Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,26,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(3.95996779952\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −48.0000 | −0.00828641 | −0.00414320 | − | 0.999991i | \(-0.501319\pi\) | ||||
−0.00414320 | + | 0.999991i | \(0.501319\pi\) | |||||||
\(3\) | −195804. | −0.212719 | −0.106359 | − | 0.994328i | \(-0.533919\pi\) | ||||
−0.106359 | + | 0.994328i | \(0.533919\pi\) | |||||||
\(4\) | −3.35521e7 | −0.999931 | ||||||||
\(5\) | −7.41990e8 | −1.35917 | −0.679584 | − | 0.733598i | \(-0.737840\pi\) | ||||
−0.679584 | + | 0.733598i | \(0.737840\pi\) | |||||||
\(6\) | 9.39859e6 | 0.00176267 | ||||||||
\(7\) | 3.90806e10 | 1.06718 | 0.533588 | − | 0.845745i | \(-0.320843\pi\) | ||||
0.533588 | + | 0.845745i | \(0.320843\pi\) | |||||||
\(8\) | 3.22111e9 | 0.0165722 | ||||||||
\(9\) | −8.08949e11 | −0.954751 | ||||||||
\(10\) | 3.56155e10 | 0.0112626 | ||||||||
\(11\) | 8.41952e12 | 0.808870 | 0.404435 | − | 0.914567i | \(-0.367468\pi\) | ||||
0.404435 | + | 0.914567i | \(0.367468\pi\) | |||||||
\(12\) | 6.56964e12 | 0.212704 | ||||||||
\(13\) | −8.16510e13 | −0.972008 | −0.486004 | − | 0.873957i | \(-0.661546\pi\) | ||||
−0.486004 | + | 0.873957i | \(0.661546\pi\) | |||||||
\(14\) | −1.87587e12 | −0.00884305 | ||||||||
\(15\) | 1.45285e14 | 0.289120 | ||||||||
\(16\) | 1.12567e15 | 0.999794 | ||||||||
\(17\) | −2.51990e15 | −1.04899 | −0.524496 | − | 0.851413i | \(-0.675746\pi\) | ||||
−0.524496 | + | 0.851413i | \(0.675746\pi\) | |||||||
\(18\) | 3.88296e13 | 0.00791145 | ||||||||
\(19\) | −6.08206e15 | −0.630421 | −0.315210 | − | 0.949022i | \(-0.602075\pi\) | ||||
−0.315210 | + | 0.949022i | \(0.602075\pi\) | |||||||
\(20\) | 2.48953e16 | 1.35907 | ||||||||
\(21\) | −7.65214e15 | −0.227008 | ||||||||
\(22\) | −4.04137e14 | −0.00670262 | ||||||||
\(23\) | −9.49953e16 | −0.903866 | −0.451933 | − | 0.892052i | \(-0.649265\pi\) | ||||
−0.451933 | + | 0.892052i | \(0.649265\pi\) | |||||||
\(24\) | −6.30707e14 | −0.00352523 | ||||||||
\(25\) | 2.52526e17 | 0.847336 | ||||||||
\(26\) | 3.91925e15 | 0.00805445 | ||||||||
\(27\) | 3.24298e17 | 0.415812 | ||||||||
\(28\) | −1.31124e18 | −1.06710 | ||||||||
\(29\) | −2.71247e17 | −0.142361 | −0.0711803 | − | 0.997463i | \(-0.522677\pi\) | ||||
−0.0711803 | + | 0.997463i | \(0.522677\pi\) | |||||||
\(30\) | −6.97366e15 | −0.00239577 | ||||||||
\(31\) | 4.29167e18 | 0.978599 | 0.489299 | − | 0.872116i | \(-0.337253\pi\) | ||||
0.489299 | + | 0.872116i | \(0.337253\pi\) | |||||||
\(32\) | −1.62115e17 | −0.0248569 | ||||||||
\(33\) | −1.64857e18 | −0.172062 | ||||||||
\(34\) | 1.20955e17 | 0.00869237 | ||||||||
\(35\) | −2.89974e19 | −1.45047 | ||||||||
\(36\) | 2.71420e19 | 0.954685 | ||||||||
\(37\) | 2.03015e19 | 0.506998 | 0.253499 | − | 0.967336i | \(-0.418419\pi\) | ||||
0.253499 | + | 0.967336i | \(0.418419\pi\) | |||||||
\(38\) | 2.91939e17 | 0.00522392 | ||||||||
\(39\) | 1.59876e19 | 0.206764 | ||||||||
\(40\) | −2.39003e18 | −0.0225245 | ||||||||
\(41\) | −1.83744e20 | −1.27179 | −0.635895 | − | 0.771775i | \(-0.719369\pi\) | ||||
−0.635895 | + | 0.771775i | \(0.719369\pi\) | |||||||
\(42\) | 3.67303e17 | 0.00188108 | ||||||||
\(43\) | 3.00902e20 | 1.14834 | 0.574168 | − | 0.818737i | \(-0.305326\pi\) | ||||
0.574168 | + | 0.818737i | \(0.305326\pi\) | |||||||
\(44\) | −2.82493e20 | −0.808814 | ||||||||
\(45\) | 6.00232e20 | 1.29767 | ||||||||
\(46\) | 4.55977e18 | 0.00748980 | ||||||||
\(47\) | −9.24361e20 | −1.16043 | −0.580214 | − | 0.814464i | \(-0.697031\pi\) | ||||
−0.580214 | + | 0.814464i | \(0.697031\pi\) | |||||||
\(48\) | −2.20410e20 | −0.212675 | ||||||||
\(49\) | 1.86224e20 | 0.138863 | ||||||||
\(50\) | −1.21212e19 | −0.00702137 | ||||||||
\(51\) | 4.93407e20 | 0.223140 | ||||||||
\(52\) | 2.73957e21 | 0.971941 | ||||||||
\(53\) | −9.90292e20 | −0.276895 | −0.138447 | − | 0.990370i | \(-0.544211\pi\) | ||||
−0.138447 | + | 0.990370i | \(0.544211\pi\) | |||||||
\(54\) | −1.55663e19 | −0.00344559 | ||||||||
\(55\) | −6.24719e21 | −1.09939 | ||||||||
\(56\) | 1.25883e20 | 0.0176855 | ||||||||
\(57\) | 1.19089e21 | 0.134102 | ||||||||
\(58\) | 1.30199e19 | 0.00117966 | ||||||||
\(59\) | 1.30526e22 | 0.955093 | 0.477547 | − | 0.878606i | \(-0.341526\pi\) | ||||
0.477547 | + | 0.878606i | \(0.341526\pi\) | |||||||
\(60\) | −4.87461e21 | −0.289101 | ||||||||
\(61\) | 9.01545e21 | 0.434875 | 0.217438 | − | 0.976074i | \(-0.430230\pi\) | ||||
0.217438 | + | 0.976074i | \(0.430230\pi\) | |||||||
\(62\) | −2.06000e20 | −0.00810907 | ||||||||
\(63\) | −3.16142e22 | −1.01889 | ||||||||
\(64\) | −3.77634e22 | −0.999588 | ||||||||
\(65\) | 6.05842e22 | 1.32112 | ||||||||
\(66\) | 7.91316e19 | 0.00142577 | ||||||||
\(67\) | −2.66891e22 | −0.398473 | −0.199236 | − | 0.979951i | \(-0.563846\pi\) | ||||
−0.199236 | + | 0.979951i | \(0.563846\pi\) | |||||||
\(68\) | 8.45480e22 | 1.04892 | ||||||||
\(69\) | 1.86005e22 | 0.192269 | ||||||||
\(70\) | 1.39188e21 | 0.0120192 | ||||||||
\(71\) | −1.92391e23 | −1.39141 | −0.695704 | − | 0.718329i | \(-0.744907\pi\) | ||||
−0.695704 | + | 0.718329i | \(0.744907\pi\) | |||||||
\(72\) | −2.60572e21 | −0.0158224 | ||||||||
\(73\) | 4.24046e22 | 0.216709 | 0.108355 | − | 0.994112i | \(-0.465442\pi\) | ||||
0.108355 | + | 0.994112i | \(0.465442\pi\) | |||||||
\(74\) | −9.74471e20 | −0.00420119 | ||||||||
\(75\) | −4.94455e22 | −0.180244 | ||||||||
\(76\) | 2.04066e23 | 0.630377 | ||||||||
\(77\) | 3.29040e23 | 0.863206 | ||||||||
\(78\) | −7.67405e20 | −0.00171333 | ||||||||
\(79\) | −2.71681e23 | −0.517274 | −0.258637 | − | 0.965975i | \(-0.583273\pi\) | ||||
−0.258637 | + | 0.965975i | \(0.583273\pi\) | |||||||
\(80\) | −8.35234e23 | −1.35889 | ||||||||
\(81\) | 6.21915e23 | 0.866300 | ||||||||
\(82\) | 8.81972e21 | 0.0105386 | ||||||||
\(83\) | −9.31454e23 | −0.956501 | −0.478251 | − | 0.878223i | \(-0.658729\pi\) | ||||
−0.478251 | + | 0.878223i | \(0.658729\pi\) | |||||||
\(84\) | 2.56745e23 | 0.226993 | ||||||||
\(85\) | 1.86974e24 | 1.42575 | ||||||||
\(86\) | −1.44433e22 | −0.00951558 | ||||||||
\(87\) | 5.31112e22 | 0.0302828 | ||||||||
\(88\) | 2.71202e22 | 0.0134048 | ||||||||
\(89\) | −1.76364e24 | −0.756892 | −0.378446 | − | 0.925623i | \(-0.623541\pi\) | ||||
−0.378446 | + | 0.925623i | \(0.623541\pi\) | |||||||
\(90\) | −2.88111e22 | −0.0107530 | ||||||||
\(91\) | −3.19097e24 | −1.03730 | ||||||||
\(92\) | 3.18729e24 | 0.903804 | ||||||||
\(93\) | −8.40325e23 | −0.208166 | ||||||||
\(94\) | 4.43693e22 | 0.00961578 | ||||||||
\(95\) | 4.51282e24 | 0.856847 | ||||||||
\(96\) | 3.17427e22 | 0.00528754 | ||||||||
\(97\) | 2.82924e24 | 0.414022 | 0.207011 | − | 0.978339i | \(-0.433626\pi\) | ||||
0.207011 | + | 0.978339i | \(0.433626\pi\) | |||||||
\(98\) | −8.93877e21 | −0.00115067 | ||||||||
\(99\) | −6.81096e24 | −0.772269 | ||||||||
\(100\) | −8.47278e24 | −0.847278 | ||||||||
\(101\) | 1.86342e24 | 0.164549 | 0.0822744 | − | 0.996610i | \(-0.473782\pi\) | ||||
0.0822744 | + | 0.996610i | \(0.473782\pi\) | |||||||
\(102\) | −2.36835e22 | −0.00184903 | ||||||||
\(103\) | 4.85812e24 | 0.335740 | 0.167870 | − | 0.985809i | \(-0.446311\pi\) | ||||
0.167870 | + | 0.985809i | \(0.446311\pi\) | |||||||
\(104\) | −2.63007e23 | −0.0161084 | ||||||||
\(105\) | 5.67781e24 | 0.308542 | ||||||||
\(106\) | 4.75340e22 | 0.00229446 | ||||||||
\(107\) | 3.58304e25 | 1.53799 | 0.768997 | − | 0.639252i | \(-0.220756\pi\) | ||||
0.768997 | + | 0.639252i | \(0.220756\pi\) | |||||||
\(108\) | −1.08809e25 | −0.415784 | ||||||||
\(109\) | −4.77795e25 | −1.62709 | −0.813543 | − | 0.581505i | \(-0.802464\pi\) | ||||
−0.813543 | + | 0.581505i | \(0.802464\pi\) | |||||||
\(110\) | 2.99865e23 | 0.00910999 | ||||||||
\(111\) | −3.97511e24 | −0.107848 | ||||||||
\(112\) | 4.39918e25 | 1.06696 | ||||||||
\(113\) | −7.46476e25 | −1.62008 | −0.810038 | − | 0.586378i | \(-0.800553\pi\) | ||||
−0.810038 | + | 0.586378i | \(0.800553\pi\) | |||||||
\(114\) | −5.71628e22 | −0.00111123 | ||||||||
\(115\) | 7.04855e25 | 1.22851 | ||||||||
\(116\) | 9.10091e24 | 0.142351 | ||||||||
\(117\) | 6.60516e25 | 0.928025 | ||||||||
\(118\) | −6.26523e23 | −0.00791429 | ||||||||
\(119\) | −9.84792e25 | −1.11946 | ||||||||
\(120\) | 4.67978e23 | 0.00479137 | ||||||||
\(121\) | −3.74588e25 | −0.345730 | ||||||||
\(122\) | −4.32742e23 | −0.00360355 | ||||||||
\(123\) | 3.59779e25 | 0.270534 | ||||||||
\(124\) | −1.43995e26 | −0.978532 | ||||||||
\(125\) | 3.37587e25 | 0.207496 | ||||||||
\(126\) | 1.51748e24 | 0.00844291 | ||||||||
\(127\) | 3.35905e26 | 1.69305 | 0.846524 | − | 0.532350i | \(-0.178691\pi\) | ||||
0.846524 | + | 0.532350i | \(0.178691\pi\) | |||||||
\(128\) | 7.25231e24 | 0.0331399 | ||||||||
\(129\) | −5.89178e25 | −0.244273 | ||||||||
\(130\) | −2.90804e24 | −0.0109474 | ||||||||
\(131\) | −1.74971e26 | −0.598513 | −0.299257 | − | 0.954173i | \(-0.596739\pi\) | ||||
−0.299257 | + | 0.954173i | \(0.596739\pi\) | |||||||
\(132\) | 5.53132e25 | 0.172050 | ||||||||
\(133\) | −2.37690e26 | −0.672769 | ||||||||
\(134\) | 1.28108e24 | 0.00330191 | ||||||||
\(135\) | −2.40626e26 | −0.565158 | ||||||||
\(136\) | −8.11689e24 | −0.0173841 | ||||||||
\(137\) | 6.18313e26 | 1.20837 | 0.604187 | − | 0.796843i | \(-0.293498\pi\) | ||||
0.604187 | + | 0.796843i | \(0.293498\pi\) | |||||||
\(138\) | −8.92822e23 | −0.00159322 | ||||||||
\(139\) | −4.84462e26 | −0.789905 | −0.394952 | − | 0.918702i | \(-0.629239\pi\) | ||||
−0.394952 | + | 0.918702i | \(0.629239\pi\) | |||||||
\(140\) | 9.72925e26 | 1.45037 | ||||||||
\(141\) | 1.80994e26 | 0.246845 | ||||||||
\(142\) | 9.23474e24 | 0.0115298 | ||||||||
\(143\) | −6.87462e26 | −0.786228 | ||||||||
\(144\) | −9.10608e26 | −0.954554 | ||||||||
\(145\) | 2.01262e26 | 0.193492 | ||||||||
\(146\) | −2.03542e24 | −0.00179574 | ||||||||
\(147\) | −3.64635e25 | −0.0295387 | ||||||||
\(148\) | −6.81158e26 | −0.506963 | ||||||||
\(149\) | 9.05569e26 | 0.619574 | 0.309787 | − | 0.950806i | \(-0.399742\pi\) | ||||
0.309787 | + | 0.950806i | \(0.399742\pi\) | |||||||
\(150\) | 2.37339e24 | 0.00149358 | ||||||||
\(151\) | 1.16190e27 | 0.672907 | 0.336454 | − | 0.941700i | \(-0.390772\pi\) | ||||
0.336454 | + | 0.941700i | \(0.390772\pi\) | |||||||
\(152\) | −1.95910e25 | −0.0104475 | ||||||||
\(153\) | 2.03847e27 | 1.00152 | ||||||||
\(154\) | −1.57939e25 | −0.00715287 | ||||||||
\(155\) | −3.18437e27 | −1.33008 | ||||||||
\(156\) | −5.36418e26 | −0.206750 | ||||||||
\(157\) | −3.41505e26 | −0.121521 | −0.0607605 | − | 0.998152i | \(-0.519353\pi\) | ||||
−0.0607605 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(158\) | 1.30407e25 | 0.00428634 | ||||||||
\(159\) | 1.93903e26 | 0.0589008 | ||||||||
\(160\) | 1.20287e26 | 0.0337847 | ||||||||
\(161\) | −3.71247e27 | −0.964583 | ||||||||
\(162\) | −2.98519e25 | −0.00717851 | ||||||||
\(163\) | 4.63202e27 | 1.03140 | 0.515698 | − | 0.856771i | \(-0.327533\pi\) | ||||
0.515698 | + | 0.856771i | \(0.327533\pi\) | |||||||
\(164\) | 6.16501e27 | 1.27170 | ||||||||
\(165\) | 1.22323e27 | 0.233861 | ||||||||
\(166\) | 4.47098e25 | 0.00792596 | ||||||||
\(167\) | −8.26470e27 | −1.35916 | −0.679581 | − | 0.733600i | \(-0.737838\pi\) | ||||
−0.679581 | + | 0.733600i | \(0.737838\pi\) | |||||||
\(168\) | −2.46484e25 | −0.00376204 | ||||||||
\(169\) | −3.89517e26 | −0.0552004 | ||||||||
\(170\) | −8.97475e25 | −0.0118144 | ||||||||
\(171\) | 4.92008e27 | 0.601895 | ||||||||
\(172\) | −1.00959e28 | −1.14826 | ||||||||
\(173\) | −6.02602e27 | −0.637462 | −0.318731 | − | 0.947845i | \(-0.603257\pi\) | ||||
−0.318731 | + | 0.947845i | \(0.603257\pi\) | |||||||
\(174\) | −2.54934e24 | −0.000250935 0 | ||||||||
\(175\) | 9.86886e27 | 0.904256 | ||||||||
\(176\) | 9.47758e27 | 0.808703 | ||||||||
\(177\) | −2.55575e27 | −0.203166 | ||||||||
\(178\) | 8.46545e25 | 0.00627191 | ||||||||
\(179\) | 2.41023e28 | 1.66493 | 0.832463 | − | 0.554081i | \(-0.186930\pi\) | ||||
0.832463 | + | 0.554081i | \(0.186930\pi\) | |||||||
\(180\) | −2.01391e28 | −1.29758 | ||||||||
\(181\) | −8.19193e27 | −0.492498 | −0.246249 | − | 0.969207i | \(-0.579198\pi\) | ||||
−0.246249 | + | 0.969207i | \(0.579198\pi\) | |||||||
\(182\) | 1.53167e26 | 0.00859551 | ||||||||
\(183\) | −1.76526e27 | −0.0925061 | ||||||||
\(184\) | −3.05991e26 | −0.0149791 | ||||||||
\(185\) | −1.50635e28 | −0.689095 | ||||||||
\(186\) | 4.03356e25 | 0.00172495 | ||||||||
\(187\) | −2.12163e28 | −0.848497 | ||||||||
\(188\) | 3.10143e28 | 1.16035 | ||||||||
\(189\) | 1.26738e28 | 0.443744 | ||||||||
\(190\) | −2.16616e26 | −0.00710018 | ||||||||
\(191\) | 5.50602e27 | 0.169013 | 0.0845066 | − | 0.996423i | \(-0.473069\pi\) | ||||
0.0845066 | + | 0.996423i | \(0.473069\pi\) | |||||||
\(192\) | 7.39422e27 | 0.212631 | ||||||||
\(193\) | 2.08716e28 | 0.562457 | 0.281228 | − | 0.959641i | \(-0.409258\pi\) | ||||
0.281228 | + | 0.959641i | \(0.409258\pi\) | |||||||
\(194\) | −1.35804e26 | −0.00343075 | ||||||||
\(195\) | −1.18626e28 | −0.281027 | ||||||||
\(196\) | −6.24823e27 | −0.138853 | ||||||||
\(197\) | −5.99370e28 | −1.24988 | −0.624938 | − | 0.780674i | \(-0.714876\pi\) | ||||
−0.624938 | + | 0.780674i | \(0.714876\pi\) | |||||||
\(198\) | 3.26926e26 | 0.00639933 | ||||||||
\(199\) | 2.24042e27 | 0.0411782 | 0.0205891 | − | 0.999788i | \(-0.493446\pi\) | ||||
0.0205891 | + | 0.999788i | \(0.493446\pi\) | |||||||
\(200\) | 8.13414e26 | 0.0140423 | ||||||||
\(201\) | 5.22583e27 | 0.0847626 | ||||||||
\(202\) | −8.94444e25 | −0.00136352 | ||||||||
\(203\) | −1.06005e28 | −0.151924 | ||||||||
\(204\) | −1.65548e28 | −0.223125 | ||||||||
\(205\) | 1.36336e29 | 1.72858 | ||||||||
\(206\) | −2.33190e26 | −0.00278208 | ||||||||
\(207\) | 7.68464e28 | 0.862967 | ||||||||
\(208\) | −9.19120e28 | −0.971808 | ||||||||
\(209\) | −5.12080e28 | −0.509928 | ||||||||
\(210\) | −2.72535e26 | −0.00255671 | ||||||||
\(211\) | −7.52475e28 | −0.665214 | −0.332607 | − | 0.943066i | \(-0.607928\pi\) | ||||
−0.332607 | + | 0.943066i | \(0.607928\pi\) | |||||||
\(212\) | 3.32264e28 | 0.276876 | ||||||||
\(213\) | 3.76708e28 | 0.295979 | ||||||||
\(214\) | −1.71986e27 | −0.0127444 | ||||||||
\(215\) | −2.23266e29 | −1.56078 | ||||||||
\(216\) | 1.04460e27 | 0.00689094 | ||||||||
\(217\) | 1.67721e29 | 1.04434 | ||||||||
\(218\) | 2.29342e27 | 0.0134827 | ||||||||
\(219\) | −8.30299e27 | −0.0460981 | ||||||||
\(220\) | 2.09607e29 | 1.09931 | ||||||||
\(221\) | 2.05752e29 | 1.01963 | ||||||||
\(222\) | 1.90805e26 | 0.000893673 0 | ||||||||
\(223\) | −3.16696e29 | −1.40227 | −0.701135 | − | 0.713029i | \(-0.747323\pi\) | ||||
−0.701135 | + | 0.713029i | \(0.747323\pi\) | |||||||
\(224\) | −6.33554e27 | −0.0265267 | ||||||||
\(225\) | −2.04281e29 | −0.808994 | ||||||||
\(226\) | 3.58308e27 | 0.0134246 | ||||||||
\(227\) | 3.85094e29 | 1.36535 | 0.682674 | − | 0.730723i | \(-0.260817\pi\) | ||||
0.682674 | + | 0.730723i | \(0.260817\pi\) | |||||||
\(228\) | −3.99569e28 | −0.134093 | ||||||||
\(229\) | −5.68261e29 | −1.80553 | −0.902765 | − | 0.430134i | \(-0.858466\pi\) | ||||
−0.902765 | + | 0.430134i | \(0.858466\pi\) | |||||||
\(230\) | −3.38331e27 | −0.0101799 | ||||||||
\(231\) | −6.44273e28 | −0.183620 | ||||||||
\(232\) | −8.73718e26 | −0.00235924 | ||||||||
\(233\) | 4.95586e29 | 1.26815 | 0.634075 | − | 0.773272i | \(-0.281381\pi\) | ||||
0.634075 | + | 0.773272i | \(0.281381\pi\) | |||||||
\(234\) | −3.17048e27 | −0.00769000 | ||||||||
\(235\) | 6.85867e29 | 1.57722 | ||||||||
\(236\) | −4.37941e29 | −0.955028 | ||||||||
\(237\) | 5.31962e28 | 0.110034 | ||||||||
\(238\) | 4.72700e27 | 0.00927628 | ||||||||
\(239\) | −1.44023e29 | −0.268200 | −0.134100 | − | 0.990968i | \(-0.542814\pi\) | ||||
−0.134100 | + | 0.990968i | \(0.542814\pi\) | |||||||
\(240\) | 1.63542e29 | 0.289061 | ||||||||
\(241\) | −3.19456e29 | −0.536041 | −0.268020 | − | 0.963413i | \(-0.586369\pi\) | ||||
−0.268020 | + | 0.963413i | \(0.586369\pi\) | |||||||
\(242\) | 1.79802e27 | 0.00286486 | ||||||||
\(243\) | −3.96547e29 | −0.600090 | ||||||||
\(244\) | −3.02488e29 | −0.434845 | ||||||||
\(245\) | −1.38177e29 | −0.188738 | ||||||||
\(246\) | −1.72694e27 | −0.00224175 | ||||||||
\(247\) | 4.96606e29 | 0.612774 | ||||||||
\(248\) | 1.38239e28 | 0.0162176 | ||||||||
\(249\) | 1.82383e29 | 0.203466 | ||||||||
\(250\) | −1.62042e27 | −0.00171940 | ||||||||
\(251\) | 6.21677e29 | 0.627543 | 0.313771 | − | 0.949499i | \(-0.398407\pi\) | ||||
0.313771 | + | 0.949499i | \(0.398407\pi\) | |||||||
\(252\) | 1.06072e30 | 1.01882 | ||||||||
\(253\) | −7.99814e29 | −0.731110 | ||||||||
\(254\) | −1.61234e28 | −0.0140293 | ||||||||
\(255\) | −3.66103e29 | −0.303285 | ||||||||
\(256\) | 1.26678e30 | 0.999313 | ||||||||
\(257\) | −2.29446e30 | −1.72392 | −0.861960 | − | 0.506977i | \(-0.830763\pi\) | ||||
−0.861960 | + | 0.506977i | \(0.830763\pi\) | |||||||
\(258\) | 2.82805e27 | 0.00202414 | ||||||||
\(259\) | 7.93394e29 | 0.541056 | ||||||||
\(260\) | −2.03273e30 | −1.32103 | ||||||||
\(261\) | 2.19425e29 | 0.135919 | ||||||||
\(262\) | 8.39859e27 | 0.00495952 | ||||||||
\(263\) | 7.73316e29 | 0.435422 | 0.217711 | − | 0.976013i | \(-0.430141\pi\) | ||||
0.217711 | + | 0.976013i | \(0.430141\pi\) | |||||||
\(264\) | −5.31025e27 | −0.00285145 | ||||||||
\(265\) | 7.34787e29 | 0.376347 | ||||||||
\(266\) | 1.14091e28 | 0.00557484 | ||||||||
\(267\) | 3.45327e29 | 0.161005 | ||||||||
\(268\) | 8.95475e29 | 0.398445 | ||||||||
\(269\) | 3.62259e30 | 1.53856 | 0.769282 | − | 0.638910i | \(-0.220614\pi\) | ||||
0.769282 | + | 0.638910i | \(0.220614\pi\) | |||||||
\(270\) | 1.15500e28 | 0.00468313 | ||||||||
\(271\) | −3.62767e30 | −1.40447 | −0.702234 | − | 0.711946i | \(-0.747814\pi\) | ||||
−0.702234 | + | 0.711946i | \(0.747814\pi\) | |||||||
\(272\) | −2.83657e30 | −1.04877 | ||||||||
\(273\) | 6.24805e29 | 0.220654 | ||||||||
\(274\) | −2.96790e28 | −0.0100131 | ||||||||
\(275\) | 2.12614e30 | 0.685384 | ||||||||
\(276\) | −6.24085e29 | −0.192256 | ||||||||
\(277\) | −2.54808e30 | −0.750266 | −0.375133 | − | 0.926971i | \(-0.622403\pi\) | ||||
−0.375133 | + | 0.926971i | \(0.622403\pi\) | |||||||
\(278\) | 2.32542e28 | 0.00654547 | ||||||||
\(279\) | −3.47174e30 | −0.934318 | ||||||||
\(280\) | −9.34040e28 | −0.0240375 | ||||||||
\(281\) | 3.59817e30 | 0.885631 | 0.442816 | − | 0.896613i | \(-0.353980\pi\) | ||||
0.442816 | + | 0.896613i | \(0.353980\pi\) | |||||||
\(282\) | −8.68769e27 | −0.00204546 | ||||||||
\(283\) | 3.82265e30 | 0.861061 | 0.430530 | − | 0.902576i | \(-0.358327\pi\) | ||||
0.430530 | + | 0.902576i | \(0.358327\pi\) | |||||||
\(284\) | 6.45511e30 | 1.39131 | ||||||||
\(285\) | −8.83629e29 | −0.182267 | ||||||||
\(286\) | 3.29982e28 | 0.00651500 | ||||||||
\(287\) | −7.18084e30 | −1.35722 | ||||||||
\(288\) | 1.31143e29 | 0.0237322 | ||||||||
\(289\) | 5.79269e29 | 0.100382 | ||||||||
\(290\) | −9.66060e27 | −0.00160335 | ||||||||
\(291\) | −5.53977e29 | −0.0880702 | ||||||||
\(292\) | −1.42276e30 | −0.216694 | ||||||||
\(293\) | 1.30007e29 | 0.0189723 | 0.00948615 | − | 0.999955i | \(-0.496980\pi\) | ||||
0.00948615 | + | 0.999955i | \(0.496980\pi\) | |||||||
\(294\) | 1.75025e27 | 0.000244770 0 | ||||||||
\(295\) | −9.68487e30 | −1.29813 | ||||||||
\(296\) | 6.53934e28 | 0.00840210 | ||||||||
\(297\) | 2.73043e30 | 0.336338 | ||||||||
\(298\) | −4.34673e28 | −0.00513404 | ||||||||
\(299\) | 7.75646e30 | 0.878565 | ||||||||
\(300\) | 1.65900e30 | 0.180232 | ||||||||
\(301\) | 1.17594e31 | 1.22548 | ||||||||
\(302\) | −5.57710e28 | −0.00557599 | ||||||||
\(303\) | −3.64866e29 | −0.0350026 | ||||||||
\(304\) | −6.84638e30 | −0.630291 | ||||||||
\(305\) | −6.68937e30 | −0.591068 | ||||||||
\(306\) | −9.78466e28 | −0.00829904 | ||||||||
\(307\) | 1.43602e31 | 1.16931 | 0.584657 | − | 0.811281i | \(-0.301229\pi\) | ||||
0.584657 | + | 0.811281i | \(0.301229\pi\) | |||||||
\(308\) | −1.10400e31 | −0.863146 | ||||||||
\(309\) | −9.51239e29 | −0.0714182 | ||||||||
\(310\) | 1.52850e29 | 0.0110216 | ||||||||
\(311\) | −2.24630e31 | −1.55584 | −0.777918 | − | 0.628366i | \(-0.783724\pi\) | ||||
−0.777918 | + | 0.628366i | \(0.783724\pi\) | |||||||
\(312\) | 5.14979e28 | 0.00342655 | ||||||||
\(313\) | −1.37956e30 | −0.0881934 | −0.0440967 | − | 0.999027i | \(-0.514041\pi\) | ||||
−0.0440967 | + | 0.999027i | \(0.514041\pi\) | |||||||
\(314\) | 1.63922e28 | 0.00100697 | ||||||||
\(315\) | 2.34574e31 | 1.38484 | ||||||||
\(316\) | 9.11548e30 | 0.517239 | ||||||||
\(317\) | −1.02787e31 | −0.560655 | −0.280327 | − | 0.959904i | \(-0.590443\pi\) | ||||
−0.280327 | + | 0.959904i | \(0.590443\pi\) | |||||||
\(318\) | −9.30735e27 | −0.000488076 0 | ||||||||
\(319\) | −2.28377e30 | −0.115151 | ||||||||
\(320\) | 2.80200e31 | 1.35861 | ||||||||
\(321\) | −7.01574e30 | −0.327160 | ||||||||
\(322\) | 1.78199e29 | 0.00799293 | ||||||||
\(323\) | 1.53262e31 | 0.661306 | ||||||||
\(324\) | −2.08666e31 | −0.866240 | ||||||||
\(325\) | −2.06190e31 | −0.823617 | ||||||||
\(326\) | −2.22337e29 | −0.00854656 | ||||||||
\(327\) | 9.35542e30 | 0.346112 | ||||||||
\(328\) | −5.91861e29 | −0.0210764 | ||||||||
\(329\) | −3.61246e31 | −1.23838 | ||||||||
\(330\) | −5.87148e28 | −0.00193787 | ||||||||
\(331\) | −5.75356e30 | −0.182847 | −0.0914233 | − | 0.995812i | \(-0.529142\pi\) | ||||
−0.0914233 | + | 0.995812i | \(0.529142\pi\) | |||||||
\(332\) | 3.12523e31 | 0.956435 | ||||||||
\(333\) | −1.64229e31 | −0.484057 | ||||||||
\(334\) | 3.96706e29 | 0.0112626 | ||||||||
\(335\) | 1.98030e31 | 0.541591 | ||||||||
\(336\) | −8.61377e30 | −0.226961 | ||||||||
\(337\) | 6.69268e31 | 1.69913 | 0.849564 | − | 0.527485i | \(-0.176865\pi\) | ||||
0.849564 | + | 0.527485i | \(0.176865\pi\) | |||||||
\(338\) | 1.86968e28 | 0.000457413 0 | ||||||||
\(339\) | 1.46163e31 | 0.344621 | ||||||||
\(340\) | −6.27338e31 | −1.42566 | ||||||||
\(341\) | 3.61337e31 | 0.791559 | ||||||||
\(342\) | −2.36164e29 | −0.00498754 | ||||||||
\(343\) | −4.51320e31 | −0.918984 | ||||||||
\(344\) | 9.69239e29 | 0.0190305 | ||||||||
\(345\) | −1.38013e31 | −0.261326 | ||||||||
\(346\) | 2.89249e29 | 0.00528227 | ||||||||
\(347\) | 9.41781e29 | 0.0165894 | 0.00829472 | − | 0.999966i | \(-0.497360\pi\) | ||||
0.00829472 | + | 0.999966i | \(0.497360\pi\) | |||||||
\(348\) | −1.78200e30 | −0.0302807 | ||||||||
\(349\) | −3.39081e31 | −0.555886 | −0.277943 | − | 0.960598i | \(-0.589653\pi\) | ||||
−0.277943 | + | 0.960598i | \(0.589653\pi\) | |||||||
\(350\) | −4.73705e29 | −0.00749303 | ||||||||
\(351\) | −2.64793e31 | −0.404173 | ||||||||
\(352\) | −1.36493e30 | −0.0201060 | ||||||||
\(353\) | 1.30313e31 | 0.185269 | 0.0926346 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926346 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(354\) | 1.22676e29 | 0.00168352 | ||||||||
\(355\) | 1.42752e32 | 1.89116 | ||||||||
\(356\) | 5.91737e31 | 0.756840 | ||||||||
\(357\) | 1.92826e31 | 0.238130 | ||||||||
\(358\) | −1.15691e30 | −0.0137963 | ||||||||
\(359\) | −1.30336e32 | −1.50101 | −0.750506 | − | 0.660864i | \(-0.770190\pi\) | ||||
−0.750506 | + | 0.660864i | \(0.770190\pi\) | |||||||
\(360\) | 1.93342e30 | 0.0215052 | ||||||||
\(361\) | −5.60851e31 | −0.602570 | ||||||||
\(362\) | 3.93213e29 | 0.00408104 | ||||||||
\(363\) | 7.33459e30 | 0.0735433 | ||||||||
\(364\) | 1.07064e32 | 1.03723 | ||||||||
\(365\) | −3.14638e31 | −0.294544 | ||||||||
\(366\) | 8.47325e28 | 0.000766543 0 | ||||||||
\(367\) | −2.06294e32 | −1.80369 | −0.901844 | − | 0.432061i | \(-0.857786\pi\) | ||||
−0.901844 | + | 0.432061i | \(0.857786\pi\) | |||||||
\(368\) | −1.06933e32 | −0.903680 | ||||||||
\(369\) | 1.48640e32 | 1.21424 | ||||||||
\(370\) | 7.23048e29 | 0.00571012 | ||||||||
\(371\) | −3.87012e31 | −0.295495 | ||||||||
\(372\) | 2.81947e31 | 0.208152 | ||||||||
\(373\) | 2.46051e32 | 1.75657 | 0.878283 | − | 0.478142i | \(-0.158689\pi\) | ||||
0.878283 | + | 0.478142i | \(0.158689\pi\) | |||||||
\(374\) | 1.01838e30 | 0.00703099 | ||||||||
\(375\) | −6.61009e30 | −0.0441384 | ||||||||
\(376\) | −2.97747e30 | −0.0192309 | ||||||||
\(377\) | 2.21476e31 | 0.138376 | ||||||||
\(378\) | −6.08341e29 | −0.00367705 | ||||||||
\(379\) | 7.12743e31 | 0.416815 | 0.208407 | − | 0.978042i | \(-0.433172\pi\) | ||||
0.208407 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(380\) | −1.51415e32 | −0.856788 | ||||||||
\(381\) | −6.57715e31 | −0.360143 | ||||||||
\(382\) | −2.64289e29 | −0.00140051 | ||||||||
\(383\) | 1.33051e32 | 0.682393 | 0.341196 | − | 0.939992i | \(-0.389168\pi\) | ||||
0.341196 | + | 0.939992i | \(0.389168\pi\) | |||||||
\(384\) | −1.42003e30 | −0.00704949 | ||||||||
\(385\) | −2.44144e32 | −1.17324 | ||||||||
\(386\) | −1.00184e30 | −0.00466075 | ||||||||
\(387\) | −2.43414e32 | −1.09637 | ||||||||
\(388\) | −9.49271e31 | −0.413993 | ||||||||
\(389\) | 2.40509e32 | 1.01569 | 0.507844 | − | 0.861449i | \(-0.330443\pi\) | ||||
0.507844 | + | 0.861449i | \(0.330443\pi\) | |||||||
\(390\) | 5.69407e29 | 0.00232871 | ||||||||
\(391\) | 2.39379e32 | 0.948147 | ||||||||
\(392\) | 5.99850e29 | 0.00230127 | ||||||||
\(393\) | 3.42599e31 | 0.127315 | ||||||||
\(394\) | 2.87698e30 | 0.0103570 | ||||||||
\(395\) | 2.01585e32 | 0.703062 | ||||||||
\(396\) | 2.28522e32 | 0.772216 | ||||||||
\(397\) | −4.12137e32 | −1.34946 | −0.674730 | − | 0.738065i | \(-0.735740\pi\) | ||||
−0.674730 | + | 0.738065i | \(0.735740\pi\) | |||||||
\(398\) | −1.07540e29 | −0.000341219 0 | ||||||||
\(399\) | 4.65407e31 | 0.143111 | ||||||||
\(400\) | 2.84260e32 | 0.847161 | ||||||||
\(401\) | −7.16647e31 | −0.207014 | −0.103507 | − | 0.994629i | \(-0.533006\pi\) | ||||
−0.103507 | + | 0.994629i | \(0.533006\pi\) | |||||||
\(402\) | −2.50840e29 | −0.000702377 0 | ||||||||
\(403\) | −3.50419e32 | −0.951206 | ||||||||
\(404\) | −6.25219e31 | −0.164537 | ||||||||
\(405\) | −4.61454e32 | −1.17745 | ||||||||
\(406\) | 5.08824e29 | 0.00125890 | ||||||||
\(407\) | 1.70929e32 | 0.410095 | ||||||||
\(408\) | 1.58932e30 | 0.00369793 | ||||||||
\(409\) | 1.34430e32 | 0.303358 | 0.151679 | − | 0.988430i | \(-0.451532\pi\) | ||||
0.151679 | + | 0.988430i | \(0.451532\pi\) | |||||||
\(410\) | −6.54415e30 | −0.0143237 | ||||||||
\(411\) | −1.21068e32 | −0.257044 | ||||||||
\(412\) | −1.63000e32 | −0.335717 | ||||||||
\(413\) | 5.10102e32 | 1.01925 | ||||||||
\(414\) | −3.68863e30 | −0.00715089 | ||||||||
\(415\) | 6.91130e32 | 1.30004 | ||||||||
\(416\) | 1.32368e31 | 0.0241612 | ||||||||
\(417\) | 9.48596e31 | 0.168028 | ||||||||
\(418\) | 2.45798e30 | 0.00422547 | ||||||||
\(419\) | −1.71876e32 | −0.286774 | −0.143387 | − | 0.989667i | \(-0.545799\pi\) | ||||
−0.143387 | + | 0.989667i | \(0.545799\pi\) | |||||||
\(420\) | −1.90503e32 | −0.308521 | ||||||||
\(421\) | −8.27664e32 | −1.30115 | −0.650576 | − | 0.759441i | \(-0.725472\pi\) | ||||
−0.650576 | + | 0.759441i | \(0.725472\pi\) | |||||||
\(422\) | 3.61188e30 | 0.00551223 | ||||||||
\(423\) | 7.47761e32 | 1.10792 | ||||||||
\(424\) | −3.18984e30 | −0.00458877 | ||||||||
\(425\) | −6.36340e32 | −0.888848 | ||||||||
\(426\) | −1.80820e30 | −0.00245260 | ||||||||
\(427\) | 3.52329e32 | 0.464088 | ||||||||
\(428\) | −1.20219e33 | −1.53789 | ||||||||
\(429\) | 1.34608e32 | 0.167245 | ||||||||
\(430\) | 1.07168e31 | 0.0129333 | ||||||||
\(431\) | −7.83836e31 | −0.0918881 | −0.0459441 | − | 0.998944i | \(-0.514630\pi\) | ||||
−0.0459441 | + | 0.998944i | \(0.514630\pi\) | |||||||
\(432\) | 3.65052e32 | 0.415727 | ||||||||
\(433\) | 6.33273e32 | 0.700635 | 0.350318 | − | 0.936631i | \(-0.386074\pi\) | ||||
0.350318 | + | 0.936631i | \(0.386074\pi\) | |||||||
\(434\) | −8.05060e30 | −0.00865380 | ||||||||
\(435\) | −3.94080e31 | −0.0411594 | ||||||||
\(436\) | 1.60310e33 | 1.62697 | ||||||||
\(437\) | 5.77767e32 | 0.569816 | ||||||||
\(438\) | 3.98543e29 | 0.000381988 0 | ||||||||
\(439\) | −1.48299e33 | −1.38144 | −0.690718 | − | 0.723124i | \(-0.742705\pi\) | ||||
−0.690718 | + | 0.723124i | \(0.742705\pi\) | |||||||
\(440\) | −2.01229e31 | −0.0182193 | ||||||||
\(441\) | −1.50646e32 | −0.132579 | ||||||||
\(442\) | −9.87612e30 | −0.00844905 | ||||||||
\(443\) | −1.20901e33 | −1.00551 | −0.502753 | − | 0.864430i | \(-0.667679\pi\) | ||||
−0.502753 | + | 0.864430i | \(0.667679\pi\) | |||||||
\(444\) | 1.33373e32 | 0.107841 | ||||||||
\(445\) | 1.30860e33 | 1.02874 | ||||||||
\(446\) | 1.52014e31 | 0.0116198 | ||||||||
\(447\) | −1.77314e32 | −0.131795 | ||||||||
\(448\) | −1.47581e33 | −1.06674 | ||||||||
\(449\) | −9.48861e32 | −0.666996 | −0.333498 | − | 0.942751i | \(-0.608229\pi\) | ||||
−0.333498 | + | 0.942751i | \(0.608229\pi\) | |||||||
\(450\) | 9.80547e30 | 0.00670366 | ||||||||
\(451\) | −1.54704e33 | −1.02871 | ||||||||
\(452\) | 2.50459e33 | 1.61996 | ||||||||
\(453\) | −2.27504e32 | −0.143140 | ||||||||
\(454\) | −1.84845e31 | −0.0113138 | ||||||||
\(455\) | 2.36767e33 | 1.40987 | ||||||||
\(456\) | 3.83600e30 | 0.00222238 | ||||||||
\(457\) | 1.90644e33 | 1.07466 | 0.537329 | − | 0.843373i | \(-0.319433\pi\) | ||||
0.537329 | + | 0.843373i | \(0.319433\pi\) | |||||||
\(458\) | 2.72765e31 | 0.0149614 | ||||||||
\(459\) | −8.17199e32 | −0.436183 | ||||||||
\(460\) | −2.36494e33 | −1.22842 | ||||||||
\(461\) | −4.56270e31 | −0.0230653 | −0.0115327 | − | 0.999933i | \(-0.503671\pi\) | ||||
−0.0115327 | + | 0.999933i | \(0.503671\pi\) | |||||||
\(462\) | 3.09251e30 | 0.00152155 | ||||||||
\(463\) | 2.13521e33 | 1.02254 | 0.511269 | − | 0.859421i | \(-0.329176\pi\) | ||||
0.511269 | + | 0.859421i | \(0.329176\pi\) | |||||||
\(464\) | −3.05334e32 | −0.142331 | ||||||||
\(465\) | 6.23513e32 | 0.282933 | ||||||||
\(466\) | −2.37882e31 | −0.0105084 | ||||||||
\(467\) | −2.67225e33 | −1.14926 | −0.574628 | − | 0.818415i | \(-0.694853\pi\) | ||||
−0.574628 | + | 0.818415i | \(0.694853\pi\) | |||||||
\(468\) | −2.21617e33 | −0.927962 | ||||||||
\(469\) | −1.04302e33 | −0.425240 | ||||||||
\(470\) | −3.29216e31 | −0.0130695 | ||||||||
\(471\) | 6.68680e31 | 0.0258498 | ||||||||
\(472\) | 4.20438e31 | 0.0158280 | ||||||||
\(473\) | 2.53345e33 | 0.928854 | ||||||||
\(474\) | −2.55342e30 | −0.000911786 0 | ||||||||
\(475\) | −1.53588e33 | −0.534178 | ||||||||
\(476\) | 3.30419e33 | 1.11938 | ||||||||
\(477\) | 8.01096e32 | 0.264366 | ||||||||
\(478\) | 6.91313e30 | 0.00222242 | ||||||||
\(479\) | 1.97240e33 | 0.617733 | 0.308867 | − | 0.951105i | \(-0.400050\pi\) | ||||
0.308867 | + | 0.951105i | \(0.400050\pi\) | |||||||
\(480\) | −2.35528e31 | −0.00718665 | ||||||||
\(481\) | −1.65764e33 | −0.492806 | ||||||||
\(482\) | 1.53339e31 | 0.00444185 | ||||||||
\(483\) | 7.26917e32 | 0.205185 | ||||||||
\(484\) | 1.25682e33 | 0.345706 | ||||||||
\(485\) | −2.09927e33 | −0.562725 | ||||||||
\(486\) | 1.90343e31 | 0.00497259 | ||||||||
\(487\) | −3.96366e32 | −0.100922 | −0.0504608 | − | 0.998726i | \(-0.516069\pi\) | ||||
−0.0504608 | + | 0.998726i | \(0.516069\pi\) | |||||||
\(488\) | 2.90398e31 | 0.00720686 | ||||||||
\(489\) | −9.06968e32 | −0.219397 | ||||||||
\(490\) | 6.63248e30 | 0.00156396 | ||||||||
\(491\) | −7.22626e33 | −1.66110 | −0.830548 | − | 0.556947i | \(-0.811973\pi\) | ||||
−0.830548 | + | 0.556947i | \(0.811973\pi\) | |||||||
\(492\) | −1.20713e33 | −0.270515 | ||||||||
\(493\) | 6.83515e32 | 0.149335 | ||||||||
\(494\) | −2.38371e31 | −0.00507769 | ||||||||
\(495\) | 5.05366e33 | 1.04964 | ||||||||
\(496\) | 4.83099e33 | 0.978397 | ||||||||
\(497\) | −7.51874e33 | −1.48488 | ||||||||
\(498\) | −8.75436e30 | −0.00168600 | ||||||||
\(499\) | 8.19830e33 | 1.53981 | 0.769905 | − | 0.638159i | \(-0.220304\pi\) | ||||
0.769905 | + | 0.638159i | \(0.220304\pi\) | |||||||
\(500\) | −1.13268e33 | −0.207482 | ||||||||
\(501\) | 1.61826e33 | 0.289119 | ||||||||
\(502\) | −2.98405e31 | −0.00520008 | ||||||||
\(503\) | 4.72562e33 | 0.803265 | 0.401633 | − | 0.915801i | \(-0.368443\pi\) | ||||
0.401633 | + | 0.915801i | \(0.368443\pi\) | |||||||
\(504\) | −1.01833e32 | −0.0168852 | ||||||||
\(505\) | −1.38264e33 | −0.223649 | ||||||||
\(506\) | 3.83911e31 | 0.00605827 | ||||||||
\(507\) | 7.62689e31 | 0.0117422 | ||||||||
\(508\) | −1.12703e34 | −1.69293 | ||||||||
\(509\) | 1.96955e33 | 0.288665 | 0.144332 | − | 0.989529i | \(-0.453897\pi\) | ||||
0.144332 | + | 0.989529i | \(0.453897\pi\) | |||||||
\(510\) | 1.75729e31 | 0.00251314 | ||||||||
\(511\) | 1.65720e33 | 0.231267 | ||||||||
\(512\) | −3.04153e32 | −0.0414207 | ||||||||
\(513\) | −1.97240e33 | −0.262137 | ||||||||
\(514\) | 1.10134e32 | 0.0142851 | ||||||||
\(515\) | −3.60468e33 | −0.456327 | ||||||||
\(516\) | 1.97682e33 | 0.244256 | ||||||||
\(517\) | −7.78267e33 | −0.938635 | ||||||||
\(518\) | −3.80829e31 | −0.00448341 | ||||||||
\(519\) | 1.17992e33 | 0.135600 | ||||||||
\(520\) | 1.95149e32 | 0.0218940 | ||||||||
\(521\) | 7.39782e33 | 0.810274 | 0.405137 | − | 0.914256i | \(-0.367224\pi\) | ||||
0.405137 | + | 0.914256i | \(0.367224\pi\) | |||||||
\(522\) | −1.05324e31 | −0.00112628 | ||||||||
\(523\) | 1.70332e34 | 1.77838 | 0.889191 | − | 0.457535i | \(-0.151268\pi\) | ||||
0.889191 | + | 0.457535i | \(0.151268\pi\) | |||||||
\(524\) | 5.87063e33 | 0.598472 | ||||||||
\(525\) | −1.93236e33 | −0.192352 | ||||||||
\(526\) | −3.71192e31 | −0.00360808 | ||||||||
\(527\) | −1.08146e34 | −1.02654 | ||||||||
\(528\) | −1.85575e33 | −0.172026 | ||||||||
\(529\) | −2.02166e33 | −0.183026 | ||||||||
\(530\) | −3.52698e31 | −0.00311856 | ||||||||
\(531\) | −1.05589e34 | −0.911876 | ||||||||
\(532\) | 7.97502e33 | 0.672723 | ||||||||
\(533\) | 1.50029e34 | 1.23619 | ||||||||
\(534\) | −1.65757e31 | −0.00133415 | ||||||||
\(535\) | −2.65858e34 | −2.09039 | ||||||||
\(536\) | −8.59686e31 | −0.00660358 | ||||||||
\(537\) | −4.71932e33 | −0.354161 | ||||||||
\(538\) | −1.73884e32 | −0.0127492 | ||||||||
\(539\) | 1.56792e33 | 0.112322 | ||||||||
\(540\) | 8.07351e33 | 0.565120 | ||||||||
\(541\) | −1.28681e34 | −0.880134 | −0.440067 | − | 0.897965i | \(-0.645045\pi\) | ||||
−0.440067 | + | 0.897965i | \(0.645045\pi\) | |||||||
\(542\) | 1.74128e32 | 0.0116380 | ||||||||
\(543\) | 1.60401e33 | 0.104764 | ||||||||
\(544\) | 4.08513e32 | 0.0260747 | ||||||||
\(545\) | 3.54519e34 | 2.21148 | ||||||||
\(546\) | −2.99906e31 | −0.00182843 | ||||||||
\(547\) | 2.06624e34 | 1.23123 | 0.615616 | − | 0.788046i | \(-0.288907\pi\) | ||||
0.615616 | + | 0.788046i | \(0.288907\pi\) | |||||||
\(548\) | −2.07457e34 | −1.20829 | ||||||||
\(549\) | −7.29304e33 | −0.415197 | ||||||||
\(550\) | −1.02055e32 | −0.00567937 | ||||||||
\(551\) | 1.64974e33 | 0.0897471 | ||||||||
\(552\) | 5.99142e31 | 0.00318633 | ||||||||
\(553\) | −1.06175e34 | −0.552022 | ||||||||
\(554\) | 1.22308e32 | 0.00621701 | ||||||||
\(555\) | 2.94949e33 | 0.146583 | ||||||||
\(556\) | 1.62547e34 | 0.789851 | ||||||||
\(557\) | −3.28751e33 | −0.156198 | −0.0780992 | − | 0.996946i | \(-0.524885\pi\) | ||||
−0.0780992 | + | 0.996946i | \(0.524885\pi\) | |||||||
\(558\) | 1.66644e32 | 0.00774214 | ||||||||
\(559\) | −2.45689e34 | −1.11619 | ||||||||
\(560\) | −3.26415e34 | −1.45017 | ||||||||
\(561\) | 4.15424e33 | 0.180491 | ||||||||
\(562\) | −1.72712e32 | −0.00733870 | ||||||||
\(563\) | −1.80804e34 | −0.751371 | −0.375685 | − | 0.926747i | \(-0.622593\pi\) | ||||
−0.375685 | + | 0.926747i | \(0.622593\pi\) | |||||||
\(564\) | −6.07272e33 | −0.246828 | ||||||||
\(565\) | 5.53878e34 | 2.20195 | ||||||||
\(566\) | −1.83487e32 | −0.00713510 | ||||||||
\(567\) | 2.43048e34 | 0.924493 | ||||||||
\(568\) | −6.19712e32 | −0.0230587 | ||||||||
\(569\) | −3.05967e33 | −0.111371 | −0.0556854 | − | 0.998448i | \(-0.517734\pi\) | ||||
−0.0556854 | + | 0.998448i | \(0.517734\pi\) | |||||||
\(570\) | 4.24142e31 | 0.00151034 | ||||||||
\(571\) | −1.29884e34 | −0.452486 | −0.226243 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226243 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(572\) | 2.30658e34 | 0.786174 | ||||||||
\(573\) | −1.07810e33 | −0.0359523 | ||||||||
\(574\) | 3.44680e32 | 0.0112465 | ||||||||
\(575\) | −2.39888e34 | −0.765878 | ||||||||
\(576\) | 3.05487e34 | 0.954357 | ||||||||
\(577\) | −7.31490e31 | −0.00223620 | −0.00111810 | − | 0.999999i | \(-0.500356\pi\) | ||||
−0.00111810 | + | 0.999999i | \(0.500356\pi\) | |||||||
\(578\) | −2.78049e31 | −0.000831808 0 | ||||||||
\(579\) | −4.08674e33 | −0.119645 | ||||||||
\(580\) | −6.75278e33 | −0.193479 | ||||||||
\(581\) | −3.64018e34 | −1.02075 | ||||||||
\(582\) | 2.65909e31 | 0.000729786 0 | ||||||||
\(583\) | −8.33778e33 | −0.223972 | ||||||||
\(584\) | 1.36590e32 | 0.00359136 | ||||||||
\(585\) | −4.90096e34 | −1.26134 | ||||||||
\(586\) | −6.24031e30 | −0.000157212 0 | ||||||||
\(587\) | 5.16226e34 | 1.27310 | 0.636551 | − | 0.771234i | \(-0.280360\pi\) | ||||
0.636551 | + | 0.771234i | \(0.280360\pi\) | |||||||
\(588\) | 1.22343e33 | 0.0295367 | ||||||||
\(589\) | −2.61022e34 | −0.616929 | ||||||||
\(590\) | 4.64874e32 | 0.0107568 | ||||||||
\(591\) | 1.17359e34 | 0.265872 | ||||||||
\(592\) | 2.28527e34 | 0.506894 | ||||||||
\(593\) | 2.40705e34 | 0.522758 | 0.261379 | − | 0.965236i | \(-0.415823\pi\) | ||||
0.261379 | + | 0.965236i | \(0.415823\pi\) | |||||||
\(594\) | −1.31061e32 | −0.00278703 | ||||||||
\(595\) | 7.30706e34 | 1.52153 | ||||||||
\(596\) | −3.03838e34 | −0.619531 | ||||||||
\(597\) | −4.38684e32 | −0.00875937 | ||||||||
\(598\) | −3.72310e32 | −0.00728015 | ||||||||
\(599\) | −8.30672e33 | −0.159072 | −0.0795361 | − | 0.996832i | \(-0.525344\pi\) | ||||
−0.0795361 | + | 0.996832i | \(0.525344\pi\) | |||||||
\(600\) | −1.59270e32 | −0.00298705 | ||||||||
\(601\) | −3.00405e34 | −0.551792 | −0.275896 | − | 0.961187i | \(-0.588975\pi\) | ||||
−0.275896 | + | 0.961187i | \(0.588975\pi\) | |||||||
\(602\) | −5.64452e32 | −0.0101548 | ||||||||
\(603\) | 2.15901e34 | 0.380442 | ||||||||
\(604\) | −3.89841e34 | −0.672861 | ||||||||
\(605\) | 2.77941e34 | 0.469905 | ||||||||
\(606\) | 1.75136e31 | 0.000290046 0 | ||||||||
\(607\) | −1.00963e35 | −1.63796 | −0.818978 | − | 0.573825i | \(-0.805459\pi\) | ||||
−0.818978 | + | 0.573825i | \(0.805459\pi\) | |||||||
\(608\) | 9.85991e32 | 0.0156703 | ||||||||
\(609\) | 2.07562e33 | 0.0323170 | ||||||||
\(610\) | 3.21090e32 | 0.00489783 | ||||||||
\(611\) | 7.54750e34 | 1.12795 | ||||||||
\(612\) | −6.83951e34 | −1.00146 | ||||||||
\(613\) | −1.02453e33 | −0.0146983 | −0.00734915 | − | 0.999973i | \(-0.502339\pi\) | ||||
−0.00734915 | + | 0.999973i | \(0.502339\pi\) | |||||||
\(614\) | −6.89290e32 | −0.00968941 | ||||||||
\(615\) | −2.66952e34 | −0.367701 | ||||||||
\(616\) | 1.05987e33 | 0.0143053 | ||||||||
\(617\) | 4.53271e34 | 0.599505 | 0.299753 | − | 0.954017i | \(-0.403096\pi\) | ||||
0.299753 | + | 0.954017i | \(0.403096\pi\) | |||||||
\(618\) | 4.56595e31 | 0.000591800 0 | ||||||||
\(619\) | 1.24784e35 | 1.58499 | 0.792496 | − | 0.609878i | \(-0.208781\pi\) | ||||
0.792496 | + | 0.609878i | \(0.208781\pi\) | |||||||
\(620\) | 1.06842e35 | 1.32999 | ||||||||
\(621\) | −3.08068e34 | −0.375839 | ||||||||
\(622\) | 1.07823e33 | 0.0128923 | ||||||||
\(623\) | −6.89239e34 | −0.807736 | ||||||||
\(624\) | 1.79967e34 | 0.206722 | ||||||||
\(625\) | −1.00307e35 | −1.12936 | ||||||||
\(626\) | 6.62189e31 | 0.000730807 0 | ||||||||
\(627\) | 1.00267e34 | 0.108471 | ||||||||
\(628\) | 1.14582e34 | 0.121513 | ||||||||
\(629\) | −5.11577e34 | −0.531836 | ||||||||
\(630\) | −1.12596e33 | −0.0114753 | ||||||||
\(631\) | 4.83338e34 | 0.482930 | 0.241465 | − | 0.970410i | \(-0.422372\pi\) | ||||
0.241465 | + | 0.970410i | \(0.422372\pi\) | |||||||
\(632\) | −8.75116e32 | −0.00857239 | ||||||||
\(633\) | 1.47338e34 | 0.141503 | ||||||||
\(634\) | 4.93375e32 | 0.00464581 | ||||||||
\(635\) | −2.49238e35 | −2.30114 | ||||||||
\(636\) | −6.50586e33 | −0.0588967 | ||||||||
\(637\) | −1.52054e34 | −0.134976 | ||||||||
\(638\) | 1.09621e32 | 0.000954190 0 | ||||||||
\(639\) | 1.55634e35 | 1.32845 | ||||||||
\(640\) | −5.38114e33 | −0.0450427 | ||||||||
\(641\) | 8.30494e34 | 0.681728 | 0.340864 | − | 0.940113i | \(-0.389280\pi\) | ||||
0.340864 | + | 0.940113i | \(0.389280\pi\) | |||||||
\(642\) | 3.36756e32 | 0.00271098 | ||||||||
\(643\) | 5.25724e34 | 0.415069 | 0.207535 | − | 0.978228i | \(-0.433456\pi\) | ||||
0.207535 | + | 0.978228i | \(0.433456\pi\) | |||||||
\(644\) | 1.24561e35 | 0.964517 | ||||||||
\(645\) | 4.37164e34 | 0.332008 | ||||||||
\(646\) | −7.35656e32 | −0.00547985 | ||||||||
\(647\) | −2.03021e35 | −1.48333 | −0.741665 | − | 0.670770i | \(-0.765964\pi\) | ||||
−0.741665 | + | 0.670770i | \(0.765964\pi\) | |||||||
\(648\) | 2.00326e33 | 0.0143565 | ||||||||
\(649\) | 1.09896e35 | 0.772546 | ||||||||
\(650\) | 9.89711e32 | 0.00682483 | ||||||||
\(651\) | −3.28404e34 | −0.222150 | ||||||||
\(652\) | −1.55414e35 | −1.03132 | ||||||||
\(653\) | 1.67657e35 | 1.09146 | 0.545728 | − | 0.837962i | \(-0.316253\pi\) | ||||
0.545728 | + | 0.837962i | \(0.316253\pi\) | |||||||
\(654\) | −4.49060e32 | −0.00286802 | ||||||||
\(655\) | 1.29826e35 | 0.813479 | ||||||||
\(656\) | −2.06835e35 | −1.27153 | ||||||||
\(657\) | −3.43032e34 | −0.206903 | ||||||||
\(658\) | 1.73398e33 | 0.0102617 | ||||||||
\(659\) | −2.92521e35 | −1.69859 | −0.849296 | − | 0.527917i | \(-0.822973\pi\) | ||||
−0.849296 | + | 0.527917i | \(0.822973\pi\) | |||||||
\(660\) | −4.10418e34 | −0.233845 | ||||||||
\(661\) | 8.30227e34 | 0.464172 | 0.232086 | − | 0.972695i | \(-0.425445\pi\) | ||||
0.232086 | + | 0.972695i | \(0.425445\pi\) | |||||||
\(662\) | 2.76171e32 | 0.00151514 | ||||||||
\(663\) | −4.02872e34 | −0.216894 | ||||||||
\(664\) | −3.00032e33 | −0.0158514 | ||||||||
\(665\) | 1.76364e35 | 0.914406 | ||||||||
\(666\) | 7.88298e32 | 0.00401109 | ||||||||
\(667\) | 2.57672e34 | 0.128675 | ||||||||
\(668\) | 2.77298e35 | 1.35907 | ||||||||
\(669\) | 6.20103e34 | 0.298289 | ||||||||
\(670\) | −9.50545e32 | −0.00448784 | ||||||||
\(671\) | 7.59057e34 | 0.351757 | ||||||||
\(672\) | 1.24052e33 | 0.00564273 | ||||||||
\(673\) | −3.23598e35 | −1.44483 | −0.722417 | − | 0.691458i | \(-0.756969\pi\) | ||||
−0.722417 | + | 0.691458i | \(0.756969\pi\) | |||||||
\(674\) | −3.21249e33 | −0.0140797 | ||||||||
\(675\) | 8.18936e34 | 0.352333 | ||||||||
\(676\) | 1.30691e34 | 0.0551966 | ||||||||
\(677\) | 7.76333e34 | 0.321877 | 0.160938 | − | 0.986964i | \(-0.448548\pi\) | ||||
0.160938 | + | 0.986964i | \(0.448548\pi\) | |||||||
\(678\) | −7.01582e32 | −0.00285567 | ||||||||
\(679\) | 1.10568e35 | 0.441834 | ||||||||
\(680\) | 6.02265e33 | 0.0236280 | ||||||||
\(681\) | −7.54029e34 | −0.290435 | ||||||||
\(682\) | −1.73442e33 | −0.00655918 | ||||||||
\(683\) | −2.49909e35 | −0.927945 | −0.463973 | − | 0.885850i | \(-0.653576\pi\) | ||||
−0.463973 | + | 0.885850i | \(0.653576\pi\) | |||||||
\(684\) | −1.65079e35 | −0.601853 | ||||||||
\(685\) | −4.58782e35 | −1.64238 | ||||||||
\(686\) | 2.16634e33 | 0.00761508 | ||||||||
\(687\) | 1.11268e35 | 0.384070 | ||||||||
\(688\) | 3.38716e35 | 1.14810 | ||||||||
\(689\) | 8.08584e34 | 0.269144 | ||||||||
\(690\) | 6.62465e32 | 0.00216545 | ||||||||
\(691\) | −8.56964e34 | −0.275098 | −0.137549 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137549 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(692\) | 2.02186e35 | 0.637419 | ||||||||
\(693\) | −2.66176e35 | −0.824146 | ||||||||
\(694\) | −4.52055e31 | −0.000137467 0 | ||||||||
\(695\) | 3.59466e35 | 1.07361 | ||||||||
\(696\) | 1.71077e32 | 0.000501854 0 | ||||||||
\(697\) | 4.63017e35 | 1.33410 | ||||||||
\(698\) | 1.62759e33 | 0.00460630 | ||||||||
\(699\) | −9.70378e34 | −0.269759 | ||||||||
\(700\) | −3.31121e35 | −0.904193 | ||||||||
\(701\) | 4.53464e35 | 1.21637 | 0.608187 | − | 0.793793i | \(-0.291897\pi\) | ||||
0.608187 | + | 0.793793i | \(0.291897\pi\) | |||||||
\(702\) | 1.27101e33 | 0.00334914 | ||||||||
\(703\) | −1.23475e35 | −0.319622 | ||||||||
\(704\) | −3.17949e35 | −0.808536 | ||||||||
\(705\) | −1.34295e35 | −0.335504 | ||||||||
\(706\) | −6.25502e32 | −0.00153522 | ||||||||
\(707\) | 7.28238e34 | 0.175602 | ||||||||
\(708\) | 8.57507e34 | 0.203152 | ||||||||
\(709\) | −4.93254e35 | −1.14813 | −0.574067 | − | 0.818808i | \(-0.694635\pi\) | ||||
−0.574067 | + | 0.818808i | \(0.694635\pi\) | |||||||
\(710\) | −6.85209e33 | −0.0156709 | ||||||||
\(711\) | 2.19776e35 | 0.493868 | ||||||||
\(712\) | −5.68087e33 | −0.0125434 | ||||||||
\(713\) | −4.07688e35 | −0.884522 | ||||||||
\(714\) | −9.25566e32 | −0.00197324 | ||||||||
\(715\) | 5.10090e35 | 1.06862 | ||||||||
\(716\) | −8.08682e35 | −1.66481 | ||||||||
\(717\) | 2.82004e34 | 0.0570513 | ||||||||
\(718\) | 6.25613e33 | 0.0124380 | ||||||||
\(719\) | 2.13499e35 | 0.417142 | 0.208571 | − | 0.978007i | \(-0.433119\pi\) | ||||
0.208571 | + | 0.978007i | \(0.433119\pi\) | |||||||
\(720\) | 6.75662e35 | 1.29740 | ||||||||
\(721\) | 1.89858e35 | 0.358293 | ||||||||
\(722\) | 2.69208e33 | 0.00499314 | ||||||||
\(723\) | 6.25508e34 | 0.114026 | ||||||||
\(724\) | 2.74857e35 | 0.492464 | ||||||||
\(725\) | −6.84968e34 | −0.120627 | ||||||||
\(726\) | −3.52060e32 | −0.000609409 0 | ||||||||
\(727\) | 5.12190e35 | 0.871467 | 0.435734 | − | 0.900076i | \(-0.356489\pi\) | ||||
0.435734 | + | 0.900076i | \(0.356489\pi\) | |||||||
\(728\) | −1.02785e34 | −0.0171904 | ||||||||
\(729\) | −4.49296e35 | −0.738649 | ||||||||
\(730\) | 1.51026e33 | 0.00244071 | ||||||||
\(731\) | −7.58243e35 | −1.20459 | ||||||||
\(732\) | 5.92283e34 | 0.0924998 | ||||||||
\(733\) | 1.77366e35 | 0.272315 | 0.136157 | − | 0.990687i | \(-0.456525\pi\) | ||||
0.136157 | + | 0.990687i | \(0.456525\pi\) | |||||||
\(734\) | 9.90213e33 | 0.0149461 | ||||||||
\(735\) | 2.70555e34 | 0.0401481 | ||||||||
\(736\) | 1.54001e34 | 0.0224674 | ||||||||
\(737\) | −2.24709e35 | −0.322312 | ||||||||
\(738\) | −7.13471e33 | −0.0100617 | ||||||||
\(739\) | −1.13535e36 | −1.57425 | −0.787124 | − | 0.616794i | \(-0.788431\pi\) | ||||
−0.787124 | + | 0.616794i | \(0.788431\pi\) | |||||||
\(740\) | 5.05412e35 | 0.689048 | ||||||||
\(741\) | −9.72375e34 | −0.130349 | ||||||||
\(742\) | 1.85766e33 | 0.00244860 | ||||||||
\(743\) | 4.03749e34 | 0.0523301 | 0.0261651 | − | 0.999658i | \(-0.491670\pi\) | ||||
0.0261651 | + | 0.999658i | \(0.491670\pi\) | |||||||
\(744\) | −2.70678e33 | −0.00344978 | ||||||||
\(745\) | −6.71923e35 | −0.842104 | ||||||||
\(746\) | −1.18104e34 | −0.0145556 | ||||||||
\(747\) | 7.53500e35 | 0.913220 | ||||||||
\(748\) | 7.11853e35 | 0.848439 | ||||||||
\(749\) | 1.40027e36 | 1.64131 | ||||||||
\(750\) | 3.17284e32 | 0.000365749 0 | ||||||||
\(751\) | 7.72405e35 | 0.875681 | 0.437840 | − | 0.899053i | \(-0.355744\pi\) | ||||
0.437840 | + | 0.899053i | \(0.355744\pi\) | |||||||
\(752\) | −1.04052e36 | −1.16019 | ||||||||
\(753\) | −1.21727e35 | −0.133490 | ||||||||
\(754\) | −1.06308e33 | −0.00114664 | ||||||||
\(755\) | −8.62115e35 | −0.914594 | ||||||||
\(756\) | −4.25232e35 | −0.443714 | ||||||||
\(757\) | 3.31585e35 | 0.340327 | 0.170163 | − | 0.985416i | \(-0.445570\pi\) | ||||
0.170163 | + | 0.985416i | \(0.445570\pi\) | |||||||
\(758\) | −3.42117e33 | −0.00345390 | ||||||||
\(759\) | 1.56607e35 | 0.155521 | ||||||||
\(760\) | 1.45363e34 | 0.0141999 | ||||||||
\(761\) | 2.02230e36 | 1.94329 | 0.971646 | − | 0.236440i | \(-0.0759807\pi\) | ||||
0.971646 | + | 0.236440i | \(0.0759807\pi\) | |||||||
\(762\) | 3.15703e33 | 0.00298429 | ||||||||
\(763\) | −1.86725e36 | −1.73639 | ||||||||
\(764\) | −1.84739e35 | −0.169002 | ||||||||
\(765\) | −1.51253e36 | −1.36124 | ||||||||
\(766\) | −6.38646e33 | −0.00565458 | ||||||||
\(767\) | −1.06576e36 | −0.928358 | ||||||||
\(768\) | −2.48041e35 | −0.212573 | ||||||||
\(769\) | 7.71193e35 | 0.650255 | 0.325128 | − | 0.945670i | \(-0.394593\pi\) | ||||
0.325128 | + | 0.945670i | \(0.394593\pi\) | |||||||
\(770\) | 1.17189e34 | 0.00972195 | ||||||||
\(771\) | 4.49265e35 | 0.366710 | ||||||||
\(772\) | −7.00286e35 | −0.562418 | ||||||||
\(773\) | 1.96060e36 | 1.54934 | 0.774668 | − | 0.632368i | \(-0.217917\pi\) | ||||
0.774668 | + | 0.632368i | \(0.217917\pi\) | |||||||
\(774\) | 1.16839e34 | 0.00908501 | ||||||||
\(775\) | 1.08376e36 | 0.829202 | ||||||||
\(776\) | 9.11331e33 | 0.00686127 | ||||||||
\(777\) | −1.55350e35 | −0.115093 | ||||||||
\(778\) | −1.15444e34 | −0.00841641 | ||||||||
\(779\) | 1.11754e36 | 0.801763 | ||||||||
\(780\) | 3.98017e35 | 0.281008 | ||||||||
\(781\) | −1.61983e36 | −1.12547 | ||||||||
\(782\) | −1.14902e34 | −0.00785674 | ||||||||
\(783\) | −8.79649e34 | −0.0591953 | ||||||||
\(784\) | 2.09627e35 | 0.138834 | ||||||||
\(785\) | 2.53393e35 | 0.165167 | ||||||||
\(786\) | −1.64448e33 | −0.00105498 | ||||||||
\(787\) | −8.92654e35 | −0.563637 | −0.281818 | − | 0.959468i | \(-0.590938\pi\) | ||||
−0.281818 | + | 0.959468i | \(0.590938\pi\) | |||||||
\(788\) | 2.01101e36 | 1.24979 | ||||||||
\(789\) | −1.51418e35 | −0.0926224 | ||||||||
\(790\) | −9.67606e33 | −0.00582586 | ||||||||
\(791\) | −2.91727e36 | −1.72890 | ||||||||
\(792\) | −2.19389e34 | −0.0127982 | ||||||||
\(793\) | −7.36121e35 | −0.422702 | ||||||||
\(794\) | 1.97826e34 | 0.0111822 | ||||||||
\(795\) | −1.43874e35 | −0.0800560 | ||||||||
\(796\) | −7.51710e34 | −0.0411753 | ||||||||
\(797\) | −2.35494e36 | −1.26984 | −0.634921 | − | 0.772577i | \(-0.718968\pi\) | ||||
−0.634921 | + | 0.772577i | \(0.718968\pi\) | |||||||
\(798\) | −2.23396e33 | −0.00118587 | ||||||||
\(799\) | 2.32930e36 | 1.21728 | ||||||||
\(800\) | −4.09381e34 | −0.0210622 | ||||||||
\(801\) | 1.42669e36 | 0.722643 | ||||||||
\(802\) | 3.43990e33 | 0.00171541 | ||||||||
\(803\) | 3.57026e35 | 0.175289 | ||||||||
\(804\) | −1.75338e35 | −0.0847568 | ||||||||
\(805\) | 2.75462e36 | 1.31103 | ||||||||
\(806\) | 1.68201e34 | 0.00788208 | ||||||||
\(807\) | −7.09317e35 | −0.327281 | ||||||||
\(808\) | 6.00231e33 | 0.00272694 | ||||||||
\(809\) | −1.29617e36 | −0.579834 | −0.289917 | − | 0.957052i | \(-0.593628\pi\) | ||||
−0.289917 | + | 0.957052i | \(0.593628\pi\) | |||||||
\(810\) | 2.21498e34 | 0.00975680 | ||||||||
\(811\) | 2.63606e36 | 1.14339 | 0.571695 | − | 0.820467i | \(-0.306286\pi\) | ||||
0.571695 | + | 0.820467i | \(0.306286\pi\) | |||||||
\(812\) | 3.55669e35 | 0.151913 | ||||||||
\(813\) | 7.10313e35 | 0.298757 | ||||||||
\(814\) | −8.20458e33 | −0.00339822 | ||||||||
\(815\) | −3.43691e36 | −1.40184 | ||||||||
\(816\) | 5.55412e35 | 0.223094 | ||||||||
\(817\) | −1.83010e36 | −0.723935 | ||||||||
\(818\) | −6.45265e33 | −0.00251375 | ||||||||
\(819\) | 2.58133e36 | 0.990366 | ||||||||
\(820\) | −4.57438e36 | −1.72846 | ||||||||
\(821\) | −5.92271e35 | −0.220410 | −0.110205 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110205 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(822\) | 5.81127e33 | 0.00212997 | ||||||||
\(823\) | 4.76928e35 | 0.172169 | 0.0860845 | − | 0.996288i | \(-0.472564\pi\) | ||||
0.0860845 | + | 0.996288i | \(0.472564\pi\) | |||||||
\(824\) | 1.56486e34 | 0.00556396 | ||||||||
\(825\) | −4.16308e35 | −0.145794 | ||||||||
\(826\) | −2.44849e34 | −0.00844594 | ||||||||
\(827\) | 4.17794e36 | 1.41953 | 0.709763 | − | 0.704440i | \(-0.248802\pi\) | ||||
0.709763 | + | 0.704440i | \(0.248802\pi\) | |||||||
\(828\) | −2.57836e36 | −0.862908 | ||||||||
\(829\) | −3.18023e36 | −1.04840 | −0.524199 | − | 0.851596i | \(-0.675635\pi\) | ||||
−0.524199 | + | 0.851596i | \(0.675635\pi\) | |||||||
\(830\) | −3.31742e34 | −0.0107727 | ||||||||
\(831\) | 4.98924e35 | 0.159596 | ||||||||
\(832\) | 3.08342e36 | 0.971608 | ||||||||
\(833\) | −4.69267e35 | −0.145666 | ||||||||
\(834\) | −4.55326e33 | −0.00139235 | ||||||||
\(835\) | 6.13232e36 | 1.84733 | ||||||||
\(836\) | 1.71814e36 | 0.509893 | ||||||||
\(837\) | 1.39178e36 | 0.406913 | ||||||||
\(838\) | 8.25006e33 | 0.00237633 | ||||||||
\(839\) | −3.57270e36 | −1.01384 | −0.506922 | − | 0.861992i | \(-0.669217\pi\) | ||||
−0.506922 | + | 0.861992i | \(0.669217\pi\) | |||||||
\(840\) | 1.82889e34 | 0.00511324 | ||||||||
\(841\) | −3.55679e36 | −0.979733 | ||||||||
\(842\) | 3.97279e34 | 0.0107819 | ||||||||
\(843\) | −7.04537e35 | −0.188390 | ||||||||
\(844\) | 2.52471e36 | 0.665168 | ||||||||
\(845\) | 2.89018e35 | 0.0750266 | ||||||||
\(846\) | −3.58925e34 | −0.00918068 | ||||||||
\(847\) | −1.46391e36 | −0.368954 | ||||||||
\(848\) | −1.11474e36 | −0.276838 | ||||||||
\(849\) | −7.48489e35 | −0.183164 | ||||||||
\(850\) | 3.05443e34 | 0.00736535 | ||||||||
\(851\) | −1.92855e36 | −0.458258 | ||||||||
\(852\) | −1.26394e36 | −0.295958 | ||||||||
\(853\) | −1.75466e36 | −0.404884 | −0.202442 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202442 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(854\) | −1.69118e34 | −0.00384562 | ||||||||
\(855\) | −3.65065e36 | −0.818075 | ||||||||
\(856\) | 1.15414e35 | 0.0254880 | ||||||||
\(857\) | 7.10324e36 | 1.54595 | 0.772976 | − | 0.634435i | \(-0.218767\pi\) | ||||
0.772976 | + | 0.634435i | \(0.218767\pi\) | |||||||
\(858\) | −6.46118e33 | −0.00138586 | ||||||||
\(859\) | −7.56695e36 | −1.59958 | −0.799791 | − | 0.600279i | \(-0.795056\pi\) | ||||
−0.799791 | + | 0.600279i | \(0.795056\pi\) | |||||||
\(860\) | 7.49105e36 | 1.56067 | ||||||||
\(861\) | 1.40604e36 | 0.288707 | ||||||||
\(862\) | 3.76241e33 | 0.000761423 0 | ||||||||
\(863\) | 5.72195e36 | 1.14132 | 0.570662 | − | 0.821185i | \(-0.306687\pi\) | ||||
0.570662 | + | 0.821185i | \(0.306687\pi\) | |||||||
\(864\) | −5.25735e34 | −0.0103358 | ||||||||
\(865\) | 4.47125e36 | 0.866418 | ||||||||
\(866\) | −3.03971e34 | −0.00580575 | ||||||||
\(867\) | −1.13423e35 | −0.0213532 | ||||||||
\(868\) | −5.62739e36 | −1.04426 | ||||||||
\(869\) | −2.28742e36 | −0.418407 | ||||||||
\(870\) | 1.89158e33 | 0.000341063 0 | ||||||||
\(871\) | 2.17919e36 | 0.387318 | ||||||||
\(872\) | −1.53903e35 | −0.0269645 | ||||||||
\(873\) | −2.28871e36 | −0.395288 | ||||||||
\(874\) | −2.77328e34 | −0.00472173 | ||||||||
\(875\) | 1.31931e36 | 0.221435 | ||||||||
\(876\) | 2.78583e35 | 0.0460949 | ||||||||
\(877\) | 3.21926e36 | 0.525123 | 0.262561 | − | 0.964915i | \(-0.415433\pi\) | ||||
0.262561 | + | 0.964915i | \(0.415433\pi\) | |||||||
\(878\) | 7.11834e34 | 0.0114471 | ||||||||
\(879\) | −2.54558e34 | −0.00403576 | ||||||||
\(880\) | −7.03227e36 | −1.09916 | ||||||||
\(881\) | −1.04633e37 | −1.61238 | −0.806191 | − | 0.591655i | \(-0.798475\pi\) | ||||
−0.806191 | + | 0.591655i | \(0.798475\pi\) | |||||||
\(882\) | 7.23102e33 | 0.00109861 | ||||||||
\(883\) | 4.11745e36 | 0.616765 | 0.308382 | − | 0.951263i | \(-0.400212\pi\) | ||||
0.308382 | + | 0.951263i | \(0.400212\pi\) | |||||||
\(884\) | −6.90343e36 | −1.01956 | ||||||||
\(885\) | 1.89634e36 | 0.276137 | ||||||||
\(886\) | 5.80326e34 | 0.00833202 | ||||||||
\(887\) | −2.52904e36 | −0.358022 | −0.179011 | − | 0.983847i | \(-0.557290\pi\) | ||||
−0.179011 | + | 0.983847i | \(0.557290\pi\) | |||||||
\(888\) | −1.28043e34 | −0.00178728 | ||||||||
\(889\) | 1.31273e37 | 1.80678 | ||||||||
\(890\) | −6.28128e34 | −0.00852458 | ||||||||
\(891\) | 5.23622e36 | 0.700723 | ||||||||
\(892\) | 1.06258e37 | 1.40217 | ||||||||
\(893\) | 5.62202e36 | 0.731558 | ||||||||
\(894\) | 8.51107e33 | 0.00109211 | ||||||||
\(895\) | −1.78836e37 | −2.26291 | ||||||||
\(896\) | 2.83425e35 | 0.0353661 | ||||||||
\(897\) | −1.51875e36 | −0.186887 | ||||||||
\(898\) | 4.55453e34 | 0.00552700 | ||||||||
\(899\) | −1.16410e36 | −0.139314 | ||||||||
\(900\) | 6.85405e36 | 0.808939 | ||||||||
\(901\) | 2.49544e36 | 0.290460 | ||||||||
\(902\) | 7.42578e34 | 0.00852433 | ||||||||
\(903\) | −2.30254e36 | −0.260682 | ||||||||
\(904\) | −2.40448e35 | −0.0268483 | ||||||||
\(905\) | 6.07833e36 | 0.669387 | ||||||||
\(906\) | 1.09202e34 | 0.00118612 | ||||||||
\(907\) | −4.93129e36 | −0.528286 | −0.264143 | − | 0.964484i | \(-0.585089\pi\) | ||||
−0.264143 | + | 0.964484i | \(0.585089\pi\) | |||||||
\(908\) | −1.29207e37 | −1.36525 | ||||||||
\(909\) | −1.50742e36 | −0.157103 | ||||||||
\(910\) | −1.13648e35 | −0.0116827 | ||||||||
\(911\) | −7.10548e36 | −0.720466 | −0.360233 | − | 0.932862i | \(-0.617303\pi\) | ||||
−0.360233 | + | 0.932862i | \(0.617303\pi\) | |||||||
\(912\) | 1.34055e36 | 0.134075 | ||||||||
\(913\) | −7.84240e36 | −0.773685 | ||||||||
\(914\) | −9.15090e34 | −0.00890505 | ||||||||
\(915\) | 1.30981e36 | 0.125731 | ||||||||
\(916\) | 1.90664e37 | 1.80541 | ||||||||
\(917\) | −6.83795e36 | −0.638718 | ||||||||
\(918\) | 3.92255e34 | 0.00361439 | ||||||||
\(919\) | 2.64155e36 | 0.240112 | 0.120056 | − | 0.992767i | \(-0.461693\pi\) | ||||
0.120056 | + | 0.992767i | \(0.461693\pi\) | |||||||
\(920\) | 2.27042e35 | 0.0203591 | ||||||||
\(921\) | −2.81179e36 | −0.248735 | ||||||||
\(922\) | 2.19009e33 | 0.000191129 0 | ||||||||
\(923\) | 1.57089e37 | 1.35246 | ||||||||
\(924\) | 2.16167e36 | 0.183607 | ||||||||
\(925\) | 5.12665e36 | 0.429597 | ||||||||
\(926\) | −1.02490e35 | −0.00847316 | ||||||||
\(927\) | −3.92997e36 | −0.320548 | ||||||||
\(928\) | 4.39731e34 | 0.00353865 | ||||||||
\(929\) | 5.01934e36 | 0.398520 | 0.199260 | − | 0.979947i | \(-0.436146\pi\) | ||||
0.199260 | + | 0.979947i | \(0.436146\pi\) | |||||||
\(930\) | −2.99286e34 | −0.00234450 | ||||||||
\(931\) | −1.13263e36 | −0.0875419 | ||||||||
\(932\) | −1.66280e37 | −1.26806 | ||||||||
\(933\) | 4.39835e36 | 0.330955 | ||||||||
\(934\) | 1.28268e35 | 0.00952320 | ||||||||
\(935\) | 1.57423e37 | 1.15325 | ||||||||
\(936\) | 2.12760e35 | 0.0153795 | ||||||||
\(937\) | −1.70189e37 | −1.21391 | −0.606956 | − | 0.794735i | \(-0.707610\pi\) | ||||
−0.606956 | + | 0.794735i | \(0.707610\pi\) | |||||||
\(938\) | 5.00652e34 | 0.00352371 | ||||||||
\(939\) | 2.70123e35 | 0.0187604 | ||||||||
\(940\) | −2.30123e37 | −1.57711 | ||||||||
\(941\) | −1.51254e37 | −1.02291 | −0.511455 | − | 0.859310i | \(-0.670893\pi\) | ||||
−0.511455 | + | 0.859310i | \(0.670893\pi\) | |||||||
\(942\) | −3.20967e33 | −0.000214202 0 | ||||||||
\(943\) | 1.74548e37 | 1.14953 | ||||||||
\(944\) | 1.46929e37 | 0.954897 | ||||||||
\(945\) | −9.40380e36 | −0.603123 | ||||||||
\(946\) | −1.21605e35 | −0.00769687 | ||||||||
\(947\) | 1.65329e36 | 0.103270 | 0.0516351 | − | 0.998666i | \(-0.483557\pi\) | ||||
0.0516351 | + | 0.998666i | \(0.483557\pi\) | |||||||
\(948\) | −1.78485e36 | −0.110026 | ||||||||
\(949\) | −3.46238e36 | −0.210643 | ||||||||
\(950\) | 7.37220e34 | 0.00442642 | ||||||||
\(951\) | 2.01260e36 | 0.119262 | ||||||||
\(952\) | −3.17213e35 | −0.0185519 | ||||||||
\(953\) | 2.77784e37 | 1.60341 | 0.801706 | − | 0.597718i | \(-0.203926\pi\) | ||||
0.801706 | + | 0.597718i | \(0.203926\pi\) | |||||||
\(954\) | −3.84526e34 | −0.00219064 | ||||||||
\(955\) | −4.08541e36 | −0.229717 | ||||||||
\(956\) | 4.83229e36 | 0.268182 | ||||||||
\(957\) | 4.47171e35 | 0.0244948 | ||||||||
\(958\) | −9.46752e34 | −0.00511879 | ||||||||
\(959\) | 2.41640e37 | 1.28955 | ||||||||
\(960\) | −5.48644e36 | −0.289001 | ||||||||
\(961\) | −8.14395e35 | −0.0423441 | ||||||||
\(962\) | 7.95666e34 | 0.00408359 | ||||||||
\(963\) | −2.89850e37 | −1.46840 | ||||||||
\(964\) | 1.07184e37 | 0.536004 | ||||||||
\(965\) | −1.54865e37 | −0.764473 | ||||||||
\(966\) | −3.48920e34 | −0.00170025 | ||||||||
\(967\) | 3.82441e36 | 0.183965 | 0.0919823 | − | 0.995761i | \(-0.470680\pi\) | ||||
0.0919823 | + | 0.995761i | \(0.470680\pi\) | |||||||
\(968\) | −1.20659e35 | −0.00572952 | ||||||||
\(969\) | −3.00093e36 | −0.140672 | ||||||||
\(970\) | 1.00765e35 | 0.00466297 | ||||||||
\(971\) | −1.67087e37 | −0.763311 | −0.381655 | − | 0.924305i | \(-0.624646\pi\) | ||||
−0.381655 | + | 0.924305i | \(0.624646\pi\) | |||||||
\(972\) | 1.33050e37 | 0.600049 | ||||||||
\(973\) | −1.89331e37 | −0.842967 | ||||||||
\(974\) | 1.90256e34 | 0.000836277 0 | ||||||||
\(975\) | 4.03728e36 | 0.175199 | ||||||||
\(976\) | 1.01484e37 | 0.434786 | ||||||||
\(977\) | −3.54376e37 | −1.49893 | −0.749466 | − | 0.662043i | \(-0.769690\pi\) | ||||
−0.749466 | + | 0.662043i | \(0.769690\pi\) | |||||||
\(978\) | 4.35345e34 | 0.00181802 | ||||||||
\(979\) | −1.48490e37 | −0.612227 | ||||||||
\(980\) | 4.63612e36 | 0.188725 | ||||||||
\(981\) | 3.86512e37 | 1.55346 | ||||||||
\(982\) | 3.46860e35 | 0.0137645 | ||||||||
\(983\) | 2.26759e37 | 0.888476 | 0.444238 | − | 0.895909i | \(-0.353475\pi\) | ||||
0.444238 | + | 0.895909i | \(0.353475\pi\) | |||||||
\(984\) | 1.15889e35 | 0.00448335 | ||||||||
\(985\) | 4.44726e37 | 1.69879 | ||||||||
\(986\) | −3.28087e34 | −0.00123745 | ||||||||
\(987\) | 7.07334e36 | 0.263427 | ||||||||
\(988\) | −1.66622e37 | −0.612732 | ||||||||
\(989\) | −2.85843e37 | −1.03794 | ||||||||
\(990\) | −2.42576e35 | −0.00869777 | ||||||||
\(991\) | −1.82706e36 | −0.0646891 | −0.0323445 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323445 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(992\) | −6.95742e35 | −0.0243250 | ||||||||
\(993\) | 1.12657e36 | 0.0388949 | ||||||||
\(994\) | 3.60899e35 | 0.0123043 | ||||||||
\(995\) | −1.66237e36 | −0.0559680 | ||||||||
\(996\) | −6.11932e36 | −0.203452 | ||||||||
\(997\) | 2.34599e37 | 0.770260 | 0.385130 | − | 0.922862i | \(-0.374157\pi\) | ||||
0.385130 | + | 0.922862i | \(0.374157\pi\) | |||||||
\(998\) | −3.93518e35 | −0.0127595 | ||||||||
\(999\) | 6.58373e36 | 0.210816 |
(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 | 1.26.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.26.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 16.26.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 25.26.b.a.24.1 | 2 | |||
5.3 | odd | 4 | 25.26.b.a.24.2 | 2 | |||
5.4 | even | 2 | 25.26.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 49.26.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.26.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.26.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
16.26.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
25.26.a.a.1.1 | 1 | 5.4 | even | 2 | |||
25.26.b.a.24.1 | 2 | 5.2 | odd | 4 | |||
25.26.b.a.24.2 | 2 | 5.3 | odd | 4 | |||
49.26.a.a.1.1 | 1 | 7.6 | odd | 2 |