Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(74,75)]
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, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not 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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 3278 x^{18} + 4245491 x^{16} + 2854629536 x^{14} + 1117319469691 x^{12} + 266849787342054 x^{10} + \cdots + 89\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{22}\cdot 5^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.4 | ||
Root | \(12.5890i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.9.d.d.74.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −24.1370 | −1.50856 | −0.754281 | − | 0.656552i | \(-0.772014\pi\) | ||||
−0.754281 | + | 0.656552i | \(0.772014\pi\) | |||||||
\(3\) | 70.6742 | + | 39.5746i | 0.872521 | + | 0.488576i | ||||
\(4\) | 326.594 | 1.27576 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1705.86 | − | 955.212i | −1.31625 | − | 0.737047i | ||||
\(7\) | 1042.22i | 0.434077i | 0.976163 | + | 0.217039i | \(0.0696398\pi\) | ||||
−0.976163 | + | 0.217039i | \(0.930360\pi\) | |||||||
\(8\) | −1703.92 | −0.415997 | ||||||||
\(9\) | 3428.70 | + | 5593.81i | 0.522587 | + | 0.852586i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 19553.4i | − | 1.33552i | −0.744376 | − | 0.667761i | \(-0.767253\pi\) | ||
0.744376 | − | 0.667761i | \(-0.232747\pi\) | |||||||
\(12\) | 23081.8 | + | 12924.8i | 1.11313 | + | 0.623304i | ||||
\(13\) | − | 29037.8i | − | 1.01670i | −0.861152 | − | 0.508348i | \(-0.830257\pi\) | ||
0.861152 | − | 0.508348i | \(-0.169743\pi\) | |||||||
\(14\) | − | 25156.0i | − | 0.654832i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −42480.5 | −0.648200 | ||||||||
\(17\) | 122230. | 1.46346 | 0.731731 | − | 0.681594i | \(-0.238713\pi\) | ||||
0.731731 | + | 0.681594i | \(0.238713\pi\) | |||||||
\(18\) | −82758.4 | − | 135018.i | −0.788355 | − | 1.28618i | ||||
\(19\) | −189552. | −1.45450 | −0.727250 | − | 0.686373i | \(-0.759202\pi\) | ||||
−0.727250 | + | 0.686373i | \(0.759202\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −41245.5 | + | 73658.1i | −0.212080 | + | 0.378742i | ||||
\(22\) | 471959.i | 2.01472i | ||||||||
\(23\) | −112212. | −0.400985 | −0.200493 | − | 0.979695i | \(-0.564254\pi\) | ||||
−0.200493 | + | 0.979695i | \(0.564254\pi\) | |||||||
\(24\) | −120424. | − | 67432.2i | −0.362966 | − | 0.203246i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 700886.i | 1.53375i | ||||||||
\(27\) | 20947.3 | + | 531028.i | 0.0394160 | + | 0.999223i | ||||
\(28\) | 340383.i | 0.553777i | ||||||||
\(29\) | 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 | \(0.723414\pi\) | |||||||
\(32\) | 1.46155e6 | 1.39385 | ||||||||
\(33\) | 773817. | − | 1.38192e6i | 0.652503 | − | 1.16527i | ||||
\(34\) | −2.95026e6 | −2.20772 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.11979e6 | + | 1.82691e6i | 0.666695 | + | 1.08769i | ||||
\(37\) | − | 2.84100e6i | − | 1.51588i | −0.652326 | − | 0.757939i | \(-0.726207\pi\) | ||
0.652326 | − | 0.757939i | \(-0.273793\pi\) | |||||||
\(38\) | 4.57521e6 | 2.19420 | ||||||||
\(39\) | 1.14916e6 | − | 2.05223e6i | 0.496733 | − | 0.887088i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.90516e6i | − | 1.38199i | −0.722861 | − | 0.690993i | \(-0.757173\pi\) | ||
0.722861 | − | 0.690993i | \(-0.242827\pi\) | |||||||
\(42\) | 995541. | − | 1.77788e6i | 0.319935 | − | 0.571355i | ||||
\(43\) | 864712.i | 0.252928i | 0.991971 | + | 0.126464i | \(0.0403629\pi\) | ||||
−0.991971 | + | 0.126464i | \(0.959637\pi\) | |||||||
\(44\) | − | 6.38601e6i | − | 1.70380i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.70846e6 | 0.604911 | ||||||||
\(47\) | 1.48368e6 | 0.304053 | 0.152026 | − | 0.988376i | \(-0.451420\pi\) | ||||
0.152026 | + | 0.988376i | \(0.451420\pi\) | |||||||
\(48\) | −3.00227e6 | − | 1.68115e6i | −0.565569 | − | 0.316695i | ||||
\(49\) | 4.67858e6 | 0.811577 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.63850e6 | + | 4.83720e6i | 1.27690 | + | 0.715012i | ||||
\(52\) | − | 9.48358e6i | − | 1.29706i | ||||||
\(53\) | 3.65103e6 | 0.462713 | 0.231357 | − | 0.972869i | \(-0.425684\pi\) | ||||
0.231357 | + | 0.972869i | \(0.425684\pi\) | |||||||
\(54\) | −505604. | − | 1.28174e7i | −0.0594615 | − | 1.50739i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.77586e6i | − | 0.180575i | ||||||
\(57\) | −1.33964e7 | − | 7.50144e6i | −1.26908 | − | 0.710633i | ||||
\(58\) | − | 2.62712e6i | − | 0.232149i | ||||||
\(59\) | − | 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 | \(0.303742\pi\) | |||||||
\(62\) | 2.87844e7 | 1.94801 | ||||||||
\(63\) | −5.82998e6 | + | 3.57345e6i | −0.370088 | + | 0.226843i | ||||
\(64\) | −2.44025e7 | −1.45450 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.86776e7 | + | 3.33554e7i | −0.984341 | + | 1.75788i | ||||
\(67\) | 2.14382e7i | 1.06387i | 0.846784 | + | 0.531937i | \(0.178536\pi\) | ||||
−0.846784 | + | 0.531937i | \(0.821464\pi\) | |||||||
\(68\) | 3.99195e7 | 1.86702 | ||||||||
\(69\) | −7.93050e6 | − | 4.44075e6i | −0.349868 | − | 0.195912i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.10459e7i | − | 1.61524i | −0.589706 | − | 0.807618i | \(-0.700756\pi\) | ||
0.589706 | − | 0.807618i | \(-0.299244\pi\) | |||||||
\(72\) | −5.84224e6 | − | 9.53144e6i | −0.217395 | − | 0.354673i | ||||
\(73\) | − | 4.70244e7i | − | 1.65589i | −0.560808 | − | 0.827946i | \(-0.689509\pi\) | ||
0.560808 | − | 0.827946i | \(-0.310491\pi\) | |||||||
\(74\) | 6.85731e7i | 2.28679i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.19065e7 | −1.85559 | ||||||||
\(77\) | 2.03789e7 | 0.579719 | ||||||||
\(78\) | −2.77373e7 | + | 4.95346e7i | −0.749352 | + | 1.33823i | ||||
\(79\) | 2.43754e7 | 0.625811 | 0.312905 | − | 0.949784i | \(-0.398698\pi\) | ||||
0.312905 | + | 0.949784i | \(0.398698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.95348e7 | + | 3.83590e7i | −0.453805 | + | 0.891101i | ||||
\(82\) | 9.42589e7i | 2.08481i | ||||||||
\(83\) | −6.88381e6 | −0.145050 | −0.0725248 | − | 0.997367i | \(-0.523106\pi\) | ||||
−0.0725248 | + | 0.997367i | \(0.523106\pi\) | |||||||
\(84\) | −1.34705e7 | + | 2.40563e7i | −0.270562 | + | 0.483183i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 2.08715e7i | − | 0.381558i | ||||||
\(87\) | −4.30738e6 | + | 7.69233e6i | −0.0751859 | + | 0.134271i | ||||
\(88\) | 3.33174e7i | 0.555573i | ||||||||
\(89\) | 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 | ||||||||
\(92\) | −3.66478e7 | −0.511560 | ||||||||
\(93\) | −8.42822e7 | − | 4.71945e7i | −1.12669 | − | 0.630899i | ||||
\(94\) | −3.58116e7 | −0.458682 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.03294e8 | + | 5.78405e7i | 1.21616 | + | 0.681000i | ||||
\(97\) | 1.50338e7i | 0.169817i | 0.996389 | + | 0.0849086i | \(0.0270598\pi\) | ||||
−0.996389 | + | 0.0849086i | \(0.972940\pi\) | |||||||
\(98\) | −1.12927e8 | −1.22431 | ||||||||
\(99\) | 1.09378e8 | − | 6.70425e7i | 1.13865 | − | 0.697927i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.51577e8i | − | 1.45663i | −0.685244 | − | 0.728314i | \(-0.740304\pi\) | ||
0.685244 | − | 0.728314i | \(-0.259696\pi\) | |||||||
\(102\) | −2.08507e8 | − | 1.16755e8i | −1.92628 | − | 1.07864i | ||||
\(103\) | − | 4.88143e7i | − | 0.433709i | −0.976204 | − | 0.216854i | \(-0.930420\pi\) | ||
0.976204 | − | 0.216854i | \(-0.0695797\pi\) | |||||||
\(104\) | 4.94783e7i | 0.422942i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.81248e7 | −0.698031 | ||||||||
\(107\) | 1.32340e6 | 0.0100962 | 0.00504808 | − | 0.999987i | \(-0.498393\pi\) | ||||
0.00504808 | + | 0.999987i | \(0.498393\pi\) | |||||||
\(108\) | 6.84125e6 | + | 1.73431e8i | 0.0502853 | + | 1.27477i | ||||
\(109\) | 1.70973e8 | 1.21122 | 0.605608 | − | 0.795763i | \(-0.292930\pi\) | ||||
0.605608 | + | 0.795763i | \(0.292930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.12432e8 | − | 2.00785e8i | 0.740621 | − | 1.32264i | ||||
\(112\) | − | 4.42740e7i | − | 0.281369i | ||||||
\(113\) | 3.37372e7 | 0.206916 | 0.103458 | − | 0.994634i | \(-0.467009\pi\) | ||||
0.103458 | + | 0.994634i | \(0.467009\pi\) | |||||||
\(114\) | 3.23349e8 | + | 1.81062e8i | 1.91449 | + | 1.07203i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.55471e7i | 0.196324i | ||||||||
\(117\) | 1.62432e8 | − | 9.95619e7i | 0.866820 | − | 0.531312i | ||||
\(118\) | 3.53814e8i | 1.82493i | ||||||||
\(119\) | 1.27390e8i | 0.635256i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.67975e8 | −0.783617 | ||||||||
\(122\) | −3.86488e8 | −1.74460 | ||||||||
\(123\) | 1.54545e8 | − | 2.75995e8i | 0.675205 | − | 1.20581i | ||||
\(124\) | −3.89478e8 | −1.64739 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.40718e8 | − | 8.62524e7i | 0.558301 | − | 0.342207i | ||||
\(127\) | 9.39184e7i | 0.361024i | 0.983573 | + | 0.180512i | \(0.0577754\pi\) | ||||
−0.983573 | + | 0.180512i | \(0.942225\pi\) | |||||||
\(128\) | 2.14845e8 | 0.800361 | ||||||||
\(129\) | −3.42206e7 | + | 6.11128e7i | −0.123575 | + | 0.220685i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.71847e8i | 0.923079i | 0.887120 | + | 0.461540i | \(0.152703\pi\) | ||||
−0.887120 | + | 0.461540i | \(0.847297\pi\) | |||||||
\(132\) | 2.52724e8 | − | 4.51326e8i | 0.832436 | − | 1.48660i | ||||
\(133\) | − | 1.97555e8i | − | 0.631365i | ||||||
\(134\) | − | 5.17455e8i | − | 1.60492i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.08270e8 | −0.608796 | ||||||||
\(137\) | 2.18688e8 | 0.620788 | 0.310394 | − | 0.950608i | \(-0.399539\pi\) | ||||
0.310394 | + | 0.950608i | \(0.399539\pi\) | |||||||
\(138\) | 1.91418e8 | + | 1.07186e8i | 0.527798 | + | 0.295545i | ||||
\(139\) | −4.92467e8 | −1.31922 | −0.659611 | − | 0.751608i | \(-0.729279\pi\) | ||||
−0.659611 | + | 0.751608i | \(0.729279\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.04858e8 | + | 5.87161e7i | 0.265293 | + | 0.148553i | ||||
\(142\) | 9.90724e8i | 2.43668i | ||||||||
\(143\) | −5.67787e8 | −1.35782 | ||||||||
\(144\) | −1.45653e8 | − | 2.37628e8i | −0.338741 | − | 0.552646i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.13503e9i | 2.49801i | ||||||||
\(147\) | 3.30655e8 | + | 1.85153e8i | 0.708118 | + | 0.396517i | ||||
\(148\) | − | 9.27853e8i | − | 1.93389i | ||||||
\(149\) | − | 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 | \(0.591281\pi\) | |||||||
\(152\) | 3.22982e8 | 0.605067 | ||||||||
\(153\) | 4.19089e8 | + | 6.83731e8i | 0.764787 | + | 1.24773i | ||||
\(154\) | −4.91885e8 | −0.874542 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.75309e8 | − | 6.70245e8i | 0.633710 | − | 1.13171i | ||||
\(157\) | 5.15599e8i | 0.848621i | 0.905517 | + | 0.424310i | \(0.139483\pi\) | ||||
−0.905517 | + | 0.424310i | \(0.860517\pi\) | |||||||
\(158\) | −5.88348e8 | −0.944074 | ||||||||
\(159\) | 2.58034e8 | + | 1.44488e8i | 0.403727 | + | 0.226070i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.16950e8i | − | 0.174059i | ||||||
\(162\) | 4.71511e8 | − | 9.25870e8i | 0.684592 | − | 1.34428i | ||||
\(163\) | − | 7.26841e8i | − | 1.02965i | −0.857296 | − | 0.514824i | \(-0.827857\pi\) | ||
0.857296 | − | 0.514824i | \(-0.172143\pi\) | |||||||
\(164\) | − | 1.27540e9i | − | 1.76308i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.66154e8 | 0.218816 | ||||||||
\(167\) | 3.33903e8 | 0.429294 | 0.214647 | − | 0.976692i | \(-0.431140\pi\) | ||||
0.214647 | + | 0.976692i | \(0.431140\pi\) | |||||||
\(168\) | 7.02791e7 | − | 1.25508e8i | 0.0882245 | − | 0.157555i | ||||
\(169\) | −2.74650e7 | −0.0336692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.49915e8 | − | 1.06032e9i | −0.760103 | − | 1.24009i | ||||
\(172\) | 2.82410e8i | 0.322675i | ||||||||
\(173\) | 1.32165e9 | 1.47547 | 0.737737 | − | 0.675088i | \(-0.235894\pi\) | ||||
0.737737 | + | 0.675088i | \(0.235894\pi\) | |||||||
\(174\) | 1.03967e8 | − | 1.85670e8i | 0.113423 | − | 0.202555i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.30636e8i | 0.865685i | ||||||||
\(177\) | 5.80109e8 | − | 1.03599e9i | 0.591039 | − | 1.05551i | ||||
\(178\) | − | 8.20193e8i | − | 0.817026i | ||||||
\(179\) | 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 | \(0.554400\pi\) | |||||||
\(182\) | −7.30477e8 | −0.665765 | ||||||||
\(183\) | 1.13166e9 | + | 6.33680e8i | 1.00904 | + | 0.565023i | ||||
\(184\) | 1.91201e8 | 0.166809 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.03432e9 | + | 1.13913e9i | 1.69968 | + | 0.951750i | ||||
\(187\) | − | 2.39000e9i | − | 1.95448i | ||||||
\(188\) | 4.84561e8 | 0.387898 | ||||||||
\(189\) | −5.53448e8 | + | 2.18317e7i | −0.433740 | + | 0.0171096i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.14467e9i | − | 1.61148i | −0.592267 | − | 0.805742i | \(-0.701767\pi\) | ||
0.592267 | − | 0.805742i | \(-0.298233\pi\) | |||||||
\(192\) | −1.72463e9 | − | 9.65721e8i | −1.26909 | − | 0.710635i | ||||
\(193\) | 2.36470e9i | 1.70431i | 0.523293 | + | 0.852153i | \(0.324703\pi\) | ||||
−0.523293 | + | 0.852153i | \(0.675297\pi\) | |||||||
\(194\) | − | 3.62870e8i | − | 0.256180i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.52800e9 | 1.03538 | ||||||||
\(197\) | −2.37290e9 | −1.57548 | −0.787742 | − | 0.616006i | \(-0.788750\pi\) | ||||
−0.787742 | + | 0.616006i | \(0.788750\pi\) | |||||||
\(198\) | −2.64005e9 | + | 1.61820e9i | −1.71772 | + | 1.05287i | ||||
\(199\) | 8.35564e8 | 0.532804 | 0.266402 | − | 0.963862i | \(-0.414165\pi\) | ||||
0.266402 | + | 0.963862i | \(0.414165\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.48411e8 | + | 1.51513e9i | −0.519783 | + | 0.928252i | ||||
\(202\) | 3.65862e9i | 2.19741i | ||||||||
\(203\) | −1.13437e8 | −0.0667993 | ||||||||
\(204\) | 2.82128e9 | + | 1.57980e9i | 1.62902 | + | 0.912182i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.17823e9i | 0.654276i | ||||||||
\(207\) | −3.84741e8 | − | 6.27694e8i | −0.209550 | − | 0.341874i | ||||
\(208\) | 1.23354e9i | 0.659022i | ||||||||
\(209\) | 3.70638e9i | 1.94251i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.31595e9 | −1.16842 | −0.584211 | − | 0.811602i | \(-0.698596\pi\) | ||||
−0.584211 | + | 0.811602i | \(0.698596\pi\) | |||||||
\(212\) | 1.19240e9 | 0.590310 | ||||||||
\(213\) | 1.62438e9 | − | 2.90089e9i | 0.789165 | − | 1.40933i | ||||
\(214\) | −3.19429e7 | −0.0152307 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.56926e7 | − | 9.04831e8i | −0.0163969 | − | 0.415674i | ||||
\(217\) | − | 1.24289e9i | − | 0.560525i | ||||||
\(218\) | −4.12678e9 | −1.82720 | ||||||||
\(219\) | 1.86097e9 | − | 3.32341e9i | 0.809029 | − | 1.44480i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.54929e9i | − | 1.48789i | ||||||
\(222\) | −2.71376e9 | + | 4.84635e9i | −1.11727 | + | 1.99528i | ||||
\(223\) | 4.75871e8i | 0.192429i | 0.995361 | + | 0.0962144i | \(0.0306734\pi\) | ||||
−0.995361 | + | 0.0962144i | \(0.969327\pi\) | |||||||
\(224\) | 1.52326e9i | 0.605037i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.14313e8 | −0.312146 | ||||||||
\(227\) | 3.01408e9 | 1.13515 | 0.567573 | − | 0.823323i | \(-0.307882\pi\) | ||||
0.567573 | + | 0.823323i | \(0.307882\pi\) | |||||||
\(228\) | −4.37519e9 | − | 2.44993e9i | −1.61904 | − | 0.906595i | ||||
\(229\) | −3.75337e9 | −1.36483 | −0.682416 | − | 0.730964i | \(-0.739071\pi\) | ||||
−0.682416 | + | 0.730964i | \(0.739071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.44026e9 | + | 8.06488e8i | 0.505818 | + | 0.283237i | ||||
\(232\) | − | 1.85459e8i | − | 0.0640169i | ||||||
\(233\) | 3.63111e9 | 1.23201 | 0.616007 | − | 0.787741i | \(-0.288749\pi\) | ||||
0.616007 | + | 0.787741i | \(0.288749\pi\) | |||||||
\(234\) | −3.92062e9 | + | 2.40312e9i | −1.30765 | + | 0.801517i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 4.78741e9i | − | 1.54331i | ||||||
\(237\) | 1.72271e9 | + | 9.64647e8i | 0.546033 | + | 0.305756i | ||||
\(238\) | − | 3.07482e9i | − | 0.958322i | ||||||
\(239\) | 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 | \(0.671835\pi\) | |||||||
\(242\) | 4.05441e9 | 1.18213 | ||||||||
\(243\) | −2.89865e9 | + | 1.93791e9i | −0.831325 | + | 0.555787i | ||||
\(244\) | 5.22951e9 | 1.47537 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.73026e9 | + | 6.66167e9i | −1.01859 | + | 1.81904i | ||||
\(247\) | 5.50417e9i | 1.47878i | ||||||||
\(248\) | 2.03200e9 | 0.537178 | ||||||||
\(249\) | −4.86508e8 | − | 2.72424e8i | −0.126559 | − | 0.0708677i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.53777e9i | − | 0.387432i | −0.981058 | − | 0.193716i | \(-0.937946\pi\) | ||
0.981058 | − | 0.193716i | \(-0.0620541\pi\) | |||||||
\(252\) | −1.90404e9 | + | 1.16707e9i | −0.472143 | + | 0.289397i | ||||
\(253\) | 2.19412e9i | 0.535524i | ||||||||
\(254\) | − | 2.26691e9i | − | 0.544626i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.06133e9 | 0.247110 | ||||||||
\(257\) | −2.70241e9 | −0.619467 | −0.309734 | − | 0.950823i | \(-0.600240\pi\) | ||||
−0.309734 | + | 0.950823i | \(0.600240\pi\) | |||||||
\(258\) | 8.25983e8 | − | 1.47508e9i | 0.186420 | − | 0.332917i | ||||
\(259\) | 2.96095e9 | 0.658008 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.08842e8 | + | 3.73186e8i | −0.131203 | + | 0.0804199i | ||||
\(262\) | − | 6.56156e9i | − | 1.39252i | ||||||
\(263\) | −3.23085e9 | −0.675296 | −0.337648 | − | 0.941273i | \(-0.609631\pi\) | ||||
−0.337648 | + | 0.941273i | \(0.609631\pi\) | |||||||
\(264\) | −1.31853e9 | + | 2.35469e9i | −0.271439 | + | 0.484749i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.76837e9i | 0.952453i | ||||||||
\(267\) | −1.34478e9 | + | 2.40156e9i | −0.264609 | + | 0.472552i | ||||
\(268\) | 7.00160e9i | 1.35724i | ||||||||
\(269\) | − | 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 | \(0.201483\pi\) | |||||||
\(272\) | −5.19238e9 | −0.948616 | ||||||||
\(273\) | 2.13887e9 | + | 1.19768e9i | 0.385065 | + | 0.215620i | ||||
\(274\) | −5.27847e9 | −0.936496 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.59005e9 | − | 1.45032e9i | −0.446347 | − | 0.249936i | ||||
\(277\) | − | 8.57729e9i | − | 1.45690i | −0.685097 | − | 0.728452i | \(-0.740240\pi\) | ||
0.685097 | − | 0.728452i | \(-0.259760\pi\) | |||||||
\(278\) | 1.18867e10 | 1.99013 | ||||||||
\(279\) | −4.08887e9 | − | 6.67087e9i | −0.674818 | − | 1.10095i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.84302e9i | 0.455990i | 0.973662 | + | 0.227995i | \(0.0732169\pi\) | ||||
−0.973662 | + | 0.227995i | \(0.926783\pi\) | |||||||
\(282\) | −2.53096e9 | − | 1.41723e9i | −0.400210 | − | 0.224101i | ||||
\(283\) | − | 9.94012e9i | − | 1.54969i | −0.632149 | − | 0.774847i | \(-0.717827\pi\) | ||
0.632149 | − | 0.774847i | \(-0.282173\pi\) | |||||||
\(284\) | − | 1.34053e10i | − | 2.06065i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.37047e10 | 2.04835 | ||||||||
\(287\) | 4.07004e9 | 0.599889 | ||||||||
\(288\) | 5.01123e9 | + | 8.17567e9i | 0.728407 | + | 1.18837i | ||||
\(289\) | 7.96436e9 | 1.14172 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.94957e8 | + | 1.06250e9i | −0.0829686 | + | 0.148169i | ||||
\(292\) | − | 1.53579e10i | − | 2.11252i | ||||||
\(293\) | −4.76323e9 | −0.646295 | −0.323147 | − | 0.946349i | \(-0.604741\pi\) | ||||
−0.323147 | + | 0.946349i | \(0.604741\pi\) | |||||||
\(294\) | −7.98101e9 | − | 4.46904e9i | −1.06824 | − | 0.598170i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.84085e9i | 0.630601i | ||||||||
\(297\) | 1.03834e10 | − | 4.09590e8i | 1.33448 | − | 0.0526409i | ||||
\(298\) | 5.74949e7i | 0.00729062i | ||||||||
\(299\) | 3.25840e9i | 0.407680i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.01219e8 | −0.109790 | ||||||||
\(302\) | 7.09873e9 | 0.853400 | ||||||||
\(303\) | 5.99861e9 | − | 1.07126e10i | 0.711673 | − | 1.27094i | ||||
\(304\) | 8.05225e9 | 0.942807 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.01155e10 | − | 1.65032e10i | −1.15373 | − | 1.88227i | ||||
\(307\) | − | 3.26248e9i | − | 0.367277i | −0.982994 | − | 0.183639i | \(-0.941212\pi\) | ||
0.982994 | − | 0.183639i | \(-0.0587876\pi\) | |||||||
\(308\) | 6.65563e9 | 0.739581 | ||||||||
\(309\) | 1.93181e9 | − | 3.44991e9i | 0.211900 | − | 0.378420i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.13691e10i | − | 1.21530i | −0.794204 | − | 0.607651i | \(-0.792112\pi\) | ||
0.794204 | − | 0.607651i | \(-0.207888\pi\) | |||||||
\(312\) | −1.95808e9 | + | 3.49684e9i | −0.206639 | + | 0.369026i | ||||
\(313\) | − | 2.83465e9i | − | 0.295340i | −0.989037 | − | 0.147670i | \(-0.952823\pi\) | ||
0.989037 | − | 0.147670i | \(-0.0471774\pi\) | |||||||
\(314\) | − | 1.24450e10i | − | 1.28020i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.96085e9 | 0.798383 | ||||||||
\(317\) | −4.84402e9 | −0.479699 | −0.239850 | − | 0.970810i | \(-0.577098\pi\) | ||||
−0.239850 | + | 0.970810i | \(0.577098\pi\) | |||||||
\(318\) | −6.22816e9 | − | 3.48751e9i | −0.609047 | − | 0.341041i | ||||
\(319\) | 2.12823e9 | 0.205521 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.35303e7 | + | 5.23731e7i | 0.00880911 | + | 0.00493274i | ||||
\(322\) | 2.82281e9i | 0.262578i | ||||||||
\(323\) | −2.31689e10 | −2.12860 | ||||||||
\(324\) | −6.37995e9 | + | 1.25278e10i | −0.578945 | + | 1.13683i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.75437e10i | 1.55329i | ||||||||
\(327\) | 1.20834e10 | + | 6.76620e9i | 1.05681 | + | 0.591771i | ||||
\(328\) | 6.65410e9i | 0.574902i | ||||||||
\(329\) | 1.54632e9i | 0.131982i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.47410e9 | −0.456037 | −0.228019 | − | 0.973657i | \(-0.573225\pi\) | ||||
−0.228019 | + | 0.973657i | \(0.573225\pi\) | |||||||
\(332\) | −2.24821e9 | −0.185048 | ||||||||
\(333\) | 1.58920e10 | − | 9.74092e9i | 1.29242 | − | 0.792179i | ||||
\(334\) | −8.05942e9 | −0.647616 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.75213e9 | − | 3.12903e9i | 0.137470 | − | 0.245501i | ||||
\(337\) | 2.30004e10i | 1.78327i | 0.452759 | + | 0.891633i | \(0.350440\pi\) | ||||
−0.452759 | + | 0.891633i | \(0.649560\pi\) | |||||||
\(338\) | 6.62922e8 | 0.0507920 | ||||||||
\(339\) | 2.38435e9 | + | 1.33514e9i | 0.180539 | + | 0.101094i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.33183e10i | 1.72456i | ||||||||
\(342\) | 1.56870e10 | + | 2.55929e10i | 1.14666 | + | 1.87074i | ||||
\(343\) | 1.08843e10i | 0.786364i | ||||||||
\(344\) | − | 1.47340e9i | − | 0.105217i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.19006e10 | −2.22584 | ||||||||
\(347\) | −2.27792e10 | −1.57116 | −0.785582 | − | 0.618758i | \(-0.787636\pi\) | ||||
−0.785582 | + | 0.618758i | \(0.787636\pi\) | |||||||
\(348\) | −1.40677e9 | + | 2.51227e9i | −0.0959190 | + | 0.171297i | ||||
\(349\) | −2.25621e10 | −1.52082 | −0.760410 | − | 0.649444i | \(-0.775002\pi\) | ||||
−0.760410 | + | 0.649444i | \(0.775002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.54199e10 | − | 6.08264e8i | 1.01591 | − | 0.0400741i | ||||
\(352\) | − | 2.85783e10i | − | 1.86151i | ||||||
\(353\) | −8.56846e9 | −0.551828 | −0.275914 | − | 0.961182i | \(-0.588981\pi\) | ||||
−0.275914 | + | 0.961182i | \(0.588981\pi\) | |||||||
\(354\) | −1.40021e10 | + | 2.50056e10i | −0.891619 | + | 1.59229i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.10979e10i | 0.690941i | ||||||||
\(357\) | −5.04142e9 | + | 9.00321e9i | −0.310370 | + | 0.554274i | ||||
\(358\) | − | 2.64994e9i | − | 0.161326i | ||||||
\(359\) | − | 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 | ||||||||
\(362\) | 8.81177e9 | 0.513132 | ||||||||
\(363\) | −1.18715e10 | − | 6.64756e9i | −0.683722 | − | 0.382856i | ||||
\(364\) | 9.88397e9 | 0.563023 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.73148e10 | − | 1.52951e10i | −1.52220 | − | 0.852371i | ||||
\(367\) | − | 7.52594e9i | − | 0.414855i | −0.978250 | − | 0.207428i | \(-0.933491\pi\) | ||
0.978250 | − | 0.207428i | \(-0.0665092\pi\) | |||||||
\(368\) | 4.76682e9 | 0.259919 | ||||||||
\(369\) | 2.18448e10 | − | 1.33896e10i | 1.17826 | − | 0.722209i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.80518e9i | 0.200853i | ||||||||
\(372\) | −2.75260e10 | − | 1.54134e10i | −1.43738 | − | 0.804874i | ||||
\(373\) | 1.60977e10i | 0.831625i | 0.909450 | + | 0.415812i | \(0.136503\pi\) | ||||
−0.909450 | + | 0.415812i | \(0.863497\pi\) | |||||||
\(374\) | 5.76875e10i | 2.94846i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.52808e9 | −0.126485 | ||||||||
\(377\) | 3.16054e9 | 0.156457 | ||||||||
\(378\) | 1.33586e10 | − | 5.26951e8i | 0.654323 | − | 0.0258109i | ||||
\(379\) | 7.26804e9 | 0.352257 | 0.176129 | − | 0.984367i | \(-0.443642\pi\) | ||||
0.176129 | + | 0.984367i | \(0.443642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.71679e9 | + | 6.63761e9i | −0.176387 | + | 0.315001i | ||||
\(382\) | 5.17657e10i | 2.43102i | ||||||||
\(383\) | −3.84730e9 | −0.178797 | −0.0893987 | − | 0.995996i | \(-0.528495\pi\) | ||||
−0.0893987 | + | 0.995996i | \(0.528495\pi\) | |||||||
\(384\) | 1.51840e10 | + | 8.50242e9i | 0.698332 | + | 0.391037i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 5.70768e10i | − | 2.57105i | ||||||
\(387\) | −4.83704e9 | + | 2.96483e9i | −0.215643 | + | 0.132177i | ||||
\(388\) | 4.90995e9i | 0.216646i | ||||||||
\(389\) | 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 | ||||||||
\(392\) | −7.97194e9 | −0.337614 | ||||||||
\(393\) | −1.07582e10 | + | 1.92126e10i | −0.450994 | + | 0.805407i | ||||
\(394\) | 5.72746e10 | 2.37671 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.57222e10 | − | 2.18957e10i | 1.45264 | − | 0.890385i | ||||
\(397\) | − | 3.57344e10i | − | 1.43855i | −0.694727 | − | 0.719273i | \(-0.744475\pi\) | ||
0.694727 | − | 0.719273i | \(-0.255525\pi\) | |||||||
\(398\) | −2.01680e10 | −0.803767 | ||||||||
\(399\) | 7.81815e9 | − | 1.39620e10i | 0.308470 | − | 0.550880i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.65267e9i | − | 0.295962i | −0.988990 | − | 0.147981i | \(-0.952723\pi\) | ||
0.988990 | − | 0.147981i | \(-0.0472774\pi\) | |||||||
\(402\) | 2.04781e10 | − | 3.65707e10i | 0.784124 | − | 1.40033i | ||||
\(403\) | 3.46289e10i | 1.31286i | ||||||||
\(404\) | − | 4.95042e10i | − | 1.85830i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.73803e9 | 0.100771 | ||||||||
\(407\) | −5.55511e10 | −2.02449 | ||||||||
\(408\) | −1.47193e10 | − | 8.24222e9i | −0.531187 | − | 0.297443i | ||||
\(409\) | −1.89488e10 | −0.677154 | −0.338577 | − | 0.940939i | \(-0.609946\pi\) | ||||
−0.338577 | + | 0.940939i | \(0.609946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.54556e10 | + | 8.65450e9i | 0.541650 | + | 0.303302i | ||||
\(412\) | − | 1.59425e10i | − | 0.553307i | ||||||
\(413\) | 1.52775e10 | 0.525111 | ||||||||
\(414\) | 9.28649e9 | + | 1.51506e10i | 0.316119 | + | 0.515738i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4.24404e10i | − | 1.41712i | ||||||
\(417\) | −3.48047e10 | − | 1.94892e10i | −1.15105 | − | 0.644540i | ||||
\(418\) | − | 8.94607e10i | − | 2.93040i | ||||||
\(419\) | − | 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 | \(0.318909\pi\) | |||||||
\(422\) | 5.59001e10 | 1.76264 | ||||||||
\(423\) | 5.08709e9 | + | 8.29944e9i | 0.158894 | + | 0.259231i | ||||
\(424\) | −6.22108e9 | −0.192487 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.92075e10 | + | 7.00186e10i | −1.19050 | + | 2.12606i | ||||
\(427\) | 1.66883e10i | 0.501997i | ||||||||
\(428\) | 4.32214e8 | 0.0128802 | ||||||||
\(429\) | −4.01279e10 | − | 2.24700e10i | −1.18473 | − | 0.663397i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.98116e10i | 0.863924i | 0.901892 | + | 0.431962i | \(0.142179\pi\) | ||||
−0.901892 | + | 0.431962i | \(0.857821\pi\) | |||||||
\(432\) | −8.89850e8 | − | 2.25583e10i | −0.0255495 | − | 0.647697i | ||||
\(433\) | − | 2.54166e9i | − | 0.0723047i | −0.999346 | − | 0.0361524i | \(-0.988490\pi\) | ||
0.999346 | − | 0.0361524i | \(-0.0115102\pi\) | |||||||
\(434\) | 2.99997e10i | 0.845586i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.58388e10 | 1.54522 | ||||||||
\(437\) | 2.12700e10 | 0.583233 | ||||||||
\(438\) | −4.49183e10 | + | 8.02172e10i | −1.22047 | + | 2.17957i | ||||
\(439\) | −1.11261e10 | −0.299559 | −0.149780 | − | 0.988719i | \(-0.547856\pi\) | ||||
−0.149780 | + | 0.988719i | \(0.547856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.60414e10 | + | 2.61711e10i | 0.424120 | + | 0.691939i | ||||
\(442\) | 8.56691e10i | 2.24458i | ||||||||
\(443\) | 3.00907e10 | 0.781299 | 0.390650 | − | 0.920539i | \(-0.372250\pi\) | ||||
0.390650 | + | 0.920539i | \(0.372250\pi\) | |||||||
\(444\) | 3.67194e10 | − | 6.55753e10i | 0.944853 | − | 1.68736i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 1.14861e10i | − | 0.290291i | ||||||
\(447\) | 9.42678e7 | − | 1.68348e8i | 0.00236120 | − | 0.00421674i | ||||
\(448\) | − | 2.54328e10i | − | 0.631367i | ||||||
\(449\) | − | 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 | ||||||||
\(452\) | 1.10184e10 | 0.263975 | ||||||||
\(453\) | −2.07854e10 | − | 1.16390e10i | −0.493589 | − | 0.276390i | ||||
\(454\) | −7.27509e10 | −1.71244 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.28265e10 | + | 1.27819e10i | 0.527934 | + | 0.295621i | ||||
\(457\) | 1.18416e10i | 0.271486i | 0.990744 | + | 0.135743i | \(0.0433421\pi\) | ||||
−0.990744 | + | 0.135743i | \(0.956658\pi\) | |||||||
\(458\) | 9.05950e10 | 2.05893 | ||||||||
\(459\) | 2.56038e9 | + | 6.49074e10i | 0.0576838 | + | 1.46232i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.03656e10i | − | 0.450913i | −0.974253 | − | 0.225456i | \(-0.927613\pi\) | ||
0.974253 | − | 0.225456i | \(-0.0723873\pi\) | |||||||
\(462\) | −3.47636e10 | − | 1.94662e10i | −0.763057 | − | 0.427280i | ||||
\(463\) | 3.88105e10i | 0.844550i | 0.906468 | + | 0.422275i | \(0.138768\pi\) | ||||
−0.906468 | + | 0.422275i | \(0.861232\pi\) | |||||||
\(464\) | − | 4.62366e9i | − | 0.0997502i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.76440e10 | −1.85857 | ||||||||
\(467\) | 6.67567e10 | 1.40355 | 0.701774 | − | 0.712400i | \(-0.252392\pi\) | ||||
0.701774 | + | 0.712400i | \(0.252392\pi\) | |||||||
\(468\) | 5.30494e10 | − | 3.25163e10i | 1.10585 | − | 0.677825i | ||||
\(469\) | −2.23434e10 | −0.461803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.04047e10 | + | 3.64396e10i | −0.414616 | + | 0.740440i | ||||
\(472\) | 2.49771e10i | 0.503239i | ||||||||
\(473\) | 1.69080e10 | 0.337791 | ||||||||
\(474\) | −4.15810e10 | − | 2.32837e10i | −0.823725 | − | 0.461252i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.16049e10i | 0.810432i | ||||||||
\(477\) | 1.25183e10 | + | 2.04232e10i | 0.241808 | + | 0.394503i | ||||
\(478\) | − | 1.13385e11i | − | 2.17193i | ||||||
\(479\) | 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 | ||||||||
\(482\) | 8.37027e10 | 1.55078 | ||||||||
\(483\) | 4.62824e9 | − | 8.26533e9i | 0.0850408 | − | 0.151870i | ||||
\(484\) | −5.48597e10 | −0.999705 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.99647e10 | − | 4.67753e10i | 1.25410 | − | 0.838439i | ||||
\(487\) | 1.08507e10i | 0.192905i | 0.995338 | + | 0.0964526i | \(0.0307496\pi\) | ||||
−0.995338 | + | 0.0964526i | \(0.969250\pi\) | |||||||
\(488\) | −2.72837e10 | −0.481088 | ||||||||
\(489\) | 2.87645e10 | − | 5.13689e10i | 0.503061 | − | 0.898390i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.02973e10i | 0.177173i | 0.996068 | + | 0.0885864i | \(0.0282349\pi\) | ||||
−0.996068 | + | 0.0885864i | \(0.971765\pi\) | |||||||
\(492\) | 5.04736e10 | − | 9.01381e10i | 0.861398 | − | 1.53833i | ||||
\(493\) | 1.33037e10i | 0.225209i | ||||||||
\(494\) | − | 1.32854e11i | − | 2.23083i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.06598e10 | 0.837022 | ||||||||
\(497\) | 4.27788e10 | 0.701138 | ||||||||
\(498\) | 1.17428e10 | + | 6.57550e9i | 0.190922 | + | 0.106908i | ||||
\(499\) | −6.76597e10 | −1.09126 | −0.545630 | − | 0.838026i | \(-0.683710\pi\) | ||||
−0.545630 | + | 0.838026i | \(0.683710\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.35984e10 | + | 1.32141e10i | 0.374568 | + | 0.209743i | ||||
\(502\) | 3.71171e10i | 0.584465i | ||||||||
\(503\) | 2.55230e10 | 0.398712 | 0.199356 | − | 0.979927i | \(-0.436115\pi\) | ||||
0.199356 | + | 0.979927i | \(0.436115\pi\) | |||||||
\(504\) | 9.93385e9 | − | 6.08890e9i | 0.153956 | − | 0.0943662i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 5.29595e10i | − | 0.807871i | ||||||
\(507\) | −1.94107e9 | − | 1.08692e9i | −0.0293771 | − | 0.0164500i | ||||
\(508\) | 3.06732e10i | 0.460579i | ||||||||
\(509\) | − | 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 | ||||||||
\(512\) | −8.06177e10 | −1.17314 | ||||||||
\(513\) | −3.97059e9 | − | 1.00657e11i | −0.0573305 | − | 1.45337i | ||||
\(514\) | 6.52280e10 | 0.934504 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.11763e10 | + | 1.99591e10i | −0.157651 | + | 0.281541i | ||||
\(517\) | − | 2.90110e10i | − | 0.406069i | ||||||
\(518\) | −7.14683e10 | −0.992646 | ||||||||
\(519\) | 9.34065e10 | + | 5.23038e10i | 1.28738 | + | 0.720881i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.25006e10i | 0.712547i | 0.934382 | + | 0.356273i | \(0.115953\pi\) | ||||
−0.934382 | + | 0.356273i | \(0.884047\pi\) | |||||||
\(522\) | 1.46956e10 | − | 9.00759e9i | 0.197927 | − | 0.121318i | ||||
\(523\) | 8.56285e10i | 1.14449i | 0.820083 | + | 0.572245i | \(0.193927\pi\) | ||||
−0.820083 | + | 0.572245i | \(0.806073\pi\) | |||||||
\(524\) | 8.87835e10i | 1.17763i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.79830e10 | 1.01872 | ||||||||
\(527\) | −1.45764e11 | −1.88977 | ||||||||
\(528\) | −3.28721e10 | + | 5.87046e10i | −0.422953 | + | 0.755329i | ||||
\(529\) | −6.57194e10 | −0.839211 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.19975e10 | − | 5.02599e10i | 1.03139 | − | 0.632184i | ||||
\(532\) | − | 6.45201e10i | − | 0.805469i | ||||||
\(533\) | −1.13398e11 | −1.40506 | ||||||||
\(534\) | 3.24588e10 | − | 5.79665e10i | 0.399179 | − | 0.712873i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3.65291e10i | − | 0.442568i | ||||||
\(537\) | −4.34480e9 | + | 7.75915e9i | −0.0522484 | + | 0.0933076i | ||||
\(538\) | 2.13036e10i | 0.254287i | ||||||||
\(539\) | − | 9.14820e10i | − | 1.08388i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.14250e10 | −0.250111 | −0.125055 | − | 0.992150i | \(-0.539911\pi\) | ||||
−0.125055 | + | 0.992150i | \(0.539911\pi\) | |||||||
\(542\) | −2.09928e11 | −2.43261 | ||||||||
\(543\) | −2.58013e10 | − | 1.44476e10i | −0.296785 | − | 0.166187i | ||||
\(544\) | 1.78645e11 | 2.03984 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.16259e10 | − | 2.89084e10i | −0.580894 | − | 0.325277i | ||||
\(547\) | − | 9.14990e8i | − | 0.0102204i | −0.999987 | − | 0.00511019i | \(-0.998373\pi\) | ||
0.999987 | − | 0.00511019i | \(-0.00162663\pi\) | |||||||
\(548\) | 7.14222e10 | 0.791974 | ||||||||
\(549\) | 5.49012e10 | + | 8.95697e10i | 0.604356 | + | 0.985989i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.06312e10i | − | 0.223830i | ||||||
\(552\) | 1.35130e10 | + | 7.56671e9i | 0.145544 | + | 0.0814987i | ||||
\(553\) | 2.54045e10i | 0.271650i | ||||||||
\(554\) | 2.07030e11i | 2.19783i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.60837e11 | −1.68301 | ||||||||
\(557\) | 1.81764e11 | 1.88837 | 0.944185 | − | 0.329416i | \(-0.106852\pi\) | ||||
0.944185 | + | 0.329416i | \(0.106852\pi\) | |||||||
\(558\) | 9.86930e10 | + | 1.61015e11i | 1.01800 | + | 1.66084i | ||||
\(559\) | 2.51093e10 | 0.257151 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.45835e10 | − | 1.68912e11i | 0.954913 | − | 1.70533i | ||||
\(562\) | − | 6.86220e10i | − | 0.687889i | ||||||
\(563\) | −4.19023e10 | −0.417066 | −0.208533 | − | 0.978015i | \(-0.566869\pi\) | ||||
−0.208533 | + | 0.978015i | \(0.566869\pi\) | |||||||
\(564\) | 3.42460e10 | + | 1.91763e10i | 0.338449 | + | 0.189517i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.39924e11i | 2.33781i | ||||||||
\(567\) | −3.99785e10 | − | 2.03596e10i | −0.386807 | − | 0.196986i | ||||
\(568\) | 6.99391e10i | 0.671934i | ||||||||
\(569\) | − | 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 | \(0.393155\pi\) | |||||||
\(572\) | −1.85436e11 | −1.73225 | ||||||||
\(573\) | 8.48743e10 | − | 1.51573e11i | 0.787332 | − | 1.40605i | ||||
\(574\) | −9.82385e10 | −0.904970 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.36688e10 | − | 1.36503e11i | −0.760105 | − | 1.24009i | ||||
\(577\) | 5.16977e10i | 0.466410i | 0.972428 | + | 0.233205i | \(0.0749213\pi\) | ||||
−0.972428 | + | 0.233205i | \(0.925079\pi\) | |||||||
\(578\) | −1.92236e11 | −1.72235 | ||||||||
\(579\) | −9.35823e10 | + | 1.67124e11i | −0.832683 | + | 1.48704i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 7.17444e9i | − | 0.0629627i | ||||||
\(582\) | 1.43605e10 | − | 2.56456e10i | 0.125163 | − | 0.223522i | ||||
\(583\) | − | 7.13899e10i | − | 0.617963i | ||||||
\(584\) | 8.01260e10i | 0.688846i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.14970e11 | 0.974976 | ||||||||
\(587\) | 7.90362e10 | 0.665693 | 0.332846 | − | 0.942981i | \(-0.391991\pi\) | ||||
0.332846 | + | 0.942981i | \(0.391991\pi\) | |||||||
\(588\) | 1.07990e11 | + | 6.04699e10i | 0.903387 | + | 0.505859i | ||||
\(589\) | 2.26049e11 | 1.87820 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.67703e11 | − | 9.39065e10i | −1.37464 | − | 0.769743i | ||||
\(592\) | 1.20687e11i | 0.982592i | ||||||||
\(593\) | 2.38940e11 | 1.93228 | 0.966141 | − | 0.258015i | \(-0.0830683\pi\) | ||||
0.966141 | + | 0.258015i | \(0.0830683\pi\) | |||||||
\(594\) | −2.50624e11 | + | 9.88626e9i | −2.01315 | + | 0.0794120i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.77955e8i | − | 0.00616551i | ||||||
\(597\) | 5.90528e10 | + | 3.30671e10i | 0.464883 | + | 0.260315i | ||||
\(598\) | − | 7.86478e10i | − | 0.615010i | ||||||
\(599\) | 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 | \(0.596380\pi\) | |||||||
\(602\) | 2.17527e10 | 0.165626 | ||||||||
\(603\) | −1.19922e11 | + | 7.35052e10i | −0.907043 | + | 0.555967i | ||||
\(604\) | −9.60518e10 | −0.721702 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.44788e11 | + | 2.58570e11i | −1.07360 | + | 1.91729i | ||||
\(607\) | − | 1.00711e11i | − | 0.741864i | −0.928660 | − | 0.370932i | \(-0.879038\pi\) | ||
0.928660 | − | 0.370932i | \(-0.120962\pi\) | |||||||
\(608\) | −2.77040e11 | −2.02735 | ||||||||
\(609\) | −8.01710e9 | − | 4.48924e9i | −0.0582838 | − | 0.0326365i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.30829e10i | − | 0.309129i | ||||||
\(612\) | 1.36872e11 | + | 2.23302e11i | 0.975682 | + | 1.59180i | ||||
\(613\) | − | 1.66738e11i | − | 1.18084i | −0.807094 | − | 0.590422i | \(-0.798961\pi\) | ||
0.807094 | − | 0.590422i | \(-0.201039\pi\) | |||||||
\(614\) | 7.87464e10i | 0.554060i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.47241e10 | −0.241162 | ||||||||
\(617\) | −5.98004e10 | −0.412632 | −0.206316 | − | 0.978485i | \(-0.566148\pi\) | ||||
−0.206316 | + | 0.978485i | \(0.566148\pi\) | |||||||
\(618\) | −4.66280e10 | + | 8.32705e10i | −0.319664 | + | 0.570870i | ||||
\(619\) | 1.30260e11 | 0.887254 | 0.443627 | − | 0.896211i | \(-0.353691\pi\) | ||||
0.443627 | + | 0.896211i | \(0.353691\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.35054e9 | − | 5.95878e10i | −0.0158052 | − | 0.400674i | ||||
\(622\) | 2.74416e11i | 1.83336i | ||||||||
\(623\) | −3.54154e10 | −0.235093 | ||||||||
\(624\) | −4.88169e10 | + | 8.71795e10i | −0.321982 | + | 0.575011i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.84200e10i | 0.445539i | ||||||||
\(627\) | −1.46678e11 | + | 2.61945e11i | −0.949065 | + | 1.69489i | ||||
\(628\) | 1.68392e11i | 1.08263i | ||||||||
\(629\) | − | 3.47255e11i | − | 2.21843i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.11689e11 | −1.33530 | −0.667652 | − | 0.744473i | \(-0.732701\pi\) | ||||
−0.667652 | + | 0.744473i | \(0.732701\pi\) | |||||||
\(632\) | −4.15338e10 | −0.260335 | ||||||||
\(633\) | −1.63678e11 | − | 9.16529e10i | −1.01947 | − | 0.570863i | ||||
\(634\) | 1.16920e11 | 0.723656 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.42723e10 | + | 4.71890e10i | 0.515058 | + | 0.288411i | ||||
\(637\) | − | 1.35856e11i | − | 0.825126i | ||||||
\(638\) | −5.13690e10 | −0.310040 | ||||||||
\(639\) | 2.29603e11 | − | 1.40734e11i | 1.37713 | − | 0.844102i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 9.94582e9i | − | 0.0589126i | −0.999566 | − | 0.0294563i | \(-0.990622\pi\) | ||
0.999566 | − | 0.0294563i | \(-0.00937759\pi\) | |||||||
\(642\) | −2.25754e9 | − | 1.26413e9i | −0.0132891 | − | 0.00744134i | ||||
\(643\) | − | 4.35787e10i | − | 0.254935i | −0.991843 | − | 0.127468i | \(-0.959315\pi\) | ||
0.991843 | − | 0.127468i | \(-0.0406849\pi\) | |||||||
\(644\) | − | 3.81950e10i | − | 0.222057i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.59227e11 | 3.21113 | ||||||||
\(647\) | 1.00404e11 | 0.572973 | 0.286487 | − | 0.958084i | \(-0.407513\pi\) | ||||
0.286487 | + | 0.958084i | \(0.407513\pi\) | |||||||
\(648\) | 3.32858e10 | − | 6.53608e10i | 0.188781 | − | 0.370695i | ||||
\(649\) | −2.86625e11 | −1.61560 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.91871e10 | − | 8.78405e10i | 0.273859 | − | 0.489070i | ||||
\(652\) | − | 2.37382e11i | − | 1.31358i | ||||||
\(653\) | 9.51805e10 | 0.523474 | 0.261737 | − | 0.965139i | \(-0.415705\pi\) | ||||
0.261737 | + | 0.965139i | \(0.415705\pi\) | |||||||
\(654\) | −2.91657e11 | − | 1.63316e11i | −1.59427 | − | 0.892723i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.65893e11i | 0.895804i | ||||||||
\(657\) | 2.63046e11 | − | 1.61232e11i | 1.41179 | − | 0.865348i | ||||
\(658\) | − | 3.73235e10i | − | 0.199104i | ||||||
\(659\) | 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 | \(0.283675\pi\) | |||||||
\(662\) | 1.32128e11 | 0.687960 | ||||||||
\(663\) | 1.40462e11 | − | 2.50843e11i | 0.726949 | − | 1.29822i | ||||
\(664\) | 1.17295e10 | 0.0603402 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.83585e11 | + | 2.35116e11i | −1.94969 | + | 1.19505i | ||||
\(667\) | − | 1.22134e10i | − | 0.0617068i | ||||||
\(668\) | 1.09051e11 | 0.547675 | ||||||||
\(669\) | −1.88324e10 | + | 3.36318e10i | −0.0940160 | + | 0.167898i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.13094e11i | − | 1.54449i | ||||||
\(672\) | −6.02825e10 | + | 1.07655e11i | −0.295607 | + | 0.527908i | ||||
\(673\) | 1.21923e11i | 0.594326i | 0.954827 | + | 0.297163i | \(0.0960404\pi\) | ||||
−0.954827 | + | 0.297163i | \(0.903960\pi\) | |||||||
\(674\) | − | 5.55161e11i | − | 2.69017i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.96990e9 | −0.0429537 | ||||||||
\(677\) | −3.04202e10 | −0.144813 | −0.0724066 | − | 0.997375i | \(-0.523068\pi\) | ||||
−0.0724066 | + | 0.997375i | \(0.523068\pi\) | |||||||
\(678\) | −5.75510e10 | − | 3.22262e10i | −0.272354 | − | 0.152507i | ||||
\(679\) | −1.56685e10 | −0.0737138 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.13018e11 | + | 1.19281e11i | 0.990440 | + | 0.554605i | ||||
\(682\) | − | 5.62832e11i | − | 2.60161i | ||||||
\(683\) | 2.91193e11 | 1.33813 | 0.669065 | − | 0.743204i | \(-0.266695\pi\) | ||||
0.669065 | + | 0.743204i | \(0.266695\pi\) | |||||||
\(684\) | −2.12258e11 | − | 3.46293e11i | −0.969707 | − | 1.58205i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 2.62714e11i | − | 1.18628i | ||||||
\(687\) | −2.65267e11 | − | 1.48538e11i | −1.19085 | − | 0.666824i | ||||
\(688\) | − | 3.67333e10i | − | 0.163948i | ||||||
\(689\) | − | 1.06018e11i | − | 0.470438i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.48484e11 | −1.52852 | −0.764260 | − | 0.644908i | \(-0.776896\pi\) | ||||
−0.764260 | + | 0.644908i | \(0.776896\pi\) | |||||||
\(692\) | 4.31642e11 | 1.88235 | ||||||||
\(693\) | 6.98731e10 | + | 1.13996e11i | 0.302954 | + | 0.494261i | ||||
\(694\) | 5.49822e11 | 2.37020 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.33945e9 | − | 1.31071e10i | 0.0312771 | − | 0.0558562i | ||||
\(697\) | − | 4.77327e11i | − | 2.02248i | ||||||
\(698\) | 5.44581e11 | 2.29425 | ||||||||
\(699\) | 2.56626e11 | + | 1.43700e11i | 1.07496 | + | 0.601932i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.23548e11i | − | 0.511640i | −0.966724 | − | 0.255820i | \(-0.917655\pi\) | ||
0.966724 | − | 0.255820i | \(-0.0823455\pi\) | |||||||
\(702\) | −3.72190e11 | + | 1.46816e10i | −1.53256 | + | 0.0604542i | ||||
\(703\) | 5.38516e11i | 2.20484i | ||||||||
\(704\) | 4.77151e11i | 1.94252i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.06817e11 | 0.832467 | ||||||||
\(707\) | 1.57977e11 | 0.632289 | ||||||||
\(708\) | 1.89460e11 | − | 3.38346e11i | 0.754023 | − | 1.34657i | ||||
\(709\) | −3.17753e11 | −1.25749 | −0.628744 | − | 0.777612i | \(-0.716431\pi\) | ||||
−0.628744 | + | 0.777612i | \(0.716431\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.35758e10 | + | 1.36351e11i | 0.327041 | + | 0.533557i | ||||
\(712\) | − | 5.79006e10i | − | 0.225301i | ||||||
\(713\) | 1.33818e11 | 0.517793 | ||||||||
\(714\) | 1.21685e11 | − | 2.17310e11i | 0.468213 | − | 0.836156i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.58560e10i | 0.136430i | ||||||||
\(717\) | −1.85905e11 | + | 3.31997e11i | −0.703419 | + | 1.25620i | ||||
\(718\) | 8.33539e10i | 0.313638i | ||||||||
\(719\) | − | 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 | ||||||||
\(722\) | −4.57307e11 | −1.68290 | ||||||||
\(723\) | −2.45085e11 | − | 1.37238e11i | −0.896942 | − | 0.502250i | ||||
\(724\) | −1.19231e11 | −0.433944 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.86543e11 | + | 1.60452e11i | 1.03144 | + | 0.577562i | ||||
\(727\) | 2.06831e11i | 0.740420i | 0.928948 | + | 0.370210i | \(0.120714\pi\) | ||||
−0.928948 | + | 0.370210i | \(0.879286\pi\) | |||||||
\(728\) | −5.15672e10 | −0.183590 | ||||||||
\(729\) | −2.81552e11 | + | 2.22472e10i | −0.996893 | + | 0.0787707i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.05693e11i | 0.370151i | ||||||||
\(732\) | 3.69592e11 | + | 2.06956e11i | 1.28730 | + | 0.720832i | ||||
\(733\) | 2.72921e11i | 0.945412i | 0.881220 | + | 0.472706i | \(0.156723\pi\) | ||||
−0.881220 | + | 0.472706i | \(0.843277\pi\) | |||||||
\(734\) | 1.81654e11i | 0.625835i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.64004e11 | −0.558912 | ||||||||
\(737\) | 4.19190e11 | 1.42083 | ||||||||
\(738\) | −5.27267e11 | + | 3.23185e11i | −1.77748 | + | 1.08950i | ||||
\(739\) | −1.03105e10 | −0.0345702 | −0.0172851 | − | 0.999851i | \(-0.505502\pi\) | ||||
−0.0172851 | + | 0.999851i | \(0.505502\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.17826e11 | + | 3.89003e11i | −0.722497 | + | 1.29027i | ||||
\(742\) | − | 9.18454e10i | − | 0.303000i | ||||||
\(743\) | −3.12920e11 | −1.02678 | −0.513392 | − | 0.858154i | \(-0.671611\pi\) | ||||
−0.513392 | + | 0.858154i | \(0.671611\pi\) | |||||||
\(744\) | 1.43610e11 | + | 8.04159e10i | 0.468699 | + | 0.262452i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 3.88549e11i | − | 1.25456i | ||||||
\(747\) | −2.36025e10 | − | 3.85067e10i | −0.0758010 | − | 0.123667i | ||||
\(748\) | − | 7.80561e11i | − | 2.49345i | ||||||
\(749\) | 1.37927e9i | 0.00438251i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.76676e11 | 0.869783 | 0.434892 | − | 0.900483i | \(-0.356787\pi\) | ||||
0.434892 | + | 0.900483i | \(0.356787\pi\) | |||||||
\(752\) | −6.30275e10 | −0.197087 | ||||||||
\(753\) | 6.08566e10 | − | 1.08681e11i | 0.189290 | − | 0.338043i | ||||
\(754\) | −7.62858e10 | −0.236025 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.80753e11 | + | 7.13009e9i | −0.553347 | + | 0.0218277i | ||||
\(757\) | 1.25846e11i | 0.383226i | 0.981471 | + | 0.191613i | \(0.0613718\pi\) | ||||
−0.981471 | + | 0.191613i | \(0.938628\pi\) | |||||||
\(758\) | −1.75428e11 | −0.531402 | ||||||||
\(759\) | −8.68317e10 | + | 1.55068e11i | −0.261644 | + | 0.467256i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.11284e11i | 1.22632i | 0.789960 | + | 0.613159i | \(0.210101\pi\) | ||||
−0.789960 | + | 0.613159i | \(0.789899\pi\) | |||||||
\(762\) | 8.97120e10 | − | 1.60212e11i | 0.266091 | − | 0.475198i | ||||
\(763\) | 1.78192e11i | 0.525762i | ||||||||
\(764\) | − | 7.00435e11i | − | 2.05586i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.28622e10 | 0.269727 | ||||||||
\(767\) | −4.25654e11 | −1.22991 | ||||||||
\(768\) | 7.50087e10 | + | 4.20018e10i | 0.215609 | + | 0.120732i | ||||
\(769\) | −4.51287e10 | −0.129047 | −0.0645235 | − | 0.997916i | \(-0.520553\pi\) | ||||
−0.0645235 | + | 0.997916i | \(0.520553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.90991e11 | − | 1.06947e11i | −0.540498 | − | 0.302657i | ||||
\(772\) | 7.72298e11i | 2.17428i | ||||||||
\(773\) | 3.86868e11 | 1.08354 | 0.541770 | − | 0.840527i | \(-0.317755\pi\) | ||||
0.541770 | + | 0.840527i | \(0.317755\pi\) | |||||||
\(774\) | 1.16751e11 | − | 7.15621e10i | 0.325311 | − | 0.199397i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 2.56164e10i | − | 0.0706435i | ||||||
\(777\) | 2.09263e11 | + | 1.17178e11i | 0.574126 | + | 0.321487i | ||||
\(778\) | − | 3.97252e11i | − | 1.08430i | ||||||
\(779\) | 7.40231e11i | 2.01010i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.02585e11 | −2.15718 | ||||||||
\(782\) | 3.31055e11 | 0.885264 | ||||||||
\(783\) | −5.77982e10 | + | 2.27994e9i | −0.153768 | + | 0.00606565i | ||||
\(784\) | −1.98748e11 | −0.526064 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.59671e11 | − | 4.63733e11i | 0.680353 | − | 1.21501i | ||||
\(787\) | 4.31897e11i | 1.12585i | 0.826508 | + | 0.562926i | \(0.190324\pi\) | ||||
−0.826508 | + | 0.562926i | \(0.809676\pi\) | |||||||
\(788\) | −7.74973e11 | −2.00993 | ||||||||
\(789\) | −2.28338e11 | − | 1.27860e11i | −0.589210 | − | 0.329933i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.51615e10i | 0.0898177i | ||||||||
\(792\) | −1.86372e11 | + | 1.14235e11i | −0.473673 | + | 0.290335i | ||||
\(793\) | − | 4.64962e11i | − | 1.17578i | ||||||
\(794\) | 8.62519e11i | 2.17014i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.72890e11 | 0.679728 | ||||||||
\(797\) | 1.89233e11 | 0.468991 | 0.234495 | − | 0.972117i | \(-0.424656\pi\) | ||||
0.234495 | + | 0.972117i | \(0.424656\pi\) | |||||||
\(798\) | −1.88707e11 | + | 3.37001e11i | −0.465346 | + | 0.831036i | ||||
\(799\) | 1.81350e11 | 0.444970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.90082e11 | + | 1.16510e11i | −0.461754 | + | 0.283030i | ||||
\(802\) | 1.84712e11i | 0.446477i | ||||||||
\(803\) | −9.19486e11 | −2.21148 | ||||||||
\(804\) | −2.77086e11 | + | 4.94833e11i | −0.663117 | + | 1.18423i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 8.35837e11i | − | 1.98053i | ||||||
\(807\) | 3.49291e10 | − | 6.23781e10i | 0.0823557 | − | 0.147075i | ||||
\(808\) | 2.58276e11i | 0.605953i | ||||||||
\(809\) | 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 | \(0.576205\pi\) | |||||||
\(812\) | −3.70479e10 | −0.0852197 | ||||||||
\(813\) | 6.14679e11 | + | 3.44195e11i | 1.40697 | + | 0.787847i | ||||
\(814\) | 1.34084e12 | 3.05406 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.66967e11 | − | 2.05486e11i | −0.827688 | − | 0.463471i | ||||
\(817\) | − | 1.63908e11i | − | 0.367884i | ||||||
\(818\) | 4.57366e11 | 1.02153 | ||||||||
\(819\) | 1.03765e11 | + | 1.69290e11i | 0.230631 | + | 0.376267i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.41950e10i | 0.0312437i | 0.999878 | + | 0.0156218i | \(0.00497278\pi\) | ||||
−0.999878 | + | 0.0156218i | \(0.995027\pi\) | |||||||
\(822\) | −3.73052e11 | − | 2.08894e11i | −0.817113 | − | 0.457549i | ||||
\(823\) | 2.98009e11i | 0.649576i | 0.945787 | + | 0.324788i | \(0.105293\pi\) | ||||
−0.945787 | + | 0.324788i | \(0.894707\pi\) | |||||||
\(824\) | 8.31759e10i | 0.180422i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.68752e11 | −0.792163 | ||||||||
\(827\) | −3.12011e11 | −0.667034 | −0.333517 | − | 0.942744i | \(-0.608235\pi\) | ||||
−0.333517 | + | 0.942744i | \(0.608235\pi\) | |||||||
\(828\) | −1.25654e11 | − | 2.05001e11i | −0.267335 | − | 0.436149i | ||||
\(829\) | −2.42950e11 | −0.514397 | −0.257198 | − | 0.966359i | \(-0.582799\pi\) | ||||
−0.257198 | + | 0.966359i | \(0.582799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.39443e11 | − | 6.06193e11i | 0.711808 | − | 1.27118i | ||||
\(832\) | 7.08596e11i | 1.47879i | ||||||||
\(833\) | 5.71862e11 | 1.18771 | ||||||||
\(834\) | 8.40081e11 | + | 4.70410e11i | 1.73643 | + | 0.972327i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.21048e12i | 2.47818i | ||||||||
\(837\) | −2.49806e10 | − | 6.33274e11i | −0.0508980 | − | 1.29030i | ||||
\(838\) | 2.08262e11i | 0.422312i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | −8.16963e11 | −1.62538 | ||||||||
\(843\) | −1.12512e11 | + | 2.00928e11i | −0.222786 | + | 0.397861i | ||||
\(844\) | −7.56376e11 | −1.49062 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.22787e11 | − | 2.00323e11i | −0.239702 | − | 0.391066i | ||||
\(847\) | − | 1.75067e11i | − | 0.340150i | ||||||
\(848\) | −1.55097e11 | −0.299931 | ||||||||
\(849\) | 3.93377e11 | − | 7.02510e11i | 0.757143 | − | 1.35214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.18794e11i | 0.607844i | ||||||||
\(852\) | 5.30511e11 | − | 9.47412e11i | 1.00678 | − | 1.79796i | ||||
\(853\) | 2.30678e11i | 0.435723i | 0.975980 | + | 0.217861i | \(0.0699080\pi\) | ||||
−0.975980 | + | 0.217861i | \(0.930092\pi\) | |||||||
\(854\) | − | 4.02806e11i | − | 0.757293i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.25497e9 | −0.00419997 | ||||||||
\(857\) | −6.99039e11 | −1.29592 | −0.647960 | − | 0.761674i | \(-0.724378\pi\) | ||||
−0.647960 | + | 0.761674i | \(0.724378\pi\) | |||||||
\(858\) | 9.68567e11 | + | 5.42357e11i | 1.78723 | + | 1.00078i | ||||
\(859\) | −9.39004e10 | −0.172463 | −0.0862313 | − | 0.996275i | \(-0.527482\pi\) | ||||
−0.0862313 | + | 0.996275i | \(0.527482\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.87647e11 | + | 1.61070e11i | 0.523416 | + | 0.293091i | ||||
\(862\) | − | 7.19561e11i | − | 1.30328i | ||||||
\(863\) | −7.27490e11 | −1.31155 | −0.655773 | − | 0.754958i | \(-0.727657\pi\) | ||||
−0.655773 | + | 0.754958i | \(0.727657\pi\) | |||||||
\(864\) | 3.06156e10 | + | 7.76126e11i | 0.0549399 | + | 1.39276i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.13481e10i | 0.109076i | ||||||||
\(867\) | 5.62875e11 | + | 3.15187e11i | 0.996175 | + | 0.557817i | ||||
\(868\) | − | 4.05921e11i | − | 0.715094i | ||||||
\(869\) | − | 4.76621e11i | − | 0.835783i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.22520e11 | 1.08164 | ||||||||
\(872\) | −2.91325e11 | −0.503863 | ||||||||
\(873\) | −8.40963e10 | + | 5.15463e10i | −0.144784 | + | 0.0887443i | ||||
\(874\) | −5.13394e11 | −0.879842 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.07783e11 | − | 1.08541e12i | 1.03212 | − | 1.84322i | ||||
\(877\) | − | 1.49532e11i | − | 0.252775i | −0.991981 | − | 0.126388i | \(-0.959662\pi\) | ||
0.991981 | − | 0.126388i | \(-0.0403383\pi\) | |||||||
\(878\) | 2.68549e11 | 0.451904 | ||||||||
\(879\) | −3.36637e11 | − | 1.88503e11i | −0.563906 | − | 0.315764i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.01607e11i | 1.49663i | 0.663345 | + | 0.748314i | \(0.269136\pi\) | ||||
−0.663345 | + | 0.748314i | \(0.730864\pi\) | |||||||
\(882\) | −3.87192e11 | − | 6.31691e11i | −0.639811 | − | 1.04383i | ||||
\(883\) | − | 7.05614e11i | − | 1.16071i | −0.814363 | − | 0.580356i | \(-0.802914\pi\) | ||
0.814363 | − | 0.580356i | \(-0.197086\pi\) | |||||||
\(884\) | − | 1.15918e12i | − | 1.89819i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.26299e11 | −1.17864 | ||||||||
\(887\) | −1.05583e12 | −1.70568 | −0.852842 | − | 0.522170i | \(-0.825123\pi\) | ||||
−0.852842 | + | 0.522170i | \(0.825123\pi\) | |||||||
\(888\) | −1.91575e11 | + | 3.42123e11i | −0.308096 | + | 0.550213i | ||||
\(889\) | −9.78836e10 | −0.156712 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.50047e11 | + | 3.81971e11i | 1.19008 | + | 0.606066i | ||||
\(892\) | 1.55417e11i | 0.245492i | ||||||||
\(893\) | −2.81234e11 | −0.442245 | ||||||||
\(894\) | −2.27534e9 | + | 4.06341e9i | −0.00356202 | + | 0.00636122i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.23916e11i | 0.347419i | ||||||||
\(897\) | −1.28950e11 | + | 2.30285e11i | −0.199182 | + | 0.355709i | ||||
\(898\) | 5.94873e11i | 0.914785i | ||||||||
\(899\) | − | 1.29799e11i | − | 0.198716i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.46265e11 | 0.677163 | ||||||||
\(902\) | 1.84308e12 | 2.78431 | ||||||||
\(903\) | −6.36930e10 | − | 3.56654e10i | −0.0957945 | − | 0.0536410i | ||||
\(904\) | −5.74856e10 | −0.0860766 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.01697e11 | + | 2.80930e11i | 0.744610 | + | 0.416951i | ||||
\(907\) | 3.67842e11i | 0.543541i | 0.962362 | + | 0.271771i | \(0.0876092\pi\) | ||||
−0.962362 | + | 0.271771i | \(0.912391\pi\) | |||||||
\(908\) | 9.84382e11 | 1.44817 | ||||||||
\(909\) | 8.47895e11 | − | 5.19712e11i | 1.24190 | − | 0.761215i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 9.64432e11i | − | 1.40023i | −0.714032 | − | 0.700113i | \(-0.753133\pi\) | ||
0.714032 | − | 0.700113i | \(-0.246867\pi\) | |||||||
\(912\) | 5.69086e11 | + | 3.18665e11i | 0.822619 | + | 0.460633i | ||||
\(913\) | 1.34602e11i | 0.193717i | ||||||||
\(914\) | − | 2.85821e11i | − | 0.409553i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.22583e12 | −1.74120 | ||||||||
\(917\) | −2.83324e11 | −0.400688 | ||||||||
\(918\) | −6.17999e10 | − | 1.56667e12i | −0.0870196 | − | 2.20601i | ||||
\(919\) | 1.03446e12 | 1.45028 | 0.725138 | − | 0.688603i | \(-0.241776\pi\) | ||||
0.725138 | + | 0.688603i | \(0.241776\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.29111e11 | − | 2.30573e11i | 0.179443 | − | 0.320457i | ||||
\(922\) | 4.91563e11i | 0.680229i | ||||||||
\(923\) | −1.19188e12 | −1.64220 | ||||||||
\(924\) | 4.70381e11 | + | 2.63394e11i | 0.645301 | + | 0.361342i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 9.36768e11i | − | 1.27405i | ||||||
\(927\) | 2.73058e11 | − | 1.67369e11i | 0.369774 | − | 0.226651i | ||||
\(928\) | 1.59079e11i | 0.214496i | ||||||||
\(929\) | − | 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 | ||||||||
\(932\) | 1.18590e12 | 1.57175 | ||||||||
\(933\) | 4.49928e11 | − | 8.03502e11i | 0.593767 | − | 1.06038i | ||||
\(934\) | −1.61131e12 | −2.11734 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.76772e11 | + | 1.69646e11i | −0.360595 | + | 0.221024i | ||||
\(937\) | 3.27745e11i | 0.425185i | 0.977141 | + | 0.212593i | \(0.0681908\pi\) | ||||
−0.977141 | + | 0.212593i | \(0.931809\pi\) | |||||||
\(938\) | 5.39301e11 | 0.696659 | ||||||||
\(939\) | 1.12180e11 | − | 2.00337e11i | 0.144296 | − | 0.257691i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.29986e11i | 0.420860i | 0.977609 | + | 0.210430i | \(0.0674864\pi\) | ||||
−0.977609 | + | 0.210430i | \(0.932514\pi\) | |||||||
\(942\) | 4.92507e11 | − | 8.79542e11i | 0.625473 | − | 1.11700i | ||||
\(943\) | 4.38207e11i | 0.554156i | ||||||||
\(944\) | 6.22704e11i | 0.784140i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.08109e11 | −0.509579 | ||||||||
\(947\) | −2.28185e8 | −0.000283718 | −0.000141859 | − | 1.00000i | \(-0.500045\pi\) | ||||
−0.000141859 | 1.00000i | \(0.500045\pi\) | ||||||||
\(948\) | 5.62627e11 | + | 3.15048e11i | 0.696606 | + | 0.390070i | ||||
\(949\) | −1.36549e12 | −1.68354 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.42347e11 | − | 1.91700e11i | −0.418548 | − | 0.234369i | ||||
\(952\) | − | 2.17063e11i | − | 0.264264i | ||||||
\(953\) | −1.61330e11 | −0.195588 | −0.0977942 | − | 0.995207i | \(-0.531179\pi\) | ||||
−0.0977942 | + | 0.995207i | \(0.531179\pi\) | |||||||
\(954\) | −3.02153e11 | − | 4.92954e11i | −0.364782 | − | 0.595131i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.53420e12i | 1.83675i | ||||||||
\(957\) | 1.50411e11 | + | 8.42238e10i | 0.179321 | + | 0.100412i | ||||
\(958\) | − | 2.44653e12i | − | 2.90462i | ||||||
\(959\) | 2.27921e11i | 0.269470i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.69271e11 | 0.667460 | ||||||||
\(962\) | 1.99122e12 | 2.32497 | ||||||||
\(963\) | 4.53754e9 | + | 7.40286e9i | 0.00527612 | + | 0.00860784i | ||||
\(964\) | −1.13257e12 | −1.31146 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.11712e11 | + | 1.99500e11i | −0.128289 | + | 0.229105i | ||||
\(967\) | 1.49948e12i | 1.71489i | 0.514577 | + | 0.857444i | \(0.327949\pi\) | ||||
−0.514577 | + | 0.857444i | \(0.672051\pi\) | |||||||
\(968\) | 2.86217e11 | 0.325982 | ||||||||
\(969\) | −1.63744e12 | − | 9.16900e11i | −1.85725 | − | 1.03998i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.35149e11i | 0.377017i | 0.982072 | + | 0.188509i | \(0.0603654\pi\) | ||||
−0.982072 | + | 0.188509i | \(0.939635\pi\) | |||||||
\(972\) | −9.46682e11 | + | 6.32909e11i | −1.06057 | + | 0.709049i | ||||
\(973\) | − | 5.13258e11i | − | 0.572644i | ||||||
\(974\) | − | 2.61904e11i | − | 0.291009i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.80209e11 | −0.749623 | ||||||||
\(977\) | 8.22116e11 | 0.902308 | 0.451154 | − | 0.892446i | \(-0.351012\pi\) | ||||
0.451154 | + | 0.892446i | \(0.351012\pi\) | |||||||
\(978\) | −6.94287e11 | + | 1.23989e12i | −0.758898 | + | 1.35528i | ||||
\(979\) | 6.64438e11 | 0.723309 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.86215e11 | + | 9.56392e11i | 0.632967 | + | 1.03267i | ||||
\(982\) | − | 2.48545e11i | − | 0.267276i | ||||||
\(983\) | 1.23984e12 | 1.32786 | 0.663930 | − | 0.747795i | \(-0.268887\pi\) | ||||
0.663930 | + | 0.747795i | \(0.268887\pi\) | |||||||
\(984\) | −2.63334e11 | + | 4.70274e11i | −0.280883 | + | 0.501615i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 3.21112e11i | − | 0.339742i | ||||||
\(987\) | −6.11951e10 | + | 1.09285e11i | −0.0644834 | + | 0.115158i | ||||
\(988\) | 1.79763e12i | 1.88657i | ||||||||
\(989\) | − | 9.70311e10i | − | 0.101420i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.44437e12 | 1.49756 | 0.748782 | − | 0.662817i | \(-0.230639\pi\) | ||||
0.748782 | + | 0.662817i | \(0.230639\pi\) | |||||||
\(992\) | −1.74297e12 | −1.79988 | ||||||||
\(993\) | −3.86878e11 | − | 2.16635e11i | −0.397902 | − | 0.222809i | ||||
\(994\) | −1.03255e12 | −1.05771 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.58890e11 | − | 8.89721e10i | −0.161458 | − | 0.0904100i | ||||
\(997\) | − | 4.69939e11i | − | 0.475621i | −0.971312 | − | 0.237810i | \(-0.923570\pi\) | ||
0.971312 | − | 0.237810i | \(-0.0764297\pi\) | |||||||
\(998\) | 1.63310e12 | 1.64623 | ||||||||
\(999\) | 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.d.d.74.4 | 20 | ||
3.2 | odd | 2 | inner | 75.9.d.d.74.18 | 20 | ||
5.2 | odd | 4 | 75.9.c.e.26.2 | ✓ | 10 | ||
5.3 | odd | 4 | 75.9.c.f.26.9 | yes | 10 | ||
5.4 | even | 2 | inner | 75.9.d.d.74.17 | 20 | ||
15.2 | even | 4 | 75.9.c.e.26.9 | yes | 10 | ||
15.8 | even | 4 | 75.9.c.f.26.2 | yes | 10 | ||
15.14 | odd | 2 | inner | 75.9.d.d.74.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.c.e.26.2 | ✓ | 10 | 5.2 | odd | 4 | ||
75.9.c.e.26.9 | yes | 10 | 15.2 | even | 4 | ||
75.9.c.f.26.2 | yes | 10 | 15.8 | even | 4 | ||
75.9.c.f.26.9 | yes | 10 | 5.3 | odd | 4 | ||
75.9.d.d.74.3 | 20 | 15.14 | odd | 2 | inner | ||
75.9.d.d.74.4 | 20 | 1.1 | even | 1 | trivial | ||
75.9.d.d.74.17 | 20 | 5.4 | even | 2 | inner | ||
75.9.d.d.74.18 | 20 | 3.2 | odd | 2 | inner |