Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(209.608008215\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 75.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2844.00 | 1.96388 | 0.981939 | − | 0.189196i | \(-0.0605882\pi\) | ||||
0.981939 | + | 0.189196i | \(0.0605882\pi\) | |||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 5.99118e6 | 2.85682 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.67935e8 | 1.13385 | ||||||||
\(7\) | −3.63304e8 | −0.486117 | −0.243058 | − | 0.970012i | \(-0.578151\pi\) | ||||
−0.243058 | + | 0.970012i | \(0.578151\pi\) | |||||||
\(8\) | 1.10746e10 | 3.64657 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.45818e10 | 0.169508 | 0.0847538 | − | 0.996402i | \(-0.472990\pi\) | ||||
0.0847538 | + | 0.996402i | \(0.472990\pi\) | |||||||
\(12\) | 3.53773e11 | 1.64939 | ||||||||
\(13\) | −1.13351e11 | −0.228044 | −0.114022 | − | 0.993478i | \(-0.536373\pi\) | ||||
−0.114022 | + | 0.993478i | \(0.536373\pi\) | |||||||
\(14\) | −1.03324e12 | −0.954674 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.89318e13 | 4.30460 | ||||||||
\(17\) | 8.58939e12 | 1.03335 | 0.516676 | − | 0.856181i | \(-0.327169\pi\) | ||||
0.516676 | + | 0.856181i | \(0.327169\pi\) | |||||||
\(18\) | 9.91641e12 | 0.654626 | ||||||||
\(19\) | −2.92029e13 | −1.09273 | −0.546366 | − | 0.837546i | \(-0.683989\pi\) | ||||
−0.546366 | + | 0.837546i | \(0.683989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.14527e13 | −0.280660 | ||||||||
\(22\) | 4.14707e13 | 0.332892 | ||||||||
\(23\) | 1.55899e14 | 0.784696 | 0.392348 | − | 0.919817i | \(-0.371663\pi\) | ||||
0.392348 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(24\) | 6.53946e14 | 2.10535 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.22370e14 | −0.447851 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | −2.17662e15 | −1.38875 | ||||||||
\(29\) | 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 | \(-0.421079\pi\) | ||||
0.245406 | + | 0.969420i | \(0.421079\pi\) | |||||||
\(32\) | 3.06169e16 | 4.80714 | ||||||||
\(33\) | 8.61043e14 | 0.0978652 | ||||||||
\(34\) | 2.44282e16 | 2.02938 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.08900e16 | 0.952273 | ||||||||
\(37\) | 3.07851e16 | 1.05250 | 0.526250 | − | 0.850330i | \(-0.323598\pi\) | ||||
0.526250 | + | 0.850330i | \(0.323598\pi\) | |||||||
\(38\) | −8.30532e16 | −2.14599 | ||||||||
\(39\) | −6.69325e15 | −0.131661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.03208e17 | −1.20083 | −0.600414 | − | 0.799689i | \(-0.704998\pi\) | ||||
−0.600414 | + | 0.799689i | \(0.704998\pi\) | |||||||
\(42\) | −6.10116e16 | −0.551182 | ||||||||
\(43\) | 1.65557e17 | 1.16823 | 0.584117 | − | 0.811670i | \(-0.301441\pi\) | ||||
0.584117 | + | 0.811670i | \(0.301441\pi\) | |||||||
\(44\) | 8.73624e16 | 0.484252 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.43377e17 | 1.54105 | ||||||||
\(47\) | 6.65872e16 | 0.184656 | 0.0923280 | − | 0.995729i | \(-0.470569\pi\) | ||||
0.0923280 | + | 0.995729i | \(0.470569\pi\) | |||||||
\(48\) | 1.11790e18 | 2.48526 | ||||||||
\(49\) | −4.26556e17 | −0.763690 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.07195e17 | 0.596607 | ||||||||
\(52\) | −6.79105e17 | −0.651482 | ||||||||
\(53\) | −4.35423e17 | −0.341991 | −0.170995 | − | 0.985272i | \(-0.554698\pi\) | ||||
−0.170995 | + | 0.985272i | \(0.554698\pi\) | |||||||
\(54\) | 5.85554e17 | 0.377949 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.02346e18 | −1.77266 | ||||||||
\(57\) | −1.72440e18 | −0.630889 | ||||||||
\(58\) | 6.82784e18 | 2.08108 | ||||||||
\(59\) | 5.53437e18 | 1.40968 | 0.704842 | − | 0.709364i | \(-0.251018\pi\) | ||||
0.704842 | + | 0.709364i | \(0.251018\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.17621e18 | −1.28805 | −0.644023 | − | 0.765006i | \(-0.722736\pi\) | ||||
−0.644023 | + | 0.765006i | \(0.722736\pi\) | |||||||
\(62\) | 6.37005e18 | 0.963896 | ||||||||
\(63\) | −1.26676e18 | −0.162039 | ||||||||
\(64\) | 4.73716e19 | 5.13604 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.44881e18 | 0.192195 | ||||||||
\(67\) | 1.57554e19 | 1.05595 | 0.527977 | − | 0.849258i | \(-0.322951\pi\) | ||||
0.527977 | + | 0.849258i | \(0.322951\pi\) | |||||||
\(68\) | 5.14606e19 | 2.95210 | ||||||||
\(69\) | 9.20569e18 | 0.453045 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.64579e19 | 0.964588 | 0.482294 | − | 0.876009i | \(-0.339804\pi\) | ||||
0.482294 | + | 0.876009i | \(0.339804\pi\) | |||||||
\(72\) | 3.86148e19 | 1.21552 | ||||||||
\(73\) | −1.34712e19 | −0.366875 | −0.183437 | − | 0.983031i | \(-0.558722\pi\) | ||||
−0.183437 | + | 0.983031i | \(0.558722\pi\) | |||||||
\(74\) | 8.75527e19 | 2.06698 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.74960e20 | −3.12174 | ||||||||
\(77\) | −5.29764e18 | −0.0824005 | ||||||||
\(78\) | −1.90356e19 | −0.258567 | ||||||||
\(79\) | −1.68861e19 | −0.200653 | −0.100326 | − | 0.994955i | \(-0.531989\pi\) | ||||
−0.100326 | + | 0.994955i | \(0.531989\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | −2.93522e20 | −2.35828 | ||||||||
\(83\) | 1.70688e20 | 1.20749 | 0.603744 | − | 0.797178i | \(-0.293675\pi\) | ||||
0.603744 | + | 0.797178i | \(0.293675\pi\) | |||||||
\(84\) | −1.28527e20 | −0.801794 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.70845e20 | 2.29427 | ||||||||
\(87\) | 1.41764e20 | 0.611807 | ||||||||
\(88\) | 1.61488e20 | 0.618121 | ||||||||
\(89\) | −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 | ||||||||
\(92\) | 9.34021e20 | 2.24174 | ||||||||
\(93\) | 1.32259e20 | 0.283371 | ||||||||
\(94\) | 1.89374e20 | 0.362642 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.80790e21 | 2.77540 | ||||||||
\(97\) | −9.49015e20 | −1.30668 | −0.653341 | − | 0.757064i | \(-0.726633\pi\) | ||||
−0.653341 | + | 0.757064i | \(0.726633\pi\) | |||||||
\(98\) | −1.21313e21 | −1.49980 | ||||||||
\(99\) | 5.08437e19 | 0.0565025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44798e20 | 0.130433 | 0.0652166 | − | 0.997871i | \(-0.479226\pi\) | ||||
0.0652166 | + | 0.997871i | \(0.479226\pi\) | |||||||
\(102\) | 1.44246e21 | 1.17166 | ||||||||
\(103\) | −2.19627e21 | −1.61025 | −0.805127 | − | 0.593102i | \(-0.797903\pi\) | ||||
−0.805127 | + | 0.593102i | \(0.797903\pi\) | |||||||
\(104\) | −1.25532e21 | −0.831579 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.23834e21 | −0.671629 | ||||||||
\(107\) | 1.63087e20 | 0.0801473 | 0.0400737 | − | 0.999197i | \(-0.487241\pi\) | ||||
0.0400737 | + | 0.999197i | \(0.487241\pi\) | |||||||
\(108\) | 1.23353e21 | 0.549795 | ||||||||
\(109\) | 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 | ||||||||
\(112\) | −6.87800e21 | −2.09254 | ||||||||
\(113\) | 4.24118e21 | 1.17534 | 0.587670 | − | 0.809101i | \(-0.300045\pi\) | ||||
0.587670 | + | 0.809101i | \(0.300045\pi\) | |||||||
\(114\) | −4.90421e21 | −1.23899 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.43836e22 | 3.02732 | ||||||||
\(117\) | −3.95230e20 | −0.0760148 | ||||||||
\(118\) | 1.57397e22 | 2.76845 | ||||||||
\(119\) | −3.12056e21 | −0.502330 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.18762e21 | −0.971267 | ||||||||
\(122\) | −2.04091e22 | −2.52957 | ||||||||
\(123\) | −6.09430e21 | −0.693299 | ||||||||
\(124\) | 1.34192e22 | 1.40216 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.60267e21 | −0.318225 | ||||||||
\(127\) | −1.66312e21 | −0.135202 | −0.0676012 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676012 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(128\) | 7.05165e22 | 5.27942 | ||||||||
\(129\) | 9.77599e21 | 0.674480 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.40663e21 | 0.376081 | 0.188040 | − | 0.982161i | \(-0.439786\pi\) | ||||
0.188040 | + | 0.982161i | \(0.439786\pi\) | |||||||
\(132\) | 5.15867e21 | 0.279583 | ||||||||
\(133\) | 1.06095e22 | 0.531196 | ||||||||
\(134\) | 4.48085e22 | 2.07377 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.51243e22 | 3.76819 | ||||||||
\(137\) | 1.98314e22 | 0.727423 | 0.363711 | − | 0.931512i | \(-0.381509\pi\) | ||||
0.363711 | + | 0.931512i | \(0.381509\pi\) | |||||||
\(138\) | 2.61810e22 | 0.889725 | ||||||||
\(139\) | −5.20143e21 | −0.163858 | −0.0819290 | − | 0.996638i | \(-0.526108\pi\) | ||||
−0.0819290 | + | 0.996638i | \(0.526108\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.93191e21 | 0.106611 | ||||||||
\(142\) | 7.52461e22 | 1.89433 | ||||||||
\(143\) | −1.65286e21 | −0.0386552 | ||||||||
\(144\) | 6.60112e22 | 1.43487 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.83122e22 | −0.720498 | ||||||||
\(147\) | −2.51877e22 | −0.440917 | ||||||||
\(148\) | 1.84439e23 | 3.00680 | ||||||||
\(149\) | −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 | \(-0.238038\pi\) | ||||
0.733174 | + | 0.680042i | \(0.238038\pi\) | |||||||
\(152\) | −3.23412e23 | −3.98472 | ||||||||
\(153\) | 2.99493e22 | 0.344451 | ||||||||
\(154\) | −1.50665e22 | −0.161824 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.01005e22 | −0.376133 | ||||||||
\(157\) | −4.36563e22 | −0.382913 | −0.191457 | − | 0.981501i | \(-0.561321\pi\) | ||||
−0.191457 | + | 0.981501i | \(0.561321\pi\) | |||||||
\(158\) | −4.80241e22 | −0.394058 | ||||||||
\(159\) | −2.57113e22 | −0.197449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.66388e22 | −0.381454 | ||||||||
\(162\) | 3.45764e22 | 0.218209 | ||||||||
\(163\) | −2.85661e23 | −1.68998 | −0.844989 | − | 0.534783i | \(-0.820393\pi\) | ||||
−0.844989 | + | 0.534783i | \(0.820393\pi\) | |||||||
\(164\) | −6.18336e23 | −3.43055 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.85437e23 | 2.37136 | ||||||||
\(167\) | −2.66950e23 | −1.22435 | −0.612177 | − | 0.790720i | \(-0.709706\pi\) | ||||
−0.612177 | + | 0.790720i | \(0.709706\pi\) | |||||||
\(168\) | −2.37581e23 | −1.02344 | ||||||||
\(169\) | −2.34216e23 | −0.947996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.01824e23 | −0.364244 | ||||||||
\(172\) | 9.91884e23 | 3.33743 | ||||||||
\(173\) | 2.28496e23 | 0.723425 | 0.361713 | − | 0.932290i | \(-0.382192\pi\) | ||||
0.361713 | + | 0.932290i | \(0.382192\pi\) | |||||||
\(174\) | 4.03177e23 | 1.20151 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.76061e23 | 0.729661 | ||||||||
\(177\) | 3.26799e23 | 0.813881 | ||||||||
\(178\) | −8.89013e23 | −2.08688 | ||||||||
\(179\) | −1.29151e22 | −0.0285852 | −0.0142926 | − | 0.999898i | \(-0.504550\pi\) | ||||
−0.0142926 | + | 0.999898i | \(0.504550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.75338e23 | −1.72405 | −0.862026 | − | 0.506863i | \(-0.830805\pi\) | ||||
−0.862026 | + | 0.506863i | \(0.830805\pi\) | |||||||
\(182\) | 1.17118e23 | 0.217708 | ||||||||
\(183\) | −4.23748e23 | −0.743654 | ||||||||
\(184\) | 1.72653e24 | 2.86145 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.76145e23 | 0.556506 | ||||||||
\(187\) | 1.25249e23 | 0.175161 | ||||||||
\(188\) | 3.98936e23 | 0.527529 | ||||||||
\(189\) | −7.48011e22 | −0.0935532 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.33961e24 | 1.50013 | 0.750066 | − | 0.661363i | \(-0.230022\pi\) | ||||
0.750066 | + | 0.661363i | \(0.230022\pi\) | |||||||
\(192\) | 2.79725e24 | 2.96529 | ||||||||
\(193\) | 2.13970e23 | 0.214783 | 0.107392 | − | 0.994217i | \(-0.465750\pi\) | ||||
0.107392 | + | 0.994217i | \(0.465750\pi\) | |||||||
\(194\) | −2.69900e24 | −2.56616 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.55558e24 | −2.18173 | ||||||||
\(197\) | −1.42895e24 | −1.15644 | −0.578220 | − | 0.815881i | \(-0.696252\pi\) | ||||
−0.578220 | + | 0.815881i | \(0.696252\pi\) | |||||||
\(198\) | 1.44600e23 | 0.110964 | ||||||||
\(199\) | 7.45856e23 | 0.542872 | 0.271436 | − | 0.962456i | \(-0.412501\pi\) | ||||
0.271436 | + | 0.962456i | \(0.412501\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.30344e23 | 0.609656 | ||||||||
\(202\) | 4.11805e23 | 0.256155 | ||||||||
\(203\) | −8.72216e23 | −0.515129 | ||||||||
\(204\) | 3.03870e24 | 1.70440 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.24619e24 | −3.16234 | ||||||||
\(207\) | 5.43587e23 | 0.261565 | ||||||||
\(208\) | −2.14594e24 | −0.981639 | ||||||||
\(209\) | −4.25832e23 | −0.185226 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.65090e24 | −1.04334 | −0.521671 | − | 0.853147i | \(-0.674691\pi\) | ||||
−0.521671 | + | 0.853147i | \(0.674691\pi\) | |||||||
\(212\) | −2.60870e24 | −0.977006 | ||||||||
\(213\) | 1.56231e24 | 0.556905 | ||||||||
\(214\) | 4.63819e23 | 0.157400 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.28017e24 | 0.701782 | ||||||||
\(217\) | −8.13736e23 | −0.238592 | ||||||||
\(218\) | 6.39479e23 | 0.178662 | ||||||||
\(219\) | −7.95464e23 | −0.211815 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.73614e23 | −0.235650 | ||||||||
\(222\) | 5.16990e24 | 1.19337 | ||||||||
\(223\) | −3.97174e24 | −0.874539 | −0.437270 | − | 0.899330i | \(-0.644054\pi\) | ||||
−0.437270 | + | 0.899330i | \(0.644054\pi\) | |||||||
\(224\) | −1.11232e25 | −2.33683 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.20619e25 | 2.30823 | ||||||||
\(227\) | 2.14690e24 | 0.392229 | 0.196114 | − | 0.980581i | \(-0.437168\pi\) | ||||
0.196114 | + | 0.980581i | \(0.437168\pi\) | |||||||
\(228\) | −1.03312e25 | −1.80234 | ||||||||
\(229\) | 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 | ||||||||
\(232\) | 2.65878e25 | 3.86420 | ||||||||
\(233\) | 2.90921e24 | 0.404145 | 0.202073 | − | 0.979371i | \(-0.435232\pi\) | ||||
0.202073 | + | 0.979371i | \(0.435232\pi\) | |||||||
\(234\) | −1.12403e24 | −0.149284 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.31574e25 | 4.02721 | ||||||||
\(237\) | −9.97109e23 | −0.115847 | ||||||||
\(238\) | −8.87487e24 | −0.986516 | ||||||||
\(239\) | −4.80224e24 | −0.510818 | −0.255409 | − | 0.966833i | \(-0.582210\pi\) | ||||
−0.255409 | + | 0.966833i | \(0.582210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.86263e24 | 0.766282 | 0.383141 | − | 0.923690i | \(-0.374842\pi\) | ||||
0.383141 | + | 0.923690i | \(0.374842\pi\) | |||||||
\(242\) | −2.04416e25 | −1.90745 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | −4.29940e25 | −3.67972 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.73322e25 | −1.36155 | ||||||||
\(247\) | 3.31018e24 | 0.249191 | ||||||||
\(248\) | 2.48052e25 | 1.78978 | ||||||||
\(249\) | 1.00790e25 | 0.697144 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.99525e25 | −1.26889 | −0.634443 | − | 0.772969i | \(-0.718771\pi\) | ||||
−0.634443 | + | 0.772969i | \(0.718771\pi\) | |||||||
\(252\) | −7.58941e24 | −0.462916 | ||||||||
\(253\) | 2.27330e24 | 0.133012 | ||||||||
\(254\) | −4.72991e24 | −0.265521 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.01203e26 | 5.23210 | ||||||||
\(257\) | −1.33580e25 | −0.662894 | −0.331447 | − | 0.943474i | \(-0.607537\pi\) | ||||
−0.331447 | + | 0.943474i | \(0.607537\pi\) | |||||||
\(258\) | 2.78029e25 | 1.32460 | ||||||||
\(259\) | −1.11843e25 | −0.511638 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.37103e24 | 0.353227 | ||||||||
\(262\) | 1.82204e25 | 0.738576 | ||||||||
\(263\) | 5.83637e24 | 0.227304 | 0.113652 | − | 0.993521i | \(-0.463745\pi\) | ||||
0.113652 | + | 0.993521i | \(0.463745\pi\) | |||||||
\(264\) | 9.53573e24 | 0.356872 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.01735e25 | 1.04320 | ||||||||
\(267\) | −1.84583e25 | −0.613512 | ||||||||
\(268\) | 9.43938e25 | 3.01667 | ||||||||
\(269\) | 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 | \(-0.547420\pi\) | ||||
−0.148425 | + | 0.988924i | \(0.547420\pi\) | |||||||
\(272\) | 1.62613e26 | 4.44817 | ||||||||
\(273\) | 2.43168e24 | 0.0640029 | ||||||||
\(274\) | 5.64004e25 | 1.42857 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.51530e25 | 1.29427 | ||||||||
\(277\) | −3.14884e25 | −0.711399 | −0.355699 | − | 0.934600i | \(-0.615757\pi\) | ||||
−0.355699 | + | 0.934600i | \(0.615757\pi\) | |||||||
\(278\) | −1.47929e25 | −0.321797 | ||||||||
\(279\) | 7.80977e24 | 0.163604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.15887e25 | −0.225225 | −0.112613 | − | 0.993639i | \(-0.535922\pi\) | ||||
−0.112613 | + | 0.993639i | \(0.535922\pi\) | |||||||
\(282\) | 1.11823e25 | 0.209371 | ||||||||
\(283\) | 4.80399e25 | 0.866652 | 0.433326 | − | 0.901237i | \(-0.357340\pi\) | ||||
0.433326 | + | 0.901237i | \(0.357340\pi\) | |||||||
\(284\) | 1.58514e26 | 2.75565 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.70074e24 | −0.0759142 | ||||||||
\(287\) | 3.74957e25 | 0.583743 | ||||||||
\(288\) | 1.06755e26 | 1.60238 | ||||||||
\(289\) | 4.68568e24 | 0.0678180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.60384e25 | −0.754413 | ||||||||
\(292\) | −8.07087e25 | −1.04809 | ||||||||
\(293\) | 7.96714e25 | 0.998142 | 0.499071 | − | 0.866561i | \(-0.333675\pi\) | ||||
0.499071 | + | 0.866561i | \(0.333675\pi\) | |||||||
\(294\) | −7.16339e25 | −0.865907 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.40933e26 | 3.83801 | ||||||||
\(297\) | 3.00227e24 | 0.0326217 | ||||||||
\(298\) | −2.12626e26 | −2.23021 | ||||||||
\(299\) | −1.76713e25 | −0.178946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.01476e25 | −0.567898 | ||||||||
\(302\) | 3.15809e26 | 2.87973 | ||||||||
\(303\) | 8.55018e24 | 0.0753056 | ||||||||
\(304\) | −5.52865e26 | −4.70377 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.51760e25 | 0.676460 | ||||||||
\(307\) | −1.51498e26 | −1.16266 | −0.581332 | − | 0.813666i | \(-0.697468\pi\) | ||||
−0.581332 | + | 0.813666i | \(0.697468\pi\) | |||||||
\(308\) | −3.17391e25 | −0.235403 | ||||||||
\(309\) | −1.29687e26 | −0.929681 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.41406e26 | 0.947292 | 0.473646 | − | 0.880715i | \(-0.342938\pi\) | ||||
0.473646 | + | 0.880715i | \(0.342938\pi\) | |||||||
\(312\) | −7.41253e25 | −0.480112 | ||||||||
\(313\) | −4.99598e25 | −0.312899 | −0.156450 | − | 0.987686i | \(-0.550005\pi\) | ||||
−0.156450 | + | 0.987686i | \(0.550005\pi\) | |||||||
\(314\) | −1.24158e26 | −0.751995 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.01168e26 | −0.573229 | ||||||||
\(317\) | −1.81535e26 | −0.995033 | −0.497517 | − | 0.867454i | \(-0.665755\pi\) | ||||
−0.497517 | + | 0.867454i | \(0.665755\pi\) | |||||||
\(318\) | −7.31229e25 | −0.387765 | ||||||||
\(319\) | 3.50079e25 | 0.179624 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.63011e24 | 0.0462731 | ||||||||
\(322\) | −1.61081e26 | −0.749130 | ||||||||
\(323\) | −2.50835e26 | −1.12918 | ||||||||
\(324\) | 7.28388e25 | 0.317424 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.12420e26 | −3.31891 | ||||||||
\(327\) | 1.32773e25 | 0.0525240 | ||||||||
\(328\) | −1.14299e27 | −4.37890 | ||||||||
\(329\) | −2.41914e25 | −0.0897644 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.44090e26 | 0.501695 | 0.250848 | − | 0.968027i | \(-0.419291\pi\) | ||||
0.250848 | + | 0.968027i | \(0.419291\pi\) | |||||||
\(332\) | 1.02262e27 | 3.44958 | ||||||||
\(333\) | 1.07341e26 | 0.350833 | ||||||||
\(334\) | −7.59206e26 | −2.40448 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.06139e26 | −1.20813 | ||||||||
\(337\) | 3.63051e26 | 1.04678 | 0.523388 | − | 0.852095i | \(-0.324668\pi\) | ||||
0.523388 | + | 0.852095i | \(0.324668\pi\) | |||||||
\(338\) | −6.66111e26 | −1.86175 | ||||||||
\(339\) | 2.50438e26 | 0.678583 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.26607e25 | 0.0831964 | ||||||||
\(342\) | −2.89588e26 | −0.715331 | ||||||||
\(343\) | 3.57891e26 | 0.857360 | ||||||||
\(344\) | 1.83349e27 | 4.26004 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.49841e26 | 1.42072 | ||||||||
\(347\) | 7.09622e25 | 0.150511 | 0.0752554 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752554 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(348\) | 8.49335e26 | 1.74782 | ||||||||
\(349\) | −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 | ||||||||
\(352\) | 4.46451e26 | 0.814846 | ||||||||
\(353\) | 1.08085e26 | 0.191483 | 0.0957414 | − | 0.995406i | \(-0.469478\pi\) | ||||
0.0957414 | + | 0.995406i | \(0.469478\pi\) | |||||||
\(354\) | 9.29416e26 | 1.59836 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.87280e27 | −3.03575 | ||||||||
\(357\) | −1.84266e26 | −0.290020 | ||||||||
\(358\) | −3.67305e25 | −0.0561378 | ||||||||
\(359\) | −1.67492e26 | −0.248601 | −0.124301 | − | 0.992245i | \(-0.539669\pi\) | ||||
−0.124301 | + | 0.992245i | \(0.539669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.38602e26 | 0.194064 | ||||||||
\(362\) | −2.48946e27 | −3.38583 | ||||||||
\(363\) | −4.24422e26 | −0.560761 | ||||||||
\(364\) | 2.46722e26 | 0.316696 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.20514e27 | −1.46045 | ||||||||
\(367\) | −9.83667e26 | −1.15839 | −0.579194 | − | 0.815190i | \(-0.696633\pi\) | ||||
−0.579194 | + | 0.815190i | \(0.696633\pi\) | |||||||
\(368\) | 2.95146e27 | 3.37780 | ||||||||
\(369\) | −3.59863e26 | −0.400276 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.58191e26 | 0.166248 | ||||||||
\(372\) | 7.92389e26 | 0.809539 | ||||||||
\(373\) | −1.00058e26 | −0.0993824 | −0.0496912 | − | 0.998765i | \(-0.515824\pi\) | ||||
−0.0496912 | + | 0.998765i | \(0.515824\pi\) | |||||||
\(374\) | 3.56208e26 | 0.343995 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.37429e26 | 0.673360 | ||||||||
\(377\) | −2.72131e26 | −0.241654 | ||||||||
\(378\) | −2.12734e26 | −0.183727 | ||||||||
\(379\) | 9.23905e25 | 0.0776096 | 0.0388048 | − | 0.999247i | \(-0.487645\pi\) | ||||
0.0388048 | + | 0.999247i | \(0.487645\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.82055e25 | −0.0780591 | ||||||||
\(382\) | 3.80986e27 | 2.94608 | ||||||||
\(383\) | 2.13677e27 | 1.60757 | 0.803786 | − | 0.594919i | \(-0.202816\pi\) | ||||
0.803786 | + | 0.594919i | \(0.202816\pi\) | |||||||
\(384\) | 4.16393e27 | 3.04807 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.08530e26 | 0.421809 | ||||||||
\(387\) | 5.77263e26 | 0.389411 | ||||||||
\(388\) | −5.68572e27 | −3.73295 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | −4.72395e27 | −2.78485 | ||||||||
\(393\) | 3.78305e26 | 0.217130 | ||||||||
\(394\) | −4.06394e27 | −2.27111 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.04614e26 | 0.161417 | ||||||||
\(397\) | −1.78165e27 | −0.919439 | −0.459719 | − | 0.888064i | \(-0.652050\pi\) | ||||
−0.459719 | + | 0.888064i | \(0.652050\pi\) | |||||||
\(398\) | 2.12121e27 | 1.06614 | ||||||||
\(399\) | 6.26483e26 | 0.306686 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.40181e27 | 0.651141 | 0.325570 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325570 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(402\) | 2.64590e27 | 1.19729 | ||||||||
\(403\) | −2.53885e26 | −0.111927 | ||||||||
\(404\) | 8.67511e26 | 0.372624 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.48058e27 | −1.01165 | ||||||||
\(407\) | 4.48903e26 | 0.178407 | ||||||||
\(408\) | 5.61699e27 | 2.17557 | ||||||||
\(409\) | 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 | ||||||||
\(412\) | −1.31582e28 | −4.60021 | ||||||||
\(413\) | −2.01066e27 | −0.685271 | ||||||||
\(414\) | 1.54596e27 | 0.513683 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.47045e27 | −1.09624 | ||||||||
\(417\) | −3.07139e26 | −0.0946034 | ||||||||
\(418\) | −1.21107e27 | −0.363762 | ||||||||
\(419\) | −6.07636e27 | −1.77990 | −0.889952 | − | 0.456055i | \(-0.849262\pi\) | ||||
−0.889952 | + | 0.456055i | \(0.849262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.89993e27 | −0.529389 | −0.264695 | − | 0.964332i | \(-0.585271\pi\) | ||||
−0.264695 | + | 0.964332i | \(0.585271\pi\) | |||||||
\(422\) | −7.53915e27 | −2.04900 | ||||||||
\(423\) | 2.32175e26 | 0.0615520 | ||||||||
\(424\) | −4.82214e27 | −1.24709 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.44321e27 | 1.09369 | ||||||||
\(427\) | 2.60714e27 | 0.626141 | ||||||||
\(428\) | 9.77083e26 | 0.228966 | ||||||||
\(429\) | −9.75999e25 | −0.0223176 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.08572e24 | −0.00176079 | −0.000880395 | − | 1.00000i | \(-0.500280\pi\) | ||||
−0.000880395 | 1.00000i | \(0.500280\pi\) | ||||||||
\(432\) | 3.89789e27 | 0.828420 | ||||||||
\(433\) | 5.60439e27 | 1.16253 | 0.581267 | − | 0.813713i | \(-0.302557\pi\) | ||||
0.581267 | + | 0.813713i | \(0.302557\pi\) | |||||||
\(434\) | −2.31426e27 | −0.468566 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.34713e27 | 0.259897 | ||||||||
\(437\) | −4.55272e27 | −0.857463 | ||||||||
\(438\) | −2.26230e27 | −0.415979 | ||||||||
\(439\) | −8.51110e27 | −1.52795 | −0.763973 | − | 0.645248i | \(-0.776754\pi\) | ||||
−0.763973 | + | 0.645248i | \(0.776754\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.48731e27 | −0.254563 | ||||||||
\(442\) | −2.76896e27 | −0.462789 | ||||||||
\(443\) | 6.63134e27 | 1.08234 | 0.541168 | − | 0.840915i | \(-0.317982\pi\) | ||||
0.541168 | + | 0.840915i | \(0.317982\pi\) | |||||||
\(444\) | 1.08909e28 | 1.73598 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.12956e28 | −1.71749 | ||||||||
\(447\) | −4.41468e27 | −0.655648 | ||||||||
\(448\) | −1.72103e28 | −2.49671 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | 2.54097e28 | 3.35773 | ||||||||
\(453\) | 6.55703e27 | 0.846596 | ||||||||
\(454\) | 6.10577e27 | 0.770289 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.90971e28 | −2.30058 | ||||||||
\(457\) | −4.72949e27 | −0.556793 | −0.278397 | − | 0.960466i | \(-0.589803\pi\) | ||||
−0.278397 | + | 0.960466i | \(0.589803\pi\) | |||||||
\(458\) | 1.04097e28 | 1.19771 | ||||||||
\(459\) | 1.76848e27 | 0.198869 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.92722e27 | 0.529349 | 0.264675 | − | 0.964338i | \(-0.414735\pi\) | ||||
0.264675 | + | 0.964338i | \(0.414735\pi\) | |||||||
\(462\) | −8.89661e26 | −0.0934294 | ||||||||
\(463\) | −1.20207e28 | −1.23404 | −0.617021 | − | 0.786947i | \(-0.711661\pi\) | ||||
−0.617021 | + | 0.786947i | \(0.711661\pi\) | |||||||
\(464\) | 4.54513e28 | 4.56150 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.27379e27 | 0.793693 | ||||||||
\(467\) | −1.09969e28 | −1.03144 | −0.515719 | − | 0.856758i | \(-0.672475\pi\) | ||||
−0.515719 | + | 0.856758i | \(0.672475\pi\) | |||||||
\(468\) | −2.36789e27 | −0.217161 | ||||||||
\(469\) | −5.72402e27 | −0.513317 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.57786e27 | −0.221075 | ||||||||
\(472\) | 6.12910e28 | 5.14051 | ||||||||
\(473\) | 2.41413e27 | 0.198024 | ||||||||
\(474\) | −2.83578e27 | −0.227510 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.86958e28 | −1.43507 | ||||||||
\(477\) | −1.51823e27 | −0.113997 | ||||||||
\(478\) | −1.36576e28 | −1.00318 | ||||||||
\(479\) | −1.32717e28 | −0.953684 | −0.476842 | − | 0.878989i | \(-0.658219\pi\) | ||||
−0.476842 | + | 0.878989i | \(0.658219\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.48951e27 | −0.240017 | ||||||||
\(482\) | 2.23613e28 | 1.50489 | ||||||||
\(483\) | −3.34446e27 | −0.220233 | ||||||||
\(484\) | −4.30624e28 | −2.77473 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.04170e27 | 0.125983 | ||||||||
\(487\) | −2.62576e28 | −1.58563 | −0.792813 | − | 0.609466i | \(-0.791384\pi\) | ||||
−0.792813 | + | 0.609466i | \(0.791384\pi\) | |||||||
\(488\) | −7.94738e28 | −4.69695 | ||||||||
\(489\) | −1.68680e28 | −0.975710 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.54066e28 | −1.40796 | −0.703982 | − | 0.710218i | \(-0.748596\pi\) | ||||
−0.703982 | + | 0.710218i | \(0.748596\pi\) | |||||||
\(492\) | −3.65121e28 | −1.98063 | ||||||||
\(493\) | 2.06213e28 | 1.09502 | ||||||||
\(494\) | 9.41414e27 | 0.489382 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.24039e28 | 2.11275 | ||||||||
\(497\) | −9.61224e27 | −0.468903 | ||||||||
\(498\) | 2.86645e28 | 1.36911 | ||||||||
\(499\) | −1.30048e28 | −0.608204 | −0.304102 | − | 0.952640i | \(-0.598356\pi\) | ||||
−0.304102 | + | 0.952640i | \(0.598356\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.57631e28 | −0.706882 | ||||||||
\(502\) | −5.67449e28 | −2.49194 | ||||||||
\(503\) | −1.34993e27 | −0.0580559 | −0.0290280 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290280 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(504\) | −1.40289e28 | −0.590886 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.46525e27 | 0.261219 | ||||||||
\(507\) | −1.38302e28 | −0.547326 | ||||||||
\(508\) | −9.96406e27 | −0.386249 | ||||||||
\(509\) | −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 | ||||||||
\(512\) | 1.39939e29 | 4.99579 | ||||||||
\(513\) | −6.01263e27 | −0.210296 | ||||||||
\(514\) | −3.79902e28 | −1.30184 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.85698e28 | 1.92687 | ||||||||
\(517\) | 9.70964e26 | 0.0313006 | ||||||||
\(518\) | −3.18083e28 | −1.00479 | ||||||||
\(519\) | 1.34924e28 | 0.417670 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.40378e28 | 1.60658 | 0.803289 | − | 0.595590i | \(-0.203082\pi\) | ||||
0.803289 | + | 0.595590i | \(0.203082\pi\) | |||||||
\(522\) | 2.38072e28 | 0.693695 | ||||||||
\(523\) | −1.54066e28 | −0.439988 | −0.219994 | − | 0.975501i | \(-0.570604\pi\) | ||||
−0.219994 | + | 0.975501i | \(0.570604\pi\) | |||||||
\(524\) | 3.83833e28 | 1.07439 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.65986e28 | 0.446398 | ||||||||
\(527\) | 1.92387e28 | 0.507182 | ||||||||
\(528\) | 1.63011e28 | 0.421270 | ||||||||
\(529\) | −1.51670e28 | −0.384252 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.92971e28 | 0.469895 | ||||||||
\(532\) | 6.35637e28 | 1.51753 | ||||||||
\(533\) | 1.16987e28 | 0.273842 | ||||||||
\(534\) | −5.24953e28 | −1.20486 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.74486e29 | 3.85061 | ||||||||
\(537\) | −7.62623e26 | −0.0165037 | ||||||||
\(538\) | 1.52238e29 | 3.23080 | ||||||||
\(539\) | −6.21997e27 | −0.129451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.54478e28 | −1.51034 | −0.755171 | − | 0.655528i | \(-0.772446\pi\) | ||||
−0.755171 | + | 0.655528i | \(0.772446\pi\) | |||||||
\(542\) | −2.96923e28 | −0.582976 | ||||||||
\(543\) | −5.16878e28 | −0.995382 | ||||||||
\(544\) | 2.62981e29 | 4.96747 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.91571e27 | 0.125694 | ||||||||
\(547\) | −7.90524e28 | −1.40944 | −0.704722 | − | 0.709483i | \(-0.748928\pi\) | ||||
−0.704722 | + | 0.709483i | \(0.748928\pi\) | |||||||
\(548\) | 1.18813e29 | 2.07812 | ||||||||
\(549\) | −2.50219e28 | −0.429349 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.01101e28 | −1.15795 | ||||||||
\(552\) | 1.01950e29 | 1.65206 | ||||||||
\(553\) | 6.13480e27 | 0.0975408 | ||||||||
\(554\) | −8.95531e28 | −1.39710 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.11627e28 | −0.468113 | ||||||||
\(557\) | −1.17729e29 | −1.73541 | −0.867707 | − | 0.497075i | \(-0.834407\pi\) | ||||
−0.867707 | + | 0.497075i | \(0.834407\pi\) | |||||||
\(558\) | 2.22110e28 | 0.321299 | ||||||||
\(559\) | −1.87660e28 | −0.266409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.39583e27 | 0.101129 | ||||||||
\(562\) | −3.29582e28 | −0.442315 | ||||||||
\(563\) | 9.20807e28 | 1.21291 | 0.606457 | − | 0.795116i | \(-0.292590\pi\) | ||||
0.606457 | + | 0.795116i | \(0.292590\pi\) | |||||||
\(564\) | 2.35568e28 | 0.304569 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.36626e29 | 1.70200 | ||||||||
\(567\) | −4.41693e27 | −0.0540130 | ||||||||
\(568\) | 2.93011e29 | 3.51744 | ||||||||
\(569\) | −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 | \(-0.476825\pi\) | ||||
0.0727434 | + | 0.997351i | \(0.476825\pi\) | |||||||
\(572\) | −9.90260e27 | −0.110431 | ||||||||
\(573\) | 7.91029e28 | 0.866102 | ||||||||
\(574\) | 1.06638e29 | 1.14640 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.65175e29 | 1.71201 | ||||||||
\(577\) | −1.49329e29 | −1.51984 | −0.759922 | − | 0.650015i | \(-0.774763\pi\) | ||||
−0.759922 | + | 0.650015i | \(0.774763\pi\) | |||||||
\(578\) | 1.33261e28 | 0.133186 | ||||||||
\(579\) | 1.26347e28 | 0.124005 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.20116e28 | −0.586980 | ||||||||
\(582\) | −1.59373e29 | −1.48158 | ||||||||
\(583\) | −6.34926e27 | −0.0579700 | ||||||||
\(584\) | −1.49189e29 | −1.33783 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.26586e29 | 1.96023 | ||||||||
\(587\) | −2.62975e28 | −0.223468 | −0.111734 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111734 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(588\) | −1.50904e29 | −1.25962 | ||||||||
\(589\) | −6.54093e28 | −0.536326 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.43783e28 | −0.667671 | ||||||||
\(592\) | 5.82817e29 | 4.53059 | ||||||||
\(593\) | −1.92294e29 | −1.46856 | −0.734278 | − | 0.678849i | \(-0.762479\pi\) | ||||
−0.734278 | + | 0.678849i | \(0.762479\pi\) | |||||||
\(594\) | 8.53846e27 | 0.0640651 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.47919e29 | −3.24425 | ||||||||
\(597\) | 4.40421e28 | 0.313428 | ||||||||
\(598\) | −5.02572e28 | −0.351427 | ||||||||
\(599\) | −2.45874e29 | −1.68940 | −0.844699 | − | 0.535242i | \(-0.820220\pi\) | ||||
−0.844699 | + | 0.535242i | \(0.820220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.47252e28 | 0.495776 | 0.247888 | − | 0.968789i | \(-0.420264\pi\) | ||||
0.247888 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(602\) | −1.71060e29 | −1.11528 | ||||||||
\(603\) | 5.49359e28 | 0.351985 | ||||||||
\(604\) | 6.65285e29 | 4.18909 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.43167e28 | 0.147891 | ||||||||
\(607\) | 1.23466e29 | 0.738016 | 0.369008 | − | 0.929426i | \(-0.379698\pi\) | ||||
0.369008 | + | 0.929426i | \(0.379698\pi\) | |||||||
\(608\) | −8.94104e29 | −5.25291 | ||||||||
\(609\) | −5.15035e28 | −0.297410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.54771e27 | −0.0421098 | ||||||||
\(612\) | 1.79432e29 | 0.984034 | ||||||||
\(613\) | 1.59244e29 | 0.858476 | 0.429238 | − | 0.903191i | \(-0.358782\pi\) | ||||
0.429238 | + | 0.903191i | \(0.358782\pi\) | |||||||
\(614\) | −4.30861e29 | −2.28333 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.86694e28 | −0.300479 | ||||||||
\(617\) | −1.23256e29 | −0.620602 | −0.310301 | − | 0.950638i | \(-0.600430\pi\) | ||||
−0.310301 | + | 0.950638i | \(0.600430\pi\) | |||||||
\(618\) | −3.68831e29 | −1.82578 | ||||||||
\(619\) | −5.18990e28 | −0.252585 | −0.126292 | − | 0.991993i | \(-0.540308\pi\) | ||||
−0.126292 | + | 0.991993i | \(0.540308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.20983e28 | 0.151015 | ||||||||
\(622\) | 4.02159e29 | 1.86037 | ||||||||
\(623\) | 1.13566e29 | 0.516564 | ||||||||
\(624\) | −1.26715e29 | −0.566750 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.42086e29 | −0.614497 | ||||||||
\(627\) | −2.51450e28 | −0.106940 | ||||||||
\(628\) | −2.61553e29 | −1.09391 | ||||||||
\(629\) | 2.64425e29 | 1.08760 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.05208e28 | −0.0816366 | −0.0408183 | − | 0.999167i | \(-0.512996\pi\) | ||||
−0.0408183 | + | 0.999167i | \(0.512996\pi\) | |||||||
\(632\) | −1.87008e29 | −0.731694 | ||||||||
\(633\) | −1.56533e29 | −0.602374 | ||||||||
\(634\) | −5.16285e29 | −1.95412 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.54041e29 | −0.564075 | ||||||||
\(637\) | 4.83505e28 | 0.174155 | ||||||||
\(638\) | 9.95625e28 | 0.352759 | ||||||||
\(639\) | 9.22528e28 | 0.321529 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.14342e29 | 1.73477 | 0.867386 | − | 0.497636i | \(-0.165798\pi\) | ||||
0.867386 | + | 0.497636i | \(0.165798\pi\) | |||||||
\(642\) | 2.73880e28 | 0.0908747 | ||||||||
\(643\) | 8.85766e28 | 0.289137 | 0.144569 | − | 0.989495i | \(-0.453821\pi\) | ||||
0.144569 | + | 0.989495i | \(0.453821\pi\) | |||||||
\(644\) | −3.39333e29 | −1.08975 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.13376e29 | −2.21757 | ||||||||
\(647\) | −5.46916e29 | −1.67273 | −0.836364 | − | 0.548174i | \(-0.815323\pi\) | ||||
−0.836364 | + | 0.548174i | \(0.815323\pi\) | |||||||
\(648\) | 1.34642e29 | 0.405174 | ||||||||
\(649\) | 8.07012e28 | 0.238952 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.80503e28 | −0.137751 | ||||||||
\(652\) | −1.71145e30 | −4.82796 | ||||||||
\(653\) | 5.66153e29 | 1.57161 | 0.785806 | − | 0.618473i | \(-0.212248\pi\) | ||||
0.785806 | + | 0.618473i | \(0.212248\pi\) | |||||||
\(654\) | 3.77606e28 | 0.103151 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.95391e30 | −5.16908 | ||||||||
\(657\) | −4.69713e28 | −0.122292 | ||||||||
\(658\) | −6.88003e28 | −0.176286 | ||||||||
\(659\) | −1.48653e29 | −0.374867 | −0.187434 | − | 0.982277i | \(-0.560017\pi\) | ||||
−0.187434 | + | 0.982277i | \(0.560017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.04669e29 | −0.988517 | −0.494259 | − | 0.869315i | \(-0.664560\pi\) | ||||
−0.494259 | + | 0.869315i | \(0.664560\pi\) | |||||||
\(662\) | 4.09792e29 | 0.985268 | ||||||||
\(663\) | −5.74909e28 | −0.136053 | ||||||||
\(664\) | 1.89031e30 | 4.40319 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.05278e29 | 0.688994 | ||||||||
\(667\) | 3.74281e29 | 0.831527 | ||||||||
\(668\) | −1.59935e30 | −3.49776 | ||||||||
\(669\) | −2.34527e29 | −0.504916 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.04642e29 | −0.218334 | ||||||||
\(672\) | −6.56816e29 | −1.34917 | ||||||||
\(673\) | 1.54590e29 | 0.312625 | 0.156313 | − | 0.987708i | \(-0.450039\pi\) | ||||
0.156313 | + | 0.987708i | \(0.450039\pi\) | |||||||
\(674\) | 1.03252e30 | 2.05574 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.40323e30 | −2.70825 | ||||||||
\(677\) | 9.88421e29 | 1.87828 | 0.939142 | − | 0.343530i | \(-0.111623\pi\) | ||||
0.939142 | + | 0.343530i | \(0.111623\pi\) | |||||||
\(678\) | 7.12245e29 | 1.33265 | ||||||||
\(679\) | 3.44781e29 | 0.635200 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.26772e29 | 0.226453 | ||||||||
\(682\) | 9.28870e28 | 0.163388 | ||||||||
\(683\) | 1.41169e29 | 0.244524 | 0.122262 | − | 0.992498i | \(-0.460985\pi\) | ||||
0.122262 | + | 0.992498i | \(0.460985\pi\) | |||||||
\(684\) | −6.10048e29 | −1.04058 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.01784e30 | 1.68375 | ||||||||
\(687\) | 2.16133e29 | 0.352108 | ||||||||
\(688\) | 3.13430e30 | 5.02877 | ||||||||
\(689\) | 4.93555e28 | 0.0779891 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.11585e29 | 1.09070 | 0.545352 | − | 0.838207i | \(-0.316396\pi\) | ||||
0.545352 | + | 0.838207i | \(0.316396\pi\) | |||||||
\(692\) | 1.36896e30 | 2.06669 | ||||||||
\(693\) | −1.84717e28 | −0.0274668 | ||||||||
\(694\) | 2.01817e29 | 0.295585 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.56999e30 | 2.23099 | ||||||||
\(697\) | −8.86490e29 | −1.24088 | ||||||||
\(698\) | −2.00200e30 | −2.76047 | ||||||||
\(699\) | 1.71786e29 | 0.233334 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.80754e29 | −1.16096 | −0.580478 | − | 0.814276i | \(-0.697134\pi\) | ||||
−0.580478 | + | 0.814276i | \(0.697134\pi\) | |||||||
\(702\) | −6.63731e28 | −0.0861891 | ||||||||
\(703\) | −8.99015e29 | −1.15010 | ||||||||
\(704\) | 6.90765e29 | 0.870597 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.07393e29 | 0.376049 | ||||||||
\(707\) | −5.26057e28 | −0.0634058 | ||||||||
\(708\) | 1.95791e30 | 2.32511 | ||||||||
\(709\) | −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 | ||||||||
\(712\) | −3.46185e30 | −3.87496 | ||||||||
\(713\) | 3.49186e29 | 0.385139 | ||||||||
\(714\) | −5.24052e29 | −0.569565 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.73767e28 | −0.0816626 | ||||||||
\(717\) | −2.83568e29 | −0.294921 | ||||||||
\(718\) | −4.76349e29 | −0.488223 | ||||||||
\(719\) | 1.21404e30 | 1.22625 | 0.613124 | − | 0.789987i | \(-0.289913\pi\) | ||||
0.613124 | + | 0.789987i | \(0.289913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.97913e29 | 0.782772 | ||||||||
\(722\) | 3.94185e29 | 0.381118 | ||||||||
\(723\) | 4.64280e29 | 0.442413 | ||||||||
\(724\) | −5.24431e30 | −4.92531 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.20706e30 | −1.10127 | ||||||||
\(727\) | 6.54831e29 | 0.588868 | 0.294434 | − | 0.955672i | \(-0.404869\pi\) | ||||
0.294434 | + | 0.955672i | \(0.404869\pi\) | |||||||
\(728\) | 4.56062e29 | 0.404245 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.42204e30 | 1.20720 | ||||||||
\(732\) | −2.53875e30 | −2.12449 | ||||||||
\(733\) | −2.20665e29 | −0.182029 | −0.0910147 | − | 0.995850i | \(-0.529011\pi\) | ||||
−0.0910147 | + | 0.995850i | \(0.529011\pi\) | |||||||
\(734\) | −2.79755e30 | −2.27493 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.77315e30 | 3.77214 | ||||||||
\(737\) | 2.29743e29 | 0.178992 | ||||||||
\(738\) | −1.02345e30 | −0.786094 | ||||||||
\(739\) | −4.07297e29 | −0.308422 | −0.154211 | − | 0.988038i | \(-0.549283\pi\) | ||||
−0.154211 | + | 0.988038i | \(0.549283\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.95463e29 | 0.143871 | ||||||||
\(742\) | 4.49895e29 | 0.326490 | ||||||||
\(743\) | −3.97218e29 | −0.284214 | −0.142107 | − | 0.989851i | \(-0.545388\pi\) | ||||
−0.142107 | + | 0.989851i | \(0.545388\pi\) | |||||||
\(744\) | 1.46472e30 | 1.03333 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.84565e29 | −0.195175 | ||||||||
\(747\) | 5.95152e29 | 0.402496 | ||||||||
\(748\) | 7.50390e29 | 0.500403 | ||||||||
\(749\) | −5.92500e28 | −0.0389610 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.86890e30 | −1.19500 | −0.597498 | − | 0.801871i | \(-0.703838\pi\) | ||||
−0.597498 | + | 0.801871i | \(0.703838\pi\) | |||||||
\(752\) | 1.26062e30 | 0.794869 | ||||||||
\(753\) | −1.17817e30 | −0.732592 | ||||||||
\(754\) | −7.73941e29 | −0.474579 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.48147e29 | −0.267265 | ||||||||
\(757\) | 2.99103e30 | 1.75919 | 0.879597 | − | 0.475720i | \(-0.157812\pi\) | ||||
0.879597 | + | 0.475720i | \(0.157812\pi\) | |||||||
\(758\) | 2.62759e29 | 0.152416 | ||||||||
\(759\) | 1.34236e29 | 0.0767945 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.51341e30 | 0.842206 | 0.421103 | − | 0.907013i | \(-0.361643\pi\) | ||||
0.421103 | + | 0.907013i | \(0.361643\pi\) | |||||||
\(762\) | −2.79297e29 | −0.153299 | ||||||||
\(763\) | −8.16896e28 | −0.0442241 | ||||||||
\(764\) | 8.02588e30 | 4.28561 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.07697e30 | 3.15707 | ||||||||
\(767\) | −6.27325e29 | −0.321470 | ||||||||
\(768\) | 5.97596e30 | 3.02075 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 1.28193e30 | 0.613598 | ||||||||
\(773\) | 1.69545e30 | 0.800571 | 0.400285 | − | 0.916390i | \(-0.368911\pi\) | ||||
0.400285 | + | 0.916390i | \(0.368911\pi\) | |||||||
\(774\) | 1.64173e30 | 0.764756 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.05100e31 | −4.76490 | ||||||||
\(777\) | −6.60424e29 | −0.295394 | ||||||||
\(778\) | −3.57153e30 | −1.57604 | ||||||||
\(779\) | 3.01396e30 | 1.31218 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.85804e29 | 0.163505 | ||||||||
\(782\) | 3.80834e30 | 1.59245 | ||||||||
\(783\) | 4.94301e29 | 0.203936 | ||||||||
\(784\) | −8.07548e30 | −3.28738 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.07590e30 | 0.426417 | ||||||||
\(787\) | 1.87332e30 | 0.732616 | 0.366308 | − | 0.930494i | \(-0.380622\pi\) | ||||
0.366308 | + | 0.930494i | \(0.380622\pi\) | |||||||
\(788\) | −8.56113e30 | −3.30374 | ||||||||
\(789\) | 3.44632e29 | 0.131234 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.54084e30 | −0.571353 | ||||||||
\(792\) | 5.63075e29 | 0.206040 | ||||||||
\(793\) | 8.13429e29 | 0.293732 | ||||||||
\(794\) | −5.06702e30 | −1.80567 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.46856e30 | 1.55089 | ||||||||
\(797\) | 7.79664e29 | 0.267051 | 0.133526 | − | 0.991045i | \(-0.457370\pi\) | ||||
0.133526 | + | 0.991045i | \(0.457370\pi\) | |||||||
\(798\) | 1.78172e30 | 0.602294 | ||||||||
\(799\) | 5.71944e29 | 0.190815 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.08994e30 | −0.354211 | ||||||||
\(802\) | 3.98676e30 | 1.27876 | ||||||||
\(803\) | −1.96436e29 | −0.0621880 | ||||||||
\(804\) | 5.57386e30 | 1.74168 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.22050e29 | −0.219811 | ||||||||
\(807\) | 3.16088e30 | 0.949807 | ||||||||
\(808\) | 1.60358e30 | 0.475633 | ||||||||
\(809\) | 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 | \(-0.594956\pi\) | ||||
−0.293907 | + | 0.955834i | \(0.594956\pi\) | |||||||
\(812\) | −5.22561e30 | −1.47163 | ||||||||
\(813\) | −6.16490e29 | −0.171386 | ||||||||
\(814\) | 1.27668e30 | 0.350369 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.60212e30 | 2.56815 | ||||||||
\(817\) | −4.83476e30 | −1.27657 | ||||||||
\(818\) | 6.18551e30 | 1.61237 | ||||||||
\(819\) | 1.43589e29 | 0.0369521 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.83846e30 | −0.461160 | −0.230580 | − | 0.973053i | \(-0.574062\pi\) | ||||
−0.230580 | + | 0.973053i | \(0.574062\pi\) | |||||||
\(822\) | 3.33039e30 | 0.824785 | ||||||||
\(823\) | −7.73766e29 | −0.189196 | −0.0945979 | − | 0.995516i | \(-0.530157\pi\) | ||||
−0.0945979 | + | 0.995516i | \(0.530157\pi\) | |||||||
\(824\) | −2.43229e31 | −5.87190 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.71831e30 | −1.34579 | ||||||||
\(827\) | 4.59989e30 | 1.06891 | 0.534453 | − | 0.845198i | \(-0.320518\pi\) | ||||
0.534453 | + | 0.845198i | \(0.320518\pi\) | |||||||
\(828\) | 3.25673e30 | 0.747245 | ||||||||
\(829\) | 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 | ||||||||
\(832\) | −5.36961e30 | −1.17124 | ||||||||
\(833\) | −3.66386e30 | −0.789162 | ||||||||
\(834\) | −8.73504e29 | −0.185790 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.55124e30 | −0.529158 | ||||||||
\(837\) | 4.61159e29 | 0.0944569 | ||||||||
\(838\) | −1.72812e31 | −3.49551 | ||||||||
\(839\) | 4.84033e30 | 0.966884 | 0.483442 | − | 0.875376i | \(-0.339386\pi\) | ||||
0.483442 | + | 0.875376i | \(0.339386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.30944e29 | 0.122923 | ||||||||
\(842\) | −5.40340e30 | −1.03966 | ||||||||
\(843\) | −6.84300e29 | −0.130034 | ||||||||
\(844\) | −1.58820e31 | −2.98064 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.60306e29 | 0.120881 | ||||||||
\(847\) | 2.61129e30 | 0.472149 | ||||||||
\(848\) | −8.24334e30 | −1.47213 | ||||||||
\(849\) | 2.83671e30 | 0.500362 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.79937e30 | 0.825893 | ||||||||
\(852\) | 9.36009e30 | 1.59098 | ||||||||
\(853\) | −2.96903e30 | −0.498483 | −0.249242 | − | 0.968441i | \(-0.580181\pi\) | ||||
−0.249242 | + | 0.968441i | \(0.580181\pi\) | |||||||
\(854\) | 7.41472e30 | 1.22967 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.80612e30 | 0.292263 | ||||||||
\(857\) | 3.70009e30 | 0.591444 | 0.295722 | − | 0.955274i | \(-0.404440\pi\) | ||||
0.295722 | + | 0.955274i | \(0.404440\pi\) | |||||||
\(858\) | −2.77574e29 | −0.0438291 | ||||||||
\(859\) | 7.75385e29 | 0.120945 | 0.0604726 | − | 0.998170i | \(-0.480739\pi\) | ||||
0.0604726 | + | 0.998170i | \(0.480739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.21408e30 | 0.337024 | ||||||||
\(862\) | −2.29958e28 | −0.00345798 | ||||||||
\(863\) | 1.29544e31 | 1.92443 | 0.962217 | − | 0.272283i | \(-0.0877786\pi\) | ||||
0.962217 | + | 0.272283i | \(0.0877786\pi\) | |||||||
\(864\) | 6.30375e30 | 0.925134 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.59389e31 | 2.28307 | ||||||||
\(867\) | 2.76685e29 | 0.0391548 | ||||||||
\(868\) | −4.87524e30 | −0.681615 | ||||||||
\(869\) | −2.46231e29 | −0.0340122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.78589e30 | −0.240805 | ||||||||
\(872\) | 2.49015e30 | 0.331744 | ||||||||
\(873\) | −3.30901e30 | −0.435560 | ||||||||
\(874\) | −1.29479e31 | −1.68395 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.76577e30 | −0.605118 | ||||||||
\(877\) | 1.57355e31 | 1.97417 | 0.987083 | − | 0.160207i | \(-0.0512162\pi\) | ||||
0.987083 | + | 0.160207i | \(0.0512162\pi\) | |||||||
\(878\) | −2.42056e31 | −3.00070 | ||||||||
\(879\) | 4.70452e30 | 0.576278 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.47526e31 | −1.76450 | −0.882252 | − | 0.470778i | \(-0.843973\pi\) | ||||
−0.882252 | + | 0.470778i | \(0.843973\pi\) | |||||||
\(882\) | −4.22991e30 | −0.499932 | ||||||||
\(883\) | 5.64453e30 | 0.659235 | 0.329617 | − | 0.944115i | \(-0.393080\pi\) | ||||
0.329617 | + | 0.944115i | \(0.393080\pi\) | |||||||
\(884\) | −5.83310e30 | −0.673210 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.88595e31 | 2.12558 | ||||||||
\(887\) | −5.89300e30 | −0.656354 | −0.328177 | − | 0.944616i | \(-0.606434\pi\) | ||||
−0.328177 | + | 0.944616i | \(0.606434\pi\) | |||||||
\(888\) | 2.01318e31 | 2.21588 | ||||||||
\(889\) | 6.04218e29 | 0.0657242 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.77281e29 | 0.0188342 | ||||||||
\(892\) | −2.37954e31 | −2.49840 | ||||||||
\(893\) | −1.94454e30 | −0.201780 | ||||||||
\(894\) | −1.25554e31 | −1.28761 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.56189e31 | −2.56641 | ||||||||
\(897\) | −1.04347e30 | −0.103314 | ||||||||
\(898\) | 3.70840e31 | 3.62898 | ||||||||
\(899\) | 5.37734e30 | 0.520104 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.74002e30 | −0.353397 | ||||||||
\(902\) | −4.28009e30 | −0.399746 | ||||||||
\(903\) | −3.55166e30 | −0.327876 | ||||||||
\(904\) | 4.69695e31 | 4.28596 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.86482e31 | 1.66261 | ||||||||
\(907\) | −8.32782e30 | −0.733931 | −0.366965 | − | 0.930235i | \(-0.619603\pi\) | ||||
−0.366965 | + | 0.930235i | \(0.619603\pi\) | |||||||
\(908\) | 1.28624e31 | 1.12053 | ||||||||
\(909\) | 5.04879e29 | 0.0434777 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.08086e31 | 0.909548 | 0.454774 | − | 0.890607i | \(-0.349720\pi\) | ||||
0.454774 | + | 0.890607i | \(0.349720\pi\) | |||||||
\(912\) | −3.26461e31 | −2.71572 | ||||||||
\(913\) | 2.48894e30 | 0.204678 | ||||||||
\(914\) | −1.34507e31 | −1.09347 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.19291e31 | 1.74229 | ||||||||
\(917\) | −2.32755e30 | −0.182819 | ||||||||
\(918\) | 5.02955e30 | 0.390554 | ||||||||
\(919\) | 6.55205e30 | 0.502996 | 0.251498 | − | 0.967858i | \(-0.419077\pi\) | ||||
0.251498 | + | 0.967858i | \(0.419077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.94582e30 | −0.671265 | ||||||||
\(922\) | 1.40130e31 | 1.03958 | ||||||||
\(923\) | −2.99902e30 | −0.219969 | ||||||||
\(924\) | −1.87416e30 | −0.135910 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.41869e31 | −2.42351 | ||||||||
\(927\) | −7.65791e30 | −0.536752 | ||||||||
\(928\) | 7.35047e31 | 5.09403 | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 1.74296e31 | 1.15457 | ||||||||
\(933\) | 8.34989e30 | 0.546919 | ||||||||
\(934\) | −3.12752e31 | −2.02562 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.37702e30 | −0.277193 | ||||||||
\(937\) | 2.09831e31 | 1.31402 | 0.657012 | − | 0.753880i | \(-0.271820\pi\) | ||||
0.657012 | + | 0.753880i | \(0.271820\pi\) | |||||||
\(938\) | −1.62791e31 | −1.00809 | ||||||||
\(939\) | −2.95007e30 | −0.180653 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.20967e31 | 1.32323 | 0.661617 | − | 0.749842i | \(-0.269870\pi\) | ||||
0.661617 | + | 0.749842i | \(0.269870\pi\) | |||||||
\(942\) | −7.33143e30 | −0.434165 | ||||||||
\(943\) | −1.60900e31 | −0.942286 | ||||||||
\(944\) | 1.04776e32 | 6.06812 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.86578e30 | 0.388896 | ||||||||
\(947\) | 2.59604e31 | 1.45424 | 0.727121 | − | 0.686509i | \(-0.240858\pi\) | ||||
0.727121 | + | 0.686509i | \(0.240858\pi\) | |||||||
\(948\) | −5.97386e30 | −0.330954 | ||||||||
\(949\) | 1.52698e30 | 0.0836637 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.07194e31 | −0.574483 | ||||||||
\(952\) | −3.45590e31 | −1.83178 | ||||||||
\(953\) | 2.94729e31 | 1.54507 | 0.772535 | − | 0.634973i | \(-0.218989\pi\) | ||||
0.772535 | + | 0.634973i | \(0.218989\pi\) | |||||||
\(954\) | −4.31783e30 | −0.223876 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.87711e31 | −1.45931 | ||||||||
\(957\) | 2.06718e30 | 0.103706 | ||||||||
\(958\) | −3.77448e31 | −1.87292 | ||||||||
\(959\) | −7.20482e30 | −0.353612 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.58087e31 | −0.759103 | ||||||||
\(962\) | −9.92417e30 | −0.471364 | ||||||||
\(963\) | 5.68648e29 | 0.0267158 | ||||||||
\(964\) | 4.71064e31 | 2.18913 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.51166e30 | −0.432510 | ||||||||
\(967\) | −6.98077e30 | −0.313997 | −0.156998 | − | 0.987599i | \(-0.550182\pi\) | ||||
−0.156998 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(968\) | −7.96002e31 | −3.54179 | ||||||||
\(969\) | −1.48116e31 | −0.651931 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.30234e30 | −0.0560946 | −0.0280473 | − | 0.999607i | \(-0.508929\pi\) | ||||
−0.0280473 | + | 0.999607i | \(0.508929\pi\) | |||||||
\(972\) | 4.30106e30 | 0.183265 | ||||||||
\(973\) | 1.88970e30 | 0.0796541 | ||||||||
\(974\) | −7.46765e31 | −3.11398 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.35859e32 | −5.54452 | ||||||||
\(977\) | −3.06599e31 | −1.23788 | −0.618939 | − | 0.785439i | \(-0.712437\pi\) | ||||
−0.618939 | + | 0.785439i | \(0.712437\pi\) | |||||||
\(978\) | −4.79726e31 | −1.91618 | ||||||||
\(979\) | −4.55817e30 | −0.180124 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.84011e29 | 0.0303248 | ||||||||
\(982\) | −7.22564e31 | −2.76507 | ||||||||
\(983\) | −8.31325e30 | −0.314745 | −0.157373 | − | 0.987539i | \(-0.550302\pi\) | ||||
−0.157373 | + | 0.987539i | \(0.550302\pi\) | |||||||
\(984\) | −6.74921e31 | −2.52816 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.86470e31 | 2.15049 | ||||||||
\(987\) | −1.42848e30 | −0.0518255 | ||||||||
\(988\) | 1.98319e31 | 0.711895 | ||||||||
\(989\) | 2.58102e31 | 0.916708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.32568e31 | −0.460962 | −0.230481 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230481 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(992\) | 6.85764e31 | 2.35940 | ||||||||
\(993\) | 8.50837e30 | 0.289654 | ||||||||
\(994\) | −2.73372e31 | −0.920868 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.03849e31 | 1.99161 | ||||||||
\(997\) | −3.42048e31 | −1.11632 | −0.558159 | − | 0.829734i | \(-0.688492\pi\) | ||||
−0.558159 | + | 0.829734i | \(0.688492\pi\) | |||||||
\(998\) | −3.69857e31 | −1.19444 | ||||||||
\(999\) | 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 | 75.22.a.c.1.1 | 1 | ||
5.2 | odd | 4 | 75.22.b.a.49.2 | 2 | |||
5.3 | odd | 4 | 75.22.b.a.49.1 | 2 | |||
5.4 | even | 2 | 3.22.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 9.22.a.d.1.1 | 1 | |||
20.19 | odd | 2 | 48.22.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.22.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
9.22.a.d.1.1 | 1 | 15.14 | odd | 2 | |||
48.22.a.e.1.1 | 1 | 20.19 | odd | 2 | |||
75.22.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
75.22.b.a.49.1 | 2 | 5.3 | odd | 4 | |||
75.22.b.a.49.2 | 2 | 5.2 | odd | 4 |