Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,11,Mod(14,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.14");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(9.53035879011\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 17880 x^{14} + 140656106 x^{12} + 568287997200 x^{10} + \cdots + 16\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{32}\cdot 5^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 14.1 | ||
Root | \(-19.4690 + 50.0826i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.14 |
Dual form | 15.11.d.c.14.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −50.9058 | −1.59081 | −0.795404 | − | 0.606080i | \(-0.792741\pi\) | ||||
−0.795404 | + | 0.606080i | \(0.792741\pi\) | |||||||
\(3\) | −190.983 | − | 150.248i | −0.785939 | − | 0.618304i | ||||
\(4\) | 1567.41 | 1.53067 | ||||||||
\(5\) | 553.573 | + | 3075.58i | 0.177143 | + | 0.984185i | ||||
\(6\) | 9722.16 | + | 7648.49i | 1.25028 | + | 0.983603i | ||||
\(7\) | 8178.10i | 0.486589i | 0.969952 | + | 0.243294i | \(0.0782281\pi\) | ||||
−0.969952 | + | 0.243294i | \(0.921772\pi\) | |||||||
\(8\) | −27662.5 | −0.844192 | ||||||||
\(9\) | 13900.2 | + | 57389.6i | 0.235400 | + | 0.971898i | ||||
\(10\) | −28180.1 | − | 156565.i | −0.281801 | − | 1.56565i | ||||
\(11\) | − | 197407.i | − | 1.22574i | −0.790182 | − | 0.612872i | \(-0.790014\pi\) | ||
0.790182 | − | 0.612872i | \(-0.209986\pi\) | |||||||
\(12\) | −299348. | − | 235499.i | −1.20301 | − | 0.946419i | ||||
\(13\) | 212605.i | 0.572606i | 0.958139 | + | 0.286303i | \(0.0924265\pi\) | ||||
−0.958139 | + | 0.286303i | \(0.907574\pi\) | |||||||
\(14\) | − | 416313.i | − | 0.774069i | ||||||
\(15\) | 356376. | − | 670557.i | 0.469302 | − | 0.883038i | ||||
\(16\) | −196840. | −0.187721 | ||||||||
\(17\) | −2.05581e6 | −1.44790 | −0.723950 | − | 0.689852i | \(-0.757676\pi\) | ||||
−0.723950 | + | 0.689852i | \(0.757676\pi\) | |||||||
\(18\) | −707599. | − | 2.92147e6i | −0.374477 | − | 1.54610i | ||||
\(19\) | 1.39222e6 | 0.562262 | 0.281131 | − | 0.959669i | \(-0.409290\pi\) | ||||
0.281131 | + | 0.959669i | \(0.409290\pi\) | |||||||
\(20\) | 867673. | + | 4.82068e6i | 0.271148 | + | 1.50646i | ||||
\(21\) | 1.22874e6 | − | 1.56188e6i | 0.300860 | − | 0.382429i | ||||
\(22\) | 1.00492e7i | 1.94992i | ||||||||
\(23\) | 6.13773e6 | 0.953605 | 0.476802 | − | 0.879011i | \(-0.341796\pi\) | ||||
0.476802 | + | 0.879011i | \(0.341796\pi\) | |||||||
\(24\) | 5.28307e6 | + | 4.15623e6i | 0.663484 | + | 0.521967i | ||||
\(25\) | −9.15274e6 | + | 3.40511e6i | −0.937240 | + | 0.348684i | ||||
\(26\) | − | 1.08228e7i | − | 0.910907i | ||||||
\(27\) | 5.96797e6 | − | 1.30489e7i | 0.415918 | − | 0.909402i | ||||
\(28\) | 1.28184e7i | 0.744807i | ||||||||
\(29\) | − | 3.53508e7i | − | 1.72349i | −0.507339 | − | 0.861747i | \(-0.669371\pi\) | ||
0.507339 | − | 0.861747i | \(-0.330629\pi\) | |||||||
\(30\) | −1.81416e7 | + | 3.41353e7i | −0.746569 | + | 1.40474i | ||||
\(31\) | −3.56226e7 | −1.24428 | −0.622139 | − | 0.782907i | \(-0.713736\pi\) | ||||
−0.622139 | + | 0.782907i | \(0.713736\pi\) | |||||||
\(32\) | 3.83467e7 | 1.14282 | ||||||||
\(33\) | −2.96600e7 | + | 3.77015e7i | −0.757883 | + | 0.963361i | ||||
\(34\) | 1.04653e8 | 2.30333 | ||||||||
\(35\) | −2.51524e7 | + | 4.52718e6i | −0.478894 | + | 0.0861960i | ||||
\(36\) | 2.17872e7 | + | 8.99528e7i | 0.360320 | + | 1.48765i | ||||
\(37\) | − | 1.06122e8i | − | 1.53037i | −0.643810 | − | 0.765185i | \(-0.722647\pi\) | ||
0.643810 | − | 0.765185i | \(-0.277353\pi\) | |||||||
\(38\) | −7.08720e7 | −0.894451 | ||||||||
\(39\) | 3.19434e7 | − | 4.06039e7i | 0.354045 | − | 0.450034i | ||||
\(40\) | −1.53132e7 | − | 8.50782e7i | −0.149543 | − | 0.830841i | ||||
\(41\) | 1.33173e7i | 0.114947i | 0.998347 | + | 0.0574736i | \(0.0183045\pi\) | ||||
−0.998347 | + | 0.0574736i | \(0.981696\pi\) | |||||||
\(42\) | −6.25502e7 | + | 7.95088e7i | −0.478610 | + | 0.608371i | ||||
\(43\) | − | 1.18665e8i | − | 0.807200i | −0.914936 | − | 0.403600i | \(-0.867759\pi\) | ||
0.914936 | − | 0.403600i | \(-0.132241\pi\) | |||||||
\(44\) | − | 3.09417e8i | − | 1.87621i | ||||||
\(45\) | −1.68812e8 | + | 7.45204e7i | −0.914828 | + | 0.403843i | ||||
\(46\) | −3.12446e8 | −1.51700 | ||||||||
\(47\) | −2.04173e7 | −0.0890245 | −0.0445122 | − | 0.999009i | \(-0.514173\pi\) | ||||
−0.0445122 | + | 0.999009i | \(0.514173\pi\) | |||||||
\(48\) | 3.75932e7 | + | 2.95748e7i | 0.147538 | + | 0.116069i | ||||
\(49\) | 2.15594e8 | 0.763231 | ||||||||
\(50\) | 4.65928e8 | − | 1.73340e8i | 1.49097 | − | 0.554689i | ||||
\(51\) | 3.92625e8 | + | 3.08881e8i | 1.13796 | + | 0.895243i | ||||
\(52\) | 3.33238e8i | 0.876471i | ||||||||
\(53\) | −3.25193e8 | −0.777610 | −0.388805 | − | 0.921320i | \(-0.627112\pi\) | ||||
−0.388805 | + | 0.921320i | \(0.627112\pi\) | |||||||
\(54\) | −3.03805e8 | + | 6.64267e8i | −0.661646 | + | 1.44668i | ||||
\(55\) | 6.07142e8 | − | 1.09279e8i | 1.20636 | − | 0.217133i | ||||
\(56\) | − | 2.26227e8i | − | 0.410775i | ||||||
\(57\) | −2.65890e8 | − | 2.09178e8i | −0.441904 | − | 0.347649i | ||||
\(58\) | 1.79956e9i | 2.74175i | ||||||||
\(59\) | 3.81698e8i | 0.533900i | 0.963710 | + | 0.266950i | \(0.0860158\pi\) | ||||
−0.963710 | + | 0.266950i | \(0.913984\pi\) | |||||||
\(60\) | 5.58585e8 | − | 1.05103e9i | 0.718345 | − | 1.35164i | ||||
\(61\) | −4.24233e8 | −0.502291 | −0.251146 | − | 0.967949i | \(-0.580807\pi\) | ||||
−0.251146 | + | 0.967949i | \(0.580807\pi\) | |||||||
\(62\) | 1.81340e9 | 1.97941 | ||||||||
\(63\) | −4.69338e8 | + | 1.13677e8i | −0.472915 | + | 0.114543i | ||||
\(64\) | −1.75051e9 | −1.63029 | ||||||||
\(65\) | −6.53883e8 | + | 1.17692e8i | −0.563551 | + | 0.101433i | ||||
\(66\) | 1.50987e9 | − | 1.91923e9i | 1.20565 | − | 1.53252i | ||||
\(67\) | − | 1.63786e9i | − | 1.21312i | −0.795039 | − | 0.606558i | \(-0.792550\pi\) | ||
0.795039 | − | 0.606558i | \(-0.207450\pi\) | |||||||
\(68\) | −3.22229e9 | −2.21626 | ||||||||
\(69\) | −1.17220e9 | − | 9.22180e8i | −0.749475 | − | 0.589618i | ||||
\(70\) | 1.28040e9 | − | 2.30460e8i | 0.761828 | − | 0.137121i | ||||
\(71\) | − | 1.20624e9i | − | 0.668564i | −0.942473 | − | 0.334282i | \(-0.891506\pi\) | ||
0.942473 | − | 0.334282i | \(-0.108494\pi\) | |||||||
\(72\) | −3.84513e8 | − | 1.58754e9i | −0.198723 | − | 0.820469i | ||||
\(73\) | − | 1.19205e9i | − | 0.575017i | −0.957778 | − | 0.287508i | \(-0.907173\pi\) | ||
0.957778 | − | 0.287508i | \(-0.0928270\pi\) | |||||||
\(74\) | 5.40223e9i | 2.43452i | ||||||||
\(75\) | 2.25963e9 | + | 7.24860e8i | 0.952206 | + | 0.305455i | ||||
\(76\) | 2.18217e9 | 0.860638 | ||||||||
\(77\) | 1.61442e9 | 0.596434 | ||||||||
\(78\) | −1.62611e9 | + | 2.06698e9i | −0.563217 | + | 0.715917i | ||||
\(79\) | 3.77862e8 | 0.122800 | 0.0614000 | − | 0.998113i | \(-0.480443\pi\) | ||||
0.0614000 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(80\) | −1.08965e8 | − | 6.05397e8i | −0.0332536 | − | 0.184753i | ||||
\(81\) | −3.10036e9 | + | 1.59545e9i | −0.889173 | + | 0.457571i | ||||
\(82\) | − | 6.77930e8i | − | 0.182859i | ||||||
\(83\) | −1.59624e9 | −0.405236 | −0.202618 | − | 0.979258i | \(-0.564945\pi\) | ||||
−0.202618 | + | 0.979258i | \(0.564945\pi\) | |||||||
\(84\) | 1.92594e9 | − | 2.44810e9i | 0.460517 | − | 0.585373i | ||||
\(85\) | −1.13804e9 | − | 6.32281e9i | −0.256486 | − | 1.42500i | ||||
\(86\) | 6.04075e9i | 1.28410i | ||||||||
\(87\) | −5.31139e9 | + | 6.75141e9i | −1.06564 | + | 1.35456i | ||||
\(88\) | 5.46078e9i | 1.03476i | ||||||||
\(89\) | − | 8.82698e9i | − | 1.58075i | −0.612626 | − | 0.790373i | \(-0.709887\pi\) | ||
0.612626 | − | 0.790373i | \(-0.290113\pi\) | |||||||
\(90\) | 8.59349e9 | − | 3.79352e9i | 1.45532 | − | 0.642437i | ||||
\(91\) | −1.73870e9 | −0.278624 | ||||||||
\(92\) | 9.62031e9 | 1.45965 | ||||||||
\(93\) | 6.80332e9 | + | 5.35222e9i | 0.977926 | + | 0.769342i | ||||
\(94\) | 1.03936e9 | 0.141621 | ||||||||
\(95\) | 7.70694e8 | + | 4.28187e9i | 0.0996011 | + | 0.553370i | ||||
\(96\) | −7.32358e9 | − | 5.76151e9i | −0.898188 | − | 0.706611i | ||||
\(97\) | 4.83465e9i | 0.562997i | 0.959562 | + | 0.281499i | \(0.0908315\pi\) | ||||
−0.959562 | + | 0.281499i | \(0.909169\pi\) | |||||||
\(98\) | −1.09750e10 | −1.21415 | ||||||||
\(99\) | 1.13291e10 | − | 2.74399e9i | 1.19130 | − | 0.288541i | ||||
\(100\) | −1.43460e10 | + | 5.33719e9i | −1.43460 | + | 0.533719i | ||||
\(101\) | 1.31030e10i | 1.24671i | 0.781940 | + | 0.623353i | \(0.214230\pi\) | ||||
−0.781940 | + | 0.623353i | \(0.785770\pi\) | |||||||
\(102\) | −1.99869e10 | − | 1.57239e10i | −1.81028 | − | 1.42416i | ||||
\(103\) | − | 6.50730e8i | − | 0.0561325i | −0.999606 | − | 0.0280663i | \(-0.991065\pi\) | ||
0.999606 | − | 0.0280663i | \(-0.00893494\pi\) | |||||||
\(104\) | − | 5.88118e9i | − | 0.483390i | ||||||
\(105\) | 5.48388e9 | + | 2.91448e9i | 0.429677 | + | 0.228357i | ||||
\(106\) | 1.65542e10 | 1.23703 | ||||||||
\(107\) | 1.97051e10 | 1.40495 | 0.702473 | − | 0.711710i | \(-0.252079\pi\) | ||||
0.702473 | + | 0.711710i | \(0.252079\pi\) | |||||||
\(108\) | 9.35423e9 | − | 2.04530e10i | 0.636633 | − | 1.39199i | ||||
\(109\) | 1.12463e10 | 0.730932 | 0.365466 | − | 0.930825i | \(-0.380910\pi\) | ||||
0.365466 | + | 0.930825i | \(0.380910\pi\) | |||||||
\(110\) | −3.09071e10 | + | 5.56296e9i | −1.91909 | + | 0.345416i | ||||
\(111\) | −1.59446e10 | + | 2.02675e10i | −0.946234 | + | 1.20278i | ||||
\(112\) | − | 1.60978e9i | − | 0.0913432i | ||||||
\(113\) | −2.43658e9 | −0.132248 | −0.0661240 | − | 0.997811i | \(-0.521063\pi\) | ||||
−0.0661240 | + | 0.997811i | \(0.521063\pi\) | |||||||
\(114\) | 1.35354e10 | + | 1.06484e10i | 0.702984 | + | 0.553043i | ||||
\(115\) | 3.39768e9 | + | 1.88771e10i | 0.168925 | + | 0.938524i | ||||
\(116\) | − | 5.54091e10i | − | 2.63810i | ||||||
\(117\) | −1.22013e10 | + | 2.95524e9i | −0.556515 | + | 0.134792i | ||||
\(118\) | − | 1.94307e10i | − | 0.849332i | ||||||
\(119\) | − | 1.68126e10i | − | 0.704532i | ||||||
\(120\) | −9.85825e9 | + | 1.85493e10i | −0.396181 | + | 0.745454i | ||||
\(121\) | −1.30323e10 | −0.502450 | ||||||||
\(122\) | 2.15960e10 | 0.799049 | ||||||||
\(123\) | 2.00090e9 | − | 2.54339e9i | 0.0710723 | − | 0.0903415i | ||||
\(124\) | −5.58351e10 | −1.90458 | ||||||||
\(125\) | −1.55394e10 | − | 2.62650e10i | −0.509195 | − | 0.860651i | ||||
\(126\) | 2.38921e10 | − | 5.78682e9i | 0.752317 | − | 0.182216i | ||||
\(127\) | − | 1.58080e10i | − | 0.478474i | −0.970961 | − | 0.239237i | \(-0.923103\pi\) | ||
0.970961 | − | 0.239237i | \(-0.0768973\pi\) | |||||||
\(128\) | 4.98440e10 | 1.45065 | ||||||||
\(129\) | −1.78292e10 | + | 2.26631e10i | −0.499095 | + | 0.634410i | ||||
\(130\) | 3.32864e10 | − | 5.99122e9i | 0.896501 | − | 0.161361i | ||||
\(131\) | 1.02430e9i | 0.0265503i | 0.999912 | + | 0.0132752i | \(0.00422574\pi\) | ||||
−0.999912 | + | 0.0132752i | \(0.995774\pi\) | |||||||
\(132\) | −4.64893e10 | + | 5.90935e10i | −1.16007 | + | 1.47459i | ||||
\(133\) | 1.13857e10i | 0.273591i | ||||||||
\(134\) | 8.33765e10i | 1.92983i | ||||||||
\(135\) | 4.34367e10 | + | 1.11314e10i | 0.968697 | + | 0.248246i | ||||
\(136\) | 5.68689e10 | 1.22231 | ||||||||
\(137\) | −1.11459e10 | −0.230948 | −0.115474 | − | 0.993311i | \(-0.536839\pi\) | ||||
−0.115474 | + | 0.993311i | \(0.536839\pi\) | |||||||
\(138\) | 5.96720e10 | + | 4.69444e10i | 1.19227 | + | 0.937968i | ||||
\(139\) | −2.36968e10 | −0.456684 | −0.228342 | − | 0.973581i | \(-0.573330\pi\) | ||||
−0.228342 | + | 0.973581i | \(0.573330\pi\) | |||||||
\(140\) | −3.94240e10 | + | 7.09592e9i | −0.733028 | + | 0.131938i | ||||
\(141\) | 3.89936e9 | + | 3.06766e9i | 0.0699678 | + | 0.0550442i | ||||
\(142\) | 6.14048e10i | 1.06356i | ||||||||
\(143\) | 4.19698e10 | 0.701869 | ||||||||
\(144\) | −2.73611e9 | − | 1.12966e10i | −0.0441897 | − | 0.182446i | ||||
\(145\) | 1.08724e11 | − | 1.95693e10i | 1.69624 | − | 0.305305i | ||||
\(146\) | 6.06824e10i | 0.914741i | ||||||||
\(147\) | −4.11748e10 | − | 3.23925e10i | −0.599853 | − | 0.471909i | ||||
\(148\) | − | 1.66336e11i | − | 2.34249i | ||||||
\(149\) | − | 6.95286e10i | − | 0.946744i | −0.880863 | − | 0.473372i | \(-0.843037\pi\) | ||
0.880863 | − | 0.473372i | \(-0.156963\pi\) | |||||||
\(150\) | −1.15028e11 | − | 3.68996e10i | −1.51478 | − | 0.485921i | ||||
\(151\) | −1.41697e11 | −1.80499 | −0.902497 | − | 0.430695i | \(-0.858268\pi\) | ||||
−0.902497 | + | 0.430695i | \(0.858268\pi\) | |||||||
\(152\) | −3.85122e10 | −0.474658 | ||||||||
\(153\) | −2.85761e10 | − | 1.17982e11i | −0.340836 | − | 1.40721i | ||||
\(154\) | −8.21833e10 | −0.948812 | ||||||||
\(155\) | −1.97197e10 | − | 1.09560e11i | −0.220416 | − | 1.22460i | ||||
\(156\) | 5.00683e10 | − | 6.36428e10i | 0.541925 | − | 0.688853i | ||||
\(157\) | 1.68085e10i | 0.176210i | 0.996111 | + | 0.0881049i | \(0.0280811\pi\) | ||||
−0.996111 | + | 0.0881049i | \(0.971919\pi\) | |||||||
\(158\) | −1.92354e10 | −0.195351 | ||||||||
\(159\) | 6.21064e10 | + | 4.88596e10i | 0.611154 | + | 0.480800i | ||||
\(160\) | 2.12277e10 | + | 1.17938e11i | 0.202443 | + | 1.12475i | ||||
\(161\) | 5.01950e10i | 0.464014i | ||||||||
\(162\) | 1.57826e11 | − | 8.12177e10i | 1.41450 | − | 0.727907i | ||||
\(163\) | 9.31622e10i | 0.809658i | 0.914392 | + | 0.404829i | \(0.132669\pi\) | ||||
−0.914392 | + | 0.404829i | \(0.867331\pi\) | |||||||
\(164\) | 2.08737e10i | 0.175946i | ||||||||
\(165\) | −1.32373e11 | − | 7.03512e10i | −1.08238 | − | 0.575244i | ||||
\(166\) | 8.12579e10 | 0.644652 | ||||||||
\(167\) | −4.49511e10 | −0.346065 | −0.173033 | − | 0.984916i | \(-0.555357\pi\) | ||||
−0.173033 | + | 0.984916i | \(0.555357\pi\) | |||||||
\(168\) | −3.39901e10 | + | 4.32055e10i | −0.253984 | + | 0.322844i | ||||
\(169\) | 9.26577e10 | 0.672122 | ||||||||
\(170\) | 5.79330e10 | + | 3.21868e11i | 0.408020 | + | 2.26690i | ||||
\(171\) | 1.93520e10 | + | 7.98988e10i | 0.132357 | + | 0.546462i | ||||
\(172\) | − | 1.85996e11i | − | 1.23556i | ||||||
\(173\) | −1.20661e11 | −0.778638 | −0.389319 | − | 0.921103i | \(-0.627290\pi\) | ||||
−0.389319 | + | 0.921103i | \(0.627290\pi\) | |||||||
\(174\) | 2.70381e11 | − | 3.43686e11i | 1.69523 | − | 2.15485i | ||||
\(175\) | −2.78474e10 | − | 7.48520e10i | −0.169666 | − | 0.456051i | ||||
\(176\) | 3.88577e10i | 0.230099i | ||||||||
\(177\) | 5.73493e10 | − | 7.28979e10i | 0.330112 | − | 0.419613i | ||||
\(178\) | 4.49345e11i | 2.51466i | ||||||||
\(179\) | 1.25285e11i | 0.681762i | 0.940106 | + | 0.340881i | \(0.110725\pi\) | ||||
−0.940106 | + | 0.340881i | \(0.889275\pi\) | |||||||
\(180\) | −2.64596e11 | + | 1.16804e11i | −1.40030 | + | 0.618150i | ||||
\(181\) | −4.85936e10 | −0.250142 | −0.125071 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125071 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(182\) | 8.85101e10 | 0.443237 | ||||||||
\(183\) | 8.10215e10 | + | 6.37402e10i | 0.394770 | + | 0.310569i | ||||
\(184\) | −1.69785e11 | −0.805026 | ||||||||
\(185\) | 3.26386e11 | − | 5.87463e10i | 1.50617 | − | 0.271095i | ||||
\(186\) | −3.46329e11 | − | 2.72459e11i | −1.55569 | − | 1.22387i | ||||
\(187\) | 4.05832e11i | 1.77476i | ||||||||
\(188\) | −3.20022e10 | −0.136267 | ||||||||
\(189\) | 1.06715e11 | + | 4.88067e10i | 0.442505 | + | 0.202381i | ||||
\(190\) | −3.92328e10 | − | 2.17972e11i | −0.158446 | − | 0.880306i | ||||
\(191\) | − | 1.54637e11i | − | 0.608342i | −0.952618 | − | 0.304171i | \(-0.901621\pi\) | ||
0.952618 | − | 0.304171i | \(-0.0983794\pi\) | |||||||
\(192\) | 3.34317e11 | + | 2.63010e11i | 1.28131 | + | 1.00801i | ||||
\(193\) | − | 4.23429e11i | − | 1.58123i | −0.612315 | − | 0.790614i | \(-0.709762\pi\) | ||
0.612315 | − | 0.790614i | \(-0.290238\pi\) | |||||||
\(194\) | − | 2.46112e11i | − | 0.895620i | ||||||
\(195\) | 1.42564e11 | + | 7.57672e10i | 0.505633 | + | 0.268725i | ||||
\(196\) | 3.37923e11 | 1.16825 | ||||||||
\(197\) | −5.51250e11 | −1.85788 | −0.928939 | − | 0.370232i | \(-0.879278\pi\) | ||||
−0.928939 | + | 0.370232i | \(0.879278\pi\) | |||||||
\(198\) | −5.76719e11 | + | 1.39685e11i | −1.89513 | + | 0.459013i | ||||
\(199\) | −8.03909e10 | −0.257598 | −0.128799 | − | 0.991671i | \(-0.541112\pi\) | ||||
−0.128799 | + | 0.991671i | \(0.541112\pi\) | |||||||
\(200\) | 2.53188e11 | − | 9.41940e10i | 0.791211 | − | 0.294356i | ||||
\(201\) | −2.46085e11 | + | 3.12803e11i | −0.750074 | + | 0.953435i | ||||
\(202\) | − | 6.67020e11i | − | 1.98327i | ||||||
\(203\) | 2.89103e11 | 0.838633 | ||||||||
\(204\) | 6.15403e11 | + | 4.84142e11i | 1.74184 | + | 1.37032i | ||||
\(205\) | −4.09585e10 | + | 7.37212e9i | −0.113129 | + | 0.0203621i | ||||
\(206\) | 3.31260e10i | 0.0892961i | ||||||||
\(207\) | 8.53154e10 | + | 3.52242e11i | 0.224479 | + | 0.926807i | ||||
\(208\) | − | 4.18492e10i | − | 0.107490i | ||||||
\(209\) | − | 2.74834e11i | − | 0.689190i | ||||||
\(210\) | −2.79162e11 | − | 1.48364e11i | −0.683533 | − | 0.363272i | ||||
\(211\) | 5.98657e11 | 1.43142 | 0.715708 | − | 0.698399i | \(-0.246104\pi\) | ||||
0.715708 | + | 0.698399i | \(0.246104\pi\) | |||||||
\(212\) | −5.09709e11 | −1.19026 | ||||||||
\(213\) | −1.81235e11 | + | 2.30372e11i | −0.413376 | + | 0.525450i | ||||
\(214\) | −1.00311e12 | −2.23500 | ||||||||
\(215\) | 3.64964e11 | − | 6.56899e10i | 0.794434 | − | 0.142990i | ||||
\(216\) | −1.65089e11 | + | 3.60966e11i | −0.351115 | + | 0.767710i | ||||
\(217\) | − | 2.91325e11i | − | 0.605452i | ||||||
\(218\) | −5.72502e11 | −1.16277 | ||||||||
\(219\) | −1.79103e11 | + | 2.27662e11i | −0.355535 | + | 0.451928i | ||||
\(220\) | 9.51637e11 | − | 1.71285e11i | 1.84654 | − | 0.332358i | ||||
\(221\) | − | 4.37075e11i | − | 0.829077i | ||||||
\(222\) | 8.11673e11 | − | 1.03173e12i | 1.50528 | − | 1.91339i | ||||
\(223\) | 6.50824e11i | 1.18016i | 0.807346 | + | 0.590078i | \(0.200903\pi\) | ||||
−0.807346 | + | 0.590078i | \(0.799097\pi\) | |||||||
\(224\) | 3.13603e11i | 0.556084i | ||||||||
\(225\) | −3.22643e11 | − | 4.77941e11i | −0.559512 | − | 0.828822i | ||||
\(226\) | 1.24036e11 | 0.210381 | ||||||||
\(227\) | 6.29028e11 | 1.04362 | 0.521808 | − | 0.853063i | \(-0.325258\pi\) | ||||
0.521808 | + | 0.853063i | \(0.325258\pi\) | |||||||
\(228\) | −4.16757e11 | − | 3.27866e11i | −0.676409 | − | 0.532136i | ||||
\(229\) | −9.59819e11 | −1.52410 | −0.762048 | − | 0.647521i | \(-0.775806\pi\) | ||||
−0.762048 | + | 0.647521i | \(0.775806\pi\) | |||||||
\(230\) | −1.72962e11 | − | 9.60953e11i | −0.268727 | − | 1.49301i | ||||
\(231\) | −3.08327e11 | − | 2.42563e11i | −0.468761 | − | 0.368777i | ||||
\(232\) | 9.77892e11i | 1.45496i | ||||||||
\(233\) | 4.34864e10 | 0.0633248 | 0.0316624 | − | 0.999499i | \(-0.489920\pi\) | ||||
0.0316624 | + | 0.999499i | \(0.489920\pi\) | |||||||
\(234\) | 6.21118e11 | − | 1.50439e11i | 0.885309 | − | 0.214428i | ||||
\(235\) | −1.13025e10 | − | 6.27951e10i | −0.0157701 | − | 0.0876166i | ||||
\(236\) | 5.98275e11i | 0.817224i | ||||||||
\(237\) | −7.21653e10 | − | 5.67730e10i | −0.0965132 | − | 0.0759277i | ||||
\(238\) | 8.55861e11i | 1.12078i | ||||||||
\(239\) | 2.77725e11i | 0.356144i | 0.984017 | + | 0.178072i | \(0.0569860\pi\) | ||||
−0.984017 | + | 0.178072i | \(0.943014\pi\) | |||||||
\(240\) | −7.01491e10 | + | 1.31993e11i | −0.0880980 | + | 0.165765i | ||||
\(241\) | 1.81041e11 | 0.222686 | 0.111343 | − | 0.993782i | \(-0.464485\pi\) | ||||
0.111343 | + | 0.993782i | \(0.464485\pi\) | |||||||
\(242\) | 6.63418e11 | 0.799301 | ||||||||
\(243\) | 8.31829e11 | + | 1.61118e11i | 0.981754 | + | 0.190157i | ||||
\(244\) | −6.64946e11 | −0.768842 | ||||||||
\(245\) | 1.19347e11 | + | 6.63076e11i | 0.135201 | + | 0.751161i | ||||
\(246\) | −1.01858e11 | + | 1.29473e11i | −0.113062 | + | 0.143716i | ||||
\(247\) | 2.95992e11i | 0.321955i | ||||||||
\(248\) | 9.85410e11 | 1.05041 | ||||||||
\(249\) | 3.04855e11 | + | 2.39832e11i | 0.318490 | + | 0.250559i | ||||
\(250\) | 7.91047e11 | + | 1.33704e12i | 0.810032 | + | 1.36913i | ||||
\(251\) | − | 5.59687e11i | − | 0.561793i | −0.959738 | − | 0.280896i | \(-0.909368\pi\) | ||
0.959738 | − | 0.280896i | \(-0.0906318\pi\) | |||||||
\(252\) | −7.35643e11 | + | 1.78178e11i | −0.723876 | + | 0.175328i | ||||
\(253\) | − | 1.21163e12i | − | 1.16888i | ||||||
\(254\) | 8.04720e11i | 0.761160i | ||||||||
\(255\) | −7.32642e11 | + | 1.37854e12i | −0.679502 | + | 1.27855i | ||||
\(256\) | −7.44833e11 | −0.677421 | ||||||||
\(257\) | −1.73313e12 | −1.54584 | −0.772920 | − | 0.634504i | \(-0.781204\pi\) | ||||
−0.772920 | + | 0.634504i | \(0.781204\pi\) | |||||||
\(258\) | 9.07610e11 | − | 1.15368e12i | 0.793964 | − | 1.00922i | ||||
\(259\) | 8.67876e11 | 0.744661 | ||||||||
\(260\) | −1.02490e12 | + | 1.84471e11i | −0.862609 | + | 0.155261i | ||||
\(261\) | 2.02877e12 | − | 4.91382e11i | 1.67506 | − | 0.405711i | ||||
\(262\) | − | 5.21427e10i | − | 0.0422365i | ||||||
\(263\) | −3.22541e11 | −0.256334 | −0.128167 | − | 0.991753i | \(-0.540909\pi\) | ||||
−0.128167 | + | 0.991753i | \(0.540909\pi\) | |||||||
\(264\) | 8.20471e11 | − | 1.04292e12i | 0.639799 | − | 0.813262i | ||||
\(265\) | −1.80018e11 | − | 1.00016e12i | −0.137749 | − | 0.765313i | ||||
\(266\) | − | 5.79598e11i | − | 0.435230i | ||||||
\(267\) | −1.32623e12 | + | 1.68580e12i | −0.977381 | + | 1.24237i | ||||
\(268\) | − | 2.56719e12i | − | 1.85688i | ||||||
\(269\) | − | 5.70627e11i | − | 0.405127i | −0.979269 | − | 0.202564i | \(-0.935073\pi\) | ||
0.979269 | − | 0.202564i | \(-0.0649273\pi\) | |||||||
\(270\) | −2.21118e12 | − | 5.66655e11i | −1.54101 | − | 0.394912i | ||||
\(271\) | −1.77796e11 | −0.121640 | −0.0608199 | − | 0.998149i | \(-0.519372\pi\) | ||||
−0.0608199 | + | 0.998149i | \(0.519372\pi\) | |||||||
\(272\) | 4.04666e11 | 0.271802 | ||||||||
\(273\) | 3.32063e11 | + | 2.61236e11i | 0.218981 | + | 0.172274i | ||||
\(274\) | 5.67393e11 | 0.367393 | ||||||||
\(275\) | 6.72195e11 | + | 1.80682e12i | 0.427397 | + | 1.14882i | ||||
\(276\) | −1.83732e12 | − | 1.44543e12i | −1.14720 | − | 0.902509i | ||||
\(277\) | − | 5.44853e11i | − | 0.334103i | −0.985948 | − | 0.167052i | \(-0.946575\pi\) | ||
0.985948 | − | 0.167052i | \(-0.0534247\pi\) | |||||||
\(278\) | 1.20631e12 | 0.726496 | ||||||||
\(279\) | −4.95160e11 | − | 2.04437e12i | −0.292903 | − | 1.20931i | ||||
\(280\) | 6.95778e11 | − | 1.25233e11i | 0.404278 | − | 0.0727660i | ||||
\(281\) | 2.40808e12i | 1.37448i | 0.726430 | + | 0.687240i | \(0.241178\pi\) | ||||
−0.726430 | + | 0.687240i | \(0.758822\pi\) | |||||||
\(282\) | −1.98500e11 | − | 1.56162e11i | −0.111305 | − | 0.0875647i | ||||
\(283\) | − | 1.25441e12i | − | 0.691045i | −0.938410 | − | 0.345523i | \(-0.887702\pi\) | ||
0.938410 | − | 0.345523i | \(-0.112298\pi\) | |||||||
\(284\) | − | 1.89067e12i | − | 1.02335i | ||||||
\(285\) | 4.96153e11 | − | 9.33561e11i | 0.263871 | − | 0.496499i | ||||
\(286\) | −2.13651e12 | −1.11654 | ||||||||
\(287\) | −1.08911e11 | −0.0559320 | ||||||||
\(288\) | 5.33025e11 | + | 2.20070e12i | 0.269021 | + | 1.11071i | ||||
\(289\) | 2.21037e12 | 1.09642 | ||||||||
\(290\) | −5.53470e12 | + | 9.96190e11i | −2.69839 | + | 0.485682i | ||||
\(291\) | 7.26396e11 | − | 9.23337e11i | 0.348103 | − | 0.442482i | ||||
\(292\) | − | 1.86843e12i | − | 0.880161i | ||||||
\(293\) | −1.00015e12 | −0.463156 | −0.231578 | − | 0.972816i | \(-0.574389\pi\) | ||||
−0.231578 | + | 0.972816i | \(0.574389\pi\) | |||||||
\(294\) | 2.09604e12 | + | 1.64897e12i | 0.954251 | + | 0.750716i | ||||
\(295\) | −1.17394e12 | + | 2.11298e11i | −0.525456 | + | 0.0945768i | ||||
\(296\) | 2.93560e12i | 1.29193i | ||||||||
\(297\) | −2.57595e12 | − | 1.17812e12i | −1.11469 | − | 0.509810i | ||||
\(298\) | 3.53941e12i | 1.50609i | ||||||||
\(299\) | 1.30491e12i | 0.546040i | ||||||||
\(300\) | 3.54176e12 | + | 1.13615e12i | 1.45751 | + | 0.467551i | ||||
\(301\) | 9.70456e11 | 0.392775 | ||||||||
\(302\) | 7.21321e12 | 2.87140 | ||||||||
\(303\) | 1.96870e12 | − | 2.50246e12i | 0.770844 | − | 0.979835i | ||||
\(304\) | −2.74044e11 | −0.105549 | ||||||||
\(305\) | −2.34844e11 | − | 1.30476e12i | −0.0889776 | − | 0.494348i | ||||
\(306\) | 1.45469e12 | + | 6.00599e12i | 0.542205 | + | 2.23860i | ||||
\(307\) | 3.95601e12i | 1.45066i | 0.688402 | + | 0.725329i | \(0.258312\pi\) | ||||
−0.688402 | + | 0.725329i | \(0.741688\pi\) | |||||||
\(308\) | 2.53045e12 | 0.912943 | ||||||||
\(309\) | −9.77708e10 | + | 1.24278e11i | −0.0347070 | + | 0.0441168i | ||||
\(310\) | 1.00385e12 | + | 5.57725e12i | 0.350639 | + | 1.94810i | ||||
\(311\) | − | 3.90857e12i | − | 1.34343i | −0.740808 | − | 0.671717i | \(-0.765557\pi\) | ||
0.740808 | − | 0.671717i | \(-0.234443\pi\) | |||||||
\(312\) | −8.83634e11 | + | 1.12321e12i | −0.298882 | + | 0.379915i | ||||
\(313\) | − | 1.23218e11i | − | 0.0410158i | −0.999790 | − | 0.0205079i | \(-0.993472\pi\) | ||
0.999790 | − | 0.0205079i | \(-0.00652833\pi\) | |||||||
\(314\) | − | 8.55650e11i | − | 0.280316i | ||||||
\(315\) | −6.09435e11 | − | 1.38056e12i | −0.196506 | − | 0.445145i | ||||
\(316\) | 5.92263e11 | 0.187966 | ||||||||
\(317\) | 1.24152e12 | 0.387845 | 0.193923 | − | 0.981017i | \(-0.437879\pi\) | ||||
0.193923 | + | 0.981017i | \(0.437879\pi\) | |||||||
\(318\) | −3.16158e12 | − | 2.48724e12i | −0.972229 | − | 0.764860i | ||||
\(319\) | −6.97852e12 | −2.11256 | ||||||||
\(320\) | −9.69034e11 | − | 5.38382e12i | −0.288795 | − | 1.60450i | ||||
\(321\) | −3.76334e12 | − | 2.96065e12i | −1.10420 | − | 0.868684i | ||||
\(322\) | − | 2.55522e12i | − | 0.738156i | ||||||
\(323\) | −2.86214e12 | −0.814100 | ||||||||
\(324\) | −4.85951e12 | + | 2.50072e12i | −1.36103 | + | 0.700389i | ||||
\(325\) | −7.23944e11 | − | 1.94592e12i | −0.199659 | − | 0.536670i | ||||
\(326\) | − | 4.74250e12i | − | 1.28801i | ||||||
\(327\) | −2.14785e12 | − | 1.68973e12i | −0.574468 | − | 0.451938i | ||||
\(328\) | − | 3.68391e11i | − | 0.0970375i | ||||||
\(329\) | − | 1.66975e11i | − | 0.0433183i | ||||||
\(330\) | 6.73855e12 | + | 3.58129e12i | 1.72186 | + | 0.915102i | ||||
\(331\) | 3.06363e12 | 0.771075 | 0.385537 | − | 0.922692i | \(-0.374016\pi\) | ||||
0.385537 | + | 0.922692i | \(0.374016\pi\) | |||||||
\(332\) | −2.50195e12 | −0.620282 | ||||||||
\(333\) | 6.09030e12 | − | 1.47511e12i | 1.48736 | − | 0.360250i | ||||
\(334\) | 2.28827e12 | 0.550523 | ||||||||
\(335\) | 5.03736e12 | − | 9.06674e11i | 1.19393 | − | 0.214895i | ||||
\(336\) | −2.41866e11 | + | 3.07441e11i | −0.0564778 | + | 0.0717902i | ||||
\(337\) | 7.32668e12i | 1.68561i | 0.538218 | + | 0.842806i | \(0.319098\pi\) | ||||
−0.538218 | + | 0.842806i | \(0.680902\pi\) | |||||||
\(338\) | −4.71682e12 | −1.06922 | ||||||||
\(339\) | 4.65347e11 | + | 3.66092e11i | 0.103939 | + | 0.0817695i | ||||
\(340\) | −1.78377e12 | − | 9.91040e12i | −0.392595 | − | 2.18121i | ||||
\(341\) | 7.03217e12i | 1.52517i | ||||||||
\(342\) | −9.85132e11 | − | 4.06732e12i | −0.210554 | − | 0.869316i | ||||
\(343\) | 4.07326e12i | 0.857969i | ||||||||
\(344\) | 3.28257e12i | 0.681432i | ||||||||
\(345\) | 2.18734e12 | − | 4.11570e12i | 0.447528 | − | 0.842069i | ||||
\(346\) | 6.14234e12 | 1.23866 | ||||||||
\(347\) | −1.63438e12 | −0.324868 | −0.162434 | − | 0.986719i | \(-0.551934\pi\) | ||||
−0.162434 | + | 0.986719i | \(0.551934\pi\) | |||||||
\(348\) | −8.32509e12 | + | 1.05822e13i | −1.63115 | + | 2.07338i | ||||
\(349\) | 1.29926e12 | 0.250940 | 0.125470 | − | 0.992097i | \(-0.459956\pi\) | ||||
0.125470 | + | 0.992097i | \(0.459956\pi\) | |||||||
\(350\) | 1.41759e12 | + | 3.81041e12i | 0.269905 | + | 0.725489i | ||||
\(351\) | 2.77426e12 | + | 1.26882e12i | 0.520729 | + | 0.238157i | ||||
\(352\) | − | 7.56992e12i | − | 1.40081i | ||||||
\(353\) | −4.44094e12 | −0.810217 | −0.405109 | − | 0.914269i | \(-0.632766\pi\) | ||||
−0.405109 | + | 0.914269i | \(0.632766\pi\) | |||||||
\(354\) | −2.91941e12 | + | 3.71093e12i | −0.525145 | + | 0.667523i | ||||
\(355\) | 3.70989e12 | − | 6.67743e11i | 0.657990 | − | 0.118432i | ||||
\(356\) | − | 1.38355e13i | − | 2.41960i | ||||||
\(357\) | −2.52606e12 | + | 3.21093e12i | −0.435615 | + | 0.553720i | ||||
\(358\) | − | 6.37772e12i | − | 1.08455i | ||||||
\(359\) | 9.25546e12i | 1.55212i | 0.630658 | + | 0.776061i | \(0.282785\pi\) | ||||
−0.630658 | + | 0.776061i | \(0.717215\pi\) | |||||||
\(360\) | 4.66975e12 | − | 2.06142e12i | 0.772291 | − | 0.340921i | ||||
\(361\) | −4.19280e12 | −0.683861 | ||||||||
\(362\) | 2.47370e12 | 0.397927 | ||||||||
\(363\) | 2.48894e12 | + | 1.95807e12i | 0.394895 | + | 0.310667i | ||||
\(364\) | −2.72525e12 | −0.426481 | ||||||||
\(365\) | 3.66625e12 | − | 6.59888e11i | 0.565923 | − | 0.101860i | ||||
\(366\) | −4.12447e12 | − | 3.24475e12i | −0.628004 | − | 0.494055i | ||||
\(367\) | − | 1.09566e13i | − | 1.64568i | −0.568272 | − | 0.822841i | \(-0.692388\pi\) | ||
0.568272 | − | 0.822841i | \(-0.307612\pi\) | |||||||
\(368\) | −1.20815e12 | −0.179012 | ||||||||
\(369\) | −7.64277e11 | + | 1.85113e11i | −0.111717 | + | 0.0270586i | ||||
\(370\) | −1.66150e13 | + | 2.99053e12i | −2.39602 | + | 0.431260i | ||||
\(371\) | − | 2.65946e12i | − | 0.378377i | ||||||
\(372\) | 1.06636e13 | + | 8.38910e12i | 1.49688 | + | 1.17761i | ||||
\(373\) | 8.00491e12i | 1.10869i | 0.832285 | + | 0.554347i | \(0.187032\pi\) | ||||
−0.832285 | + | 0.554347i | \(0.812968\pi\) | |||||||
\(374\) | − | 2.06592e13i | − | 2.82330i | ||||||
\(375\) | −9.78492e11 | + | 7.35093e12i | −0.131947 | + | 0.991257i | ||||
\(376\) | 5.64794e11 | 0.0751538 | ||||||||
\(377\) | 7.51575e12 | 0.986883 | ||||||||
\(378\) | −5.43244e12 | − | 2.48455e12i | −0.703940 | − | 0.321950i | ||||
\(379\) | 1.30200e13 | 1.66501 | 0.832504 | − | 0.554018i | \(-0.186906\pi\) | ||||
0.832504 | + | 0.554018i | \(0.186906\pi\) | |||||||
\(380\) | 1.20799e12 | + | 6.71143e12i | 0.152456 | + | 0.847027i | ||||
\(381\) | −2.37512e12 | + | 3.01906e12i | −0.295842 | + | 0.376052i | ||||
\(382\) | 7.87194e12i | 0.967755i | ||||||||
\(383\) | 2.49577e12 | 0.302838 | 0.151419 | − | 0.988470i | \(-0.451616\pi\) | ||||
0.151419 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(384\) | −9.51937e12 | − | 7.48896e12i | −1.14012 | − | 0.896944i | ||||
\(385\) | 8.93698e11 | + | 4.96527e12i | 0.105654 | + | 0.587001i | ||||
\(386\) | 2.15550e13i | 2.51543i | ||||||||
\(387\) | 6.81015e12 | − | 1.64947e12i | 0.784516 | − | 0.190015i | ||||
\(388\) | 7.57785e12i | 0.861763i | ||||||||
\(389\) | − | 3.35910e12i | − | 0.377116i | −0.982062 | − | 0.188558i | \(-0.939619\pi\) | ||
0.982062 | − | 0.188558i | \(-0.0603814\pi\) | |||||||
\(390\) | −7.25732e12 | − | 3.85699e12i | −0.804365 | − | 0.427490i | ||||
\(391\) | −1.26180e13 | −1.38072 | ||||||||
\(392\) | −5.96387e12 | −0.644314 | ||||||||
\(393\) | 1.53899e11 | − | 1.95624e11i | 0.0164162 | − | 0.0208669i | ||||
\(394\) | 2.80618e13 | 2.95553 | ||||||||
\(395\) | 2.09174e11 | + | 1.16214e12i | 0.0217532 | + | 0.120858i | ||||
\(396\) | 1.77573e13 | − | 4.30095e12i | 1.82349 | − | 0.441661i | ||||
\(397\) | 3.31190e12i | 0.335834i | 0.985801 | + | 0.167917i | \(0.0537040\pi\) | ||||
−0.985801 | + | 0.167917i | \(0.946296\pi\) | |||||||
\(398\) | 4.09237e12 | 0.409788 | ||||||||
\(399\) | 1.71068e12 | − | 2.17448e12i | 0.169162 | − | 0.215026i | ||||
\(400\) | 1.80163e12 | − | 6.70263e11i | 0.175940 | − | 0.0654554i | ||||
\(401\) | 1.07686e13i | 1.03857i | 0.854600 | + | 0.519287i | \(0.173803\pi\) | ||||
−0.854600 | + | 0.519287i | \(0.826197\pi\) | |||||||
\(402\) | 1.25271e13 | − | 1.59235e13i | 1.19322 | − | 1.51673i | ||||
\(403\) | − | 7.57354e12i | − | 0.712481i | ||||||
\(404\) | 2.05377e13i | 1.90830i | ||||||||
\(405\) | −6.62321e12 | − | 8.65219e12i | −0.607845 | − | 0.794055i | ||||
\(406\) | −1.47170e13 | −1.33410 | ||||||||
\(407\) | −2.09493e13 | −1.87584 | ||||||||
\(408\) | −1.08610e13 | − | 8.54443e12i | −0.960658 | − | 0.755757i | ||||
\(409\) | −4.75031e12 | −0.415055 | −0.207527 | − | 0.978229i | \(-0.566542\pi\) | ||||
−0.207527 | + | 0.978229i | \(0.566542\pi\) | |||||||
\(410\) | 2.08503e12 | − | 3.75284e11i | 0.179967 | − | 0.0323922i | ||||
\(411\) | 2.12868e12 | + | 1.67465e12i | 0.181511 | + | 0.142796i | ||||
\(412\) | − | 1.01996e12i | − | 0.0859203i | ||||||
\(413\) | −3.12156e12 | −0.259790 | ||||||||
\(414\) | −4.34305e12 | − | 1.79312e13i | −0.357103 | − | 1.47437i | ||||
\(415\) | −8.83635e11 | − | 4.90936e12i | −0.0717848 | − | 0.398827i | ||||
\(416\) | 8.15269e12i | 0.654387i | ||||||||
\(417\) | 4.52569e12 | + | 3.56039e12i | 0.358926 | + | 0.282369i | ||||
\(418\) | 1.39907e13i | 1.09637i | ||||||||
\(419\) | − | 1.48450e13i | − | 1.14950i | −0.818328 | − | 0.574751i | \(-0.805099\pi\) | ||
0.818328 | − | 0.574751i | \(-0.194901\pi\) | |||||||
\(420\) | 8.59546e12 | + | 4.56817e12i | 0.657693 | + | 0.349539i | ||||
\(421\) | −1.53608e13 | −1.16146 | −0.580728 | − | 0.814098i | \(-0.697232\pi\) | ||||
−0.580728 | + | 0.814098i | \(0.697232\pi\) | |||||||
\(422\) | −3.04752e13 | −2.27711 | ||||||||
\(423\) | −2.83804e11 | − | 1.17174e12i | −0.0209564 | − | 0.0865227i | ||||
\(424\) | 8.99565e12 | 0.656453 | ||||||||
\(425\) | 1.88163e13 | − | 7.00028e12i | 1.35703 | − | 0.504859i | ||||
\(426\) | 9.22594e12 | − | 1.17273e13i | 0.657601 | − | 0.835891i | ||||
\(427\) | − | 3.46942e12i | − | 0.244409i | ||||||
\(428\) | 3.08859e13 | 2.15051 | ||||||||
\(429\) | −8.01552e12 | − | 6.30587e12i | −0.551626 | − | 0.433969i | ||||
\(430\) | −1.85788e13 | + | 3.34400e12i | −1.26379 | + | 0.227470i | ||||
\(431\) | − | 1.84497e13i | − | 1.24052i | −0.784396 | − | 0.620260i | \(-0.787027\pi\) | ||
0.784396 | − | 0.620260i | \(-0.212973\pi\) | |||||||
\(432\) | −1.17474e12 | + | 2.56855e12i | −0.0780768 | + | 0.170714i | ||||
\(433\) | − | 2.31045e13i | − | 1.51795i | −0.651121 | − | 0.758974i | \(-0.725701\pi\) | ||
0.651121 | − | 0.758974i | \(-0.274299\pi\) | |||||||
\(434\) | 1.48302e13i | 0.963157i | ||||||||
\(435\) | −2.37047e13 | − | 1.25982e13i | −1.52191 | − | 0.808838i | ||||
\(436\) | 1.76275e13 | 1.11881 | ||||||||
\(437\) | 8.54505e12 | 0.536176 | ||||||||
\(438\) | 9.11740e12 | − | 1.15893e13i | 0.565588 | − | 0.718931i | ||||
\(439\) | 9.38712e12 | 0.575718 | 0.287859 | − | 0.957673i | \(-0.407057\pi\) | ||||
0.287859 | + | 0.957673i | \(0.407057\pi\) | |||||||
\(440\) | −1.67951e13 | + | 3.02294e12i | −1.01840 | + | 0.183302i | ||||
\(441\) | 2.99679e12 | + | 1.23729e13i | 0.179665 | + | 0.741783i | ||||
\(442\) | 2.22497e13i | 1.31890i | ||||||||
\(443\) | −2.03386e13 | −1.19207 | −0.596037 | − | 0.802957i | \(-0.703259\pi\) | ||||
−0.596037 | + | 0.802957i | \(0.703259\pi\) | |||||||
\(444\) | −2.49916e13 | + | 3.17674e13i | −1.44837 | + | 1.84105i | ||||
\(445\) | 2.71481e13 | − | 4.88638e12i | 1.55575 | − | 0.280019i | ||||
\(446\) | − | 3.31308e13i | − | 1.87740i | ||||||
\(447\) | −1.04465e13 | + | 1.32788e13i | −0.585375 | + | 0.744083i | ||||
\(448\) | − | 1.43158e13i | − | 0.793280i | ||||||
\(449\) | 4.51767e11i | 0.0247561i | 0.999923 | + | 0.0123781i | \(0.00394016\pi\) | ||||
−0.999923 | + | 0.0123781i | \(0.996060\pi\) | |||||||
\(450\) | 1.64244e13 | + | 2.43300e13i | 0.890076 | + | 1.31850i | ||||
\(451\) | 2.62894e12 | 0.140896 | ||||||||
\(452\) | −3.81911e12 | −0.202428 | ||||||||
\(453\) | 2.70617e13 | + | 2.12897e13i | 1.41862 | + | 1.11604i | ||||
\(454\) | −3.20212e13 | −1.66019 | ||||||||
\(455\) | −9.62499e11 | − | 5.34752e12i | −0.0493564 | − | 0.274218i | ||||
\(456\) | 7.35518e12 | + | 5.78638e12i | 0.373052 | + | 0.293483i | ||||
\(457\) | − | 2.05500e11i | − | 0.0103093i | −0.999987 | − | 0.00515466i | \(-0.998359\pi\) | ||
0.999987 | − | 0.00515466i | \(-0.00164079\pi\) | |||||||
\(458\) | 4.88604e13 | 2.42454 | ||||||||
\(459\) | −1.22690e13 | + | 2.68261e13i | −0.602208 | + | 1.31672i | ||||
\(460\) | 5.32554e12 | + | 2.95880e13i | 0.258568 | + | 1.43657i | ||||
\(461\) | 1.85609e13i | 0.891445i | 0.895171 | + | 0.445722i | \(0.147053\pi\) | ||||
−0.895171 | + | 0.445722i | \(0.852947\pi\) | |||||||
\(462\) | 1.56956e13 | + | 1.23479e13i | 0.745708 | + | 0.586654i | ||||
\(463\) | − | 2.09809e13i | − | 0.986095i | −0.870002 | − | 0.493048i | \(-0.835883\pi\) | ||
0.870002 | − | 0.493048i | \(-0.164117\pi\) | |||||||
\(464\) | 6.95846e12i | 0.323537i | ||||||||
\(465\) | −1.26950e13 | + | 2.38870e13i | −0.583941 | + | 1.09874i | ||||
\(466\) | −2.21371e12 | −0.100738 | ||||||||
\(467\) | 2.47202e13 | 1.11293 | 0.556464 | − | 0.830872i | \(-0.312158\pi\) | ||||
0.556464 | + | 0.830872i | \(0.312158\pi\) | |||||||
\(468\) | −1.91244e13 | + | 4.63206e12i | −0.851841 | + | 0.206322i | ||||
\(469\) | 1.33946e13 | 0.590289 | ||||||||
\(470\) | 5.75362e11 | + | 3.19664e12i | 0.0250872 | + | 0.139381i | ||||
\(471\) | 2.52544e12 | − | 3.21014e12i | 0.108951 | − | 0.138490i | ||||
\(472\) | − | 1.05587e13i | − | 0.450714i | ||||||
\(473\) | −2.34254e13 | −0.989421 | ||||||||
\(474\) | 3.67364e12 | + | 2.89008e12i | 0.153534 | + | 0.120786i | ||||
\(475\) | −1.27426e13 | + | 4.74066e12i | −0.526975 | + | 0.196052i | ||||
\(476\) | − | 2.63522e13i | − | 1.07841i | ||||||
\(477\) | −4.52024e12 | − | 1.86627e13i | −0.183050 | − | 0.755758i | ||||
\(478\) | − | 1.41378e13i | − | 0.566556i | ||||||
\(479\) | − | 1.00024e13i | − | 0.396666i | −0.980135 | − | 0.198333i | \(-0.936447\pi\) | ||
0.980135 | − | 0.198333i | \(-0.0635527\pi\) | |||||||
\(480\) | 1.36658e13 | − | 2.57137e13i | 0.536328 | − | 1.00915i | ||||
\(481\) | 2.25620e13 | 0.876300 | ||||||||
\(482\) | −9.21606e12 | −0.354250 | ||||||||
\(483\) | 7.54168e12 | − | 9.58639e12i | 0.286901 | − | 0.364686i | ||||
\(484\) | −2.04268e13 | −0.769085 | ||||||||
\(485\) | −1.48693e13 | + | 2.67633e12i | −0.554094 | + | 0.0997313i | ||||
\(486\) | −4.23449e13 | − | 8.20183e12i | −1.56178 | − | 0.302503i | ||||
\(487\) | − | 3.35486e13i | − | 1.22470i | −0.790587 | − | 0.612350i | \(-0.790224\pi\) | ||
0.790587 | − | 0.612350i | \(-0.209776\pi\) | |||||||
\(488\) | 1.17354e13 | 0.424031 | ||||||||
\(489\) | 1.39974e13 | − | 1.77924e13i | 0.500615 | − | 0.636342i | ||||
\(490\) | −6.07546e12 | − | 3.37544e13i | −0.215079 | − | 1.19495i | ||||
\(491\) | − | 9.86200e12i | − | 0.345587i | −0.984958 | − | 0.172793i | \(-0.944721\pi\) | ||
0.984958 | − | 0.172793i | \(-0.0552793\pi\) | |||||||
\(492\) | 3.13622e12 | − | 3.98652e12i | 0.108788 | − | 0.138283i | ||||
\(493\) | 7.26746e13i | 2.49545i | ||||||||
\(494\) | − | 1.50677e13i | − | 0.512168i | ||||||
\(495\) | 1.47109e13 | + | 3.33247e13i | 0.495008 | + | 1.12135i | ||||
\(496\) | 7.01196e12 | 0.233578 | ||||||||
\(497\) | 9.86477e12 | 0.325316 | ||||||||
\(498\) | −1.55189e13 | − | 1.22088e13i | −0.506657 | − | 0.398591i | ||||
\(499\) | −3.23855e13 | −1.04676 | −0.523381 | − | 0.852099i | \(-0.675330\pi\) | ||||
−0.523381 | + | 0.852099i | \(0.675330\pi\) | |||||||
\(500\) | −2.43565e13 | − | 4.11679e13i | −0.779409 | − | 1.31737i | ||||
\(501\) | 8.58491e12 | + | 6.75381e12i | 0.271986 | + | 0.213974i | ||||
\(502\) | 2.84913e13i | 0.893705i | ||||||||
\(503\) | −6.38005e12 | −0.198145 | −0.0990727 | − | 0.995080i | \(-0.531588\pi\) | ||||
−0.0990727 | + | 0.995080i | \(0.531588\pi\) | |||||||
\(504\) | 1.29831e13 | − | 3.14459e12i | 0.399231 | − | 0.0966965i | ||||
\(505\) | −4.02993e13 | + | 7.25348e12i | −1.22699 | + | 0.220846i | ||||
\(506\) | 6.16792e13i | 1.85946i | ||||||||
\(507\) | −1.76961e13 | − | 1.39216e13i | −0.528247 | − | 0.415576i | ||||
\(508\) | − | 2.47775e13i | − | 0.732386i | ||||||
\(509\) | − | 6.47112e12i | − | 0.189404i | −0.995506 | − | 0.0947022i | \(-0.969810\pi\) | ||
0.995506 | − | 0.0947022i | \(-0.0301899\pi\) | |||||||
\(510\) | 3.72957e13 | − | 7.01757e13i | 1.08096 | − | 2.03393i | ||||
\(511\) | 9.74872e12 | 0.279797 | ||||||||
\(512\) | −1.31239e13 | −0.373005 | ||||||||
\(513\) | 8.30871e12 | − | 1.81669e13i | 0.233855 | − | 0.511323i | ||||
\(514\) | 8.82262e13 | 2.45913 | ||||||||
\(515\) | 2.00137e12 | − | 3.60227e11i | 0.0552448 | − | 0.00994351i | ||||
\(516\) | −2.79456e13 | + | 3.55222e13i | −0.763949 | + | 0.971072i | ||||
\(517\) | 4.03053e12i | 0.109121i | ||||||||
\(518\) | −4.41800e13 | −1.18461 | ||||||||
\(519\) | 2.30442e13 | + | 1.81290e13i | 0.611962 | + | 0.481435i | ||||
\(520\) | 1.80880e13 | − | 3.25566e12i | 0.475745 | − | 0.0856293i | ||||
\(521\) | − | 1.32724e13i | − | 0.345748i | −0.984944 | − | 0.172874i | \(-0.944695\pi\) | ||
0.984944 | − | 0.172874i | \(-0.0553054\pi\) | |||||||
\(522\) | −1.03276e14 | + | 2.50142e13i | −2.66470 | + | 0.645408i | ||||
\(523\) | − | 5.67492e12i | − | 0.145028i | −0.997367 | − | 0.0725139i | \(-0.976898\pi\) | ||
0.997367 | − | 0.0725139i | \(-0.0231022\pi\) | |||||||
\(524\) | 1.60549e12i | 0.0406398i | ||||||||
\(525\) | −5.92798e12 | + | 1.84795e13i | −0.148631 | + | 0.463333i | ||||
\(526\) | 1.64192e13 | 0.407778 | ||||||||
\(527\) | 7.32334e13 | 1.80159 | ||||||||
\(528\) | 5.83829e12 | − | 7.42117e12i | 0.142271 | − | 0.180843i | ||||
\(529\) | −3.75481e12 | −0.0906379 | ||||||||
\(530\) | 9.16398e12 | + | 5.09138e13i | 0.219131 | + | 1.21746i | ||||
\(531\) | −2.19055e13 | + | 5.30566e12i | −0.518896 | + | 0.125680i | ||||
\(532\) | 1.78460e13i | 0.418777i | ||||||||
\(533\) | −2.83133e12 | −0.0658195 | ||||||||
\(534\) | 6.75131e13 | − | 8.58173e13i | 1.55483 | − | 1.97637i | ||||
\(535\) | 1.09082e13 | + | 6.06046e13i | 0.248877 | + | 1.38273i | ||||
\(536\) | 4.53072e13i | 1.02410i | ||||||||
\(537\) | 1.88238e13 | − | 2.39273e13i | 0.421536 | − | 0.535823i | ||||
\(538\) | 2.90483e13i | 0.644479i | ||||||||
\(539\) | − | 4.25598e13i | − | 0.935527i | ||||||
\(540\) | 6.80829e13 | + | 1.74475e13i | 1.48275 | + | 0.379982i | ||||
\(541\) | −4.08953e13 | −0.882444 | −0.441222 | − | 0.897398i | \(-0.645455\pi\) | ||||
−0.441222 | + | 0.897398i | \(0.645455\pi\) | |||||||
\(542\) | 9.05086e12 | 0.193506 | ||||||||
\(543\) | 9.28056e12 | + | 7.30109e12i | 0.196596 | + | 0.154664i | ||||
\(544\) | −7.88336e13 | −1.65469 | ||||||||
\(545\) | 6.22565e12 | + | 3.45889e13i | 0.129480 | + | 0.719372i | ||||
\(546\) | −1.69039e13 | − | 1.32985e13i | −0.348357 | − | 0.274055i | ||||
\(547\) | 6.40347e13i | 1.30761i | 0.756663 | + | 0.653806i | \(0.226829\pi\) | ||||
−0.756663 | + | 0.653806i | \(0.773171\pi\) | |||||||
\(548\) | −1.74702e13 | −0.353504 | ||||||||
\(549\) | −5.89691e12 | − | 2.43466e13i | −0.118240 | − | 0.488176i | ||||
\(550\) | −3.42187e13 | − | 9.19776e13i | −0.679907 | − | 1.82755i | ||||
\(551\) | − | 4.92160e13i | − | 0.969055i | ||||||
\(552\) | 3.24261e13 | + | 2.55098e13i | 0.632701 | + | 0.497751i | ||||
\(553\) | 3.09020e12i | 0.0597531i | ||||||||
\(554\) | 2.77362e13i | 0.531494i | ||||||||
\(555\) | −7.11608e13 | − | 3.78193e13i | −1.35138 | − | 0.718205i | ||||
\(556\) | −3.71425e13 | −0.699032 | ||||||||
\(557\) | 4.26311e13 | 0.795152 | 0.397576 | − | 0.917569i | \(-0.369851\pi\) | ||||
0.397576 | + | 0.917569i | \(0.369851\pi\) | |||||||
\(558\) | 2.52065e13 | + | 1.04070e14i | 0.465953 | + | 1.92378i | ||||
\(559\) | 2.52288e13 | 0.462208 | ||||||||
\(560\) | 4.95100e12 | − | 8.91130e11i | 0.0898986 | − | 0.0161808i | ||||
\(561\) | 6.09755e13 | − | 7.75072e13i | 1.09734 | − | 1.39485i | ||||
\(562\) | − | 1.22585e14i | − | 2.18653i | ||||||
\(563\) | −4.95070e13 | −0.875235 | −0.437617 | − | 0.899161i | \(-0.644178\pi\) | ||||
−0.437617 | + | 0.899161i | \(0.644178\pi\) | |||||||
\(564\) | 6.11188e12 | + | 4.80826e12i | 0.107098 | + | 0.0842544i | ||||
\(565\) | −1.34883e12 | − | 7.49391e12i | −0.0234269 | − | 0.130157i | ||||
\(566\) | 6.38567e13i | 1.09932i | ||||||||
\(567\) | −1.30478e13 | − | 2.53550e13i | −0.222649 | − | 0.432662i | ||||
\(568\) | 3.33677e13i | 0.564396i | ||||||||
\(569\) | 8.12271e13i | 1.36188i | 0.732338 | + | 0.680941i | \(0.238429\pi\) | ||||
−0.732338 | + | 0.680941i | \(0.761571\pi\) | |||||||
\(570\) | −2.52571e13 | + | 4.75237e13i | −0.419767 | + | 0.789834i | ||||
\(571\) | 5.43146e13 | 0.894821 | 0.447411 | − | 0.894329i | \(-0.352346\pi\) | ||||
0.447411 | + | 0.894329i | \(0.352346\pi\) | |||||||
\(572\) | 6.57836e13 | 1.07433 | ||||||||
\(573\) | −2.32339e13 | + | 2.95331e13i | −0.376140 | + | 0.478119i | ||||
\(574\) | 5.54418e12 | 0.0889771 | ||||||||
\(575\) | −5.61770e13 | + | 2.08997e13i | −0.893757 | + | 0.332507i | ||||
\(576\) | −2.43323e13 | − | 1.00461e14i | −0.383770 | − | 1.58447i | ||||
\(577\) | − | 9.61550e13i | − | 1.50346i | −0.659469 | − | 0.751731i | \(-0.729219\pi\) | ||
0.659469 | − | 0.751731i | \(-0.270781\pi\) | |||||||
\(578\) | −1.12521e14 | −1.74419 | ||||||||
\(579\) | −6.36193e13 | + | 8.08679e13i | −0.977679 | + | 1.24275i | ||||
\(580\) | 1.70415e14 | − | 3.06730e13i | 2.59638 | − | 0.467322i | ||||
\(581\) | − | 1.30542e13i | − | 0.197183i | ||||||
\(582\) | −3.69778e13 | + | 4.70032e13i | −0.553766 | + | 0.703903i | ||||
\(583\) | 6.41955e13i | 0.953152i | ||||||||
\(584\) | 3.29751e13i | 0.485425i | ||||||||
\(585\) | −1.58434e13 | − | 3.58901e13i | −0.231243 | − | 0.523837i | ||||
\(586\) | 5.09135e13 | 0.736792 | ||||||||
\(587\) | 6.14398e13 | 0.881575 | 0.440787 | − | 0.897612i | \(-0.354699\pi\) | ||||
0.440787 | + | 0.897612i | \(0.354699\pi\) | |||||||
\(588\) | −6.45376e13 | − | 5.07722e13i | −0.918177 | − | 0.722336i | ||||
\(589\) | −4.95944e13 | −0.699610 | ||||||||
\(590\) | 5.97605e13 | − | 1.07563e13i | 0.835900 | − | 0.150454i | ||||
\(591\) | 1.05279e14 | + | 8.28241e13i | 1.46018 | + | 1.14873i | ||||
\(592\) | 2.08891e13i | 0.287283i | ||||||||
\(593\) | −4.15267e13 | −0.566310 | −0.283155 | − | 0.959074i | \(-0.591381\pi\) | ||||
−0.283155 | + | 0.959074i | \(0.591381\pi\) | |||||||
\(594\) | 1.31131e14 | + | 5.99733e13i | 1.77326 | + | 0.811009i | ||||
\(595\) | 5.17086e13 | − | 9.30702e12i | 0.693390 | − | 0.124803i | ||||
\(596\) | − | 1.08980e14i | − | 1.44915i | ||||||
\(597\) | 1.53533e13 | + | 1.20786e13i | 0.202456 | + | 0.159274i | ||||
\(598\) | − | 6.64275e13i | − | 0.868645i | ||||||
\(599\) | − | 3.38848e12i | − | 0.0439410i | −0.999759 | − | 0.0219705i | \(-0.993006\pi\) | ||
0.999759 | − | 0.0219705i | \(-0.00699399\pi\) | |||||||
\(600\) | −6.25070e13 | − | 2.00514e13i | −0.803845 | − | 0.257863i | ||||
\(601\) | −2.41599e13 | −0.308123 | −0.154061 | − | 0.988061i | \(-0.549235\pi\) | ||||
−0.154061 | + | 0.988061i | \(0.549235\pi\) | |||||||
\(602\) | −4.94019e13 | −0.624829 | ||||||||
\(603\) | 9.39961e13 | − | 2.27665e13i | 1.17903 | − | 0.285568i | ||||
\(604\) | −2.22097e14 | −2.76285 | ||||||||
\(605\) | −7.21431e12 | − | 4.00817e13i | −0.0890057 | − | 0.494504i | ||||
\(606\) | −1.00218e14 | + | 1.27390e14i | −1.22626 | + | 1.55873i | ||||
\(607\) | 7.14259e12i | 0.0866787i | 0.999060 | + | 0.0433394i | \(0.0137997\pi\) | ||||
−0.999060 | + | 0.0433394i | \(0.986200\pi\) | |||||||
\(608\) | 5.33869e13 | 0.642565 | ||||||||
\(609\) | −5.52137e13 | − | 4.34370e13i | −0.659114 | − | 0.518530i | ||||
\(610\) | 1.19549e13 | + | 6.64201e13i | 0.141546 | + | 0.786412i | ||||
\(611\) | − | 4.34082e12i | − | 0.0509760i | ||||||
\(612\) | −4.47903e13 | − | 1.84926e14i | −0.521708 | − | 2.15398i | ||||
\(613\) | − | 8.67406e13i | − | 1.00212i | −0.865412 | − | 0.501060i | \(-0.832944\pi\) | ||
0.865412 | − | 0.501060i | \(-0.167056\pi\) | |||||||
\(614\) | − | 2.01384e14i | − | 2.30772i | ||||||
\(615\) | 8.93003e12 | + | 4.74598e12i | 0.101503 | + | 0.0539449i | ||||
\(616\) | −4.46588e13 | −0.503505 | ||||||||
\(617\) | −1.30072e14 | −1.45465 | −0.727325 | − | 0.686293i | \(-0.759237\pi\) | ||||
−0.727325 | + | 0.686293i | \(0.759237\pi\) | |||||||
\(618\) | 4.97710e12 | − | 6.32650e12i | 0.0552121 | − | 0.0701813i | ||||
\(619\) | −1.19936e12 | −0.0131977 | −0.00659885 | − | 0.999978i | \(-0.502100\pi\) | ||||
−0.00659885 | + | 0.999978i | \(0.502100\pi\) | |||||||
\(620\) | −3.09088e13 | − | 1.71725e14i | −0.337383 | − | 1.87446i | ||||
\(621\) | 3.66298e13 | − | 8.00907e13i | 0.396622 | − | 0.867210i | ||||
\(622\) | 1.98969e14i | 2.13714i | ||||||||
\(623\) | 7.21879e13 | 0.769173 | ||||||||
\(624\) | −6.28775e12 | + | 7.99248e12i | −0.0664618 | + | 0.0844810i | ||||
\(625\) | 7.21778e13 | − | 6.23323e13i | 0.756839 | − | 0.653601i | ||||
\(626\) | 6.27250e12i | 0.0652483i | ||||||||
\(627\) | −4.12932e13 | + | 5.24887e13i | −0.426129 | + | 0.541661i | ||||
\(628\) | 2.63457e13i | 0.269719i | ||||||||
\(629\) | 2.18167e14i | 2.21582i | ||||||||
\(630\) | 3.10238e13 | + | 7.02785e13i | 0.312603 | + | 0.708141i | ||||
\(631\) | −8.90644e13 | −0.890343 | −0.445172 | − | 0.895445i | \(-0.646857\pi\) | ||||
−0.445172 | + | 0.895445i | \(0.646857\pi\) | |||||||
\(632\) | −1.04526e13 | −0.103667 | ||||||||
\(633\) | −1.14334e14 | − | 8.99470e13i | −1.12501 | − | 0.885051i | ||||
\(634\) | −6.32007e13 | −0.616987 | ||||||||
\(635\) | 4.86188e13 | − | 8.75089e12i | 0.470907 | − | 0.0847585i | ||||
\(636\) | 9.73459e13 | + | 7.65827e13i | 0.935475 | + | 0.735945i | ||||
\(637\) | 4.58363e13i | 0.437031i | ||||||||
\(638\) | 3.55247e14 | 3.36068 | ||||||||
\(639\) | 6.92258e13 | − | 1.67670e13i | 0.649776 | − | 0.157380i | ||||
\(640\) | 2.75923e13 | + | 1.53299e14i | 0.256973 | + | 1.42771i | ||||
\(641\) | 3.65233e13i | 0.337505i | 0.985658 | + | 0.168752i | \(0.0539738\pi\) | ||||
−0.985658 | + | 0.168752i | \(0.946026\pi\) | |||||||
\(642\) | 1.91576e14 | + | 1.50714e14i | 1.75657 | + | 1.38191i | ||||
\(643\) | 5.65540e13i | 0.514527i | 0.966341 | + | 0.257263i | \(0.0828208\pi\) | ||||
−0.966341 | + | 0.257263i | \(0.917179\pi\) | |||||||
\(644\) | 7.86758e13i | 0.710251i | ||||||||
\(645\) | −7.95718e13 | − | 4.22894e13i | −0.712788 | − | 0.378820i | ||||
\(646\) | 1.45699e14 | 1.29508 | ||||||||
\(647\) | −1.04260e14 | −0.919594 | −0.459797 | − | 0.888024i | \(-0.652078\pi\) | ||||
−0.459797 | + | 0.888024i | \(0.652078\pi\) | |||||||
\(648\) | 8.57636e13 | − | 4.41341e13i | 0.750633 | − | 0.386278i | ||||
\(649\) | 7.53500e13 | 0.654425 | ||||||||
\(650\) | 3.68530e13 | + | 9.90585e13i | 0.317618 | + | 0.853738i | ||||
\(651\) | −4.37710e13 | + | 5.56382e13i | −0.374353 | + | 0.475848i | ||||
\(652\) | 1.46023e14i | 1.23932i | ||||||||
\(653\) | −7.77253e13 | −0.654631 | −0.327315 | − | 0.944915i | \(-0.606144\pi\) | ||||
−0.327315 | + | 0.944915i | \(0.606144\pi\) | |||||||
\(654\) | 1.09338e14 | + | 8.60172e13i | 0.913868 | + | 0.718947i | ||||
\(655\) | −3.15031e12 | + | 5.67024e11i | −0.0261304 | + | 0.00470321i | ||||
\(656\) | − | 2.62139e12i | − | 0.0215780i | ||||||
\(657\) | 6.84114e13 | − | 1.65697e13i | 0.558858 | − | 0.135359i | ||||
\(658\) | 8.50000e12i | 0.0689111i | ||||||||
\(659\) | − | 1.33902e14i | − | 1.07736i | −0.842510 | − | 0.538680i | \(-0.818923\pi\) | ||
0.842510 | − | 0.538680i | \(-0.181077\pi\) | |||||||
\(660\) | −2.07482e14 | − | 1.10269e14i | −1.65676 | − | 0.880508i | ||||
\(661\) | 6.42011e13 | 0.508786 | 0.254393 | − | 0.967101i | \(-0.418124\pi\) | ||||
0.254393 | + | 0.967101i | \(0.418124\pi\) | |||||||
\(662\) | −1.55957e14 | −1.22663 | ||||||||
\(663\) | −6.56696e13 | + | 8.34740e13i | −0.512622 | + | 0.651604i | ||||
\(664\) | 4.41560e13 | 0.342097 | ||||||||
\(665\) | −3.50176e13 | + | 6.30281e12i | −0.269264 | + | 0.0484648i | ||||
\(666\) | −3.10032e14 | + | 7.50918e13i | −2.36611 | + | 0.573088i | ||||
\(667\) | − | 2.16974e14i | − | 1.64353i | ||||||
\(668\) | −7.04566e13 | −0.529711 | ||||||||
\(669\) | 9.77850e13 | − | 1.24297e14i | 0.729695 | − | 0.927531i | ||||
\(670\) | −2.56431e14 | + | 4.61550e13i | −1.89931 | + | 0.341857i | ||||
\(671\) | 8.37468e13i | 0.615681i | ||||||||
\(672\) | 4.71182e13 | − | 5.98929e13i | 0.343829 | − | 0.437048i | ||||
\(673\) | − | 1.45739e14i | − | 1.05560i | −0.849368 | − | 0.527802i | \(-0.823016\pi\) | ||
0.849368 | − | 0.527802i | \(-0.176984\pi\) | |||||||
\(674\) | − | 3.72971e14i | − | 2.68148i | ||||||
\(675\) | −1.01902e13 | + | 1.39755e14i | −0.0727217 | + | 0.997352i | ||||
\(676\) | 1.45232e14 | 1.02880 | ||||||||
\(677\) | 8.91145e13 | 0.626621 | 0.313311 | − | 0.949651i | \(-0.398562\pi\) | ||||
0.313311 | + | 0.949651i | \(0.398562\pi\) | |||||||
\(678\) | −2.36889e13 | − | 1.86362e13i | −0.165347 | − | 0.130080i | ||||
\(679\) | −3.95382e13 | −0.273948 | ||||||||
\(680\) | 3.14811e13 | + | 1.74905e14i | 0.216524 | + | 1.20298i | ||||
\(681\) | −1.20134e14 | − | 9.45101e13i | −0.820218 | − | 0.645272i | ||||
\(682\) | − | 3.57978e14i | − | 2.42625i | ||||||
\(683\) | 2.86475e14 | 1.92745 | 0.963726 | − | 0.266894i | \(-0.0859975\pi\) | ||||
0.963726 | + | 0.266894i | \(0.0859975\pi\) | |||||||
\(684\) | 3.03325e13 | + | 1.25234e14i | 0.202594 | + | 0.836452i | ||||
\(685\) | −6.17009e12 | − | 3.42802e13i | −0.0409108 | − | 0.227295i | ||||
\(686\) | − | 2.07353e14i | − | 1.36486i | ||||||
\(687\) | 1.83309e14 | + | 1.44211e14i | 1.19785 | + | 0.942354i | ||||
\(688\) | 2.33581e13i | 0.151529i | ||||||||
\(689\) | − | 6.91376e13i | − | 0.445265i | ||||||
\(690\) | −1.11348e14 | + | 2.09513e14i | −0.711931 | + | 1.33957i | ||||
\(691\) | −2.46521e14 | −1.56482 | −0.782408 | − | 0.622767i | \(-0.786009\pi\) | ||||
−0.782408 | + | 0.622767i | \(0.786009\pi\) | |||||||
\(692\) | −1.89124e14 | −1.19184 | ||||||||
\(693\) | 2.24407e13 | + | 9.26508e13i | 0.140401 | + | 0.579673i | ||||
\(694\) | 8.31997e13 | 0.516802 | ||||||||
\(695\) | −1.31179e13 | − | 7.28813e13i | −0.0808985 | − | 0.449461i | ||||
\(696\) | 1.46926e14 | − | 1.86761e14i | 0.899607 | − | 1.14351i | ||||
\(697\) | − | 2.73779e13i | − | 0.166432i | ||||||
\(698\) | −6.61400e13 | −0.399197 | ||||||||
\(699\) | −8.30517e12 | − | 6.53374e12i | −0.0497694 | − | 0.0391540i | ||||
\(700\) | −4.36481e13 | − | 1.17323e14i | −0.259702 | − | 0.698063i | ||||
\(701\) | 3.94207e13i | 0.232881i | 0.993198 | + | 0.116441i | \(0.0371485\pi\) | ||||
−0.993198 | + | 0.116441i | \(0.962852\pi\) | |||||||
\(702\) | −1.41226e14 | − | 6.45903e13i | −0.828380 | − | 0.378863i | ||||
\(703\) | − | 1.47745e14i | − | 0.860470i | ||||||
\(704\) | 3.45563e14i | 1.99832i | ||||||||
\(705\) | −7.27624e12 | + | 1.36910e13i | −0.0417793 | + | 0.0786120i | ||||
\(706\) | 2.26070e14 | 1.28890 | ||||||||
\(707\) | −1.07158e14 | −0.606634 | ||||||||
\(708\) | 8.98896e13 | − | 1.14260e14i | 0.505293 | − | 0.642288i | ||||
\(709\) | 9.14117e13 | 0.510236 | 0.255118 | − | 0.966910i | \(-0.417886\pi\) | ||||
0.255118 | + | 0.966910i | \(0.417886\pi\) | |||||||
\(710\) | −1.88855e14 | + | 3.39920e13i | −1.04674 | + | 0.188402i | ||||
\(711\) | 5.25235e12 | + | 2.16854e13i | 0.0289072 | + | 0.119349i | ||||
\(712\) | 2.44176e14i | 1.33445i | ||||||||
\(713\) | −2.18642e14 | −1.18655 | ||||||||
\(714\) | 1.28591e14 | − | 1.63455e14i | 0.692980 | − | 0.880861i | ||||
\(715\) | 2.32333e13 | + | 1.29081e14i | 0.124332 | + | 0.690769i | ||||
\(716\) | 1.96372e14i | 1.04355i | ||||||||
\(717\) | 4.17276e13 | − | 5.30408e13i | 0.220205 | − | 0.279907i | ||||
\(718\) | − | 4.71157e14i | − | 2.46913i | ||||||
\(719\) | − | 1.72327e14i | − | 0.896829i | −0.893826 | − | 0.448415i | \(-0.851989\pi\) | ||
0.893826 | − | 0.448415i | \(-0.148011\pi\) | |||||||
\(720\) | 3.32289e13 | − | 1.46686e13i | 0.171733 | − | 0.0758100i | ||||
\(721\) | 5.32174e12 | 0.0273135 | ||||||||
\(722\) | 2.13438e14 | 1.08789 | ||||||||
\(723\) | −3.45759e13 | − | 2.72011e13i | −0.175018 | − | 0.137688i | ||||
\(724\) | −7.61659e13 | −0.382884 | ||||||||
\(725\) | 1.20374e14 | + | 3.23557e14i | 0.600954 | + | 1.61533i | ||||
\(726\) | −1.26702e14 | − | 9.96772e13i | −0.628202 | − | 0.494211i | ||||
\(727\) | 2.82412e14i | 1.39063i | 0.718705 | + | 0.695315i | \(0.244735\pi\) | ||||
−0.718705 | + | 0.695315i | \(0.755265\pi\) | |||||||
\(728\) | 4.80969e13 | 0.235212 | ||||||||
\(729\) | −1.34658e14 | − | 1.55751e14i | −0.654024 | − | 0.756474i | ||||
\(730\) | −1.86633e14 | + | 3.35921e13i | −0.900275 | + | 0.162040i | ||||
\(731\) | 2.43953e14i | 1.16875i | ||||||||
\(732\) | 1.26993e14 | + | 9.99067e13i | 0.604263 | + | 0.475378i | ||||
\(733\) | 3.17769e14i | 1.50173i | 0.660455 | + | 0.750866i | \(0.270364\pi\) | ||||
−0.660455 | + | 0.750866i | \(0.729636\pi\) | |||||||
\(734\) | 5.57755e14i | 2.61796i | ||||||||
\(735\) | 7.68325e13 | − | 1.44568e14i | 0.358186 | − | 0.673962i | ||||
\(736\) | 2.35362e14 | 1.08980 | ||||||||
\(737\) | −3.23325e14 | −1.48697 | ||||||||
\(738\) | 3.89062e13 | − | 9.42334e12i | 0.177720 | − | 0.0430450i | ||||
\(739\) | 1.19381e14 | 0.541643 | 0.270822 | − | 0.962630i | \(-0.412705\pi\) | ||||
0.270822 | + | 0.962630i | \(0.412705\pi\) | |||||||
\(740\) | 5.11580e14 | − | 9.20792e13i | 2.30544 | − | 0.414957i | ||||
\(741\) | 4.44722e13 | − | 5.65295e13i | 0.199066 | − | 0.253037i | ||||
\(742\) | 1.35382e14i | 0.601924i | ||||||||
\(743\) | 4.04198e14 | 1.78505 | 0.892525 | − | 0.450997i | \(-0.148932\pi\) | ||||
0.892525 | + | 0.450997i | \(0.148932\pi\) | |||||||
\(744\) | −1.88197e14 | − | 1.48056e14i | −0.825558 | − | 0.649472i | ||||
\(745\) | 2.13841e14 | − | 3.84892e13i | 0.931771 | − | 0.167709i | ||||
\(746\) | − | 4.07496e14i | − | 1.76372i | ||||||
\(747\) | −2.21880e13 | − | 9.16076e13i | −0.0953926 | − | 0.393848i | ||||
\(748\) | 6.36104e14i | 2.71656i | ||||||||
\(749\) | 1.61150e14i | 0.683632i | ||||||||
\(750\) | 4.98110e13 | − | 3.74205e14i | 0.209903 | − | 1.57690i | ||||
\(751\) | −3.96757e14 | −1.66083 | −0.830415 | − | 0.557145i | \(-0.811897\pi\) | ||||
−0.830415 | + | 0.557145i | \(0.811897\pi\) | |||||||
\(752\) | 4.01895e12 | 0.0167118 | ||||||||
\(753\) | −8.40917e13 | + | 1.06891e14i | −0.347359 | + | 0.441535i | ||||
\(754\) | −3.82596e14 | −1.56994 | ||||||||
\(755\) | −7.84397e13 | − | 4.35800e14i | −0.319743 | − | 1.77645i | ||||
\(756\) | 1.67266e14 | + | 7.64998e13i | 0.677329 | + | 0.309779i | ||||
\(757\) | 1.22108e14i | 0.491208i | 0.969370 | + | 0.245604i | \(0.0789863\pi\) | ||||
−0.969370 | + | 0.245604i | \(0.921014\pi\) | |||||||
\(758\) | −6.62797e14 | −2.64871 | ||||||||
\(759\) | −1.82045e14 | + | 2.31402e14i | −0.722721 | + | 0.918665i | ||||
\(760\) | −2.13193e13 | − | 1.18447e14i | −0.0840825 | − | 0.467151i | ||||
\(761\) | 2.36730e14i | 0.927536i | 0.885957 | + | 0.463768i | \(0.153503\pi\) | ||||
−0.885957 | + | 0.463768i | \(0.846497\pi\) | |||||||
\(762\) | 1.20907e14 | − | 1.53688e14i | 0.470628 | − | 0.598226i | ||||
\(763\) | 9.19733e13i | 0.355663i | ||||||||
\(764\) | − | 2.42379e14i | − | 0.931170i | ||||||
\(765\) | 3.47045e14 | − | 1.53200e14i | 1.32458 | − | 0.584724i | ||||
\(766\) | −1.27049e14 | −0.481758 | ||||||||
\(767\) | −8.11508e13 | −0.305714 | ||||||||
\(768\) | 1.42251e14 | + | 1.11910e14i | 0.532412 | + | 0.418852i | ||||
\(769\) | 2.25082e14 | 0.836968 | 0.418484 | − | 0.908224i | \(-0.362562\pi\) | ||||
0.418484 | + | 0.908224i | \(0.362562\pi\) | |||||||
\(770\) | −4.54945e13 | − | 2.52761e14i | −0.168076 | − | 0.933806i | ||||
\(771\) | 3.30998e14 | + | 2.60398e14i | 1.21494 | + | 0.955799i | ||||
\(772\) | − | 6.63685e14i | − | 2.42034i | ||||||
\(773\) | 5.14382e14 | 1.86375 | 0.931877 | − | 0.362776i | \(-0.118171\pi\) | ||||
0.931877 | + | 0.362776i | \(0.118171\pi\) | |||||||
\(774\) | −3.46677e14 | + | 8.39674e13i | −1.24801 | + | 0.302278i | ||||
\(775\) | 3.26044e14 | − | 1.21299e14i | 1.16619 | − | 0.433859i | ||||
\(776\) | − | 1.33738e14i | − | 0.475278i | ||||||
\(777\) | −1.65750e14 | − | 1.30396e14i | −0.585258 | − | 0.460427i | ||||
\(778\) | 1.70998e14i | 0.599919i | ||||||||
\(779\) | 1.85406e13i | 0.0646305i | ||||||||
\(780\) | 2.23455e14 | + | 1.18758e14i | 0.773957 | + | 0.411329i | ||||
\(781\) | −2.38121e14 | −0.819489 | ||||||||
\(782\) | 6.42331e14 | 2.19647 | ||||||||
\(783\) | −4.61290e14 | − | 2.10973e14i | −1.56735 | − | 0.716832i | ||||
\(784\) | −4.24375e13 | −0.143275 | ||||||||
\(785\) | −5.16958e13 | + | 9.30472e12i | −0.173423 | + | 0.0312144i | ||||
\(786\) | −7.83434e12 | + | 9.95839e12i | −0.0261150 | + | 0.0331953i | ||||
\(787\) | 4.58515e14i | 1.51873i | 0.650666 | + | 0.759364i | \(0.274490\pi\) | ||||
−0.650666 | + | 0.759364i | \(0.725510\pi\) | |||||||
\(788\) | −8.64032e14 | −2.84380 | ||||||||
\(789\) | 6.15999e13 | + | 4.84611e13i | 0.201463 | + | 0.158492i | ||||
\(790\) | −1.06482e13 | − | 5.91600e13i | −0.0346051 | − | 0.192262i | ||||
\(791\) | − | 1.99266e13i | − | 0.0643504i | ||||||
\(792\) | −3.13392e14 | + | 7.59057e13i | −1.00569 | + | 0.243584i | ||||
\(793\) | − | 9.01940e13i | − | 0.287615i | ||||||
\(794\) | − | 1.68595e14i | − | 0.534247i | ||||||
\(795\) | −1.15891e14 | + | 2.18061e14i | −0.364934 | + | 0.686659i | ||||
\(796\) | −1.26005e14 | −0.394297 | ||||||||
\(797\) | 3.36528e14 | 1.04648 | 0.523238 | − | 0.852186i | \(-0.324724\pi\) | ||||
0.523238 | + | 0.852186i | \(0.324724\pi\) | |||||||
\(798\) | −8.70834e13 | + | 1.10694e14i | −0.269104 | + | 0.342064i | ||||
\(799\) | 4.19742e13 | 0.128899 | ||||||||
\(800\) | −3.50977e14 | + | 1.30575e14i | −1.07110 | + | 0.398483i | ||||
\(801\) | 5.06577e14 | − | 1.22696e14i | 1.53632 | − | 0.372108i | ||||
\(802\) | − | 5.48185e14i | − | 1.65217i | ||||||
\(803\) | −2.35320e14 | −0.704824 | ||||||||
\(804\) | −3.85714e14 | + | 4.90290e14i | −1.14812 | + | 1.45939i | ||||
\(805\) | −1.54379e14 | + | 2.77866e13i | −0.456675 | + | 0.0821969i | ||||
\(806\) | 3.85537e14i | 1.13342i | ||||||||
\(807\) | −8.57356e13 | + | 1.08980e14i | −0.250492 | + | 0.318405i | ||||
\(808\) | − | 3.62462e14i | − | 1.05246i | ||||||
\(809\) | − | 1.05361e14i | − | 0.304044i | −0.988377 | − | 0.152022i | \(-0.951422\pi\) | ||
0.988377 | − | 0.152022i | \(-0.0485784\pi\) | |||||||
\(810\) | 3.37160e14 | + | 4.40447e14i | 0.966965 | + | 1.26319i | ||||
\(811\) | 2.34283e14 | 0.667786 | 0.333893 | − | 0.942611i | \(-0.391638\pi\) | ||||
0.333893 | + | 0.942611i | \(0.391638\pi\) | |||||||
\(812\) | 4.53141e14 | 1.28367 | ||||||||
\(813\) | 3.39561e13 | + | 2.67135e13i | 0.0956015 | + | 0.0752104i | ||||
\(814\) | 1.06644e15 | 2.98411 | ||||||||
\(815\) | −2.86528e14 | + | 5.15721e13i | −0.796853 | + | 0.143426i | ||||
\(816\) | −7.72845e13 | − | 6.08002e13i | −0.213620 | − | 0.168056i | ||||
\(817\) | − | 1.65208e14i | − | 0.453858i | ||||||
\(818\) | 2.41819e14 | 0.660272 | ||||||||
\(819\) | −2.41682e13 | − | 9.97835e13i | −0.0655882 | − | 0.270794i | ||||
\(820\) | −6.41986e13 | + | 1.15551e13i | −0.173163 | + | 0.0311677i | ||||
\(821\) | − | 5.17294e14i | − | 1.38682i | −0.720541 | − | 0.693412i | \(-0.756106\pi\) | ||
0.720541 | − | 0.693412i | \(-0.243894\pi\) | |||||||
\(822\) | −1.08363e14 | − | 8.52496e13i | −0.288749 | − | 0.227161i | ||||
\(823\) | − | 5.83446e14i | − | 1.54526i | −0.634857 | − | 0.772630i | \(-0.718941\pi\) | ||
0.634857 | − | 0.772630i | \(-0.281059\pi\) | |||||||
\(824\) | 1.80008e13i | 0.0473867i | ||||||||
\(825\) | 1.43093e14 | − | 4.46068e14i | 0.374410 | − | 1.16716i | ||||
\(826\) | 1.58906e14 | 0.413275 | ||||||||
\(827\) | −4.13226e14 | −1.06822 | −0.534109 | − | 0.845415i | \(-0.679353\pi\) | ||||
−0.534109 | + | 0.845415i | \(0.679353\pi\) | |||||||
\(828\) | 1.33724e14 | + | 5.52106e14i | 0.343603 | + | 1.41863i | ||||
\(829\) | −5.47753e14 | −1.39898 | −0.699491 | − | 0.714641i | \(-0.746590\pi\) | ||||
−0.699491 | + | 0.714641i | \(0.746590\pi\) | |||||||
\(830\) | 4.49822e13 | + | 2.49915e14i | 0.114196 | + | 0.634457i | ||||
\(831\) | −8.18630e13 | + | 1.04058e14i | −0.206577 | + | 0.262585i | ||||
\(832\) | − | 3.72166e14i | − | 0.933513i | ||||||
\(833\) | −4.43221e14 | −1.10508 | ||||||||
\(834\) | −2.30384e14 | − | 1.81245e14i | −0.570982 | − | 0.449195i | ||||
\(835\) | −2.48837e13 | − | 1.38251e14i | −0.0613032 | − | 0.340592i | ||||
\(836\) | − | 4.30776e14i | − | 1.05492i | ||||||
\(837\) | −2.12595e14 | + | 4.64837e14i | −0.517518 | + | 1.13155i | ||||
\(838\) | 7.55697e14i | 1.82864i | ||||||||
\(839\) | − | 5.67198e14i | − | 1.36435i | −0.731191 | − | 0.682173i | \(-0.761035\pi\) | ||
0.731191 | − | 0.682173i | \(-0.238965\pi\) | |||||||
\(840\) | −1.51698e14 | − | 8.06217e13i | −0.362730 | − | 0.192777i | ||||
\(841\) | −8.28974e14 | −1.97043 | ||||||||
\(842\) | 7.81953e14 | 1.84765 | ||||||||
\(843\) | 3.61808e14 | − | 4.59902e14i | 0.849847 | − | 1.08026i | ||||
\(844\) | 9.38339e14 | 2.19103 | ||||||||
\(845\) | 5.12928e13 | + | 2.84976e14i | 0.119062 | + | 0.661492i | ||||
\(846\) | 1.44473e13 | + | 5.96485e13i | 0.0333376 | + | 0.137641i | ||||
\(847\) | − | 1.06579e14i | − | 0.244487i | ||||||
\(848\) | 6.40111e13 | 0.145974 | ||||||||
\(849\) | −1.88472e14 | + | 2.39571e14i | −0.427276 | + | 0.543119i | ||||
\(850\) | −9.57860e14 | + | 3.56355e14i | −2.15878 | + | 0.803134i | ||||
\(851\) | − | 6.51348e14i | − | 1.45937i | ||||||
\(852\) | −2.84069e14 | + | 3.61086e14i | −0.632741 | + | 0.804291i | ||||
\(853\) | 7.64152e14i | 1.69213i | 0.533077 | + | 0.846067i | \(0.321036\pi\) | ||||
−0.533077 | + | 0.846067i | \(0.678964\pi\) | |||||||
\(854\) | 1.76614e14i | 0.388808i | ||||||||
\(855\) | −2.35022e14 | + | 1.03749e14i | −0.514374 | + | 0.227066i | ||||
\(856\) | −5.45092e14 | −1.18605 | ||||||||
\(857\) | 1.15205e14 | 0.249211 | 0.124606 | − | 0.992206i | \(-0.460233\pi\) | ||||
0.124606 | + | 0.992206i | \(0.460233\pi\) | |||||||
\(858\) | 4.08037e14 | + | 3.21005e14i | 0.877532 | + | 0.690360i | ||||
\(859\) | 6.54322e14 | 1.39903 | 0.699513 | − | 0.714620i | \(-0.253400\pi\) | ||||
0.699513 | + | 0.714620i | \(0.253400\pi\) | |||||||
\(860\) | 5.72047e14 | − | 1.02963e14i | 1.21602 | − | 0.218871i | ||||
\(861\) | 2.08001e13 | + | 1.63636e13i | 0.0439592 | + | 0.0345830i | ||||
\(862\) | 9.39199e14i | 1.97343i | ||||||||
\(863\) | 6.58785e14 | 1.37623 | 0.688113 | − | 0.725604i | \(-0.258439\pi\) | ||||
0.688113 | + | 0.725604i | \(0.258439\pi\) | |||||||
\(864\) | 2.28852e14 | − | 5.00383e14i | 0.475320 | − | 1.03928i | ||||
\(865\) | −6.67946e13 | − | 3.71102e14i | −0.137931 | − | 0.766324i | ||||
\(866\) | 1.17615e15i | 2.41476i | ||||||||
\(867\) | −4.22143e14 | − | 3.32103e14i | −0.861716 | − | 0.677918i | ||||
\(868\) | − | 4.56625e14i | − | 0.926746i | ||||||
\(869\) | − | 7.45928e13i | − | 0.150521i | ||||||
\(870\) | 1.20671e15 | + | 6.41321e14i | 2.42107 | + | 1.28671i | ||||
\(871\) | 3.48216e14 | 0.694638 | ||||||||
\(872\) | −3.11101e14 | −0.617047 | ||||||||
\(873\) | −2.77459e14 | + | 6.72024e13i | −0.547176 | + | 0.132530i | ||||
\(874\) | −4.34993e14 | −0.852953 | ||||||||
\(875\) | 2.14798e14 | − | 1.27083e14i | 0.418783 | − | 0.247769i | ||||
\(876\) | −2.80727e14 | + | 3.56838e14i | −0.544207 | + | 0.691753i | ||||
\(877\) | 3.46323e14i | 0.667550i | 0.942653 | + | 0.333775i | \(0.108323\pi\) | ||||
−0.942653 | + | 0.333775i | \(0.891677\pi\) | |||||||
\(878\) | −4.77859e14 | −0.915857 | ||||||||
\(879\) | 1.91012e14 | + | 1.50270e14i | 0.364012 | + | 0.286371i | ||||
\(880\) | −1.19510e14 | + | 2.15106e13i | −0.226460 | + | 0.0407604i | ||||
\(881\) | 6.56655e13i | 0.123725i | 0.998085 | + | 0.0618625i | \(0.0197040\pi\) | ||||
−0.998085 | + | 0.0618625i | \(0.980296\pi\) | |||||||
\(882\) | −1.52554e14 | − | 6.29851e14i | −0.285812 | − | 1.18003i | ||||
\(883\) | − | 7.17599e14i | − | 1.33684i | −0.743785 | − | 0.668418i | \(-0.766972\pi\) | ||
0.743785 | − | 0.668418i | \(-0.233028\pi\) | |||||||
\(884\) | − | 6.85074e14i | − | 1.26904i | ||||||
\(885\) | 2.55950e14 | + | 1.36028e14i | 0.471454 | + | 0.250560i | ||||
\(886\) | 1.03536e15 | 1.89636 | ||||||||
\(887\) | −2.72208e14 | −0.495773 | −0.247887 | − | 0.968789i | \(-0.579736\pi\) | ||||
−0.247887 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(888\) | 4.41067e14 | − | 5.60650e14i | 0.798804 | − | 1.01538i | ||||
\(889\) | 1.29279e14 | 0.232820 | ||||||||
\(890\) | −1.38200e15 | + | 2.48745e14i | −2.47489 | + | 0.445456i | ||||
\(891\) | 3.14954e14 | + | 6.12033e14i | 0.560865 | + | 1.08990i | ||||
\(892\) | 1.02011e15i | 1.80643i | ||||||||
\(893\) | −2.84253e13 | −0.0500551 | ||||||||
\(894\) | 5.31789e14 | − | 6.75969e14i | 0.931219 | − | 1.18369i | ||||
\(895\) | −3.85323e14 | + | 6.93542e13i | −0.670980 | + | 0.120770i | ||||
\(896\) | 4.07629e14i | 0.705871i | ||||||||
\(897\) | 1.96060e14 | − | 2.49216e14i | 0.337619 | − | 0.429154i | ||||
\(898\) | − | 2.29976e13i | − | 0.0393822i | ||||||
\(899\) | 1.25929e15i | 2.14450i | ||||||||
\(900\) | −5.05712e14 | − | 7.49127e14i | −0.856428 | − | 1.26865i | ||||
\(901\) | 6.68536e14 | 1.12590 | ||||||||
\(902\) | −1.33828e14 | −0.224138 | ||||||||
\(903\) | −1.85341e14 | − | 1.45809e14i | −0.308697 | − | 0.242854i | ||||
\(904\) | 6.74020e13 | 0.111643 | ||||||||
\(905\) | −2.69001e13 | − | 1.49453e14i | −0.0443110 | − | 0.246186i | ||||
\(906\) | −1.37760e15 | − | 1.08377e15i | −2.25674 | − | 1.77540i | ||||
\(907\) | − | 2.16615e14i | − | 0.352900i | −0.984310 | − | 0.176450i | \(-0.943539\pi\) | ||
0.984310 | − | 0.176450i | \(-0.0564613\pi\) | |||||||
\(908\) | 9.85941e14 | 1.59743 | ||||||||
\(909\) | −7.51977e14 | + | 1.82134e14i | −1.21167 | + | 0.293475i | ||||
\(910\) | 4.89968e13 | + | 2.72220e14i | 0.0785165 | + | 0.436227i | ||||
\(911\) | − | 8.10639e14i | − | 1.29192i | −0.763371 | − | 0.645960i | \(-0.776457\pi\) | ||
0.763371 | − | 0.645960i | \(-0.223543\pi\) | |||||||
\(912\) | 5.23378e13 | + | 4.11746e13i | 0.0829548 | + | 0.0652612i | ||||
\(913\) | 3.15109e14i | 0.496715i | ||||||||
\(914\) | 1.04611e13i | 0.0164001i | ||||||||
\(915\) | −1.51187e14 | + | 2.84473e14i | −0.235726 | + | 0.443542i | ||||
\(916\) | −1.50443e15 | −2.33289 | ||||||||
\(917\) | −8.37681e12 | −0.0129191 | ||||||||
\(918\) | 6.24565e14 | − | 1.36561e15i | 0.957998 | − | 2.09465i | ||||
\(919\) | −2.39232e14 | −0.364957 | −0.182478 | − | 0.983210i | \(-0.558412\pi\) | ||||
−0.182478 | + | 0.983210i | \(0.558412\pi\) | |||||||
\(920\) | −9.39883e13 | − | 5.22187e14i | −0.142605 | − | 0.792294i | ||||
\(921\) | 5.94382e14 | − | 7.55531e14i | 0.896948 | − | 1.14013i | ||||
\(922\) | − | 9.44858e14i | − | 1.41812i | ||||||
\(923\) | 2.56453e14 | 0.382824 | ||||||||
\(924\) | −4.83273e14 | − | 3.80194e14i | −0.717517 | − | 0.564476i | ||||
\(925\) | 3.61357e14 | + | 9.71306e14i | 0.533615 | + | 1.43432i | ||||
\(926\) | 1.06805e15i | 1.56869i | ||||||||
\(927\) | 3.73452e13 | − | 9.04525e12i | 0.0545551 | − | 0.0132136i | ||||
\(928\) | − | 1.35559e15i | − | 1.96964i | ||||||
\(929\) | 3.85573e14i | 0.557222i | 0.960404 | + | 0.278611i | \(0.0898740\pi\) | ||||
−0.960404 | + | 0.278611i | \(0.910126\pi\) | |||||||
\(930\) | 6.46252e14 | − | 1.21599e15i | 0.928938 | − | 1.74789i | ||||
\(931\) | 3.00154e14 | 0.429136 | ||||||||
\(932\) | 6.81608e13 | 0.0969293 | ||||||||
\(933\) | −5.87255e14 | + | 7.46472e14i | −0.830650 | + | 1.05586i | ||||
\(934\) | −1.25840e15 | −1.77045 | ||||||||
\(935\) | −1.24817e15 | + | 2.24658e14i | −1.74669 | + | 0.314386i | ||||
\(936\) | 3.37519e14 | − | 8.17493e13i | 0.469806 | − | 0.113790i | ||||
\(937\) | − | 1.09450e15i | − | 1.51537i | −0.652619 | − | 0.757686i | \(-0.726330\pi\) | ||
0.652619 | − | 0.757686i | \(-0.273670\pi\) | |||||||
\(938\) | −6.81862e14 | −0.939036 | ||||||||
\(939\) | −1.85132e13 | + | 2.35325e13i | −0.0253602 | + | 0.0322359i | ||||
\(940\) | −1.77156e13 | − | 9.84253e13i | −0.0241388 | − | 0.134112i | ||||
\(941\) | 8.03737e14i | 1.08935i | 0.838649 | + | 0.544673i | \(0.183346\pi\) | ||||
−0.838649 | + | 0.544673i | \(0.816654\pi\) | |||||||
\(942\) | −1.28560e14 | + | 1.63415e14i | −0.173320 | + | 0.220311i | ||||
\(943\) | 8.17382e13i | 0.109614i | ||||||||
\(944\) | − | 7.51335e13i | − | 0.100224i | ||||||
\(945\) | −9.10340e13 | + | 3.55230e14i | −0.120794 | + | 0.471357i | ||||
\(946\) | 1.19249e15 | 1.57398 | ||||||||
\(947\) | −1.74430e14 | −0.229019 | −0.114510 | − | 0.993422i | \(-0.536530\pi\) | ||||
−0.114510 | + | 0.993422i | \(0.536530\pi\) | |||||||
\(948\) | −1.13112e14 | − | 8.89863e13i | −0.147730 | − | 0.116220i | ||||
\(949\) | 2.53436e14 | 0.329258 | ||||||||
\(950\) | 6.48673e14 | − | 2.41327e14i | 0.838316 | − | 0.311881i | ||||
\(951\) | −2.37110e14 | − | 1.86536e14i | −0.304823 | − | 0.239806i | ||||
\(952\) | 4.65079e14i | 0.594761i | ||||||||
\(953\) | 9.73346e14 | 1.23823 | 0.619117 | − | 0.785299i | \(-0.287491\pi\) | ||||
0.619117 | + | 0.785299i | \(0.287491\pi\) | |||||||
\(954\) | 2.30106e14 | + | 9.50041e14i | 0.291197 | + | 1.20227i | ||||
\(955\) | 4.75599e14 | − | 8.56031e13i | 0.598721 | − | 0.107764i | ||||
\(956\) | 4.35308e14i | 0.545138i | ||||||||
\(957\) | 1.33278e15 | + | 1.04851e15i | 1.66035 | + | 1.30621i | ||||
\(958\) | 5.09178e14i | 0.631019i | ||||||||
\(959\) | − | 9.11525e13i | − | 0.112377i | ||||||
\(960\) | −6.23839e14 | + | 1.17381e15i | −0.765096 | + | 1.43961i | ||||
\(961\) | 4.49342e14 | 0.548227 | ||||||||
\(962\) | −1.14854e15 | −1.39402 | ||||||||
\(963\) | 2.73904e14 | + | 1.13087e15i | 0.330725 | + | 1.36547i | ||||
\(964\) | 2.83765e14 | 0.340858 | ||||||||
\(965\) | 1.30229e15 | − | 2.34399e14i | 1.55622 | − | 0.280104i | ||||
\(966\) | −3.83916e14 | + | 4.88003e14i | −0.456405 | + | 0.580146i | ||||
\(967\) | − | 2.54476e13i | − | 0.0300964i | −0.999887 | − | 0.0150482i | \(-0.995210\pi\) | ||
0.999887 | − | 0.0150482i | \(-0.00479018\pi\) | |||||||
\(968\) | 3.60505e14 | 0.424165 | ||||||||
\(969\) | 5.46620e14 | + | 4.30030e14i | 0.639833 | + | 0.503361i | ||||
\(970\) | 7.56936e14 | − | 1.36241e14i | 0.881456 | − | 0.158653i | ||||
\(971\) | − | 7.60628e14i | − | 0.881204i | −0.897703 | − | 0.440602i | \(-0.854765\pi\) | ||
0.897703 | − | 0.440602i | \(-0.145235\pi\) | |||||||
\(972\) | 1.30381e15 | + | 2.52537e14i | 1.50274 | + | 0.291067i | ||||
\(973\) | − | 1.93795e14i | − | 0.222217i | ||||||
\(974\) | 1.70782e15i | 1.94826i | ||||||||
\(975\) | −1.54109e14 | + | 4.80408e14i | −0.174906 | + | 0.545239i | ||||
\(976\) | 8.35062e13 | 0.0942908 | ||||||||
\(977\) | 8.51350e13 | 0.0956391 | 0.0478195 | − | 0.998856i | \(-0.484773\pi\) | ||||
0.0478195 | + | 0.998856i | \(0.484773\pi\) | |||||||
\(978\) | −7.12551e14 | + | 9.05738e14i | −0.796382 | + | 1.01230i | ||||
\(979\) | −1.74251e15 | −1.93759 | ||||||||
\(980\) | 1.87065e14 | + | 1.03931e15i | 0.206949 | + | 1.14978i | ||||
\(981\) | 1.56325e14 | + | 6.45421e14i | 0.172062 | + | 0.710392i | ||||
\(982\) | 5.02033e14i | 0.549762i | ||||||||
\(983\) | 4.91406e14 | 0.535393 | 0.267696 | − | 0.963503i | \(-0.413738\pi\) | ||||
0.267696 | + | 0.963503i | \(0.413738\pi\) | |||||||
\(984\) | −5.53499e13 | + | 7.03565e13i | −0.0599987 | + | 0.0762656i | ||||
\(985\) | −3.05157e14 | − | 1.69541e15i | −0.329111 | − | 1.82850i | ||||
\(986\) | − | 3.69956e15i | − | 3.96978i | ||||||
\(987\) | −2.50876e13 | + | 3.18894e13i | −0.0267839 | + | 0.0340456i | ||||
\(988\) | 4.63939e14i | 0.492807i | ||||||||
\(989\) | − | 7.28335e14i | − | 0.769750i | ||||||
\(990\) | −7.48870e14 | − | 1.69642e15i | −0.787463 | − | 1.78385i | ||||
\(991\) | −1.07070e15 | −1.12021 | −0.560104 | − | 0.828422i | \(-0.689239\pi\) | ||||
−0.560104 | + | 0.828422i | \(0.689239\pi\) | |||||||
\(992\) | −1.36601e15 | −1.42199 | ||||||||
\(993\) | −5.85102e14 | − | 4.60304e14i | −0.606018 | − | 0.476759i | ||||
\(994\) | −5.02175e14 | −0.517515 | ||||||||
\(995\) | −4.45023e13 | − | 2.47249e14i | −0.0456317 | − | 0.253524i | ||||
\(996\) | 4.77831e14 | + | 3.75913e14i | 0.487503 | + | 0.383523i | ||||
\(997\) | 1.60992e15i | 1.63428i | 0.576436 | + | 0.817142i | \(0.304443\pi\) | ||||
−0.576436 | + | 0.817142i | \(0.695557\pi\) | |||||||
\(998\) | 1.64861e15 | 1.66520 | ||||||||
\(999\) | −1.38478e15 | − | 6.33333e14i | −1.39172 | − | 0.636509i |
(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 | 15.11.d.c.14.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 15.11.d.c.14.15 | yes | 16 | |
5.2 | odd | 4 | 75.11.c.h.26.1 | 16 | |||
5.3 | odd | 4 | 75.11.c.h.26.16 | 16 | |||
5.4 | even | 2 | inner | 15.11.d.c.14.16 | yes | 16 | |
15.2 | even | 4 | 75.11.c.h.26.15 | 16 | |||
15.8 | even | 4 | 75.11.c.h.26.2 | 16 | |||
15.14 | odd | 2 | inner | 15.11.d.c.14.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.11.d.c.14.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
15.11.d.c.14.2 | yes | 16 | 15.14 | odd | 2 | inner | |
15.11.d.c.14.15 | yes | 16 | 3.2 | odd | 2 | inner | |
15.11.d.c.14.16 | yes | 16 | 5.4 | even | 2 | inner | |
75.11.c.h.26.1 | 16 | 5.2 | odd | 4 | |||
75.11.c.h.26.2 | 16 | 15.8 | even | 4 | |||
75.11.c.h.26.15 | 16 | 15.2 | even | 4 | |||
75.11.c.h.26.16 | 16 | 5.3 | odd | 4 |