Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,34,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, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
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: | \(68.9828288810\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3937184160 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-62746.5\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 65536.0 | 0.707107 | ||||||||
\(3\) | −3.44083e6 | −0.0461491 | −0.0230745 | − | 0.999734i | \(-0.507346\pi\) | ||||
−0.0230745 | + | 0.999734i | \(0.507346\pi\) | |||||||
\(4\) | 4.29497e9 | 0.500000 | ||||||||
\(5\) | 1.52588e11 | 0.447214 | ||||||||
\(6\) | −2.25498e11 | −0.0326323 | ||||||||
\(7\) | 9.65954e13 | 1.09860 | 0.549299 | − | 0.835626i | \(-0.314895\pi\) | ||||
0.549299 | + | 0.835626i | \(0.314895\pi\) | |||||||
\(8\) | 2.81475e14 | 0.353553 | ||||||||
\(9\) | −5.54722e15 | −0.997870 | ||||||||
\(10\) | 1.00000e16 | 0.316228 | ||||||||
\(11\) | −1.25630e17 | −0.824356 | −0.412178 | − | 0.911103i | \(-0.635232\pi\) | ||||
−0.412178 | + | 0.911103i | \(0.635232\pi\) | |||||||
\(12\) | −1.47783e16 | −0.0230745 | ||||||||
\(13\) | −3.83776e18 | −1.59960 | −0.799801 | − | 0.600265i | \(-0.795062\pi\) | ||||
−0.799801 | + | 0.600265i | \(0.795062\pi\) | |||||||
\(14\) | 6.33048e18 | 0.776826 | ||||||||
\(15\) | −5.25030e17 | −0.0206385 | ||||||||
\(16\) | 1.84467e19 | 0.250000 | ||||||||
\(17\) | −1.12561e19 | −0.0561023 | −0.0280512 | − | 0.999606i | \(-0.508930\pi\) | ||||
−0.0280512 | + | 0.999606i | \(0.508930\pi\) | |||||||
\(18\) | −3.63543e20 | −0.705601 | ||||||||
\(19\) | −1.21644e21 | −0.967512 | −0.483756 | − | 0.875203i | \(-0.660728\pi\) | ||||
−0.483756 | + | 0.875203i | \(0.660728\pi\) | |||||||
\(20\) | 6.55360e20 | 0.223607 | ||||||||
\(21\) | −3.32369e20 | −0.0506993 | ||||||||
\(22\) | −8.23330e21 | −0.582907 | ||||||||
\(23\) | 3.30661e22 | 1.12428 | 0.562139 | − | 0.827043i | \(-0.309979\pi\) | ||||
0.562139 | + | 0.827043i | \(0.309979\pi\) | |||||||
\(24\) | −9.68509e20 | −0.0163162 | ||||||||
\(25\) | 2.32831e22 | 0.200000 | ||||||||
\(26\) | −2.51511e23 | −1.13109 | ||||||||
\(27\) | 3.82149e22 | 0.0921999 | ||||||||
\(28\) | 4.14874e23 | 0.549299 | ||||||||
\(29\) | 5.37492e23 | 0.398846 | 0.199423 | − | 0.979914i | \(-0.436093\pi\) | ||||
0.199423 | + | 0.979914i | \(0.436093\pi\) | |||||||
\(30\) | −3.44083e22 | −0.0145936 | ||||||||
\(31\) | −4.22167e24 | −1.04236 | −0.521178 | − | 0.853448i | \(-0.674507\pi\) | ||||
−0.521178 | + | 0.853448i | \(0.674507\pi\) | |||||||
\(32\) | 1.20893e24 | 0.176777 | ||||||||
\(33\) | 4.32273e23 | 0.0380432 | ||||||||
\(34\) | −7.37680e23 | −0.0396704 | ||||||||
\(35\) | 1.47393e25 | 0.491308 | ||||||||
\(36\) | −2.38251e25 | −0.498935 | ||||||||
\(37\) | −1.37889e26 | −1.83739 | −0.918696 | − | 0.394966i | \(-0.870756\pi\) | ||||
−0.918696 | + | 0.394966i | \(0.870756\pi\) | |||||||
\(38\) | −7.97206e25 | −0.684134 | ||||||||
\(39\) | 1.32051e25 | 0.0738202 | ||||||||
\(40\) | 4.29497e25 | 0.158114 | ||||||||
\(41\) | 4.39352e26 | 1.07617 | 0.538083 | − | 0.842892i | \(-0.319149\pi\) | ||||
0.538083 | + | 0.842892i | \(0.319149\pi\) | |||||||
\(42\) | −2.17821e25 | −0.0358498 | ||||||||
\(43\) | −1.20456e27 | −1.34462 | −0.672312 | − | 0.740268i | \(-0.734699\pi\) | ||||
−0.672312 | + | 0.740268i | \(0.734699\pi\) | |||||||
\(44\) | −5.39577e26 | −0.412178 | ||||||||
\(45\) | −8.46439e26 | −0.446261 | ||||||||
\(46\) | 2.16702e27 | 0.794984 | ||||||||
\(47\) | −3.56629e27 | −0.917493 | −0.458746 | − | 0.888567i | \(-0.651701\pi\) | ||||
−0.458746 | + | 0.888567i | \(0.651701\pi\) | |||||||
\(48\) | −6.34722e25 | −0.0115373 | ||||||||
\(49\) | 1.59968e27 | 0.206918 | ||||||||
\(50\) | 1.52588e27 | 0.141421 | ||||||||
\(51\) | 3.87304e25 | 0.00258907 | ||||||||
\(52\) | −1.64830e28 | −0.799801 | ||||||||
\(53\) | 3.20094e28 | 1.13429 | 0.567147 | − | 0.823617i | \(-0.308047\pi\) | ||||
0.567147 | + | 0.823617i | \(0.308047\pi\) | |||||||
\(54\) | 2.50445e27 | 0.0651952 | ||||||||
\(55\) | −1.91696e28 | −0.368663 | ||||||||
\(56\) | 2.71892e28 | 0.388413 | ||||||||
\(57\) | 4.18557e27 | 0.0446498 | ||||||||
\(58\) | 3.52251e28 | 0.282027 | ||||||||
\(59\) | 2.08570e29 | 1.25949 | 0.629744 | − | 0.776803i | \(-0.283160\pi\) | ||||
0.629744 | + | 0.776803i | \(0.283160\pi\) | |||||||
\(60\) | −2.25498e27 | −0.0103192 | ||||||||
\(61\) | −1.84408e29 | −0.642448 | −0.321224 | − | 0.947003i | \(-0.604094\pi\) | ||||
−0.321224 | + | 0.947003i | \(0.604094\pi\) | |||||||
\(62\) | −2.76671e29 | −0.737057 | ||||||||
\(63\) | −5.35836e29 | −1.09626 | ||||||||
\(64\) | 7.92282e28 | 0.125000 | ||||||||
\(65\) | −5.85595e29 | −0.715364 | ||||||||
\(66\) | 2.83294e28 | 0.0269006 | ||||||||
\(67\) | −3.61772e29 | −0.268040 | −0.134020 | − | 0.990979i | \(-0.542789\pi\) | ||||
−0.134020 | + | 0.990979i | \(0.542789\pi\) | |||||||
\(68\) | −4.83446e28 | −0.0280512 | ||||||||
\(69\) | −1.13775e29 | −0.0518844 | ||||||||
\(70\) | 9.65954e29 | 0.347407 | ||||||||
\(71\) | −5.64849e30 | −1.60757 | −0.803784 | − | 0.594921i | \(-0.797183\pi\) | ||||
−0.803784 | + | 0.594921i | \(0.797183\pi\) | |||||||
\(72\) | −1.56140e30 | −0.352800 | ||||||||
\(73\) | −6.52836e29 | −0.117484 | −0.0587418 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587418 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(74\) | −9.03671e30 | −1.29923 | ||||||||
\(75\) | −8.01132e28 | −0.00922982 | ||||||||
\(76\) | −5.22457e30 | −0.483756 | ||||||||
\(77\) | −1.21353e31 | −0.905636 | ||||||||
\(78\) | 8.65408e29 | 0.0521988 | ||||||||
\(79\) | −2.61534e31 | −1.27844 | −0.639221 | − | 0.769023i | \(-0.720743\pi\) | ||||
−0.639221 | + | 0.769023i | \(0.720743\pi\) | |||||||
\(80\) | 2.81475e30 | 0.111803 | ||||||||
\(81\) | 3.07058e31 | 0.993615 | ||||||||
\(82\) | 2.87934e31 | 0.760965 | ||||||||
\(83\) | −7.88667e31 | −1.70650 | −0.853248 | − | 0.521505i | \(-0.825371\pi\) | ||||
−0.853248 | + | 0.521505i | \(0.825371\pi\) | |||||||
\(84\) | −1.42751e30 | −0.0253496 | ||||||||
\(85\) | −1.71755e30 | −0.0250897 | ||||||||
\(86\) | −7.89424e31 | −0.950792 | ||||||||
\(87\) | −1.84942e30 | −0.0184064 | ||||||||
\(88\) | −3.53617e31 | −0.291454 | ||||||||
\(89\) | 6.51043e31 | 0.445323 | 0.222661 | − | 0.974896i | \(-0.428526\pi\) | ||||
0.222661 | + | 0.974896i | \(0.428526\pi\) | |||||||
\(90\) | −5.54722e31 | −0.315554 | ||||||||
\(91\) | −3.70710e32 | −1.75732 | ||||||||
\(92\) | 1.42018e32 | 0.562139 | ||||||||
\(93\) | 1.45261e31 | 0.0481038 | ||||||||
\(94\) | −2.33721e32 | −0.648765 | ||||||||
\(95\) | −1.85614e32 | −0.432685 | ||||||||
\(96\) | −4.15971e30 | −0.00815808 | ||||||||
\(97\) | −7.62730e32 | −1.26077 | −0.630387 | − | 0.776281i | \(-0.717104\pi\) | ||||
−0.630387 | + | 0.776281i | \(0.717104\pi\) | |||||||
\(98\) | 1.04837e32 | 0.146313 | ||||||||
\(99\) | 6.96898e32 | 0.822600 | ||||||||
\(100\) | 1.00000e32 | 0.100000 | ||||||||
\(101\) | −3.89030e32 | −0.330127 | −0.165063 | − | 0.986283i | \(-0.552783\pi\) | ||||
−0.165063 | + | 0.986283i | \(0.552783\pi\) | |||||||
\(102\) | 2.53824e30 | 0.00183075 | ||||||||
\(103\) | 1.75553e33 | 1.07794 | 0.538970 | − | 0.842325i | \(-0.318814\pi\) | ||||
0.538970 | + | 0.842325i | \(0.318814\pi\) | |||||||
\(104\) | −1.08023e33 | −0.565545 | ||||||||
\(105\) | −5.07155e31 | −0.0226734 | ||||||||
\(106\) | 2.09777e33 | 0.802067 | ||||||||
\(107\) | 2.84461e33 | 0.931517 | 0.465759 | − | 0.884912i | \(-0.345781\pi\) | ||||
0.465759 | + | 0.884912i | \(0.345781\pi\) | |||||||
\(108\) | 1.64132e32 | 0.0460999 | ||||||||
\(109\) | 7.03753e33 | 1.69779 | 0.848894 | − | 0.528564i | \(-0.177269\pi\) | ||||
0.848894 | + | 0.528564i | \(0.177269\pi\) | |||||||
\(110\) | −1.25630e33 | −0.260684 | ||||||||
\(111\) | 4.74454e32 | 0.0847939 | ||||||||
\(112\) | 1.78187e33 | 0.274650 | ||||||||
\(113\) | −3.22217e33 | −0.428898 | −0.214449 | − | 0.976735i | \(-0.568796\pi\) | ||||
−0.214449 | + | 0.976735i | \(0.568796\pi\) | |||||||
\(114\) | 2.74305e32 | 0.0315722 | ||||||||
\(115\) | 5.04548e33 | 0.502792 | ||||||||
\(116\) | 2.30851e33 | 0.199423 | ||||||||
\(117\) | 2.12889e34 | 1.59620 | ||||||||
\(118\) | 1.36689e34 | 0.890593 | ||||||||
\(119\) | −1.08729e33 | −0.0616339 | ||||||||
\(120\) | −1.47783e32 | −0.00729681 | ||||||||
\(121\) | −7.44222e33 | −0.320438 | ||||||||
\(122\) | −1.20854e34 | −0.454279 | ||||||||
\(123\) | −1.51174e33 | −0.0496641 | ||||||||
\(124\) | −1.81319e34 | −0.521178 | ||||||||
\(125\) | 3.55271e33 | 0.0894427 | ||||||||
\(126\) | −3.51166e34 | −0.775172 | ||||||||
\(127\) | −2.14069e33 | −0.0414756 | −0.0207378 | − | 0.999785i | \(-0.506602\pi\) | ||||
−0.0207378 | + | 0.999785i | \(0.506602\pi\) | |||||||
\(128\) | 5.19230e33 | 0.0883883 | ||||||||
\(129\) | 4.14471e33 | 0.0620531 | ||||||||
\(130\) | −3.83776e34 | −0.505839 | ||||||||
\(131\) | 7.71149e34 | 0.895699 | 0.447850 | − | 0.894109i | \(-0.352190\pi\) | ||||
0.447850 | + | 0.894109i | \(0.352190\pi\) | |||||||
\(132\) | 1.85660e33 | 0.0190216 | ||||||||
\(133\) | −1.17503e35 | −1.06291 | ||||||||
\(134\) | −2.37091e34 | −0.189533 | ||||||||
\(135\) | 5.83113e33 | 0.0412330 | ||||||||
\(136\) | −3.16831e33 | −0.0198352 | ||||||||
\(137\) | −2.86481e35 | −1.58930 | −0.794650 | − | 0.607068i | \(-0.792345\pi\) | ||||
−0.794650 | + | 0.607068i | \(0.792345\pi\) | |||||||
\(138\) | −7.45635e33 | −0.0366878 | ||||||||
\(139\) | 4.17053e34 | 0.182158 | 0.0910788 | − | 0.995844i | \(-0.470968\pi\) | ||||
0.0910788 | + | 0.995844i | \(0.470968\pi\) | |||||||
\(140\) | 6.33048e34 | 0.245654 | ||||||||
\(141\) | 1.22710e34 | 0.0423414 | ||||||||
\(142\) | −3.70179e35 | −1.13672 | ||||||||
\(143\) | 4.82138e35 | 1.31864 | ||||||||
\(144\) | −1.02328e35 | −0.249468 | ||||||||
\(145\) | 8.20148e34 | 0.178369 | ||||||||
\(146\) | −4.27843e34 | −0.0830734 | ||||||||
\(147\) | −5.50424e33 | −0.00954907 | ||||||||
\(148\) | −5.92230e35 | −0.918696 | ||||||||
\(149\) | 2.17706e35 | 0.302201 | 0.151101 | − | 0.988518i | \(-0.451718\pi\) | ||||
0.151101 | + | 0.988518i | \(0.451718\pi\) | |||||||
\(150\) | −5.25030e33 | −0.00652646 | ||||||||
\(151\) | −3.80622e35 | −0.424008 | −0.212004 | − | 0.977269i | \(-0.567999\pi\) | ||||
−0.212004 | + | 0.977269i | \(0.567999\pi\) | |||||||
\(152\) | −3.42398e35 | −0.342067 | ||||||||
\(153\) | 6.24401e34 | 0.0559829 | ||||||||
\(154\) | −7.95299e35 | −0.640381 | ||||||||
\(155\) | −6.44175e35 | −0.466156 | ||||||||
\(156\) | 5.67154e34 | 0.0369101 | ||||||||
\(157\) | 1.98603e36 | 1.16316 | 0.581582 | − | 0.813488i | \(-0.302434\pi\) | ||||
0.581582 | + | 0.813488i | \(0.302434\pi\) | |||||||
\(158\) | −1.71399e36 | −0.903995 | ||||||||
\(159\) | −1.10139e35 | −0.0523466 | ||||||||
\(160\) | 1.84467e35 | 0.0790569 | ||||||||
\(161\) | 3.19403e36 | 1.23513 | ||||||||
\(162\) | 2.01234e36 | 0.702592 | ||||||||
\(163\) | 4.49451e36 | 1.41771 | 0.708854 | − | 0.705355i | \(-0.249212\pi\) | ||||
0.708854 | + | 0.705355i | \(0.249212\pi\) | |||||||
\(164\) | 1.88700e36 | 0.538083 | ||||||||
\(165\) | 6.59596e34 | 0.0170135 | ||||||||
\(166\) | −5.16861e36 | −1.20668 | ||||||||
\(167\) | −1.58924e36 | −0.336023 | −0.168012 | − | 0.985785i | \(-0.553735\pi\) | ||||
−0.168012 | + | 0.985785i | \(0.553735\pi\) | |||||||
\(168\) | −9.35535e34 | −0.0179249 | ||||||||
\(169\) | 8.97224e36 | 1.55873 | ||||||||
\(170\) | −1.12561e35 | −0.0177411 | ||||||||
\(171\) | 6.74786e36 | 0.965452 | ||||||||
\(172\) | −5.17357e36 | −0.672312 | ||||||||
\(173\) | 6.81608e36 | 0.804960 | 0.402480 | − | 0.915429i | \(-0.368148\pi\) | ||||
0.402480 | + | 0.915429i | \(0.368148\pi\) | |||||||
\(174\) | −1.21204e35 | −0.0130153 | ||||||||
\(175\) | 2.24904e36 | 0.219720 | ||||||||
\(176\) | −2.31747e36 | −0.206089 | ||||||||
\(177\) | −7.17655e35 | −0.0581242 | ||||||||
\(178\) | 4.26668e36 | 0.314891 | ||||||||
\(179\) | 7.04020e36 | 0.473707 | 0.236853 | − | 0.971545i | \(-0.423884\pi\) | ||||
0.236853 | + | 0.971545i | \(0.423884\pi\) | |||||||
\(180\) | −3.63543e36 | −0.223131 | ||||||||
\(181\) | 1.81472e36 | 0.101651 | 0.0508257 | − | 0.998708i | \(-0.483815\pi\) | ||||
0.0508257 | + | 0.998708i | \(0.483815\pi\) | |||||||
\(182\) | −2.42948e37 | −1.24261 | ||||||||
\(183\) | 6.34518e35 | 0.0296484 | ||||||||
\(184\) | 9.30728e36 | 0.397492 | ||||||||
\(185\) | −2.10402e37 | −0.821707 | ||||||||
\(186\) | 9.51980e35 | 0.0340145 | ||||||||
\(187\) | 1.41411e36 | 0.0462483 | ||||||||
\(188\) | −1.53171e37 | −0.458746 | ||||||||
\(189\) | 3.69138e36 | 0.101291 | ||||||||
\(190\) | −1.21644e37 | −0.305954 | ||||||||
\(191\) | −5.47196e37 | −1.26209 | −0.631047 | − | 0.775744i | \(-0.717375\pi\) | ||||
−0.631047 | + | 0.775744i | \(0.717375\pi\) | |||||||
\(192\) | −2.72611e35 | −0.00576863 | ||||||||
\(193\) | −4.57793e37 | −0.889148 | −0.444574 | − | 0.895742i | \(-0.646645\pi\) | ||||
−0.444574 | + | 0.895742i | \(0.646645\pi\) | |||||||
\(194\) | −4.99863e37 | −0.891502 | ||||||||
\(195\) | 2.01494e36 | 0.0330134 | ||||||||
\(196\) | 6.87058e36 | 0.103459 | ||||||||
\(197\) | −7.48669e37 | −1.03657 | −0.518284 | − | 0.855209i | \(-0.673429\pi\) | ||||
−0.518284 | + | 0.855209i | \(0.673429\pi\) | |||||||
\(198\) | 4.56719e37 | 0.581666 | ||||||||
\(199\) | 3.94421e37 | 0.462258 | 0.231129 | − | 0.972923i | \(-0.425758\pi\) | ||||
0.231129 | + | 0.972923i | \(0.425758\pi\) | |||||||
\(200\) | 6.55360e36 | 0.0707107 | ||||||||
\(201\) | 1.24480e36 | 0.0123698 | ||||||||
\(202\) | −2.54955e37 | −0.233435 | ||||||||
\(203\) | 5.19193e37 | 0.438171 | ||||||||
\(204\) | 1.66346e35 | 0.00129454 | ||||||||
\(205\) | 6.70399e37 | 0.481276 | ||||||||
\(206\) | 1.15051e38 | 0.762219 | ||||||||
\(207\) | −1.83425e38 | −1.12188 | ||||||||
\(208\) | −7.07941e37 | −0.399901 | ||||||||
\(209\) | 1.52822e38 | 0.797574 | ||||||||
\(210\) | −3.32369e36 | −0.0160325 | ||||||||
\(211\) | 2.10514e38 | 0.938905 | 0.469452 | − | 0.882958i | \(-0.344451\pi\) | ||||
0.469452 | + | 0.882958i | \(0.344451\pi\) | |||||||
\(212\) | 1.37479e38 | 0.567147 | ||||||||
\(213\) | 1.94355e37 | 0.0741878 | ||||||||
\(214\) | 1.86425e38 | 0.658682 | ||||||||
\(215\) | −1.83802e38 | −0.601334 | ||||||||
\(216\) | 1.07565e37 | 0.0325976 | ||||||||
\(217\) | −4.07794e38 | −1.14513 | ||||||||
\(218\) | 4.61212e38 | 1.20052 | ||||||||
\(219\) | 2.24630e36 | 0.00542176 | ||||||||
\(220\) | −8.23330e37 | −0.184332 | ||||||||
\(221\) | 4.31982e37 | 0.0897415 | ||||||||
\(222\) | 3.10938e37 | 0.0599584 | ||||||||
\(223\) | 2.49660e38 | 0.447012 | 0.223506 | − | 0.974703i | \(-0.428250\pi\) | ||||
0.223506 | + | 0.974703i | \(0.428250\pi\) | |||||||
\(224\) | 1.16777e38 | 0.194207 | ||||||||
\(225\) | −1.29156e38 | −0.199574 | ||||||||
\(226\) | −2.11168e38 | −0.303276 | ||||||||
\(227\) | −3.49100e38 | −0.466147 | −0.233073 | − | 0.972459i | \(-0.574878\pi\) | ||||
−0.233073 | + | 0.972459i | \(0.574878\pi\) | |||||||
\(228\) | 1.79769e37 | 0.0223249 | ||||||||
\(229\) | 8.78358e38 | 1.01481 | 0.507406 | − | 0.861707i | \(-0.330604\pi\) | ||||
0.507406 | + | 0.861707i | \(0.330604\pi\) | |||||||
\(230\) | 3.30661e38 | 0.355528 | ||||||||
\(231\) | 4.17555e37 | 0.0417942 | ||||||||
\(232\) | 1.51291e38 | 0.141013 | ||||||||
\(233\) | 1.89180e38 | 0.164249 | 0.0821245 | − | 0.996622i | \(-0.473829\pi\) | ||||
0.0821245 | + | 0.996622i | \(0.473829\pi\) | |||||||
\(234\) | 1.39519e39 | 1.12868 | ||||||||
\(235\) | −5.44173e38 | −0.410315 | ||||||||
\(236\) | 8.95802e38 | 0.629744 | ||||||||
\(237\) | 8.99895e37 | 0.0589989 | ||||||||
\(238\) | −7.12565e37 | −0.0435818 | ||||||||
\(239\) | −2.46744e39 | −1.40825 | −0.704126 | − | 0.710075i | \(-0.748661\pi\) | ||||
−0.704126 | + | 0.710075i | \(0.748661\pi\) | |||||||
\(240\) | −9.68509e36 | −0.00515962 | ||||||||
\(241\) | −3.30287e39 | −1.64289 | −0.821447 | − | 0.570284i | \(-0.806833\pi\) | ||||
−0.821447 | + | 0.570284i | \(0.806833\pi\) | |||||||
\(242\) | −4.87733e38 | −0.226584 | ||||||||
\(243\) | −3.18093e38 | −0.138054 | ||||||||
\(244\) | −7.92027e38 | −0.321224 | ||||||||
\(245\) | 2.44092e38 | 0.0925365 | ||||||||
\(246\) | −9.90733e37 | −0.0351178 | ||||||||
\(247\) | 4.66840e39 | 1.54764 | ||||||||
\(248\) | −1.18829e39 | −0.368529 | ||||||||
\(249\) | 2.71367e38 | 0.0787532 | ||||||||
\(250\) | 2.32831e38 | 0.0632456 | ||||||||
\(251\) | 2.80676e39 | 0.713820 | 0.356910 | − | 0.934139i | \(-0.383830\pi\) | ||||
0.356910 | + | 0.934139i | \(0.383830\pi\) | |||||||
\(252\) | −2.30140e39 | −0.548129 | ||||||||
\(253\) | −4.15410e39 | −0.926804 | ||||||||
\(254\) | −1.40292e38 | −0.0293277 | ||||||||
\(255\) | 5.90979e36 | 0.00115787 | ||||||||
\(256\) | 3.40282e38 | 0.0625000 | ||||||||
\(257\) | −7.29261e39 | −1.25599 | −0.627996 | − | 0.778217i | \(-0.716124\pi\) | ||||
−0.627996 | + | 0.778217i | \(0.716124\pi\) | |||||||
\(258\) | 2.71628e38 | 0.0438782 | ||||||||
\(259\) | −1.33195e40 | −2.01856 | ||||||||
\(260\) | −2.51511e39 | −0.357682 | ||||||||
\(261\) | −2.98159e39 | −0.397996 | ||||||||
\(262\) | 5.05380e39 | 0.633355 | ||||||||
\(263\) | 8.76662e39 | 1.03172 | 0.515861 | − | 0.856673i | \(-0.327472\pi\) | ||||
0.515861 | + | 0.856673i | \(0.327472\pi\) | |||||||
\(264\) | 1.21674e38 | 0.0134503 | ||||||||
\(265\) | 4.88425e39 | 0.507272 | ||||||||
\(266\) | −7.70065e39 | −0.751589 | ||||||||
\(267\) | −2.24013e38 | −0.0205512 | ||||||||
\(268\) | −1.55380e39 | −0.134020 | ||||||||
\(269\) | 2.09117e40 | 1.69620 | 0.848098 | − | 0.529839i | \(-0.177748\pi\) | ||||
0.848098 | + | 0.529839i | \(0.177748\pi\) | |||||||
\(270\) | 3.82149e38 | 0.0291562 | ||||||||
\(271\) | 1.15067e39 | 0.0825958 | 0.0412979 | − | 0.999147i | \(-0.486851\pi\) | ||||
0.0412979 | + | 0.999147i | \(0.486851\pi\) | |||||||
\(272\) | −2.07639e38 | −0.0140256 | ||||||||
\(273\) | 1.27555e39 | 0.0810987 | ||||||||
\(274\) | −1.87748e40 | −1.12380 | ||||||||
\(275\) | −2.92506e39 | −0.164871 | ||||||||
\(276\) | −4.88660e38 | −0.0259422 | ||||||||
\(277\) | 2.78662e40 | 1.39367 | 0.696837 | − | 0.717229i | \(-0.254590\pi\) | ||||
0.696837 | + | 0.717229i | \(0.254590\pi\) | |||||||
\(278\) | 2.73320e39 | 0.128805 | ||||||||
\(279\) | 2.34185e40 | 1.04014 | ||||||||
\(280\) | 4.14874e39 | 0.173704 | ||||||||
\(281\) | 4.93528e40 | 1.94831 | 0.974153 | − | 0.225888i | \(-0.0725283\pi\) | ||||
0.974153 | + | 0.225888i | \(0.0725283\pi\) | |||||||
\(282\) | 8.04194e38 | 0.0299399 | ||||||||
\(283\) | −1.57701e40 | −0.553806 | −0.276903 | − | 0.960898i | \(-0.589308\pi\) | ||||
−0.276903 | + | 0.960898i | \(0.589308\pi\) | |||||||
\(284\) | −2.42601e40 | −0.803784 | ||||||||
\(285\) | 6.38667e38 | 0.0199680 | ||||||||
\(286\) | 3.15974e40 | 0.932420 | ||||||||
\(287\) | 4.24394e40 | 1.18227 | ||||||||
\(288\) | −6.70618e39 | −0.176400 | ||||||||
\(289\) | −4.01278e40 | −0.996853 | ||||||||
\(290\) | 5.37492e39 | 0.126126 | ||||||||
\(291\) | 2.62443e39 | 0.0581836 | ||||||||
\(292\) | −2.80391e39 | −0.0587418 | ||||||||
\(293\) | 3.85942e40 | 0.764199 | 0.382100 | − | 0.924121i | \(-0.375201\pi\) | ||||
0.382100 | + | 0.924121i | \(0.375201\pi\) | |||||||
\(294\) | −3.60726e38 | −0.00675221 | ||||||||
\(295\) | 3.18253e40 | 0.563260 | ||||||||
\(296\) | −3.88124e40 | −0.649616 | ||||||||
\(297\) | −4.80094e39 | −0.0760055 | ||||||||
\(298\) | 1.42676e40 | 0.213689 | ||||||||
\(299\) | −1.26900e41 | −1.79840 | ||||||||
\(300\) | −3.44083e38 | −0.00461491 | ||||||||
\(301\) | −1.16355e41 | −1.47720 | ||||||||
\(302\) | −2.49444e40 | −0.299819 | ||||||||
\(303\) | 1.33859e39 | 0.0152351 | ||||||||
\(304\) | −2.24394e40 | −0.241878 | ||||||||
\(305\) | −2.81385e40 | −0.287311 | ||||||||
\(306\) | 4.09208e39 | 0.0395859 | ||||||||
\(307\) | 8.29043e40 | 0.759965 | 0.379983 | − | 0.924994i | \(-0.375930\pi\) | ||||
0.379983 | + | 0.924994i | \(0.375930\pi\) | |||||||
\(308\) | −5.21207e40 | −0.452818 | ||||||||
\(309\) | −6.04050e39 | −0.0497460 | ||||||||
\(310\) | −4.22167e40 | −0.329622 | ||||||||
\(311\) | 1.68520e40 | 0.124769 | 0.0623844 | − | 0.998052i | \(-0.480130\pi\) | ||||
0.0623844 | + | 0.998052i | \(0.480130\pi\) | |||||||
\(312\) | 3.71690e39 | 0.0260994 | ||||||||
\(313\) | −5.51347e39 | −0.0367235 | −0.0183617 | − | 0.999831i | \(-0.505845\pi\) | ||||
−0.0183617 | + | 0.999831i | \(0.505845\pi\) | |||||||
\(314\) | 1.30156e41 | 0.822482 | ||||||||
\(315\) | −8.17621e40 | −0.490262 | ||||||||
\(316\) | −1.12328e41 | −0.639221 | ||||||||
\(317\) | −2.09450e41 | −1.13136 | −0.565682 | − | 0.824624i | \(-0.691387\pi\) | ||||
−0.565682 | + | 0.824624i | \(0.691387\pi\) | |||||||
\(318\) | −7.21807e39 | −0.0370147 | ||||||||
\(319\) | −6.75252e40 | −0.328791 | ||||||||
\(320\) | 1.20893e40 | 0.0559017 | ||||||||
\(321\) | −9.78784e39 | −0.0429887 | ||||||||
\(322\) | 2.09324e41 | 0.873368 | ||||||||
\(323\) | 1.36924e40 | 0.0542797 | ||||||||
\(324\) | 1.31881e41 | 0.496808 | ||||||||
\(325\) | −8.93547e40 | −0.319921 | ||||||||
\(326\) | 2.94552e41 | 1.00247 | ||||||||
\(327\) | −2.42150e40 | −0.0783513 | ||||||||
\(328\) | 1.23667e41 | 0.380482 | ||||||||
\(329\) | −3.44488e41 | −1.00796 | ||||||||
\(330\) | 4.32273e39 | 0.0120303 | ||||||||
\(331\) | 1.39181e41 | 0.368485 | 0.184242 | − | 0.982881i | \(-0.441017\pi\) | ||||
0.184242 | + | 0.982881i | \(0.441017\pi\) | |||||||
\(332\) | −3.38730e41 | −0.853248 | ||||||||
\(333\) | 7.64902e41 | 1.83348 | ||||||||
\(334\) | −1.04153e41 | −0.237604 | ||||||||
\(335\) | −5.52020e40 | −0.119871 | ||||||||
\(336\) | −6.13112e39 | −0.0126748 | ||||||||
\(337\) | −4.64639e41 | −0.914582 | −0.457291 | − | 0.889317i | \(-0.651180\pi\) | ||||
−0.457291 | + | 0.889317i | \(0.651180\pi\) | |||||||
\(338\) | 5.88005e41 | 1.10219 | ||||||||
\(339\) | 1.10869e40 | 0.0197932 | ||||||||
\(340\) | −7.37680e39 | −0.0125449 | ||||||||
\(341\) | 5.30369e41 | 0.859272 | ||||||||
\(342\) | 4.42228e41 | 0.682677 | ||||||||
\(343\) | −5.92257e41 | −0.871279 | ||||||||
\(344\) | −3.39055e41 | −0.475396 | ||||||||
\(345\) | −1.73607e40 | −0.0232034 | ||||||||
\(346\) | 4.46699e41 | 0.569192 | ||||||||
\(347\) | 3.74401e41 | 0.454884 | 0.227442 | − | 0.973792i | \(-0.426964\pi\) | ||||
0.227442 | + | 0.973792i | \(0.426964\pi\) | |||||||
\(348\) | −7.94320e39 | −0.00920318 | ||||||||
\(349\) | −3.17132e41 | −0.350446 | −0.175223 | − | 0.984529i | \(-0.556065\pi\) | ||||
−0.175223 | + | 0.984529i | \(0.556065\pi\) | |||||||
\(350\) | 1.47393e41 | 0.155365 | ||||||||
\(351\) | −1.46659e41 | −0.147483 | ||||||||
\(352\) | −1.51878e41 | −0.145727 | ||||||||
\(353\) | 1.29547e42 | 1.18616 | 0.593080 | − | 0.805144i | \(-0.297912\pi\) | ||||
0.593080 | + | 0.805144i | \(0.297912\pi\) | |||||||
\(354\) | −4.70323e40 | −0.0411000 | ||||||||
\(355\) | −8.61891e41 | −0.718926 | ||||||||
\(356\) | 2.79621e41 | 0.222661 | ||||||||
\(357\) | 3.74118e39 | 0.00284435 | ||||||||
\(358\) | 4.61386e41 | 0.334961 | ||||||||
\(359\) | 1.19616e42 | 0.829338 | 0.414669 | − | 0.909972i | \(-0.363897\pi\) | ||||
0.414669 | + | 0.909972i | \(0.363897\pi\) | |||||||
\(360\) | −2.38251e41 | −0.157777 | ||||||||
\(361\) | −1.01043e41 | −0.0639202 | ||||||||
\(362\) | 1.18930e41 | 0.0718784 | ||||||||
\(363\) | 2.56074e40 | 0.0147879 | ||||||||
\(364\) | −1.59219e42 | −0.878660 | ||||||||
\(365\) | −9.96149e40 | −0.0525402 | ||||||||
\(366\) | 4.15838e40 | 0.0209646 | ||||||||
\(367\) | −2.24871e42 | −1.08378 | −0.541892 | − | 0.840448i | \(-0.682292\pi\) | ||||
−0.541892 | + | 0.840448i | \(0.682292\pi\) | |||||||
\(368\) | 6.09962e41 | 0.281069 | ||||||||
\(369\) | −2.43719e42 | −1.07387 | ||||||||
\(370\) | −1.37889e42 | −0.581034 | ||||||||
\(371\) | 3.09196e42 | 1.24613 | ||||||||
\(372\) | 6.23890e40 | 0.0240519 | ||||||||
\(373\) | 4.82851e42 | 1.78081 | 0.890404 | − | 0.455171i | \(-0.150422\pi\) | ||||
0.890404 | + | 0.455171i | \(0.150422\pi\) | |||||||
\(374\) | 9.26749e40 | 0.0327025 | ||||||||
\(375\) | −1.22243e40 | −0.00412770 | ||||||||
\(376\) | −1.00382e42 | −0.324383 | ||||||||
\(377\) | −2.06276e42 | −0.637995 | ||||||||
\(378\) | 2.41918e41 | 0.0716233 | ||||||||
\(379\) | −4.26076e42 | −1.20765 | −0.603823 | − | 0.797118i | \(-0.706357\pi\) | ||||
−0.603823 | + | 0.797118i | \(0.706357\pi\) | |||||||
\(380\) | −7.97206e41 | −0.216342 | ||||||||
\(381\) | 7.36576e39 | 0.00191406 | ||||||||
\(382\) | −3.58610e42 | −0.892436 | ||||||||
\(383\) | 8.60164e41 | 0.205023 | 0.102511 | − | 0.994732i | \(-0.467312\pi\) | ||||
0.102511 | + | 0.994732i | \(0.467312\pi\) | |||||||
\(384\) | −1.78658e40 | −0.00407904 | ||||||||
\(385\) | −1.85170e42 | −0.405013 | ||||||||
\(386\) | −3.00020e42 | −0.628722 | ||||||||
\(387\) | 6.68199e42 | 1.34176 | ||||||||
\(388\) | −3.27590e42 | −0.630387 | ||||||||
\(389\) | −1.00931e43 | −1.86148 | −0.930739 | − | 0.365685i | \(-0.880835\pi\) | ||||
−0.930739 | + | 0.365685i | \(0.880835\pi\) | |||||||
\(390\) | 1.32051e41 | 0.0233440 | ||||||||
\(391\) | −3.72195e41 | −0.0630746 | ||||||||
\(392\) | 4.50270e41 | 0.0731565 | ||||||||
\(393\) | −2.65340e41 | −0.0413357 | ||||||||
\(394\) | −4.90648e42 | −0.732964 | ||||||||
\(395\) | −3.99069e42 | −0.571737 | ||||||||
\(396\) | 2.99316e42 | 0.411300 | ||||||||
\(397\) | 8.51038e42 | 1.12177 | 0.560887 | − | 0.827892i | \(-0.310460\pi\) | ||||
0.560887 | + | 0.827892i | \(0.310460\pi\) | |||||||
\(398\) | 2.58488e42 | 0.326866 | ||||||||
\(399\) | 4.04307e41 | 0.0490522 | ||||||||
\(400\) | 4.29497e41 | 0.0500000 | ||||||||
\(401\) | 5.69759e42 | 0.636516 | 0.318258 | − | 0.948004i | \(-0.396902\pi\) | ||||
0.318258 | + | 0.948004i | \(0.396902\pi\) | |||||||
\(402\) | 8.15789e40 | 0.00874678 | ||||||||
\(403\) | 1.62017e43 | 1.66736 | ||||||||
\(404\) | −1.67087e42 | −0.165063 | ||||||||
\(405\) | 4.68534e42 | 0.444358 | ||||||||
\(406\) | 3.40258e42 | 0.309834 | ||||||||
\(407\) | 1.73230e43 | 1.51466 | ||||||||
\(408\) | 1.09016e40 | 0.000915375 0 | ||||||||
\(409\) | −1.52688e43 | −1.23132 | −0.615660 | − | 0.788012i | \(-0.711111\pi\) | ||||
−0.615660 | + | 0.788012i | \(0.711111\pi\) | |||||||
\(410\) | 4.39352e42 | 0.340314 | ||||||||
\(411\) | 9.85732e41 | 0.0733447 | ||||||||
\(412\) | 7.53996e42 | 0.538970 | ||||||||
\(413\) | 2.01469e43 | 1.38367 | ||||||||
\(414\) | −1.20209e43 | −0.793291 | ||||||||
\(415\) | −1.20341e43 | −0.763168 | ||||||||
\(416\) | −4.63956e42 | −0.282772 | ||||||||
\(417\) | −1.43501e41 | −0.00840640 | ||||||||
\(418\) | 1.00153e43 | 0.563970 | ||||||||
\(419\) | −2.95628e43 | −1.60035 | −0.800173 | − | 0.599769i | \(-0.795259\pi\) | ||||
−0.800173 | + | 0.599769i | \(0.795259\pi\) | |||||||
\(420\) | −2.17821e41 | −0.0113367 | ||||||||
\(421\) | 2.45835e43 | 1.23024 | 0.615119 | − | 0.788434i | \(-0.289108\pi\) | ||||
0.615119 | + | 0.788434i | \(0.289108\pi\) | |||||||
\(422\) | 1.37963e43 | 0.663906 | ||||||||
\(423\) | 1.97830e43 | 0.915539 | ||||||||
\(424\) | 9.00985e42 | 0.401034 | ||||||||
\(425\) | −2.62077e41 | −0.0112205 | ||||||||
\(426\) | 1.27373e42 | 0.0524587 | ||||||||
\(427\) | −1.78130e43 | −0.705792 | ||||||||
\(428\) | 1.22175e43 | 0.465759 | ||||||||
\(429\) | −1.65896e42 | −0.0608541 | ||||||||
\(430\) | −1.20456e43 | −0.425207 | ||||||||
\(431\) | 1.54742e43 | 0.525693 | 0.262846 | − | 0.964838i | \(-0.415339\pi\) | ||||
0.262846 | + | 0.964838i | \(0.415339\pi\) | |||||||
\(432\) | 7.04940e41 | 0.0230500 | ||||||||
\(433\) | −4.36385e43 | −1.37347 | −0.686735 | − | 0.726907i | \(-0.740957\pi\) | ||||
−0.686735 | + | 0.726907i | \(0.740957\pi\) | |||||||
\(434\) | −2.67252e43 | −0.809730 | ||||||||
\(435\) | −2.82199e41 | −0.00823158 | ||||||||
\(436\) | 3.02260e43 | 0.848894 | ||||||||
\(437\) | −4.02229e43 | −1.08775 | ||||||||
\(438\) | 1.47214e41 | 0.00383376 | ||||||||
\(439\) | −6.44930e43 | −1.61751 | −0.808757 | − | 0.588144i | \(-0.799859\pi\) | ||||
−0.808757 | + | 0.588144i | \(0.799859\pi\) | |||||||
\(440\) | −5.39577e42 | −0.130342 | ||||||||
\(441\) | −8.87379e42 | −0.206477 | ||||||||
\(442\) | 2.83104e42 | 0.0634568 | ||||||||
\(443\) | 3.04125e43 | 0.656736 | 0.328368 | − | 0.944550i | \(-0.393501\pi\) | ||||
0.328368 | + | 0.944550i | \(0.393501\pi\) | |||||||
\(444\) | 2.03776e42 | 0.0423970 | ||||||||
\(445\) | 9.93413e42 | 0.199154 | ||||||||
\(446\) | 1.63617e43 | 0.316085 | ||||||||
\(447\) | −7.49089e41 | −0.0139463 | ||||||||
\(448\) | 7.65308e42 | 0.137325 | ||||||||
\(449\) | −6.70336e43 | −1.15939 | −0.579693 | − | 0.814835i | \(-0.696827\pi\) | ||||
−0.579693 | + | 0.814835i | \(0.696827\pi\) | |||||||
\(450\) | −8.46439e42 | −0.141120 | ||||||||
\(451\) | −5.51959e43 | −0.887144 | ||||||||
\(452\) | −1.38391e43 | −0.214449 | ||||||||
\(453\) | 1.30966e42 | 0.0195676 | ||||||||
\(454\) | −2.28786e43 | −0.329616 | ||||||||
\(455\) | −5.65658e43 | −0.785898 | ||||||||
\(456\) | 1.17813e42 | 0.0157861 | ||||||||
\(457\) | 5.09970e43 | 0.659064 | 0.329532 | − | 0.944144i | \(-0.393109\pi\) | ||||
0.329532 | + | 0.944144i | \(0.393109\pi\) | |||||||
\(458\) | 5.75640e43 | 0.717581 | ||||||||
\(459\) | −4.30151e41 | −0.00517263 | ||||||||
\(460\) | 2.16702e43 | 0.251396 | ||||||||
\(461\) | −7.70670e43 | −0.862588 | −0.431294 | − | 0.902211i | \(-0.641943\pi\) | ||||
−0.431294 | + | 0.902211i | \(0.641943\pi\) | |||||||
\(462\) | 2.73649e42 | 0.0295530 | ||||||||
\(463\) | 4.19125e43 | 0.436774 | 0.218387 | − | 0.975862i | \(-0.429921\pi\) | ||||
0.218387 | + | 0.975862i | \(0.429921\pi\) | |||||||
\(464\) | 9.91498e42 | 0.0997115 | ||||||||
\(465\) | 2.21650e42 | 0.0215127 | ||||||||
\(466\) | 1.23981e43 | 0.116142 | ||||||||
\(467\) | 1.16618e44 | 1.05448 | 0.527238 | − | 0.849717i | \(-0.323227\pi\) | ||||
0.527238 | + | 0.849717i | \(0.323227\pi\) | |||||||
\(468\) | 9.14351e43 | 0.798098 | ||||||||
\(469\) | −3.49455e43 | −0.294469 | ||||||||
\(470\) | −3.56629e43 | −0.290137 | ||||||||
\(471\) | −6.83359e42 | −0.0536790 | ||||||||
\(472\) | 5.87073e43 | 0.445296 | ||||||||
\(473\) | 1.51330e44 | 1.10845 | ||||||||
\(474\) | 5.89755e42 | 0.0417185 | ||||||||
\(475\) | −2.83225e43 | −0.193502 | ||||||||
\(476\) | −4.66987e42 | −0.0308170 | ||||||||
\(477\) | −1.77563e44 | −1.13188 | ||||||||
\(478\) | −1.61706e44 | −0.995785 | ||||||||
\(479\) | 1.47459e44 | 0.877276 | 0.438638 | − | 0.898664i | \(-0.355461\pi\) | ||||
0.438638 | + | 0.898664i | \(0.355461\pi\) | |||||||
\(480\) | −6.34722e41 | −0.00364840 | ||||||||
\(481\) | 5.29185e44 | 2.93910 | ||||||||
\(482\) | −2.16457e44 | −1.16170 | ||||||||
\(483\) | −1.09901e43 | −0.0570001 | ||||||||
\(484\) | −3.19641e43 | −0.160219 | ||||||||
\(485\) | −1.16383e44 | −0.563835 | ||||||||
\(486\) | −2.08465e43 | −0.0976191 | ||||||||
\(487\) | 1.46242e44 | 0.661979 | 0.330990 | − | 0.943634i | \(-0.392618\pi\) | ||||
0.330990 | + | 0.943634i | \(0.392618\pi\) | |||||||
\(488\) | −5.19063e43 | −0.227140 | ||||||||
\(489\) | −1.54649e43 | −0.0654260 | ||||||||
\(490\) | 1.59968e43 | 0.0654332 | ||||||||
\(491\) | −1.96551e44 | −0.777374 | −0.388687 | − | 0.921370i | \(-0.627071\pi\) | ||||
−0.388687 | + | 0.921370i | \(0.627071\pi\) | |||||||
\(492\) | −6.49287e42 | −0.0248320 | ||||||||
\(493\) | −6.05007e42 | −0.0223762 | ||||||||
\(494\) | 3.05948e44 | 1.09434 | ||||||||
\(495\) | 1.06338e44 | 0.367878 | ||||||||
\(496\) | −7.78760e43 | −0.260589 | ||||||||
\(497\) | −5.45618e44 | −1.76607 | ||||||||
\(498\) | 1.77843e43 | 0.0556869 | ||||||||
\(499\) | 5.06608e44 | 1.53466 | 0.767332 | − | 0.641250i | \(-0.221584\pi\) | ||||
0.767332 | + | 0.641250i | \(0.221584\pi\) | |||||||
\(500\) | 1.52588e43 | 0.0447214 | ||||||||
\(501\) | 5.46833e42 | 0.0155072 | ||||||||
\(502\) | 1.83944e44 | 0.504747 | ||||||||
\(503\) | 6.45463e44 | 1.71395 | 0.856977 | − | 0.515354i | \(-0.172340\pi\) | ||||
0.856977 | + | 0.515354i | \(0.172340\pi\) | |||||||
\(504\) | −1.50824e44 | −0.387586 | ||||||||
\(505\) | −5.93613e43 | −0.147637 | ||||||||
\(506\) | −2.72243e44 | −0.655350 | ||||||||
\(507\) | −3.08720e43 | −0.0719339 | ||||||||
\(508\) | −9.19419e42 | −0.0207378 | ||||||||
\(509\) | −1.22512e44 | −0.267507 | −0.133753 | − | 0.991015i | \(-0.542703\pi\) | ||||
−0.133753 | + | 0.991015i | \(0.542703\pi\) | |||||||
\(510\) | 3.87304e41 | 0.000818736 0 | ||||||||
\(511\) | −6.30610e43 | −0.129067 | ||||||||
\(512\) | 2.23007e43 | 0.0441942 | ||||||||
\(513\) | −4.64861e43 | −0.0892045 | ||||||||
\(514\) | −4.77929e44 | −0.888120 | ||||||||
\(515\) | 2.67873e44 | 0.482070 | ||||||||
\(516\) | 1.78014e43 | 0.0310266 | ||||||||
\(517\) | 4.48034e44 | 0.756340 | ||||||||
\(518\) | −8.72904e44 | −1.42733 | ||||||||
\(519\) | −2.34530e43 | −0.0371481 | ||||||||
\(520\) | −1.64830e44 | −0.252919 | ||||||||
\(521\) | 4.86872e43 | 0.0723757 | 0.0361878 | − | 0.999345i | \(-0.488479\pi\) | ||||
0.0361878 | + | 0.999345i | \(0.488479\pi\) | |||||||
\(522\) | −1.95401e44 | −0.281426 | ||||||||
\(523\) | −1.13407e45 | −1.58257 | −0.791283 | − | 0.611450i | \(-0.790587\pi\) | ||||
−0.791283 | + | 0.611450i | \(0.790587\pi\) | |||||||
\(524\) | 3.31206e44 | 0.447850 | ||||||||
\(525\) | −7.73856e42 | −0.0101399 | ||||||||
\(526\) | 5.74529e44 | 0.729537 | ||||||||
\(527\) | 4.75196e43 | 0.0584786 | ||||||||
\(528\) | 7.97402e42 | 0.00951081 | ||||||||
\(529\) | 2.28361e44 | 0.264000 | ||||||||
\(530\) | 3.20094e44 | 0.358695 | ||||||||
\(531\) | −1.15699e45 | −1.25681 | ||||||||
\(532\) | −5.04670e44 | −0.531454 | ||||||||
\(533\) | −1.68613e45 | −1.72144 | ||||||||
\(534\) | −1.46809e43 | −0.0145319 | ||||||||
\(535\) | 4.34054e44 | 0.416587 | ||||||||
\(536\) | −1.01830e44 | −0.0947666 | ||||||||
\(537\) | −2.42241e43 | −0.0218611 | ||||||||
\(538\) | 1.37047e45 | 1.19939 | ||||||||
\(539\) | −2.00968e44 | −0.170574 | ||||||||
\(540\) | 2.50445e43 | 0.0206165 | ||||||||
\(541\) | −6.78227e44 | −0.541527 | −0.270763 | − | 0.962646i | \(-0.587276\pi\) | ||||
−0.270763 | + | 0.962646i | \(0.587276\pi\) | |||||||
\(542\) | 7.54104e43 | 0.0584041 | ||||||||
\(543\) | −6.24415e42 | −0.00469112 | ||||||||
\(544\) | −1.36078e43 | −0.00991759 | ||||||||
\(545\) | 1.07384e45 | 0.759273 | ||||||||
\(546\) | 8.35945e43 | 0.0573455 | ||||||||
\(547\) | 6.38198e44 | 0.424780 | 0.212390 | − | 0.977185i | \(-0.431875\pi\) | ||||
0.212390 | + | 0.977185i | \(0.431875\pi\) | |||||||
\(548\) | −1.23042e45 | −0.794650 | ||||||||
\(549\) | 1.02295e45 | 0.641080 | ||||||||
\(550\) | −1.91696e44 | −0.116581 | ||||||||
\(551\) | −6.53827e44 | −0.385888 | ||||||||
\(552\) | −3.20248e43 | −0.0183439 | ||||||||
\(553\) | −2.52630e45 | −1.40449 | ||||||||
\(554\) | 1.82624e45 | 0.985477 | ||||||||
\(555\) | 7.23959e43 | 0.0379210 | ||||||||
\(556\) | 1.79123e44 | 0.0910788 | ||||||||
\(557\) | −1.02802e45 | −0.507447 | −0.253724 | − | 0.967277i | \(-0.581655\pi\) | ||||
−0.253724 | + | 0.967277i | \(0.581655\pi\) | |||||||
\(558\) | 1.53476e45 | 0.735487 | ||||||||
\(559\) | 4.62283e45 | 2.15086 | ||||||||
\(560\) | 2.71892e44 | 0.122827 | ||||||||
\(561\) | −4.86571e42 | −0.00213432 | ||||||||
\(562\) | 3.23438e45 | 1.37766 | ||||||||
\(563\) | 1.16743e45 | 0.482885 | 0.241442 | − | 0.970415i | \(-0.422380\pi\) | ||||
0.241442 | + | 0.970415i | \(0.422380\pi\) | |||||||
\(564\) | 5.27037e43 | 0.0211707 | ||||||||
\(565\) | −4.91664e44 | −0.191809 | ||||||||
\(566\) | −1.03351e45 | −0.391600 | ||||||||
\(567\) | 2.96604e45 | 1.09158 | ||||||||
\(568\) | −1.58991e45 | −0.568361 | ||||||||
\(569\) | −1.70096e45 | −0.590666 | −0.295333 | − | 0.955394i | \(-0.595431\pi\) | ||||
−0.295333 | + | 0.955394i | \(0.595431\pi\) | |||||||
\(570\) | 4.18557e43 | 0.0141195 | ||||||||
\(571\) | 2.65488e45 | 0.870060 | 0.435030 | − | 0.900416i | \(-0.356738\pi\) | ||||
0.435030 | + | 0.900416i | \(0.356738\pi\) | |||||||
\(572\) | 2.07077e45 | 0.659321 | ||||||||
\(573\) | 1.88281e44 | 0.0582445 | ||||||||
\(574\) | 2.78131e45 | 0.835994 | ||||||||
\(575\) | 7.69880e44 | 0.224855 | ||||||||
\(576\) | −4.39496e44 | −0.124734 | ||||||||
\(577\) | −2.36511e45 | −0.652304 | −0.326152 | − | 0.945317i | \(-0.605752\pi\) | ||||
−0.326152 | + | 0.945317i | \(0.605752\pi\) | |||||||
\(578\) | −2.62982e45 | −0.704881 | ||||||||
\(579\) | 1.57519e44 | 0.0410334 | ||||||||
\(580\) | 3.52251e44 | 0.0891846 | ||||||||
\(581\) | −7.61817e45 | −1.87475 | ||||||||
\(582\) | 1.71994e44 | 0.0411420 | ||||||||
\(583\) | −4.02135e45 | −0.935062 | ||||||||
\(584\) | −1.83757e44 | −0.0415367 | ||||||||
\(585\) | 3.24843e45 | 0.713840 | ||||||||
\(586\) | 2.52931e45 | 0.540370 | ||||||||
\(587\) | −1.20601e45 | −0.250508 | −0.125254 | − | 0.992125i | \(-0.539975\pi\) | ||||
−0.125254 | + | 0.992125i | \(0.539975\pi\) | |||||||
\(588\) | −2.36405e43 | −0.00477454 | ||||||||
\(589\) | 5.13541e45 | 1.00849 | ||||||||
\(590\) | 2.08570e45 | 0.398285 | ||||||||
\(591\) | 2.57605e44 | 0.0478366 | ||||||||
\(592\) | −2.54361e45 | −0.459348 | ||||||||
\(593\) | −2.17738e45 | −0.382413 | −0.191206 | − | 0.981550i | \(-0.561240\pi\) | ||||
−0.191206 | + | 0.981550i | \(0.561240\pi\) | |||||||
\(594\) | −3.14634e44 | −0.0537440 | ||||||||
\(595\) | −1.65907e44 | −0.0275635 | ||||||||
\(596\) | 9.35039e44 | 0.151101 | ||||||||
\(597\) | −1.35714e44 | −0.0213328 | ||||||||
\(598\) | −8.31649e45 | −1.27166 | ||||||||
\(599\) | −4.67713e45 | −0.695724 | −0.347862 | − | 0.937546i | \(-0.613092\pi\) | ||||
−0.347862 | + | 0.937546i | \(0.613092\pi\) | |||||||
\(600\) | −2.25498e43 | −0.00326323 | ||||||||
\(601\) | −1.01814e46 | −1.43344 | −0.716722 | − | 0.697359i | \(-0.754358\pi\) | ||||
−0.716722 | + | 0.697359i | \(0.754358\pi\) | |||||||
\(602\) | −7.62547e45 | −1.04454 | ||||||||
\(603\) | 2.00683e45 | 0.267470 | ||||||||
\(604\) | −1.63476e45 | −0.212004 | ||||||||
\(605\) | −1.13559e45 | −0.143304 | ||||||||
\(606\) | 8.77258e43 | 0.0107728 | ||||||||
\(607\) | −8.73331e45 | −1.04368 | −0.521838 | − | 0.853045i | \(-0.674753\pi\) | ||||
−0.521838 | + | 0.853045i | \(0.674753\pi\) | |||||||
\(608\) | −1.47059e45 | −0.171034 | ||||||||
\(609\) | −1.78646e44 | −0.0202212 | ||||||||
\(610\) | −1.84408e45 | −0.203160 | ||||||||
\(611\) | 1.36866e46 | 1.46762 | ||||||||
\(612\) | 2.68178e44 | 0.0279914 | ||||||||
\(613\) | −8.45222e44 | −0.0858763 | −0.0429381 | − | 0.999078i | \(-0.513672\pi\) | ||||
−0.0429381 | + | 0.999078i | \(0.513672\pi\) | |||||||
\(614\) | 5.43321e45 | 0.537377 | ||||||||
\(615\) | −2.30673e44 | −0.0222105 | ||||||||
\(616\) | −3.41578e45 | −0.320191 | ||||||||
\(617\) | −6.99843e44 | −0.0638698 | −0.0319349 | − | 0.999490i | \(-0.510167\pi\) | ||||
−0.0319349 | + | 0.999490i | \(0.510167\pi\) | |||||||
\(618\) | −3.95870e44 | −0.0351757 | ||||||||
\(619\) | 1.82399e46 | 1.57807 | 0.789037 | − | 0.614345i | \(-0.210580\pi\) | ||||
0.789037 | + | 0.614345i | \(0.210580\pi\) | |||||||
\(620\) | −2.76671e45 | −0.233078 | ||||||||
\(621\) | 1.26362e45 | 0.103658 | ||||||||
\(622\) | 1.10442e45 | 0.0882249 | ||||||||
\(623\) | 6.28878e45 | 0.489231 | ||||||||
\(624\) | 2.43591e44 | 0.0184550 | ||||||||
\(625\) | 5.42101e44 | 0.0400000 | ||||||||
\(626\) | −3.61331e44 | −0.0259674 | ||||||||
\(627\) | −5.25834e44 | −0.0368073 | ||||||||
\(628\) | 8.52993e45 | 0.581582 | ||||||||
\(629\) | 1.55210e45 | 0.103082 | ||||||||
\(630\) | −5.35836e45 | −0.346667 | ||||||||
\(631\) | 1.71214e46 | 1.07908 | 0.539540 | − | 0.841960i | \(-0.318598\pi\) | ||||
0.539540 | + | 0.841960i | \(0.318598\pi\) | |||||||
\(632\) | −7.36153e45 | −0.451998 | ||||||||
\(633\) | −7.24345e44 | −0.0433296 | ||||||||
\(634\) | −1.37265e46 | −0.799995 | ||||||||
\(635\) | −3.26643e44 | −0.0185484 | ||||||||
\(636\) | −4.73044e44 | −0.0261733 | ||||||||
\(637\) | −6.13919e45 | −0.330986 | ||||||||
\(638\) | −4.42533e45 | −0.232490 | ||||||||
\(639\) | 3.13334e46 | 1.60414 | ||||||||
\(640\) | 7.92282e44 | 0.0395285 | ||||||||
\(641\) | −3.25948e46 | −1.58486 | −0.792429 | − | 0.609964i | \(-0.791184\pi\) | ||||
−0.792429 | + | 0.609964i | \(0.791184\pi\) | |||||||
\(642\) | −6.41456e44 | −0.0303976 | ||||||||
\(643\) | 3.81037e46 | 1.75989 | 0.879947 | − | 0.475073i | \(-0.157578\pi\) | ||||
0.879947 | + | 0.475073i | \(0.157578\pi\) | |||||||
\(644\) | 1.37183e46 | 0.617565 | ||||||||
\(645\) | 6.32432e44 | 0.0277510 | ||||||||
\(646\) | 8.97344e44 | 0.0383815 | ||||||||
\(647\) | 1.23656e46 | 0.515580 | 0.257790 | − | 0.966201i | \(-0.417006\pi\) | ||||
0.257790 | + | 0.966201i | \(0.417006\pi\) | |||||||
\(648\) | 8.64293e45 | 0.351296 | ||||||||
\(649\) | −2.62027e46 | −1.03827 | ||||||||
\(650\) | −5.85595e45 | −0.226218 | ||||||||
\(651\) | 1.40315e45 | 0.0528467 | ||||||||
\(652\) | 1.93038e46 | 0.708854 | ||||||||
\(653\) | 4.34456e45 | 0.155553 | 0.0777764 | − | 0.996971i | \(-0.475218\pi\) | ||||
0.0777764 | + | 0.996971i | \(0.475218\pi\) | |||||||
\(654\) | −1.58695e45 | −0.0554027 | ||||||||
\(655\) | 1.17668e46 | 0.400569 | ||||||||
\(656\) | 8.10462e45 | 0.269042 | ||||||||
\(657\) | 3.62143e45 | 0.117233 | ||||||||
\(658\) | −2.25763e46 | −0.712732 | ||||||||
\(659\) | −3.61863e46 | −1.11413 | −0.557063 | − | 0.830470i | \(-0.688072\pi\) | ||||
−0.557063 | + | 0.830470i | \(0.688072\pi\) | |||||||
\(660\) | 2.83294e44 | 0.00850673 | ||||||||
\(661\) | −1.31841e46 | −0.386124 | −0.193062 | − | 0.981187i | \(-0.561842\pi\) | ||||
−0.193062 | + | 0.981187i | \(0.561842\pi\) | |||||||
\(662\) | 9.12140e45 | 0.260558 | ||||||||
\(663\) | −1.48638e44 | −0.00414149 | ||||||||
\(664\) | −2.21990e46 | −0.603338 | ||||||||
\(665\) | −1.79295e46 | −0.475347 | ||||||||
\(666\) | 5.01286e46 | 1.29647 | ||||||||
\(667\) | 1.77728e46 | 0.448413 | ||||||||
\(668\) | −6.82575e45 | −0.168012 | ||||||||
\(669\) | −8.59040e44 | −0.0206292 | ||||||||
\(670\) | −3.61772e45 | −0.0847618 | ||||||||
\(671\) | 2.31672e46 | 0.529606 | ||||||||
\(672\) | −4.01809e44 | −0.00896245 | ||||||||
\(673\) | 4.84617e46 | 1.05475 | 0.527375 | − | 0.849633i | \(-0.323176\pi\) | ||||
0.527375 | + | 0.849633i | \(0.323176\pi\) | |||||||
\(674\) | −3.04506e46 | −0.646707 | ||||||||
\(675\) | 8.89759e44 | 0.0184400 | ||||||||
\(676\) | 3.85355e46 | 0.779364 | ||||||||
\(677\) | −4.32560e46 | −0.853755 | −0.426877 | − | 0.904310i | \(-0.640386\pi\) | ||||
−0.426877 | + | 0.904310i | \(0.640386\pi\) | |||||||
\(678\) | 7.26594e44 | 0.0139959 | ||||||||
\(679\) | −7.36762e46 | −1.38508 | ||||||||
\(680\) | −4.83446e44 | −0.00887056 | ||||||||
\(681\) | 1.20119e45 | 0.0215122 | ||||||||
\(682\) | 3.47583e46 | 0.607597 | ||||||||
\(683\) | −6.34451e45 | −0.108257 | −0.0541286 | − | 0.998534i | \(-0.517238\pi\) | ||||
−0.0541286 | + | 0.998534i | \(0.517238\pi\) | |||||||
\(684\) | 2.89819e46 | 0.482726 | ||||||||
\(685\) | −4.37135e46 | −0.710756 | ||||||||
\(686\) | −3.88141e46 | −0.616087 | ||||||||
\(687\) | −3.02228e45 | −0.0468327 | ||||||||
\(688\) | −2.22203e46 | −0.336156 | ||||||||
\(689\) | −1.22844e47 | −1.81442 | ||||||||
\(690\) | −1.13775e45 | −0.0164073 | ||||||||
\(691\) | −5.27291e46 | −0.742442 | −0.371221 | − | 0.928545i | \(-0.621061\pi\) | ||||
−0.371221 | + | 0.928545i | \(0.621061\pi\) | |||||||
\(692\) | 2.92749e46 | 0.402480 | ||||||||
\(693\) | 6.73172e46 | 0.903707 | ||||||||
\(694\) | 2.45367e46 | 0.321652 | ||||||||
\(695\) | 6.36373e45 | 0.0814633 | ||||||||
\(696\) | −5.20566e44 | −0.00650763 | ||||||||
\(697\) | −4.94540e45 | −0.0603755 | ||||||||
\(698\) | −2.07836e46 | −0.247803 | ||||||||
\(699\) | −6.50937e44 | −0.00757994 | ||||||||
\(700\) | 9.65954e45 | 0.109860 | ||||||||
\(701\) | −1.32738e47 | −1.47451 | −0.737255 | − | 0.675614i | \(-0.763879\pi\) | ||||
−0.737255 | + | 0.675614i | \(0.763879\pi\) | |||||||
\(702\) | −9.61147e45 | −0.104286 | ||||||||
\(703\) | 1.67734e47 | 1.77770 | ||||||||
\(704\) | −9.95345e45 | −0.103044 | ||||||||
\(705\) | 1.87241e45 | 0.0189357 | ||||||||
\(706\) | 8.48996e46 | 0.838741 | ||||||||
\(707\) | −3.75786e46 | −0.362677 | ||||||||
\(708\) | −3.08231e45 | −0.0290621 | ||||||||
\(709\) | −1.89943e47 | −1.74968 | −0.874841 | − | 0.484409i | \(-0.839035\pi\) | ||||
−0.874841 | + | 0.484409i | \(0.839035\pi\) | |||||||
\(710\) | −5.64849e46 | −0.508358 | ||||||||
\(711\) | 1.45079e47 | 1.27572 | ||||||||
\(712\) | 1.83252e46 | 0.157445 | ||||||||
\(713\) | −1.39594e47 | −1.17190 | ||||||||
\(714\) | 2.45182e44 | 0.00201126 | ||||||||
\(715\) | 7.35684e46 | 0.589714 | ||||||||
\(716\) | 3.02374e46 | 0.236853 | ||||||||
\(717\) | 8.49004e45 | 0.0649895 | ||||||||
\(718\) | 7.83917e46 | 0.586430 | ||||||||
\(719\) | −1.12722e47 | −0.824104 | −0.412052 | − | 0.911160i | \(-0.635188\pi\) | ||||
−0.412052 | + | 0.911160i | \(0.635188\pi\) | |||||||
\(720\) | −1.56140e46 | −0.111565 | ||||||||
\(721\) | 1.69576e47 | 1.18422 | ||||||||
\(722\) | −6.62196e45 | −0.0451984 | ||||||||
\(723\) | 1.13646e46 | 0.0758181 | ||||||||
\(724\) | 7.79417e45 | 0.0508257 | ||||||||
\(725\) | 1.25145e46 | 0.0797692 | ||||||||
\(726\) | 1.67821e45 | 0.0104566 | ||||||||
\(727\) | 1.60341e47 | 0.976626 | 0.488313 | − | 0.872669i | \(-0.337613\pi\) | ||||
0.488313 | + | 0.872669i | \(0.337613\pi\) | |||||||
\(728\) | −1.04346e47 | −0.621307 | ||||||||
\(729\) | −1.69601e47 | −0.987244 | ||||||||
\(730\) | −6.52836e45 | −0.0371516 | ||||||||
\(731\) | 1.35587e46 | 0.0754365 | ||||||||
\(732\) | 2.72523e45 | 0.0148242 | ||||||||
\(733\) | 3.44847e47 | 1.83405 | 0.917024 | − | 0.398832i | \(-0.130584\pi\) | ||||
0.917024 | + | 0.398832i | \(0.130584\pi\) | |||||||
\(734\) | −1.47371e47 | −0.766351 | ||||||||
\(735\) | −8.39880e44 | −0.00427047 | ||||||||
\(736\) | 3.99744e46 | 0.198746 | ||||||||
\(737\) | 4.54494e46 | 0.220961 | ||||||||
\(738\) | −1.59723e47 | −0.759344 | ||||||||
\(739\) | 2.87632e47 | 1.33722 | 0.668611 | − | 0.743612i | \(-0.266889\pi\) | ||||
0.668611 | + | 0.743612i | \(0.266889\pi\) | |||||||
\(740\) | −9.03671e46 | −0.410853 | ||||||||
\(741\) | −1.60632e46 | −0.0714219 | ||||||||
\(742\) | 2.02635e47 | 0.881149 | ||||||||
\(743\) | 3.46436e47 | 1.47335 | 0.736677 | − | 0.676244i | \(-0.236394\pi\) | ||||
0.736677 | + | 0.676244i | \(0.236394\pi\) | |||||||
\(744\) | 4.08872e45 | 0.0170073 | ||||||||
\(745\) | 3.32193e46 | 0.135149 | ||||||||
\(746\) | 3.16441e47 | 1.25922 | ||||||||
\(747\) | 4.37491e47 | 1.70286 | ||||||||
\(748\) | 6.07354e45 | 0.0231241 | ||||||||
\(749\) | 2.74777e47 | 1.02336 | ||||||||
\(750\) | −8.01132e44 | −0.00291872 | ||||||||
\(751\) | −4.94603e47 | −1.76278 | −0.881389 | − | 0.472391i | \(-0.843391\pi\) | ||||
−0.881389 | + | 0.472391i | \(0.843391\pi\) | |||||||
\(752\) | −6.57865e46 | −0.229373 | ||||||||
\(753\) | −9.65759e45 | −0.0329421 | ||||||||
\(754\) | −1.35185e47 | −0.451131 | ||||||||
\(755\) | −5.80783e46 | −0.189622 | ||||||||
\(756\) | 1.58544e46 | 0.0506453 | ||||||||
\(757\) | −5.29375e47 | −1.65456 | −0.827278 | − | 0.561793i | \(-0.810112\pi\) | ||||
−0.827278 | + | 0.561793i | \(0.810112\pi\) | |||||||
\(758\) | −2.79233e47 | −0.853935 | ||||||||
\(759\) | 1.42936e46 | 0.0427712 | ||||||||
\(760\) | −5.22457e46 | −0.152977 | ||||||||
\(761\) | −5.45469e47 | −1.56287 | −0.781436 | − | 0.623985i | \(-0.785513\pi\) | ||||
−0.781436 | + | 0.623985i | \(0.785513\pi\) | |||||||
\(762\) | 4.82722e44 | 0.00135344 | ||||||||
\(763\) | 6.79793e47 | 1.86519 | ||||||||
\(764\) | −2.35019e47 | −0.631047 | ||||||||
\(765\) | 9.52761e45 | 0.0250363 | ||||||||
\(766\) | 5.63717e46 | 0.144973 | ||||||||
\(767\) | −8.00442e47 | −2.01468 | ||||||||
\(768\) | −1.17086e45 | −0.00288432 | ||||||||
\(769\) | 6.99140e47 | 1.68570 | 0.842848 | − | 0.538151i | \(-0.180877\pi\) | ||||
0.842848 | + | 0.538151i | \(0.180877\pi\) | |||||||
\(770\) | −1.21353e47 | −0.286387 | ||||||||
\(771\) | 2.50927e46 | 0.0579628 | ||||||||
\(772\) | −1.96621e47 | −0.444574 | ||||||||
\(773\) | −7.98533e47 | −1.76738 | −0.883692 | − | 0.468069i | \(-0.844950\pi\) | ||||
−0.883692 | + | 0.468069i | \(0.844950\pi\) | |||||||
\(774\) | 4.37911e47 | 0.948767 | ||||||||
\(775\) | −9.82934e46 | −0.208471 | ||||||||
\(776\) | −2.14689e47 | −0.445751 | ||||||||
\(777\) | 4.58301e46 | 0.0931545 | ||||||||
\(778\) | −6.61464e47 | −1.31626 | ||||||||
\(779\) | −5.34446e47 | −1.04120 | ||||||||
\(780\) | 8.65408e45 | 0.0165067 | ||||||||
\(781\) | 7.09620e47 | 1.32521 | ||||||||
\(782\) | −2.43922e46 | −0.0446005 | ||||||||
\(783\) | 2.05402e46 | 0.0367735 | ||||||||
\(784\) | 2.95089e46 | 0.0517295 | ||||||||
\(785\) | 3.03044e47 | 0.520183 | ||||||||
\(786\) | −1.73893e46 | −0.0292287 | ||||||||
\(787\) | −3.34859e47 | −0.551161 | −0.275580 | − | 0.961278i | \(-0.588870\pi\) | ||||
−0.275580 | + | 0.961278i | \(0.588870\pi\) | |||||||
\(788\) | −3.21551e47 | −0.518284 | ||||||||
\(789\) | −3.01645e46 | −0.0476130 | ||||||||
\(790\) | −2.61534e47 | −0.404279 | ||||||||
\(791\) | −3.11246e47 | −0.471186 | ||||||||
\(792\) | 1.96159e47 | 0.290833 | ||||||||
\(793\) | 7.07714e47 | 1.02766 | ||||||||
\(794\) | 5.57736e47 | 0.793214 | ||||||||
\(795\) | −1.68059e46 | −0.0234101 | ||||||||
\(796\) | 1.69403e47 | 0.231129 | ||||||||
\(797\) | −9.43634e47 | −1.26108 | −0.630538 | − | 0.776159i | \(-0.717166\pi\) | ||||
−0.630538 | + | 0.776159i | \(0.717166\pi\) | |||||||
\(798\) | 2.64967e46 | 0.0346851 | ||||||||
\(799\) | 4.01426e46 | 0.0514735 | ||||||||
\(800\) | 2.81475e46 | 0.0353553 | ||||||||
\(801\) | −3.61148e47 | −0.444374 | ||||||||
\(802\) | 3.73397e47 | 0.450084 | ||||||||
\(803\) | 8.20159e46 | 0.0968482 | ||||||||
\(804\) | 5.34636e45 | 0.00618491 | ||||||||
\(805\) | 4.87371e47 | 0.552367 | ||||||||
\(806\) | 1.06180e48 | 1.17900 | ||||||||
\(807\) | −7.19536e46 | −0.0782779 | ||||||||
\(808\) | −1.09502e47 | −0.116717 | ||||||||
\(809\) | −2.25513e47 | −0.235516 | −0.117758 | − | 0.993042i | \(-0.537571\pi\) | ||||
−0.117758 | + | 0.993042i | \(0.537571\pi\) | |||||||
\(810\) | 3.07058e47 | 0.314209 | ||||||||
\(811\) | −1.37037e48 | −1.37402 | −0.687009 | − | 0.726649i | \(-0.741077\pi\) | ||||
−0.687009 | + | 0.726649i | \(0.741077\pi\) | |||||||
\(812\) | 2.22992e47 | 0.219086 | ||||||||
\(813\) | −3.95927e45 | −0.00381172 | ||||||||
\(814\) | 1.13528e48 | 1.07103 | ||||||||
\(815\) | 6.85808e47 | 0.634019 | ||||||||
\(816\) | 7.14450e44 | 0.000647268 0 | ||||||||
\(817\) | 1.46528e48 | 1.30094 | ||||||||
\(818\) | −1.00066e48 | −0.870675 | ||||||||
\(819\) | 2.05641e48 | 1.75358 | ||||||||
\(820\) | 2.87934e47 | 0.240638 | ||||||||
\(821\) | −4.56387e47 | −0.373827 | −0.186914 | − | 0.982376i | \(-0.559848\pi\) | ||||
−0.186914 | + | 0.982376i | \(0.559848\pi\) | |||||||
\(822\) | 6.46009e46 | 0.0518625 | ||||||||
\(823\) | −8.98179e47 | −0.706750 | −0.353375 | − | 0.935482i | \(-0.614966\pi\) | ||||
−0.353375 | + | 0.935482i | \(0.614966\pi\) | |||||||
\(824\) | 4.94139e47 | 0.381109 | ||||||||
\(825\) | 1.00646e46 | 0.00760865 | ||||||||
\(826\) | 1.32035e48 | 0.978403 | ||||||||
\(827\) | 4.00288e47 | 0.290758 | 0.145379 | − | 0.989376i | \(-0.453560\pi\) | ||||
0.145379 | + | 0.989376i | \(0.453560\pi\) | |||||||
\(828\) | −7.87804e47 | −0.560942 | ||||||||
\(829\) | −7.44189e47 | −0.519437 | −0.259719 | − | 0.965684i | \(-0.583630\pi\) | ||||
−0.259719 | + | 0.965684i | \(0.583630\pi\) | |||||||
\(830\) | −7.88667e47 | −0.539642 | ||||||||
\(831\) | −9.58829e46 | −0.0643168 | ||||||||
\(832\) | −3.04058e47 | −0.199950 | ||||||||
\(833\) | −1.80062e46 | −0.0116086 | ||||||||
\(834\) | −9.40449e45 | −0.00594422 | ||||||||
\(835\) | −2.42500e47 | −0.150274 | ||||||||
\(836\) | 6.56364e47 | 0.398787 | ||||||||
\(837\) | −1.61331e47 | −0.0961051 | ||||||||
\(838\) | −1.93743e48 | −1.13162 | ||||||||
\(839\) | 2.38585e48 | 1.36638 | 0.683188 | − | 0.730243i | \(-0.260593\pi\) | ||||
0.683188 | + | 0.730243i | \(0.260593\pi\) | |||||||
\(840\) | −1.42751e46 | −0.00801626 | ||||||||
\(841\) | −1.52718e48 | −0.840922 | ||||||||
\(842\) | 1.61111e48 | 0.869910 | ||||||||
\(843\) | −1.69815e47 | −0.0899126 | ||||||||
\(844\) | 9.04153e47 | 0.469452 | ||||||||
\(845\) | 1.36906e48 | 0.697085 | ||||||||
\(846\) | 1.29650e48 | 0.647384 | ||||||||
\(847\) | −7.18884e47 | −0.352032 | ||||||||
\(848\) | 5.90469e47 | 0.283574 | ||||||||
\(849\) | 5.42622e46 | 0.0255576 | ||||||||
\(850\) | −1.71755e46 | −0.00793407 | ||||||||
\(851\) | −4.55946e48 | −2.06574 | ||||||||
\(852\) | 8.34749e46 | 0.0370939 | ||||||||
\(853\) | 1.91914e48 | 0.836466 | 0.418233 | − | 0.908340i | \(-0.362650\pi\) | ||||
0.418233 | + | 0.908340i | \(0.362650\pi\) | |||||||
\(854\) | −1.16739e48 | −0.499070 | ||||||||
\(855\) | 1.02964e48 | 0.431763 | ||||||||
\(856\) | 8.00687e47 | 0.329341 | ||||||||
\(857\) | −4.27431e48 | −1.72458 | −0.862289 | − | 0.506417i | \(-0.830970\pi\) | ||||
−0.862289 | + | 0.506417i | \(0.830970\pi\) | |||||||
\(858\) | −1.08721e47 | −0.0430303 | ||||||||
\(859\) | −2.08295e48 | −0.808707 | −0.404353 | − | 0.914603i | \(-0.632503\pi\) | ||||
−0.404353 | + | 0.914603i | \(0.632503\pi\) | |||||||
\(860\) | −7.89424e47 | −0.300667 | ||||||||
\(861\) | −1.46027e47 | −0.0545609 | ||||||||
\(862\) | 1.01411e48 | 0.371721 | ||||||||
\(863\) | −2.59078e48 | −0.931650 | −0.465825 | − | 0.884877i | \(-0.654242\pi\) | ||||
−0.465825 | + | 0.884877i | \(0.654242\pi\) | |||||||
\(864\) | 4.61989e46 | 0.0162988 | ||||||||
\(865\) | 1.04005e48 | 0.359989 | ||||||||
\(866\) | −2.85989e48 | −0.971191 | ||||||||
\(867\) | 1.38073e47 | 0.0460038 | ||||||||
\(868\) | −1.75146e48 | −0.572565 | ||||||||
\(869\) | 3.28566e48 | 1.05389 | ||||||||
\(870\) | −1.84942e46 | −0.00582060 | ||||||||
\(871\) | 1.38839e48 | 0.428758 | ||||||||
\(872\) | 1.98089e48 | 0.600258 | ||||||||
\(873\) | 4.23103e48 | 1.25809 | ||||||||
\(874\) | −2.63605e48 | −0.769157 | ||||||||
\(875\) | 3.43176e47 | 0.0982616 | ||||||||
\(876\) | 9.64779e45 | 0.00271088 | ||||||||
\(877\) | 5.50587e48 | 1.51821 | 0.759107 | − | 0.650966i | \(-0.225636\pi\) | ||||
0.759107 | + | 0.650966i | \(0.225636\pi\) | |||||||
\(878\) | −4.22661e48 | −1.14375 | ||||||||
\(879\) | −1.32796e47 | −0.0352671 | ||||||||
\(880\) | −3.53617e47 | −0.0921658 | ||||||||
\(881\) | −1.00108e48 | −0.256076 | −0.128038 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128038 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(882\) | −5.81552e47 | −0.146001 | ||||||||
\(883\) | −7.50570e48 | −1.84944 | −0.924719 | − | 0.380652i | \(-0.875700\pi\) | ||||
−0.924719 | + | 0.380652i | \(0.875700\pi\) | |||||||
\(884\) | 1.85535e47 | 0.0448707 | ||||||||
\(885\) | −1.09506e47 | −0.0259939 | ||||||||
\(886\) | 1.99311e48 | 0.464382 | ||||||||
\(887\) | −1.00895e48 | −0.230744 | −0.115372 | − | 0.993322i | \(-0.536806\pi\) | ||||
−0.115372 | + | 0.993322i | \(0.536806\pi\) | |||||||
\(888\) | 1.33547e47 | 0.0299792 | ||||||||
\(889\) | −2.06781e47 | −0.0455650 | ||||||||
\(890\) | 6.51043e47 | 0.140823 | ||||||||
\(891\) | −3.85758e48 | −0.819092 | ||||||||
\(892\) | 1.07228e48 | 0.223506 | ||||||||
\(893\) | 4.33819e48 | 0.887685 | ||||||||
\(894\) | −4.90923e46 | −0.00986154 | ||||||||
\(895\) | 1.07425e48 | 0.211848 | ||||||||
\(896\) | 5.01552e47 | 0.0971033 | ||||||||
\(897\) | 4.36640e47 | 0.0829944 | ||||||||
\(898\) | −4.39311e48 | −0.819809 | ||||||||
\(899\) | −2.26911e48 | −0.415739 | ||||||||
\(900\) | −5.54722e47 | −0.0997870 | ||||||||
\(901\) | −3.60301e47 | −0.0636366 | ||||||||
\(902\) | −3.61732e48 | −0.627305 | ||||||||
\(903\) | 4.00360e47 | 0.0681715 | ||||||||
\(904\) | −9.06959e47 | −0.151638 | ||||||||
\(905\) | 2.76904e47 | 0.0454599 | ||||||||
\(906\) | 8.58296e46 | 0.0138364 | ||||||||
\(907\) | −4.59452e47 | −0.0727310 | −0.0363655 | − | 0.999339i | \(-0.511578\pi\) | ||||
−0.0363655 | + | 0.999339i | \(0.511578\pi\) | |||||||
\(908\) | −1.49937e48 | −0.233073 | ||||||||
\(909\) | 2.15804e48 | 0.329424 | ||||||||
\(910\) | −3.70710e48 | −0.555714 | ||||||||
\(911\) | 6.61697e48 | 0.974105 | 0.487053 | − | 0.873373i | \(-0.338072\pi\) | ||||
0.487053 | + | 0.873373i | \(0.338072\pi\) | |||||||
\(912\) | 7.72101e46 | 0.0111624 | ||||||||
\(913\) | 9.90804e48 | 1.40676 | ||||||||
\(914\) | 3.34214e48 | 0.466028 | ||||||||
\(915\) | 9.68198e46 | 0.0132592 | ||||||||
\(916\) | 3.77252e48 | 0.507406 | ||||||||
\(917\) | 7.44895e48 | 0.984013 | ||||||||
\(918\) | −2.81904e46 | −0.00365760 | ||||||||
\(919\) | −1.20821e49 | −1.53971 | −0.769854 | − | 0.638220i | \(-0.779671\pi\) | ||||
−0.769854 | + | 0.638220i | \(0.779671\pi\) | |||||||
\(920\) | 1.42018e48 | 0.177764 | ||||||||
\(921\) | −2.85260e47 | −0.0350717 | ||||||||
\(922\) | −5.05066e48 | −0.609942 | ||||||||
\(923\) | 2.16775e49 | 2.57147 | ||||||||
\(924\) | 1.79339e47 | 0.0208971 | ||||||||
\(925\) | −3.21048e48 | −0.367478 | ||||||||
\(926\) | 2.74677e48 | 0.308846 | ||||||||
\(927\) | −9.73833e48 | −1.07564 | ||||||||
\(928\) | 6.49788e47 | 0.0705067 | ||||||||
\(929\) | 5.93684e48 | 0.632843 | 0.316422 | − | 0.948619i | \(-0.397519\pi\) | ||||
0.316422 | + | 0.948619i | \(0.397519\pi\) | |||||||
\(930\) | 1.45261e47 | 0.0152118 | ||||||||
\(931\) | −1.94592e48 | −0.200196 | ||||||||
\(932\) | 8.12522e47 | 0.0821245 | ||||||||
\(933\) | −5.79851e46 | −0.00575797 | ||||||||
\(934\) | 7.64268e48 | 0.745628 | ||||||||
\(935\) | 2.15776e47 | 0.0206829 | ||||||||
\(936\) | 5.99229e48 | 0.564340 | ||||||||
\(937\) | −1.17439e49 | −1.08670 | −0.543349 | − | 0.839507i | \(-0.682844\pi\) | ||||
−0.543349 | + | 0.839507i | \(0.682844\pi\) | |||||||
\(938\) | −2.29019e48 | −0.208221 | ||||||||
\(939\) | 1.89709e46 | 0.00169475 | ||||||||
\(940\) | −2.33721e48 | −0.205158 | ||||||||
\(941\) | 1.07666e49 | 0.928646 | 0.464323 | − | 0.885666i | \(-0.346298\pi\) | ||||
0.464323 | + | 0.885666i | \(0.346298\pi\) | |||||||
\(942\) | −4.47846e47 | −0.0379568 | ||||||||
\(943\) | 1.45277e49 | 1.20991 | ||||||||
\(944\) | 3.84744e48 | 0.314872 | ||||||||
\(945\) | 5.63260e47 | 0.0452985 | ||||||||
\(946\) | 9.91754e48 | 0.783791 | ||||||||
\(947\) | −2.67196e48 | −0.207518 | −0.103759 | − | 0.994602i | \(-0.533087\pi\) | ||||
−0.103759 | + | 0.994602i | \(0.533087\pi\) | |||||||
\(948\) | 3.86502e47 | 0.0294995 | ||||||||
\(949\) | 2.50543e48 | 0.187927 | ||||||||
\(950\) | −1.85614e48 | −0.136827 | ||||||||
\(951\) | 7.20682e47 | 0.0522114 | ||||||||
\(952\) | −3.06044e47 | −0.0217909 | ||||||||
\(953\) | −5.75060e48 | −0.402421 | −0.201210 | − | 0.979548i | \(-0.564487\pi\) | ||||
−0.201210 | + | 0.979548i | \(0.564487\pi\) | |||||||
\(954\) | −1.16368e49 | −0.800359 | ||||||||
\(955\) | −8.34954e48 | −0.564426 | ||||||||
\(956\) | −1.05976e49 | −0.704126 | ||||||||
\(957\) | 2.32343e47 | 0.0151734 | ||||||||
\(958\) | 9.66390e48 | 0.620328 | ||||||||
\(959\) | −2.76727e49 | −1.74600 | ||||||||
\(960\) | −4.15971e46 | −0.00257981 | ||||||||
\(961\) | 1.41901e48 | 0.0865066 | ||||||||
\(962\) | 3.46807e49 | 2.07826 | ||||||||
\(963\) | −1.57797e49 | −0.929533 | ||||||||
\(964\) | −1.41857e49 | −0.821447 | ||||||||
\(965\) | −6.98537e48 | −0.397639 | ||||||||
\(966\) | −7.20250e47 | −0.0403051 | ||||||||
\(967\) | −1.91342e49 | −1.05262 | −0.526311 | − | 0.850292i | \(-0.676425\pi\) | ||||
−0.526311 | + | 0.850292i | \(0.676425\pi\) | |||||||
\(968\) | −2.09480e48 | −0.113292 | ||||||||
\(969\) | −4.71132e46 | −0.00250496 | ||||||||
\(970\) | −7.62730e48 | −0.398692 | ||||||||
\(971\) | −1.56571e49 | −0.804625 | −0.402313 | − | 0.915502i | \(-0.631794\pi\) | ||||
−0.402313 | + | 0.915502i | \(0.631794\pi\) | |||||||
\(972\) | −1.36620e48 | −0.0690271 | ||||||||
\(973\) | 4.02854e48 | 0.200118 | ||||||||
\(974\) | 9.58412e48 | 0.468090 | ||||||||
\(975\) | 3.07455e47 | 0.0147640 | ||||||||
\(976\) | −3.40173e48 | −0.160612 | ||||||||
\(977\) | 1.35623e49 | 0.629614 | 0.314807 | − | 0.949156i | \(-0.398060\pi\) | ||||
0.314807 | + | 0.949156i | \(0.398060\pi\) | |||||||
\(978\) | −1.01351e48 | −0.0462631 | ||||||||
\(979\) | −8.17907e48 | −0.367104 | ||||||||
\(980\) | 1.04837e48 | 0.0462683 | ||||||||
\(981\) | −3.90388e49 | −1.69417 | ||||||||
\(982\) | −1.28811e49 | −0.549686 | ||||||||
\(983\) | 1.58986e49 | 0.667155 | 0.333578 | − | 0.942723i | \(-0.391744\pi\) | ||||
0.333578 | + | 0.942723i | \(0.391744\pi\) | |||||||
\(984\) | −4.25517e47 | −0.0175589 | ||||||||
\(985\) | −1.14238e49 | −0.463567 | ||||||||
\(986\) | −3.96497e47 | −0.0158224 | ||||||||
\(987\) | 1.18533e48 | 0.0465162 | ||||||||
\(988\) | 2.00506e49 | 0.773818 | ||||||||
\(989\) | −3.98302e49 | −1.51173 | ||||||||
\(990\) | 6.96898e48 | 0.260129 | ||||||||
\(991\) | 1.36513e49 | 0.501141 | 0.250570 | − | 0.968098i | \(-0.419382\pi\) | ||||
0.250570 | + | 0.968098i | \(0.419382\pi\) | |||||||
\(992\) | −5.10368e48 | −0.184264 | ||||||||
\(993\) | −4.78900e47 | −0.0170052 | ||||||||
\(994\) | −3.57576e49 | −1.24880 | ||||||||
\(995\) | 6.01839e48 | 0.206728 | ||||||||
\(996\) | 1.16551e48 | 0.0393766 | ||||||||
\(997\) | 3.08204e49 | 1.02416 | 0.512081 | − | 0.858937i | \(-0.328875\pi\) | ||||
0.512081 | + | 0.858937i | \(0.328875\pi\) | |||||||
\(998\) | 3.32011e49 | 1.08517 | ||||||||
\(999\) | −5.26942e48 | −0.169407 |
(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 | 10.34.a.a.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.34.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |