Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(26,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.26");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.c (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: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 1634x^{8} + 776307x^{6} + 148116566x^{4} + 10575941812x^{2} + 105274575720 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{11}\cdot 5^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.9 | ||
Root | \(-13.5890i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.26 |
Dual form | 75.9.c.e.26.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 24.1370i | 1.50856i | 0.656552 | + | 0.754281i | \(0.272014\pi\) | ||||
−0.656552 | + | 0.754281i | \(0.727986\pi\) | |||||||
\(3\) | 39.5746 | + | 70.6742i | 0.488576 | + | 0.872521i | ||||
\(4\) | −326.594 | −1.27576 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1705.86 | + | 955.212i | −1.31625 | + | 0.737047i | ||||
\(7\) | −1042.22 | −0.434077 | −0.217039 | − | 0.976163i | \(-0.569640\pi\) | ||||
−0.217039 | + | 0.976163i | \(0.569640\pi\) | |||||||
\(8\) | − | 1703.92i | − | 0.415997i | ||||||
\(9\) | −3428.70 | + | 5593.81i | −0.522587 | + | 0.852586i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19553.4i | 1.33552i | 0.744376 | + | 0.667761i | \(0.232747\pi\) | ||||
−0.744376 | + | 0.667761i | \(0.767253\pi\) | |||||||
\(12\) | −12924.8 | − | 23081.8i | −0.623304 | − | 1.11313i | ||||
\(13\) | −29037.8 | −1.01670 | −0.508348 | − | 0.861152i | \(-0.669743\pi\) | ||||
−0.508348 | + | 0.861152i | \(0.669743\pi\) | |||||||
\(14\) | − | 25156.0i | − | 0.654832i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −42480.5 | −0.648200 | ||||||||
\(17\) | − | 122230.i | − | 1.46346i | −0.681594 | − | 0.731731i | \(-0.738713\pi\) | ||
0.681594 | − | 0.731731i | \(-0.261287\pi\) | |||||||
\(18\) | −135018. | − | 82758.4i | −1.28618 | − | 0.788355i | ||||
\(19\) | 189552. | 1.45450 | 0.727250 | − | 0.686373i | \(-0.240798\pi\) | ||||
0.727250 | + | 0.686373i | \(0.240798\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −41245.5 | − | 73658.1i | −0.212080 | − | 0.378742i | ||||
\(22\) | −471959. | −2.01472 | ||||||||
\(23\) | − | 112212.i | − | 0.400985i | −0.979695 | − | 0.200493i | \(-0.935746\pi\) | ||
0.979695 | − | 0.200493i | \(-0.0642543\pi\) | |||||||
\(24\) | 120424. | − | 67432.2i | 0.362966 | − | 0.203246i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 700886.i | − | 1.53375i | ||||||
\(27\) | −531028. | − | 20947.3i | −0.999223 | − | 0.0394160i | ||||
\(28\) | 340383. | 0.553777 | ||||||||
\(29\) | 108842.i | 0.153888i | 0.997035 | + | 0.0769440i | \(0.0245163\pi\) | ||||
−0.997035 | + | 0.0769440i | \(0.975484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.19254e6 | −1.29130 | −0.645651 | − | 0.763633i | \(-0.723414\pi\) | ||||
−0.645651 | + | 0.763633i | \(0.723414\pi\) | |||||||
\(32\) | − | 1.46155e6i | − | 1.39385i | ||||||
\(33\) | −1.38192e6 | + | 773817.i | −1.16527 | + | 0.652503i | ||||
\(34\) | 2.95026e6 | 2.20772 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.11979e6 | − | 1.82691e6i | 0.666695 | − | 1.08769i | ||||
\(37\) | 2.84100e6 | 1.51588 | 0.757939 | − | 0.652326i | \(-0.226207\pi\) | ||||
0.757939 | + | 0.652326i | \(0.226207\pi\) | |||||||
\(38\) | 4.57521e6i | 2.19420i | ||||||||
\(39\) | −1.14916e6 | − | 2.05223e6i | −0.496733 | − | 0.887088i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.90516e6i | 1.38199i | 0.722861 | + | 0.690993i | \(0.242827\pi\) | ||||
−0.722861 | + | 0.690993i | \(0.757173\pi\) | |||||||
\(42\) | 1.77788e6 | − | 995541.i | 0.571355 | − | 0.319935i | ||||
\(43\) | 864712. | 0.252928 | 0.126464 | − | 0.991971i | \(-0.459637\pi\) | ||||
0.126464 | + | 0.991971i | \(0.459637\pi\) | |||||||
\(44\) | − | 6.38601e6i | − | 1.70380i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.70846e6 | 0.604911 | ||||||||
\(47\) | − | 1.48368e6i | − | 0.304053i | −0.988376 | − | 0.152026i | \(-0.951420\pi\) | ||
0.988376 | − | 0.152026i | \(-0.0485799\pi\) | |||||||
\(48\) | −1.68115e6 | − | 3.00227e6i | −0.316695 | − | 0.565569i | ||||
\(49\) | −4.67858e6 | −0.811577 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.63850e6 | − | 4.83720e6i | 1.27690 | − | 0.715012i | ||||
\(52\) | 9.48358e6 | 1.29706 | ||||||||
\(53\) | 3.65103e6i | 0.462713i | 0.972869 | + | 0.231357i | \(0.0743164\pi\) | ||||
−0.972869 | + | 0.231357i | \(0.925684\pi\) | |||||||
\(54\) | 505604. | − | 1.28174e7i | 0.0594615 | − | 1.50739i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.77586e6i | 0.180575i | ||||||||
\(57\) | 7.50144e6 | + | 1.33964e7i | 0.710633 | + | 1.26908i | ||||
\(58\) | −2.62712e6 | −0.232149 | ||||||||
\(59\) | − | 1.46586e7i | − | 1.20972i | −0.796332 | − | 0.604859i | \(-0.793229\pi\) | ||
0.796332 | − | 0.604859i | \(-0.206771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.60123e7 | 1.15647 | 0.578234 | − | 0.815871i | \(-0.303742\pi\) | ||||
0.578234 | + | 0.815871i | \(0.303742\pi\) | |||||||
\(62\) | − | 2.87844e7i | − | 1.94801i | ||||||
\(63\) | 3.57345e6 | − | 5.82998e6i | 0.226843 | − | 0.370088i | ||||
\(64\) | 2.44025e7 | 1.45450 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.86776e7 | − | 3.33554e7i | −0.984341 | − | 1.75788i | ||||
\(67\) | −2.14382e7 | −1.06387 | −0.531937 | − | 0.846784i | \(-0.678536\pi\) | ||||
−0.531937 | + | 0.846784i | \(0.678536\pi\) | |||||||
\(68\) | 3.99195e7i | 1.86702i | ||||||||
\(69\) | 7.93050e6 | − | 4.44075e6i | 0.349868 | − | 0.195912i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.10459e7i | 1.61524i | 0.589706 | + | 0.807618i | \(0.299244\pi\) | ||||
−0.589706 | + | 0.807618i | \(0.700756\pi\) | |||||||
\(72\) | 9.53144e6 | + | 5.84224e6i | 0.354673 | + | 0.217395i | ||||
\(73\) | −4.70244e7 | −1.65589 | −0.827946 | − | 0.560808i | \(-0.810491\pi\) | ||||
−0.827946 | + | 0.560808i | \(0.810491\pi\) | |||||||
\(74\) | 6.85731e7i | 2.28679i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.19065e7 | −1.85559 | ||||||||
\(77\) | − | 2.03789e7i | − | 0.579719i | ||||||
\(78\) | 4.95346e7 | − | 2.77373e7i | 1.33823 | − | 0.749352i | ||||
\(79\) | −2.43754e7 | −0.625811 | −0.312905 | − | 0.949784i | \(-0.601302\pi\) | ||||
−0.312905 | + | 0.949784i | \(0.601302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.95348e7 | − | 3.83590e7i | −0.453805 | − | 0.891101i | ||||
\(82\) | −9.42589e7 | −2.08481 | ||||||||
\(83\) | − | 6.88381e6i | − | 0.145050i | −0.997367 | − | 0.0725248i | \(-0.976894\pi\) | ||
0.997367 | − | 0.0725248i | \(-0.0231056\pi\) | |||||||
\(84\) | 1.34705e7 | + | 2.40563e7i | 0.270562 | + | 0.483183i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.08715e7i | 0.381558i | ||||||||
\(87\) | −7.69233e6 | + | 4.30738e6i | −0.134271 | + | 0.0751859i | ||||
\(88\) | 3.33174e7 | 0.555573 | ||||||||
\(89\) | 3.39808e7i | 0.541593i | 0.962637 | + | 0.270796i | \(0.0872870\pi\) | ||||
−0.962637 | + | 0.270796i | \(0.912713\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.02638e7 | 0.441324 | ||||||||
\(92\) | 3.66478e7i | 0.511560i | ||||||||
\(93\) | −4.71945e7 | − | 8.42822e7i | −0.630899 | − | 1.12669i | ||||
\(94\) | 3.58116e7 | 0.458682 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.03294e8 | − | 5.78405e7i | 1.21616 | − | 0.681000i | ||||
\(97\) | −1.50338e7 | −0.169817 | −0.0849086 | − | 0.996389i | \(-0.527060\pi\) | ||||
−0.0849086 | + | 0.996389i | \(0.527060\pi\) | |||||||
\(98\) | − | 1.12927e8i | − | 1.22431i | ||||||
\(99\) | −1.09378e8 | − | 6.70425e7i | −1.13865 | − | 0.697927i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.51577e8i | 1.45663i | 0.685244 | + | 0.728314i | \(0.259696\pi\) | ||||
−0.685244 | + | 0.728314i | \(0.740304\pi\) | |||||||
\(102\) | 1.16755e8 | + | 2.08507e8i | 1.07864 | + | 1.92628i | ||||
\(103\) | −4.88143e7 | −0.433709 | −0.216854 | − | 0.976204i | \(-0.569580\pi\) | ||||
−0.216854 | + | 0.976204i | \(0.569580\pi\) | |||||||
\(104\) | 4.94783e7i | 0.422942i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.81248e7 | −0.698031 | ||||||||
\(107\) | − | 1.32340e6i | − | 0.0100962i | −0.999987 | − | 0.00504808i | \(-0.998393\pi\) | ||
0.999987 | − | 0.00504808i | \(-0.00160686\pi\) | |||||||
\(108\) | 1.73431e8 | + | 6.84125e6i | 1.27477 | + | 0.0502853i | ||||
\(109\) | −1.70973e8 | −1.21122 | −0.605608 | − | 0.795763i | \(-0.707070\pi\) | ||||
−0.605608 | + | 0.795763i | \(0.707070\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.12432e8 | + | 2.00785e8i | 0.740621 | + | 1.32264i | ||||
\(112\) | 4.42740e7 | 0.281369 | ||||||||
\(113\) | 3.37372e7i | 0.206916i | 0.994634 | + | 0.103458i | \(0.0329908\pi\) | ||||
−0.994634 | + | 0.103458i | \(0.967009\pi\) | |||||||
\(114\) | −3.23349e8 | + | 1.81062e8i | −1.91449 | + | 1.07203i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3.55471e7i | − | 0.196324i | ||||||
\(117\) | 9.95619e7 | − | 1.62432e8i | 0.531312 | − | 0.866820i | ||||
\(118\) | 3.53814e8 | 1.82493 | ||||||||
\(119\) | 1.27390e8i | 0.635256i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.67975e8 | −0.783617 | ||||||||
\(122\) | 3.86488e8i | 1.74460i | ||||||||
\(123\) | −2.75995e8 | + | 1.54545e8i | −1.20581 | + | 0.675205i | ||||
\(124\) | 3.89478e8 | 1.64739 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.40718e8 | + | 8.62524e7i | 0.558301 | + | 0.342207i | ||||
\(127\) | −9.39184e7 | −0.361024 | −0.180512 | − | 0.983573i | \(-0.557775\pi\) | ||||
−0.180512 | + | 0.983573i | \(0.557775\pi\) | |||||||
\(128\) | 2.14845e8i | 0.800361i | ||||||||
\(129\) | 3.42206e7 | + | 6.11128e7i | 0.123575 | + | 0.220685i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.71847e8i | − | 0.923079i | −0.887120 | − | 0.461540i | \(-0.847297\pi\) | ||
0.887120 | − | 0.461540i | \(-0.152703\pi\) | |||||||
\(132\) | 4.51326e8 | − | 2.52724e8i | 1.48660 | − | 0.832436i | ||||
\(133\) | −1.97555e8 | −0.631365 | ||||||||
\(134\) | − | 5.17455e8i | − | 1.60492i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.08270e8 | −0.608796 | ||||||||
\(137\) | − | 2.18688e8i | − | 0.620788i | −0.950608 | − | 0.310394i | \(-0.899539\pi\) | ||
0.950608 | − | 0.310394i | \(-0.100461\pi\) | |||||||
\(138\) | 1.07186e8 | + | 1.91418e8i | 0.295545 | + | 0.527798i | ||||
\(139\) | 4.92467e8 | 1.31922 | 0.659611 | − | 0.751608i | \(-0.270721\pi\) | ||||
0.659611 | + | 0.751608i | \(0.270721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.04858e8 | − | 5.87161e7i | 0.265293 | − | 0.148553i | ||||
\(142\) | −9.90724e8 | −2.43668 | ||||||||
\(143\) | − | 5.67787e8i | − | 1.35782i | ||||||
\(144\) | 1.45653e8 | − | 2.37628e8i | 0.338741 | − | 0.552646i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 1.13503e9i | − | 2.49801i | ||||||
\(147\) | −1.85153e8 | − | 3.30655e8i | −0.396517 | − | 0.708118i | ||||
\(148\) | −9.27853e8 | −1.93389 | ||||||||
\(149\) | − | 2.38202e6i | − | 0.00483283i | −0.999997 | − | 0.00241641i | \(-0.999231\pi\) | ||
0.999997 | − | 0.00241641i | \(-0.000769169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.94102e8 | −0.565705 | −0.282852 | − | 0.959163i | \(-0.591281\pi\) | ||||
−0.282852 | + | 0.959163i | \(0.591281\pi\) | |||||||
\(152\) | − | 3.22982e8i | − | 0.605067i | ||||||
\(153\) | 6.83731e8 | + | 4.19089e8i | 1.24773 | + | 0.764787i | ||||
\(154\) | 4.91885e8 | 0.874542 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.75309e8 | + | 6.70245e8i | 0.633710 | + | 1.13171i | ||||
\(157\) | −5.15599e8 | −0.848621 | −0.424310 | − | 0.905517i | \(-0.639483\pi\) | ||||
−0.424310 | + | 0.905517i | \(0.639483\pi\) | |||||||
\(158\) | − | 5.88348e8i | − | 0.944074i | ||||||
\(159\) | −2.58034e8 | + | 1.44488e8i | −0.403727 | + | 0.226070i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.16950e8i | 0.174059i | ||||||||
\(162\) | 9.25870e8 | − | 4.71511e8i | 1.34428 | − | 0.684592i | ||||
\(163\) | −7.26841e8 | −1.02965 | −0.514824 | − | 0.857296i | \(-0.672143\pi\) | ||||
−0.514824 | + | 0.857296i | \(0.672143\pi\) | |||||||
\(164\) | − | 1.27540e9i | − | 1.76308i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.66154e8 | 0.218816 | ||||||||
\(167\) | − | 3.33903e8i | − | 0.429294i | −0.976692 | − | 0.214647i | \(-0.931140\pi\) | ||
0.976692 | − | 0.214647i | \(-0.0688601\pi\) | |||||||
\(168\) | −1.25508e8 | + | 7.02791e7i | −0.157555 | + | 0.0882245i | ||||
\(169\) | 2.74650e7 | 0.0336692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.49915e8 | + | 1.06032e9i | −0.760103 | + | 1.24009i | ||||
\(172\) | −2.82410e8 | −0.322675 | ||||||||
\(173\) | 1.32165e9i | 1.47547i | 0.675088 | + | 0.737737i | \(0.264106\pi\) | ||||
−0.675088 | + | 0.737737i | \(0.735894\pi\) | |||||||
\(174\) | −1.03967e8 | − | 1.85670e8i | −0.113423 | − | 0.202555i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 8.30636e8i | − | 0.865685i | ||||||
\(177\) | 1.03599e9 | − | 5.80109e8i | 1.05551 | − | 0.591039i | ||||
\(178\) | −8.20193e8 | −0.817026 | ||||||||
\(179\) | 1.09788e8i | 0.106940i | 0.998569 | + | 0.0534701i | \(0.0170282\pi\) | ||||
−0.998569 | + | 0.0534701i | \(0.982972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.65073e8 | −0.340146 | −0.170073 | − | 0.985431i | \(-0.554400\pi\) | ||||
−0.170073 | + | 0.985431i | \(0.554400\pi\) | |||||||
\(182\) | 7.30477e8i | 0.665765i | ||||||||
\(183\) | 6.33680e8 | + | 1.13166e9i | 0.565023 | + | 1.00904i | ||||
\(184\) | −1.91201e8 | −0.166809 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.03432e9 | − | 1.13913e9i | 1.69968 | − | 0.951750i | ||||
\(187\) | 2.39000e9 | 1.95448 | ||||||||
\(188\) | 4.84561e8i | 0.387898i | ||||||||
\(189\) | 5.53448e8 | + | 2.18317e7i | 0.433740 | + | 0.0171096i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.14467e9i | 1.61148i | 0.592267 | + | 0.805742i | \(0.298233\pi\) | ||||
−0.592267 | + | 0.805742i | \(0.701767\pi\) | |||||||
\(192\) | 9.65721e8 | + | 1.72463e9i | 0.710635 | + | 1.26909i | ||||
\(193\) | 2.36470e9 | 1.70431 | 0.852153 | − | 0.523293i | \(-0.175297\pi\) | ||||
0.852153 | + | 0.523293i | \(0.175297\pi\) | |||||||
\(194\) | − | 3.62870e8i | − | 0.256180i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.52800e9 | 1.03538 | ||||||||
\(197\) | 2.37290e9i | 1.57548i | 0.616006 | + | 0.787742i | \(0.288750\pi\) | ||||
−0.616006 | + | 0.787742i | \(0.711250\pi\) | |||||||
\(198\) | 1.61820e9 | − | 2.64005e9i | 1.05287 | − | 1.71772i | ||||
\(199\) | −8.35564e8 | −0.532804 | −0.266402 | − | 0.963862i | \(-0.585835\pi\) | ||||
−0.266402 | + | 0.963862i | \(0.585835\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.48411e8 | − | 1.51513e9i | −0.519783 | − | 0.928252i | ||||
\(202\) | −3.65862e9 | −2.19741 | ||||||||
\(203\) | − | 1.13437e8i | − | 0.0667993i | ||||||
\(204\) | −2.82128e9 | + | 1.57980e9i | −1.62902 | + | 0.912182i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 1.17823e9i | − | 0.654276i | ||||||
\(207\) | 6.27694e8 | + | 3.84741e8i | 0.341874 | + | 0.209550i | ||||
\(208\) | 1.23354e9 | 0.659022 | ||||||||
\(209\) | 3.70638e9i | 1.94251i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.31595e9 | −1.16842 | −0.584211 | − | 0.811602i | \(-0.698596\pi\) | ||||
−0.584211 | + | 0.811602i | \(0.698596\pi\) | |||||||
\(212\) | − | 1.19240e9i | − | 0.590310i | ||||||
\(213\) | −2.90089e9 | + | 1.62438e9i | −1.40933 | + | 0.789165i | ||||
\(214\) | 3.19429e7 | 0.0152307 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.56926e7 | + | 9.04831e8i | −0.0163969 | + | 0.415674i | ||||
\(217\) | 1.24289e9 | 0.560525 | ||||||||
\(218\) | − | 4.12678e9i | − | 1.82720i | ||||||
\(219\) | −1.86097e9 | − | 3.32341e9i | −0.809029 | − | 1.44480i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.54929e9i | 1.48789i | ||||||||
\(222\) | −4.84635e9 | + | 2.71376e9i | −1.99528 | + | 1.11727i | ||||
\(223\) | 4.75871e8 | 0.192429 | 0.0962144 | − | 0.995361i | \(-0.469327\pi\) | ||||
0.0962144 | + | 0.995361i | \(0.469327\pi\) | |||||||
\(224\) | 1.52326e9i | 0.605037i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.14313e8 | −0.312146 | ||||||||
\(227\) | − | 3.01408e9i | − | 1.13515i | −0.823323 | − | 0.567573i | \(-0.807882\pi\) | ||
0.823323 | − | 0.567573i | \(-0.192118\pi\) | |||||||
\(228\) | −2.44993e9 | − | 4.37519e9i | −0.906595 | − | 1.61904i | ||||
\(229\) | 3.75337e9 | 1.36483 | 0.682416 | − | 0.730964i | \(-0.260929\pi\) | ||||
0.682416 | + | 0.730964i | \(0.260929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.44026e9 | − | 8.06488e8i | 0.505818 | − | 0.283237i | ||||
\(232\) | 1.85459e8 | 0.0640169 | ||||||||
\(233\) | 3.63111e9i | 1.23201i | 0.787741 | + | 0.616007i | \(0.211251\pi\) | ||||
−0.787741 | + | 0.616007i | \(0.788749\pi\) | |||||||
\(234\) | 3.92062e9 | + | 2.40312e9i | 1.30765 | + | 0.801517i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.78741e9i | 1.54331i | ||||||||
\(237\) | −9.64647e8 | − | 1.72271e9i | −0.305756 | − | 0.546033i | ||||
\(238\) | −3.07482e9 | −0.958322 | ||||||||
\(239\) | 4.69757e9i | 1.43973i | 0.694112 | + | 0.719867i | \(0.255797\pi\) | ||||
−0.694112 | + | 0.719867i | \(0.744203\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.46782e9 | −1.02799 | −0.513994 | − | 0.857794i | \(-0.671835\pi\) | ||||
−0.513994 | + | 0.857794i | \(0.671835\pi\) | |||||||
\(242\) | − | 4.05441e9i | − | 1.18213i | ||||||
\(243\) | 1.93791e9 | − | 2.89865e9i | 0.555787 | − | 0.831325i | ||||
\(244\) | −5.22951e9 | −1.47537 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.73026e9 | − | 6.66167e9i | −1.01859 | − | 1.81904i | ||||
\(247\) | −5.50417e9 | −1.47878 | ||||||||
\(248\) | 2.03200e9i | 0.537178i | ||||||||
\(249\) | 4.86508e8 | − | 2.72424e8i | 0.126559 | − | 0.0708677i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.53777e9i | 0.387432i | 0.981058 | + | 0.193716i | \(0.0620541\pi\) | ||||
−0.981058 | + | 0.193716i | \(0.937946\pi\) | |||||||
\(252\) | −1.16707e9 | + | 1.90404e9i | −0.289397 | + | 0.472143i | ||||
\(253\) | 2.19412e9 | 0.535524 | ||||||||
\(254\) | − | 2.26691e9i | − | 0.544626i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.06133e9 | 0.247110 | ||||||||
\(257\) | 2.70241e9i | 0.619467i | 0.950823 | + | 0.309734i | \(0.100240\pi\) | ||||
−0.950823 | + | 0.309734i | \(0.899760\pi\) | |||||||
\(258\) | −1.47508e9 | + | 8.25983e8i | −0.332917 | + | 0.186420i | ||||
\(259\) | −2.96095e9 | −0.658008 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.08842e8 | − | 3.73186e8i | −0.131203 | − | 0.0804199i | ||||
\(262\) | 6.56156e9 | 1.39252 | ||||||||
\(263\) | − | 3.23085e9i | − | 0.675296i | −0.941273 | − | 0.337648i | \(-0.890369\pi\) | ||
0.941273 | − | 0.337648i | \(-0.109631\pi\) | |||||||
\(264\) | 1.31853e9 | + | 2.35469e9i | 0.271439 | + | 0.484749i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 4.76837e9i | − | 0.952453i | ||||||
\(267\) | −2.40156e9 | + | 1.34478e9i | −0.472552 | + | 0.264609i | ||||
\(268\) | 7.00160e9 | 1.35724 | ||||||||
\(269\) | − | 8.82614e8i | − | 0.168563i | −0.996442 | − | 0.0842814i | \(-0.973141\pi\) | ||
0.996442 | − | 0.0842814i | \(-0.0268595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.69735e9 | 1.61254 | 0.806269 | − | 0.591549i | \(-0.201483\pi\) | ||||
0.806269 | + | 0.591549i | \(0.201483\pi\) | |||||||
\(272\) | 5.19238e9i | 0.948616i | ||||||||
\(273\) | 1.19768e9 | + | 2.13887e9i | 0.215620 | + | 0.385065i | ||||
\(274\) | 5.27847e9 | 0.936496 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.59005e9 | + | 1.45032e9i | −0.446347 | + | 0.249936i | ||||
\(277\) | 8.57729e9 | 1.45690 | 0.728452 | − | 0.685097i | \(-0.240240\pi\) | ||||
0.728452 | + | 0.685097i | \(0.240240\pi\) | |||||||
\(278\) | 1.18867e10i | 1.99013i | ||||||||
\(279\) | 4.08887e9 | − | 6.67087e9i | 0.674818 | − | 1.10095i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.84302e9i | − | 0.455990i | −0.973662 | − | 0.227995i | \(-0.926783\pi\) | ||
0.973662 | − | 0.227995i | \(-0.0732169\pi\) | |||||||
\(282\) | 1.41723e9 | + | 2.53096e9i | 0.224101 | + | 0.400210i | ||||
\(283\) | −9.94012e9 | −1.54969 | −0.774847 | − | 0.632149i | \(-0.782173\pi\) | ||||
−0.774847 | + | 0.632149i | \(0.782173\pi\) | |||||||
\(284\) | − | 1.34053e10i | − | 2.06065i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.37047e10 | 2.04835 | ||||||||
\(287\) | − | 4.07004e9i | − | 0.599889i | ||||||
\(288\) | 8.17567e9 | + | 5.01123e9i | 1.18837 | + | 0.728407i | ||||
\(289\) | −7.96436e9 | −1.14172 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.94957e8 | − | 1.06250e9i | −0.0829686 | − | 0.148169i | ||||
\(292\) | 1.53579e10 | 2.11252 | ||||||||
\(293\) | − | 4.76323e9i | − | 0.646295i | −0.946349 | − | 0.323147i | \(-0.895259\pi\) | ||
0.946349 | − | 0.323147i | \(-0.104741\pi\) | |||||||
\(294\) | 7.98101e9 | − | 4.46904e9i | 1.06824 | − | 0.598170i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4.84085e9i | − | 0.630601i | ||||||
\(297\) | 4.09590e8 | − | 1.03834e10i | 0.0526409 | − | 1.33448i | ||||
\(298\) | 5.74949e7 | 0.00729062 | ||||||||
\(299\) | 3.25840e9i | 0.407680i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.01219e8 | −0.109790 | ||||||||
\(302\) | − | 7.09873e9i | − | 0.853400i | ||||||
\(303\) | −1.07126e10 | + | 5.99861e9i | −1.27094 | + | 0.711673i | ||||
\(304\) | −8.05225e9 | −0.942807 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.01155e10 | + | 1.65032e10i | −1.15373 | + | 1.88227i | ||||
\(307\) | 3.26248e9 | 0.367277 | 0.183639 | − | 0.982994i | \(-0.441212\pi\) | ||||
0.183639 | + | 0.982994i | \(0.441212\pi\) | |||||||
\(308\) | 6.65563e9i | 0.739581i | ||||||||
\(309\) | −1.93181e9 | − | 3.44991e9i | −0.211900 | − | 0.378420i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.13691e10i | 1.21530i | 0.794204 | + | 0.607651i | \(0.207888\pi\) | ||||
−0.794204 | + | 0.607651i | \(0.792112\pi\) | |||||||
\(312\) | −3.49684e9 | + | 1.95808e9i | −0.369026 | + | 0.206639i | ||||
\(313\) | −2.83465e9 | −0.295340 | −0.147670 | − | 0.989037i | \(-0.547177\pi\) | ||||
−0.147670 | + | 0.989037i | \(0.547177\pi\) | |||||||
\(314\) | − | 1.24450e10i | − | 1.28020i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.96085e9 | 0.798383 | ||||||||
\(317\) | 4.84402e9i | 0.479699i | 0.970810 | + | 0.239850i | \(0.0770981\pi\) | ||||
−0.970810 | + | 0.239850i | \(0.922902\pi\) | |||||||
\(318\) | −3.48751e9 | − | 6.22816e9i | −0.341041 | − | 0.609047i | ||||
\(319\) | −2.12823e9 | −0.205521 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.35303e7 | − | 5.23731e7i | 0.00880911 | − | 0.00493274i | ||||
\(322\) | −2.82281e9 | −0.262578 | ||||||||
\(323\) | − | 2.31689e10i | − | 2.12860i | ||||||
\(324\) | 6.37995e9 | + | 1.25278e10i | 0.578945 | + | 1.13683i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.75437e10i | − | 1.55329i | ||||||
\(327\) | −6.76620e9 | − | 1.20834e10i | −0.591771 | − | 1.05681i | ||||
\(328\) | 6.65410e9 | 0.574902 | ||||||||
\(329\) | 1.54632e9i | 0.131982i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.47410e9 | −0.456037 | −0.228019 | − | 0.973657i | \(-0.573225\pi\) | ||||
−0.228019 | + | 0.973657i | \(0.573225\pi\) | |||||||
\(332\) | 2.24821e9i | 0.185048i | ||||||||
\(333\) | −9.74092e9 | + | 1.58920e10i | −0.792179 | + | 1.29242i | ||||
\(334\) | 8.05942e9 | 0.647616 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.75213e9 | + | 3.12903e9i | 0.137470 | + | 0.245501i | ||||
\(337\) | −2.30004e10 | −1.78327 | −0.891633 | − | 0.452759i | \(-0.850440\pi\) | ||||
−0.891633 | + | 0.452759i | \(0.850440\pi\) | |||||||
\(338\) | 6.62922e8i | 0.0507920i | ||||||||
\(339\) | −2.38435e9 | + | 1.33514e9i | −0.180539 | + | 0.101094i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.33183e10i | − | 1.72456i | ||||||
\(342\) | −2.55929e10 | − | 1.56870e10i | −1.87074 | − | 1.14666i | ||||
\(343\) | 1.08843e10 | 0.786364 | ||||||||
\(344\) | − | 1.47340e9i | − | 0.105217i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.19006e10 | −2.22584 | ||||||||
\(347\) | 2.27792e10i | 1.57116i | 0.618758 | + | 0.785582i | \(0.287636\pi\) | ||||
−0.618758 | + | 0.785582i | \(0.712364\pi\) | |||||||
\(348\) | 2.51227e9 | − | 1.40677e9i | 0.171297 | − | 0.0959190i | ||||
\(349\) | 2.25621e10 | 1.52082 | 0.760410 | − | 0.649444i | \(-0.224998\pi\) | ||||
0.760410 | + | 0.649444i | \(0.224998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54199e10 | + | 6.08264e8i | 1.01591 | + | 0.0400741i | ||||
\(352\) | 2.85783e10 | 1.86151 | ||||||||
\(353\) | − | 8.56846e9i | − | 0.551828i | −0.961182 | − | 0.275914i | \(-0.911019\pi\) | ||
0.961182 | − | 0.275914i | \(-0.0889806\pi\) | |||||||
\(354\) | 1.40021e10 | + | 2.50056e10i | 0.891619 | + | 1.59229i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.10979e10i | − | 0.690941i | ||||||
\(357\) | −9.00321e9 | + | 5.04142e9i | −0.554274 | + | 0.310370i | ||||
\(358\) | −2.64994e9 | −0.161326 | ||||||||
\(359\) | − | 3.45337e9i | − | 0.207905i | −0.994582 | − | 0.103953i | \(-0.966851\pi\) | ||
0.994582 | − | 0.103953i | \(-0.0331490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.89463e10 | 1.11557 | ||||||||
\(362\) | − | 8.81177e9i | − | 0.513132i | ||||||
\(363\) | −6.64756e9 | − | 1.18715e10i | −0.382856 | − | 0.683722i | ||||
\(364\) | −9.88397e9 | −0.563023 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.73148e10 | + | 1.52951e10i | −1.52220 | + | 0.852371i | ||||
\(367\) | 7.52594e9 | 0.414855 | 0.207428 | − | 0.978250i | \(-0.433491\pi\) | ||||
0.207428 | + | 0.978250i | \(0.433491\pi\) | |||||||
\(368\) | 4.76682e9i | 0.259919i | ||||||||
\(369\) | −2.18448e10 | − | 1.33896e10i | −1.17826 | − | 0.722209i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.80518e9i | − | 0.200853i | ||||||
\(372\) | 1.54134e10 | + | 2.75260e10i | 0.804874 | + | 1.43738i | ||||
\(373\) | 1.60977e10 | 0.831625 | 0.415812 | − | 0.909450i | \(-0.363497\pi\) | ||||
0.415812 | + | 0.909450i | \(0.363497\pi\) | |||||||
\(374\) | 5.76875e10i | 2.94846i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.52808e9 | −0.126485 | ||||||||
\(377\) | − | 3.16054e9i | − | 0.156457i | ||||||
\(378\) | −5.26951e8 | + | 1.33586e10i | −0.0258109 | + | 0.654323i | ||||
\(379\) | −7.26804e9 | −0.352257 | −0.176129 | − | 0.984367i | \(-0.556358\pi\) | ||||
−0.176129 | + | 0.984367i | \(0.556358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.71679e9 | − | 6.63761e9i | −0.176387 | − | 0.315001i | ||||
\(382\) | −5.17657e10 | −2.43102 | ||||||||
\(383\) | − | 3.84730e9i | − | 0.178797i | −0.995996 | − | 0.0893987i | \(-0.971505\pi\) | ||
0.995996 | − | 0.0893987i | \(-0.0284945\pi\) | |||||||
\(384\) | −1.51840e10 | + | 8.50242e9i | −0.698332 | + | 0.391037i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.70768e10i | 2.57105i | ||||||||
\(387\) | −2.96483e9 | + | 4.83704e9i | −0.132177 | + | 0.215643i | ||||
\(388\) | 4.90995e9 | 0.216646 | ||||||||
\(389\) | 1.64582e10i | 0.718761i | 0.933191 | + | 0.359380i | \(0.117012\pi\) | ||||
−0.933191 | + | 0.359380i | \(0.882988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.37157e10 | −0.586826 | ||||||||
\(392\) | 7.97194e9i | 0.337614i | ||||||||
\(393\) | 1.92126e10 | − | 1.07582e10i | 0.805407 | − | 0.450994i | ||||
\(394\) | −5.72746e10 | −2.37671 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.57222e10 | + | 2.18957e10i | 1.45264 | + | 0.890385i | ||||
\(397\) | 3.57344e10 | 1.43855 | 0.719273 | − | 0.694727i | \(-0.244475\pi\) | ||||
0.719273 | + | 0.694727i | \(0.244475\pi\) | |||||||
\(398\) | − | 2.01680e10i | − | 0.803767i | ||||||
\(399\) | −7.81815e9 | − | 1.39620e10i | −0.308470 | − | 0.550880i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.65267e9i | 0.295962i | 0.988990 | + | 0.147981i | \(0.0472774\pi\) | ||||
−0.988990 | + | 0.147981i | \(0.952723\pi\) | |||||||
\(402\) | 3.65707e10 | − | 2.04781e10i | 1.40033 | − | 0.784124i | ||||
\(403\) | 3.46289e10 | 1.31286 | ||||||||
\(404\) | − | 4.95042e10i | − | 1.85830i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.73803e9 | 0.100771 | ||||||||
\(407\) | 5.55511e10i | 2.02449i | ||||||||
\(408\) | −8.24222e9 | − | 1.47193e10i | −0.297443 | − | 0.531187i | ||||
\(409\) | 1.89488e10 | 0.677154 | 0.338577 | − | 0.940939i | \(-0.390054\pi\) | ||||
0.338577 | + | 0.940939i | \(0.390054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.54556e10 | − | 8.65450e9i | 0.541650 | − | 0.303302i | ||||
\(412\) | 1.59425e10 | 0.553307 | ||||||||
\(413\) | 1.52775e10i | 0.525111i | ||||||||
\(414\) | −9.28649e9 | + | 1.51506e10i | −0.316119 | + | 0.515738i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.24404e10i | 1.41712i | ||||||||
\(417\) | 1.94892e10 | + | 3.48047e10i | 0.644540 | + | 1.15105i | ||||
\(418\) | −8.94607e10 | −2.93040 | ||||||||
\(419\) | − | 8.62832e9i | − | 0.279943i | −0.990156 | − | 0.139972i | \(-0.955299\pi\) | ||
0.990156 | − | 0.139972i | \(-0.0447012\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.38470e10 | 1.07744 | 0.538718 | − | 0.842486i | \(-0.318909\pi\) | ||||
0.538718 | + | 0.842486i | \(0.318909\pi\) | |||||||
\(422\) | − | 5.59001e10i | − | 1.76264i | ||||||
\(423\) | 8.29944e9 | + | 5.08709e9i | 0.259231 | + | 0.158894i | ||||
\(424\) | 6.22108e9 | 0.192487 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.92075e10 | − | 7.00186e10i | −1.19050 | − | 2.12606i | ||||
\(427\) | −1.66883e10 | −0.501997 | ||||||||
\(428\) | 4.32214e8i | 0.0128802i | ||||||||
\(429\) | 4.01279e10 | − | 2.24700e10i | 1.18473 | − | 0.663397i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.98116e10i | − | 0.863924i | −0.901892 | − | 0.431962i | \(-0.857821\pi\) | ||
0.901892 | − | 0.431962i | \(-0.142179\pi\) | |||||||
\(432\) | 2.25583e10 | + | 8.89850e8i | 0.647697 | + | 0.0255495i | ||||
\(433\) | −2.54166e9 | −0.0723047 | −0.0361524 | − | 0.999346i | \(-0.511510\pi\) | ||||
−0.0361524 | + | 0.999346i | \(0.511510\pi\) | |||||||
\(434\) | 2.99997e10i | 0.845586i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.58388e10 | 1.54522 | ||||||||
\(437\) | − | 2.12700e10i | − | 0.583233i | ||||||
\(438\) | 8.02172e10 | − | 4.49183e10i | 2.17957 | − | 1.22047i | ||||
\(439\) | 1.11261e10 | 0.299559 | 0.149780 | − | 0.988719i | \(-0.452144\pi\) | ||||
0.149780 | + | 0.988719i | \(0.452144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.60414e10 | − | 2.61711e10i | 0.424120 | − | 0.691939i | ||||
\(442\) | −8.56691e10 | −2.24458 | ||||||||
\(443\) | 3.00907e10i | 0.781299i | 0.920539 | + | 0.390650i | \(0.127750\pi\) | ||||
−0.920539 | + | 0.390650i | \(0.872250\pi\) | |||||||
\(444\) | −3.67194e10 | − | 6.55753e10i | −0.944853 | − | 1.68736i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.14861e10i | 0.290291i | ||||||||
\(447\) | 1.68348e8 | − | 9.42678e7i | 0.00421674 | − | 0.00236120i | ||||
\(448\) | −2.54328e10 | −0.631367 | ||||||||
\(449\) | − | 2.46457e10i | − | 0.606396i | −0.952928 | − | 0.303198i | \(-0.901946\pi\) | ||
0.952928 | − | 0.303198i | \(-0.0980543\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.63591e10 | −1.84567 | ||||||||
\(452\) | − | 1.10184e10i | − | 0.263975i | ||||||
\(453\) | −1.16390e10 | − | 2.07854e10i | −0.276390 | − | 0.493589i | ||||
\(454\) | 7.27509e10 | 1.71244 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.28265e10 | − | 1.27819e10i | 0.527934 | − | 0.295621i | ||||
\(457\) | −1.18416e10 | −0.271486 | −0.135743 | − | 0.990744i | \(-0.543342\pi\) | ||||
−0.135743 | + | 0.990744i | \(0.543342\pi\) | |||||||
\(458\) | 9.05950e10i | 2.05893i | ||||||||
\(459\) | −2.56038e9 | + | 6.49074e10i | −0.0576838 | + | 1.46232i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.03656e10i | 0.450913i | 0.974253 | + | 0.225456i | \(0.0723873\pi\) | ||||
−0.974253 | + | 0.225456i | \(0.927613\pi\) | |||||||
\(462\) | 1.94662e10 | + | 3.47636e10i | 0.427280 | + | 0.763057i | ||||
\(463\) | 3.88105e10 | 0.844550 | 0.422275 | − | 0.906468i | \(-0.361232\pi\) | ||||
0.422275 | + | 0.906468i | \(0.361232\pi\) | |||||||
\(464\) | − | 4.62366e9i | − | 0.0997502i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.76440e10 | −1.85857 | ||||||||
\(467\) | − | 6.67567e10i | − | 1.40355i | −0.712400 | − | 0.701774i | \(-0.752392\pi\) | ||
0.712400 | − | 0.701774i | \(-0.247608\pi\) | |||||||
\(468\) | −3.25163e10 | + | 5.30494e10i | −0.677825 | + | 1.10585i | ||||
\(469\) | 2.23434e10 | 0.461803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.04047e10 | − | 3.64396e10i | −0.414616 | − | 0.740440i | ||||
\(472\) | −2.49771e10 | −0.503239 | ||||||||
\(473\) | 1.69080e10i | 0.337791i | ||||||||
\(474\) | 4.15810e10 | − | 2.32837e10i | 0.823725 | − | 0.461252i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.16049e10i | − | 0.810432i | ||||||
\(477\) | −2.04232e10 | − | 1.25183e10i | −0.394503 | − | 0.241808i | ||||
\(478\) | −1.13385e11 | −2.17193 | ||||||||
\(479\) | 1.01360e11i | 1.92542i | 0.270529 | + | 0.962712i | \(0.412801\pi\) | ||||
−0.270529 | + | 0.962712i | \(0.587199\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.24964e10 | −1.54119 | ||||||||
\(482\) | − | 8.37027e10i | − | 1.55078i | ||||||
\(483\) | −8.26533e9 | + | 4.62824e9i | −0.151870 | + | 0.0850408i | ||||
\(484\) | 5.48597e10 | 0.999705 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.99647e10 | + | 4.67753e10i | 1.25410 | + | 0.838439i | ||||
\(487\) | −1.08507e10 | −0.192905 | −0.0964526 | − | 0.995338i | \(-0.530750\pi\) | ||||
−0.0964526 | + | 0.995338i | \(0.530750\pi\) | |||||||
\(488\) | − | 2.72837e10i | − | 0.481088i | ||||||
\(489\) | −2.87645e10 | − | 5.13689e10i | −0.503061 | − | 0.898390i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.02973e10i | − | 0.177173i | −0.996068 | − | 0.0885864i | \(-0.971765\pi\) | ||
0.996068 | − | 0.0885864i | \(-0.0282349\pi\) | |||||||
\(492\) | 9.01381e10 | − | 5.04736e10i | 1.53833 | − | 0.861398i | ||||
\(493\) | 1.33037e10 | 0.225209 | ||||||||
\(494\) | − | 1.32854e11i | − | 2.23083i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.06598e10 | 0.837022 | ||||||||
\(497\) | − | 4.27788e10i | − | 0.701138i | ||||||
\(498\) | 6.57550e9 | + | 1.17428e10i | 0.106908 | + | 0.190922i | ||||
\(499\) | 6.76597e10 | 1.09126 | 0.545630 | − | 0.838026i | \(-0.316290\pi\) | ||||
0.545630 | + | 0.838026i | \(0.316290\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.35984e10 | − | 1.32141e10i | 0.374568 | − | 0.209743i | ||||
\(502\) | −3.71171e10 | −0.584465 | ||||||||
\(503\) | 2.55230e10i | 0.398712i | 0.979927 | + | 0.199356i | \(0.0638850\pi\) | ||||
−0.979927 | + | 0.199356i | \(0.936115\pi\) | |||||||
\(504\) | −9.93385e9 | − | 6.08890e9i | −0.153956 | − | 0.0943662i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.29595e10i | 0.807871i | ||||||||
\(507\) | 1.08692e9 | + | 1.94107e9i | 0.0164500 | + | 0.0293771i | ||||
\(508\) | 3.06732e10 | 0.460579 | ||||||||
\(509\) | − | 1.02891e11i | − | 1.53287i | −0.642320 | − | 0.766437i | \(-0.722028\pi\) | ||
0.642320 | − | 0.766437i | \(-0.277972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.90098e10 | 0.718785 | ||||||||
\(512\) | 8.06177e10i | 1.17314i | ||||||||
\(513\) | −1.00657e11 | − | 3.97059e9i | −1.45337 | − | 0.0573305i | ||||
\(514\) | −6.52280e10 | −0.934504 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.11763e10 | − | 1.99591e10i | −0.157651 | − | 0.281541i | ||||
\(517\) | 2.90110e10 | 0.406069 | ||||||||
\(518\) | − | 7.14683e10i | − | 0.992646i | ||||||
\(519\) | −9.34065e10 | + | 5.23038e10i | −1.28738 | + | 0.720881i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.25006e10i | − | 0.712547i | −0.934382 | − | 0.356273i | \(-0.884047\pi\) | ||
0.934382 | − | 0.356273i | \(-0.115953\pi\) | |||||||
\(522\) | 9.00759e9 | − | 1.46956e10i | 0.121318 | − | 0.197927i | ||||
\(523\) | 8.56285e10 | 1.14449 | 0.572245 | − | 0.820083i | \(-0.306073\pi\) | ||||
0.572245 | + | 0.820083i | \(0.306073\pi\) | |||||||
\(524\) | 8.87835e10i | 1.17763i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.79830e10 | 1.01872 | ||||||||
\(527\) | 1.45764e11i | 1.88977i | ||||||||
\(528\) | 5.87046e10 | − | 3.28721e10i | 0.755329 | − | 0.422953i | ||||
\(529\) | 6.57194e10 | 0.839211 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.19975e10 | + | 5.02599e10i | 1.03139 | + | 0.632184i | ||||
\(532\) | 6.45201e10 | 0.805469 | ||||||||
\(533\) | − | 1.13398e11i | − | 1.40506i | ||||||
\(534\) | −3.24588e10 | − | 5.79665e10i | −0.399179 | − | 0.712873i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.65291e10i | 0.442568i | ||||||||
\(537\) | −7.75915e9 | + | 4.34480e9i | −0.0933076 | + | 0.0522484i | ||||
\(538\) | 2.13036e10 | 0.254287 | ||||||||
\(539\) | − | 9.14820e10i | − | 1.08388i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.14250e10 | −0.250111 | −0.125055 | − | 0.992150i | \(-0.539911\pi\) | ||||
−0.125055 | + | 0.992150i | \(0.539911\pi\) | |||||||
\(542\) | 2.09928e11i | 2.43261i | ||||||||
\(543\) | −1.44476e10 | − | 2.58013e10i | −0.166187 | − | 0.296785i | ||||
\(544\) | −1.78645e11 | −2.03984 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.16259e10 | + | 2.89084e10i | −0.580894 | + | 0.325277i | ||||
\(547\) | 9.14990e8 | 0.0102204 | 0.00511019 | − | 0.999987i | \(-0.498373\pi\) | ||||
0.00511019 | + | 0.999987i | \(0.498373\pi\) | |||||||
\(548\) | 7.14222e10i | 0.791974i | ||||||||
\(549\) | −5.49012e10 | + | 8.95697e10i | −0.604356 | + | 0.985989i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.06312e10i | 0.223830i | ||||||||
\(552\) | −7.56671e9 | − | 1.35130e10i | −0.0814987 | − | 0.145544i | ||||
\(553\) | 2.54045e10 | 0.271650 | ||||||||
\(554\) | 2.07030e11i | 2.19783i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.60837e11 | −1.68301 | ||||||||
\(557\) | − | 1.81764e11i | − | 1.88837i | −0.329416 | − | 0.944185i | \(-0.606852\pi\) | ||
0.329416 | − | 0.944185i | \(-0.393148\pi\) | |||||||
\(558\) | 1.61015e11 | + | 9.86930e10i | 1.66084 | + | 1.01800i | ||||
\(559\) | −2.51093e10 | −0.257151 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.45835e10 | + | 1.68912e11i | 0.954913 | + | 1.70533i | ||||
\(562\) | 6.86220e10 | 0.687889 | ||||||||
\(563\) | − | 4.19023e10i | − | 0.417066i | −0.978015 | − | 0.208533i | \(-0.933131\pi\) | ||
0.978015 | − | 0.208533i | \(-0.0668689\pi\) | |||||||
\(564\) | −3.42460e10 | + | 1.91763e10i | −0.338449 | + | 0.189517i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 2.39924e11i | − | 2.33781i | ||||||
\(567\) | 2.03596e10 | + | 3.99785e10i | 0.196986 | + | 0.386807i | ||||
\(568\) | 6.99391e10 | 0.671934 | ||||||||
\(569\) | − | 9.98358e10i | − | 0.952439i | −0.879326 | − | 0.476220i | \(-0.842007\pi\) | ||
0.879326 | − | 0.476220i | \(-0.157993\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00315e10 | 0.658793 | 0.329397 | − | 0.944192i | \(-0.393155\pi\) | ||||
0.329397 | + | 0.944192i | \(0.393155\pi\) | |||||||
\(572\) | 1.85436e11i | 1.73225i | ||||||||
\(573\) | −1.51573e11 | + | 8.48743e10i | −1.40605 | + | 0.787332i | ||||
\(574\) | 9.82385e10 | 0.904970 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.36688e10 | + | 1.36503e11i | −0.760105 | + | 1.24009i | ||||
\(577\) | −5.16977e10 | −0.466410 | −0.233205 | − | 0.972428i | \(-0.574921\pi\) | ||||
−0.233205 | + | 0.972428i | \(0.574921\pi\) | |||||||
\(578\) | − | 1.92236e11i | − | 1.72235i | ||||||
\(579\) | 9.35823e10 | + | 1.67124e11i | 0.832683 | + | 1.48704i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.17444e9i | 0.0629627i | ||||||||
\(582\) | 2.56456e10 | − | 1.43605e10i | 0.223522 | − | 0.125163i | ||||
\(583\) | −7.13899e10 | −0.617963 | ||||||||
\(584\) | 8.01260e10i | 0.688846i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.14970e11 | 0.974976 | ||||||||
\(587\) | − | 7.90362e10i | − | 0.665693i | −0.942981 | − | 0.332846i | \(-0.891991\pi\) | ||
0.942981 | − | 0.332846i | \(-0.108009\pi\) | |||||||
\(588\) | 6.04699e10 | + | 1.07990e11i | 0.505859 | + | 0.903387i | ||||
\(589\) | −2.26049e11 | −1.87820 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.67703e11 | + | 9.39065e10i | −1.37464 | + | 0.769743i | ||||
\(592\) | −1.20687e11 | −0.982592 | ||||||||
\(593\) | 2.38940e11i | 1.93228i | 0.258015 | + | 0.966141i | \(0.416932\pi\) | ||||
−0.258015 | + | 0.966141i | \(0.583068\pi\) | |||||||
\(594\) | 2.50624e11 | + | 9.88626e9i | 2.01315 | + | 0.0794120i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.77955e8i | 0.00616551i | ||||||||
\(597\) | −3.30671e10 | − | 5.90528e10i | −0.260315 | − | 0.464883i | ||||
\(598\) | −7.86478e10 | −0.615010 | ||||||||
\(599\) | 1.75042e11i | 1.35968i | 0.733363 | + | 0.679838i | \(0.237950\pi\) | ||||
−0.733363 | + | 0.679838i | \(0.762050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.78052e10 | −0.596363 | −0.298181 | − | 0.954509i | \(-0.596380\pi\) | ||||
−0.298181 | + | 0.954509i | \(0.596380\pi\) | |||||||
\(602\) | − | 2.17527e10i | − | 0.165626i | ||||||
\(603\) | 7.35052e10 | − | 1.19922e11i | 0.555967 | − | 0.907043i | ||||
\(604\) | 9.60518e10 | 0.721702 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.44788e11 | − | 2.58570e11i | −1.07360 | − | 1.91729i | ||||
\(607\) | 1.00711e11 | 0.741864 | 0.370932 | − | 0.928660i | \(-0.379038\pi\) | ||||
0.370932 | + | 0.928660i | \(0.379038\pi\) | |||||||
\(608\) | − | 2.77040e11i | − | 2.02735i | ||||||
\(609\) | 8.01710e9 | − | 4.48924e9i | 0.0582838 | − | 0.0326365i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.30829e10i | 0.309129i | ||||||||
\(612\) | −2.23302e11 | − | 1.36872e11i | −1.59180 | − | 0.975682i | ||||
\(613\) | −1.66738e11 | −1.18084 | −0.590422 | − | 0.807094i | \(-0.701039\pi\) | ||||
−0.590422 | + | 0.807094i | \(0.701039\pi\) | |||||||
\(614\) | 7.87464e10i | 0.554060i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.47241e10 | −0.241162 | ||||||||
\(617\) | 5.98004e10i | 0.412632i | 0.978485 | + | 0.206316i | \(0.0661475\pi\) | ||||
−0.978485 | + | 0.206316i | \(0.933852\pi\) | |||||||
\(618\) | 8.32705e10 | − | 4.66280e10i | 0.570870 | − | 0.319664i | ||||
\(619\) | −1.30260e11 | −0.887254 | −0.443627 | − | 0.896211i | \(-0.646309\pi\) | ||||
−0.443627 | + | 0.896211i | \(0.646309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.35054e9 | + | 5.95878e10i | −0.0158052 | + | 0.400674i | ||||
\(622\) | −2.74416e11 | −1.83336 | ||||||||
\(623\) | − | 3.54154e10i | − | 0.235093i | ||||||
\(624\) | 4.88169e10 | + | 8.71795e10i | 0.321982 | + | 0.575011i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 6.84200e10i | − | 0.445539i | ||||||
\(627\) | −2.61945e11 | + | 1.46678e11i | −1.69489 | + | 0.949065i | ||||
\(628\) | 1.68392e11 | 1.08263 | ||||||||
\(629\) | − | 3.47255e11i | − | 2.21843i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.11689e11 | −1.33530 | −0.667652 | − | 0.744473i | \(-0.732701\pi\) | ||||
−0.667652 | + | 0.744473i | \(0.732701\pi\) | |||||||
\(632\) | 4.15338e10i | 0.260335i | ||||||||
\(633\) | −9.16529e10 | − | 1.63678e11i | −0.570863 | − | 1.01947i | ||||
\(634\) | −1.16920e11 | −0.723656 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.42723e10 | − | 4.71890e10i | 0.515058 | − | 0.288411i | ||||
\(637\) | 1.35856e11 | 0.825126 | ||||||||
\(638\) | − | 5.13690e10i | − | 0.310040i | ||||||
\(639\) | −2.29603e11 | − | 1.40734e11i | −1.37713 | − | 0.844102i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.94582e9i | 0.0589126i | 0.999566 | + | 0.0294563i | \(0.00937759\pi\) | ||||
−0.999566 | + | 0.0294563i | \(0.990622\pi\) | |||||||
\(642\) | 1.26413e9 | + | 2.25754e9i | 0.00744134 | + | 0.0132891i | ||||
\(643\) | −4.35787e10 | −0.254935 | −0.127468 | − | 0.991843i | \(-0.540685\pi\) | ||||
−0.127468 | + | 0.991843i | \(0.540685\pi\) | |||||||
\(644\) | − | 3.81950e10i | − | 0.222057i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.59227e11 | 3.21113 | ||||||||
\(647\) | − | 1.00404e11i | − | 0.572973i | −0.958084 | − | 0.286487i | \(-0.907513\pi\) | ||
0.958084 | − | 0.286487i | \(-0.0924874\pi\) | |||||||
\(648\) | −6.53608e10 | + | 3.32858e10i | −0.370695 | + | 0.188781i | ||||
\(649\) | 2.86625e11 | 1.61560 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.91871e10 | + | 8.78405e10i | 0.273859 | + | 0.489070i | ||||
\(652\) | 2.37382e11 | 1.31358 | ||||||||
\(653\) | 9.51805e10i | 0.523474i | 0.965139 | + | 0.261737i | \(0.0842954\pi\) | ||||
−0.965139 | + | 0.261737i | \(0.915705\pi\) | |||||||
\(654\) | 2.91657e11 | − | 1.63316e11i | 1.59427 | − | 0.892723i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.65893e11i | − | 0.895804i | ||||||
\(657\) | 1.61232e11 | − | 2.63046e11i | 0.865348 | − | 1.41179i | ||||
\(658\) | −3.73235e10 | −0.199104 | ||||||||
\(659\) | 2.93955e11i | 1.55862i | 0.626641 | + | 0.779308i | \(0.284429\pi\) | ||||
−0.626641 | + | 0.779308i | \(0.715571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.39956e11 | 1.25697 | 0.628485 | − | 0.777822i | \(-0.283675\pi\) | ||||
0.628485 | + | 0.777822i | \(0.283675\pi\) | |||||||
\(662\) | − | 1.32128e11i | − | 0.687960i | ||||||
\(663\) | −2.50843e11 | + | 1.40462e11i | −1.29822 | + | 0.726949i | ||||
\(664\) | −1.17295e10 | −0.0603402 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.83585e11 | − | 2.35116e11i | −1.94969 | − | 1.19505i | ||||
\(667\) | 1.22134e10 | 0.0617068 | ||||||||
\(668\) | 1.09051e11i | 0.547675i | ||||||||
\(669\) | 1.88324e10 | + | 3.36318e10i | 0.0940160 | + | 0.167898i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.13094e11i | 1.54449i | ||||||||
\(672\) | −1.07655e11 | + | 6.02825e10i | −0.527908 | + | 0.295607i | ||||
\(673\) | 1.21923e11 | 0.594326 | 0.297163 | − | 0.954827i | \(-0.403960\pi\) | ||||
0.297163 | + | 0.954827i | \(0.403960\pi\) | |||||||
\(674\) | − | 5.55161e11i | − | 2.69017i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.96990e9 | −0.0429537 | ||||||||
\(677\) | 3.04202e10i | 0.144813i | 0.997375 | + | 0.0724066i | \(0.0230679\pi\) | ||||
−0.997375 | + | 0.0724066i | \(0.976932\pi\) | |||||||
\(678\) | −3.22262e10 | − | 5.75510e10i | −0.152507 | − | 0.272354i | ||||
\(679\) | 1.56685e10 | 0.0737138 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.13018e11 | − | 1.19281e11i | 0.990440 | − | 0.554605i | ||||
\(682\) | 5.62832e11 | 2.60161 | ||||||||
\(683\) | 2.91193e11i | 1.33813i | 0.743204 | + | 0.669065i | \(0.233305\pi\) | ||||
−0.743204 | + | 0.669065i | \(0.766695\pi\) | |||||||
\(684\) | 2.12258e11 | − | 3.46293e11i | 0.969707 | − | 1.58205i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.62714e11i | 1.18628i | ||||||||
\(687\) | 1.48538e11 | + | 2.65267e11i | 0.666824 | + | 1.19085i | ||||
\(688\) | −3.67333e10 | −0.163948 | ||||||||
\(689\) | − | 1.06018e11i | − | 0.470438i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.48484e11 | −1.52852 | −0.764260 | − | 0.644908i | \(-0.776896\pi\) | ||||
−0.764260 | + | 0.644908i | \(0.776896\pi\) | |||||||
\(692\) | − | 4.31642e11i | − | 1.88235i | ||||||
\(693\) | 1.13996e11 | + | 6.98731e10i | 0.494261 | + | 0.302954i | ||||
\(694\) | −5.49822e11 | −2.37020 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.33945e9 | + | 1.31071e10i | 0.0312771 | + | 0.0558562i | ||||
\(697\) | 4.77327e11 | 2.02248 | ||||||||
\(698\) | 5.44581e11i | 2.29425i | ||||||||
\(699\) | −2.56626e11 | + | 1.43700e11i | −1.07496 | + | 0.601932i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.23548e11i | 0.511640i | 0.966724 | + | 0.255820i | \(0.0823455\pi\) | ||||
−0.966724 | + | 0.255820i | \(0.917655\pi\) | |||||||
\(702\) | −1.46816e10 | + | 3.72190e11i | −0.0604542 | + | 1.53256i | ||||
\(703\) | 5.38516e11 | 2.20484 | ||||||||
\(704\) | 4.77151e11i | 1.94252i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.06817e11 | 0.832467 | ||||||||
\(707\) | − | 1.57977e11i | − | 0.632289i | ||||||
\(708\) | −3.38346e11 | + | 1.89460e11i | −1.34657 | + | 0.754023i | ||||
\(709\) | 3.17753e11 | 1.25749 | 0.628744 | − | 0.777612i | \(-0.283569\pi\) | ||||
0.628744 | + | 0.777612i | \(0.283569\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.35758e10 | − | 1.36351e11i | 0.327041 | − | 0.533557i | ||||
\(712\) | 5.79006e10 | 0.225301 | ||||||||
\(713\) | 1.33818e11i | 0.517793i | ||||||||
\(714\) | −1.21685e11 | − | 2.17310e11i | −0.468213 | − | 0.836156i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 3.58560e10i | − | 0.136430i | ||||||
\(717\) | −3.31997e11 | + | 1.85905e11i | −1.25620 | + | 0.703419i | ||||
\(718\) | 8.33539e10 | 0.313638 | ||||||||
\(719\) | − | 2.47720e11i | − | 0.926926i | −0.886116 | − | 0.463463i | \(-0.846607\pi\) | ||
0.886116 | − | 0.463463i | \(-0.153393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.08752e10 | 0.188263 | ||||||||
\(722\) | 4.57307e11i | 1.68290i | ||||||||
\(723\) | −1.37238e11 | − | 2.45085e11i | −0.502250 | − | 0.896942i | ||||
\(724\) | 1.19231e11 | 0.433944 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.86543e11 | − | 1.60452e11i | 1.03144 | − | 0.577562i | ||||
\(727\) | −2.06831e11 | −0.740420 | −0.370210 | − | 0.928948i | \(-0.620714\pi\) | ||||
−0.370210 | + | 0.928948i | \(0.620714\pi\) | |||||||
\(728\) | − | 5.15672e10i | − | 0.183590i | ||||||
\(729\) | 2.81552e11 | + | 2.22472e10i | 0.996893 | + | 0.0787707i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.05693e11i | − | 0.370151i | ||||||
\(732\) | −2.06956e11 | − | 3.69592e11i | −0.720832 | − | 1.28730i | ||||
\(733\) | 2.72921e11 | 0.945412 | 0.472706 | − | 0.881220i | \(-0.343277\pi\) | ||||
0.472706 | + | 0.881220i | \(0.343277\pi\) | |||||||
\(734\) | 1.81654e11i | 0.625835i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.64004e11 | −0.558912 | ||||||||
\(737\) | − | 4.19190e11i | − | 1.42083i | ||||||
\(738\) | 3.23185e11 | − | 5.27267e11i | 1.08950 | − | 1.77748i | ||||
\(739\) | 1.03105e10 | 0.0345702 | 0.0172851 | − | 0.999851i | \(-0.494498\pi\) | ||||
0.0172851 | + | 0.999851i | \(0.494498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.17826e11 | − | 3.89003e11i | −0.722497 | − | 1.29027i | ||||
\(742\) | 9.18454e10 | 0.303000 | ||||||||
\(743\) | − | 3.12920e11i | − | 1.02678i | −0.858154 | − | 0.513392i | \(-0.828389\pi\) | ||
0.858154 | − | 0.513392i | \(-0.171611\pi\) | |||||||
\(744\) | −1.43610e11 | + | 8.04159e10i | −0.468699 | + | 0.262452i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.88549e11i | 1.25456i | ||||||||
\(747\) | 3.85067e10 | + | 2.36025e10i | 0.123667 | + | 0.0758010i | ||||
\(748\) | −7.80561e11 | −2.49345 | ||||||||
\(749\) | 1.37927e9i | 0.00438251i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.76676e11 | 0.869783 | 0.434892 | − | 0.900483i | \(-0.356787\pi\) | ||||
0.434892 | + | 0.900483i | \(0.356787\pi\) | |||||||
\(752\) | 6.30275e10i | 0.197087i | ||||||||
\(753\) | −1.08681e11 | + | 6.08566e10i | −0.338043 | + | 0.189290i | ||||
\(754\) | 7.62858e10 | 0.236025 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.80753e11 | − | 7.13009e9i | −0.553347 | − | 0.0218277i | ||||
\(757\) | −1.25846e11 | −0.383226 | −0.191613 | − | 0.981471i | \(-0.561372\pi\) | ||||
−0.191613 | + | 0.981471i | \(0.561372\pi\) | |||||||
\(758\) | − | 1.75428e11i | − | 0.531402i | ||||||
\(759\) | 8.68317e10 | + | 1.55068e11i | 0.261644 | + | 0.467256i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.11284e11i | − | 1.22632i | −0.789960 | − | 0.613159i | \(-0.789899\pi\) | ||
0.789960 | − | 0.613159i | \(-0.210101\pi\) | |||||||
\(762\) | 1.60212e11 | − | 8.97120e10i | 0.475198 | − | 0.266091i | ||||
\(763\) | 1.78192e11 | 0.525762 | ||||||||
\(764\) | − | 7.00435e11i | − | 2.05586i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.28622e10 | 0.269727 | ||||||||
\(767\) | 4.25654e11i | 1.22991i | ||||||||
\(768\) | 4.20018e10 | + | 7.50087e10i | 0.120732 | + | 0.215609i | ||||
\(769\) | 4.51287e10 | 0.129047 | 0.0645235 | − | 0.997916i | \(-0.479447\pi\) | ||||
0.0645235 | + | 0.997916i | \(0.479447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.90991e11 | + | 1.06947e11i | −0.540498 | + | 0.302657i | ||||
\(772\) | −7.72298e11 | −2.17428 | ||||||||
\(773\) | 3.86868e11i | 1.08354i | 0.840527 | + | 0.541770i | \(0.182245\pi\) | ||||
−0.840527 | + | 0.541770i | \(0.817755\pi\) | |||||||
\(774\) | −1.16751e11 | − | 7.15621e10i | −0.325311 | − | 0.199397i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.56164e10i | 0.0706435i | ||||||||
\(777\) | −1.17178e11 | − | 2.09263e11i | −0.321487 | − | 0.574126i | ||||
\(778\) | −3.97252e11 | −1.08430 | ||||||||
\(779\) | 7.40231e11i | 2.01010i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.02585e11 | −2.15718 | ||||||||
\(782\) | − | 3.31055e11i | − | 0.885264i | ||||||
\(783\) | 2.27994e9 | − | 5.77982e10i | 0.00606565 | − | 0.153768i | ||||
\(784\) | 1.98748e11 | 0.526064 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.59671e11 | + | 4.63733e11i | 0.680353 | + | 1.21501i | ||||
\(787\) | −4.31897e11 | −1.12585 | −0.562926 | − | 0.826508i | \(-0.690324\pi\) | ||||
−0.562926 | + | 0.826508i | \(0.690324\pi\) | |||||||
\(788\) | − | 7.74973e11i | − | 2.00993i | ||||||
\(789\) | 2.28338e11 | − | 1.27860e11i | 0.589210 | − | 0.329933i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.51615e10i | − | 0.0898177i | ||||||
\(792\) | −1.14235e11 | + | 1.86372e11i | −0.290335 | + | 0.473673i | ||||
\(793\) | −4.64962e11 | −1.17578 | ||||||||
\(794\) | 8.62519e11i | 2.17014i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.72890e11 | 0.679728 | ||||||||
\(797\) | − | 1.89233e11i | − | 0.468991i | −0.972117 | − | 0.234495i | \(-0.924656\pi\) | ||
0.972117 | − | 0.234495i | \(-0.0753438\pi\) | |||||||
\(798\) | 3.37001e11 | − | 1.88707e11i | 0.831036 | − | 0.465346i | ||||
\(799\) | −1.81350e11 | −0.444970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.90082e11 | − | 1.16510e11i | −0.461754 | − | 0.283030i | ||||
\(802\) | −1.84712e11 | −0.446477 | ||||||||
\(803\) | − | 9.19486e11i | − | 2.21148i | ||||||
\(804\) | 2.77086e11 | + | 4.94833e11i | 0.663117 | + | 1.18423i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.35837e11i | 1.98053i | ||||||||
\(807\) | 6.23781e10 | − | 3.49291e10i | 0.147075 | − | 0.0823557i | ||||
\(808\) | 2.58276e11 | 0.605953 | ||||||||
\(809\) | 8.16650e10i | 0.190652i | 0.995446 | + | 0.0953261i | \(0.0303894\pi\) | ||||
−0.995446 | + | 0.0953261i | \(0.969611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.05160e11 | −0.474252 | −0.237126 | − | 0.971479i | \(-0.576205\pi\) | ||||
−0.237126 | + | 0.971479i | \(0.576205\pi\) | |||||||
\(812\) | 3.70479e10i | 0.0852197i | ||||||||
\(813\) | 3.44195e11 | + | 6.14679e11i | 0.787847 | + | 1.40697i | ||||
\(814\) | −1.34084e12 | −3.05406 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.66967e11 | + | 2.05486e11i | −0.827688 | + | 0.463471i | ||||
\(817\) | 1.63908e11 | 0.367884 | ||||||||
\(818\) | 4.57366e11i | 1.02153i | ||||||||
\(819\) | −1.03765e11 | + | 1.69290e11i | −0.230631 | + | 0.376267i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.41950e10i | − | 0.0312437i | −0.999878 | − | 0.0156218i | \(-0.995027\pi\) | ||
0.999878 | − | 0.0156218i | \(-0.00497278\pi\) | |||||||
\(822\) | 2.08894e11 | + | 3.73052e11i | 0.457549 | + | 0.817113i | ||||
\(823\) | 2.98009e11 | 0.649576 | 0.324788 | − | 0.945787i | \(-0.394707\pi\) | ||||
0.324788 | + | 0.945787i | \(0.394707\pi\) | |||||||
\(824\) | 8.31759e10i | 0.180422i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.68752e11 | −0.792163 | ||||||||
\(827\) | 3.12011e11i | 0.667034i | 0.942744 | + | 0.333517i | \(0.108235\pi\) | ||||
−0.942744 | + | 0.333517i | \(0.891765\pi\) | |||||||
\(828\) | −2.05001e11 | − | 1.25654e11i | −0.436149 | − | 0.267335i | ||||
\(829\) | 2.42950e11 | 0.514397 | 0.257198 | − | 0.966359i | \(-0.417201\pi\) | ||||
0.257198 | + | 0.966359i | \(0.417201\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.39443e11 | + | 6.06193e11i | 0.711808 | + | 1.27118i | ||||
\(832\) | −7.08596e11 | −1.47879 | ||||||||
\(833\) | 5.71862e11i | 1.18771i | ||||||||
\(834\) | −8.40081e11 | + | 4.70410e11i | −1.73643 | + | 0.972327i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 1.21048e12i | − | 2.47818i | ||||||
\(837\) | 6.33274e11 | + | 2.49806e10i | 1.29030 | + | 0.0508980i | ||||
\(838\) | 2.08262e11 | 0.422312 | ||||||||
\(839\) | 1.16205e11i | 0.234519i | 0.993101 | + | 0.117259i | \(0.0374109\pi\) | ||||
−0.993101 | + | 0.117259i | \(0.962589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.88400e11 | 0.976318 | ||||||||
\(842\) | 8.16963e11i | 1.62538i | ||||||||
\(843\) | 2.00928e11 | − | 1.12512e11i | 0.397861 | − | 0.222786i | ||||
\(844\) | 7.56376e11 | 1.49062 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.22787e11 | + | 2.00323e11i | −0.239702 | + | 0.391066i | ||||
\(847\) | 1.75067e11 | 0.340150 | ||||||||
\(848\) | − | 1.55097e11i | − | 0.299931i | ||||||
\(849\) | −3.93377e11 | − | 7.02510e11i | −0.757143 | − | 1.35214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.18794e11i | − | 0.607844i | ||||||
\(852\) | 9.47412e11 | − | 5.30511e11i | 1.79796 | − | 1.00678i | ||||
\(853\) | 2.30678e11 | 0.435723 | 0.217861 | − | 0.975980i | \(-0.430092\pi\) | ||||
0.217861 | + | 0.975980i | \(0.430092\pi\) | |||||||
\(854\) | − | 4.02806e11i | − | 0.757293i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.25497e9 | −0.00419997 | ||||||||
\(857\) | 6.99039e11i | 1.29592i | 0.761674 | + | 0.647960i | \(0.224378\pi\) | ||||
−0.761674 | + | 0.647960i | \(0.775622\pi\) | |||||||
\(858\) | 5.42357e11 | + | 9.68567e11i | 1.00078 | + | 1.78723i | ||||
\(859\) | 9.39004e10 | 0.172463 | 0.0862313 | − | 0.996275i | \(-0.472518\pi\) | ||||
0.0862313 | + | 0.996275i | \(0.472518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.87647e11 | − | 1.61070e11i | 0.523416 | − | 0.293091i | ||||
\(862\) | 7.19561e11 | 1.30328 | ||||||||
\(863\) | − | 7.27490e11i | − | 1.31155i | −0.754958 | − | 0.655773i | \(-0.772343\pi\) | ||
0.754958 | − | 0.655773i | \(-0.227657\pi\) | |||||||
\(864\) | −3.06156e10 | + | 7.76126e11i | −0.0549399 | + | 1.39276i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 6.13481e10i | − | 0.109076i | ||||||
\(867\) | −3.15187e11 | − | 5.62875e11i | −0.557817 | − | 0.996175i | ||||
\(868\) | −4.05921e11 | −0.715094 | ||||||||
\(869\) | − | 4.76621e11i | − | 0.835783i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.22520e11 | 1.08164 | ||||||||
\(872\) | 2.91325e11i | 0.503863i | ||||||||
\(873\) | 5.15463e10 | − | 8.40963e10i | 0.0887443 | − | 0.144784i | ||||
\(874\) | 5.13394e11 | 0.879842 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.07783e11 | + | 1.08541e12i | 1.03212 | + | 1.84322i | ||||
\(877\) | 1.49532e11 | 0.252775 | 0.126388 | − | 0.991981i | \(-0.459662\pi\) | ||||
0.126388 | + | 0.991981i | \(0.459662\pi\) | |||||||
\(878\) | 2.68549e11i | 0.451904i | ||||||||
\(879\) | 3.36637e11 | − | 1.88503e11i | 0.563906 | − | 0.315764i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9.01607e11i | − | 1.49663i | −0.663345 | − | 0.748314i | \(-0.730864\pi\) | ||
0.663345 | − | 0.748314i | \(-0.269136\pi\) | |||||||
\(882\) | 6.31691e11 | + | 3.87192e11i | 1.04383 | + | 0.639811i | ||||
\(883\) | −7.05614e11 | −1.16071 | −0.580356 | − | 0.814363i | \(-0.697086\pi\) | ||||
−0.580356 | + | 0.814363i | \(0.697086\pi\) | |||||||
\(884\) | − | 1.15918e12i | − | 1.89819i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.26299e11 | −1.17864 | ||||||||
\(887\) | 1.05583e12i | 1.70568i | 0.522170 | + | 0.852842i | \(0.325123\pi\) | ||||
−0.522170 | + | 0.852842i | \(0.674877\pi\) | |||||||
\(888\) | 3.42123e11 | − | 1.91575e11i | 0.550213 | − | 0.308096i | ||||
\(889\) | 9.78836e10 | 0.156712 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.50047e11 | − | 3.81971e11i | 1.19008 | − | 0.606066i | ||||
\(892\) | −1.55417e11 | −0.245492 | ||||||||
\(893\) | − | 2.81234e11i | − | 0.442245i | ||||||
\(894\) | 2.27534e9 | + | 4.06341e9i | 0.00356202 | + | 0.00636122i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 2.23916e11i | − | 0.347419i | ||||||
\(897\) | −2.30285e11 | + | 1.28950e11i | −0.355709 | + | 0.199182i | ||||
\(898\) | 5.94873e11 | 0.914785 | ||||||||
\(899\) | − | 1.29799e11i | − | 0.198716i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.46265e11 | 0.677163 | ||||||||
\(902\) | − | 1.84308e12i | − | 2.78431i | ||||||
\(903\) | −3.56654e10 | − | 6.36930e10i | −0.0536410 | − | 0.0957945i | ||||
\(904\) | 5.74856e10 | 0.0860766 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.01697e11 | − | 2.80930e11i | 0.744610 | − | 0.416951i | ||||
\(907\) | −3.67842e11 | −0.543541 | −0.271771 | − | 0.962362i | \(-0.587609\pi\) | ||||
−0.271771 | + | 0.962362i | \(0.587609\pi\) | |||||||
\(908\) | 9.84382e11i | 1.44817i | ||||||||
\(909\) | −8.47895e11 | − | 5.19712e11i | −1.24190 | − | 0.761215i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.64432e11i | 1.40023i | 0.714032 | + | 0.700113i | \(0.246867\pi\) | ||||
−0.714032 | + | 0.700113i | \(0.753133\pi\) | |||||||
\(912\) | −3.18665e11 | − | 5.69086e11i | −0.460633 | − | 0.822619i | ||||
\(913\) | 1.34602e11 | 0.193717 | ||||||||
\(914\) | − | 2.85821e11i | − | 0.409553i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.22583e12 | −1.74120 | ||||||||
\(917\) | 2.83324e11i | 0.400688i | ||||||||
\(918\) | −1.56667e12 | − | 6.17999e10i | −2.20601 | − | 0.0870196i | ||||
\(919\) | −1.03446e12 | −1.45028 | −0.725138 | − | 0.688603i | \(-0.758224\pi\) | ||||
−0.725138 | + | 0.688603i | \(0.758224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.29111e11 | + | 2.30573e11i | 0.179443 | + | 0.320457i | ||||
\(922\) | −4.91563e11 | −0.680229 | ||||||||
\(923\) | − | 1.19188e12i | − | 1.64220i | ||||||
\(924\) | −4.70381e11 | + | 2.63394e11i | −0.645301 | + | 0.361342i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.36768e11i | 1.27405i | ||||||||
\(927\) | 1.67369e11 | − | 2.73058e11i | 0.226651 | − | 0.369774i | ||||
\(928\) | 1.59079e11 | 0.214496 | ||||||||
\(929\) | − | 1.47659e11i | − | 0.198242i | −0.995075 | − | 0.0991212i | \(-0.968397\pi\) | ||
0.995075 | − | 0.0991212i | \(-0.0316031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.86833e11 | −1.18044 | ||||||||
\(932\) | − | 1.18590e12i | − | 1.57175i | ||||||
\(933\) | −8.03502e11 | + | 4.49928e11i | −1.06038 | + | 0.593767i | ||||
\(934\) | 1.61131e12 | 2.11734 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.76772e11 | − | 1.69646e11i | −0.360595 | − | 0.221024i | ||||
\(937\) | −3.27745e11 | −0.425185 | −0.212593 | − | 0.977141i | \(-0.568191\pi\) | ||||
−0.212593 | + | 0.977141i | \(0.568191\pi\) | |||||||
\(938\) | 5.39301e11i | 0.696659i | ||||||||
\(939\) | −1.12180e11 | − | 2.00337e11i | −0.144296 | − | 0.257691i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.29986e11i | − | 0.420860i | −0.977609 | − | 0.210430i | \(-0.932514\pi\) | ||
0.977609 | − | 0.210430i | \(-0.0674864\pi\) | |||||||
\(942\) | 8.79542e11 | − | 4.92507e11i | 1.11700 | − | 0.625473i | ||||
\(943\) | 4.38207e11 | 0.554156 | ||||||||
\(944\) | 6.22704e11i | 0.784140i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.08109e11 | −0.509579 | ||||||||
\(947\) | 2.28185e8i | 0.000283718i | 1.00000 | 0.000141859i | \(4.51551e-5\pi\) | |||||
−1.00000 | 0.000141859i | \(0.999955\pi\) | ||||||||
\(948\) | 3.15048e11 | + | 5.62627e11i | 0.390070 | + | 0.696606i | ||||
\(949\) | 1.36549e12 | 1.68354 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.42347e11 | + | 1.91700e11i | −0.418548 | + | 0.234369i | ||||
\(952\) | 2.17063e11 | 0.264264 | ||||||||
\(953\) | − | 1.61330e11i | − | 0.195588i | −0.995207 | − | 0.0977942i | \(-0.968821\pi\) | ||
0.995207 | − | 0.0977942i | \(-0.0311787\pi\) | |||||||
\(954\) | 3.02153e11 | − | 4.92954e11i | 0.364782 | − | 0.595131i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 1.53420e12i | − | 1.83675i | ||||||
\(957\) | −8.42238e10 | − | 1.50411e11i | −0.100412 | − | 0.179321i | ||||
\(958\) | −2.44653e12 | −2.90462 | ||||||||
\(959\) | 2.27921e11i | 0.269470i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.69271e11 | 0.667460 | ||||||||
\(962\) | − | 1.99122e12i | − | 2.32497i | ||||||
\(963\) | 7.40286e9 | + | 4.53754e9i | 0.00860784 | + | 0.00527612i | ||||
\(964\) | 1.13257e12 | 1.31146 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.11712e11 | − | 1.99500e11i | −0.128289 | − | 0.229105i | ||||
\(967\) | −1.49948e12 | −1.71489 | −0.857444 | − | 0.514577i | \(-0.827949\pi\) | ||||
−0.857444 | + | 0.514577i | \(0.827949\pi\) | |||||||
\(968\) | 2.86217e11i | 0.325982i | ||||||||
\(969\) | 1.63744e12 | − | 9.16900e11i | 1.85725 | − | 1.03998i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 3.35149e11i | − | 0.377017i | −0.982072 | − | 0.188509i | \(-0.939635\pi\) | ||
0.982072 | − | 0.188509i | \(-0.0603654\pi\) | |||||||
\(972\) | −6.32909e11 | + | 9.46682e11i | −0.709049 | + | 1.06057i | ||||
\(973\) | −5.13258e11 | −0.572644 | ||||||||
\(974\) | − | 2.61904e11i | − | 0.291009i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.80209e11 | −0.749623 | ||||||||
\(977\) | − | 8.22116e11i | − | 0.902308i | −0.892446 | − | 0.451154i | \(-0.851012\pi\) | ||
0.892446 | − | 0.451154i | \(-0.148988\pi\) | |||||||
\(978\) | 1.23989e12 | − | 6.94287e11i | 1.35528 | − | 0.758898i | ||||
\(979\) | −6.64438e11 | −0.723309 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.86215e11 | − | 9.56392e11i | 0.632967 | − | 1.03267i | ||||
\(982\) | 2.48545e11 | 0.267276 | ||||||||
\(983\) | 1.23984e12i | 1.32786i | 0.747795 | + | 0.663930i | \(0.231113\pi\) | ||||
−0.747795 | + | 0.663930i | \(0.768887\pi\) | |||||||
\(984\) | 2.63334e11 | + | 4.70274e11i | 0.280883 | + | 0.501615i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.21112e11i | 0.339742i | ||||||||
\(987\) | −1.09285e11 | + | 6.11951e10i | −0.115158 | + | 0.0644834i | ||||
\(988\) | 1.79763e12 | 1.88657 | ||||||||
\(989\) | − | 9.70311e10i | − | 0.101420i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.44437e12 | 1.49756 | 0.748782 | − | 0.662817i | \(-0.230639\pi\) | ||||
0.748782 | + | 0.662817i | \(0.230639\pi\) | |||||||
\(992\) | 1.74297e12i | 1.79988i | ||||||||
\(993\) | −2.16635e11 | − | 3.86878e11i | −0.222809 | − | 0.397902i | ||||
\(994\) | 1.03255e12 | 1.05771 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.58890e11 | + | 8.89721e10i | −0.161458 | + | 0.0904100i | ||||
\(997\) | 4.69939e11 | 0.475621 | 0.237810 | − | 0.971312i | \(-0.423570\pi\) | ||||
0.237810 | + | 0.971312i | \(0.423570\pi\) | |||||||
\(998\) | 1.63310e12i | 1.64623i | ||||||||
\(999\) | −1.50865e12 | − | 5.95112e10i | −1.51470 | − | 0.0597498i |
(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 | 75.9.c.e.26.9 | yes | 10 | |
3.2 | odd | 2 | inner | 75.9.c.e.26.2 | ✓ | 10 | |
5.2 | odd | 4 | 75.9.d.d.74.3 | 20 | |||
5.3 | odd | 4 | 75.9.d.d.74.18 | 20 | |||
5.4 | even | 2 | 75.9.c.f.26.2 | yes | 10 | ||
15.2 | even | 4 | 75.9.d.d.74.17 | 20 | |||
15.8 | even | 4 | 75.9.d.d.74.4 | 20 | |||
15.14 | odd | 2 | 75.9.c.f.26.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.c.e.26.2 | ✓ | 10 | 3.2 | odd | 2 | inner | |
75.9.c.e.26.9 | yes | 10 | 1.1 | even | 1 | trivial | |
75.9.c.f.26.2 | yes | 10 | 5.4 | even | 2 | ||
75.9.c.f.26.9 | yes | 10 | 15.14 | odd | 2 | ||
75.9.d.d.74.3 | 20 | 5.2 | odd | 4 | |||
75.9.d.d.74.4 | 20 | 15.8 | even | 4 | |||
75.9.d.d.74.17 | 20 | 15.2 | even | 4 | |||
75.9.d.d.74.18 | 20 | 5.3 | odd | 4 |