.310826 | ||||||||
\(302\) | −3.59066e13 | −0.822500 | ||||||||
\(303\) | 7.65456e12 | 0.172181 | ||||||||
\(304\) | 4.73819e12 | 0.104667 | ||||||||
\(305\) | 1.25134e13 | 0.271472 | ||||||||
\(306\) | −5.18612e12 | −0.110503 | ||||||||
\(307\) | 7.26163e13 | 1.51975 | 0.759877 | − | 0.650067i | \(-0.225259\pi\) | ||||
0.759877 | + | 0.650067i | \(0.225259\pi\) | |||||||
\(308\) | 3.22519e13 | 0.663020 | ||||||||
\(309\) | 2.74910e13 | 0.555162 | ||||||||
\(310\) | 5.05177e13 | 1.00220 | ||||||||
\(311\) | −5.96904e13 | −1.16338 | −0.581691 | − | 0.813410i | \(-0.697609\pi\) | ||||
−0.581691 | + | 0.813410i | \(0.697609\pi\) | |||||||
\(312\) | 1.86567e13 | 0.357260 | ||||||||
\(313\) | −6.28890e13 | −1.18326 | −0.591630 | − | 0.806209i | \(-0.701516\pi\) | ||||
−0.591630 | + | 0.806209i | \(0.701516\pi\) | |||||||
\(314\) | −3.16144e13 | −0.584483 | ||||||||
\(315\) | 1.00083e13 | 0.181825 | ||||||||
\(316\) | −3.68794e13 | −0.658423 | ||||||||
\(317\) | −9.60991e13 | −1.68614 | −0.843070 | − | 0.537804i | \(-0.819254\pi\) | ||||
−0.843070 | + | 0.537804i | \(0.819254\pi\) | |||||||
\(318\) | 1.40633e13 | 0.242515 | ||||||||
\(319\) | −1.82881e14 | −3.09970 | ||||||||
\(320\) | 1.76170e13 | 0.293500 | ||||||||
\(321\) | −6.03864e13 | −0.988921 | ||||||||
\(322\) | 4.52147e12 | 0.0727901 | ||||||||
\(323\) | −1.68210e13 | −0.266219 | ||||||||
\(324\) | −5.16973e12 | −0.0804397 | ||||||||
\(325\) | 8.37828e11 | 0.0128173 | ||||||||
\(326\) | 5.30746e13 | 0.798344 | ||||||||
\(327\) | 4.90933e13 | 0.726122 | ||||||||
\(328\) | 6.08330e12 | 0.0884775 | ||||||||
\(329\) | −1.12560e13 | −0.160993 | ||||||||
\(330\) | −3.55278e13 | −0.499737 | ||||||||
\(331\) | −4.93954e13 | −0.683333 | −0.341667 | − | 0.939821i | \(-0.610991\pi\) | ||||
−0.341667 | + | 0.939821i | \(0.610991\pi\) | |||||||
\(332\) | −9.41397e12 | −0.128089 | ||||||||
\(333\) | 1.71302e13 | 0.229256 | ||||||||
\(334\) | 1.61374e13 | 0.212436 | ||||||||
\(335\) | 1.14703e13 | 0.148534 | ||||||||
\(336\) | 6.19111e12 | 0.0788683 | ||||||||
\(337\) | 6.72011e13 | 0.842193 | 0.421097 | − | 0.907016i | \(-0.361645\pi\) | ||||
0.421097 | + | 0.907016i | \(0.361645\pi\) | |||||||
\(338\) | −2.27238e13 | −0.280182 | ||||||||
\(339\) | 3.68724e13 | 0.447305 | ||||||||
\(340\) | 3.79090e13 | 0.452489 | ||||||||
\(341\) | −2.72681e14 | −3.20262 | ||||||||
\(342\) | 6.39354e12 | 0.0738921 | ||||||||
\(343\) | −8.21537e13 | −0.934349 | ||||||||
\(344\) | 4.56791e13 | 0.511265 | ||||||||
\(345\) | 1.30626e13 | 0.143888 | ||||||||
\(346\) | 7.52764e13 | 0.816094 | ||||||||
\(347\) | −1.31316e14 | −1.40121 | −0.700607 | − | 0.713547i | \(-0.747087\pi\) | ||||
−0.700607 | + | 0.713547i | \(0.747087\pi\) | |||||||
\(348\) | −7.41705e13 | −0.779014 | ||||||||
\(349\) | −5.29347e13 | −0.547269 | −0.273635 | − | 0.961834i | \(-0.588226\pi\) | ||||
−0.273635 | + | 0.961834i | \(0.588226\pi\) | |||||||
\(350\) | −5.33353e11 | −0.00542801 | ||||||||
\(351\) | −1.31231e13 | −0.131477 | ||||||||
\(352\) | −1.74708e14 | −1.72317 | ||||||||
\(353\) | 6.86471e13 | 0.666594 | 0.333297 | − | 0.942822i | \(-0.391839\pi\) | ||||
0.333297 | + | 0.942822i | \(0.391839\pi\) | |||||||
\(354\) | 4.13066e12 | 0.0394913 | ||||||||
\(355\) | 1.69260e14 | 1.59330 | ||||||||
\(356\) | −1.24229e14 | −1.15146 | ||||||||
\(357\) | −2.19790e13 | −0.200601 | ||||||||
\(358\) | −4.36363e13 | −0.392185 | ||||||||
\(359\) | 1.03179e14 | 0.913215 | 0.456607 | − | 0.889668i | \(-0.349064\pi\) | ||||
0.456607 | + | 0.889668i | \(0.349064\pi\) | |||||||
\(360\) | −3.43119e13 | −0.299075 | ||||||||
\(361\) | −9.57530e13 | −0.821983 | ||||||||
\(362\) | 1.02982e13 | 0.0870695 | ||||||||
\(363\) | 1.22439e14 | 1.01961 | ||||||||
\(364\) | 3.32038e13 | 0.272352 | ||||||||
\(365\) | −2.32335e14 | −1.87717 | ||||||||
\(366\) | 1.04451e13 | 0.0831315 | ||||||||
\(367\) | 5.44575e12 | 0.0426967 | 0.0213484 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213484 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(368\) | 8.08049e12 | 0.0624129 | ||||||||
\(369\) | −4.27900e12 | −0.0325609 | ||||||||
\(370\) | 4.77448e13 | 0.357945 | ||||||||
\(371\) | 5.96010e13 | 0.440247 | ||||||||
\(372\) | −1.10590e14 | −0.804880 | ||||||||
\(373\) | −7.26263e13 | −0.520829 | −0.260414 | − | 0.965497i | \(-0.583859\pi\) | ||||
−0.260414 | + | 0.965497i | \(0.583859\pi\) | |||||||
\(374\) | 7.80219e13 | 0.551344 | ||||||||
\(375\) | −8.36703e13 | −0.582638 | ||||||||
\(376\) | 3.85895e13 | 0.264811 | ||||||||
\(377\) | −1.88279e14 | −1.27328 | ||||||||
\(378\) | 8.35406e12 | 0.0556792 | ||||||||
\(379\) | −2.08008e14 | −1.36636 | −0.683179 | − | 0.730251i | \(-0.739403\pi\) | ||||
−0.683179 | + | 0.730251i | \(0.739403\pi\) | |||||||
\(380\) | −4.67349e13 | −0.302574 | ||||||||
\(381\) | −6.06193e13 | −0.386833 | ||||||||
\(382\) | −1.47540e14 | −0.928030 | ||||||||
\(383\) | 2.06489e14 | 1.28027 | 0.640137 | − | 0.768261i | \(-0.278878\pi\) | ||||
0.640137 | + | 0.768261i | \(0.278878\pi\) | |||||||
\(384\) | −8.31677e13 | −0.508315 | ||||||||
\(385\) | −1.50569e14 | −0.907195 | ||||||||
\(386\) | 6.10787e13 | 0.362794 | ||||||||
\(387\) | −3.21307e13 | −0.188152 | ||||||||
\(388\) | −1.88327e14 | −1.08727 | ||||||||
\(389\) | 2.16026e14 | 1.22966 | 0.614828 | − | 0.788661i | \(-0.289225\pi\) | ||||
0.614828 | + | 0.788661i | \(0.289225\pi\) | |||||||
\(390\) | −3.65764e13 | −0.205279 | ||||||||
\(391\) | −2.86865e13 | −0.158747 | ||||||||
\(392\) | 1.15658e14 | 0.631108 | ||||||||
\(393\) | −7.73034e13 | −0.415949 | ||||||||
\(394\) | 1.53301e14 | 0.813424 | ||||||||
\(395\) | 1.72172e14 | 0.900905 | ||||||||
\(396\) | 7.77754e13 | 0.401346 | ||||||||
\(397\) | −6.66369e13 | −0.339131 | −0.169565 | − | 0.985519i | \(-0.554236\pi\) | ||||
−0.169565 | + | 0.985519i | \(0.554236\pi\) | |||||||
\(398\) | 5.37940e13 | 0.270008 | ||||||||
\(399\) | 2.70962e13 | 0.134140 | ||||||||
\(400\) | −9.53175e11 | −0.00465418 | ||||||||
\(401\) | 9.42589e13 | 0.453971 | 0.226986 | − | 0.973898i | \(-0.427113\pi\) | ||||
0.226986 | + | 0.973898i | \(0.427113\pi\) | |||||||
\(402\) | 9.57437e12 | 0.0454849 | ||||||||
\(403\) | −2.80729e14 | −1.31556 | ||||||||
\(404\) | −4.67043e13 | −0.215903 | ||||||||
\(405\) | 2.41350e13 | 0.110064 | ||||||||
\(406\) | 1.19856e14 | 0.539222 | ||||||||
\(407\) | −2.57714e14 | −1.14385 | ||||||||
\(408\) | 7.53516e13 | 0.329960 | ||||||||
\(409\) | 1.68108e14 | 0.726288 | 0.363144 | − | 0.931733i | \(-0.381703\pi\) | ||||
0.363144 | + | 0.931733i | \(0.381703\pi\) | |||||||
\(410\) | −1.19263e13 | −0.0508386 | ||||||||
\(411\) | 1.52716e14 | 0.642326 | ||||||||
\(412\) | −1.67737e14 | −0.696135 | ||||||||
\(413\) | 1.75060e13 | 0.0716903 | ||||||||
\(414\) | 1.09035e13 | 0.0440620 | ||||||||
\(415\) | 4.39493e13 | 0.175262 | ||||||||
\(416\) | −1.79864e14 | −0.707835 | ||||||||
\(417\) | 2.67132e14 | 1.03747 | ||||||||
\(418\) | −9.61869e13 | −0.368677 | ||||||||
\(419\) | −5.52023e13 | −0.208824 | −0.104412 | − | 0.994534i | \(-0.533296\pi\) | ||||
−0.104412 | + | 0.994534i | \(0.533296\pi\) | |||||||
\(420\) | −6.10657e13 | −0.227995 | ||||||||
\(421\) | −2.98720e14 | −1.10081 | −0.550406 | − | 0.834897i | \(-0.685527\pi\) | ||||
−0.550406 | + | 0.834897i | \(0.685527\pi\) | |||||||
\(422\) | 1.46221e14 | 0.531853 | ||||||||
\(423\) | −2.71439e13 | −0.0974541 | ||||||||
\(424\) | −2.04332e14 | −0.724144 | ||||||||
\(425\) | 3.38386e12 | 0.0118379 | ||||||||
\(426\) | 1.41283e14 | 0.487908 | ||||||||
\(427\) | 4.42668e13 | 0.150912 | ||||||||
\(428\) | 3.68448e14 | 1.24004 | ||||||||
\(429\) | 1.97429e14 | 0.655989 | ||||||||
\(430\) | −8.95536e13 | −0.293769 | ||||||||
\(431\) | −4.61512e14 | −1.49471 | −0.747357 | − | 0.664423i | \(-0.768677\pi\) | ||||
−0.747357 | + | 0.664423i | \(0.768677\pi\) | |||||||
\(432\) | 1.49299e13 | 0.0477414 | ||||||||
\(433\) | −6.14093e13 | −0.193888 | −0.0969440 | − | 0.995290i | \(-0.530907\pi\) | ||||
−0.0969440 | + | 0.995290i | \(0.530907\pi\) | |||||||
\(434\) | 1.78709e14 | 0.557126 | ||||||||
\(435\) | 3.46267e14 | 1.06591 | ||||||||
\(436\) | −2.99543e14 | −0.910506 | ||||||||
\(437\) | 3.53653e13 | 0.106152 | ||||||||
\(438\) | −1.93933e14 | −0.574837 | ||||||||
\(439\) | 2.71791e14 | 0.795573 | 0.397786 | − | 0.917478i | \(-0.369779\pi\) | ||||
0.397786 | + | 0.917478i | \(0.369779\pi\) | |||||||
\(440\) | 5.16201e14 | 1.49221 | ||||||||
\(441\) | −8.13542e13 | −0.232256 | ||||||||
\(442\) | 8.03246e13 | 0.226478 | ||||||||
\(443\) | 2.08496e14 | 0.580600 | 0.290300 | − | 0.956936i | \(-0.406245\pi\) | ||||
0.290300 | + | 0.956936i | \(0.406245\pi\) | |||||||
\(444\) | −1.04520e14 | −0.287471 | ||||||||
\(445\) | 5.79967e14 | 1.57552 | ||||||||
\(446\) | −2.92716e14 | −0.785425 | ||||||||
\(447\) | −1.59503e14 | −0.422743 | ||||||||
\(448\) | 6.23213e13 | 0.163158 | ||||||||
\(449\) | −1.30410e14 | −0.337254 | −0.168627 | − | 0.985680i | \(-0.553933\pi\) | ||||
−0.168627 | + | 0.985680i | \(0.553933\pi\) | |||||||
\(450\) | −1.28618e12 | −0.00328574 | ||||||||
\(451\) | 6.43748e13 | 0.162460 | ||||||||
\(452\) | −2.24977e14 | −0.560889 | ||||||||
\(453\) | −3.66967e14 | −0.903831 | ||||||||
\(454\) | 3.33613e14 | 0.811775 | ||||||||
\(455\) | −1.55013e14 | −0.372653 | ||||||||
\(456\) | −9.28949e13 | −0.220641 | ||||||||
\(457\) | 6.29919e14 | 1.47824 | 0.739121 | − | 0.673573i | \(-0.235241\pi\) | ||||
0.739121 | + | 0.673573i | \(0.235241\pi\) | |||||||
\(458\) | −3.90773e13 | −0.0906077 | ||||||||
\(459\) | −5.30024e13 | −0.121430 | ||||||||
\(460\) | −7.97014e13 | −0.180426 | ||||||||
\(461\) | −4.96432e14 | −1.11046 | −0.555232 | − | 0.831696i | \(-0.687371\pi\) | ||||
−0.555232 | + | 0.831696i | \(0.687371\pi\) | |||||||
\(462\) | −1.25682e14 | −0.277806 | ||||||||
\(463\) | 4.11958e14 | 0.899824 | 0.449912 | − | 0.893073i | \(-0.351455\pi\) | ||||
0.449912 | + | 0.893073i | \(0.351455\pi\) | |||||||
\(464\) | 2.14200e14 | 0.462349 | ||||||||
\(465\) | 5.16294e14 | 1.10130 | ||||||||
\(466\) | −4.60079e14 | −0.969861 | ||||||||
\(467\) | −2.15183e13 | −0.0448297 | −0.0224149 | − | 0.999749i | \(-0.507135\pi\) | ||||
−0.0224149 | + | 0.999749i | \(0.507135\pi\) | |||||||
\(468\) | 8.00708e13 | 0.164863 | ||||||||
\(469\) | 4.05767e13 | 0.0825707 | ||||||||
\(470\) | −7.56545e13 | −0.152159 | ||||||||
\(471\) | −3.23101e14 | −0.642278 | ||||||||
\(472\) | −6.00164e13 | −0.117920 | ||||||||
\(473\) | 4.83386e14 | 0.938768 | ||||||||
\(474\) | 1.43714e14 | 0.275879 | ||||||||
\(475\) | −4.17169e12 | −0.00791584 | ||||||||
\(476\) | 1.34105e14 | 0.251540 | ||||||||
\(477\) | 1.43728e14 | 0.266495 | ||||||||
\(478\) | 4.54383e14 | 0.832854 | ||||||||
\(479\) | 2.18237e14 | 0.395443 | 0.197721 | − | 0.980258i | \(-0.436646\pi\) | ||||
0.197721 | + | 0.980258i | \(0.436646\pi\) | |||||||
\(480\) | 3.30792e14 | 0.592554 | ||||||||
\(481\) | −2.65320e14 | −0.469864 | ||||||||
\(482\) | −3.42591e13 | −0.0599815 | ||||||||
\(483\) | 4.62097e13 | 0.0799878 | ||||||||
\(484\) | −7.47061e14 | −1.27852 | ||||||||
\(485\) | 8.79207e14 | 1.48769 | ||||||||
\(486\) | 2.01458e13 | 0.0337043 | ||||||||
\(487\) | −6.93472e14 | −1.14715 | −0.573574 | − | 0.819154i | \(-0.694443\pi\) | ||||
−0.573574 | + | 0.819154i | \(0.694443\pi\) | |||||||
\(488\) | −1.51762e14 | −0.248229 | ||||||||
\(489\) | 5.42425e14 | 0.877286 | ||||||||
\(490\) | −2.26748e14 | −0.362631 | ||||||||
\(491\) | 5.82804e14 | 0.921668 | 0.460834 | − | 0.887486i | \(-0.347550\pi\) | ||||
0.460834 | + | 0.887486i | \(0.347550\pi\) | |||||||
\(492\) | 2.61083e13 | 0.0408292 | ||||||||
\(493\) | −7.60429e14 | −1.17598 | ||||||||
\(494\) | −9.90257e13 | −0.151443 | ||||||||
\(495\) | −3.63096e14 | −0.549153 | ||||||||
\(496\) | 3.19378e14 | 0.477701 | ||||||||
\(497\) | 5.98766e14 | 0.885722 | ||||||||
\(498\) | 3.66851e13 | 0.0536695 | ||||||||
\(499\) | −6.41955e14 | −0.928863 | −0.464431 | − | 0.885609i | \(-0.653741\pi\) | ||||
−0.464431 | + | 0.885609i | \(0.653741\pi\) | |||||||
\(500\) | 5.10514e14 | 0.730588 | ||||||||
\(501\) | 1.64925e14 | 0.233442 | ||||||||
\(502\) | 1.55697e14 | 0.217976 | ||||||||
\(503\) | 1.02609e15 | 1.42090 | 0.710448 | − | 0.703750i | \(-0.248492\pi\) | ||||
0.710448 | + | 0.703750i | \(0.248492\pi\) | |||||||
\(504\) | −1.21380e14 | −0.166257 | ||||||||
\(505\) | 2.18040e14 | 0.295416 | ||||||||
\(506\) | −1.64037e14 | −0.219843 | ||||||||
\(507\) | −2.32239e14 | −0.307887 | ||||||||
\(508\) | 3.69868e14 | 0.485062 | ||||||||
\(509\) | 4.61233e14 | 0.598374 | 0.299187 | − | 0.954194i | \(-0.403285\pi\) | ||||
0.299187 | + | 0.954194i | \(0.403285\pi\) | |||||||
\(510\) | −1.47726e14 | −0.189593 | ||||||||
\(511\) | −8.21899e14 | −1.04353 | ||||||||
\(512\) | 3.83513e14 | 0.481721 | ||||||||
\(513\) | 6.53424e13 | 0.0811988 | ||||||||
\(514\) | −4.16921e13 | −0.0512575 | ||||||||
\(515\) | 7.83082e14 | 0.952506 | ||||||||
\(516\) | 1.96045e14 | 0.235930 | ||||||||
\(517\) | 4.08363e14 | 0.486237 | ||||||||
\(518\) | 1.68900e14 | 0.198983 | ||||||||
\(519\) | 7.69329e14 | 0.896792 | ||||||||
\(520\) | 5.31436e14 | 0.612960 | ||||||||
\(521\) | −4.43782e13 | −0.0506479 | −0.0253240 | − | 0.999679i | \(-0.508062\pi\) | ||||
−0.0253240 | + | 0.999679i | \(0.508062\pi\) | |||||||
\(522\) | 2.89033e14 | 0.326407 | ||||||||
\(523\) | 3.21587e14 | 0.359367 | 0.179684 | − | 0.983724i | \(-0.442493\pi\) | ||||
0.179684 | + | 0.983724i | \(0.442493\pi\) | |||||||
\(524\) | 4.71667e14 | 0.521571 | ||||||||
\(525\) | −5.45090e12 | −0.00596474 | ||||||||
\(526\) | 3.56506e14 | 0.386052 | ||||||||
\(527\) | −1.13382e15 | −1.21503 | ||||||||
\(528\) | −2.24610e14 | −0.238201 | ||||||||
\(529\) | −8.92498e14 | −0.936701 | ||||||||
\(530\) | 4.00593e14 | 0.416089 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −1.65327e14 | −0.168202 | ||||||||
\(533\) | 6.62748e13 | 0.0667342 | ||||||||
\(534\) | 4.84106e14 | 0.482462 | ||||||||
\(535\) | −1.72011e15 | −1.69672 | ||||||||
\(536\) | −1.39111e14 | −0.135817 | ||||||||
\(537\) | −4.45965e14 | −0.430965 | ||||||||
\(538\) | 5.27892e14 | 0.504943 | ||||||||
\(539\) | 1.22392e15 | 1.15882 | ||||||||
\(540\) | −1.47260e14 | −0.138012 | ||||||||
\(541\) | −8.14845e14 | −0.755945 | −0.377972 | − | 0.925817i | \(-0.623379\pi\) | ||||
−0.377972 | + | 0.925817i | \(0.623379\pi\) | |||||||
\(542\) | −2.05277e14 | −0.188514 | ||||||||
\(543\) | 1.05249e14 | 0.0956792 | ||||||||
\(544\) | −7.26445e14 | −0.653746 | ||||||||
\(545\) | 1.39842e15 | 1.24583 | ||||||||
\(546\) | −1.29391e14 | −0.114115 | ||||||||
\(547\) | 8.04498e14 | 0.702416 | 0.351208 | − | 0.936297i | \(-0.385771\pi\) | ||||
0.351208 | + | 0.936297i | \(0.385771\pi\) | |||||||
\(548\) | −9.31799e14 | −0.805433 | ||||||||
\(549\) | 1.06749e14 | 0.0913518 | ||||||||
\(550\) | 1.93498e13 | 0.0163939 | ||||||||
\(551\) | 9.37471e14 | 0.786365 | ||||||||
\(552\) | −1.58422e14 | −0.131568 | ||||||||
\(553\) | 6.09069e14 | 0.500816 | ||||||||
\(554\) | 1.21985e15 | 0.993122 | ||||||||
\(555\) | 4.87955e14 | 0.393340 | ||||||||
\(556\) | −1.62991e15 | −1.30092 | ||||||||
\(557\) | −1.28858e15 | −1.01837 | −0.509186 | − | 0.860656i | \(-0.670053\pi\) | ||||
−0.509186 | + | 0.860656i | \(0.670053\pi\) | |||||||
\(558\) | 4.30957e14 | 0.337245 | ||||||||
\(559\) | 4.97653e14 | 0.385622 | ||||||||
\(560\) | 1.76354e14 | 0.135316 | ||||||||
\(561\) | 7.97388e14 | 0.605862 | ||||||||
\(562\) | 5.38140e14 | 0.404898 | ||||||||
\(563\) | −1.13486e15 | −0.845564 | −0.422782 | − | 0.906231i | \(-0.638946\pi\) | ||||
−0.422782 | + | 0.906231i | \(0.638946\pi\) | |||||||
\(564\) | 1.65618e14 | 0.122201 | ||||||||
\(565\) | 1.05031e15 | 0.767453 | ||||||||
\(566\) | 6.11704e14 | 0.442640 | ||||||||
\(567\) | 8.53789e13 | 0.0611849 | ||||||||
\(568\) | −2.05277e15 | −1.45689 | ||||||||
\(569\) | −3.63483e14 | −0.255486 | −0.127743 | − | 0.991807i | \(-0.540773\pi\) | ||||
−0.127743 | + | 0.991807i | \(0.540773\pi\) | |||||||
\(570\) | 1.82120e14 | 0.126779 | ||||||||
\(571\) | 5.35440e14 | 0.369158 | 0.184579 | − | 0.982818i | \(-0.440908\pi\) | ||||
0.184579 | + | 0.982818i | \(0.440908\pi\) | |||||||
\(572\) | −1.20462e15 | −0.822565 | ||||||||
\(573\) | −1.50787e15 | −1.01980 | ||||||||
\(574\) | −4.21899e13 | −0.0282613 | ||||||||
\(575\) | −7.11438e12 | −0.00472024 | ||||||||
\(576\) | 1.50288e14 | 0.0987642 | ||||||||
\(577\) | −1.71645e15 | −1.11728 | −0.558642 | − | 0.829409i | \(-0.688678\pi\) | ||||
−0.558642 | + | 0.829409i | \(0.688678\pi\) | |||||||
\(578\) | −4.90456e14 | −0.316226 | ||||||||
\(579\) | 6.24228e14 | 0.398668 | ||||||||
\(580\) | −2.11275e15 | −1.33657 | ||||||||
\(581\) | 1.55473e14 | 0.0974287 | ||||||||
\(582\) | 7.33885e14 | 0.455566 | ||||||||
\(583\) | −2.16229e15 | −1.32965 | ||||||||
\(584\) | 2.81775e15 | 1.71645 | ||||||||
\(585\) | −3.73812e14 | −0.225578 | ||||||||
\(586\) | −1.27242e15 | −0.760667 | ||||||||
\(587\) | 1.33142e15 | 0.788508 | 0.394254 | − | 0.919002i | \(-0.371003\pi\) | ||||
0.394254 | + | 0.919002i | \(0.371003\pi\) | |||||||
\(588\) | 4.96383e14 | 0.291234 | ||||||||
\(589\) | 1.39780e15 | 0.812475 | ||||||||
\(590\) | 1.17662e14 | 0.0677563 | ||||||||
\(591\) | 1.56675e15 | 0.893857 | ||||||||
\(592\) | 3.01848e14 | 0.170615 | ||||||||
\(593\) | 7.24920e14 | 0.405965 | 0.202983 | − | 0.979182i | \(-0.434936\pi\) | ||||
0.202983 | + | 0.979182i | \(0.434936\pi\) | |||||||
\(594\) | −3.03081e14 | −0.168164 | ||||||||
\(595\) | −6.26072e14 | −0.344177 | ||||||||
\(596\) | 9.73205e14 | 0.530090 | ||||||||
\(597\) | 5.49777e14 | 0.296707 | ||||||||
\(598\) | −1.68878e14 | −0.0903059 | ||||||||
\(599\) | −1.70755e15 | −0.904743 | −0.452371 | − | 0.891830i | \(-0.649422\pi\) | ||||
−0.452371 | + | 0.891830i | \(0.649422\pi\) | |||||||
\(600\) | 1.86875e13 | 0.00981115 | ||||||||
\(601\) | −1.03547e15 | −0.538675 | −0.269337 | − | 0.963046i | \(-0.586805\pi\) | ||||
−0.269337 | + | 0.963046i | \(0.586805\pi\) | |||||||
\(602\) | −3.16801e14 | −0.163307 | ||||||||
\(603\) | 9.78506e13 | 0.0499825 | ||||||||
\(604\) | 2.23905e15 | 1.13334 | ||||||||
\(605\) | 3.48767e15 | 1.74937 | ||||||||
\(606\) | 1.82001e14 | 0.0904636 | ||||||||
\(607\) | 3.90639e15 | 1.92414 | 0.962072 | − | 0.272797i | \(-0.0879488\pi\) | ||||
0.962072 | + | 0.272797i | \(0.0879488\pi\) | |||||||
\(608\) | 8.95576e14 | 0.437152 | ||||||||
\(609\) | 1.22494e15 | 0.592542 | ||||||||
\(610\) | 2.97528e14 | 0.142631 | ||||||||
\(611\) | 4.20415e14 | 0.199734 | ||||||||
\(612\) | 3.23394e14 | 0.152265 | ||||||||
\(613\) | −1.81046e15 | −0.844805 | −0.422402 | − | 0.906408i | \(-0.638813\pi\) | ||||
−0.422402 | + | 0.906408i | \(0.638813\pi\) | |||||||
\(614\) | 1.72658e15 | 0.798475 | ||||||||
\(615\) | −1.21887e14 | −0.0558657 | ||||||||
\(616\) | 1.82609e15 | 0.829522 | ||||||||
\(617\) | −1.18367e15 | −0.532921 | −0.266460 | − | 0.963846i | \(-0.585854\pi\) | ||||
−0.266460 | + | 0.963846i | \(0.585854\pi\) | |||||||
\(618\) | 6.53649e14 | 0.291681 | ||||||||
\(619\) | −3.52172e15 | −1.55760 | −0.778800 | − | 0.627273i | \(-0.784171\pi\) | ||||
−0.778800 | + | 0.627273i | \(0.784171\pi\) | |||||||
\(620\) | −3.15017e15 | −1.38095 | ||||||||
\(621\) | 1.11435e14 | 0.0484190 | ||||||||
\(622\) | −1.41925e15 | −0.611238 | ||||||||
\(623\) | 2.05167e15 | 0.875835 | ||||||||
\(624\) | −2.31239e14 | −0.0978468 | ||||||||
\(625\) | −2.33862e15 | −0.980887 | ||||||||
\(626\) | −1.49530e15 | −0.621682 | ||||||||
\(627\) | −9.83035e14 | −0.405133 | ||||||||
\(628\) | 1.97140e15 | 0.805372 | ||||||||
\(629\) | −1.07159e15 | −0.433959 | ||||||||
\(630\) | 2.37965e14 | 0.0955302 | ||||||||
\(631\) | −1.23880e15 | −0.492992 | −0.246496 | − | 0.969144i | \(-0.579279\pi\) | ||||
−0.246496 | + | 0.969144i | \(0.579279\pi\) | |||||||
\(632\) | −2.08810e15 | −0.823771 | ||||||||
\(633\) | 1.49439e15 | 0.584444 | ||||||||
\(634\) | −2.28493e15 | −0.885894 | ||||||||
\(635\) | −1.72674e15 | −0.663699 | ||||||||
\(636\) | −8.76954e14 | −0.334166 | ||||||||
\(637\) | 1.26005e15 | 0.476014 | ||||||||
\(638\) | −4.34832e15 | −1.62858 | ||||||||
\(639\) | 1.44392e15 | 0.536154 | ||||||||
\(640\) | −2.36903e15 | −0.872130 | ||||||||
\(641\) | 2.54832e15 | 0.930112 | 0.465056 | − | 0.885281i | \(-0.346034\pi\) | ||||
0.465056 | + | 0.885281i | \(0.346034\pi\) | |||||||
\(642\) | −1.43579e15 | −0.519577 | ||||||||
\(643\) | 1.45911e14 | 0.0523513 | 0.0261757 | − | 0.999657i | \(-0.491667\pi\) | ||||
0.0261757 | + | 0.999657i | \(0.491667\pi\) | |||||||
\(644\) | −2.81948e14 | −0.100299 | ||||||||
\(645\) | −9.15243e14 | −0.322818 | ||||||||
\(646\) | −3.99950e14 | −0.139871 | ||||||||
\(647\) | 1.99009e14 | 0.0690080 | 0.0345040 | − | 0.999405i | \(-0.489015\pi\) | ||||
0.0345040 | + | 0.999405i | \(0.489015\pi\) | |||||||
\(648\) | −2.92708e14 | −0.100640 | ||||||||
\(649\) | −6.35107e14 | −0.216521 | ||||||||
\(650\) | 1.99209e13 | 0.00673418 | ||||||||
\(651\) | 1.82642e15 | 0.612216 | ||||||||
\(652\) | −3.30961e15 | −1.10006 | ||||||||
\(653\) | 4.24825e14 | 0.140019 | 0.0700096 | − | 0.997546i | \(-0.477697\pi\) | ||||
0.0700096 | + | 0.997546i | \(0.477697\pi\) | |||||||
\(654\) | 1.16728e15 | 0.381503 | ||||||||
\(655\) | −2.20199e15 | −0.713654 | ||||||||
\(656\) | −7.53991e13 | −0.0242323 | ||||||||
\(657\) | −1.98201e15 | −0.631678 | ||||||||
\(658\) | −2.67632e14 | −0.0845855 | ||||||||
\(659\) | −4.66835e15 | −1.46317 | −0.731583 | − | 0.681752i | \(-0.761218\pi\) | ||||
−0.731583 | + | 0.681752i | \(0.761218\pi\) | |||||||
\(660\) | 2.21543e15 | 0.688599 | ||||||||
\(661\) | 2.49961e14 | 0.0770484 | 0.0385242 | − | 0.999258i | \(-0.487734\pi\) | ||||
0.0385242 | + | 0.999258i | \(0.487734\pi\) | |||||||
\(662\) | −1.17446e15 | −0.359022 | ||||||||
\(663\) | 8.20922e14 | 0.248873 | ||||||||
\(664\) | −5.33015e14 | −0.160256 | ||||||||
\(665\) | 7.71834e14 | 0.230147 | ||||||||
\(666\) | 4.07302e14 | 0.120450 | ||||||||
\(667\) | 1.59876e15 | 0.468911 | ||||||||
\(668\) | −1.00629e15 | −0.292720 | ||||||||
\(669\) | −2.99157e15 | −0.863089 | ||||||||
\(670\) | 2.72726e14 | 0.0780396 | ||||||||
\(671\) | −1.60598e15 | −0.455791 | ||||||||
\(672\) | 1.17019e15 | 0.329403 | ||||||||
\(673\) | 4.01308e15 | 1.12046 | 0.560228 | − | 0.828338i | \(-0.310713\pi\) | ||||
0.560228 | + | 0.828338i | \(0.310713\pi\) | |||||||
\(674\) | 1.59783e15 | 0.442486 | ||||||||
\(675\) | −1.31448e13 | −0.00361064 | ||||||||
\(676\) | 1.41700e15 | 0.386069 | ||||||||
\(677\) | 3.65865e15 | 0.988743 | 0.494371 | − | 0.869251i | \(-0.335398\pi\) | ||||
0.494371 | + | 0.869251i | \(0.335398\pi\) | |||||||
\(678\) | 8.76708e14 | 0.235013 | ||||||||
\(679\) | 3.11024e15 | 0.827010 | ||||||||
\(680\) | 2.14639e15 | 0.566121 | ||||||||
\(681\) | 3.40954e15 | 0.892045 | ||||||||
\(682\) | −6.48348e15 | −1.68265 | ||||||||
\(683\) | 6.60913e15 | 1.70149 | 0.850747 | − | 0.525575i | \(-0.176150\pi\) | ||||
0.850747 | + | 0.525575i | \(0.176150\pi\) | |||||||
\(684\) | −3.98686e14 | −0.101818 | ||||||||
\(685\) | 4.35013e15 | 1.10206 | ||||||||
\(686\) | −1.95335e15 | −0.490905 | ||||||||
\(687\) | −3.99373e14 | −0.0995672 | ||||||||
\(688\) | −5.66167e14 | −0.140026 | ||||||||
\(689\) | −2.22611e15 | −0.546186 | ||||||||
\(690\) | 3.10586e14 | 0.0755984 | ||||||||
\(691\) | −4.05146e15 | −0.978322 | −0.489161 | − | 0.872193i | \(-0.662697\pi\) | ||||
−0.489161 | + | 0.872193i | \(0.662697\pi\) | |||||||
\(692\) | −4.69406e15 | −1.12451 | ||||||||
\(693\) | −1.28447e15 | −0.305276 | ||||||||
\(694\) | −3.12226e15 | −0.736195 | ||||||||
\(695\) | 7.60925e15 | 1.78002 | ||||||||
\(696\) | −4.19950e15 | −0.974646 | ||||||||
\(697\) | 2.67674e14 | 0.0616348 | ||||||||
\(698\) | −1.25862e15 | −0.287534 | ||||||||
\(699\) | −4.70203e15 | −1.06576 | ||||||||
\(700\) | 3.32586e13 | 0.00747938 | ||||||||
\(701\) | 3.60994e15 | 0.805473 | 0.402736 | − | 0.915316i | \(-0.368059\pi\) | ||||
0.402736 | + | 0.915316i | \(0.368059\pi\) | |||||||
\(702\) | −3.12026e14 | −0.0690775 | ||||||||
\(703\) | 1.32107e15 | 0.290183 | ||||||||
\(704\) | −2.26098e15 | −0.492774 | ||||||||
\(705\) | −7.73193e14 | −0.167205 | ||||||||
\(706\) | 1.63221e15 | 0.350227 | ||||||||
\(707\) | 7.71329e14 | 0.164223 | ||||||||
\(708\) | −2.57578e14 | −0.0544160 | ||||||||
\(709\) | −4.47467e15 | −0.938009 | −0.469004 | − | 0.883196i | \(-0.655387\pi\) | ||||
−0.469004 | + | 0.883196i | \(0.655387\pi\) | |||||||
\(710\) | 4.02446e15 | 0.837117 | ||||||||
\(711\) | 1.46877e15 | 0.303159 | ||||||||
\(712\) | −7.03381e15 | −1.44062 | ||||||||
\(713\) | 2.38380e15 | 0.484481 | ||||||||
\(714\) | −5.22591e14 | −0.105395 | ||||||||
\(715\) | 5.62377e15 | 1.12550 | ||||||||
\(716\) | 2.72106e15 | 0.540401 | ||||||||
\(717\) | 4.64382e15 | 0.915208 | ||||||||
\(718\) | 2.45327e15 | 0.479801 | ||||||||
\(719\) | 5.79191e15 | 1.12412 | 0.562061 | − | 0.827096i | \(-0.310009\pi\) | ||||
0.562061 | + | 0.827096i | \(0.310009\pi\) | |||||||
\(720\) | 4.25277e14 | 0.0819111 | ||||||||
\(721\) | 2.77020e15 | 0.529501 | ||||||||
\(722\) | −2.27670e15 | −0.431868 | ||||||||
\(723\) | −3.50130e14 | −0.0659126 | ||||||||
\(724\) | −6.42175e14 | −0.119975 | ||||||||
\(725\) | −1.88590e14 | −0.0349670 | ||||||||
\(726\) | 2.91120e15 | 0.535699 | ||||||||
\(727\) | −1.72964e15 | −0.315875 | −0.157938 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157938 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(728\) | 1.87998e15 | 0.340747 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −5.52418e15 | −0.986262 | ||||||||
\(731\) | 2.00995e15 | 0.356155 | ||||||||
\(732\) | −6.51331e14 | −0.114549 | ||||||||
\(733\) | −1.53166e15 | −0.267356 | −0.133678 | − | 0.991025i | \(-0.542679\pi\) | ||||
−0.133678 | + | 0.991025i | \(0.542679\pi\) | |||||||
\(734\) | 1.29482e14 | 0.0224328 | ||||||||
\(735\) | −2.31737e15 | −0.398488 | ||||||||
\(736\) | 1.52731e15 | 0.260675 | ||||||||
\(737\) | −1.47210e15 | −0.249383 | ||||||||
\(738\) | −1.01741e14 | −0.0171074 | ||||||||
\(739\) | 4.50150e15 | 0.751299 | 0.375650 | − | 0.926762i | \(-0.377420\pi\) | ||||
0.375650 | + | 0.926762i | \(0.377420\pi\) | |||||||
\(740\) | −2.97726e15 | −0.493221 | ||||||||
\(741\) | −1.01205e15 | −0.166418 | ||||||||
\(742\) | 1.41712e15 | 0.231305 | ||||||||
\(743\) | 9.19848e15 | 1.49031 | 0.745157 | − | 0.666889i | \(-0.232375\pi\) | ||||
0.745157 | + | 0.666889i | \(0.232375\pi\) | |||||||
\(744\) | −6.26158e15 | −1.00701 | ||||||||
\(745\) | −4.54343e15 | −0.725311 | ||||||||
\(746\) | −1.72682e15 | −0.273642 | ||||||||
\(747\) | 3.74923e14 | 0.0589765 | ||||||||
\(748\) | −4.86526e15 | −0.759709 | ||||||||
\(749\) | −6.08497e15 | −0.943211 | ||||||||
\(750\) | −1.98941e15 | −0.306117 | ||||||||
\(751\) | −4.33394e15 | −0.662008 | −0.331004 | − | 0.943629i | \(-0.607387\pi\) | ||||
−0.331004 | + | 0.943629i | \(0.607387\pi\) | |||||||
\(752\) | −4.78296e14 | −0.0725268 | ||||||||
\(753\) | 1.59123e15 | 0.239530 | ||||||||
\(754\) | −4.47666e15 | −0.668977 | ||||||||
\(755\) | −1.04531e16 | −1.55073 | ||||||||
\(756\) | −5.20940e14 | −0.0767216 | ||||||||
\(757\) | 5.41348e15 | 0.791496 | 0.395748 | − | 0.918359i | \(-0.370485\pi\) | ||||
0.395748 | + | 0.918359i | \(0.370485\pi\) | |||||||
\(758\) | −4.94577e15 | −0.717882 | ||||||||
\(759\) | −1.67646e15 | −0.241582 | ||||||||
\(760\) | −2.64611e15 | −0.378559 | ||||||||
\(761\) | −4.17764e15 | −0.593356 | −0.296678 | − | 0.954978i | \(-0.595879\pi\) | ||||
−0.296678 | + | 0.954978i | \(0.595879\pi\) | |||||||
\(762\) | −1.44133e15 | −0.203241 | ||||||||
\(763\) | 4.94699e15 | 0.692559 | ||||||||
\(764\) | 9.20027e15 | 1.27875 | ||||||||
\(765\) | −1.50977e15 | −0.208340 | ||||||||
\(766\) | 4.90963e15 | 0.672653 | ||||||||
\(767\) | −6.53851e14 | −0.0889415 | ||||||||
\(768\) | −3.24408e15 | −0.438132 | ||||||||
\(769\) | −2.00420e15 | −0.268748 | −0.134374 | − | 0.990931i | \(-0.542902\pi\) | ||||
−0.134374 | + | 0.990931i | \(0.542902\pi\) | |||||||
\(770\) | −3.58004e15 | −0.476638 | ||||||||
\(771\) | −4.26096e14 | −0.0563259 | ||||||||
\(772\) | −3.80873e15 | −0.499902 | ||||||||
\(773\) | −8.64697e15 | −1.12688 | −0.563439 | − | 0.826158i | \(-0.690522\pi\) | ||||
−0.563439 | + | 0.826158i | \(0.690522\pi\) | |||||||
\(774\) | −7.63965e14 | −0.0988549 | ||||||||
\(775\) | −2.81193e14 | −0.0361281 | ||||||||
\(776\) | −1.06630e16 | −1.36031 | ||||||||
\(777\) | 1.72617e15 | 0.218659 | ||||||||
\(778\) | 5.13641e15 | 0.646058 | ||||||||
\(779\) | −3.29994e14 | −0.0412144 | ||||||||
\(780\) | 2.28082e15 | 0.282859 | ||||||||
\(781\) | −2.17229e16 | −2.67509 | ||||||||
\(782\) | −6.82072e14 | −0.0834052 | ||||||||
\(783\) | 2.95393e15 | 0.358683 | ||||||||
\(784\) | −1.43352e15 | −0.172849 | ||||||||
\(785\) | −9.20352e15 | −1.10197 | ||||||||
\(786\) | −1.83803e15 | −0.218538 | ||||||||
\(787\) | −2.22935e15 | −0.263219 | −0.131610 | − | 0.991302i | \(-0.542015\pi\) | ||||
−0.131610 | + | 0.991302i | \(0.542015\pi\) | |||||||
\(788\) | −9.55952e15 | −1.12084 | ||||||||
\(789\) | 3.64351e15 | 0.424226 | ||||||||
\(790\) | 4.09370e15 | 0.473334 | ||||||||
\(791\) | 3.71553e15 | 0.426629 | ||||||||
\(792\) | 4.40361e15 | 0.502135 | ||||||||
\(793\) | −1.65337e15 | −0.187227 | ||||||||
\(794\) | −1.58441e15 | −0.178179 | ||||||||
\(795\) | 4.09408e15 | 0.457233 | ||||||||
\(796\) | −3.35447e15 | −0.372050 | ||||||||
\(797\) | 2.86409e15 | 0.315476 | 0.157738 | − | 0.987481i | \(-0.449580\pi\) | ||||
0.157738 | + | 0.987481i | \(0.449580\pi\) | |||||||
\(798\) | 6.44260e14 | 0.0704766 | ||||||||
\(799\) | 1.69799e15 | 0.184471 | ||||||||
\(800\) | −1.80162e14 | −0.0194387 | ||||||||
\(801\) | 4.94759e15 | 0.530169 | ||||||||
\(802\) | 2.24117e15 | 0.238515 | ||||||||
\(803\) | 2.98181e16 | 3.15169 | ||||||||
\(804\) | −5.97035e14 | −0.0626746 | ||||||||
\(805\) | 1.31628e15 | 0.137237 | ||||||||
\(806\) | −6.67483e15 | −0.691190 | ||||||||
\(807\) | 5.39509e15 | 0.554873 | ||||||||
\(808\) | −2.64438e15 | −0.270123 | ||||||||
\(809\) | −1.24502e16 | −1.26316 | −0.631581 | − | 0.775310i | \(-0.717594\pi\) | ||||
−0.631581 | + | 0.775310i | \(0.717594\pi\) | |||||||
\(810\) | 5.73853e14 | 0.0578273 | ||||||||
\(811\) | −1.62012e16 | −1.62156 | −0.810778 | − | 0.585354i | \(-0.800956\pi\) | ||||
−0.810778 | + | 0.585354i | \(0.800956\pi\) | |||||||
\(812\) | −7.47396e15 | −0.743006 | ||||||||
\(813\) | −2.09794e15 | −0.207155 | ||||||||
\(814\) | −6.12761e15 | −0.600975 | ||||||||
\(815\) | 1.54510e16 | 1.50518 | ||||||||
\(816\) | −9.33941e14 | −0.0903699 | ||||||||
\(817\) | −2.47790e15 | −0.238156 | ||||||||
\(818\) | 3.99706e15 | 0.381590 | ||||||||
\(819\) | −1.32238e15 | −0.125399 | ||||||||
\(820\) | 7.43695e14 | 0.0700517 | ||||||||
\(821\) | −7.47532e15 | −0.699427 | −0.349713 | − | 0.936857i | \(-0.613721\pi\) | ||||
−0.349713 | + | 0.936857i | \(0.613721\pi\) | |||||||
\(822\) | 3.63111e15 | 0.337477 | ||||||||
\(823\) | −5.76646e13 | −0.00532366 | −0.00266183 | − | 0.999996i | \(-0.500847\pi\) | ||||
−0.00266183 | + | 0.999996i | \(0.500847\pi\) | |||||||
\(824\) | −9.49718e15 | −0.870953 | ||||||||
\(825\) | 1.97756e14 | 0.0180149 | ||||||||
\(826\) | 4.16235e14 | 0.0376659 | ||||||||
\(827\) | −4.43940e13 | −0.00399065 | −0.00199532 | − | 0.999998i | \(-0.500635\pi\) | ||||
−0.00199532 | + | 0.999998i | \(0.500635\pi\) | |||||||
\(828\) | −6.79918e14 | −0.0607141 | ||||||||
\(829\) | 1.05447e16 | 0.935372 | 0.467686 | − | 0.883895i | \(-0.345088\pi\) | ||||
0.467686 | + | 0.883895i | \(0.345088\pi\) | |||||||
\(830\) | 1.04497e15 | 0.0920822 | ||||||||
\(831\) | 1.24669e16 | 1.09132 | ||||||||
\(832\) | −2.32771e15 | −0.202419 | ||||||||
\(833\) | 5.08914e15 | 0.439639 | ||||||||
\(834\) | 6.35154e15 | 0.545087 | ||||||||
\(835\) | 4.69788e15 | 0.400522 | ||||||||
\(836\) | 5.99799e15 | 0.508009 | ||||||||
\(837\) | 4.40440e15 | 0.370593 | ||||||||
\(838\) | −1.31253e15 | −0.109716 | ||||||||
\(839\) | −6.14078e15 | −0.509956 | −0.254978 | − | 0.966947i | \(-0.582068\pi\) | ||||
−0.254978 | + | 0.966947i | \(0.582068\pi\) | |||||||
\(840\) | −3.45751e15 | −0.285251 | ||||||||
\(841\) | 3.01798e16 | 2.47365 | ||||||||
\(842\) | −7.10261e15 | −0.578364 | ||||||||
\(843\) | 5.49982e15 | 0.444935 | ||||||||
\(844\) | −9.11800e15 | −0.732852 | ||||||||
\(845\) | −6.61532e15 | −0.528249 | ||||||||
\(846\) | −6.45394e14 | −0.0512022 | ||||||||
\(847\) | 1.23378e16 | 0.972478 | ||||||||
\(848\) | 2.53259e15 | 0.198329 | ||||||||
\(849\) | 6.25165e15 | 0.486410 | ||||||||
\(850\) | 8.04573e13 | 0.00621959 | ||||||||
\(851\) | 2.25295e15 | 0.173037 | ||||||||
\(852\) | −8.81010e15 | −0.672300 | ||||||||
\(853\) | 1.02253e16 | 0.775277 | 0.387638 | − | 0.921812i | \(-0.373291\pi\) | ||||
0.387638 | + | 0.921812i | \(0.373291\pi\) | |||||||
\(854\) | 1.05252e15 | 0.0792890 | ||||||||
\(855\) | 1.86128e15 | 0.139315 | ||||||||
\(856\) | 2.08614e16 | 1.55145 | ||||||||
\(857\) | −1.43797e15 | −0.106257 | −0.0531283 | − | 0.998588i | \(-0.516919\pi\) | ||||
−0.0531283 | + | 0.998588i | \(0.516919\pi\) | |||||||
\(858\) | 4.69424e15 | 0.344655 | ||||||||
\(859\) | −5.05945e15 | −0.369097 | −0.184549 | − | 0.982823i | \(-0.559082\pi\) | ||||
−0.184549 | + | 0.982823i | \(0.559082\pi\) | |||||||
\(860\) | 5.58435e15 | 0.404792 | ||||||||
\(861\) | −4.31183e14 | −0.0310559 | ||||||||
\(862\) | −1.09733e16 | −0.785319 | ||||||||
\(863\) | −1.23610e16 | −0.879012 | −0.439506 | − | 0.898240i | \(-0.644846\pi\) | ||||
−0.439506 | + | 0.898240i | \(0.644846\pi\) | |||||||
\(864\) | 2.82192e15 | 0.199397 | ||||||||
\(865\) | 2.19143e16 | 1.53865 | ||||||||
\(866\) | −1.46012e15 | −0.101868 | ||||||||
\(867\) | −5.01249e15 | −0.347495 | ||||||||
\(868\) | −1.11439e16 | −0.767677 | ||||||||
\(869\) | −2.20967e16 | −1.51258 | ||||||||
\(870\) | 8.23310e15 | 0.560025 | ||||||||
\(871\) | −1.51555e15 | −0.102440 | ||||||||
\(872\) | −1.69600e16 | −1.13916 | ||||||||
\(873\) | 7.50035e15 | 0.500614 | ||||||||
\(874\) | 8.40872e14 | 0.0557721 | ||||||||
\(875\) | −8.43122e15 | −0.555708 | ||||||||
\(876\) | 1.20932e16 | 0.792081 | ||||||||
\(877\) | 6.38167e15 | 0.415372 | 0.207686 | − | 0.978196i | \(-0.433407\pi\) | ||||
0.207686 | + | 0.978196i | \(0.433407\pi\) | |||||||
\(878\) | 6.46231e15 | 0.417992 | ||||||||
\(879\) | −1.30042e16 | −0.835884 | ||||||||
\(880\) | −6.39802e15 | −0.408687 | ||||||||
\(881\) | −9.60382e15 | −0.609644 | −0.304822 | − | 0.952409i | \(-0.598597\pi\) | ||||
−0.304822 | + | 0.952409i | \(0.598597\pi\) | |||||||
\(882\) | −1.93434e15 | −0.122027 | ||||||||
\(883\) | 2.03319e16 | 1.27466 | 0.637329 | − | 0.770592i | \(-0.280039\pi\) | ||||
0.637329 | + | 0.770592i | \(0.280039\pi\) | |||||||
\(884\) | −5.00885e15 | −0.312069 | ||||||||
\(885\) | 1.20251e15 | 0.0744562 | ||||||||
\(886\) | 4.95737e15 | 0.305046 | ||||||||
\(887\) | 1.16294e16 | 0.711178 | 0.355589 | − | 0.934642i | \(-0.384280\pi\) | ||||
0.355589 | + | 0.934642i | \(0.384280\pi\) | |||||||
\(888\) | −5.91789e15 | −0.359663 | ||||||||
\(889\) | −6.10844e15 | −0.368952 | ||||||||
\(890\) | 1.37897e16 | 0.827773 | ||||||||
\(891\) | −3.09750e15 | −0.184793 | ||||||||
\(892\) | 1.82531e16 | 1.08225 | ||||||||
\(893\) | −2.09332e15 | −0.123354 | ||||||||
\(894\) | −3.79246e15 | −0.222108 | ||||||||
\(895\) | −1.27033e16 | −0.739418 | ||||||||
\(896\) | −8.38058e15 | −0.484820 | ||||||||
\(897\) | −1.72594e15 | −0.0992356 | ||||||||
\(898\) | −3.10074e15 | −0.177192 | ||||||||
\(899\) | 6.31903e16 | 3.58899 | ||||||||
\(900\) | 8.02032e13 | 0.00452749 | ||||||||
\(901\) | −8.99092e15 | −0.504450 | ||||||||
\(902\) | 1.53063e15 | 0.0853559 | ||||||||
\(903\) | −3.23772e15 | −0.179456 | ||||||||
\(904\) | −1.27381e16 | −0.701744 | ||||||||
\(905\) | 2.99801e15 | 0.164159 | ||||||||
\(906\) | −8.72530e15 | −0.474871 | ||||||||
\(907\) | −2.64117e16 | −1.42875 | −0.714375 | − | 0.699763i | \(-0.753289\pi\) | ||||
−0.714375 | + | 0.699763i | \(0.753289\pi\) | |||||||
\(908\) | −2.08033e16 | −1.11856 | ||||||||
\(909\) | 1.86006e15 | 0.0994088 | ||||||||
\(910\) | −3.68570e15 | −0.195791 | ||||||||
\(911\) | 4.28301e15 | 0.226151 | 0.113075 | − | 0.993586i | \(-0.463930\pi\) | ||||
0.113075 | + | 0.993586i | \(0.463930\pi\) | |||||||
\(912\) | 1.15138e15 | 0.0604293 | ||||||||
\(913\) | −5.64049e15 | −0.294257 | ||||||||
\(914\) | 1.49774e16 | 0.776665 | ||||||||
\(915\) | 3.04075e15 | 0.156735 | ||||||||
\(916\) | 2.43677e15 | 0.124850 | ||||||||
\(917\) | −7.78965e15 | −0.396722 | ||||||||
\(918\) | −1.26023e15 | −0.0637990 | ||||||||
\(919\) | 8.05938e15 | 0.405571 | 0.202785 | − | 0.979223i | \(-0.435001\pi\) | ||||
0.202785 | + | 0.979223i | \(0.435001\pi\) | |||||||
\(920\) | −4.51266e15 | −0.225735 | ||||||||
\(921\) | 1.76458e16 | 0.877430 | ||||||||
\(922\) | −1.18035e16 | −0.583435 | ||||||||
\(923\) | −2.23641e16 | −1.09886 | ||||||||
\(924\) | 7.83721e15 | 0.382795 | ||||||||
\(925\) | −2.65758e14 | −0.0129035 | ||||||||
\(926\) | 9.79504e15 | 0.472765 | ||||||||
\(927\) | 6.68032e15 | 0.320523 | ||||||||
\(928\) | 4.04863e16 | 1.93105 | ||||||||
\(929\) | 2.56238e15 | 0.121495 | 0.0607474 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607474 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(930\) | 1.22758e16 | 0.578620 | ||||||||
\(931\) | −6.27399e15 | −0.293982 | ||||||||
\(932\) | 2.86894e16 | 1.33639 | ||||||||
\(933\) | −1.45048e16 | −0.671679 | ||||||||
\(934\) | −5.11637e14 | −0.0235534 | ||||||||
\(935\) | 2.27136e16 | 1.03949 | ||||||||
\(936\) | 4.53358e15 | 0.206264 | ||||||||
\(937\) | 1.21684e16 | 0.550385 | 0.275193 | − | 0.961389i | \(-0.411258\pi\) | ||||
0.275193 | + | 0.961389i | \(0.411258\pi\) | |||||||
\(938\) | 9.64783e14 | 0.0433825 | ||||||||
\(939\) | −1.52820e16 | −0.683156 | ||||||||
\(940\) | 4.71764e15 | 0.209663 | ||||||||
\(941\) | 2.93994e16 | 1.29896 | 0.649479 | − | 0.760379i | \(-0.274987\pi\) | ||||
0.649479 | + | 0.760379i | \(0.274987\pi\) | |||||||
\(942\) | −7.68229e15 | −0.337451 | ||||||||
\(943\) | −5.62769e14 | −0.0245763 | ||||||||
\(944\) | 7.43870e14 | 0.0322962 | ||||||||
\(945\) | 2.43202e15 | 0.104976 | ||||||||
\(946\) | 1.14934e16 | 0.493226 | ||||||||
\(947\) | 1.40267e16 | 0.598455 | 0.299228 | − | 0.954182i | \(-0.403271\pi\) | ||||
0.299228 | + | 0.954182i | \(0.403271\pi\) | |||||||
\(948\) | −8.96169e15 | −0.380141 | ||||||||
\(949\) | 3.06981e16 | 1.29464 | ||||||||
\(950\) | −9.91894e13 | −0.00415897 | ||||||||
\(951\) | −2.33521e16 | −0.973493 | ||||||||
\(952\) | 7.59297e15 | 0.314709 | ||||||||
\(953\) | 3.03827e16 | 1.25203 | 0.626015 | − | 0.779811i | \(-0.284685\pi\) | ||||
0.626015 | + | 0.779811i | \(0.284685\pi\) | |||||||
\(954\) | 3.41738e15 | 0.140016 | ||||||||
\(955\) | −4.29516e16 | −1.74969 | ||||||||
\(956\) | −2.83343e16 | −1.14761 | ||||||||
\(957\) | −4.44401e16 | −1.78961 | ||||||||
\(958\) | 5.18898e15 | 0.207765 | ||||||||
\(959\) | 1.53888e16 | 0.612637 | ||||||||
\(960\) | 4.28094e15 | 0.169452 | ||||||||
\(961\) | 6.88100e16 | 2.70815 | ||||||||
\(962\) | −6.30845e15 | −0.246865 | ||||||||
\(963\) | −1.46739e16 | −0.570954 | ||||||||
\(964\) | 2.13632e15 | 0.0826499 | ||||||||
\(965\) | 1.77811e16 | 0.684005 | ||||||||
\(966\) | 1.09872e15 | 0.0420254 | ||||||||
\(967\) | −3.25574e16 | −1.23824 | −0.619120 | − | 0.785296i | \(-0.712511\pi\) | ||||
−0.619120 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(968\) | −4.22983e16 | −1.59959 | ||||||||
\(969\) | −4.08751e15 | −0.153702 | ||||||||
\(970\) | 2.09047e16 | 0.781627 | ||||||||
\(971\) | 4.36365e16 | 1.62235 | 0.811174 | − | 0.584805i | \(-0.198829\pi\) | ||||
0.811174 | + | 0.584805i | \(0.198829\pi\) | |||||||
\(972\) | −1.25624e15 | −0.0464419 | ||||||||
\(973\) | 2.69182e16 | 0.989520 | ||||||||
\(974\) | −1.64885e16 | −0.602709 | ||||||||
\(975\) | 2.03592e14 | 0.00740007 | ||||||||
\(976\) | 1.88100e15 | 0.0679853 | ||||||||
\(977\) | −1.98101e16 | −0.711979 | −0.355989 | − | 0.934490i | \(-0.615856\pi\) | ||||
−0.355989 | + | 0.934490i | \(0.615856\pi\) | |||||||
\(978\) | 1.28971e16 | 0.460924 | ||||||||
\(979\) | −7.44334e16 | −2.64523 | ||||||||
\(980\) | 1.41395e16 | 0.499677 | ||||||||
\(981\) | 1.19297e16 | 0.419227 | ||||||||
\(982\) | 1.38572e16 | 0.484242 | ||||||||
\(983\) | −4.32181e16 | −1.50183 | −0.750916 | − | 0.660398i | \(-0.770388\pi\) | ||||
−0.750916 | + | 0.660398i | \(0.770388\pi\) | |||||||
\(984\) | 1.47824e15 | 0.0510825 | ||||||||
\(985\) | 4.46288e16 | 1.53361 | ||||||||
\(986\) | −1.80805e16 | −0.617858 | ||||||||
\(987\) | −2.73522e15 | −0.0929495 | ||||||||
\(988\) | 6.17501e15 | 0.208677 | ||||||||
\(989\) | −4.22580e15 | −0.142013 | ||||||||
\(990\) | −8.63326e15 | −0.288523 | ||||||||
\(991\) | 2.96218e16 | 0.984478 | 0.492239 | − | 0.870460i | \(-0.336179\pi\) | ||||
0.492239 | + | 0.870460i | \(0.336179\pi\) | |||||||
\(992\) | 6.03663e16 | 1.99517 | ||||||||
\(993\) | −1.20031e16 | −0.394523 | ||||||||
\(994\) | 1.42367e16 | 0.465356 | ||||||||
\(995\) | 1.56604e16 | 0.509068 | ||||||||
\(996\) | −2.28759e15 | −0.0739525 | ||||||||
\(997\) | −4.68798e16 | −1.50717 | −0.753585 | − | 0.657350i | \(-0.771677\pi\) | ||||
−0.753585 | + | 0.657350i | \(0.771677\pi\) | |||||||
\(998\) | −1.52636e16 | −0.488022 | ||||||||
\(999\) | 4.16265e15 | 0.132361 |
(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 | 177.12.a.d.1.17 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.17 | ✓ | 28 | 1.1 | even | 1 | trivial |