Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,24,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(33.5204037345\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{219241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 54810 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(234.616\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2048.00 | −0.707107 | ||||||||
\(3\) | −248056. | −0.808455 | −0.404227 | − | 0.914659i | \(-0.632460\pi\) | ||||
−0.404227 | + | 0.914659i | \(0.632460\pi\) | |||||||
\(4\) | 4.19430e6 | 0.500000 | ||||||||
\(5\) | 4.88281e7 | 0.447214 | ||||||||
\(6\) | 5.08019e8 | 0.571664 | ||||||||
\(7\) | −5.53518e9 | −1.05805 | −0.529023 | − | 0.848607i | \(-0.677441\pi\) | ||||
−0.529023 | + | 0.848607i | \(0.677441\pi\) | |||||||
\(8\) | −8.58993e9 | −0.353553 | ||||||||
\(9\) | −3.26113e10 | −0.346401 | ||||||||
\(10\) | −1.00000e11 | −0.316228 | ||||||||
\(11\) | 1.14906e12 | 1.21431 | 0.607153 | − | 0.794585i | \(-0.292311\pi\) | ||||
0.607153 | + | 0.794585i | \(0.292311\pi\) | |||||||
\(12\) | −1.04042e12 | −0.404227 | ||||||||
\(13\) | 5.00457e12 | 0.774495 | 0.387247 | − | 0.921976i | \(-0.373426\pi\) | ||||
0.387247 | + | 0.921976i | \(0.373426\pi\) | |||||||
\(14\) | 1.13361e13 | 0.748152 | ||||||||
\(15\) | −1.21121e13 | −0.361552 | ||||||||
\(16\) | 1.75922e13 | 0.250000 | ||||||||
\(17\) | 2.66925e14 | 1.88897 | 0.944487 | − | 0.328549i | \(-0.106560\pi\) | ||||
0.944487 | + | 0.328549i | \(0.106560\pi\) | |||||||
\(18\) | 6.67879e13 | 0.244943 | ||||||||
\(19\) | −8.29918e14 | −1.63444 | −0.817219 | − | 0.576327i | \(-0.804486\pi\) | ||||
−0.817219 | + | 0.576327i | \(0.804486\pi\) | |||||||
\(20\) | 2.04800e14 | 0.223607 | ||||||||
\(21\) | 1.37304e15 | 0.855382 | ||||||||
\(22\) | −2.35328e15 | −0.858644 | ||||||||
\(23\) | 4.09173e15 | 0.895441 | 0.447721 | − | 0.894173i | \(-0.352236\pi\) | ||||
0.447721 | + | 0.894173i | \(0.352236\pi\) | |||||||
\(24\) | 2.13079e15 | 0.285832 | ||||||||
\(25\) | 2.38419e15 | 0.200000 | ||||||||
\(26\) | −1.02494e16 | −0.547650 | ||||||||
\(27\) | 3.14422e16 | 1.08850 | ||||||||
\(28\) | −2.32162e16 | −0.529023 | ||||||||
\(29\) | −7.61938e16 | −1.15969 | −0.579846 | − | 0.814726i | \(-0.696887\pi\) | ||||
−0.579846 | + | 0.814726i | \(0.696887\pi\) | |||||||
\(30\) | 2.48056e16 | 0.255656 | ||||||||
\(31\) | −9.68453e16 | −0.684572 | −0.342286 | − | 0.939596i | \(-0.611201\pi\) | ||||
−0.342286 | + | 0.939596i | \(0.611201\pi\) | |||||||
\(32\) | −3.60288e16 | −0.176777 | ||||||||
\(33\) | −2.85032e17 | −0.981712 | ||||||||
\(34\) | −5.46662e17 | −1.33571 | ||||||||
\(35\) | −2.70273e17 | −0.473173 | ||||||||
\(36\) | −1.36782e17 | −0.173201 | ||||||||
\(37\) | 4.73319e16 | 0.0437355 | 0.0218678 | − | 0.999761i | \(-0.493039\pi\) | ||||
0.0218678 | + | 0.999761i | \(0.493039\pi\) | |||||||
\(38\) | 1.69967e18 | 1.15572 | ||||||||
\(39\) | −1.24142e18 | −0.626144 | ||||||||
\(40\) | −4.19430e17 | −0.158114 | ||||||||
\(41\) | −2.15162e18 | −0.610592 | −0.305296 | − | 0.952257i | \(-0.598755\pi\) | ||||
−0.305296 | + | 0.952257i | \(0.598755\pi\) | |||||||
\(42\) | −2.81198e18 | −0.604847 | ||||||||
\(43\) | −7.08076e18 | −1.16196 | −0.580982 | − | 0.813916i | \(-0.697331\pi\) | ||||
−0.580982 | + | 0.813916i | \(0.697331\pi\) | |||||||
\(44\) | 4.81952e18 | 0.607153 | ||||||||
\(45\) | −1.59235e18 | −0.154915 | ||||||||
\(46\) | −8.37987e18 | −0.633173 | ||||||||
\(47\) | −1.89843e19 | −1.12013 | −0.560065 | − | 0.828448i | \(-0.689224\pi\) | ||||
−0.560065 | + | 0.828448i | \(0.689224\pi\) | |||||||
\(48\) | −4.36385e18 | −0.202114 | ||||||||
\(49\) | 3.26951e18 | 0.119461 | ||||||||
\(50\) | −4.88281e18 | −0.141421 | ||||||||
\(51\) | −6.62123e19 | −1.52715 | ||||||||
\(52\) | 2.09907e19 | 0.387247 | ||||||||
\(53\) | 3.73319e19 | 0.553233 | 0.276616 | − | 0.960980i | \(-0.410787\pi\) | ||||
0.276616 | + | 0.960980i | \(0.410787\pi\) | |||||||
\(54\) | −6.43937e19 | −0.769689 | ||||||||
\(55\) | 5.61066e19 | 0.543054 | ||||||||
\(56\) | 4.75469e19 | 0.374076 | ||||||||
\(57\) | 2.05866e20 | 1.32137 | ||||||||
\(58\) | 1.56045e20 | 0.820026 | ||||||||
\(59\) | 2.48317e20 | 1.07203 | 0.536016 | − | 0.844208i | \(-0.319929\pi\) | ||||
0.536016 | + | 0.844208i | \(0.319929\pi\) | |||||||
\(60\) | −5.08019e19 | −0.180776 | ||||||||
\(61\) | −2.46263e20 | −0.724613 | −0.362306 | − | 0.932059i | \(-0.618011\pi\) | ||||
−0.362306 | + | 0.932059i | \(0.618011\pi\) | |||||||
\(62\) | 1.98339e20 | 0.484065 | ||||||||
\(63\) | 1.80510e20 | 0.366508 | ||||||||
\(64\) | 7.37870e19 | 0.125000 | ||||||||
\(65\) | 2.44364e20 | 0.346365 | ||||||||
\(66\) | 5.83747e20 | 0.694175 | ||||||||
\(67\) | −8.02335e20 | −0.802594 | −0.401297 | − | 0.915948i | \(-0.631440\pi\) | ||||
−0.401297 | + | 0.915948i | \(0.631440\pi\) | |||||||
\(68\) | 1.11956e21 | 0.944487 | ||||||||
\(69\) | −1.01498e21 | −0.723924 | ||||||||
\(70\) | 5.53518e20 | 0.334584 | ||||||||
\(71\) | −9.67342e20 | −0.496717 | −0.248358 | − | 0.968668i | \(-0.579891\pi\) | ||||
−0.248358 | + | 0.968668i | \(0.579891\pi\) | |||||||
\(72\) | 2.80129e20 | 0.122471 | ||||||||
\(73\) | 1.76339e21 | 0.657864 | 0.328932 | − | 0.944354i | \(-0.393311\pi\) | ||||
0.328932 | + | 0.944354i | \(0.393311\pi\) | |||||||
\(74\) | −9.69358e19 | −0.0309257 | ||||||||
\(75\) | −5.91412e20 | −0.161691 | ||||||||
\(76\) | −3.48093e21 | −0.817219 | ||||||||
\(77\) | −6.36028e21 | −1.28479 | ||||||||
\(78\) | 2.54242e21 | 0.442751 | ||||||||
\(79\) | −6.00291e21 | −0.902921 | −0.451461 | − | 0.892291i | \(-0.649097\pi\) | ||||
−0.451461 | + | 0.892291i | \(0.649097\pi\) | |||||||
\(80\) | 8.58993e20 | 0.111803 | ||||||||
\(81\) | −4.72931e21 | −0.533605 | ||||||||
\(82\) | 4.40652e21 | 0.431754 | ||||||||
\(83\) | −1.90063e22 | −1.61994 | −0.809969 | − | 0.586472i | \(-0.800516\pi\) | ||||
−0.809969 | + | 0.586472i | \(0.800516\pi\) | |||||||
\(84\) | 5.75893e21 | 0.427691 | ||||||||
\(85\) | 1.30334e22 | 0.844775 | ||||||||
\(86\) | 1.45014e22 | 0.821633 | ||||||||
\(87\) | 1.89003e22 | 0.937558 | ||||||||
\(88\) | −9.87039e21 | −0.429322 | ||||||||
\(89\) | −4.51150e22 | −1.72320 | −0.861601 | − | 0.507587i | \(-0.830538\pi\) | ||||
−0.861601 | + | 0.507587i | \(0.830538\pi\) | |||||||
\(90\) | 3.26113e21 | 0.109542 | ||||||||
\(91\) | −2.77012e22 | −0.819451 | ||||||||
\(92\) | 1.71620e22 | 0.447721 | ||||||||
\(93\) | 2.40231e22 | 0.553445 | ||||||||
\(94\) | 3.88798e22 | 0.792052 | ||||||||
\(95\) | −4.05233e22 | −0.730943 | ||||||||
\(96\) | 8.93717e21 | 0.142916 | ||||||||
\(97\) | 1.75770e22 | 0.249499 | 0.124750 | − | 0.992188i | \(-0.460187\pi\) | ||||
0.124750 | + | 0.992188i | \(0.460187\pi\) | |||||||
\(98\) | −6.69595e21 | −0.0844720 | ||||||||
\(99\) | −3.74725e22 | −0.420637 | ||||||||
\(100\) | 1.00000e22 | 0.100000 | ||||||||
\(101\) | 1.72636e23 | 1.53970 | 0.769850 | − | 0.638225i | \(-0.220331\pi\) | ||||
0.769850 | + | 0.638225i | \(0.220331\pi\) | |||||||
\(102\) | 1.35603e23 | 1.07986 | ||||||||
\(103\) | −7.39196e22 | −0.526176 | −0.263088 | − | 0.964772i | \(-0.584741\pi\) | ||||
−0.263088 | + | 0.964772i | \(0.584741\pi\) | |||||||
\(104\) | −4.29890e22 | −0.273825 | ||||||||
\(105\) | 6.70428e22 | 0.382539 | ||||||||
\(106\) | −7.64558e22 | −0.391195 | ||||||||
\(107\) | 3.64152e23 | 1.67251 | 0.836255 | − | 0.548340i | \(-0.184740\pi\) | ||||
0.836255 | + | 0.548340i | \(0.184740\pi\) | |||||||
\(108\) | 1.31878e23 | 0.544252 | ||||||||
\(109\) | 2.32344e23 | 0.862434 | 0.431217 | − | 0.902248i | \(-0.358084\pi\) | ||||
0.431217 | + | 0.902248i | \(0.358084\pi\) | |||||||
\(110\) | −1.14906e23 | −0.383997 | ||||||||
\(111\) | −1.17410e22 | −0.0353582 | ||||||||
\(112\) | −9.73760e22 | −0.264512 | ||||||||
\(113\) | −6.52015e23 | −1.59902 | −0.799512 | − | 0.600650i | \(-0.794909\pi\) | ||||
−0.799512 | + | 0.600650i | \(0.794909\pi\) | |||||||
\(114\) | −4.21614e23 | −0.934349 | ||||||||
\(115\) | 1.99792e23 | 0.400454 | ||||||||
\(116\) | −3.19580e23 | −0.579846 | ||||||||
\(117\) | −1.63206e23 | −0.268286 | ||||||||
\(118\) | −5.08552e23 | −0.758041 | ||||||||
\(119\) | −1.47748e24 | −1.99862 | ||||||||
\(120\) | 1.04042e23 | 0.127828 | ||||||||
\(121\) | 4.24918e23 | 0.474541 | ||||||||
\(122\) | 5.04347e23 | 0.512379 | ||||||||
\(123\) | 5.33723e23 | 0.493636 | ||||||||
\(124\) | −4.06199e23 | −0.342286 | ||||||||
\(125\) | 1.16415e23 | 0.0894427 | ||||||||
\(126\) | −3.69683e23 | −0.259160 | ||||||||
\(127\) | −8.69127e23 | −0.556340 | −0.278170 | − | 0.960532i | \(-0.589728\pi\) | ||||
−0.278170 | + | 0.960532i | \(0.589728\pi\) | |||||||
\(128\) | −1.51116e23 | −0.0883883 | ||||||||
\(129\) | 1.75643e24 | 0.939396 | ||||||||
\(130\) | −5.00457e23 | −0.244917 | ||||||||
\(131\) | 1.54721e23 | 0.0693311 | 0.0346656 | − | 0.999399i | \(-0.488963\pi\) | ||||
0.0346656 | + | 0.999399i | \(0.488963\pi\) | |||||||
\(132\) | −1.19551e24 | −0.490856 | ||||||||
\(133\) | 4.59375e24 | 1.72931 | ||||||||
\(134\) | 1.64318e24 | 0.567519 | ||||||||
\(135\) | 1.53527e24 | 0.486794 | ||||||||
\(136\) | −2.29286e24 | −0.667853 | ||||||||
\(137\) | −5.27775e23 | −0.141307 | −0.0706533 | − | 0.997501i | \(-0.522508\pi\) | ||||
−0.0706533 | + | 0.997501i | \(0.522508\pi\) | |||||||
\(138\) | 2.07868e24 | 0.511891 | ||||||||
\(139\) | −3.13469e24 | −0.710435 | −0.355217 | − | 0.934784i | \(-0.615593\pi\) | ||||
−0.355217 | + | 0.934784i | \(0.615593\pi\) | |||||||
\(140\) | −1.13361e24 | −0.236586 | ||||||||
\(141\) | 4.70917e24 | 0.905575 | ||||||||
\(142\) | 1.98112e24 | 0.351232 | ||||||||
\(143\) | 5.75057e24 | 0.940474 | ||||||||
\(144\) | −5.73704e23 | −0.0866003 | ||||||||
\(145\) | −3.72040e24 | −0.518630 | ||||||||
\(146\) | −3.61143e24 | −0.465180 | ||||||||
\(147\) | −8.11022e23 | −0.0965791 | ||||||||
\(148\) | 1.98525e23 | 0.0218678 | ||||||||
\(149\) | −2.68240e24 | −0.273453 | −0.136726 | − | 0.990609i | \(-0.543658\pi\) | ||||
−0.136726 | + | 0.990609i | \(0.543658\pi\) | |||||||
\(150\) | 1.21121e24 | 0.114333 | ||||||||
\(151\) | 9.87063e24 | 0.863197 | 0.431599 | − | 0.902066i | \(-0.357950\pi\) | ||||
0.431599 | + | 0.902066i | \(0.357950\pi\) | |||||||
\(152\) | 7.12894e24 | 0.577861 | ||||||||
\(153\) | −8.70476e24 | −0.654343 | ||||||||
\(154\) | 1.30259e25 | 0.908485 | ||||||||
\(155\) | −4.72877e24 | −0.306150 | ||||||||
\(156\) | −5.20687e24 | −0.313072 | ||||||||
\(157\) | −2.58352e25 | −1.44333 | −0.721666 | − | 0.692242i | \(-0.756623\pi\) | ||||
−0.721666 | + | 0.692242i | \(0.756623\pi\) | |||||||
\(158\) | 1.22940e25 | 0.638462 | ||||||||
\(159\) | −9.26042e24 | −0.447264 | ||||||||
\(160\) | −1.75922e24 | −0.0790569 | ||||||||
\(161\) | −2.26485e25 | −0.947418 | ||||||||
\(162\) | 9.68563e24 | 0.377316 | ||||||||
\(163\) | −3.31455e24 | −0.120301 | −0.0601503 | − | 0.998189i | \(-0.519158\pi\) | ||||
−0.0601503 | + | 0.998189i | \(0.519158\pi\) | |||||||
\(164\) | −9.02455e24 | −0.305296 | ||||||||
\(165\) | −1.39176e25 | −0.439035 | ||||||||
\(166\) | 3.89248e25 | 1.14547 | ||||||||
\(167\) | −9.23000e24 | −0.253491 | −0.126745 | − | 0.991935i | \(-0.540453\pi\) | ||||
−0.126745 | + | 0.991935i | \(0.540453\pi\) | |||||||
\(168\) | −1.17943e25 | −0.302423 | ||||||||
\(169\) | −1.67082e25 | −0.400158 | ||||||||
\(170\) | −2.66925e25 | −0.597346 | ||||||||
\(171\) | 2.70647e25 | 0.566171 | ||||||||
\(172\) | −2.96989e25 | −0.580982 | ||||||||
\(173\) | 2.50481e25 | 0.458400 | 0.229200 | − | 0.973379i | \(-0.426389\pi\) | ||||
0.229200 | + | 0.973379i | \(0.426389\pi\) | |||||||
\(174\) | −3.87079e25 | −0.662954 | ||||||||
\(175\) | −1.31969e25 | −0.211609 | ||||||||
\(176\) | 2.02145e25 | 0.303577 | ||||||||
\(177\) | −6.15965e25 | −0.866689 | ||||||||
\(178\) | 9.23955e25 | 1.21849 | ||||||||
\(179\) | −7.76500e25 | −0.960133 | −0.480067 | − | 0.877232i | \(-0.659388\pi\) | ||||
−0.480067 | + | 0.877232i | \(0.659388\pi\) | |||||||
\(180\) | −6.67879e24 | −0.0774576 | ||||||||
\(181\) | 1.79026e26 | 1.94810 | 0.974050 | − | 0.226331i | \(-0.0726731\pi\) | ||||
0.974050 | + | 0.226331i | \(0.0726731\pi\) | |||||||
\(182\) | 5.67321e25 | 0.579439 | ||||||||
\(183\) | 6.10871e25 | 0.585817 | ||||||||
\(184\) | −3.51477e25 | −0.316586 | ||||||||
\(185\) | 2.31113e24 | 0.0195591 | ||||||||
\(186\) | −4.91993e25 | −0.391345 | ||||||||
\(187\) | 3.06713e26 | 2.29379 | ||||||||
\(188\) | −7.96258e25 | −0.560065 | ||||||||
\(189\) | −1.74039e26 | −1.15169 | ||||||||
\(190\) | 8.29918e25 | 0.516855 | ||||||||
\(191\) | −1.87629e26 | −1.10006 | −0.550031 | − | 0.835144i | \(-0.685384\pi\) | ||||
−0.550031 | + | 0.835144i | \(0.685384\pi\) | |||||||
\(192\) | −1.83033e25 | −0.101057 | ||||||||
\(193\) | 3.19948e26 | 1.66407 | 0.832033 | − | 0.554726i | \(-0.187177\pi\) | ||||
0.832033 | + | 0.554726i | \(0.187177\pi\) | |||||||
\(194\) | −3.59977e25 | −0.176423 | ||||||||
\(195\) | −6.06160e25 | −0.280020 | ||||||||
\(196\) | 1.37133e25 | 0.0597307 | ||||||||
\(197\) | 2.32413e26 | 0.954770 | 0.477385 | − | 0.878694i | \(-0.341585\pi\) | ||||
0.477385 | + | 0.878694i | \(0.341585\pi\) | |||||||
\(198\) | 7.67436e25 | 0.297435 | ||||||||
\(199\) | −1.44151e26 | −0.527237 | −0.263619 | − | 0.964627i | \(-0.584916\pi\) | ||||
−0.263619 | + | 0.964627i | \(0.584916\pi\) | |||||||
\(200\) | −2.04800e25 | −0.0707107 | ||||||||
\(201\) | 1.99024e26 | 0.648861 | ||||||||
\(202\) | −3.53559e26 | −1.08873 | ||||||||
\(203\) | 4.21747e26 | 1.22701 | ||||||||
\(204\) | −2.77714e26 | −0.763575 | ||||||||
\(205\) | −1.05060e26 | −0.273065 | ||||||||
\(206\) | 1.51387e26 | 0.372063 | ||||||||
\(207\) | −1.33437e26 | −0.310182 | ||||||||
\(208\) | 8.80414e25 | 0.193624 | ||||||||
\(209\) | −9.53629e26 | −1.98471 | ||||||||
\(210\) | −1.37304e26 | −0.270496 | ||||||||
\(211\) | −9.00904e26 | −1.68047 | −0.840234 | − | 0.542223i | \(-0.817583\pi\) | ||||
−0.840234 | + | 0.542223i | \(0.817583\pi\) | |||||||
\(212\) | 1.56581e26 | 0.276616 | ||||||||
\(213\) | 2.39955e26 | 0.401573 | ||||||||
\(214\) | −7.45783e26 | −1.18264 | ||||||||
\(215\) | −3.45740e26 | −0.519646 | ||||||||
\(216\) | −2.70087e26 | −0.384844 | ||||||||
\(217\) | 5.36056e26 | 0.724308 | ||||||||
\(218\) | −4.75840e26 | −0.609833 | ||||||||
\(219\) | −4.37420e26 | −0.531853 | ||||||||
\(220\) | 2.35328e26 | 0.271527 | ||||||||
\(221\) | 1.33584e27 | 1.46300 | ||||||||
\(222\) | 2.40455e25 | 0.0250020 | ||||||||
\(223\) | 1.12234e27 | 1.10820 | 0.554100 | − | 0.832450i | \(-0.313063\pi\) | ||||
0.554100 | + | 0.832450i | \(0.313063\pi\) | |||||||
\(224\) | 1.99426e26 | 0.187038 | ||||||||
\(225\) | −7.77514e25 | −0.0692802 | ||||||||
\(226\) | 1.33533e27 | 1.13068 | ||||||||
\(227\) | −1.38912e26 | −0.111800 | −0.0558999 | − | 0.998436i | \(-0.517803\pi\) | ||||
−0.0558999 | + | 0.998436i | \(0.517803\pi\) | |||||||
\(228\) | 8.63466e26 | 0.660685 | ||||||||
\(229\) | −1.03506e27 | −0.753105 | −0.376553 | − | 0.926395i | \(-0.622891\pi\) | ||||
−0.376553 | + | 0.926395i | \(0.622891\pi\) | |||||||
\(230\) | −4.09173e26 | −0.283163 | ||||||||
\(231\) | 1.57771e27 | 1.03870 | ||||||||
\(232\) | 6.54500e26 | 0.410013 | ||||||||
\(233\) | −1.03552e27 | −0.617398 | −0.308699 | − | 0.951160i | \(-0.599894\pi\) | ||||
−0.308699 | + | 0.951160i | \(0.599894\pi\) | |||||||
\(234\) | 3.34245e26 | 0.189707 | ||||||||
\(235\) | −9.26967e26 | −0.500938 | ||||||||
\(236\) | 1.04151e27 | 0.536016 | ||||||||
\(237\) | 1.48906e27 | 0.729971 | ||||||||
\(238\) | 3.02587e27 | 1.41324 | ||||||||
\(239\) | −1.71220e27 | −0.762041 | −0.381021 | − | 0.924567i | \(-0.624427\pi\) | ||||
−0.381021 | + | 0.924567i | \(0.624427\pi\) | |||||||
\(240\) | −2.13079e26 | −0.0903880 | ||||||||
\(241\) | −8.11502e26 | −0.328166 | −0.164083 | − | 0.986447i | \(-0.552466\pi\) | ||||
−0.164083 | + | 0.986447i | \(0.552466\pi\) | |||||||
\(242\) | −8.70232e26 | −0.335551 | ||||||||
\(243\) | −1.78694e27 | −0.657109 | ||||||||
\(244\) | −1.03290e27 | −0.362306 | ||||||||
\(245\) | 1.59644e26 | 0.0534248 | ||||||||
\(246\) | −1.09306e27 | −0.349053 | ||||||||
\(247\) | −4.15338e27 | −1.26586 | ||||||||
\(248\) | 8.31895e26 | 0.242033 | ||||||||
\(249\) | 4.71462e27 | 1.30965 | ||||||||
\(250\) | −2.38419e26 | −0.0632456 | ||||||||
\(251\) | 2.20197e27 | 0.557910 | 0.278955 | − | 0.960304i | \(-0.410012\pi\) | ||||
0.278955 | + | 0.960304i | \(0.410012\pi\) | |||||||
\(252\) | 7.57112e26 | 0.183254 | ||||||||
\(253\) | 4.70166e27 | 1.08734 | ||||||||
\(254\) | 1.77997e27 | 0.393392 | ||||||||
\(255\) | −3.23302e27 | −0.682962 | ||||||||
\(256\) | 3.09485e26 | 0.0625000 | ||||||||
\(257\) | −8.24281e27 | −1.59164 | −0.795819 | − | 0.605534i | \(-0.792959\pi\) | ||||
−0.795819 | + | 0.605534i | \(0.792959\pi\) | |||||||
\(258\) | −3.59716e27 | −0.664253 | ||||||||
\(259\) | −2.61991e26 | −0.0462742 | ||||||||
\(260\) | 1.02494e27 | 0.173182 | ||||||||
\(261\) | 2.48478e27 | 0.401718 | ||||||||
\(262\) | −3.16868e26 | −0.0490245 | ||||||||
\(263\) | 1.16638e27 | 0.172722 | 0.0863610 | − | 0.996264i | \(-0.472476\pi\) | ||||
0.0863610 | + | 0.996264i | \(0.472476\pi\) | |||||||
\(264\) | 2.44841e27 | 0.347088 | ||||||||
\(265\) | 1.82285e27 | 0.247413 | ||||||||
\(266\) | −9.40799e27 | −1.22281 | ||||||||
\(267\) | 1.11911e28 | 1.39313 | ||||||||
\(268\) | −3.36524e27 | −0.401297 | ||||||||
\(269\) | −1.48702e28 | −1.69890 | −0.849448 | − | 0.527673i | \(-0.823065\pi\) | ||||
−0.849448 | + | 0.527673i | \(0.823065\pi\) | |||||||
\(270\) | −3.14422e27 | −0.344215 | ||||||||
\(271\) | −1.44238e28 | −1.51333 | −0.756665 | − | 0.653803i | \(-0.773172\pi\) | ||||
−0.756665 | + | 0.653803i | \(0.773172\pi\) | |||||||
\(272\) | 4.69579e27 | 0.472243 | ||||||||
\(273\) | 6.87146e27 | 0.662489 | ||||||||
\(274\) | 1.08088e27 | 0.0999188 | ||||||||
\(275\) | 2.73958e27 | 0.242861 | ||||||||
\(276\) | −4.25713e27 | −0.361962 | ||||||||
\(277\) | −1.19544e28 | −0.975013 | −0.487507 | − | 0.873119i | \(-0.662094\pi\) | ||||
−0.487507 | + | 0.873119i | \(0.662094\pi\) | |||||||
\(278\) | 6.41984e27 | 0.502353 | ||||||||
\(279\) | 3.15825e27 | 0.237136 | ||||||||
\(280\) | 2.32162e27 | 0.167292 | ||||||||
\(281\) | 2.06996e28 | 1.43166 | 0.715831 | − | 0.698274i | \(-0.246048\pi\) | ||||
0.715831 | + | 0.698274i | \(0.246048\pi\) | |||||||
\(282\) | −9.64438e27 | −0.640338 | ||||||||
\(283\) | −1.14948e28 | −0.732753 | −0.366376 | − | 0.930467i | \(-0.619402\pi\) | ||||
−0.366376 | + | 0.930467i | \(0.619402\pi\) | |||||||
\(284\) | −4.05733e27 | −0.248358 | ||||||||
\(285\) | 1.00521e28 | 0.590934 | ||||||||
\(286\) | −1.17772e28 | −0.665016 | ||||||||
\(287\) | 1.19096e28 | 0.646035 | ||||||||
\(288\) | 1.17495e27 | 0.0612356 | ||||||||
\(289\) | 5.12812e28 | 2.56822 | ||||||||
\(290\) | 7.61938e27 | 0.366727 | ||||||||
\(291\) | −4.36008e27 | −0.201709 | ||||||||
\(292\) | 7.39620e27 | 0.328932 | ||||||||
\(293\) | −3.69791e28 | −1.58117 | −0.790586 | − | 0.612352i | \(-0.790224\pi\) | ||||
−0.790586 | + | 0.612352i | \(0.790224\pi\) | |||||||
\(294\) | 1.66097e27 | 0.0682917 | ||||||||
\(295\) | 1.21248e28 | 0.479427 | ||||||||
\(296\) | −4.06578e26 | −0.0154628 | ||||||||
\(297\) | 3.61291e28 | 1.32178 | ||||||||
\(298\) | 5.49356e27 | 0.193360 | ||||||||
\(299\) | 2.04774e28 | 0.693515 | ||||||||
\(300\) | −2.48056e27 | −0.0808455 | ||||||||
\(301\) | 3.91933e28 | 1.22941 | ||||||||
\(302\) | −2.02150e28 | −0.610372 | ||||||||
\(303\) | −4.28235e28 | −1.24478 | ||||||||
\(304\) | −1.46001e28 | −0.408610 | ||||||||
\(305\) | −1.20246e28 | −0.324057 | ||||||||
\(306\) | 1.78273e28 | 0.462690 | ||||||||
\(307\) | −3.17969e28 | −0.794866 | −0.397433 | − | 0.917631i | \(-0.630099\pi\) | ||||
−0.397433 | + | 0.917631i | \(0.630099\pi\) | |||||||
\(308\) | −2.66770e28 | −0.642396 | ||||||||
\(309\) | 1.83362e28 | 0.425390 | ||||||||
\(310\) | 9.68453e27 | 0.216481 | ||||||||
\(311\) | −4.33022e28 | −0.932750 | −0.466375 | − | 0.884587i | \(-0.654440\pi\) | ||||
−0.466375 | + | 0.884587i | \(0.654440\pi\) | |||||||
\(312\) | 1.06637e28 | 0.221375 | ||||||||
\(313\) | 4.55810e26 | 0.00912061 | 0.00456030 | − | 0.999990i | \(-0.498548\pi\) | ||||
0.00456030 | + | 0.999990i | \(0.498548\pi\) | |||||||
\(314\) | 5.29105e28 | 1.02059 | ||||||||
\(315\) | 8.81394e27 | 0.163907 | ||||||||
\(316\) | −2.51780e28 | −0.451461 | ||||||||
\(317\) | 5.36147e28 | 0.927049 | 0.463524 | − | 0.886084i | \(-0.346585\pi\) | ||||
0.463524 | + | 0.886084i | \(0.346585\pi\) | |||||||
\(318\) | 1.89653e28 | 0.316263 | ||||||||
\(319\) | −8.75515e28 | −1.40822 | ||||||||
\(320\) | 3.60288e27 | 0.0559017 | ||||||||
\(321\) | −9.03301e28 | −1.35215 | ||||||||
\(322\) | 4.63841e28 | 0.669926 | ||||||||
\(323\) | −2.21525e29 | −3.08741 | ||||||||
\(324\) | −1.98362e28 | −0.266803 | ||||||||
\(325\) | 1.19318e28 | 0.154899 | ||||||||
\(326\) | 6.78820e27 | 0.0850653 | ||||||||
\(327\) | −5.76343e28 | −0.697239 | ||||||||
\(328\) | 1.84823e28 | 0.215877 | ||||||||
\(329\) | 1.05081e29 | 1.18515 | ||||||||
\(330\) | 2.85032e28 | 0.310445 | ||||||||
\(331\) | 3.04232e28 | 0.320025 | 0.160012 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160012 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(332\) | −7.97180e28 | −0.809969 | ||||||||
\(333\) | −1.54356e27 | −0.0151500 | ||||||||
\(334\) | 1.89030e28 | 0.179245 | ||||||||
\(335\) | −3.91765e28 | −0.358931 | ||||||||
\(336\) | 2.41547e28 | 0.213846 | ||||||||
\(337\) | 5.57310e28 | 0.476819 | 0.238409 | − | 0.971165i | \(-0.423374\pi\) | ||||
0.238409 | + | 0.971165i | \(0.423374\pi\) | |||||||
\(338\) | 3.42183e28 | 0.282954 | ||||||||
\(339\) | 1.61736e29 | 1.29274 | ||||||||
\(340\) | 5.46662e28 | 0.422387 | ||||||||
\(341\) | −1.11281e29 | −0.831280 | ||||||||
\(342\) | −5.54285e28 | −0.400344 | ||||||||
\(343\) | 1.33394e29 | 0.931650 | ||||||||
\(344\) | 6.08233e28 | 0.410816 | ||||||||
\(345\) | −4.95596e28 | −0.323749 | ||||||||
\(346\) | −5.12985e28 | −0.324138 | ||||||||
\(347\) | −2.05152e29 | −1.25397 | −0.626985 | − | 0.779031i | \(-0.715711\pi\) | ||||
−0.626985 | + | 0.779031i | \(0.715711\pi\) | |||||||
\(348\) | 7.92738e28 | 0.468779 | ||||||||
\(349\) | 2.36329e29 | 1.35215 | 0.676074 | − | 0.736834i | \(-0.263680\pi\) | ||||
0.676074 | + | 0.736834i | \(0.263680\pi\) | |||||||
\(350\) | 2.70273e28 | 0.149630 | ||||||||
\(351\) | 1.57355e29 | 0.843041 | ||||||||
\(352\) | −4.13994e28 | −0.214661 | ||||||||
\(353\) | 1.09725e29 | 0.550677 | 0.275339 | − | 0.961347i | \(-0.411210\pi\) | ||||
0.275339 | + | 0.961347i | \(0.411210\pi\) | |||||||
\(354\) | 1.26150e29 | 0.612841 | ||||||||
\(355\) | −4.72335e28 | −0.222139 | ||||||||
\(356\) | −1.89226e29 | −0.861601 | ||||||||
\(357\) | 3.66497e29 | 1.61579 | ||||||||
\(358\) | 1.59027e29 | 0.678917 | ||||||||
\(359\) | −3.26602e29 | −1.35031 | −0.675153 | − | 0.737677i | \(-0.735923\pi\) | ||||
−0.675153 | + | 0.737677i | \(0.735923\pi\) | |||||||
\(360\) | 1.36782e28 | 0.0547708 | ||||||||
\(361\) | 4.30934e29 | 1.67139 | ||||||||
\(362\) | −3.66644e29 | −1.37752 | ||||||||
\(363\) | −1.05404e29 | −0.383645 | ||||||||
\(364\) | −1.16187e29 | −0.409726 | ||||||||
\(365\) | 8.61031e28 | 0.294206 | ||||||||
\(366\) | −1.25106e29 | −0.414235 | ||||||||
\(367\) | −8.85081e28 | −0.284003 | −0.142002 | − | 0.989866i | \(-0.545354\pi\) | ||||
−0.142002 | + | 0.989866i | \(0.545354\pi\) | |||||||
\(368\) | 7.19825e28 | 0.223860 | ||||||||
\(369\) | 7.01671e28 | 0.211510 | ||||||||
\(370\) | −4.73319e27 | −0.0138304 | ||||||||
\(371\) | −2.06639e29 | −0.585346 | ||||||||
\(372\) | 1.00760e29 | 0.276723 | ||||||||
\(373\) | −3.93901e29 | −1.04890 | −0.524452 | − | 0.851440i | \(-0.675730\pi\) | ||||
−0.524452 | + | 0.851440i | \(0.675730\pi\) | |||||||
\(374\) | −6.28149e29 | −1.62196 | ||||||||
\(375\) | −2.88775e28 | −0.0723104 | ||||||||
\(376\) | 1.63074e29 | 0.396026 | ||||||||
\(377\) | −3.81317e29 | −0.898175 | ||||||||
\(378\) | 3.56431e29 | 0.814366 | ||||||||
\(379\) | 1.29839e29 | 0.287777 | 0.143888 | − | 0.989594i | \(-0.454039\pi\) | ||||
0.143888 | + | 0.989594i | \(0.454039\pi\) | |||||||
\(380\) | −1.69967e29 | −0.365472 | ||||||||
\(381\) | 2.15592e29 | 0.449776 | ||||||||
\(382\) | 3.84265e29 | 0.777861 | ||||||||
\(383\) | 2.17964e29 | 0.428153 | 0.214076 | − | 0.976817i | \(-0.431326\pi\) | ||||
0.214076 | + | 0.976817i | \(0.431326\pi\) | |||||||
\(384\) | 3.74852e28 | 0.0714580 | ||||||||
\(385\) | −3.10561e29 | −0.574577 | ||||||||
\(386\) | −6.55254e29 | −1.17667 | ||||||||
\(387\) | 2.30913e29 | 0.402506 | ||||||||
\(388\) | 7.37232e28 | 0.124750 | ||||||||
\(389\) | −9.04905e29 | −1.48656 | −0.743280 | − | 0.668980i | \(-0.766731\pi\) | ||||
−0.743280 | + | 0.668980i | \(0.766731\pi\) | |||||||
\(390\) | 1.24142e29 | 0.198004 | ||||||||
\(391\) | 1.09218e30 | 1.69147 | ||||||||
\(392\) | −2.80849e28 | −0.0422360 | ||||||||
\(393\) | −3.83794e28 | −0.0560511 | ||||||||
\(394\) | −4.75982e29 | −0.675125 | ||||||||
\(395\) | −2.93111e29 | −0.403799 | ||||||||
\(396\) | −1.57171e29 | −0.210319 | ||||||||
\(397\) | 1.18206e30 | 1.53656 | 0.768279 | − | 0.640116i | \(-0.221114\pi\) | ||||
0.768279 | + | 0.640116i | \(0.221114\pi\) | |||||||
\(398\) | 2.95221e29 | 0.372813 | ||||||||
\(399\) | −1.13951e30 | −1.39807 | ||||||||
\(400\) | 4.19430e28 | 0.0500000 | ||||||||
\(401\) | 9.75353e29 | 1.12980 | 0.564900 | − | 0.825159i | \(-0.308915\pi\) | ||||
0.564900 | + | 0.825159i | \(0.308915\pi\) | |||||||
\(402\) | −4.07602e29 | −0.458814 | ||||||||
\(403\) | −4.84669e29 | −0.530197 | ||||||||
\(404\) | 7.24089e29 | 0.769850 | ||||||||
\(405\) | −2.30923e29 | −0.238636 | ||||||||
\(406\) | −8.63737e29 | −0.867625 | ||||||||
\(407\) | 5.43874e28 | 0.0531084 | ||||||||
\(408\) | 5.68759e29 | 0.539929 | ||||||||
\(409\) | 3.52564e29 | 0.325402 | 0.162701 | − | 0.986675i | \(-0.447979\pi\) | ||||
0.162701 | + | 0.986675i | \(0.447979\pi\) | |||||||
\(410\) | 2.15162e29 | 0.193086 | ||||||||
\(411\) | 1.30918e29 | 0.114240 | ||||||||
\(412\) | −3.10041e29 | −0.263088 | ||||||||
\(413\) | −1.37448e30 | −1.13426 | ||||||||
\(414\) | 2.73278e29 | 0.219332 | ||||||||
\(415\) | −9.28040e29 | −0.724459 | ||||||||
\(416\) | −1.80309e29 | −0.136913 | ||||||||
\(417\) | 7.77579e29 | 0.574354 | ||||||||
\(418\) | 1.95303e30 | 1.40340 | ||||||||
\(419\) | −1.40788e30 | −0.984246 | −0.492123 | − | 0.870526i | \(-0.663779\pi\) | ||||
−0.492123 | + | 0.870526i | \(0.663779\pi\) | |||||||
\(420\) | 2.81198e29 | 0.191269 | ||||||||
\(421\) | 7.36867e29 | 0.487691 | 0.243845 | − | 0.969814i | \(-0.421591\pi\) | ||||
0.243845 | + | 0.969814i | \(0.421591\pi\) | |||||||
\(422\) | 1.84505e30 | 1.18827 | ||||||||
\(423\) | 6.19102e29 | 0.388014 | ||||||||
\(424\) | −3.20679e29 | −0.195597 | ||||||||
\(425\) | 6.36398e29 | 0.377795 | ||||||||
\(426\) | −4.91428e29 | −0.283955 | ||||||||
\(427\) | 1.36311e30 | 0.766674 | ||||||||
\(428\) | 1.52736e30 | 0.836255 | ||||||||
\(429\) | −1.42647e30 | −0.760331 | ||||||||
\(430\) | 7.08076e29 | 0.367445 | ||||||||
\(431\) | 1.71259e30 | 0.865298 | 0.432649 | − | 0.901562i | \(-0.357579\pi\) | ||||
0.432649 | + | 0.901562i | \(0.357579\pi\) | |||||||
\(432\) | 5.53138e29 | 0.272126 | ||||||||
\(433\) | 3.34373e30 | 1.60184 | 0.800921 | − | 0.598770i | \(-0.204343\pi\) | ||||
0.800921 | + | 0.598770i | \(0.204343\pi\) | |||||||
\(434\) | −1.09784e30 | −0.512163 | ||||||||
\(435\) | 9.22868e29 | 0.419289 | ||||||||
\(436\) | 9.74520e29 | 0.431217 | ||||||||
\(437\) | −3.39580e30 | −1.46354 | ||||||||
\(438\) | 8.95837e29 | 0.376077 | ||||||||
\(439\) | −3.95516e30 | −1.61742 | −0.808710 | − | 0.588208i | \(-0.799834\pi\) | ||||
−0.808710 | + | 0.588208i | \(0.799834\pi\) | |||||||
\(440\) | −4.81952e29 | −0.191999 | ||||||||
\(441\) | −1.06623e29 | −0.0413816 | ||||||||
\(442\) | −2.73581e30 | −1.03450 | ||||||||
\(443\) | −3.40082e30 | −1.25297 | −0.626486 | − | 0.779433i | \(-0.715507\pi\) | ||||
−0.626486 | + | 0.779433i | \(0.715507\pi\) | |||||||
\(444\) | −4.92452e28 | −0.0176791 | ||||||||
\(445\) | −2.20288e30 | −0.770639 | ||||||||
\(446\) | −2.29855e30 | −0.783616 | ||||||||
\(447\) | 6.65387e29 | 0.221074 | ||||||||
\(448\) | −4.08424e29 | −0.132256 | ||||||||
\(449\) | 3.24298e30 | 1.02355 | 0.511777 | − | 0.859118i | \(-0.328987\pi\) | ||||
0.511777 | + | 0.859118i | \(0.328987\pi\) | |||||||
\(450\) | 1.59235e29 | 0.0489885 | ||||||||
\(451\) | −2.47235e30 | −0.741446 | ||||||||
\(452\) | −2.73475e30 | −0.799512 | ||||||||
\(453\) | −2.44847e30 | −0.697856 | ||||||||
\(454\) | 2.84491e29 | 0.0790545 | ||||||||
\(455\) | −1.35260e30 | −0.366470 | ||||||||
\(456\) | −1.76838e30 | −0.467175 | ||||||||
\(457\) | −2.32028e30 | −0.597729 | −0.298864 | − | 0.954296i | \(-0.596608\pi\) | ||||
−0.298864 | + | 0.954296i | \(0.596608\pi\) | |||||||
\(458\) | 2.11979e30 | 0.532526 | ||||||||
\(459\) | 8.39270e30 | 2.05616 | ||||||||
\(460\) | 8.37987e29 | 0.200227 | ||||||||
\(461\) | −1.77997e30 | −0.414813 | −0.207406 | − | 0.978255i | \(-0.566502\pi\) | ||||
−0.207406 | + | 0.978255i | \(0.566502\pi\) | |||||||
\(462\) | −3.23114e30 | −0.734469 | ||||||||
\(463\) | −1.16490e30 | −0.258291 | −0.129145 | − | 0.991626i | \(-0.541223\pi\) | ||||
−0.129145 | + | 0.991626i | \(0.541223\pi\) | |||||||
\(464\) | −1.34042e30 | −0.289923 | ||||||||
\(465\) | 1.17300e30 | 0.247508 | ||||||||
\(466\) | 2.12074e30 | 0.436566 | ||||||||
\(467\) | 4.42414e30 | 0.888555 | 0.444278 | − | 0.895889i | \(-0.353460\pi\) | ||||
0.444278 | + | 0.895889i | \(0.353460\pi\) | |||||||
\(468\) | −6.84534e29 | −0.134143 | ||||||||
\(469\) | 4.44107e30 | 0.849181 | ||||||||
\(470\) | 1.89843e30 | 0.354216 | ||||||||
\(471\) | 6.40858e30 | 1.16687 | ||||||||
\(472\) | −2.13302e30 | −0.379020 | ||||||||
\(473\) | −8.13625e30 | −1.41098 | ||||||||
\(474\) | −3.04959e30 | −0.516167 | ||||||||
\(475\) | −1.97868e30 | −0.326888 | ||||||||
\(476\) | −6.19699e30 | −0.999311 | ||||||||
\(477\) | −1.21744e30 | −0.191640 | ||||||||
\(478\) | 3.50659e30 | 0.538845 | ||||||||
\(479\) | 1.17747e31 | 1.76641 | 0.883207 | − | 0.468983i | \(-0.155379\pi\) | ||||
0.883207 | + | 0.468983i | \(0.155379\pi\) | |||||||
\(480\) | 4.36385e29 | 0.0639140 | ||||||||
\(481\) | 2.36876e29 | 0.0338729 | ||||||||
\(482\) | 1.66196e30 | 0.232048 | ||||||||
\(483\) | 5.61810e30 | 0.765945 | ||||||||
\(484\) | 1.78224e30 | 0.237270 | ||||||||
\(485\) | 8.58252e29 | 0.111580 | ||||||||
\(486\) | 3.65965e30 | 0.464646 | ||||||||
\(487\) | 8.71950e30 | 1.08121 | 0.540603 | − | 0.841278i | \(-0.318196\pi\) | ||||
0.540603 | + | 0.841278i | \(0.318196\pi\) | |||||||
\(488\) | 2.11538e30 | 0.256189 | ||||||||
\(489\) | 8.22195e29 | 0.0972575 | ||||||||
\(490\) | −3.26951e29 | −0.0377770 | ||||||||
\(491\) | 3.31430e30 | 0.374071 | 0.187036 | − | 0.982353i | \(-0.440112\pi\) | ||||
0.187036 | + | 0.982353i | \(0.440112\pi\) | |||||||
\(492\) | 2.23860e30 | 0.246818 | ||||||||
\(493\) | −2.03380e31 | −2.19063 | ||||||||
\(494\) | 8.50613e30 | 0.895101 | ||||||||
\(495\) | −1.82971e30 | −0.188115 | ||||||||
\(496\) | −1.70372e30 | −0.171143 | ||||||||
\(497\) | 5.35441e30 | 0.525549 | ||||||||
\(498\) | −9.65554e30 | −0.926060 | ||||||||
\(499\) | −4.41221e30 | −0.413523 | −0.206762 | − | 0.978391i | \(-0.566292\pi\) | ||||
−0.206762 | + | 0.978391i | \(0.566292\pi\) | |||||||
\(500\) | 4.88281e29 | 0.0447214 | ||||||||
\(501\) | 2.28956e30 | 0.204936 | ||||||||
\(502\) | −4.50964e30 | −0.394502 | ||||||||
\(503\) | 8.86520e30 | 0.757978 | 0.378989 | − | 0.925401i | \(-0.376272\pi\) | ||||
0.378989 | + | 0.925401i | \(0.376272\pi\) | |||||||
\(504\) | −1.55056e30 | −0.129580 | ||||||||
\(505\) | 8.42950e30 | 0.688575 | ||||||||
\(506\) | −9.62901e30 | −0.768866 | ||||||||
\(507\) | 4.14456e30 | 0.323510 | ||||||||
\(508\) | −3.64538e30 | −0.278170 | ||||||||
\(509\) | 4.77364e30 | 0.356119 | 0.178059 | − | 0.984020i | \(-0.443018\pi\) | ||||
0.178059 | + | 0.984020i | \(0.443018\pi\) | |||||||
\(510\) | 6.62123e30 | 0.482927 | ||||||||
\(511\) | −9.76070e30 | −0.696050 | ||||||||
\(512\) | −6.33825e29 | −0.0441942 | ||||||||
\(513\) | −2.60945e31 | −1.77909 | ||||||||
\(514\) | 1.68813e31 | 1.12546 | ||||||||
\(515\) | −3.60935e30 | −0.235313 | ||||||||
\(516\) | 7.36699e30 | 0.469698 | ||||||||
\(517\) | −2.18142e31 | −1.36018 | ||||||||
\(518\) | 5.36558e29 | 0.0327208 | ||||||||
\(519\) | −6.21334e30 | −0.370596 | ||||||||
\(520\) | −2.09907e30 | −0.122458 | ||||||||
\(521\) | −8.76488e30 | −0.500164 | −0.250082 | − | 0.968225i | \(-0.580458\pi\) | ||||
−0.250082 | + | 0.968225i | \(0.580458\pi\) | |||||||
\(522\) | −5.08882e30 | −0.284058 | ||||||||
\(523\) | 1.88160e31 | 1.02744 | 0.513721 | − | 0.857957i | \(-0.328266\pi\) | ||||
0.513721 | + | 0.857957i | \(0.328266\pi\) | |||||||
\(524\) | 6.48945e29 | 0.0346656 | ||||||||
\(525\) | 3.27357e30 | 0.171076 | ||||||||
\(526\) | −2.38874e30 | −0.122133 | ||||||||
\(527\) | −2.58504e31 | −1.29314 | ||||||||
\(528\) | −5.01434e30 | −0.245428 | ||||||||
\(529\) | −4.13819e30 | −0.198185 | ||||||||
\(530\) | −3.73319e30 | −0.174948 | ||||||||
\(531\) | −8.09792e30 | −0.371353 | ||||||||
\(532\) | 1.92676e31 | 0.864656 | ||||||||
\(533\) | −1.07679e31 | −0.472900 | ||||||||
\(534\) | −2.29193e31 | −0.985092 | ||||||||
\(535\) | 1.77808e31 | 0.747970 | ||||||||
\(536\) | 6.89201e30 | 0.283760 | ||||||||
\(537\) | 1.92616e31 | 0.776224 | ||||||||
\(538\) | 3.04542e31 | 1.20130 | ||||||||
\(539\) | 3.75687e30 | 0.145063 | ||||||||
\(540\) | 6.43937e30 | 0.243397 | ||||||||
\(541\) | −2.61136e31 | −0.966269 | −0.483135 | − | 0.875546i | \(-0.660502\pi\) | ||||
−0.483135 | + | 0.875546i | \(0.660502\pi\) | |||||||
\(542\) | 2.95400e31 | 1.07009 | ||||||||
\(543\) | −4.44084e31 | −1.57495 | ||||||||
\(544\) | −9.61697e30 | −0.333927 | ||||||||
\(545\) | 1.13449e31 | 0.385692 | ||||||||
\(546\) | −1.40728e31 | −0.468450 | ||||||||
\(547\) | 3.35569e29 | 0.0109377 | 0.00546887 | − | 0.999985i | \(-0.498259\pi\) | ||||
0.00546887 | + | 0.999985i | \(0.498259\pi\) | |||||||
\(548\) | −2.21365e30 | −0.0706533 | ||||||||
\(549\) | 8.03095e30 | 0.251007 | ||||||||
\(550\) | −5.61066e30 | −0.171729 | ||||||||
\(551\) | 6.32346e31 | 1.89544 | ||||||||
\(552\) | 8.71861e30 | 0.255946 | ||||||||
\(553\) | 3.32272e31 | 0.955332 | ||||||||
\(554\) | 2.44826e31 | 0.689438 | ||||||||
\(555\) | −5.73290e29 | −0.0158127 | ||||||||
\(556\) | −1.31478e31 | −0.355217 | ||||||||
\(557\) | 1.24154e31 | 0.328567 | 0.164284 | − | 0.986413i | \(-0.447469\pi\) | ||||
0.164284 | + | 0.986413i | \(0.447469\pi\) | |||||||
\(558\) | −6.46810e30 | −0.167681 | ||||||||
\(559\) | −3.54362e31 | −0.899935 | ||||||||
\(560\) | −4.75469e30 | −0.118293 | ||||||||
\(561\) | −7.60822e31 | −1.85443 | ||||||||
\(562\) | −4.23929e31 | −1.01234 | ||||||||
\(563\) | 6.53842e31 | 1.52977 | 0.764885 | − | 0.644166i | \(-0.222796\pi\) | ||||
0.764885 | + | 0.644166i | \(0.222796\pi\) | |||||||
\(564\) | 1.97517e31 | 0.452787 | ||||||||
\(565\) | −3.18366e31 | −0.715106 | ||||||||
\(566\) | 2.35413e31 | 0.518134 | ||||||||
\(567\) | 2.61776e31 | 0.564579 | ||||||||
\(568\) | 8.30940e30 | 0.175616 | ||||||||
\(569\) | 2.71677e31 | 0.562680 | 0.281340 | − | 0.959608i | \(-0.409221\pi\) | ||||
0.281340 | + | 0.959608i | \(0.409221\pi\) | |||||||
\(570\) | −2.05866e31 | −0.417854 | ||||||||
\(571\) | 5.92712e31 | 1.17904 | 0.589520 | − | 0.807754i | \(-0.299317\pi\) | ||||
0.589520 | + | 0.807754i | \(0.299317\pi\) | |||||||
\(572\) | 2.41197e31 | 0.470237 | ||||||||
\(573\) | 4.65426e31 | 0.889350 | ||||||||
\(574\) | −2.43909e31 | −0.456815 | ||||||||
\(575\) | 9.75545e30 | 0.179088 | ||||||||
\(576\) | −2.40629e30 | −0.0433001 | ||||||||
\(577\) | −2.23935e31 | −0.395003 | −0.197502 | − | 0.980303i | \(-0.563283\pi\) | ||||
−0.197502 | + | 0.980303i | \(0.563283\pi\) | |||||||
\(578\) | −1.05024e32 | −1.81601 | ||||||||
\(579\) | −7.93651e31 | −1.34532 | ||||||||
\(580\) | −1.56045e31 | −0.259315 | ||||||||
\(581\) | 1.05203e32 | 1.71397 | ||||||||
\(582\) | 8.92945e30 | 0.142630 | ||||||||
\(583\) | 4.28968e31 | 0.671794 | ||||||||
\(584\) | −1.51474e31 | −0.232590 | ||||||||
\(585\) | −7.96902e30 | −0.119981 | ||||||||
\(586\) | 7.57332e31 | 1.11806 | ||||||||
\(587\) | −6.49190e31 | −0.939796 | −0.469898 | − | 0.882721i | \(-0.655709\pi\) | ||||
−0.469898 | + | 0.882721i | \(0.655709\pi\) | |||||||
\(588\) | −3.40167e30 | −0.0482896 | ||||||||
\(589\) | 8.03736e31 | 1.11889 | ||||||||
\(590\) | −2.48317e31 | −0.339006 | ||||||||
\(591\) | −5.76515e31 | −0.771889 | ||||||||
\(592\) | 8.32672e29 | 0.0109339 | ||||||||
\(593\) | 1.27637e32 | 1.64379 | 0.821895 | − | 0.569638i | \(-0.192917\pi\) | ||||
0.821895 | + | 0.569638i | \(0.192917\pi\) | |||||||
\(594\) | −7.39925e31 | −0.934638 | ||||||||
\(595\) | −7.21424e31 | −0.893811 | ||||||||
\(596\) | −1.12508e31 | −0.136726 | ||||||||
\(597\) | 3.57575e31 | 0.426248 | ||||||||
\(598\) | −4.19377e31 | −0.490389 | ||||||||
\(599\) | −4.35980e31 | −0.500101 | −0.250051 | − | 0.968233i | \(-0.580447\pi\) | ||||
−0.250051 | + | 0.968233i | \(0.580447\pi\) | |||||||
\(600\) | 5.08019e30 | 0.0571664 | ||||||||
\(601\) | −8.94982e31 | −0.988002 | −0.494001 | − | 0.869461i | \(-0.664466\pi\) | ||||
−0.494001 | + | 0.869461i | \(0.664466\pi\) | |||||||
\(602\) | −8.02679e31 | −0.869326 | ||||||||
\(603\) | 2.61652e31 | 0.278019 | ||||||||
\(604\) | 4.14004e31 | 0.431599 | ||||||||
\(605\) | 2.07480e31 | 0.212221 | ||||||||
\(606\) | 8.77025e31 | 0.880191 | ||||||||
\(607\) | −8.25995e31 | −0.813406 | −0.406703 | − | 0.913560i | \(-0.633322\pi\) | ||||
−0.406703 | + | 0.913560i | \(0.633322\pi\) | |||||||
\(608\) | 2.99009e31 | 0.288931 | ||||||||
\(609\) | −1.04617e32 | −0.991980 | ||||||||
\(610\) | 2.46263e31 | 0.229143 | ||||||||
\(611\) | −9.50082e31 | −0.867535 | ||||||||
\(612\) | −3.65104e31 | −0.327171 | ||||||||
\(613\) | −1.75363e32 | −1.54221 | −0.771104 | − | 0.636710i | \(-0.780295\pi\) | ||||
−0.771104 | + | 0.636710i | \(0.780295\pi\) | |||||||
\(614\) | 6.51201e31 | 0.562055 | ||||||||
\(615\) | 2.60607e31 | 0.220761 | ||||||||
\(616\) | 5.46344e31 | 0.454243 | ||||||||
\(617\) | −9.32726e31 | −0.761158 | −0.380579 | − | 0.924749i | \(-0.624275\pi\) | ||||
−0.380579 | + | 0.924749i | \(0.624275\pi\) | |||||||
\(618\) | −3.75526e31 | −0.300796 | ||||||||
\(619\) | −2.11173e32 | −1.66034 | −0.830169 | − | 0.557512i | \(-0.811756\pi\) | ||||
−0.830169 | + | 0.557512i | \(0.811756\pi\) | |||||||
\(620\) | −1.98339e31 | −0.153075 | ||||||||
\(621\) | 1.28653e32 | 0.974692 | ||||||||
\(622\) | 8.86828e31 | 0.659554 | ||||||||
\(623\) | 2.49720e32 | 1.82323 | ||||||||
\(624\) | −2.18392e31 | −0.156536 | ||||||||
\(625\) | 5.68434e30 | 0.0400000 | ||||||||
\(626\) | −9.33498e29 | −0.00644924 | ||||||||
\(627\) | 2.36553e32 | 1.60455 | ||||||||
\(628\) | −1.08361e32 | −0.721666 | ||||||||
\(629\) | 1.26341e31 | 0.0826153 | ||||||||
\(630\) | −1.80510e31 | −0.115900 | ||||||||
\(631\) | −1.01929e32 | −0.642628 | −0.321314 | − | 0.946973i | \(-0.604125\pi\) | ||||
−0.321314 | + | 0.946973i | \(0.604125\pi\) | |||||||
\(632\) | 5.15646e31 | 0.319231 | ||||||||
\(633\) | 2.23475e32 | 1.35858 | ||||||||
\(634\) | −1.09803e32 | −0.655522 | ||||||||
\(635\) | −4.24379e31 | −0.248803 | ||||||||
\(636\) | −3.88410e31 | −0.223632 | ||||||||
\(637\) | 1.63625e31 | 0.0925222 | ||||||||
\(638\) | 1.79306e32 | 0.995763 | ||||||||
\(639\) | 3.15463e31 | 0.172063 | ||||||||
\(640\) | −7.37870e30 | −0.0395285 | ||||||||
\(641\) | −8.95507e31 | −0.471196 | −0.235598 | − | 0.971851i | \(-0.575705\pi\) | ||||
−0.235598 | + | 0.971851i | \(0.575705\pi\) | |||||||
\(642\) | 1.84996e32 | 0.956114 | ||||||||
\(643\) | 1.55072e32 | 0.787242 | 0.393621 | − | 0.919273i | \(-0.371222\pi\) | ||||
0.393621 | + | 0.919273i | \(0.371222\pi\) | |||||||
\(644\) | −9.49947e31 | −0.473709 | ||||||||
\(645\) | 8.57631e31 | 0.420110 | ||||||||
\(646\) | 4.53684e32 | 2.18313 | ||||||||
\(647\) | −7.18599e31 | −0.339693 | −0.169847 | − | 0.985470i | \(-0.554327\pi\) | ||||
−0.169847 | + | 0.985470i | \(0.554327\pi\) | |||||||
\(648\) | 4.06245e31 | 0.188658 | ||||||||
\(649\) | 2.85332e32 | 1.30177 | ||||||||
\(650\) | −2.44364e31 | −0.109530 | ||||||||
\(651\) | −1.32972e32 | −0.585571 | ||||||||
\(652\) | −1.39022e31 | −0.0601503 | ||||||||
\(653\) | 1.03893e32 | 0.441658 | 0.220829 | − | 0.975313i | \(-0.429124\pi\) | ||||
0.220829 | + | 0.975313i | \(0.429124\pi\) | |||||||
\(654\) | 1.18035e32 | 0.493022 | ||||||||
\(655\) | 7.55472e30 | 0.0310058 | ||||||||
\(656\) | −3.78517e31 | −0.152648 | ||||||||
\(657\) | −5.75065e31 | −0.227885 | ||||||||
\(658\) | −2.15207e32 | −0.838028 | ||||||||
\(659\) | −2.67825e31 | −0.102487 | −0.0512435 | − | 0.998686i | \(-0.516318\pi\) | ||||
−0.0512435 | + | 0.998686i | \(0.516318\pi\) | |||||||
\(660\) | −5.83747e31 | −0.219517 | ||||||||
\(661\) | −3.87116e32 | −1.43062 | −0.715310 | − | 0.698807i | \(-0.753715\pi\) | ||||
−0.715310 | + | 0.698807i | \(0.753715\pi\) | |||||||
\(662\) | −6.23068e31 | −0.226292 | ||||||||
\(663\) | −3.31364e32 | −1.18277 | ||||||||
\(664\) | 1.63263e32 | 0.572735 | ||||||||
\(665\) | 2.24304e32 | 0.773371 | ||||||||
\(666\) | 3.16120e30 | 0.0107127 | ||||||||
\(667\) | −3.11765e32 | −1.03844 | ||||||||
\(668\) | −3.87134e31 | −0.126745 | ||||||||
\(669\) | −2.78403e32 | −0.895929 | ||||||||
\(670\) | 8.02335e31 | 0.253802 | ||||||||
\(671\) | −2.82972e32 | −0.879902 | ||||||||
\(672\) | −4.94689e31 | −0.151212 | ||||||||
\(673\) | −2.33531e32 | −0.701733 | −0.350867 | − | 0.936425i | \(-0.614113\pi\) | ||||
−0.350867 | + | 0.936425i | \(0.614113\pi\) | |||||||
\(674\) | −1.14137e32 | −0.337162 | ||||||||
\(675\) | 7.49641e31 | 0.217701 | ||||||||
\(676\) | −7.00791e31 | −0.200079 | ||||||||
\(677\) | 6.22149e32 | 1.74632 | 0.873161 | − | 0.487432i | \(-0.162066\pi\) | ||||
0.873161 | + | 0.487432i | \(0.162066\pi\) | |||||||
\(678\) | −3.31236e32 | −0.914104 | ||||||||
\(679\) | −9.72919e31 | −0.263982 | ||||||||
\(680\) | −1.11956e32 | −0.298673 | ||||||||
\(681\) | 3.44579e31 | 0.0903851 | ||||||||
\(682\) | 2.27904e32 | 0.587804 | ||||||||
\(683\) | −5.18176e32 | −1.31413 | −0.657067 | − | 0.753833i | \(-0.728203\pi\) | ||||
−0.657067 | + | 0.753833i | \(0.728203\pi\) | |||||||
\(684\) | 1.13518e32 | 0.283086 | ||||||||
\(685\) | −2.57703e31 | −0.0631942 | ||||||||
\(686\) | −2.73190e32 | −0.658776 | ||||||||
\(687\) | 2.56752e32 | 0.608851 | ||||||||
\(688\) | −1.24566e32 | −0.290491 | ||||||||
\(689\) | 1.86830e32 | 0.428476 | ||||||||
\(690\) | 1.01498e32 | 0.228925 | ||||||||
\(691\) | 5.78541e32 | 1.28333 | 0.641663 | − | 0.766987i | \(-0.278245\pi\) | ||||
0.641663 | + | 0.766987i | \(0.278245\pi\) | |||||||
\(692\) | 1.05059e32 | 0.229200 | ||||||||
\(693\) | 2.07417e32 | 0.445053 | ||||||||
\(694\) | 4.20151e32 | 0.886690 | ||||||||
\(695\) | −1.53061e32 | −0.317716 | ||||||||
\(696\) | −1.62353e32 | −0.331477 | ||||||||
\(697\) | −5.74320e32 | −1.15339 | ||||||||
\(698\) | −4.84001e32 | −0.956113 | ||||||||
\(699\) | 2.56867e32 | 0.499138 | ||||||||
\(700\) | −5.53518e31 | −0.105805 | ||||||||
\(701\) | 7.25665e32 | 1.36452 | 0.682259 | − | 0.731111i | \(-0.260998\pi\) | ||||
0.682259 | + | 0.731111i | \(0.260998\pi\) | |||||||
\(702\) | −3.22263e32 | −0.596120 | ||||||||
\(703\) | −3.92816e31 | −0.0714831 | ||||||||
\(704\) | 8.47860e31 | 0.151788 | ||||||||
\(705\) | 2.29940e32 | 0.404985 | ||||||||
\(706\) | −2.24717e32 | −0.389388 | ||||||||
\(707\) | −9.55573e32 | −1.62907 | ||||||||
\(708\) | −2.58354e32 | −0.433344 | ||||||||
\(709\) | 6.96702e32 | 1.14978 | 0.574891 | − | 0.818230i | \(-0.305044\pi\) | ||||
0.574891 | + | 0.818230i | \(0.305044\pi\) | |||||||
\(710\) | 9.67342e31 | 0.157076 | ||||||||
\(711\) | 1.95763e32 | 0.312773 | ||||||||
\(712\) | 3.87535e32 | 0.609244 | ||||||||
\(713\) | −3.96265e32 | −0.612994 | ||||||||
\(714\) | −7.50586e32 | −1.14254 | ||||||||
\(715\) | 2.80790e32 | 0.420593 | ||||||||
\(716\) | −3.25688e32 | −0.480067 | ||||||||
\(717\) | 4.24722e32 | 0.616076 | ||||||||
\(718\) | 6.68880e32 | 0.954811 | ||||||||
\(719\) | 7.58207e32 | 1.06514 | 0.532569 | − | 0.846387i | \(-0.321227\pi\) | ||||
0.532569 | + | 0.846387i | \(0.321227\pi\) | |||||||
\(720\) | −2.80129e31 | −0.0387288 | ||||||||
\(721\) | 4.09158e32 | 0.556719 | ||||||||
\(722\) | −8.82552e32 | −1.18185 | ||||||||
\(723\) | 2.01298e32 | 0.265307 | ||||||||
\(724\) | 7.50888e32 | 0.974050 | ||||||||
\(725\) | −1.81660e32 | −0.231938 | ||||||||
\(726\) | 2.15866e32 | 0.271278 | ||||||||
\(727\) | 2.69772e32 | 0.333696 | 0.166848 | − | 0.985983i | \(-0.446641\pi\) | ||||
0.166848 | + | 0.985983i | \(0.446641\pi\) | |||||||
\(728\) | 2.37952e32 | 0.289720 | ||||||||
\(729\) | 8.88493e32 | 1.06485 | ||||||||
\(730\) | −1.76339e32 | −0.208035 | ||||||||
\(731\) | −1.89003e33 | −2.19492 | ||||||||
\(732\) | 2.56218e32 | 0.292908 | ||||||||
\(733\) | −3.67420e32 | −0.413492 | −0.206746 | − | 0.978395i | \(-0.566287\pi\) | ||||
−0.206746 | + | 0.978395i | \(0.566287\pi\) | |||||||
\(734\) | 1.81265e32 | 0.200821 | ||||||||
\(735\) | −3.96007e31 | −0.0431915 | ||||||||
\(736\) | −1.47420e32 | −0.158293 | ||||||||
\(737\) | −9.21935e32 | −0.974595 | ||||||||
\(738\) | −1.43702e32 | −0.149560 | ||||||||
\(739\) | 1.50918e33 | 1.54643 | 0.773216 | − | 0.634143i | \(-0.218647\pi\) | ||||
0.773216 | + | 0.634143i | \(0.218647\pi\) | |||||||
\(740\) | 9.69358e30 | 0.00977956 | ||||||||
\(741\) | 1.03027e33 | 1.02339 | ||||||||
\(742\) | 4.23197e32 | 0.413902 | ||||||||
\(743\) | 8.64193e32 | 0.832222 | 0.416111 | − | 0.909314i | \(-0.363393\pi\) | ||||
0.416111 | + | 0.909314i | \(0.363393\pi\) | |||||||
\(744\) | −2.06357e32 | −0.195672 | ||||||||
\(745\) | −1.30977e32 | −0.122292 | ||||||||
\(746\) | 8.06709e32 | 0.741687 | ||||||||
\(747\) | 6.19819e32 | 0.561148 | ||||||||
\(748\) | 1.28645e33 | 1.14690 | ||||||||
\(749\) | −2.01565e33 | −1.76959 | ||||||||
\(750\) | 5.91412e31 | 0.0511312 | ||||||||
\(751\) | −8.02515e32 | −0.683272 | −0.341636 | − | 0.939832i | \(-0.610981\pi\) | ||||
−0.341636 | + | 0.939832i | \(0.610981\pi\) | |||||||
\(752\) | −3.33975e32 | −0.280033 | ||||||||
\(753\) | −5.46213e32 | −0.451045 | ||||||||
\(754\) | 7.80938e32 | 0.635106 | ||||||||
\(755\) | 4.81964e32 | 0.386033 | ||||||||
\(756\) | −7.29971e32 | −0.575844 | ||||||||
\(757\) | −7.46047e32 | −0.579647 | −0.289823 | − | 0.957080i | \(-0.593597\pi\) | ||||
−0.289823 | + | 0.957080i | \(0.593597\pi\) | |||||||
\(758\) | −2.65911e32 | −0.203489 | ||||||||
\(759\) | −1.16628e33 | −0.879066 | ||||||||
\(760\) | 3.48093e32 | 0.258427 | ||||||||
\(761\) | −2.23694e33 | −1.63580 | −0.817901 | − | 0.575359i | \(-0.804863\pi\) | ||||
−0.817901 | + | 0.575359i | \(0.804863\pi\) | |||||||
\(762\) | −4.41533e32 | −0.318040 | ||||||||
\(763\) | −1.28606e33 | −0.912495 | ||||||||
\(764\) | −7.86974e32 | −0.550031 | ||||||||
\(765\) | −4.25037e32 | −0.292631 | ||||||||
\(766\) | −4.46390e32 | −0.302750 | ||||||||
\(767\) | 1.24272e33 | 0.830283 | ||||||||
\(768\) | −7.67697e31 | −0.0505284 | ||||||||
\(769\) | −8.84798e32 | −0.573708 | −0.286854 | − | 0.957974i | \(-0.592609\pi\) | ||||
−0.286854 | + | 0.957974i | \(0.592609\pi\) | |||||||
\(770\) | 6.36028e32 | 0.406287 | ||||||||
\(771\) | 2.04468e33 | 1.28677 | ||||||||
\(772\) | 1.34196e33 | 0.832033 | ||||||||
\(773\) | 4.12211e32 | 0.251800 | 0.125900 | − | 0.992043i | \(-0.459818\pi\) | ||||
0.125900 | + | 0.992043i | \(0.459818\pi\) | |||||||
\(774\) | −4.72910e32 | −0.284615 | ||||||||
\(775\) | −2.30897e32 | −0.136914 | ||||||||
\(776\) | −1.50985e32 | −0.0882114 | ||||||||
\(777\) | 6.49885e31 | 0.0374106 | ||||||||
\(778\) | 1.85325e33 | 1.05116 | ||||||||
\(779\) | 1.78567e33 | 0.997975 | ||||||||
\(780\) | −2.54242e32 | −0.140010 | ||||||||
\(781\) | −1.11154e33 | −0.603167 | ||||||||
\(782\) | −2.23679e33 | −1.19605 | ||||||||
\(783\) | −2.39570e33 | −1.26233 | ||||||||
\(784\) | 5.75178e31 | 0.0298653 | ||||||||
\(785\) | −1.26148e33 | −0.645477 | ||||||||
\(786\) | 7.86010e31 | 0.0396341 | ||||||||
\(787\) | −9.29443e31 | −0.0461863 | −0.0230931 | − | 0.999733i | \(-0.507351\pi\) | ||||
−0.0230931 | + | 0.999733i | \(0.507351\pi\) | |||||||
\(788\) | 9.74811e32 | 0.477385 | ||||||||
\(789\) | −2.89327e32 | −0.139638 | ||||||||
\(790\) | 6.00291e32 | 0.285529 | ||||||||
\(791\) | 3.60902e33 | 1.69184 | ||||||||
\(792\) | 3.21886e32 | 0.148718 | ||||||||
\(793\) | −1.23244e33 | −0.561209 | ||||||||
\(794\) | −2.42086e33 | −1.08651 | ||||||||
\(795\) | −4.52169e32 | −0.200022 | ||||||||
\(796\) | −6.04612e32 | −0.263619 | ||||||||
\(797\) | −1.01244e32 | −0.0435108 | −0.0217554 | − | 0.999763i | \(-0.506926\pi\) | ||||
−0.0217554 | + | 0.999763i | \(0.506926\pi\) | |||||||
\(798\) | 2.33371e33 | 0.988585 | ||||||||
\(799\) | −5.06737e33 | −2.11590 | ||||||||
\(800\) | −8.58993e31 | −0.0353553 | ||||||||
\(801\) | 1.47126e33 | 0.596919 | ||||||||
\(802\) | −1.99752e33 | −0.798890 | ||||||||
\(803\) | 2.02625e33 | 0.798848 | ||||||||
\(804\) | 8.34768e32 | 0.324430 | ||||||||
\(805\) | −1.10588e33 | −0.423698 | ||||||||
\(806\) | 9.92603e32 | 0.374906 | ||||||||
\(807\) | 3.68865e33 | 1.37348 | ||||||||
\(808\) | −1.48293e33 | −0.544366 | ||||||||
\(809\) | −3.30371e33 | −1.19562 | −0.597811 | − | 0.801637i | \(-0.703963\pi\) | ||||
−0.597811 | + | 0.801637i | \(0.703963\pi\) | |||||||
\(810\) | 4.72931e32 | 0.168741 | ||||||||
\(811\) | 3.27520e33 | 1.15212 | 0.576061 | − | 0.817407i | \(-0.304589\pi\) | ||||
0.576061 | + | 0.817407i | \(0.304589\pi\) | |||||||
\(812\) | 1.76893e33 | 0.613504 | ||||||||
\(813\) | 3.57792e33 | 1.22346 | ||||||||
\(814\) | −1.11385e32 | −0.0375533 | ||||||||
\(815\) | −1.61843e32 | −0.0538000 | ||||||||
\(816\) | −1.16482e33 | −0.381787 | ||||||||
\(817\) | 5.87645e33 | 1.89916 | ||||||||
\(818\) | −7.22051e32 | −0.230094 | ||||||||
\(819\) | 9.03373e32 | 0.283859 | ||||||||
\(820\) | −4.40652e32 | −0.136533 | ||||||||
\(821\) | −2.62789e32 | −0.0802900 | −0.0401450 | − | 0.999194i | \(-0.512782\pi\) | ||||
−0.0401450 | + | 0.999194i | \(0.512782\pi\) | |||||||
\(822\) | −2.68120e32 | −0.0807799 | ||||||||
\(823\) | 1.32429e33 | 0.393447 | 0.196724 | − | 0.980459i | \(-0.436970\pi\) | ||||
0.196724 | + | 0.980459i | \(0.436970\pi\) | |||||||
\(824\) | 6.34964e32 | 0.186031 | ||||||||
\(825\) | −6.79570e32 | −0.196342 | ||||||||
\(826\) | 2.81493e33 | 0.802042 | ||||||||
\(827\) | 6.86820e32 | 0.192988 | 0.0964938 | − | 0.995334i | \(-0.469237\pi\) | ||||
0.0964938 | + | 0.995334i | \(0.469237\pi\) | |||||||
\(828\) | −5.59674e32 | −0.155091 | ||||||||
\(829\) | −3.52526e33 | −0.963416 | −0.481708 | − | 0.876332i | \(-0.659983\pi\) | ||||
−0.481708 | + | 0.876332i | \(0.659983\pi\) | |||||||
\(830\) | 1.90063e33 | 0.512270 | ||||||||
\(831\) | 2.96536e33 | 0.788254 | ||||||||
\(832\) | 3.69272e32 | 0.0968118 | ||||||||
\(833\) | 8.72712e32 | 0.225659 | ||||||||
\(834\) | −1.59248e33 | −0.406130 | ||||||||
\(835\) | −4.50684e32 | −0.113365 | ||||||||
\(836\) | −3.99981e33 | −0.992355 | ||||||||
\(837\) | −3.04503e33 | −0.745159 | ||||||||
\(838\) | 2.88333e33 | 0.695967 | ||||||||
\(839\) | 7.77027e33 | 1.85001 | 0.925004 | − | 0.379958i | \(-0.124061\pi\) | ||||
0.925004 | + | 0.379958i | \(0.124061\pi\) | |||||||
\(840\) | −5.75893e32 | −0.135248 | ||||||||
\(841\) | 1.48877e33 | 0.344885 | ||||||||
\(842\) | −1.50910e33 | −0.344850 | ||||||||
\(843\) | −5.13468e33 | −1.15743 | ||||||||
\(844\) | −3.77867e33 | −0.840234 | ||||||||
\(845\) | −8.15828e32 | −0.178956 | ||||||||
\(846\) | −1.26792e33 | −0.274368 | ||||||||
\(847\) | −2.35200e33 | −0.502086 | ||||||||
\(848\) | 6.56750e32 | 0.138308 | ||||||||
\(849\) | 2.85136e33 | 0.592397 | ||||||||
\(850\) | −1.30334e33 | −0.267141 | ||||||||
\(851\) | 1.93670e32 | 0.0391626 | ||||||||
\(852\) | 1.00644e33 | 0.200787 | ||||||||
\(853\) | −5.19512e33 | −1.02254 | −0.511272 | − | 0.859419i | \(-0.670825\pi\) | ||||
−0.511272 | + | 0.859419i | \(0.670825\pi\) | |||||||
\(854\) | −2.79165e33 | −0.542120 | ||||||||
\(855\) | 1.32152e33 | 0.253199 | ||||||||
\(856\) | −3.12804e33 | −0.591322 | ||||||||
\(857\) | 9.62211e33 | 1.79469 | 0.897347 | − | 0.441325i | \(-0.145491\pi\) | ||||
0.897347 | + | 0.441325i | \(0.145491\pi\) | |||||||
\(858\) | 2.92140e33 | 0.537635 | ||||||||
\(859\) | −6.92148e33 | −1.25683 | −0.628417 | − | 0.777877i | \(-0.716297\pi\) | ||||
−0.628417 | + | 0.777877i | \(0.716297\pi\) | |||||||
\(860\) | −1.45014e33 | −0.259823 | ||||||||
\(861\) | −2.95425e33 | −0.522290 | ||||||||
\(862\) | −3.50739e33 | −0.611858 | ||||||||
\(863\) | 4.39935e33 | 0.757294 | 0.378647 | − | 0.925541i | \(-0.376389\pi\) | ||||
0.378647 | + | 0.925541i | \(0.376389\pi\) | |||||||
\(864\) | −1.13283e33 | −0.192422 | ||||||||
\(865\) | 1.22305e33 | 0.205003 | ||||||||
\(866\) | −6.84795e33 | −1.13267 | ||||||||
\(867\) | −1.27206e34 | −2.07629 | ||||||||
\(868\) | 2.24838e33 | 0.362154 | ||||||||
\(869\) | −6.89772e33 | −1.09642 | ||||||||
\(870\) | −1.89003e33 | −0.296482 | ||||||||
\(871\) | −4.01535e33 | −0.621605 | ||||||||
\(872\) | −1.99582e33 | −0.304917 | ||||||||
\(873\) | −5.73208e32 | −0.0864269 | ||||||||
\(874\) | 6.95460e33 | 1.03488 | ||||||||
\(875\) | −6.44380e32 | −0.0946345 | ||||||||
\(876\) | −1.83467e33 | −0.265927 | ||||||||
\(877\) | −8.80187e33 | −1.25916 | −0.629578 | − | 0.776937i | \(-0.716772\pi\) | ||||
−0.629578 | + | 0.776937i | \(0.716772\pi\) | |||||||
\(878\) | 8.10018e33 | 1.14369 | ||||||||
\(879\) | 9.17290e33 | 1.27831 | ||||||||
\(880\) | 9.87039e32 | 0.135764 | ||||||||
\(881\) | 6.20312e33 | 0.842146 | 0.421073 | − | 0.907027i | \(-0.361654\pi\) | ||||
0.421073 | + | 0.907027i | \(0.361654\pi\) | |||||||
\(882\) | 2.18364e32 | 0.0292612 | ||||||||
\(883\) | −7.33525e32 | −0.0970213 | −0.0485106 | − | 0.998823i | \(-0.515447\pi\) | ||||
−0.0485106 | + | 0.998823i | \(0.515447\pi\) | |||||||
\(884\) | 5.60293e33 | 0.731500 | ||||||||
\(885\) | −3.00764e33 | −0.387595 | ||||||||
\(886\) | 6.96489e33 | 0.885985 | ||||||||
\(887\) | −5.08588e33 | −0.638623 | −0.319311 | − | 0.947650i | \(-0.603452\pi\) | ||||
−0.319311 | + | 0.947650i | \(0.603452\pi\) | |||||||
\(888\) | 1.00854e32 | 0.0125010 | ||||||||
\(889\) | 4.81078e33 | 0.588634 | ||||||||
\(890\) | 4.51150e33 | 0.544924 | ||||||||
\(891\) | −5.43428e33 | −0.647960 | ||||||||
\(892\) | 4.70743e33 | 0.554100 | ||||||||
\(893\) | 1.57554e34 | 1.83079 | ||||||||
\(894\) | −1.36271e33 | −0.156323 | ||||||||
\(895\) | −3.79150e33 | −0.429385 | ||||||||
\(896\) | 8.36453e32 | 0.0935189 | ||||||||
\(897\) | −5.07954e33 | −0.560675 | ||||||||
\(898\) | −6.64162e33 | −0.723763 | ||||||||
\(899\) | 7.37901e33 | 0.793892 | ||||||||
\(900\) | −3.26113e32 | −0.0346401 | ||||||||
\(901\) | 9.96481e33 | 1.04504 | ||||||||
\(902\) | 5.06337e33 | 0.524282 | ||||||||
\(903\) | −9.72215e33 | −0.993924 | ||||||||
\(904\) | 5.60076e33 | 0.565341 | ||||||||
\(905\) | 8.74148e33 | 0.871217 | ||||||||
\(906\) | 5.01447e33 | 0.493458 | ||||||||
\(907\) | 1.39867e34 | 1.35904 | 0.679521 | − | 0.733656i | \(-0.262188\pi\) | ||||
0.679521 | + | 0.733656i | \(0.262188\pi\) | |||||||
\(908\) | −5.82638e32 | −0.0558999 | ||||||||
\(909\) | −5.62989e33 | −0.533354 | ||||||||
\(910\) | 2.77012e33 | 0.259133 | ||||||||
\(911\) | −1.11628e34 | −1.03112 | −0.515561 | − | 0.856853i | \(-0.672417\pi\) | ||||
−0.515561 | + | 0.856853i | \(0.672417\pi\) | |||||||
\(912\) | 3.62164e33 | 0.330342 | ||||||||
\(913\) | −2.18394e34 | −1.96710 | ||||||||
\(914\) | 4.75194e33 | 0.422658 | ||||||||
\(915\) | 2.98277e33 | 0.261985 | ||||||||
\(916\) | −4.34134e33 | −0.376553 | ||||||||
\(917\) | −8.56407e32 | −0.0733555 | ||||||||
\(918\) | −1.71883e34 | −1.45392 | ||||||||
\(919\) | 8.24058e33 | 0.688382 | 0.344191 | − | 0.938900i | \(-0.388153\pi\) | ||||
0.344191 | + | 0.938900i | \(0.388153\pi\) | |||||||
\(920\) | −1.71620e33 | −0.141582 | ||||||||
\(921\) | 7.88743e33 | 0.642613 | ||||||||
\(922\) | 3.64538e33 | 0.293317 | ||||||||
\(923\) | −4.84113e33 | −0.384705 | ||||||||
\(924\) | 6.61738e33 | 0.519348 | ||||||||
\(925\) | 1.12848e32 | 0.00874711 | ||||||||
\(926\) | 2.38572e33 | 0.182639 | ||||||||
\(927\) | 2.41061e33 | 0.182268 | ||||||||
\(928\) | 2.74517e33 | 0.205006 | ||||||||
\(929\) | 1.03061e33 | 0.0760178 | 0.0380089 | − | 0.999277i | \(-0.487898\pi\) | ||||
0.0380089 | + | 0.999277i | \(0.487898\pi\) | |||||||
\(930\) | −2.40231e33 | −0.175015 | ||||||||
\(931\) | −2.71342e33 | −0.195252 | ||||||||
\(932\) | −4.34328e33 | −0.308699 | ||||||||
\(933\) | 1.07414e34 | 0.754086 | ||||||||
\(934\) | −9.06063e33 | −0.628303 | ||||||||
\(935\) | 1.49762e34 | 1.02582 | ||||||||
\(936\) | 1.40193e33 | 0.0948533 | ||||||||
\(937\) | −1.43845e34 | −0.961368 | −0.480684 | − | 0.876894i | \(-0.659612\pi\) | ||||
−0.480684 | + | 0.876894i | \(0.659612\pi\) | |||||||
\(938\) | −9.09532e33 | −0.600462 | ||||||||
\(939\) | −1.13066e32 | −0.00737360 | ||||||||
\(940\) | −3.88798e33 | −0.250469 | ||||||||
\(941\) | −9.09450e33 | −0.578760 | −0.289380 | − | 0.957214i | \(-0.593449\pi\) | ||||
−0.289380 | + | 0.957214i | \(0.593449\pi\) | |||||||
\(942\) | −1.31248e34 | −0.825100 | ||||||||
\(943\) | −8.80386e33 | −0.546750 | ||||||||
\(944\) | 4.36843e33 | 0.268008 | ||||||||
\(945\) | −8.49798e33 | −0.515050 | ||||||||
\(946\) | 1.66630e34 | 0.997714 | ||||||||
\(947\) | 9.97145e33 | 0.589839 | 0.294920 | − | 0.955522i | \(-0.404707\pi\) | ||||
0.294920 | + | 0.955522i | \(0.404707\pi\) | |||||||
\(948\) | 6.24556e33 | 0.364986 | ||||||||
\(949\) | 8.82502e33 | 0.509512 | ||||||||
\(950\) | 4.05233e33 | 0.231145 | ||||||||
\(951\) | −1.32995e34 | −0.749477 | ||||||||
\(952\) | 1.26914e34 | 0.706619 | ||||||||
\(953\) | −7.81126e33 | −0.429688 | −0.214844 | − | 0.976648i | \(-0.568924\pi\) | ||||
−0.214844 | + | 0.976648i | \(0.568924\pi\) | |||||||
\(954\) | 2.49332e33 | 0.135510 | ||||||||
\(955\) | −9.16159e33 | −0.491962 | ||||||||
\(956\) | −7.18149e33 | −0.381021 | ||||||||
\(957\) | 2.17177e34 | 1.13848 | ||||||||
\(958\) | −2.41146e34 | −1.24904 | ||||||||
\(959\) | 2.92133e33 | 0.149509 | ||||||||
\(960\) | −8.93717e32 | −0.0451940 | ||||||||
\(961\) | −1.06343e34 | −0.531361 | ||||||||
\(962\) | −4.85122e32 | −0.0239518 | ||||||||
\(963\) | −1.18755e34 | −0.579360 | ||||||||
\(964\) | −3.40368e33 | −0.164083 | ||||||||
\(965\) | 1.56225e34 | 0.744193 | ||||||||
\(966\) | −1.15059e34 | −0.541605 | ||||||||
\(967\) | 9.65442e33 | 0.449078 | 0.224539 | − | 0.974465i | \(-0.427912\pi\) | ||||
0.224539 | + | 0.974465i | \(0.427912\pi\) | |||||||
\(968\) | −3.65002e33 | −0.167775 | ||||||||
\(969\) | 5.49508e34 | 2.49603 | ||||||||
\(970\) | −1.75770e33 | −0.0788987 | ||||||||
\(971\) | −2.59685e34 | −1.15193 | −0.575965 | − | 0.817474i | \(-0.695374\pi\) | ||||
−0.575965 | + | 0.817474i | \(0.695374\pi\) | |||||||
\(972\) | −7.49496e33 | −0.328554 | ||||||||
\(973\) | 1.73511e34 | 0.751673 | ||||||||
\(974\) | −1.78575e34 | −0.764529 | ||||||||
\(975\) | −2.95976e33 | −0.125229 | ||||||||
\(976\) | −4.33230e33 | −0.181153 | ||||||||
\(977\) | −7.90048e33 | −0.326487 | −0.163244 | − | 0.986586i | \(-0.552196\pi\) | ||||
−0.163244 | + | 0.986586i | \(0.552196\pi\) | |||||||
\(978\) | −1.68386e33 | −0.0687714 | ||||||||
\(979\) | −5.18400e34 | −2.09249 | ||||||||
\(980\) | 6.69595e32 | 0.0267124 | ||||||||
\(981\) | −7.57703e33 | −0.298748 | ||||||||
\(982\) | −6.78769e33 | −0.264508 | ||||||||
\(983\) | 9.20116e33 | 0.354387 | 0.177193 | − | 0.984176i | \(-0.443298\pi\) | ||||
0.177193 | + | 0.984176i | \(0.443298\pi\) | |||||||
\(984\) | −4.58464e33 | −0.174527 | ||||||||
\(985\) | 1.13483e34 | 0.426986 | ||||||||
\(986\) | 4.16522e34 | 1.54901 | ||||||||
\(987\) | −2.60661e34 | −0.958140 | ||||||||
\(988\) | −1.74206e34 | −0.632932 | ||||||||
\(989\) | −2.89726e34 | −1.04047 | ||||||||
\(990\) | 3.74725e33 | 0.133017 | ||||||||
\(991\) | 2.65253e34 | 0.930708 | 0.465354 | − | 0.885125i | \(-0.345927\pi\) | ||||
0.465354 | + | 0.885125i | \(0.345927\pi\) | |||||||
\(992\) | 3.48922e33 | 0.121016 | ||||||||
\(993\) | −7.54667e33 | −0.258725 | ||||||||
\(994\) | −1.09658e34 | −0.371619 | ||||||||
\(995\) | −7.03861e33 | −0.235788 | ||||||||
\(996\) | 1.97746e34 | 0.654824 | ||||||||
\(997\) | 4.79679e34 | 1.57021 | 0.785103 | − | 0.619365i | \(-0.212610\pi\) | ||||
0.785103 | + | 0.619365i | \(0.212610\pi\) | |||||||
\(998\) | 9.03621e33 | 0.292405 | ||||||||
\(999\) | 1.48822e33 | 0.0476063 |
(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 | 10.24.a.a.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 50.24.b.d.49.2 | 4 | |||
5.3 | odd | 4 | 50.24.b.d.49.3 | 4 | |||
5.4 | even | 2 | 50.24.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.24.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.24.a.d.1.2 | 2 | 5.4 | even | 2 | |||
50.24.b.d.49.2 | 4 | 5.2 | odd | 4 | |||
50.24.b.d.49.3 | 4 | 5.3 | odd | 4 |