Newspace parameters
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(134.149125258\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.10995e6 | 0.142419 | 0.0712096 | − | 0.997461i | \(-0.477314\pi\) | ||||
0.0712096 | + | 0.997461i | \(0.477314\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.63304e8 | −0.486117 | −0.243058 | − | 0.970012i | \(-0.578151\pi\) | ||||
−0.243058 | + | 0.970012i | \(0.578151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.45818e10 | −0.169508 | −0.0847538 | − | 0.996402i | \(-0.527010\pi\) | ||||
−0.0847538 | + | 0.996402i | \(0.527010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13351e11 | 0.228044 | 0.114022 | − | 0.993478i | \(-0.463627\pi\) | ||||
0.114022 | + | 0.993478i | \(0.463627\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.83639e11 | 0.0822257 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.58939e12 | −1.03335 | −0.516676 | − | 0.856181i | \(-0.672831\pi\) | ||||
−0.516676 | + | 0.856181i | \(0.672831\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.92029e13 | 1.09273 | 0.546366 | − | 0.837546i | \(-0.316011\pi\) | ||||
0.546366 | + | 0.837546i | \(0.316011\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.14527e13 | −0.280660 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.55899e14 | 0.784696 | 0.392348 | − | 0.919817i | \(-0.371663\pi\) | ||||
0.392348 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.67165e14 | −0.979717 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.40079e15 | 1.05968 | 0.529840 | − | 0.848097i | \(-0.322252\pi\) | ||||
0.529840 | + | 0.848097i | \(0.322252\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.23982e15 | −0.490812 | −0.245406 | − | 0.969420i | \(-0.578921\pi\) | ||||
−0.245406 | + | 0.969420i | \(0.578921\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.61043e14 | −0.0978652 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.12986e15 | −0.0692323 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.07851e16 | −1.05250 | −0.526250 | − | 0.850330i | \(-0.676402\pi\) | ||||
−0.526250 | + | 0.850330i | \(0.676402\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.69325e15 | 0.131661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.03208e17 | −1.20083 | −0.600414 | − | 0.799689i | \(-0.704998\pi\) | ||||
−0.600414 | + | 0.799689i | \(0.704998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65557e17 | 1.16823 | 0.584117 | − | 0.811670i | \(-0.301441\pi\) | ||||
0.584117 | + | 0.811670i | \(0.301441\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.08437e16 | 0.0474730 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.65872e16 | 0.184656 | 0.0923280 | − | 0.995729i | \(-0.470569\pi\) | ||||
0.0923280 | + | 0.995729i | \(0.470569\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.26556e17 | −0.763690 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.07195e17 | −0.596607 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.35423e17 | 0.341991 | 0.170995 | − | 0.985272i | \(-0.445302\pi\) | ||||
0.170995 | + | 0.985272i | \(0.445302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.53488e16 | −0.0241411 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.72440e18 | 0.630889 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.53437e18 | −1.40968 | −0.704842 | − | 0.709364i | \(-0.748982\pi\) | ||||
−0.704842 | + | 0.709364i | \(0.748982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.17621e18 | −1.28805 | −0.644023 | − | 0.765006i | \(-0.722736\pi\) | ||||
−0.644023 | + | 0.765006i | \(0.722736\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.26676e18 | −0.162039 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.52515e17 | 0.0324779 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.57554e19 | 1.05595 | 0.527977 | − | 0.849258i | \(-0.322951\pi\) | ||||
0.527977 | + | 0.849258i | \(0.322951\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.20569e18 | 0.453045 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.64579e19 | −0.964588 | −0.482294 | − | 0.876009i | \(-0.660196\pi\) | ||||
−0.482294 | + | 0.876009i | \(0.660196\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.34712e19 | 0.366875 | 0.183437 | − | 0.983031i | \(-0.441278\pi\) | ||||
0.183437 | + | 0.983031i | \(0.441278\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.75856e19 | −0.565640 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.29764e18 | 0.0824005 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.68861e19 | 0.200653 | 0.100326 | − | 0.994955i | \(-0.468011\pi\) | ||||
0.100326 | + | 0.994955i | \(0.468011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.70688e20 | 1.20749 | 0.603744 | − | 0.797178i | \(-0.293675\pi\) | ||||
0.603744 | + | 0.797178i | \(0.293675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.67126e19 | −0.147169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.41764e20 | 0.611807 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.12592e20 | −1.06263 | −0.531317 | − | 0.847173i | \(-0.678303\pi\) | ||||
−0.531317 | + | 0.847173i | \(0.678303\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.11808e19 | −0.110856 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.32259e20 | −0.283371 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.08197e19 | 0.155626 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.49015e20 | 1.30668 | 0.653341 | − | 0.757064i | \(-0.273367\pi\) | ||||
0.653341 | + | 0.757064i | \(0.273367\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.08437e19 | −0.0565025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44798e20 | 0.130433 | 0.0652166 | − | 0.997871i | \(-0.479226\pi\) | ||||
0.0652166 | + | 0.997871i | \(0.479226\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19627e21 | −1.61025 | −0.805127 | − | 0.593102i | \(-0.797903\pi\) | ||||
−0.805127 | + | 0.593102i | \(0.797903\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.67169e19 | −0.0399713 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.63087e20 | 0.0801473 | 0.0400737 | − | 0.999197i | \(-0.487241\pi\) | ||||
0.0400737 | + | 0.999197i | \(0.487241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.24852e20 | 0.0909743 | 0.0454871 | − | 0.998965i | \(-0.485516\pi\) | ||||
0.0454871 | + | 0.998965i | \(0.485516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.81783e21 | −0.607661 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24118e21 | −1.17534 | −0.587670 | − | 0.809101i | \(-0.699955\pi\) | ||||
−0.587670 | + | 0.809101i | \(0.699955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.84839e20 | 0.111756 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.95230e20 | 0.0760148 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.12056e21 | 0.502330 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.18762e21 | −0.971267 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.09430e21 | −0.693299 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.93580e21 | −0.281950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.66312e21 | −0.135202 | −0.0676012 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676012 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.77599e21 | 0.674480 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.40663e21 | −0.376081 | −0.188040 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188040 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.06095e22 | −0.531196 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.40311e20 | 0.0274086 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.98314e22 | −0.727423 | −0.363711 | − | 0.931512i | \(-0.618491\pi\) | ||||
−0.363711 | + | 0.931512i | \(0.618491\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.20143e21 | 0.163858 | 0.0819290 | − | 0.996638i | \(-0.473892\pi\) | ||||
0.0819290 | + | 0.996638i | \(0.473892\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.93191e21 | 0.106611 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.65286e21 | −0.0386552 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.46633e21 | 0.150919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.51877e22 | −0.440917 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.47631e22 | −1.13562 | −0.567808 | − | 0.823161i | \(-0.692208\pi\) | ||||
−0.567808 | + | 0.823161i | \(0.692208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.11044e23 | −1.46635 | −0.733174 | − | 0.680042i | \(-0.761962\pi\) | ||||
−0.733174 | + | 0.680042i | \(0.761962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.99493e22 | −0.344451 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.96573e21 | −0.0699011 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.36563e22 | 0.382913 | 0.191457 | − | 0.981501i | \(-0.438679\pi\) | ||||
0.191457 | + | 0.981501i | \(0.438679\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.57113e22 | 0.197449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.66388e22 | −0.381454 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.85661e23 | −1.68998 | −0.844989 | − | 0.534783i | \(-0.820393\pi\) | ||||
−0.844989 | + | 0.534783i | \(0.820393\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.67780e21 | −0.0139379 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.66950e23 | −1.22435 | −0.612177 | − | 0.790720i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790720i | \(0.709706\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.34216e23 | −0.947996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.01824e23 | 0.364244 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.28496e23 | −0.723425 | −0.361713 | − | 0.932290i | \(-0.617808\pi\) | ||||
−0.361713 | + | 0.932290i | \(0.617808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.69723e23 | 0.476257 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.26799e23 | −0.813881 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.29151e22 | 0.0285852 | 0.0142926 | − | 0.999898i | \(-0.495450\pi\) | ||||
0.0142926 | + | 0.999898i | \(0.495450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.75338e23 | −1.72405 | −0.862026 | − | 0.506863i | \(-0.830805\pi\) | ||||
−0.862026 | + | 0.506863i | \(0.830805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.23748e23 | −0.743654 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.57400e22 | −0.149896 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.25249e23 | 0.175161 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.48011e22 | −0.0935532 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.33961e24 | −1.50013 | −0.750066 | − | 0.661363i | \(-0.769978\pi\) | ||||
−0.750066 | + | 0.661363i | \(0.769978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.13970e23 | −0.214783 | −0.107392 | − | 0.994217i | \(-0.534250\pi\) | ||||
−0.107392 | + | 0.994217i | \(0.534250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.08157e22 | 0.0187511 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.42895e24 | 1.15644 | 0.578220 | − | 0.815881i | \(-0.303748\pi\) | ||||
0.578220 | + | 0.815881i | \(0.303748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.45856e23 | −0.542872 | −0.271436 | − | 0.962456i | \(-0.587499\pi\) | ||||
−0.271436 | + | 0.962456i | \(0.587499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.30344e23 | 0.609656 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.72216e23 | −0.515129 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.20970e23 | −0.171021 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.43587e23 | 0.261565 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.25832e23 | −0.185226 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.65090e24 | 1.04334 | 0.521671 | − | 0.853147i | \(-0.325309\pi\) | ||||
0.521671 | + | 0.853147i | \(0.325309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.56231e24 | −0.556905 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.14875e23 | 0.166379 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.13736e23 | 0.238592 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.95464e23 | 0.211815 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.73614e23 | −0.235650 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.97174e24 | −0.874539 | −0.437270 | − | 0.899330i | \(-0.644054\pi\) | ||||
−0.437270 | + | 0.899330i | \(0.644054\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.62890e24 | −0.326572 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.14690e24 | 0.392229 | 0.196114 | − | 0.980581i | \(-0.437168\pi\) | ||||
0.196114 | + | 0.980581i | \(0.437168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.66024e24 | 0.609869 | 0.304934 | − | 0.952373i | \(-0.401365\pi\) | ||||
0.304934 | + | 0.952373i | \(0.401365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.12820e23 | 0.0475739 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.90921e24 | −0.404145 | −0.202073 | − | 0.979371i | \(-0.564768\pi\) | ||||
−0.202073 | + | 0.979371i | \(0.564768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.07083e23 | 0.0262985 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.97109e23 | 0.115847 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.80224e24 | 0.510818 | 0.255409 | − | 0.966833i | \(-0.417790\pi\) | ||||
0.255409 | + | 0.966833i | \(0.417790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.86263e24 | 0.766282 | 0.383141 | − | 0.923690i | \(-0.374842\pi\) | ||||
0.383141 | + | 0.923690i | \(0.374842\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.32657e24 | −0.108764 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.31018e24 | 0.249191 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.00790e25 | 0.697144 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.99525e25 | 1.26889 | 0.634443 | − | 0.772969i | \(-0.281229\pi\) | ||||
0.634443 | + | 0.772969i | \(0.281229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.27330e24 | −0.133012 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.57735e24 | −0.0849682 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.33580e25 | 0.662894 | 0.331447 | − | 0.943474i | \(-0.392463\pi\) | ||||
0.331447 | + | 0.943474i | \(0.392463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.11843e25 | 0.511638 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.37103e24 | 0.353227 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.83637e24 | 0.227304 | 0.113652 | − | 0.993521i | \(-0.463745\pi\) | ||||
0.113652 | + | 0.993521i | \(0.463745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.35414e24 | 0.0487060 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.84583e25 | −0.613512 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.35297e25 | 1.64511 | 0.822557 | − | 0.568683i | \(-0.192547\pi\) | ||||
0.822557 | + | 0.568683i | \(0.192547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.04403e25 | 0.296849 | 0.148425 | − | 0.988924i | \(-0.452580\pi\) | ||||
0.148425 | + | 0.988924i | \(0.452580\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.43168e24 | −0.0640029 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.81213e24 | 0.166069 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.14884e25 | 0.711399 | 0.355699 | − | 0.934600i | \(-0.384243\pi\) | ||||
0.355699 | + | 0.934600i | \(0.384243\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.80977e24 | −0.163604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.15887e25 | −0.225225 | −0.112613 | − | 0.993639i | \(-0.535922\pi\) | ||||
−0.112613 | + | 0.993639i | \(0.535922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.80399e25 | 0.866652 | 0.433326 | − | 0.901237i | \(-0.357340\pi\) | ||||
0.433326 | + | 0.901237i | \(0.357340\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.36281e24 | 0.0898507 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.74957e25 | 0.583743 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.68568e24 | 0.0678180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.60384e25 | 0.754413 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.96714e25 | −0.998142 | −0.499071 | − | 0.866561i | \(-0.666325\pi\) | ||||
−0.499071 | + | 0.866561i | \(0.666325\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.72116e25 | −0.200766 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00227e24 | −0.0326217 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.76713e25 | 0.178946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.01476e25 | −0.567898 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.55018e24 | 0.0753056 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.23176e25 | −0.183442 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.51498e26 | −1.16266 | −0.581332 | − | 0.813666i | \(-0.697468\pi\) | ||||
−0.581332 | + | 0.813666i | \(0.697468\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.29687e26 | −0.929681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.41406e26 | −0.947292 | −0.473646 | − | 0.880715i | \(-0.657062\pi\) | ||||
−0.473646 | + | 0.880715i | \(0.657062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.99598e25 | 0.312899 | 0.156450 | − | 0.987686i | \(-0.449995\pi\) | ||||
0.156450 | + | 0.987686i | \(0.449995\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.93957e24 | −0.0230774 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.81535e26 | 0.995033 | 0.497517 | − | 0.867454i | \(-0.334245\pi\) | ||||
0.497517 | + | 0.867454i | \(0.334245\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.50079e25 | −0.179624 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.63011e24 | 0.0462731 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.50835e26 | −1.12918 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.29536e25 | −0.223419 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.32773e25 | 0.0525240 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.41914e25 | −0.0897644 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.44090e26 | −0.501695 | −0.250848 | − | 0.968027i | \(-0.580709\pi\) | ||||
−0.250848 | + | 0.968027i | \(0.580709\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.07341e26 | −0.350833 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.89987e25 | 0.150388 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.63051e26 | −1.04678 | −0.523388 | − | 0.852095i | \(-0.675332\pi\) | ||||
−0.523388 | + | 0.852095i | \(0.675332\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.50438e26 | −0.678583 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.26607e25 | 0.0831964 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.57891e26 | 0.857360 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.86292e25 | 0.0645222 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.09622e25 | 0.150511 | 0.0752554 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752554 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.03939e26 | −1.40562 | −0.702810 | − | 0.711378i | \(-0.748072\pi\) | ||||
−0.702810 | + | 0.711378i | \(0.748072\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.33379e25 | 0.0438872 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.08085e26 | −0.191483 | −0.0957414 | − | 0.995406i | \(-0.530522\pi\) | ||||
−0.0957414 | + | 0.995406i | \(0.530522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.22826e25 | −0.137376 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.84266e26 | 0.290020 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.67492e26 | 0.248601 | 0.124301 | − | 0.992245i | \(-0.460331\pi\) | ||||
0.124301 | + | 0.992245i | \(0.460331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.38602e26 | 0.194064 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.24422e26 | −0.560761 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.18949e25 | 0.0522500 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.83667e26 | −1.15839 | −0.579194 | − | 0.815190i | \(-0.696633\pi\) | ||||
−0.579194 | + | 0.815190i | \(0.696633\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.59863e26 | −0.400276 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.58191e26 | −0.166248 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00058e26 | 0.0993824 | 0.0496912 | − | 0.998765i | \(-0.484176\pi\) | ||||
0.0496912 | + | 0.998765i | \(0.484176\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.73356e26 | −0.162784 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.72131e26 | 0.241654 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.23905e25 | −0.0776096 | −0.0388048 | − | 0.999247i | \(-0.512355\pi\) | ||||
−0.0388048 | + | 0.999247i | \(0.512355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.82055e25 | −0.0780591 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.13677e27 | 1.60757 | 0.803786 | − | 0.594919i | \(-0.202816\pi\) | ||||
0.803786 | + | 0.594919i | \(0.202816\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.64754e25 | 0.0117354 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.77263e26 | 0.389411 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.25581e27 | −0.802516 | −0.401258 | − | 0.915965i | \(-0.631427\pi\) | ||||
−0.401258 | + | 0.915965i | \(0.631427\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.33908e27 | −0.810868 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.78305e26 | −0.217130 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.25150e25 | 0.0285768 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.78165e27 | 0.919439 | 0.459719 | − | 0.888064i | \(-0.347950\pi\) | ||||
0.459719 | + | 0.888064i | \(0.347950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.26483e26 | −0.306686 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.40181e27 | 0.651141 | 0.325570 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325570 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.53885e26 | −0.111927 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.78097e25 | 0.0158243 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.48903e26 | 0.178407 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.17493e27 | 0.821015 | 0.410507 | − | 0.911857i | \(-0.365352\pi\) | ||||
0.410507 | + | 0.911857i | \(0.365352\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.17102e27 | −0.419978 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.01066e27 | 0.685271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.30831e26 | 0.171969 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.07139e26 | 0.0946034 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.07636e27 | 1.77990 | 0.889952 | − | 0.456055i | \(-0.150738\pi\) | ||||
0.889952 | + | 0.456055i | \(0.150738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.89993e27 | −0.529389 | −0.264695 | − | 0.964332i | \(-0.585271\pi\) | ||||
−0.264695 | + | 0.964332i | \(0.585271\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.32175e26 | 0.0615520 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.01267e27 | 1.01239 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.60714e27 | 0.626141 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.75999e25 | −0.0223176 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.08572e24 | 0.00176079 | 0.000880395 | − | 1.00000i | \(-0.499720\pi\) | ||||
0.000880395 | 1.00000i | \(0.499720\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.60439e27 | −1.16253 | −0.581267 | − | 0.813713i | \(-0.697443\pi\) | ||||
−0.581267 | + | 0.813713i | \(0.697443\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.40879e26 | 0.0871330 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.55272e27 | 0.857463 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.51110e27 | 1.52795 | 0.763973 | − | 0.645248i | \(-0.223246\pi\) | ||||
0.763973 | + | 0.645248i | \(0.223246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.48731e27 | −0.254563 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.63134e27 | 1.08234 | 0.541168 | − | 0.840915i | \(-0.317982\pi\) | ||||
0.541168 | + | 0.840915i | \(0.317982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.72147e26 | −0.151339 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.41468e27 | −0.655648 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.30394e28 | 1.84787 | 0.923933 | − | 0.382555i | \(-0.124956\pi\) | ||||
0.923933 | + | 0.382555i | \(0.124956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.50496e27 | 0.203549 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.55703e27 | −0.846596 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.28070e26 | −0.0157880 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.72949e27 | 0.556793 | 0.278397 | − | 0.960466i | \(-0.410197\pi\) | ||||
0.278397 | + | 0.960466i | \(0.410197\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.76848e27 | −0.198869 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.92722e27 | 0.529349 | 0.264675 | − | 0.964338i | \(-0.414735\pi\) | ||||
0.264675 | + | 0.964338i | \(0.414735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.20207e28 | −1.23404 | −0.617021 | − | 0.786947i | \(-0.711661\pi\) | ||||
−0.617021 | + | 0.786947i | \(0.711661\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.11319e26 | −0.0403574 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.09969e28 | −1.03144 | −0.515719 | − | 0.856758i | \(-0.672475\pi\) | ||||
−0.515719 | + | 0.856758i | \(0.672475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.72402e27 | −0.513317 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.57786e27 | 0.221075 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.41413e27 | −0.198024 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.36426e28 | −1.07057 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.51823e27 | 0.113997 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.32717e28 | 0.953684 | 0.476842 | − | 0.878989i | \(-0.341781\pi\) | ||||
0.476842 | + | 0.878989i | \(0.341781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.48951e27 | −0.240017 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.34446e27 | −0.220233 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.95139e27 | 0.186096 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.62576e28 | −1.58563 | −0.792813 | − | 0.609466i | \(-0.791384\pi\) | ||||
−0.792813 | + | 0.609466i | \(0.791384\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.68680e28 | −0.975710 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.54066e28 | 1.40796 | 0.703982 | − | 0.710218i | \(-0.251404\pi\) | ||||
0.703982 | + | 0.710218i | \(0.251404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.06213e28 | −1.09502 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.58121e26 | −0.00804704 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.61224e27 | 0.468903 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.30048e28 | 0.608204 | 0.304102 | − | 0.952640i | \(-0.401644\pi\) | ||||
0.304102 | + | 0.952640i | \(0.401644\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.57631e28 | −0.706882 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.34993e27 | −0.0580559 | −0.0290280 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290280 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.50314e26 | 0.0185762 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.38302e28 | −0.547326 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.04902e28 | −1.53749 | −0.768746 | − | 0.639554i | \(-0.779119\pi\) | ||||
−0.768746 | + | 0.639554i | \(0.779119\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.89416e27 | −0.178344 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.01263e27 | 0.210296 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.83028e27 | −0.229331 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.70964e26 | −0.0313006 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.34924e28 | −0.417670 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.40378e28 | 1.60658 | 0.803289 | − | 0.595590i | \(-0.203082\pi\) | ||||
0.803289 | + | 0.595590i | \(0.203082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.54066e28 | −0.439988 | −0.219994 | − | 0.975501i | \(-0.570604\pi\) | ||||
−0.219994 | + | 0.975501i | \(0.570604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00220e28 | 0.274967 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.92387e28 | 0.507182 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.51670e28 | −0.384252 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.92971e28 | −0.469895 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.16987e28 | −0.273842 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.07192e26 | 0.0114145 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.62623e26 | 0.0165037 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.21997e27 | 0.129451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.54478e28 | −1.51034 | −0.755171 | − | 0.655528i | \(-0.772446\pi\) | ||||
−0.755171 | + | 0.655528i | \(0.772446\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.16878e28 | −0.995382 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.99279e26 | 0.0129565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.90524e28 | −1.40944 | −0.704722 | − | 0.709483i | \(-0.748928\pi\) | ||||
−0.704722 | + | 0.709483i | \(0.748928\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.50219e28 | −0.429349 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.01101e28 | 1.15795 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.13480e27 | −0.0975408 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.65335e27 | −0.0865426 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.17729e29 | 1.73541 | 0.867707 | − | 0.497075i | \(-0.165593\pi\) | ||||
0.867707 | + | 0.497075i | \(0.165593\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.87660e28 | 0.266409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.39583e27 | 0.101129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.20807e28 | 1.21291 | 0.606457 | − | 0.795116i | \(-0.292590\pi\) | ||||
0.606457 | + | 0.795116i | \(0.292590\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.31899e28 | −0.167391 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.41693e27 | −0.0540130 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.71795e27 | −0.0320304 | −0.0160152 | − | 0.999872i | \(-0.505098\pi\) | ||||
−0.0160152 | + | 0.999872i | \(0.505098\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.28086e28 | −0.145487 | −0.0727434 | − | 0.997351i | \(-0.523175\pi\) | ||||
−0.0727434 | + | 0.997351i | \(0.523175\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.91029e28 | −0.866102 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.28307e28 | −0.768780 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.49329e29 | 1.51984 | 0.759922 | − | 0.650015i | \(-0.225237\pi\) | ||||
0.759922 | + | 0.650015i | \(0.225237\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.26347e28 | −0.124005 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.20116e28 | −0.586980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.34926e27 | −0.0579700 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.22914e27 | 0.0108260 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.62975e28 | −0.223468 | −0.111734 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111734 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.54093e28 | −0.536326 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.43783e28 | 0.667671 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.92294e29 | 1.46856 | 0.734278 | − | 0.678849i | \(-0.237521\pi\) | ||||
0.734278 | + | 0.678849i | \(0.237521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.70478e27 | 0.0715414 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.40421e28 | −0.313428 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.45874e29 | 1.68940 | 0.844699 | − | 0.535242i | \(-0.179780\pi\) | ||||
0.844699 | + | 0.535242i | \(0.179780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.47252e28 | 0.495776 | 0.247888 | − | 0.968789i | \(-0.420264\pi\) | ||||
0.247888 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.49359e28 | 0.351985 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.23531e28 | −0.138327 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.23466e29 | 0.738016 | 0.369008 | − | 0.929426i | \(-0.379698\pi\) | ||||
0.369008 | + | 0.929426i | \(0.379698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.15035e28 | −0.297410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.54771e27 | 0.0421098 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.59244e29 | −0.858476 | −0.429238 | − | 0.903191i | \(-0.641218\pi\) | ||||
−0.429238 | + | 0.903191i | \(0.641218\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.89530e28 | −0.0987390 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.23256e29 | 0.620602 | 0.310301 | − | 0.950638i | \(-0.399570\pi\) | ||||
0.310301 | + | 0.950638i | \(0.399570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.18990e28 | 0.252585 | 0.126292 | − | 0.991993i | \(-0.459692\pi\) | ||||
0.126292 | + | 0.991993i | \(0.459692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.20983e28 | 0.151015 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.13566e29 | 0.516564 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.13632e29 | 0.939562 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.51450e28 | −0.106940 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.64425e29 | 1.08760 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.05208e28 | 0.0816366 | 0.0408183 | − | 0.999167i | \(-0.487004\pi\) | ||||
0.0408183 | + | 0.999167i | \(0.487004\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.56533e29 | 0.602374 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.17222e27 | −0.0192554 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.83505e28 | −0.174155 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.22528e28 | −0.321529 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.14342e29 | 1.73477 | 0.867386 | − | 0.497636i | \(-0.165798\pi\) | ||||
0.867386 | + | 0.497636i | \(0.165798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.85766e28 | 0.289137 | 0.144569 | − | 0.989495i | \(-0.453821\pi\) | ||||
0.144569 | + | 0.989495i | \(0.453821\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.04028e28 | 0.0960588 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.46916e29 | −1.67273 | −0.836364 | − | 0.548174i | \(-0.815323\pi\) | ||||
−0.836364 | + | 0.548174i | \(0.815323\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.07012e28 | 0.238952 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.80503e28 | 0.137751 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.66153e29 | −1.57161 | −0.785806 | − | 0.618473i | \(-0.787752\pi\) | ||||
−0.785806 | + | 0.618473i | \(0.787752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.99243e28 | −0.0535611 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.69713e28 | 0.122292 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.48653e29 | 0.374867 | 0.187434 | − | 0.982277i | \(-0.439983\pi\) | ||||
0.187434 | + | 0.982277i | \(0.439983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.04669e29 | −0.988517 | −0.494259 | − | 0.869315i | \(-0.664560\pi\) | ||||
−0.494259 | + | 0.869315i | \(0.664560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.74909e28 | −0.136053 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.29951e28 | −0.0756524 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.74281e29 | 0.831527 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.34527e29 | −0.504916 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.04642e29 | 0.218334 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.54590e29 | −0.312625 | −0.156313 | − | 0.987708i | \(-0.549961\pi\) | ||||
−0.156313 | + | 0.987708i | \(0.549961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.61852e28 | −0.188547 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.88421e29 | −1.87828 | −0.939142 | − | 0.343530i | \(-0.888377\pi\) | ||||
−0.939142 | + | 0.343530i | \(0.888377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.44781e29 | −0.635200 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.26772e29 | 0.226453 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.41169e29 | 0.244524 | 0.122262 | − | 0.992498i | \(-0.460985\pi\) | ||||
0.122262 | + | 0.992498i | \(0.460985\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.16746e28 | −0.103599 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.16133e29 | 0.352108 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.93555e28 | 0.0779891 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.11585e29 | −1.09070 | −0.545352 | − | 0.838207i | \(-0.683604\pi\) | ||||
−0.545352 | + | 0.838207i | \(0.683604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.84717e28 | 0.0274668 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.61762e28 | 0.0233365 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.86490e29 | 1.24088 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.71786e29 | −0.233334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.80754e29 | −1.16096 | −0.580478 | − | 0.814276i | \(-0.697134\pi\) | ||||
−0.580478 | + | 0.814276i | \(0.697134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.99015e29 | −1.15010 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.22280e28 | 0.0151835 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.26057e28 | −0.0634058 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.79000e29 | −0.326452 | −0.163226 | − | 0.986589i | \(-0.552190\pi\) | ||||
−0.163226 | + | 0.986589i | \(0.552190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.88783e28 | 0.0668843 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.49186e29 | −0.385139 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.14032e27 | −0.00550524 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.83568e29 | 0.294921 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.21404e30 | −1.22625 | −0.613124 | − | 0.789987i | \(-0.710087\pi\) | ||||
−0.613124 | + | 0.789987i | \(0.710087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.97913e29 | 0.782772 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.64280e29 | 0.442413 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.12157e30 | −1.03819 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.54831e29 | 0.588868 | 0.294434 | − | 0.955672i | \(-0.404869\pi\) | ||||
0.294434 | + | 0.955672i | \(0.404869\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.42204e30 | −1.20720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.20665e29 | 0.182029 | 0.0910147 | − | 0.995850i | \(-0.470989\pi\) | ||||
0.0910147 | + | 0.995850i | \(0.470989\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.83325e28 | −0.0627950 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.29743e29 | −0.178992 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.07297e29 | 0.308422 | 0.154211 | − | 0.988038i | \(-0.450717\pi\) | ||||
0.154211 | + | 0.988038i | \(0.450717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.95463e29 | 0.143871 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.97218e29 | −0.284214 | −0.142107 | − | 0.989851i | \(-0.545388\pi\) | ||||
−0.142107 | + | 0.989851i | \(0.545388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.32509e29 | −0.161733 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.95152e29 | 0.402496 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.92500e28 | −0.0389610 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.86890e30 | 1.19500 | 0.597498 | − | 0.801871i | \(-0.296162\pi\) | ||||
0.597498 | + | 0.801871i | \(0.296162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.17817e30 | 0.732592 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.45341e29 | −0.208836 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.99103e30 | −1.75919 | −0.879597 | − | 0.475720i | \(-0.842188\pi\) | ||||
−0.879597 | + | 0.475720i | \(0.842188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.34236e29 | −0.0767945 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.51341e30 | 0.842206 | 0.421103 | − | 0.907013i | \(-0.361643\pi\) | ||||
0.421103 | + | 0.907013i | \(0.361643\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.16896e28 | −0.0442241 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.31410e28 | −0.0490564 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.27325e29 | −0.321470 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.53401e30 | 1.26352 | 0.631759 | − | 0.775165i | \(-0.282333\pi\) | ||||
0.631759 | + | 0.775165i | \(0.282333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.88777e29 | 0.382722 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.69545e30 | −0.800571 | −0.400285 | − | 0.916390i | \(-0.631089\pi\) | ||||
−0.400285 | + | 0.916390i | \(0.631089\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.04637e30 | 0.480857 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.60424e29 | 0.295394 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.01396e30 | −1.31218 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.85804e29 | 0.163505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.94301e29 | 0.203936 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.35769e29 | 0.0545342 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.87332e30 | 0.732616 | 0.366308 | − | 0.930494i | \(-0.380622\pi\) | ||||
0.366308 | + | 0.930494i | \(0.380622\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.44632e29 | 0.131234 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.54084e30 | 0.571353 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.13429e29 | −0.293732 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.99608e28 | 0.0281204 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.79664e29 | −0.267051 | −0.133526 | − | 0.991045i | \(-0.542630\pi\) | ||||
−0.133526 | + | 0.991045i | \(0.542630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.71944e29 | −0.190815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.08994e30 | −0.354211 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.96436e29 | −0.0621880 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.76144e29 | −0.0543264 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.16088e30 | 0.949807 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.82262e29 | 0.258308 | 0.129154 | − | 0.991625i | \(-0.458774\pi\) | ||||
0.129154 | + | 0.991625i | \(0.458774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.06044e30 | 0.587815 | 0.293907 | − | 0.955834i | \(-0.405044\pi\) | ||||
0.293907 | + | 0.955834i | \(0.405044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.16490e29 | 0.171386 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.88392e29 | −0.240685 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.83476e30 | 1.27657 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.43589e29 | −0.0369521 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.83846e30 | −0.461160 | −0.230580 | − | 0.973053i | \(-0.574062\pi\) | ||||
−0.230580 | + | 0.973053i | \(0.574062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.73766e29 | −0.189196 | −0.0945979 | − | 0.995516i | \(-0.530157\pi\) | ||||
−0.0945979 | + | 0.995516i | \(0.530157\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.02249e29 | 0.0958802 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.59989e30 | 1.06891 | 0.534453 | − | 0.845198i | \(-0.320518\pi\) | ||||
0.534453 | + | 0.845198i | \(0.320518\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.93000e30 | 1.79660 | 0.898298 | − | 0.439386i | \(-0.144804\pi\) | ||||
0.898298 | + | 0.439386i | \(0.144804\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.85936e30 | 0.410726 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.66386e30 | 0.789162 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.30202e29 | −0.174372 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.61159e29 | −0.0944569 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.84033e30 | −0.966884 | −0.483442 | − | 0.875376i | \(-0.660614\pi\) | ||||
−0.483442 | + | 0.875376i | \(0.660614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.30944e29 | 0.122923 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.84300e29 | −0.130034 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.28400e29 | −0.135013 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.61129e30 | 0.472149 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.83671e30 | 0.500362 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.79937e30 | −0.825893 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.96903e30 | 0.498483 | 0.249242 | − | 0.968441i | \(-0.419819\pi\) | ||||
0.249242 | + | 0.968441i | \(0.419819\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.16669e29 | 0.0518753 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.70009e30 | −0.591444 | −0.295722 | − | 0.955274i | \(-0.595560\pi\) | ||||
−0.295722 | + | 0.955274i | \(0.595560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.75385e29 | −0.120945 | −0.0604726 | − | 0.998170i | \(-0.519261\pi\) | ||||
−0.0604726 | + | 0.998170i | \(0.519261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.21408e30 | 0.337024 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.29544e31 | 1.92443 | 0.962217 | − | 0.272283i | \(-0.0877786\pi\) | ||||
0.962217 | + | 0.272283i | \(0.0877786\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.10610e29 | −0.103030 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.76685e29 | 0.0391548 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.46231e29 | −0.0340122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.78589e30 | 0.240805 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.30901e30 | 0.435560 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.06659e30 | 0.137060 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.57355e31 | −1.97417 | −0.987083 | − | 0.160207i | \(-0.948784\pi\) | ||||
−0.987083 | + | 0.160207i | \(0.948784\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.70452e30 | −0.576278 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.47526e31 | −1.76450 | −0.882252 | − | 0.470778i | \(-0.843973\pi\) | ||||
−0.882252 | + | 0.470778i | \(0.843973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.64453e30 | 0.659235 | 0.329617 | − | 0.944115i | \(-0.393080\pi\) | ||||
0.329617 | + | 0.944115i | \(0.393080\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.01633e30 | −0.115912 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.89300e30 | −0.656354 | −0.328177 | − | 0.944616i | \(-0.606434\pi\) | ||||
−0.328177 | + | 0.944616i | \(0.606434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.04218e29 | 0.0657242 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.77281e29 | −0.0188342 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.94454e30 | 0.201780 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.01653e28 | 0.00407107 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.04347e30 | 0.103314 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.37734e30 | −0.520104 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.74002e30 | −0.353397 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.55166e30 | −0.327876 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.72226e30 | −0.245538 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.32782e30 | −0.733931 | −0.366965 | − | 0.930235i | \(-0.619603\pi\) | ||||
−0.366965 | + | 0.930235i | \(0.619603\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.04879e29 | 0.0434777 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.08086e31 | −0.909548 | −0.454774 | − | 0.890607i | \(-0.650280\pi\) | ||||
−0.454774 | + | 0.890607i | \(0.650280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.48894e30 | −0.204678 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.31783e30 | −0.105911 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.32755e30 | 0.182819 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.55205e30 | −0.502996 | −0.251498 | − | 0.967858i | \(-0.580923\pi\) | ||||
−0.251498 | + | 0.967858i | \(0.580923\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.94582e30 | −0.671265 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.99902e30 | −0.219969 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.43817e31 | 1.03115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.65791e30 | −0.536752 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.04036e31 | 0.712883 | 0.356442 | − | 0.934318i | \(-0.383990\pi\) | ||||
0.356442 | + | 0.934318i | \(0.383990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.24567e31 | −0.834509 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.34989e30 | −0.546919 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.89518e29 | 0.0249463 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.09831e31 | −1.31402 | −0.657012 | − | 0.753880i | \(-0.728180\pi\) | ||||
−0.657012 | + | 0.753880i | \(0.728180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.95007e30 | 0.180653 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.20967e31 | 1.32323 | 0.661617 | − | 0.749842i | \(-0.269870\pi\) | ||||
0.661617 | + | 0.749842i | \(0.269870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.60900e31 | −0.942286 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.32628e29 | −0.0133238 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.59604e31 | 1.45424 | 0.727121 | − | 0.686509i | \(-0.240858\pi\) | ||||
0.727121 | + | 0.686509i | \(0.240858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.52698e30 | 0.0836637 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.07194e31 | 0.574483 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.94729e31 | −1.54507 | −0.772535 | − | 0.634973i | \(-0.781011\pi\) | ||||
−0.772535 | + | 0.634973i | \(0.781011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.16613e30 | −0.213648 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.06718e30 | −0.103706 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.20482e30 | 0.353612 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.58087e31 | −0.759103 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.68648e29 | 0.0267158 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.65436e29 | −0.0305893 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.98077e30 | −0.313997 | −0.156998 | − | 0.987599i | \(-0.550182\pi\) | ||||
−0.156998 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.48116e31 | −0.651931 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.30234e30 | 0.0560946 | 0.0280473 | − | 0.999607i | \(-0.491071\pi\) | ||||
0.0280473 | + | 0.999607i | \(0.491071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.88970e30 | −0.0796541 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.12685e30 | −0.128991 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.06599e31 | 1.23788 | 0.618939 | − | 0.785439i | \(-0.287563\pi\) | ||||
0.618939 | + | 0.785439i | \(0.287563\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.55817e30 | 0.180124 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.84011e29 | 0.0303248 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.31325e30 | −0.314745 | −0.157373 | − | 0.987539i | \(-0.550302\pi\) | ||||
−0.157373 | + | 0.987539i | \(0.550302\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.44398e30 | 0.164699 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.42848e30 | −0.0518255 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.58102e31 | 0.916708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.32568e31 | 0.460962 | 0.230481 | − | 0.973077i | \(-0.425970\pi\) | ||||
0.230481 | + | 0.973077i | \(0.425970\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.50837e30 | −0.289654 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.31958e30 | −0.0773154 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.42048e31 | 1.11632 | 0.558159 | − | 0.829734i | \(-0.311508\pi\) | ||||
0.558159 | + | 0.829734i | \(0.311508\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.33837e30 | −0.202554 |
(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 | 48.22.a.e.1.1 | 1 | ||
4.3 | odd | 2 | 3.22.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 9.22.a.d.1.1 | 1 | |||
20.3 | even | 4 | 75.22.b.a.49.2 | 2 | |||
20.7 | even | 4 | 75.22.b.a.49.1 | 2 | |||
20.19 | odd | 2 | 75.22.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.22.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
9.22.a.d.1.1 | 1 | 12.11 | even | 2 | |||
48.22.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
75.22.a.c.1.1 | 1 | 20.19 | odd | 2 | |||
75.22.b.a.49.1 | 2 | 20.7 | even | 4 | |||
75.22.b.a.49.2 | 2 | 20.3 | even | 4 |