Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,10,Mod(1,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.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: | \(25.2367559720\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 426x + 2016 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-22.2358\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.3607 | 0.590466 | 0.295233 | − | 0.955425i | \(-0.404603\pi\) | ||||
0.295233 | + | 0.955425i | \(0.404603\pi\) | |||||||
\(3\) | −163.415 | −1.16478 | −0.582392 | − | 0.812908i | \(-0.697883\pi\) | ||||
−0.582392 | + | 0.812908i | \(0.697883\pi\) | |||||||
\(4\) | −333.491 | −0.651350 | ||||||||
\(5\) | −1922.19 | −1.37541 | −0.687703 | − | 0.725992i | \(-0.741381\pi\) | ||||
−0.687703 | + | 0.725992i | \(0.741381\pi\) | |||||||
\(6\) | −2183.34 | −0.687765 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −11296.4 | −0.975066 | ||||||||
\(9\) | 7021.32 | 0.356720 | ||||||||
\(10\) | −25681.8 | −0.812131 | ||||||||
\(11\) | −90199.9 | −1.85754 | −0.928772 | − | 0.370652i | \(-0.879134\pi\) | ||||
−0.928772 | + | 0.370652i | \(0.879134\pi\) | |||||||
\(12\) | 54497.3 | 0.758681 | ||||||||
\(13\) | 3199.89 | 0.0310734 | 0.0155367 | − | 0.999879i | \(-0.495054\pi\) | ||||
0.0155367 | + | 0.999879i | \(0.495054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 314114. | 1.60205 | ||||||||
\(16\) | 19819.7 | 0.0756061 | ||||||||
\(17\) | −116494. | −0.338286 | −0.169143 | − | 0.985591i | \(-0.554100\pi\) | ||||
−0.169143 | + | 0.985591i | \(0.554100\pi\) | |||||||
\(18\) | 93809.9 | 0.210631 | ||||||||
\(19\) | 142449. | 0.250767 | 0.125383 | − | 0.992108i | \(-0.459984\pi\) | ||||
0.125383 | + | 0.992108i | \(0.459984\pi\) | |||||||
\(20\) | 641033. | 0.895870 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.20514e6 | −1.09682 | ||||||||
\(23\) | 1.27391e6 | 0.949213 | 0.474606 | − | 0.880198i | \(-0.342590\pi\) | ||||
0.474606 | + | 0.880198i | \(0.342590\pi\) | |||||||
\(24\) | 1.84599e6 | 1.13574 | ||||||||
\(25\) | 1.74168e6 | 0.891742 | ||||||||
\(26\) | 42752.8 | 0.0183478 | ||||||||
\(27\) | 2.06910e6 | 0.749282 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.42931e6 | −0.375262 | −0.187631 | − | 0.982240i | \(-0.560081\pi\) | ||||
−0.187631 | + | 0.982240i | \(0.560081\pi\) | |||||||
\(30\) | 4.19679e6 | 0.945956 | ||||||||
\(31\) | −9.67494e6 | −1.88157 | −0.940786 | − | 0.339001i | \(-0.889911\pi\) | ||||
−0.940786 | + | 0.339001i | \(0.889911\pi\) | |||||||
\(32\) | 6.04855e6 | 1.01971 | ||||||||
\(33\) | 1.47400e7 | 2.16364 | ||||||||
\(34\) | −1.55645e6 | −0.199747 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.34155e6 | −0.232349 | ||||||||
\(37\) | −8.67744e6 | −0.761174 | −0.380587 | − | 0.924745i | \(-0.624278\pi\) | ||||
−0.380587 | + | 0.924745i | \(0.624278\pi\) | |||||||
\(38\) | 1.90323e6 | 0.148069 | ||||||||
\(39\) | −522908. | −0.0361938 | ||||||||
\(40\) | 2.17138e7 | 1.34111 | ||||||||
\(41\) | −1.32544e7 | −0.732541 | −0.366271 | − | 0.930508i | \(-0.619366\pi\) | ||||
−0.366271 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97554e7 | −1.32726 | −0.663632 | − | 0.748060i | \(-0.730986\pi\) | ||||
−0.663632 | + | 0.748060i | \(0.730986\pi\) | |||||||
\(44\) | 3.00809e7 | 1.20991 | ||||||||
\(45\) | −1.34963e7 | −0.490635 | ||||||||
\(46\) | 1.70204e7 | 0.560478 | ||||||||
\(47\) | 1.07969e7 | 0.322745 | 0.161373 | − | 0.986894i | \(-0.448408\pi\) | ||||
0.161373 | + | 0.986894i | \(0.448408\pi\) | |||||||
\(48\) | −3.23882e6 | −0.0880647 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.32702e7 | 0.526544 | ||||||||
\(51\) | 1.90369e7 | 0.394030 | ||||||||
\(52\) | −1.06713e6 | −0.0202397 | ||||||||
\(53\) | 7.07399e7 | 1.23147 | 0.615734 | − | 0.787954i | \(-0.288860\pi\) | ||||
0.615734 | + | 0.787954i | \(0.288860\pi\) | |||||||
\(54\) | 2.76447e7 | 0.442426 | ||||||||
\(55\) | 1.73381e8 | 2.55488 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.32783e7 | −0.292089 | ||||||||
\(58\) | −1.90966e7 | −0.221579 | ||||||||
\(59\) | −6.40400e6 | −0.0688046 | −0.0344023 | − | 0.999408i | \(-0.510953\pi\) | ||||
−0.0344023 | + | 0.999408i | \(0.510953\pi\) | |||||||
\(60\) | −1.04754e8 | −1.04349 | ||||||||
\(61\) | −1.69190e8 | −1.56455 | −0.782275 | − | 0.622933i | \(-0.785941\pi\) | ||||
−0.782275 | + | 0.622933i | \(0.785941\pi\) | |||||||
\(62\) | −1.29264e8 | −1.11100 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.06653e7 | 0.526498 | ||||||||
\(65\) | −6.15078e6 | −0.0427386 | ||||||||
\(66\) | 1.96937e8 | 1.27755 | ||||||||
\(67\) | −1.16276e8 | −0.704943 | −0.352471 | − | 0.935823i | \(-0.614659\pi\) | ||||
−0.352471 | + | 0.935823i | \(0.614659\pi\) | |||||||
\(68\) | 3.88498e7 | 0.220343 | ||||||||
\(69\) | −2.08176e8 | −1.10563 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.44496e8 | 0.674826 | 0.337413 | − | 0.941357i | \(-0.390448\pi\) | ||||
0.337413 | + | 0.941357i | \(0.390448\pi\) | |||||||
\(72\) | −7.93154e7 | −0.347825 | ||||||||
\(73\) | −1.60155e8 | −0.660066 | −0.330033 | − | 0.943969i | \(-0.607060\pi\) | ||||
−0.330033 | + | 0.943969i | \(0.607060\pi\) | |||||||
\(74\) | −1.15937e8 | −0.449447 | ||||||||
\(75\) | −2.84617e8 | −1.03869 | ||||||||
\(76\) | −4.75056e7 | −0.163337 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.98643e6 | −0.0213712 | ||||||||
\(79\) | −4.89322e8 | −1.41343 | −0.706713 | − | 0.707500i | \(-0.749823\pi\) | ||||
−0.706713 | + | 0.707500i | \(0.749823\pi\) | |||||||
\(80\) | −3.80972e7 | −0.103989 | ||||||||
\(81\) | −4.76322e8 | −1.22947 | ||||||||
\(82\) | −1.77088e8 | −0.432541 | ||||||||
\(83\) | 8.31590e7 | 0.192335 | 0.0961674 | − | 0.995365i | \(-0.469342\pi\) | ||||
0.0961674 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.23924e8 | 0.465281 | ||||||||
\(86\) | −3.97553e8 | −0.783704 | ||||||||
\(87\) | 2.33569e8 | 0.437098 | ||||||||
\(88\) | 1.01893e9 | 1.81123 | ||||||||
\(89\) | −2.08083e6 | −0.00351546 | −0.00175773 | − | 0.999998i | \(-0.500560\pi\) | ||||
−0.00175773 | + | 0.999998i | \(0.500560\pi\) | |||||||
\(90\) | −1.80320e8 | −0.289703 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.24838e8 | −0.618270 | ||||||||
\(93\) | 1.58103e9 | 2.19162 | ||||||||
\(94\) | 1.44255e8 | 0.190570 | ||||||||
\(95\) | −2.73815e8 | −0.344906 | ||||||||
\(96\) | −9.88421e8 | −1.18774 | ||||||||
\(97\) | 3.15885e8 | 0.362290 | 0.181145 | − | 0.983456i | \(-0.442020\pi\) | ||||
0.181145 | + | 0.983456i | \(0.442020\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.33322e8 | −0.662623 | ||||||||
\(100\) | −5.80836e8 | −0.580836 | ||||||||
\(101\) | 5.74841e8 | 0.549669 | 0.274835 | − | 0.961492i | \(-0.411377\pi\) | ||||
0.274835 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(102\) | 2.54346e8 | 0.232662 | ||||||||
\(103\) | 1.51870e9 | 1.32955 | 0.664775 | − | 0.747044i | \(-0.268527\pi\) | ||||
0.664775 | + | 0.747044i | \(0.268527\pi\) | |||||||
\(104\) | −3.61471e7 | −0.0302987 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.45137e8 | 0.727140 | ||||||||
\(107\) | −2.01863e8 | −0.148878 | −0.0744390 | − | 0.997226i | \(-0.523717\pi\) | ||||
−0.0744390 | + | 0.997226i | \(0.523717\pi\) | |||||||
\(108\) | −6.90027e8 | −0.488044 | ||||||||
\(109\) | −8.73952e8 | −0.593019 | −0.296509 | − | 0.955030i | \(-0.595823\pi\) | ||||
−0.296509 | + | 0.955030i | \(0.595823\pi\) | |||||||
\(110\) | 2.31650e9 | 1.50857 | ||||||||
\(111\) | 1.41802e9 | 0.886603 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.52955e9 | 0.882491 | 0.441245 | − | 0.897386i | \(-0.354537\pi\) | ||||
0.441245 | + | 0.897386i | \(0.354537\pi\) | |||||||
\(114\) | −3.11015e8 | −0.172469 | ||||||||
\(115\) | −2.44870e9 | −1.30555 | ||||||||
\(116\) | 4.76661e8 | 0.244427 | ||||||||
\(117\) | 2.24674e7 | 0.0110845 | ||||||||
\(118\) | −8.55621e7 | −0.0406268 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.54834e9 | −1.56210 | ||||||||
\(121\) | 5.77807e9 | 2.45047 | ||||||||
\(122\) | −2.26050e9 | −0.923814 | ||||||||
\(123\) | 2.16596e9 | 0.853252 | ||||||||
\(124\) | 3.22651e9 | 1.22556 | ||||||||
\(125\) | 4.06429e8 | 0.148898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.71958e8 | −0.297426 | −0.148713 | − | 0.988880i | \(-0.547513\pi\) | ||||
−0.148713 | + | 0.988880i | \(0.547513\pi\) | |||||||
\(128\) | −2.15272e9 | −0.708830 | ||||||||
\(129\) | 4.86246e9 | 1.54597 | ||||||||
\(130\) | −8.21789e7 | −0.0252357 | ||||||||
\(131\) | −2.24404e9 | −0.665747 | −0.332874 | − | 0.942971i | \(-0.608018\pi\) | ||||
−0.332874 | + | 0.942971i | \(0.608018\pi\) | |||||||
\(132\) | −4.91565e9 | −1.40928 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.55353e9 | −0.416245 | ||||||||
\(135\) | −3.97721e9 | −1.03057 | ||||||||
\(136\) | 1.31596e9 | 0.329852 | ||||||||
\(137\) | 4.16141e9 | 1.00925 | 0.504624 | − | 0.863339i | \(-0.331631\pi\) | ||||
0.504624 | + | 0.863339i | \(0.331631\pi\) | |||||||
\(138\) | −2.78138e9 | −0.652836 | ||||||||
\(139\) | 6.03383e9 | 1.37097 | 0.685483 | − | 0.728089i | \(-0.259591\pi\) | ||||
0.685483 | + | 0.728089i | \(0.259591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.76438e9 | −0.375928 | ||||||||
\(142\) | 1.93057e9 | 0.398462 | ||||||||
\(143\) | −2.88629e8 | −0.0577203 | ||||||||
\(144\) | 1.39160e8 | 0.0269702 | ||||||||
\(145\) | 2.74740e9 | 0.516137 | ||||||||
\(146\) | −2.13979e9 | −0.389747 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.89385e9 | 0.495790 | ||||||||
\(149\) | −4.37832e9 | −0.727728 | −0.363864 | − | 0.931452i | \(-0.618543\pi\) | ||||
−0.363864 | + | 0.931452i | \(0.618543\pi\) | |||||||
\(150\) | −3.80268e9 | −0.613309 | ||||||||
\(151\) | −2.69365e9 | −0.421642 | −0.210821 | − | 0.977525i | \(-0.567614\pi\) | ||||
−0.210821 | + | 0.977525i | \(0.567614\pi\) | |||||||
\(152\) | −1.60916e9 | −0.244514 | ||||||||
\(153\) | −8.17943e8 | −0.120673 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.85971e10 | 2.58793 | ||||||||
\(156\) | 1.74385e8 | 0.0235748 | ||||||||
\(157\) | 1.33044e9 | 0.174762 | 0.0873810 | − | 0.996175i | \(-0.472150\pi\) | ||||
0.0873810 | + | 0.996175i | \(0.472150\pi\) | |||||||
\(158\) | −6.53770e9 | −0.834580 | ||||||||
\(159\) | −1.15599e10 | −1.43439 | ||||||||
\(160\) | −1.16265e10 | −1.40251 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.36401e9 | −0.725961 | ||||||||
\(163\) | −3.56094e9 | −0.395112 | −0.197556 | − | 0.980292i | \(-0.563301\pi\) | ||||
−0.197556 | + | 0.980292i | \(0.563301\pi\) | |||||||
\(164\) | 4.42022e9 | 0.477140 | ||||||||
\(165\) | −2.83330e10 | −2.97588 | ||||||||
\(166\) | 1.11106e9 | 0.113567 | ||||||||
\(167\) | 1.04285e10 | 1.03752 | 0.518762 | − | 0.854919i | \(-0.326393\pi\) | ||||
0.518762 | + | 0.854919i | \(0.326393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.05943e10 | −0.999034 | ||||||||
\(170\) | 2.99179e9 | 0.274733 | ||||||||
\(171\) | 1.00018e9 | 0.0894534 | ||||||||
\(172\) | 9.92314e9 | 0.864512 | ||||||||
\(173\) | −2.04717e10 | −1.73759 | −0.868793 | − | 0.495176i | \(-0.835104\pi\) | ||||
−0.868793 | + | 0.495176i | \(0.835104\pi\) | |||||||
\(174\) | 3.12066e9 | 0.258092 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.78773e9 | −0.140442 | ||||||||
\(177\) | 1.04651e9 | 0.0801424 | ||||||||
\(178\) | −2.78014e7 | −0.00207576 | ||||||||
\(179\) | 5.46705e9 | 0.398029 | 0.199014 | − | 0.979997i | \(-0.436226\pi\) | ||||
0.199014 | + | 0.979997i | \(0.436226\pi\) | |||||||
\(180\) | 4.50089e9 | 0.319575 | ||||||||
\(181\) | 2.11628e9 | 0.146561 | 0.0732807 | − | 0.997311i | \(-0.476653\pi\) | ||||
0.0732807 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.76481e10 | 1.82236 | ||||||||
\(184\) | −1.43906e10 | −0.925545 | ||||||||
\(185\) | 1.66797e10 | 1.04692 | ||||||||
\(186\) | 2.11237e10 | 1.29408 | ||||||||
\(187\) | 1.05078e10 | 0.628381 | ||||||||
\(188\) | −3.60068e9 | −0.210220 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.65836e9 | −0.203655 | ||||||||
\(191\) | 1.72421e10 | 0.937431 | 0.468715 | − | 0.883349i | \(-0.344717\pi\) | ||||
0.468715 | + | 0.883349i | \(0.344717\pi\) | |||||||
\(192\) | −1.15477e10 | −0.613256 | ||||||||
\(193\) | 2.02030e10 | 1.04811 | 0.524055 | − | 0.851684i | \(-0.324418\pi\) | ||||
0.524055 | + | 0.851684i | \(0.324418\pi\) | |||||||
\(194\) | 4.22045e9 | 0.213920 | ||||||||
\(195\) | 1.00513e9 | 0.0497812 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.22592e10 | −1.05296 | −0.526481 | − | 0.850187i | \(-0.676489\pi\) | ||||
−0.526481 | + | 0.850187i | \(0.676489\pi\) | |||||||
\(198\) | −8.46164e9 | −0.391256 | ||||||||
\(199\) | −1.70588e10 | −0.771098 | −0.385549 | − | 0.922687i | \(-0.625988\pi\) | ||||
−0.385549 | + | 0.922687i | \(0.625988\pi\) | |||||||
\(200\) | −1.96747e10 | −0.869508 | ||||||||
\(201\) | 1.90012e10 | 0.821105 | ||||||||
\(202\) | 7.68029e9 | 0.324561 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.34862e9 | −0.256651 | ||||||||
\(205\) | 2.54774e10 | 1.00754 | ||||||||
\(206\) | 2.02909e10 | 0.785054 | ||||||||
\(207\) | 8.94453e9 | 0.338603 | ||||||||
\(208\) | 6.34207e7 | 0.00234934 | ||||||||
\(209\) | −1.28489e10 | −0.465810 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.19873e10 | −1.11098 | −0.555490 | − | 0.831523i | \(-0.687469\pi\) | ||||
−0.555490 | + | 0.831523i | \(0.687469\pi\) | |||||||
\(212\) | −2.35911e10 | −0.802116 | ||||||||
\(213\) | −2.36127e10 | −0.786026 | ||||||||
\(214\) | −2.69704e9 | −0.0879074 | ||||||||
\(215\) | 5.71954e10 | 1.82553 | ||||||||
\(216\) | −2.33734e10 | −0.730599 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.16766e10 | −0.350157 | ||||||||
\(219\) | 2.61717e10 | 0.768834 | ||||||||
\(220\) | −5.78211e10 | −1.66412 | ||||||||
\(221\) | −3.72768e8 | −0.0105117 | ||||||||
\(222\) | 1.89458e10 | 0.523509 | ||||||||
\(223\) | 2.30967e10 | 0.625428 | 0.312714 | − | 0.949847i | \(-0.398762\pi\) | ||||
0.312714 | + | 0.949847i | \(0.398762\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.22289e10 | 0.318102 | ||||||||
\(226\) | 2.04359e10 | 0.521081 | ||||||||
\(227\) | 2.30894e10 | 0.577160 | 0.288580 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288580 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(228\) | 7.76311e9 | 0.190252 | ||||||||
\(229\) | −4.25496e10 | −1.02244 | −0.511218 | − | 0.859451i | \(-0.670805\pi\) | ||||
−0.511218 | + | 0.859451i | \(0.670805\pi\) | |||||||
\(230\) | −3.27164e10 | −0.770885 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.61460e10 | 0.365905 | ||||||||
\(233\) | −1.26679e10 | −0.281582 | −0.140791 | − | 0.990039i | \(-0.544964\pi\) | ||||
−0.140791 | + | 0.990039i | \(0.544964\pi\) | |||||||
\(234\) | 3.00181e8 | 0.00654503 | ||||||||
\(235\) | −2.07537e10 | −0.443906 | ||||||||
\(236\) | 2.13568e9 | 0.0448158 | ||||||||
\(237\) | 7.99624e10 | 1.64633 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.37875e10 | 1.26458 | 0.632289 | − | 0.774733i | \(-0.282116\pi\) | ||||
0.632289 | + | 0.774733i | \(0.282116\pi\) | |||||||
\(240\) | 6.22563e9 | 0.121125 | ||||||||
\(241\) | 2.91604e10 | 0.556823 | 0.278412 | − | 0.960462i | \(-0.410192\pi\) | ||||
0.278412 | + | 0.960462i | \(0.410192\pi\) | |||||||
\(242\) | 7.71992e10 | 1.44692 | ||||||||
\(243\) | 3.71118e10 | 0.682785 | ||||||||
\(244\) | 5.64232e10 | 1.01907 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.89388e10 | 0.503816 | ||||||||
\(247\) | 4.55822e8 | 0.00779218 | ||||||||
\(248\) | 1.09292e11 | 1.83466 | ||||||||
\(249\) | −1.35894e10 | −0.224028 | ||||||||
\(250\) | 5.43018e9 | 0.0879194 | ||||||||
\(251\) | −6.28939e10 | −1.00018 | −0.500088 | − | 0.865974i | \(-0.666699\pi\) | ||||
−0.500088 | + | 0.865974i | \(0.666699\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.14907e11 | −1.76320 | ||||||||
\(254\) | −1.16500e10 | −0.175620 | ||||||||
\(255\) | −3.65924e10 | −0.541952 | ||||||||
\(256\) | −6.49425e10 | −0.945038 | ||||||||
\(257\) | −1.14480e11 | −1.63694 | −0.818469 | − | 0.574551i | \(-0.805177\pi\) | ||||
−0.818469 | + | 0.574551i | \(0.805177\pi\) | |||||||
\(258\) | 6.49660e10 | 0.912845 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.05123e9 | 0.0278378 | ||||||||
\(261\) | −1.00356e10 | −0.133863 | ||||||||
\(262\) | −2.99820e10 | −0.393101 | ||||||||
\(263\) | 1.40705e10 | 0.181346 | 0.0906728 | − | 0.995881i | \(-0.471098\pi\) | ||||
0.0906728 | + | 0.995881i | \(0.471098\pi\) | |||||||
\(264\) | −1.66508e11 | −2.10969 | ||||||||
\(265\) | −1.35975e11 | −1.69377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.40038e8 | 0.00409475 | ||||||||
\(268\) | 3.87770e10 | 0.459164 | ||||||||
\(269\) | −8.39143e10 | −0.977127 | −0.488563 | − | 0.872528i | \(-0.662479\pi\) | ||||
−0.488563 | + | 0.872528i | \(0.662479\pi\) | |||||||
\(270\) | −5.31384e10 | −0.608515 | ||||||||
\(271\) | −1.98401e10 | −0.223451 | −0.111726 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111726 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(272\) | −2.30888e9 | −0.0255765 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.55995e10 | 0.595927 | ||||||||
\(275\) | −1.57100e11 | −1.65645 | ||||||||
\(276\) | 6.94247e10 | 0.720150 | ||||||||
\(277\) | −7.17911e10 | −0.732675 | −0.366338 | − | 0.930482i | \(-0.619389\pi\) | ||||
−0.366338 | + | 0.930482i | \(0.619389\pi\) | |||||||
\(278\) | 8.06163e10 | 0.809508 | ||||||||
\(279\) | −6.79308e10 | −0.671194 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.02853e11 | 0.984101 | 0.492050 | − | 0.870567i | \(-0.336248\pi\) | ||||
0.492050 | + | 0.870567i | \(0.336248\pi\) | |||||||
\(282\) | −2.35733e10 | −0.221973 | ||||||||
\(283\) | 5.52883e10 | 0.512382 | 0.256191 | − | 0.966626i | \(-0.417532\pi\) | ||||
0.256191 | + | 0.966626i | \(0.417532\pi\) | |||||||
\(284\) | −4.81880e10 | −0.439548 | ||||||||
\(285\) | 4.47453e10 | 0.401741 | ||||||||
\(286\) | −3.85630e9 | −0.0340819 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.24688e10 | 0.363750 | ||||||||
\(289\) | −1.05017e11 | −0.885562 | ||||||||
\(290\) | 3.67072e10 | 0.304762 | ||||||||
\(291\) | −5.16202e10 | −0.421989 | ||||||||
\(292\) | 5.34102e10 | 0.429934 | ||||||||
\(293\) | −1.05721e11 | −0.838028 | −0.419014 | − | 0.907980i | \(-0.637624\pi\) | ||||
−0.419014 | + | 0.907980i | \(0.637624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.23097e10 | 0.0946343 | ||||||||
\(296\) | 9.80236e10 | 0.742195 | ||||||||
\(297\) | −1.86633e11 | −1.39182 | ||||||||
\(298\) | −5.84975e10 | −0.429699 | ||||||||
\(299\) | 4.07637e9 | 0.0294953 | ||||||||
\(300\) | 9.49171e10 | 0.676548 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.59891e10 | −0.248966 | ||||||||
\(303\) | −9.39374e10 | −0.640246 | ||||||||
\(304\) | 2.82330e9 | 0.0189595 | ||||||||
\(305\) | 3.25214e11 | 2.15189 | ||||||||
\(306\) | −1.09283e10 | −0.0712536 | ||||||||
\(307\) | 8.10064e10 | 0.520471 | 0.260236 | − | 0.965545i | \(-0.416200\pi\) | ||||
0.260236 | + | 0.965545i | \(0.416200\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.48178e11 | −1.54864 | ||||||||
\(310\) | 2.48470e11 | 1.52808 | ||||||||
\(311\) | 3.18435e11 | 1.93018 | 0.965091 | − | 0.261913i | \(-0.0843534\pi\) | ||||
0.965091 | + | 0.261913i | \(0.0843534\pi\) | |||||||
\(312\) | 5.90696e9 | 0.0352914 | ||||||||
\(313\) | −1.28876e11 | −0.758965 | −0.379483 | − | 0.925199i | \(-0.623898\pi\) | ||||
−0.379483 | + | 0.925199i | \(0.623898\pi\) | |||||||
\(314\) | 1.77757e10 | 0.103191 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.63185e11 | 0.920635 | ||||||||
\(317\) | −7.44722e10 | −0.414217 | −0.207108 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207108 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(318\) | −1.54449e11 | −0.846961 | ||||||||
\(319\) | 1.28923e11 | 0.697065 | ||||||||
\(320\) | −1.35832e11 | −0.724148 | ||||||||
\(321\) | 3.29874e10 | 0.173411 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.65945e10 | −0.0848309 | ||||||||
\(324\) | 1.58849e11 | 0.800815 | ||||||||
\(325\) | 5.57319e9 | 0.0277095 | ||||||||
\(326\) | −4.75768e10 | −0.233301 | ||||||||
\(327\) | 1.42816e11 | 0.690738 | ||||||||
\(328\) | 1.49726e11 | 0.714276 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.78550e11 | −1.75715 | ||||||||
\(331\) | 2.83840e11 | 1.29971 | 0.649857 | − | 0.760057i | \(-0.274829\pi\) | ||||
0.649857 | + | 0.760057i | \(0.274829\pi\) | |||||||
\(332\) | −2.77328e10 | −0.125277 | ||||||||
\(333\) | −6.09271e10 | −0.271526 | ||||||||
\(334\) | 1.39332e11 | 0.612623 | ||||||||
\(335\) | 2.23505e11 | 0.969583 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.61414e9 | −0.0237109 | −0.0118555 | − | 0.999930i | \(-0.503774\pi\) | ||||
−0.0118555 | + | 0.999930i | \(0.503774\pi\) | |||||||
\(338\) | −1.41547e11 | −0.589896 | ||||||||
\(339\) | −2.49950e11 | −1.02791 | ||||||||
\(340\) | −7.46766e10 | −0.303061 | ||||||||
\(341\) | 8.72679e11 | 3.49510 | ||||||||
\(342\) | 1.33632e10 | 0.0528192 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.36128e11 | 1.29417 | ||||||||
\(345\) | 4.00153e11 | 1.52069 | ||||||||
\(346\) | −2.73517e11 | −1.02599 | ||||||||
\(347\) | 3.39846e11 | 1.25834 | 0.629171 | − | 0.777267i | \(-0.283394\pi\) | ||||
0.629171 | + | 0.777267i | \(0.283394\pi\) | |||||||
\(348\) | −7.78933e10 | −0.284704 | ||||||||
\(349\) | −3.46718e10 | −0.125101 | −0.0625506 | − | 0.998042i | \(-0.519923\pi\) | ||||
−0.0625506 | + | 0.998042i | \(0.519923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.62089e9 | 0.0232828 | ||||||||
\(352\) | −5.45578e11 | −1.89415 | ||||||||
\(353\) | 3.46900e11 | 1.18910 | 0.594550 | − | 0.804059i | \(-0.297330\pi\) | ||||
0.594550 | + | 0.804059i | \(0.297330\pi\) | |||||||
\(354\) | 1.39821e10 | 0.0473214 | ||||||||
\(355\) | −2.77748e11 | −0.928160 | ||||||||
\(356\) | 6.93939e8 | 0.00228979 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.30438e10 | 0.235023 | ||||||||
\(359\) | −2.51011e11 | −0.797569 | −0.398785 | − | 0.917045i | \(-0.630568\pi\) | ||||
−0.398785 | + | 0.917045i | \(0.630568\pi\) | |||||||
\(360\) | 1.52459e11 | 0.478401 | ||||||||
\(361\) | −3.02396e11 | −0.937116 | ||||||||
\(362\) | 2.82750e10 | 0.0865396 | ||||||||
\(363\) | −9.44221e11 | −2.85426 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.07848e11 | 0.907859 | ||||||||
\(366\) | 3.69398e11 | 1.07604 | ||||||||
\(367\) | −4.79871e11 | −1.38079 | −0.690394 | − | 0.723433i | \(-0.742563\pi\) | ||||
−0.690394 | + | 0.723433i | \(0.742563\pi\) | |||||||
\(368\) | 2.52485e10 | 0.0717663 | ||||||||
\(369\) | −9.30632e10 | −0.261312 | ||||||||
\(370\) | 2.22853e11 | 0.618173 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.27258e11 | −1.42751 | ||||||||
\(373\) | −1.84794e11 | −0.494308 | −0.247154 | − | 0.968976i | \(-0.579495\pi\) | ||||
−0.247154 | + | 0.968976i | \(0.579495\pi\) | |||||||
\(374\) | 1.40391e11 | 0.371038 | ||||||||
\(375\) | −6.64164e10 | −0.173434 | ||||||||
\(376\) | −1.21966e11 | −0.314698 | ||||||||
\(377\) | −4.57361e9 | −0.0116607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.08908e11 | −1.76487 | −0.882437 | − | 0.470431i | \(-0.844098\pi\) | ||||
−0.882437 | + | 0.470431i | \(0.844098\pi\) | |||||||
\(380\) | 9.13148e10 | 0.224654 | ||||||||
\(381\) | 1.42491e11 | 0.346437 | ||||||||
\(382\) | 2.30367e11 | 0.553521 | ||||||||
\(383\) | −1.23789e11 | −0.293959 | −0.146980 | − | 0.989140i | \(-0.546955\pi\) | ||||
−0.146980 | + | 0.989140i | \(0.546955\pi\) | |||||||
\(384\) | 3.51785e11 | 0.825633 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.69926e11 | 0.618874 | ||||||||
\(387\) | −2.08922e11 | −0.473461 | ||||||||
\(388\) | −1.05345e11 | −0.235977 | ||||||||
\(389\) | −2.97971e11 | −0.659782 | −0.329891 | − | 0.944019i | \(-0.607012\pi\) | ||||
−0.329891 | + | 0.944019i | \(0.607012\pi\) | |||||||
\(390\) | 1.34292e10 | 0.0293941 | ||||||||
\(391\) | −1.48403e11 | −0.321106 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.66708e11 | 0.775451 | ||||||||
\(394\) | −2.97400e11 | −0.621738 | ||||||||
\(395\) | 9.40570e11 | 1.94404 | ||||||||
\(396\) | 2.11207e11 | 0.431599 | ||||||||
\(397\) | −5.33426e11 | −1.07775 | −0.538873 | − | 0.842387i | \(-0.681150\pi\) | ||||
−0.538873 | + | 0.842387i | \(0.681150\pi\) | |||||||
\(398\) | −2.27918e11 | −0.455307 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.45196e10 | 0.0674212 | ||||||||
\(401\) | 4.15640e11 | 0.802726 | 0.401363 | − | 0.915919i | \(-0.368537\pi\) | ||||
0.401363 | + | 0.915919i | \(0.368537\pi\) | |||||||
\(402\) | 2.53870e11 | 0.484835 | ||||||||
\(403\) | −3.09587e10 | −0.0584669 | ||||||||
\(404\) | −1.91704e11 | −0.358027 | ||||||||
\(405\) | 9.15581e11 | 1.69102 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.82704e11 | 1.41391 | ||||||||
\(408\) | −2.15047e11 | −0.384206 | ||||||||
\(409\) | −1.07978e12 | −1.90801 | −0.954006 | − | 0.299788i | \(-0.903084\pi\) | ||||
−0.954006 | + | 0.299788i | \(0.903084\pi\) | |||||||
\(410\) | 3.40397e11 | 0.594919 | ||||||||
\(411\) | −6.80035e11 | −1.17556 | ||||||||
\(412\) | −5.06473e11 | −0.866002 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.19505e11 | 0.199934 | ||||||||
\(415\) | −1.59847e11 | −0.264539 | ||||||||
\(416\) | 1.93547e10 | 0.0316859 | ||||||||
\(417\) | −9.86015e11 | −1.59688 | ||||||||
\(418\) | −1.71671e11 | −0.275045 | ||||||||
\(419\) | 2.20998e11 | 0.350289 | 0.175144 | − | 0.984543i | \(-0.443961\pi\) | ||||
0.175144 | + | 0.984543i | \(0.443961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.47478e11 | 0.539086 | 0.269543 | − | 0.962988i | \(-0.413127\pi\) | ||||
0.269543 | + | 0.962988i | \(0.413127\pi\) | |||||||
\(422\) | −4.27373e11 | −0.655996 | ||||||||
\(423\) | 7.58087e10 | 0.115130 | ||||||||
\(424\) | −7.99105e11 | −1.20076 | ||||||||
\(425\) | −2.02896e11 | −0.301664 | ||||||||
\(426\) | −3.15483e11 | −0.464122 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.73196e10 | 0.0969716 | ||||||||
\(429\) | 4.71662e10 | 0.0672316 | ||||||||
\(430\) | 7.64172e11 | 1.07791 | ||||||||
\(431\) | 1.23574e11 | 0.172496 | 0.0862479 | − | 0.996274i | \(-0.472512\pi\) | ||||
0.0862479 | + | 0.996274i | \(0.472512\pi\) | |||||||
\(432\) | 4.10090e10 | 0.0566503 | ||||||||
\(433\) | 7.27679e11 | 0.994820 | 0.497410 | − | 0.867516i | \(-0.334284\pi\) | ||||
0.497410 | + | 0.867516i | \(0.334284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.48964e11 | −0.601188 | ||||||||
\(436\) | 2.91455e11 | 0.386262 | ||||||||
\(437\) | 1.81468e11 | 0.238031 | ||||||||
\(438\) | 3.49672e11 | 0.453970 | ||||||||
\(439\) | 5.85966e11 | 0.752977 | 0.376489 | − | 0.926421i | \(-0.377131\pi\) | ||||
0.376489 | + | 0.926421i | \(0.377131\pi\) | |||||||
\(440\) | −1.95858e12 | −2.49117 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.98045e9 | −0.00620681 | ||||||||
\(443\) | −2.11546e11 | −0.260969 | −0.130484 | − | 0.991450i | \(-0.541653\pi\) | ||||
−0.130484 | + | 0.991450i | \(0.541653\pi\) | |||||||
\(444\) | −4.72897e11 | −0.577488 | ||||||||
\(445\) | 3.99975e9 | 0.00483519 | ||||||||
\(446\) | 3.08588e11 | 0.369294 | ||||||||
\(447\) | 7.15480e11 | 0.847645 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.21048e11 | −1.06948 | −0.534741 | − | 0.845016i | \(-0.679591\pi\) | ||||
−0.534741 | + | 0.845016i | \(0.679591\pi\) | |||||||
\(450\) | 1.63387e11 | 0.187829 | ||||||||
\(451\) | 1.19554e12 | 1.36073 | ||||||||
\(452\) | −5.10091e11 | −0.574810 | ||||||||
\(453\) | 4.40181e11 | 0.491122 | ||||||||
\(454\) | 3.08491e11 | 0.340794 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.62961e11 | 0.284806 | ||||||||
\(457\) | 8.11185e11 | 0.869955 | 0.434977 | − | 0.900441i | \(-0.356756\pi\) | ||||
0.434977 | + | 0.900441i | \(0.356756\pi\) | |||||||
\(458\) | −5.68493e11 | −0.603713 | ||||||||
\(459\) | −2.41039e11 | −0.253472 | ||||||||
\(460\) | 8.16618e11 | 0.850372 | ||||||||
\(461\) | 1.90069e11 | 0.196001 | 0.0980004 | − | 0.995186i | \(-0.468755\pi\) | ||||
0.0980004 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.76945e11 | 0.482341 | 0.241170 | − | 0.970483i | \(-0.422469\pi\) | ||||
0.241170 | + | 0.970483i | \(0.422469\pi\) | |||||||
\(464\) | −2.83284e10 | −0.0283721 | ||||||||
\(465\) | −3.03903e12 | −3.01437 | ||||||||
\(466\) | −1.69253e11 | −0.166264 | ||||||||
\(467\) | −1.06392e12 | −1.03510 | −0.517549 | − | 0.855653i | \(-0.673156\pi\) | ||||
−0.517549 | + | 0.855653i | \(0.673156\pi\) | |||||||
\(468\) | −7.49268e9 | −0.00721990 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.77285e11 | −0.262111 | ||||||||
\(471\) | −2.17413e11 | −0.203560 | ||||||||
\(472\) | 7.23420e10 | 0.0670890 | ||||||||
\(473\) | 2.68393e12 | 2.46545 | ||||||||
\(474\) | 1.06836e12 | 0.972105 | ||||||||
\(475\) | 2.48102e11 | 0.223619 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.96687e11 | 0.439289 | ||||||||
\(478\) | 8.52248e11 | 0.746690 | ||||||||
\(479\) | 8.43415e11 | 0.732034 | 0.366017 | − | 0.930608i | \(-0.380721\pi\) | ||||
0.366017 | + | 0.930608i | \(0.380721\pi\) | |||||||
\(480\) | 1.89993e12 | 1.63362 | ||||||||
\(481\) | −2.77668e10 | −0.0236523 | ||||||||
\(482\) | 3.89605e11 | 0.328785 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.92694e12 | −1.59611 | ||||||||
\(485\) | −6.07191e11 | −0.498296 | ||||||||
\(486\) | 4.95841e11 | 0.403162 | ||||||||
\(487\) | 1.15202e12 | 0.928065 | 0.464032 | − | 0.885818i | \(-0.346402\pi\) | ||||
0.464032 | + | 0.885818i | \(0.346402\pi\) | |||||||
\(488\) | 1.91123e12 | 1.52554 | ||||||||
\(489\) | 5.81910e11 | 0.460220 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.68703e11 | −0.752184 | −0.376092 | − | 0.926582i | \(-0.622732\pi\) | ||||
−0.376092 | + | 0.926582i | \(0.622732\pi\) | |||||||
\(492\) | −7.22328e11 | −0.555765 | ||||||||
\(493\) | 1.66506e11 | 0.126946 | ||||||||
\(494\) | 6.09011e9 | 0.00460102 | ||||||||
\(495\) | 1.21736e12 | 0.911375 | ||||||||
\(496\) | −1.91754e11 | −0.142258 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.81564e11 | −0.132281 | ||||||||
\(499\) | 2.62821e12 | 1.89761 | 0.948805 | − | 0.315863i | \(-0.102294\pi\) | ||||
0.948805 | + | 0.315863i | \(0.102294\pi\) | |||||||
\(500\) | −1.35540e11 | −0.0969848 | ||||||||
\(501\) | −1.70417e12 | −1.20849 | ||||||||
\(502\) | −8.40308e11 | −0.590570 | ||||||||
\(503\) | −3.95070e11 | −0.275181 | −0.137590 | − | 0.990489i | \(-0.543936\pi\) | ||||
−0.137590 | + | 0.990489i | \(0.543936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.10495e12 | −0.756019 | ||||||||
\(506\) | −1.53524e12 | −1.04111 | ||||||||
\(507\) | 1.73126e12 | 1.16366 | ||||||||
\(508\) | 2.90790e11 | 0.193728 | ||||||||
\(509\) | −6.64157e11 | −0.438572 | −0.219286 | − | 0.975661i | \(-0.570373\pi\) | ||||
−0.219286 | + | 0.975661i | \(0.570373\pi\) | |||||||
\(510\) | −4.88901e11 | −0.320004 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.34512e11 | 0.150817 | ||||||||
\(513\) | 2.94743e11 | 0.187895 | ||||||||
\(514\) | −1.52954e12 | −0.966556 | ||||||||
\(515\) | −2.91923e12 | −1.82867 | ||||||||
\(516\) | −1.62159e12 | −1.00697 | ||||||||
\(517\) | −9.73882e11 | −0.599513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.34537e12 | 2.02391 | ||||||||
\(520\) | 6.94815e10 | 0.0416730 | ||||||||
\(521\) | −5.22766e11 | −0.310841 | −0.155420 | − | 0.987848i | \(-0.549673\pi\) | ||||
−0.155420 | + | 0.987848i | \(0.549673\pi\) | |||||||
\(522\) | −1.34083e11 | −0.0790417 | ||||||||
\(523\) | 3.09135e12 | 1.80672 | 0.903360 | − | 0.428882i | \(-0.141093\pi\) | ||||
0.903360 | + | 0.428882i | \(0.141093\pi\) | |||||||
\(524\) | 7.48366e11 | 0.433634 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.87991e11 | 0.107078 | ||||||||
\(527\) | 1.12708e12 | 0.636510 | ||||||||
\(528\) | 2.92142e11 | 0.163584 | ||||||||
\(529\) | −1.78305e11 | −0.0989947 | ||||||||
\(530\) | −1.81673e12 | −1.00011 | ||||||||
\(531\) | −4.49645e10 | −0.0245440 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24125e10 | −0.0227626 | ||||||||
\(534\) | 4.54316e9 | 0.00241781 | ||||||||
\(535\) | 3.88019e11 | 0.204768 | ||||||||
\(536\) | 1.31350e12 | 0.687366 | ||||||||
\(537\) | −8.93396e11 | −0.463617 | ||||||||
\(538\) | −1.12116e12 | −0.576960 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.32636e12 | 0.671259 | ||||||||
\(541\) | −1.47490e12 | −0.740243 | −0.370121 | − | 0.928983i | \(-0.620684\pi\) | ||||
−0.370121 | + | 0.928983i | \(0.620684\pi\) | |||||||
\(542\) | −2.65079e11 | −0.131940 | ||||||||
\(543\) | −3.45831e11 | −0.170712 | ||||||||
\(544\) | −7.04621e11 | −0.344954 | ||||||||
\(545\) | 1.67990e12 | 0.815642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.12294e12 | 1.01390 | 0.506949 | − | 0.861976i | \(-0.330773\pi\) | ||||
0.506949 | + | 0.861976i | \(0.330773\pi\) | |||||||
\(548\) | −1.38779e12 | −0.657374 | ||||||||
\(549\) | −1.18793e12 | −0.558106 | ||||||||
\(550\) | −2.09897e12 | −0.978078 | ||||||||
\(551\) | −2.03604e11 | −0.0941031 | ||||||||
\(552\) | 2.35163e12 | 1.07806 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.59181e11 | −0.432620 | ||||||||
\(555\) | −2.72570e12 | −1.21944 | ||||||||
\(556\) | −2.01223e12 | −0.892978 | ||||||||
\(557\) | −3.52857e12 | −1.55328 | −0.776641 | − | 0.629943i | \(-0.783078\pi\) | ||||
−0.776641 | + | 0.629943i | \(0.783078\pi\) | |||||||
\(558\) | −9.07605e11 | −0.396317 | ||||||||
\(559\) | −9.52137e10 | −0.0412426 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.71712e12 | −0.731928 | ||||||||
\(562\) | 1.37419e12 | 0.581078 | ||||||||
\(563\) | 3.35280e12 | 1.40644 | 0.703218 | − | 0.710974i | \(-0.251746\pi\) | ||||
0.703218 | + | 0.710974i | \(0.251746\pi\) | |||||||
\(564\) | 5.88403e11 | 0.244861 | ||||||||
\(565\) | −2.94008e12 | −1.21378 | ||||||||
\(566\) | 7.38691e11 | 0.302544 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.63228e12 | −0.658000 | ||||||||
\(569\) | 2.99364e12 | 1.19727 | 0.598637 | − | 0.801020i | \(-0.295709\pi\) | ||||
0.598637 | + | 0.801020i | \(0.295709\pi\) | |||||||
\(570\) | 5.97830e11 | 0.237214 | ||||||||
\(571\) | 4.67267e12 | 1.83951 | 0.919756 | − | 0.392490i | \(-0.128386\pi\) | ||||
0.919756 | + | 0.392490i | \(0.128386\pi\) | |||||||
\(572\) | 9.62553e10 | 0.0375961 | ||||||||
\(573\) | −2.81761e12 | −1.09190 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.21875e12 | 0.846453 | ||||||||
\(576\) | 4.96164e11 | 0.187812 | ||||||||
\(577\) | 3.62799e12 | 1.36262 | 0.681310 | − | 0.731995i | \(-0.261411\pi\) | ||||
0.681310 | + | 0.731995i | \(0.261411\pi\) | |||||||
\(578\) | −1.40310e12 | −0.522895 | ||||||||
\(579\) | −3.30146e12 | −1.22082 | ||||||||
\(580\) | −9.16232e11 | −0.336186 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.89683e11 | −0.249170 | ||||||||
\(583\) | −6.38073e12 | −2.28751 | ||||||||
\(584\) | 1.80917e12 | 0.643608 | ||||||||
\(585\) | −4.31866e10 | −0.0152457 | ||||||||
\(586\) | −1.41252e12 | −0.494827 | ||||||||
\(587\) | −3.97200e12 | −1.38082 | −0.690411 | − | 0.723417i | \(-0.742570\pi\) | ||||
−0.690411 | + | 0.723417i | \(0.742570\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.37819e12 | −0.471835 | ||||||||
\(590\) | 1.64466e11 | 0.0558783 | ||||||||
\(591\) | 3.63748e12 | 1.22647 | ||||||||
\(592\) | −1.71984e11 | −0.0575494 | ||||||||
\(593\) | −2.67436e12 | −0.888123 | −0.444061 | − | 0.895996i | \(-0.646463\pi\) | ||||
−0.444061 | + | 0.895996i | \(0.646463\pi\) | |||||||
\(594\) | −2.49355e12 | −0.821825 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.46013e12 | 0.474005 | ||||||||
\(597\) | 2.78765e12 | 0.898162 | ||||||||
\(598\) | 5.44632e10 | 0.0174160 | ||||||||
\(599\) | 4.84522e12 | 1.53777 | 0.768887 | − | 0.639384i | \(-0.220811\pi\) | ||||
0.768887 | + | 0.639384i | \(0.220811\pi\) | |||||||
\(600\) | 3.21513e12 | 1.01279 | ||||||||
\(601\) | 4.64764e12 | 1.45311 | 0.726553 | − | 0.687110i | \(-0.241121\pi\) | ||||
0.726553 | + | 0.687110i | \(0.241121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.16411e11 | −0.251467 | ||||||||
\(604\) | 8.98307e11 | 0.274637 | ||||||||
\(605\) | −1.11065e13 | −3.37039 | ||||||||
\(606\) | −1.25507e12 | −0.378043 | ||||||||
\(607\) | 6.52447e12 | 1.95073 | 0.975363 | − | 0.220604i | \(-0.0708030\pi\) | ||||
0.975363 | + | 0.220604i | \(0.0708030\pi\) | |||||||
\(608\) | 8.61613e11 | 0.255709 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.34510e12 | 1.27062 | ||||||||
\(611\) | 3.45489e10 | 0.0100288 | ||||||||
\(612\) | 2.72777e11 | 0.0786006 | ||||||||
\(613\) | −9.54536e11 | −0.273036 | −0.136518 | − | 0.990638i | \(-0.543591\pi\) | ||||
−0.136518 | + | 0.990638i | \(0.543591\pi\) | |||||||
\(614\) | 1.08230e12 | 0.307321 | ||||||||
\(615\) | −4.16338e12 | −1.17357 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.50764e12 | −1.25218 | −0.626088 | − | 0.779752i | \(-0.715345\pi\) | ||||
−0.626088 | + | 0.779752i | \(0.715345\pi\) | |||||||
\(618\) | −3.31583e12 | −0.914418 | ||||||||
\(619\) | −3.64346e12 | −0.997484 | −0.498742 | − | 0.866750i | \(-0.666204\pi\) | ||||
−0.498742 | + | 0.866750i | \(0.666204\pi\) | |||||||
\(620\) | −6.20195e12 | −1.68564 | ||||||||
\(621\) | 2.63585e12 | 0.711228 | ||||||||
\(622\) | 4.25452e12 | 1.13971 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.03639e10 | −0.00273647 | ||||||||
\(625\) | −4.18296e12 | −1.09654 | ||||||||
\(626\) | −1.72187e12 | −0.448143 | ||||||||
\(627\) | 2.09970e12 | 0.542567 | ||||||||
\(628\) | −4.43690e11 | −0.113831 | ||||||||
\(629\) | 1.01087e12 | 0.257495 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.61498e12 | 0.907766 | 0.453883 | − | 0.891061i | \(-0.350038\pi\) | ||||
0.453883 | + | 0.891061i | \(0.350038\pi\) | |||||||
\(632\) | 5.52757e12 | 1.37818 | ||||||||
\(633\) | 5.22718e12 | 1.29405 | ||||||||
\(634\) | −9.95003e11 | −0.244581 | ||||||||
\(635\) | 1.67607e12 | 0.409081 | ||||||||
\(636\) | 3.85513e12 | 0.934292 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.72251e12 | 0.411593 | ||||||||
\(639\) | 1.01455e12 | 0.240724 | ||||||||
\(640\) | 4.13793e12 | 0.974929 | ||||||||
\(641\) | −2.66304e12 | −0.623041 | −0.311521 | − | 0.950239i | \(-0.600838\pi\) | ||||
−0.311521 | + | 0.950239i | \(0.600838\pi\) | |||||||
\(642\) | 4.40736e11 | 0.102393 | ||||||||
\(643\) | −4.09899e12 | −0.945644 | −0.472822 | − | 0.881158i | \(-0.656765\pi\) | ||||
−0.472822 | + | 0.881158i | \(0.656765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.34656e12 | −2.12634 | ||||||||
\(646\) | −2.21715e11 | −0.0500898 | ||||||||
\(647\) | −6.11325e12 | −1.37152 | −0.685761 | − | 0.727827i | \(-0.740531\pi\) | ||||
−0.685761 | + | 0.727827i | \(0.740531\pi\) | |||||||
\(648\) | 5.38071e12 | 1.19882 | ||||||||
\(649\) | 5.77640e11 | 0.127807 | ||||||||
\(650\) | 7.44619e10 | 0.0163615 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.18754e12 | 0.257356 | ||||||||
\(653\) | 7.66270e12 | 1.64920 | 0.824598 | − | 0.565719i | \(-0.191401\pi\) | ||||
0.824598 | + | 0.565719i | \(0.191401\pi\) | |||||||
\(654\) | 1.90813e12 | 0.407858 | ||||||||
\(655\) | 4.31346e12 | 0.915673 | ||||||||
\(656\) | −2.62698e11 | −0.0553846 | ||||||||
\(657\) | −1.12450e12 | −0.235459 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.20110e9 | −0.00169390 | −0.000846950 | − | 1.00000i | \(-0.500270\pi\) | ||||
−0.000846950 | 1.00000i | \(0.500270\pi\) | ||||||||
\(660\) | 9.44881e12 | 1.93834 | ||||||||
\(661\) | −3.20922e12 | −0.653872 | −0.326936 | − | 0.945046i | \(-0.606016\pi\) | ||||
−0.326936 | + | 0.945046i | \(0.606016\pi\) | |||||||
\(662\) | 3.79231e12 | 0.767437 | ||||||||
\(663\) | 6.09158e10 | 0.0122439 | ||||||||
\(664\) | −9.39395e11 | −0.187539 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.14030e11 | −0.160327 | ||||||||
\(667\) | −1.82081e12 | −0.356203 | ||||||||
\(668\) | −3.47781e12 | −0.675791 | ||||||||
\(669\) | −3.77433e12 | −0.728488 | ||||||||
\(670\) | 2.98618e12 | 0.572506 | ||||||||
\(671\) | 1.52609e13 | 2.90622 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.91229e12 | −0.923031 | −0.461515 | − | 0.887132i | \(-0.652694\pi\) | ||||
−0.461515 | + | 0.887132i | \(0.652694\pi\) | |||||||
\(674\) | −7.50089e10 | −0.0140005 | ||||||||
\(675\) | 3.60372e12 | 0.668166 | ||||||||
\(676\) | 3.53309e12 | 0.650721 | ||||||||
\(677\) | 3.11910e12 | 0.570664 | 0.285332 | − | 0.958429i | \(-0.407896\pi\) | ||||
0.285332 | + | 0.958429i | \(0.407896\pi\) | |||||||
\(678\) | −3.33952e12 | −0.606946 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.52953e12 | −0.453680 | ||||||||
\(681\) | −3.77315e12 | −0.672267 | ||||||||
\(682\) | 1.16596e13 | 2.06374 | ||||||||
\(683\) | 2.91806e12 | 0.513099 | 0.256550 | − | 0.966531i | \(-0.417414\pi\) | ||||
0.256550 | + | 0.966531i | \(0.417414\pi\) | |||||||
\(684\) | −3.33552e11 | −0.0582655 | ||||||||
\(685\) | −7.99902e12 | −1.38813 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.95322e12 | 1.19092 | ||||||||
\(688\) | −5.89742e11 | −0.100349 | ||||||||
\(689\) | 2.26360e11 | 0.0382660 | ||||||||
\(690\) | 5.34633e12 | 0.897914 | ||||||||
\(691\) | −4.74697e12 | −0.792073 | −0.396037 | − | 0.918235i | \(-0.629615\pi\) | ||||
−0.396037 | + | 0.918235i | \(0.629615\pi\) | |||||||
\(692\) | 6.82712e12 | 1.13178 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.54058e12 | 0.743009 | ||||||||
\(695\) | −1.15982e13 | −1.88563 | ||||||||
\(696\) | −2.63849e12 | −0.426200 | ||||||||
\(697\) | 1.54406e12 | 0.247809 | ||||||||
\(698\) | −4.63240e11 | −0.0738680 | ||||||||
\(699\) | 2.07013e12 | 0.327981 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.24423e11 | −0.0351023 | −0.0175512 | − | 0.999846i | \(-0.505587\pi\) | ||||
−0.0175512 | + | 0.999846i | \(0.505587\pi\) | |||||||
\(702\) | 8.84599e10 | 0.0137477 | ||||||||
\(703\) | −1.23610e12 | −0.190877 | ||||||||
\(704\) | −6.37400e12 | −0.977992 | ||||||||
\(705\) | 3.39146e12 | 0.517054 | ||||||||
\(706\) | 4.63484e12 | 0.702123 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.49001e11 | −0.0522007 | ||||||||
\(709\) | 4.25463e12 | 0.632344 | 0.316172 | − | 0.948702i | \(-0.397602\pi\) | ||||
0.316172 | + | 0.948702i | \(0.397602\pi\) | |||||||
\(710\) | −3.71091e12 | −0.548047 | ||||||||
\(711\) | −3.43569e12 | −0.504197 | ||||||||
\(712\) | 2.35059e10 | 0.00342781 | ||||||||
\(713\) | −1.23250e13 | −1.78601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.54800e11 | 0.0793888 | ||||||||
\(716\) | −1.82321e12 | −0.259256 | ||||||||
\(717\) | −1.04238e13 | −1.47296 | ||||||||
\(718\) | −3.35369e12 | −0.470938 | ||||||||
\(719\) | 4.28931e12 | 0.598559 | 0.299280 | − | 0.954165i | \(-0.403254\pi\) | ||||
0.299280 | + | 0.954165i | \(0.403254\pi\) | |||||||
\(720\) | −2.67492e11 | −0.0370950 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.04023e12 | −0.553335 | ||||||||
\(723\) | −4.76524e12 | −0.648578 | ||||||||
\(724\) | −7.05761e11 | −0.0954627 | ||||||||
\(725\) | −2.48940e12 | −0.334637 | ||||||||
\(726\) | −1.26155e13 | −1.68535 | ||||||||
\(727\) | −1.28935e13 | −1.71185 | −0.855926 | − | 0.517098i | \(-0.827012\pi\) | ||||
−0.855926 | + | 0.517098i | \(0.827012\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.31084e12 | 0.434174 | ||||||||
\(730\) | 4.11307e12 | 0.536060 | ||||||||
\(731\) | 3.46633e12 | 0.448995 | ||||||||
\(732\) | −9.22038e12 | −1.18699 | ||||||||
\(733\) | −2.71447e12 | −0.347310 | −0.173655 | − | 0.984807i | \(-0.555558\pi\) | ||||
−0.173655 | + | 0.984807i | \(0.555558\pi\) | |||||||
\(734\) | −6.41143e12 | −0.815309 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.70531e12 | 0.967921 | ||||||||
\(737\) | 1.04881e13 | 1.30946 | ||||||||
\(738\) | −1.24339e12 | −0.154296 | ||||||||
\(739\) | −9.62579e12 | −1.18723 | −0.593617 | − | 0.804747i | \(-0.702301\pi\) | ||||
−0.593617 | + | 0.804747i | \(0.702301\pi\) | |||||||
\(740\) | −5.56252e12 | −0.681913 | ||||||||
\(741\) | −7.44880e10 | −0.00907620 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.24362e13 | −1.49706 | −0.748529 | − | 0.663103i | \(-0.769239\pi\) | ||||
−0.748529 | + | 0.663103i | \(0.769239\pi\) | |||||||
\(744\) | −1.78599e13 | −2.13698 | ||||||||
\(745\) | 8.41595e12 | 1.00092 | ||||||||
\(746\) | −2.46898e12 | −0.291872 | ||||||||
\(747\) | 5.83886e11 | 0.0686097 | ||||||||
\(748\) | −3.50425e12 | −0.409296 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.87371e11 | −0.102407 | ||||||||
\(751\) | 4.26959e12 | 0.489786 | 0.244893 | − | 0.969550i | \(-0.421247\pi\) | ||||
0.244893 | + | 0.969550i | \(0.421247\pi\) | |||||||
\(752\) | 2.13992e11 | 0.0244015 | ||||||||
\(753\) | 1.02778e13 | 1.16499 | ||||||||
\(754\) | −6.11068e10 | −0.00688523 | ||||||||
\(755\) | 5.17770e12 | 0.579930 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.76840e12 | 1.08116 | 0.540582 | − | 0.841291i | \(-0.318204\pi\) | ||||
0.540582 | + | 0.841291i | \(0.318204\pi\) | |||||||
\(758\) | −9.47153e12 | −1.04210 | ||||||||
\(759\) | 1.87774e13 | 2.05375 | ||||||||
\(760\) | 3.09311e12 | 0.336306 | ||||||||
\(761\) | −1.23336e13 | −1.33309 | −0.666543 | − | 0.745466i | \(-0.732227\pi\) | ||||
−0.666543 | + | 0.745466i | \(0.732227\pi\) | |||||||
\(762\) | 1.90378e12 | 0.204559 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.75008e12 | −0.610595 | ||||||||
\(765\) | 1.57224e12 | 0.165975 | ||||||||
\(766\) | −1.65391e12 | −0.173573 | ||||||||
\(767\) | −2.04921e10 | −0.00213800 | ||||||||
\(768\) | 1.06125e13 | 1.10076 | ||||||||
\(769\) | 1.68919e13 | 1.74185 | 0.870926 | − | 0.491415i | \(-0.163520\pi\) | ||||
0.870926 | + | 0.491415i | \(0.163520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.87078e13 | 1.90668 | ||||||||
\(772\) | −6.73751e12 | −0.682687 | ||||||||
\(773\) | −1.47186e13 | −1.48272 | −0.741359 | − | 0.671109i | \(-0.765818\pi\) | ||||
−0.741359 | + | 0.671109i | \(0.765818\pi\) | |||||||
\(774\) | −2.79135e12 | −0.279563 | ||||||||
\(775\) | −1.68507e13 | −1.67788 | ||||||||
\(776\) | −3.56835e12 | −0.353257 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.98111e12 | −0.389579 | ||||||||
\(779\) | −1.88808e12 | −0.183697 | ||||||||
\(780\) | −3.35201e11 | −0.0324250 | ||||||||
\(781\) | −1.30335e13 | −1.25352 | ||||||||
\(782\) | −1.98278e12 | −0.189602 | ||||||||
\(783\) | −2.95738e12 | −0.281177 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.55736e12 | −0.240369 | ||||||||
\(786\) | 4.89949e12 | 0.457878 | ||||||||
\(787\) | 1.82466e13 | 1.69549 | 0.847744 | − | 0.530406i | \(-0.177960\pi\) | ||||
0.847744 | + | 0.530406i | \(0.177960\pi\) | |||||||
\(788\) | 7.42326e12 | 0.685846 | ||||||||
\(789\) | −2.29932e12 | −0.211228 | ||||||||
\(790\) | 1.25667e13 | 1.14789 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.15424e12 | 0.646101 | ||||||||
\(793\) | −5.41388e11 | −0.0486160 | ||||||||
\(794\) | −7.12695e12 | −0.636373 | ||||||||
\(795\) | 2.22204e13 | 1.97287 | ||||||||
\(796\) | 5.68895e12 | 0.502254 | ||||||||
\(797\) | 1.21558e13 | 1.06714 | 0.533568 | − | 0.845757i | \(-0.320851\pi\) | ||||
0.533568 | + | 0.845757i | \(0.320851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.25778e12 | −0.109180 | ||||||||
\(800\) | 1.05347e13 | 0.909318 | ||||||||
\(801\) | −1.46102e10 | −0.00125403 | ||||||||
\(802\) | 5.55325e12 | 0.473982 | ||||||||
\(803\) | 1.44460e13 | 1.22610 | ||||||||
\(804\) | −6.33673e12 | −0.534827 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.13631e11 | −0.0345227 | ||||||||
\(807\) | 1.37128e13 | 1.13814 | ||||||||
\(808\) | −6.49362e12 | −0.535964 | ||||||||
\(809\) | −2.61893e12 | −0.214959 | −0.107479 | − | 0.994207i | \(-0.534278\pi\) | ||||
−0.107479 | + | 0.994207i | \(0.534278\pi\) | |||||||
\(810\) | 1.22328e13 | 0.998491 | ||||||||
\(811\) | −1.16994e13 | −0.949662 | −0.474831 | − | 0.880077i | \(-0.657491\pi\) | ||||
−0.474831 | + | 0.880077i | \(0.657491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.24217e12 | 0.260272 | ||||||||
\(814\) | 1.04575e13 | 0.834868 | ||||||||
\(815\) | 6.84480e12 | 0.543440 | ||||||||
\(816\) | 3.77305e11 | 0.0297911 | ||||||||
\(817\) | −4.23863e12 | −0.332833 | ||||||||
\(818\) | −1.44267e13 | −1.12662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.49649e12 | −0.656262 | ||||||||
\(821\) | 5.17673e12 | 0.397659 | 0.198830 | − | 0.980034i | \(-0.436286\pi\) | ||||
0.198830 | + | 0.980034i | \(0.436286\pi\) | |||||||
\(822\) | −9.08577e12 | −0.694126 | ||||||||
\(823\) | −7.84017e12 | −0.595698 | −0.297849 | − | 0.954613i | \(-0.596269\pi\) | ||||
−0.297849 | + | 0.954613i | \(0.596269\pi\) | |||||||
\(824\) | −1.71558e13 | −1.29640 | ||||||||
\(825\) | 2.56724e13 | 1.92941 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.43263e13 | −1.06502 | −0.532512 | − | 0.846422i | \(-0.678752\pi\) | ||||
−0.532512 | + | 0.846422i | \(0.678752\pi\) | |||||||
\(828\) | −2.98292e12 | −0.220549 | ||||||||
\(829\) | −4.95546e12 | −0.364408 | −0.182204 | − | 0.983261i | \(-0.558323\pi\) | ||||
−0.182204 | + | 0.983261i | \(0.558323\pi\) | |||||||
\(830\) | −2.13568e12 | −0.156201 | ||||||||
\(831\) | 1.17317e13 | 0.853408 | ||||||||
\(832\) | 2.26121e11 | 0.0163601 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.31739e13 | −0.942902 | ||||||||
\(835\) | −2.00456e13 | −1.42702 | ||||||||
\(836\) | 4.28500e12 | 0.303405 | ||||||||
\(837\) | −2.00185e13 | −1.40983 | ||||||||
\(838\) | 2.95270e12 | 0.206834 | ||||||||
\(839\) | −7.38235e12 | −0.514358 | −0.257179 | − | 0.966364i | \(-0.582793\pi\) | ||||
−0.257179 | + | 0.966364i | \(0.582793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.24642e13 | −0.859179 | ||||||||
\(842\) | 4.64256e12 | 0.318312 | ||||||||
\(843\) | −1.68077e13 | −1.14626 | ||||||||
\(844\) | 1.06675e13 | 0.723636 | ||||||||
\(845\) | 2.03642e13 | 1.37408 | ||||||||
\(846\) | 1.01286e12 | 0.0679802 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.40204e12 | 0.0931065 | ||||||||
\(849\) | −9.03491e12 | −0.596814 | ||||||||
\(850\) | −2.71084e12 | −0.178123 | ||||||||
\(851\) | −1.10543e13 | −0.722516 | ||||||||
\(852\) | 7.87462e12 | 0.511978 | ||||||||
\(853\) | −2.13356e13 | −1.37985 | −0.689927 | − | 0.723879i | \(-0.742357\pi\) | ||||
−0.689927 | + | 0.723879i | \(0.742357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.92254e12 | −0.123035 | ||||||||
\(856\) | 2.28032e12 | 0.145166 | ||||||||
\(857\) | −1.65008e13 | −1.04494 | −0.522468 | − | 0.852659i | \(-0.674989\pi\) | ||||
−0.522468 | + | 0.852659i | \(0.674989\pi\) | |||||||
\(858\) | 6.30175e11 | 0.0396980 | ||||||||
\(859\) | 1.94817e13 | 1.22083 | 0.610417 | − | 0.792080i | \(-0.291002\pi\) | ||||
0.610417 | + | 0.792080i | \(0.291002\pi\) | |||||||
\(860\) | −1.90742e13 | −1.18906 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.65103e12 | 0.101853 | ||||||||
\(863\) | 1.61059e13 | 0.988411 | 0.494205 | − | 0.869345i | \(-0.335459\pi\) | ||||
0.494205 | + | 0.869345i | \(0.335459\pi\) | |||||||
\(864\) | 1.25151e13 | 0.764049 | ||||||||
\(865\) | 3.93504e13 | 2.38989 | ||||||||
\(866\) | 9.72232e12 | 0.587408 | ||||||||
\(867\) | 1.71613e13 | 1.03149 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.41368e13 | 2.62550 | ||||||||
\(870\) | −5.99849e12 | −0.354981 | ||||||||
\(871\) | −3.72070e11 | −0.0219050 | ||||||||
\(872\) | 9.87249e12 | 0.578232 | ||||||||
\(873\) | 2.21793e12 | 0.129236 | ||||||||
\(874\) | 2.42454e12 | 0.140549 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.72801e12 | −0.500780 | ||||||||
\(877\) | −1.84919e13 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(878\) | 7.82892e12 | 0.444607 | ||||||||
\(879\) | 1.72764e13 | 0.976121 | ||||||||
\(880\) | 3.43636e12 | 0.193164 | ||||||||
\(881\) | 2.83078e13 | 1.58312 | 0.791562 | − | 0.611089i | \(-0.209268\pi\) | ||||
0.791562 | + | 0.611089i | \(0.209268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.32328e12 | −0.405399 | −0.202700 | − | 0.979241i | \(-0.564971\pi\) | ||||
−0.202700 | + | 0.979241i | \(0.564971\pi\) | |||||||
\(884\) | 1.24315e11 | 0.00684681 | ||||||||
\(885\) | −2.01158e12 | −0.110228 | ||||||||
\(886\) | −2.82641e12 | −0.154093 | ||||||||
\(887\) | −1.51372e13 | −0.821087 | −0.410544 | − | 0.911841i | \(-0.634661\pi\) | ||||
−0.410544 | + | 0.911841i | \(0.634661\pi\) | |||||||
\(888\) | −1.60185e13 | −0.864496 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.34396e10 | 0.00285501 | ||||||||
\(891\) | 4.29642e13 | 2.28380 | ||||||||
\(892\) | −7.70253e12 | −0.407372 | ||||||||
\(893\) | 1.53802e12 | 0.0809337 | ||||||||
\(894\) | 9.55934e12 | 0.500506 | ||||||||
\(895\) | −1.05087e13 | −0.547451 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.66138e11 | −0.0343556 | ||||||||
\(898\) | −1.23059e13 | −0.631493 | ||||||||
\(899\) | 1.38285e13 | 0.706082 | ||||||||
\(900\) | −4.07823e12 | −0.207196 | ||||||||
\(901\) | −8.24080e12 | −0.416589 | ||||||||
\(902\) | 1.59733e13 | 0.803463 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.72783e13 | −0.860487 | ||||||||
\(905\) | −4.06789e12 | −0.201582 | ||||||||
\(906\) | 5.88114e12 | 0.289991 | ||||||||
\(907\) | −2.24337e13 | −1.10070 | −0.550349 | − | 0.834935i | \(-0.685505\pi\) | ||||
−0.550349 | + | 0.834935i | \(0.685505\pi\) | |||||||
\(908\) | −7.70011e12 | −0.375933 | ||||||||
\(909\) | 4.03614e12 | 0.196078 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.34178e12 | −0.305055 | −0.152528 | − | 0.988299i | \(-0.548741\pi\) | ||||
−0.152528 | + | 0.988299i | \(0.548741\pi\) | |||||||
\(912\) | −4.61369e11 | −0.0220837 | ||||||||
\(913\) | −7.50094e12 | −0.357270 | ||||||||
\(914\) | 1.08380e13 | 0.513679 | ||||||||
\(915\) | −5.31448e13 | −2.50649 | ||||||||
\(916\) | 1.41899e13 | 0.665963 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.22045e12 | −0.149667 | ||||||||
\(919\) | 9.04471e12 | 0.418288 | 0.209144 | − | 0.977885i | \(-0.432932\pi\) | ||||
0.209144 | + | 0.977885i | \(0.432932\pi\) | |||||||
\(920\) | 2.76614e13 | 1.27300 | ||||||||
\(921\) | −1.32376e13 | −0.606236 | ||||||||
\(922\) | 2.53946e12 | 0.115732 | ||||||||
\(923\) | 4.62369e11 | 0.0209692 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.51134e13 | −0.678771 | ||||||||
\(926\) | 6.37233e12 | 0.284806 | ||||||||
\(927\) | 1.06633e13 | 0.474277 | ||||||||
\(928\) | −8.64522e12 | −0.382658 | ||||||||
\(929\) | −8.50641e12 | −0.374693 | −0.187346 | − | 0.982294i | \(-0.559989\pi\) | ||||
−0.187346 | + | 0.982294i | \(0.559989\pi\) | |||||||
\(930\) | −4.06037e13 | −1.77988 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.22464e12 | 0.183408 | ||||||||
\(933\) | −5.20368e13 | −2.24824 | ||||||||
\(934\) | −1.42147e13 | −0.611191 | ||||||||
\(935\) | −2.01979e13 | −0.864280 | ||||||||
\(936\) | −2.53800e11 | −0.0108081 | ||||||||
\(937\) | 3.00276e13 | 1.27260 | 0.636300 | − | 0.771442i | \(-0.280464\pi\) | ||||
0.636300 | + | 0.771442i | \(0.280464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.10602e13 | 0.884030 | ||||||||
\(940\) | 6.92118e12 | 0.289138 | ||||||||
\(941\) | 3.15982e13 | 1.31374 | 0.656870 | − | 0.754004i | \(-0.271880\pi\) | ||||
0.656870 | + | 0.754004i | \(0.271880\pi\) | |||||||
\(942\) | −2.90480e12 | −0.120195 | ||||||||
\(943\) | −1.68849e13 | −0.695338 | ||||||||
\(944\) | −1.26925e11 | −0.00520205 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.58592e13 | 1.45576 | ||||||||
\(947\) | −8.84885e12 | −0.357529 | −0.178765 | − | 0.983892i | \(-0.557210\pi\) | ||||
−0.178765 | + | 0.983892i | \(0.557210\pi\) | |||||||
\(948\) | −2.66667e13 | −1.07234 | ||||||||
\(949\) | −5.12477e11 | −0.0205105 | ||||||||
\(950\) | 3.31482e12 | 0.132040 | ||||||||
\(951\) | 1.21698e13 | 0.482473 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.90260e12 | −0.192534 | −0.0962672 | − | 0.995356i | \(-0.530690\pi\) | ||||
−0.0962672 | + | 0.995356i | \(0.530690\pi\) | |||||||
\(954\) | 6.63610e12 | 0.259385 | ||||||||
\(955\) | −3.31425e13 | −1.28935 | ||||||||
\(956\) | −2.12726e13 | −0.823682 | ||||||||
\(957\) | −2.10679e13 | −0.811929 | ||||||||
\(958\) | 1.12686e13 | 0.432241 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.21969e13 | 0.843476 | ||||||||
\(961\) | 6.71649e13 | 2.54031 | ||||||||
\(962\) | −3.70985e11 | −0.0139659 | ||||||||
\(963\) | −1.41735e12 | −0.0531077 | ||||||||
\(964\) | −9.72475e12 | −0.362687 | ||||||||
\(965\) | −3.88339e13 | −1.44158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55633e13 | 0.572378 | 0.286189 | − | 0.958173i | \(-0.407612\pi\) | ||||
0.286189 | + | 0.958173i | \(0.407612\pi\) | |||||||
\(968\) | −6.52713e13 | −2.38937 | ||||||||
\(969\) | 2.71179e12 | 0.0988096 | ||||||||
\(970\) | −8.11251e12 | −0.294227 | ||||||||
\(971\) | 2.49197e13 | 0.899613 | 0.449806 | − | 0.893126i | \(-0.351493\pi\) | ||||
0.449806 | + | 0.893126i | \(0.351493\pi\) | |||||||
\(972\) | −1.23765e13 | −0.444732 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.53918e13 | 0.547991 | ||||||||
\(975\) | −9.10740e11 | −0.0322756 | ||||||||
\(976\) | −3.35329e12 | −0.118290 | ||||||||
\(977\) | 4.47898e12 | 0.157273 | 0.0786364 | − | 0.996903i | \(-0.474943\pi\) | ||||
0.0786364 | + | 0.996903i | \(0.474943\pi\) | |||||||
\(978\) | 7.77474e12 | 0.271745 | ||||||||
\(979\) | 1.87691e11 | 0.00653012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.13629e12 | −0.211542 | ||||||||
\(982\) | −1.29426e13 | −0.444139 | ||||||||
\(983\) | 1.43233e13 | 0.489275 | 0.244637 | − | 0.969615i | \(-0.421331\pi\) | ||||
0.244637 | + | 0.969615i | \(0.421331\pi\) | |||||||
\(984\) | −2.44675e13 | −0.831977 | ||||||||
\(985\) | 4.27865e13 | 1.44825 | ||||||||
\(986\) | 2.22464e12 | 0.0749572 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.52013e11 | −0.00507543 | ||||||||
\(989\) | −3.79057e13 | −1.25986 | ||||||||
\(990\) | 1.62649e13 | 0.538136 | ||||||||
\(991\) | −2.28575e13 | −0.752829 | −0.376415 | − | 0.926451i | \(-0.622843\pi\) | ||||
−0.376415 | + | 0.926451i | \(0.622843\pi\) | |||||||
\(992\) | −5.85194e13 | −1.91866 | ||||||||
\(993\) | −4.63836e13 | −1.51388 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.27902e13 | 1.06057 | ||||||||
\(996\) | 4.53194e12 | 0.145921 | ||||||||
\(997\) | 2.67132e13 | 0.856243 | 0.428121 | − | 0.903721i | \(-0.359176\pi\) | ||||
0.428121 | + | 0.903721i | \(0.359176\pi\) | |||||||
\(998\) | 3.51147e13 | 1.12047 | ||||||||
\(999\) | −1.79545e13 | −0.570334 |
(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 | 49.10.a.c.1.2 | 3 | ||
7.2 | even | 3 | 49.10.c.e.18.2 | 6 | |||
7.3 | odd | 6 | 49.10.c.d.30.2 | 6 | |||
7.4 | even | 3 | 49.10.c.e.30.2 | 6 | |||
7.5 | odd | 6 | 49.10.c.d.18.2 | 6 | |||
7.6 | odd | 2 | 7.10.a.b.1.2 | ✓ | 3 | ||
21.20 | even | 2 | 63.10.a.e.1.2 | 3 | |||
28.27 | even | 2 | 112.10.a.h.1.1 | 3 | |||
35.13 | even | 4 | 175.10.b.d.99.3 | 6 | |||
35.27 | even | 4 | 175.10.b.d.99.4 | 6 | |||
35.34 | odd | 2 | 175.10.a.d.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.10.a.b.1.2 | ✓ | 3 | 7.6 | odd | 2 | ||
49.10.a.c.1.2 | 3 | 1.1 | even | 1 | trivial | ||
49.10.c.d.18.2 | 6 | 7.5 | odd | 6 | |||
49.10.c.d.30.2 | 6 | 7.3 | odd | 6 | |||
49.10.c.e.18.2 | 6 | 7.2 | even | 3 | |||
49.10.c.e.30.2 | 6 | 7.4 | even | 3 | |||
63.10.a.e.1.2 | 3 | 21.20 | even | 2 | |||
112.10.a.h.1.1 | 3 | 28.27 | even | 2 | |||
175.10.a.d.1.2 | 3 | 35.34 | odd | 2 | |||
175.10.b.d.99.3 | 6 | 35.13 | even | 4 | |||
175.10.b.d.99.4 | 6 | 35.27 | even | 4 |