Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,3,Mod(65,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.e (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: | \(5.23162107572\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.3 | ||
Root | \(1.16372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.65 |
Dual form | 192.3.e.f.65.4 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.64575 | − | 1.41421i | 0.881917 | − | 0.471405i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.48331i | 1.49666i | 0.663325 | + | 0.748331i | \(0.269145\pi\) | ||||
−0.663325 | + | 0.748331i | \(0.730855\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.29150 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000 | − | 7.48331i | 0.555556 | − | 0.831479i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.1421i | 1.28565i | 0.766014 | + | 0.642824i | \(0.222237\pi\) | ||||
−0.766014 | + | 0.642824i | \(0.777763\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.0000 | −0.769231 | −0.384615 | − | 0.923077i | \(-0.625666\pi\) | ||||
−0.384615 | + | 0.923077i | \(0.625666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.5830 | + | 19.7990i | 0.705534 | + | 1.31993i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.4575 | 1.39250 | 0.696250 | − | 0.717799i | \(-0.254850\pi\) | ||||
0.696250 | + | 0.717799i | \(0.254850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.0000 | − | 7.48331i | 0.666667 | − | 0.356348i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 16.9706i | − | 0.737851i | −0.929459 | − | 0.368925i | \(-0.879726\pi\) | ||
0.929459 | − | 0.368925i | \(-0.120274\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −31.0000 | −1.24000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575 | − | 26.8701i | 0.0979908 | − | 0.995187i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 37.4166i | − | 1.29023i | −0.764087 | − | 0.645113i | \(-0.776810\pi\) | ||
0.764087 | − | 0.645113i | \(-0.223190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.4575 | 0.853468 | 0.426734 | − | 0.904377i | \(-0.359664\pi\) | ||||
0.426734 | + | 0.904377i | \(0.359664\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 20.0000 | + | 37.4166i | 0.606061 | + | 1.13384i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 39.5980i | 1.13137i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −0.270270 | −0.135135 | − | 0.990827i | \(-0.543147\pi\) | ||||
−0.135135 | + | 0.990827i | \(0.543147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −26.4575 | + | 14.1421i | −0.678398 | + | 0.362619i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14.9666i | 0.365040i | 0.983202 | + | 0.182520i | \(0.0584254\pi\) | ||||
−0.983202 | + | 0.182520i | \(0.941575\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −58.2065 | −1.35364 | −0.676820 | − | 0.736148i | \(-0.736643\pi\) | ||||
−0.676820 | + | 0.736148i | \(0.736643\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 56.0000 | + | 37.4166i | 1.24444 | + | 0.831479i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.3137i | − | 0.240717i | −0.992730 | − | 0.120359i | \(-0.961596\pi\) | ||
0.992730 | − | 0.120359i | \(-0.0384044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.0000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37.4166i | 0.705973i | 0.935628 | + | 0.352987i | \(0.114834\pi\) | ||||
−0.935628 | + | 0.352987i | \(0.885166\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −105.830 | −1.92418 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 70.0000 | − | 37.4166i | 1.22807 | − | 0.656431i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 98.9949i | − | 1.67788i | −0.544224 | − | 0.838940i | \(-0.683176\pi\) | ||
0.544224 | − | 0.838940i | \(-0.316824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −90.0000 | −1.47541 | −0.737705 | − | 0.675123i | \(-0.764090\pi\) | ||||
−0.737705 | + | 0.675123i | \(0.764090\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 26.4575 | − | 39.5980i | 0.419961 | − | 0.628539i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 74.8331i | − | 1.15128i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.29150 | 0.0789777 | 0.0394888 | − | 0.999220i | \(-0.487427\pi\) | ||||
0.0394888 | + | 0.999220i | \(0.487427\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.0000 | − | 44.8999i | −0.347826 | − | 0.650723i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 28.2843i | − | 0.398370i | −0.979962 | − | 0.199185i | \(-0.936171\pi\) | ||
0.979962 | − | 0.199185i | \(-0.0638295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −30.0000 | −0.410959 | −0.205479 | − | 0.978661i | \(-0.565875\pi\) | ||||
−0.205479 | + | 0.978661i | \(0.565875\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −82.0183 | + | 43.8406i | −1.09358 | + | 0.584542i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 74.8331i | 0.971859i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26.4575 | 0.334905 | 0.167453 | − | 0.985880i | \(-0.446446\pi\) | ||||
0.167453 | + | 0.985880i | \(0.446446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −31.0000 | − | 74.8331i | −0.382716 | − | 0.923866i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 25.4558i | − | 0.306697i | −0.988172 | − | 0.153348i | \(-0.950994\pi\) | ||
0.988172 | − | 0.153348i | \(-0.0490057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −52.9150 | − | 98.9949i | −0.608219 | − | 1.13787i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 74.8331i | 0.840822i | 0.907334 | + | 0.420411i | \(0.138114\pi\) | ||||
−0.907334 | + | 0.420411i | \(0.861886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −52.9150 | −0.581484 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 70.0000 | − | 37.4166i | 0.752688 | − | 0.402329i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 197.990i | 2.08410i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 0.103093 | 0.0515464 | − | 0.998671i | \(-0.483585\pi\) | ||||
0.0515464 | + | 0.998671i | \(0.483585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 105.830 | + | 70.7107i | 1.06899 | + | 0.714249i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 112.250i | − | 1.11138i | −0.831388 | − | 0.555692i | \(-0.812454\pi\) | ||
0.831388 | − | 0.555692i | \(-0.187546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 47.6235 | 0.462364 | 0.231182 | − | 0.972910i | \(-0.425741\pi\) | ||||
0.231182 | + | 0.972910i | \(0.425741\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 56.0000 | + | 104.766i | 0.533333 | + | 0.997775i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843i | 0.0264339i | 0.999913 | + | 0.0132169i | \(0.00420721\pi\) | ||||
−0.999913 | + | 0.0132169i | \(0.995793\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 70.0000 | 0.642202 | 0.321101 | − | 0.947045i | \(-0.395947\pi\) | ||||
0.321101 | + | 0.947045i | \(0.395947\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.4575 | + | 14.1421i | −0.238356 | + | 0.127407i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 149.666i | 1.32448i | 0.749292 | + | 0.662240i | \(0.230394\pi\) | ||||
−0.749292 | + | 0.662240i | \(0.769606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 126.996 | 1.10431 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −50.0000 | + | 74.8331i | −0.427350 | + | 0.639600i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −79.0000 | −0.652893 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.1660 | + | 39.5980i | 0.172081 | + | 0.321935i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 44.8999i | − | 0.359199i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 153.454 | 1.20830 | 0.604148 | − | 0.796872i | \(-0.293514\pi\) | ||||
0.604148 | + | 0.796872i | \(0.293514\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −154.000 | + | 82.3165i | −1.19380 | + | 0.638112i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 70.7107i | − | 0.539776i | −0.962892 | − | 0.269888i | \(-0.913013\pi\) | ||
0.962892 | − | 0.269888i | \(-0.0869867\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 140.000 | 1.05263 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 201.077 | + | 19.7990i | 1.48946 | + | 0.146659i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 224.499i | − | 1.63868i | −0.573306 | − | 0.819341i | \(-0.694340\pi\) | ||
0.573306 | − | 0.819341i | \(-0.305660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 132.288 | 0.951709 | 0.475855 | − | 0.879524i | \(-0.342139\pi\) | ||||
0.475855 | + | 0.879524i | \(0.342139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.0000 | − | 29.9333i | −0.113475 | − | 0.212293i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 141.421i | − | 0.988961i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 280.000 | 1.93103 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −55.5608 | + | 29.6985i | −0.377964 | + | 0.202031i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 22.4499i | − | 0.150671i | −0.997158 | − | 0.0753354i | \(-0.975997\pi\) | ||
0.997158 | − | 0.0753354i | \(-0.0240027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −79.3725 | −0.525646 | −0.262823 | − | 0.964844i | \(-0.584654\pi\) | ||||
−0.262823 | + | 0.964844i | \(0.584654\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 197.990i | 1.27735i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −170.000 | −1.08280 | −0.541401 | − | 0.840764i | \(-0.682106\pi\) | ||||
−0.541401 | + | 0.840764i | \(0.682106\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 52.9150 | + | 98.9949i | 0.332799 | + | 0.622610i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 89.7998i | − | 0.557763i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −100.539 | −0.616801 | −0.308400 | − | 0.951257i | \(-0.599794\pi\) | ||||
−0.308400 | + | 0.951257i | \(0.599794\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −280.000 | + | 149.666i | −1.69697 | + | 0.907068i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 243.245i | 1.45656i | 0.685282 | + | 0.728278i | \(0.259679\pi\) | ||||
−0.685282 | + | 0.728278i | \(0.740321\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −69.0000 | −0.408284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 132.288 | − | 197.990i | 0.773611 | − | 1.15784i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 112.250i | 0.648842i | 0.945913 | + | 0.324421i | \(0.105169\pi\) | ||||
−0.945913 | + | 0.324421i | \(0.894831\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −164.037 | −0.937352 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −140.000 | − | 261.916i | −0.790960 | − | 1.47975i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 212.132i | 1.18510i | 0.805535 | + | 0.592548i | \(0.201878\pi\) | ||||
−0.805535 | + | 0.592548i | \(0.798122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 262.000 | 1.44751 | 0.723757 | − | 0.690055i | \(-0.242414\pi\) | ||||
0.723757 | + | 0.690055i | \(0.242414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −238.118 | + | 127.279i | −1.30119 | + | 0.695515i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 74.8331i | − | 0.404504i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.0000 | − | 142.183i | 0.0740741 | − | 0.752291i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 339.411i | − | 1.77702i | −0.458855 | − | 0.888511i | \(-0.651740\pi\) | ||
0.458855 | − | 0.888511i | \(-0.348260\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 210.000 | 1.08808 | 0.544041 | − | 0.839058i | \(-0.316893\pi\) | ||||
0.544041 | + | 0.839058i | \(0.316893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −105.830 | − | 197.990i | −0.542718 | − | 1.01533i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 187.083i | 0.949659i | 0.880078 | + | 0.474830i | \(0.157490\pi\) | ||||
−0.880078 | + | 0.474830i | \(0.842510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 343.948 | 1.72838 | 0.864190 | − | 0.503165i | \(-0.167831\pi\) | ||||
0.864190 | + | 0.503165i | \(0.167831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0000 | − | 7.48331i | 0.0696517 | − | 0.0372304i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 197.990i | − | 0.975320i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −112.000 | −0.546341 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −126.996 | − | 84.8528i | −0.613508 | − | 0.409917i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 374.166i | 1.79027i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −291.033 | −1.37930 | −0.689651 | − | 0.724142i | \(-0.742236\pi\) | ||||
−0.689651 | + | 0.724142i | \(0.742236\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −40.0000 | − | 74.8331i | −0.187793 | − | 0.351329i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 435.578i | − | 2.02594i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 140.000 | 0.645161 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −79.3725 | + | 42.4264i | −0.362432 | + | 0.193728i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −312.199 | −1.39999 | −0.699997 | − | 0.714146i | \(-0.746815\pi\) | ||||
−0.699997 | + | 0.714146i | \(0.746815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −155.000 | + | 231.983i | −0.688889 | + | 1.03103i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 59.3970i | − | 0.261661i | −0.991405 | − | 0.130830i | \(-0.958236\pi\) | ||
0.991405 | − | 0.130830i | \(-0.0417643\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 358.000 | 1.56332 | 0.781659 | − | 0.623706i | \(-0.214374\pi\) | ||||
0.781659 | + | 0.623706i | \(0.214374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 105.830 | + | 197.990i | 0.458139 | + | 0.857099i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 224.499i | 0.963517i | 0.876304 | + | 0.481758i | \(0.160002\pi\) | ||||
−0.876304 | + | 0.481758i | \(0.839998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 84.6640 | 0.360273 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 70.0000 | − | 37.4166i | 0.295359 | − | 0.157876i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 169.706i | 0.710065i | 0.934854 | + | 0.355033i | \(0.115530\pi\) | ||||
−0.934854 | + | 0.355033i | \(0.884470\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −110.000 | −0.456432 | −0.228216 | − | 0.973611i | \(-0.573289\pi\) | ||||
−0.228216 | + | 0.973611i | \(0.573289\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −187.848 | − | 154.149i | −0.773038 | − | 0.634359i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 157.150i | − | 0.641427i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −264.575 | −1.07115 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −36.0000 | − | 67.3498i | −0.144578 | − | 0.270481i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 296.985i | 1.18321i | 0.806229 | + | 0.591603i | \(0.201505\pi\) | ||||
−0.806229 | + | 0.591603i | \(0.798495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 240.000 | 0.948617 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 299.333i | − | 1.16472i | −0.812932 | − | 0.582359i | \(-0.802130\pi\) | ||
0.812932 | − | 0.582359i | \(-0.197870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −52.9150 | −0.204305 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −280.000 | − | 187.083i | −1.07280 | − | 0.716793i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 152.735i | 0.580742i | 0.956914 | + | 0.290371i | \(0.0937787\pi\) | ||||
−0.956914 | + | 0.290371i | \(0.906221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −280.000 | −1.05660 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 105.830 | + | 197.990i | 0.396367 | + | 0.741535i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 426.549i | − | 1.58568i | −0.609427 | − | 0.792842i | \(-0.708601\pi\) | ||
0.609427 | − | 0.792842i | \(-0.291399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −396.863 | −1.46444 | −0.732219 | − | 0.681069i | \(-0.761515\pi\) | ||||
−0.732219 | + | 0.681069i | \(0.761515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −140.000 | + | 74.8331i | −0.512821 | + | 0.274114i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 438.406i | − | 1.59420i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −490.000 | −1.76895 | −0.884477 | − | 0.466585i | \(-0.845484\pi\) | ||||
−0.884477 | + | 0.466585i | \(0.845484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 132.288 | − | 197.990i | 0.474149 | − | 0.709641i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 134.700i | 0.479358i | 0.970852 | + | 0.239679i | \(0.0770422\pi\) | ||||
−0.970852 | + | 0.239679i | \(0.922958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.29150 | 0.0186979 | 0.00934894 | − | 0.999956i | \(-0.497024\pi\) | ||||
0.00934894 | + | 0.999956i | \(0.497024\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 280.000 | + | 523.832i | 0.982456 | + | 1.83801i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 79.1960i | 0.275944i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.4575 | − | 14.1421i | 0.0909193 | − | 0.0485984i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 112.250i | − | 0.383105i | −0.981482 | − | 0.191552i | \(-0.938648\pi\) | ||
0.981482 | − | 0.191552i | \(-0.0613522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 740.810 | 2.51122 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 380.000 | + | 37.4166i | 1.27946 | + | 0.125982i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 169.706i | 0.567577i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −308.000 | −1.02326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −158.745 | − | 296.985i | −0.523911 | − | 0.980148i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 673.498i | − | 2.20819i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 47.6235 | 0.155125 | 0.0775627 | − | 0.996987i | \(-0.475286\pi\) | ||||
0.0775627 | + | 0.996987i | \(0.475286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 126.000 | − | 67.3498i | 0.407767 | − | 0.217961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 254.558i | 0.818516i | 0.912419 | + | 0.409258i | \(0.134212\pi\) | ||||
−0.912419 | + | 0.409258i | \(0.865788\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −230.000 | −0.734824 | −0.367412 | − | 0.930058i | \(-0.619756\pi\) | ||||
−0.367412 | + | 0.930058i | \(0.619756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 296.324 | + | 197.990i | 0.940712 | + | 0.628539i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 561.249i | 1.77050i | 0.465115 | + | 0.885250i | \(0.346013\pi\) | ||||
−0.465115 | + | 0.885250i | \(0.653987\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 529.150 | 1.65878 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | + | 7.48331i | 0.0124611 | + | 0.0233125i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 310.000 | 0.953846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 185.203 | − | 98.9949i | 0.566369 | − | 0.302737i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 59.8665i | − | 0.181965i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 132.288 | 0.399660 | 0.199830 | − | 0.979831i | \(-0.435961\pi\) | ||||
0.199830 | + | 0.979831i | \(0.435961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −50.0000 | + | 74.8331i | −0.150150 | + | 0.224724i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 39.5980i | 0.118203i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −70.0000 | −0.207715 | −0.103858 | − | 0.994592i | \(-0.533119\pi\) | ||||
−0.103858 | + | 0.994592i | \(0.533119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 211.660 | + | 395.980i | 0.624366 | + | 1.16808i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 374.166i | 1.09726i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −370.405 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 336.000 | − | 179.600i | 0.973913 | − | 0.520578i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 540.230i | − | 1.55686i | −0.627733 | − | 0.778429i | \(-0.716017\pi\) | ||
0.627733 | − | 0.778429i | \(-0.283983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −298.000 | −0.853868 | −0.426934 | − | 0.904283i | \(-0.640406\pi\) | ||||
−0.426934 | + | 0.904283i | \(0.640406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.4575 | + | 268.701i | −0.0753775 | + | 0.765529i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 299.333i | 0.847968i | 0.905670 | + | 0.423984i | \(0.139369\pi\) | ||||
−0.905670 | + | 0.423984i | \(0.860631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 211.660 | 0.596226 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 537.401i | 1.49694i | 0.663169 | + | 0.748470i | \(0.269211\pi\) | ||||
−0.663169 | + | 0.748470i | \(0.730789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 339.000 | 0.939058 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −209.014 | + | 111.723i | −0.575797 | + | 0.307777i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 224.499i | − | 0.615067i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 111.122 | 0.302784 | 0.151392 | − | 0.988474i | \(-0.451625\pi\) | ||||
0.151392 | + | 0.988474i | \(0.451625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 112.000 | + | 74.8331i | 0.303523 | + | 0.202800i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 197.990i | 0.533665i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −410.000 | −1.09920 | −0.549598 | − | 0.835429i | \(-0.685219\pi\) | ||||
−0.549598 | + | 0.835429i | \(0.685219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −63.4980 | − | 118.794i | −0.169328 | − | 0.316784i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 374.166i | 0.992482i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 661.438 | 1.74522 | 0.872609 | − | 0.488419i | \(-0.162426\pi\) | ||||
0.872609 | + | 0.488419i | \(0.162426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 406.000 | − | 217.016i | 1.06562 | − | 0.569596i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 158.392i | 0.413556i | 0.978388 | + | 0.206778i | \(0.0662978\pi\) | ||||
−0.978388 | + | 0.206778i | \(0.933702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −560.000 | −1.45455 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −291.033 | + | 435.578i | −0.752022 | + | 1.12552i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 246.949i | 0.634831i | 0.948287 | + | 0.317416i | \(0.102815\pi\) | ||||
−0.948287 | + | 0.317416i | \(0.897185\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −100.000 | − | 187.083i | −0.254453 | − | 0.476038i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 197.990i | 0.501240i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 230.000 | 0.579345 | 0.289673 | − | 0.957126i | \(-0.406454\pi\) | ||||
0.289673 | + | 0.957126i | \(0.406454\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 370.405 | − | 197.990i | 0.928334 | − | 0.496215i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 299.333i | 0.746465i | 0.927738 | + | 0.373233i | \(0.121751\pi\) | ||||
−0.927738 | + | 0.373233i | \(0.878249\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −264.575 | −0.656514 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 560.000 | − | 231.983i | 1.38272 | − | 0.572797i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 141.421i | − | 0.347473i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −590.000 | −1.44254 | −0.721271 | − | 0.692653i | \(-0.756442\pi\) | ||||
−0.721271 | + | 0.692653i | \(0.756442\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −317.490 | − | 593.970i | −0.772482 | − | 1.44518i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 523.832i | − | 1.26836i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 190.494 | 0.459022 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 350.000 | − | 187.083i | 0.839329 | − | 0.448640i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 98.9949i | 0.236265i | 0.992998 | + | 0.118132i | \(0.0376907\pi\) | ||||
−0.992998 | + | 0.118132i | \(0.962309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 70.0000 | 0.166271 | 0.0831354 | − | 0.996538i | \(-0.473507\pi\) | ||||
0.0831354 | + | 0.996538i | \(0.473507\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −84.6640 | − | 56.5685i | −0.200151 | − | 0.133732i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −476.235 | −1.11531 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −200.000 | − | 374.166i | −0.466200 | − | 0.872181i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 509.117i | − | 1.18125i | −0.806948 | − | 0.590623i | \(-0.798882\pi\) | ||
0.806948 | − | 0.590623i | \(-0.201118\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000 | 0.0230947 | 0.0115473 | − | 0.999933i | \(-0.496324\pi\) | ||||
0.0115473 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 740.810 | − | 395.980i | 1.70301 | − | 0.910298i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 448.999i | − | 1.02746i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −502.693 | −1.14509 | −0.572543 | − | 0.819875i | \(-0.694043\pi\) | ||||
−0.572543 | + | 0.819875i | \(0.694043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −105.000 | + | 157.150i | −0.238095 | + | 0.356348i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 313.955i | − | 0.708703i | −0.935112 | − | 0.354351i | \(-0.884702\pi\) | ||
0.935112 | − | 0.354351i | \(-0.115298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −560.000 | −1.25843 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.7490 | − | 59.3970i | −0.0710269 | − | 0.132879i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 209.533i | 0.466666i | 0.972397 | + | 0.233333i | \(0.0749631\pi\) | ||||
−0.972397 | + | 0.233333i | \(0.925037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −211.660 | −0.469313 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −210.000 | + | 112.250i | −0.463576 | + | 0.247792i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 395.980i | − | 0.870285i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −430.000 | −0.940919 | −0.470460 | − | 0.882422i | \(-0.655912\pi\) | ||||
−0.470460 | + | 0.882422i | \(0.655912\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 112.250i | 0.243492i | 0.992561 | + | 0.121746i | \(0.0388493\pi\) | ||||
−0.992561 | + | 0.121746i | \(0.961151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −100.539 | −0.217146 | −0.108573 | − | 0.994088i | \(-0.534628\pi\) | ||||
−0.108573 | + | 0.994088i | \(0.534628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 280.000 | + | 523.832i | 0.602151 | + | 1.12652i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 138.593i | − | 0.296773i | −0.988929 | − | 0.148386i | \(-0.952592\pi\) | ||
0.988929 | − | 0.148386i | \(-0.0474079\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000 | 0.0597015 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −449.778 | + | 240.416i | −0.954942 | + | 0.510438i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 823.165i | − | 1.74031i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −820.183 | −1.72670 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 280.000 | + | 187.083i | 0.587002 | + | 0.392207i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 339.411i | 0.708583i | 0.935135 | + | 0.354291i | \(0.115278\pi\) | ||||
−0.935135 | + | 0.354291i | \(0.884722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 100.000 | 0.207900 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −126.996 | − | 237.588i | −0.262932 | − | 0.491900i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 74.8331i | 0.154295i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −375.697 | −0.771451 | −0.385726 | − | 0.922614i | \(-0.626049\pi\) | ||||
−0.385726 | + | 0.922614i | \(0.626049\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −266.000 | + | 142.183i | −0.543967 | + | 0.290763i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 523.259i | 1.06570i | 0.846210 | + | 0.532850i | \(0.178879\pi\) | ||||
−0.846210 | + | 0.532850i | \(0.821121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −529.150 | + | 791.960i | −1.06899 | + | 1.59992i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 149.666i | − | 0.301139i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 555.608 | 1.11344 | 0.556721 | − | 0.830699i | \(-0.312059\pi\) | ||||
0.556721 | + | 0.830699i | \(0.312059\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 344.000 | + | 643.565i | 0.686627 | + | 1.28456i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 831.558i | − | 1.65320i | −0.562793 | − | 0.826598i | \(-0.690273\pi\) | ||
0.562793 | − | 0.826598i | \(-0.309727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 840.000 | 1.66337 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −182.557 | + | 97.5807i | −0.360073 | + | 0.192467i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 561.249i | 1.10265i | 0.834291 | + | 0.551325i | \(0.185877\pi\) | ||||
−0.834291 | + | 0.551325i | \(0.814123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −158.745 | −0.310656 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 70.0000 | − | 710.915i | 0.136452 | − | 1.38580i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 356.382i | 0.692004i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 160.000 | 0.309478 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 158.745 | + | 296.985i | 0.305867 | + | 0.572225i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 224.499i | − | 0.430901i | −0.976515 | − | 0.215451i | \(-0.930878\pi\) | ||
0.976515 | − | 0.215451i | \(-0.0691220\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −904.847 | −1.73011 | −0.865054 | − | 0.501678i | \(-0.832716\pi\) | ||||
−0.865054 | + | 0.501678i | \(0.832716\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −434.000 | + | 231.983i | −0.826667 | + | 0.441872i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 241.000 | 0.455577 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −740.810 | − | 494.975i | −1.39512 | − | 0.932156i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 149.666i | − | 0.280800i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.1660 | −0.0395626 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 300.000 | + | 561.249i | 0.558659 | + | 1.04516i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 296.985i | − | 0.550992i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 518.000 | 0.957486 | 0.478743 | − | 0.877955i | \(-0.341093\pi\) | ||||
0.478743 | + | 0.877955i | \(0.341093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 693.187 | − | 370.524i | 1.27659 | − | 0.682365i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 523.832i | 0.961160i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1000.09 | 1.82833 | 0.914163 | − | 0.405347i | \(-0.132849\pi\) | ||||
0.914163 | + | 0.405347i | \(0.132849\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −450.000 | + | 673.498i | −0.819672 | + | 1.22677i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 989.949i | − | 1.79664i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 140.000 | 0.253165 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −105.830 | − | 197.990i | −0.190685 | − | 0.356739i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 411.582i | 0.738927i | 0.929245 | + | 0.369463i | \(0.120459\pi\) | ||||
−0.929245 | + | 0.369463i | \(0.879541\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 582.065 | 1.04126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 653.367i | 1.16051i | 0.814435 | + | 0.580255i | \(0.197047\pi\) | ||||
−0.814435 | + | 0.580255i | \(0.802953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1120.00 | −1.98230 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −164.037 | − | 395.980i | −0.289306 | − | 0.698377i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 613.632i | − | 1.07844i | −0.842165 | − | 0.539220i | \(-0.818719\pi\) | ||
0.842165 | − | 0.539220i | \(-0.181281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 343.948 | 0.602360 | 0.301180 | − | 0.953567i | \(-0.402619\pi\) | ||||
0.301180 | + | 0.953567i | \(0.402619\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −480.000 | − | 897.998i | −0.837696 | − | 1.56719i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 526.087i | 0.914935i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −390.000 | −0.675910 | −0.337955 | − | 0.941162i | \(-0.609735\pi\) | ||||
−0.337955 | + | 0.941162i | \(0.609735\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 555.608 | − | 296.985i | 0.959599 | − | 0.512927i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 134.700i | − | 0.231841i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −529.150 | −0.907633 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −560.000 | − | 374.166i | −0.957265 | − | 0.639600i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 653.367i | − | 1.11306i | −0.830827 | − | 0.556530i | \(-0.812132\pi\) | ||
0.830827 | − | 0.556530i | \(-0.187868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 700.000 | 1.18846 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 264.575 | + | 494.975i | 0.447674 | + | 0.837521i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 448.999i | − | 0.757165i | −0.925568 | − | 0.378583i | \(-0.876412\pi\) | ||
0.925568 | − | 0.378583i | \(-0.123588\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 910.000 | − | 486.415i | 1.52429 | − | 0.814766i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 480.833i | 0.802726i | 0.915919 | + | 0.401363i | \(0.131463\pi\) | ||||
−0.915919 | + | 0.401363i | \(0.868537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 130.000 | 0.216306 | 0.108153 | − | 0.994134i | \(-0.465506\pi\) | ||||
0.108153 | + | 0.994134i | \(0.465506\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.4575 | − | 39.5980i | 0.0438765 | − | 0.0656683i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 591.182i | − | 0.977160i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 153.454 | 0.252807 | 0.126403 | − | 0.991979i | \(-0.459657\pi\) | ||||
0.126403 | + | 0.991979i | \(0.459657\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −280.000 | − | 523.832i | −0.459770 | − | 0.860151i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 113.137i | 0.185167i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 630.000 | 1.02773 | 0.513866 | − | 0.857870i | \(-0.328213\pi\) | ||||
0.513866 | + | 0.857870i | \(0.328213\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −296.324 | + | 158.392i | −0.481828 | + | 0.257548i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1122.50i | 1.81928i | 0.415395 | + | 0.909641i | \(0.363643\pi\) | ||||
−0.415395 | + | 0.909641i | \(0.636357\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 555.608 | 0.897589 | 0.448795 | − | 0.893635i | \(-0.351853\pi\) | ||||
0.448795 | + | 0.893635i | \(0.351853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −456.000 | − | 44.8999i | −0.734300 | − | 0.0723026i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 395.980i | 0.635602i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −439.000 | −0.702400 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 529.150 | + | 989.949i | 0.843940 | + | 1.57887i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 978.928 | 1.55139 | 0.775696 | − | 0.631107i | \(-0.217399\pi\) | ||||
0.775696 | + | 0.631107i | \(0.217399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −770.000 | + | 411.582i | −1.21643 | + | 0.650209i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1148.34i | 1.80841i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 210.000 | 0.329670 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −211.660 | − | 141.421i | −0.331236 | − | 0.221317i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 389.132i | 0.607071i | 0.952820 | + | 0.303535i | \(0.0981671\pi\) | ||||
−0.952820 | + | 0.303535i | \(0.901833\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −269.867 | −0.419699 | −0.209850 | − | 0.977734i | \(-0.567297\pi\) | ||||
−0.209850 | + | 0.977734i | \(0.567297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −616.000 | − | 1152.43i | −0.955039 | − | 1.78671i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1170.97i | 1.80984i | 0.425578 | + | 0.904922i | \(0.360071\pi\) | ||||
−0.425578 | + | 0.904922i | \(0.639929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1400.00 | 2.15716 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 370.405 | − | 197.990i | 0.568979 | − | 0.304132i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 710.915i | 1.08869i | 0.838861 | + | 0.544345i | \(0.183222\pi\) | ||||
−0.838861 | + | 0.544345i | \(0.816778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 529.150 | 0.807863 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −150.000 | + | 224.499i | −0.228311 | + | 0.341704i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 127.279i | − | 0.193140i | −0.995326 | − | 0.0965700i | \(-0.969213\pi\) | ||
0.995326 | − | 0.0965700i | \(-0.0307872\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −170.000 | −0.257186 | −0.128593 | − | 0.991697i | \(-0.541046\pi\) | ||||
−0.128593 | + | 0.991697i | \(0.541046\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1047.66i | 1.57543i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −634.980 | −0.951994 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −826.000 | + | 441.516i | −1.23468 | + | 0.659963i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1272.79i | − | 1.89686i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −310.000 | −0.460624 | −0.230312 | − | 0.973117i | \(-0.573975\pi\) | ||||
−0.230312 | + | 0.973117i | \(0.573975\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −82.0183 | + | 832.972i | −0.121509 | + | 1.23403i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1309.58i | − | 1.93439i | −0.254041 | − | 0.967194i | \(-0.581760\pi\) | ||
0.254041 | − | 0.967194i | \(-0.418240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 52.9150 | 0.0779308 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −84.0000 | − | 157.150i | −0.123348 | − | 0.230763i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1162.48i | − | 1.70203i | −0.525145 | − | 0.851013i | \(-0.675989\pi\) | ||
0.525145 | − | 0.851013i | \(-0.324011\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1680.00 | 2.45255 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 947.179 | − | 506.288i | 1.37872 | − | 0.736956i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 374.166i | − | 0.543056i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.4575 | 0.0382887 | 0.0191444 | − | 0.999817i | \(-0.493906\pi\) | ||||
0.0191444 | + | 0.999817i | \(0.493906\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 560.000 | + | 374.166i | 0.808081 | + | 0.539922i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 989.949i | 1.42439i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 317.490 | + | 593.970i | 0.454206 | + | 0.849742i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.4499i | 0.0320256i | 0.999872 | + | 0.0160128i | \(0.00509725\pi\) | ||||
−0.999872 | + | 0.0160128i | \(0.994903\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −264.575 | −0.376352 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 224.000 | − | 119.733i | 0.317730 | − | 0.169834i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 593.970i | − | 0.840127i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 182.000 | 0.256700 | 0.128350 | − | 0.991729i | \(-0.459032\pi\) | ||||
0.128350 | + | 0.991729i | \(0.459032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 132.288 | − | 197.990i | 0.186058 | − | 0.278467i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 448.999i | − | 0.629732i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1058.30 | 1.48014 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 240.000 | + | 448.999i | 0.334728 | + | 0.626219i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 395.980i | 0.550737i | 0.961339 | + | 0.275368i | \(0.0887998\pi\) | ||||
−0.961339 | + | 0.275368i | \(0.911200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 252.000 | 0.349515 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −291.033 | + | 155.563i | −0.402535 | + | 0.215164i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1159.91i | 1.59988i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.6235 | 0.0655069 | 0.0327535 | − | 0.999463i | \(-0.489572\pi\) | ||||
0.0327535 | + | 0.999463i | \(0.489572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −715.000 | − | 142.183i | −0.980796 | − | 0.195038i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −650.000 | −0.886767 | −0.443383 | − | 0.896332i | \(-0.646222\pi\) | ||||
−0.443383 | + | 0.896332i | \(0.646222\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −222.243 | − | 415.779i | −0.302372 | − | 0.565685i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 74.8331i | 0.101538i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 343.948 | 0.465423 | 0.232712 | − | 0.972546i | \(-0.425240\pi\) | ||||
0.232712 | + | 0.972546i | \(0.425240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −700.000 | + | 374.166i | −0.944669 | + | 0.504947i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 661.852i | − | 0.890783i | −0.895336 | − | 0.445392i | \(-0.853064\pi\) | ||
0.895336 | − | 0.445392i | \(-0.146936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 168.000 | 0.225503 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −190.494 | − | 127.279i | −0.255012 | − | 0.170387i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.9666i | 0.0199821i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −608.523 | −0.810283 | −0.405142 | − | 0.914254i | \(-0.632778\pi\) | ||||
−0.405142 | + | 0.914254i | \(0.632778\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 420.000 | + | 785.748i | 0.557769 | + | 1.04349i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 593.970i | − | 0.786715i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1050.00 | −1.38705 | −0.693527 | − | 0.720431i | \(-0.743944\pi\) | ||||
−0.693527 | + | 0.720431i | \(0.743944\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 634.980 | − | 339.411i | 0.836601 | − | 0.447182i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 673.498i | − | 0.885018i | −0.896764 | − | 0.442509i | \(-0.854089\pi\) | ||
0.896764 | − | 0.442509i | \(-0.145911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 370.405 | 0.485459 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 989.949i | 1.29068i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1138.00 | 1.47984 | 0.739922 | − | 0.672693i | \(-0.234862\pi\) | ||||
0.739922 | + | 0.672693i | \(0.234862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −423.320 | − | 791.960i | −0.549053 | − | 1.02718i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 785.748i | 1.01649i | 0.861212 | + | 0.508246i | \(0.169706\pi\) | ||||
−0.861212 | + | 0.508246i | \(0.830294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −820.183 | −1.05830 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −140.000 | + | 74.8331i | −0.180180 | + | 0.0963104i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 395.980i | 0.508318i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 400.000 | 0.512164 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1005.39 | − | 98.9949i | −1.28402 | − | 0.126430i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1272.16i | − | 1.62059i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −904.847 | −1.14974 | −0.574871 | − | 0.818244i | \(-0.694948\pi\) | ||||
−0.574871 | + | 0.818244i | \(0.694948\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 216.000 | + | 404.099i | 0.273764 | + | 0.512166i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 791.960i | 1.00121i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 900.000 | 1.13493 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −740.810 | + | 395.980i | −0.931837 | + | 0.498088i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1234.75i | − | 1.54924i | −0.632425 | − | 0.774622i | \(-0.717940\pi\) | ||
0.632425 | − | 0.774622i | \(-0.282060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 560.000 | + | 374.166i | 0.699126 | + | 0.467123i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 424.264i | − | 0.528349i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 672.000 | 0.834783 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −603.231 | − | 1128.54i | −0.747499 | − | 1.39844i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 823.165i | − | 1.01751i | −0.860912 | − | 0.508754i | \(-0.830106\pi\) | ||
0.860912 | − | 0.508754i | \(-0.169894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.4575 | 0.0326233 | 0.0163117 | − | 0.999867i | \(-0.494808\pi\) | ||||
0.0163117 | + | 0.999867i | \(0.494808\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1050.00 | + | 561.249i | −1.29151 | + | 0.690343i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 752.362i | − | 0.923143i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1540.00 | −1.88494 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −264.575 | + | 395.980i | −0.323047 | + | 0.483492i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 97.2831i | 0.118493i | 0.998243 | + | 0.0592467i | \(0.0188699\pi\) | ||||
−0.998243 | + | 0.0592467i | \(0.981130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 894.264 | 1.08659 | 0.543295 | − | 0.839542i | \(-0.317176\pi\) | ||||
0.543295 | + | 0.839542i | \(0.317176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −620.000 | − | 1159.91i | −0.751515 | − | 1.40596i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 285.671i | 0.345431i | 0.984972 | + | 0.172715i | \(0.0552541\pi\) | ||||
−0.984972 | + | 0.172715i | \(0.944746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −170.000 | −0.205066 | −0.102533 | − | 0.994730i | \(-0.532695\pi\) | ||||
−0.102533 | + | 0.994730i | \(0.532695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1296.42 | + | 692.965i | −1.56007 | + | 0.833892i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1820.28 | −2.17997 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 70.0000 | − | 710.915i | 0.0836320 | − | 0.849361i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 707.107i | − | 0.842797i | −0.906876 | − | 0.421399i | \(-0.861539\pi\) | ||
0.906876 | − | 0.421399i | \(-0.138461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −559.000 | −0.664685 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 190.494 | + | 356.382i | 0.225972 | + | 0.422754i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 516.349i | − | 0.611064i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −418.029 | −0.493540 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.0000 | − | 7.48331i | 0.0164900 | − | 0.00881427i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 169.706i | 0.199419i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −570.000 | −0.668230 | −0.334115 | − | 0.942532i | \(-0.608437\pi\) | ||||
−0.334115 | + | 0.942532i | \(0.608437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1481.62 | + | 989.949i | 1.73289 | + | 1.15784i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 523.832i | 0.611239i | 0.952154 | + | 0.305620i | \(0.0988636\pi\) | ||||
−0.952154 | + | 0.305620i | \(0.901136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1455.16 | −1.69402 | −0.847010 | − | 0.531577i | \(-0.821600\pi\) | ||||
−0.847010 | + | 0.531577i | \(0.821600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 112.000 | + | 209.533i | 0.130081 | + | 0.243360i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 181.019i | − | 0.209756i | −0.994485 | − | 0.104878i | \(-0.966555\pi\) | ||
0.994485 | − | 0.104878i | \(-0.0334452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −840.000 | −0.971098 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 764.622 | − | 408.708i | 0.881917 | − | 0.471405i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 374.166i | 0.430570i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.9150 | −0.0607520 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 50.0000 | − | 74.8331i | 0.0572738 | − | 0.0857195i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 237.588i | − | 0.271529i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −490.000 | −0.558723 | −0.279361 | − | 0.960186i | \(-0.590123\pi\) | ||||
−0.279361 | + | 0.960186i | \(0.590123\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −158.745 | − | 296.985i | −0.180597 | − | 0.337867i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 987.798i | 1.12122i | 0.828079 | + | 0.560612i | \(0.189434\pi\) | ||||
−0.828079 | + | 0.560612i | \(0.810566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 957.762 | 1.08467 | 0.542334 | − | 0.840163i | \(-0.317541\pi\) | ||||
0.542334 | + | 0.840163i | \(0.317541\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1960.00 | − | 1047.66i | 2.21469 | − | 1.18380i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1374.62i | − | 1.54974i | −0.632123 | − | 0.774868i | \(-0.717816\pi\) | ||
0.632123 | − | 0.774868i | \(-0.282184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 812.000 | 0.913386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1058.30 | − | 438.406i | 1.18777 | − | 0.492038i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 299.333i | − | 0.335199i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1587.45 | −1.77369 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 240.000 | + | 448.999i | 0.267559 | + | 0.500556i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 989.949i | − | 1.10117i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −814.891 | + | 435.578i | −0.902427 | + | 0.482367i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1960.63i | 2.16644i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 534.442 | 0.589241 | 0.294621 | − | 0.955614i | \(-0.404807\pi\) | ||||
0.294621 | + | 0.955614i | \(0.404807\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −840.000 | − | 561.249i | −0.924092 | − | 0.617435i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 169.706i | − | 0.186285i | −0.995653 | − | 0.0931425i | \(-0.970309\pi\) | ||
0.995653 | − | 0.0931425i | \(-0.0296912\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 360.000 | 0.394304 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −952.470 | − | 1781.91i | −1.04095 | − | 1.94744i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 374.166i | − | 0.408032i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 555.608 | 0.604579 | 0.302289 | − | 0.953216i | \(-0.402249\pi\) | ||||
0.302289 | + | 0.953216i | \(0.402249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 126.000 | − | 67.3498i | 0.136808 | − | 0.0731269i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 282.843i | 0.306438i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 310.000 | 0.335135 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 238.118 | − | 356.382i | 0.256869 | − | 0.384446i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 89.7998i | 0.0966628i | 0.998831 | + | 0.0483314i | \(0.0153904\pi\) | ||||
−0.998831 | + | 0.0483314i | \(0.984610\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −555.608 | −0.596786 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 360.000 | + | 673.498i | 0.385852 | + | 0.721863i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1270.00 | −1.35539 | −0.677695 | − | 0.735343i | \(-0.737021\pi\) | ||||
−0.677695 | + | 0.735343i | \(0.737021\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −608.523 | + | 325.269i | −0.648054 | + | 0.346399i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 187.083i | − | 0.198813i | −0.995047 | − | 0.0994064i | \(-0.968306\pi\) | ||
0.995047 | − | 0.0994064i | \(-0.0316944\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 253.992 | 0.269345 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1064.00 | + | 104.766i | 1.12593 | + | 0.110864i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 280.014i | 0.295686i | 0.989011 | + | 0.147843i | \(0.0472330\pi\) | ||||
−0.989011 | + | 0.147843i | \(0.952767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 300.000 | 0.316122 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 793.725 | + | 1484.92i | 0.834622 | + | 1.56143i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 224.499i | 0.235571i | 0.993039 | + | 0.117786i | \(0.0375796\pi\) | ||||
−0.993039 | + | 0.117786i | \(0.962420\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2539.92 | 2.65960 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1400.00 | − | 748.331i | 1.46290 | − | 0.781956i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1187.94i | − | 1.23873i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −261.000 | −0.271592 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.1660 | + | 14.1421i | 0.0219792 | + | 0.0146855i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1571.50i | 1.62849i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −206.369 | −0.213411 | −0.106706 | − | 0.994291i | \(-0.534030\pi\) | ||||
−0.106706 | + | 0.994291i | \(0.534030\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1711.20i | 1.76231i | 0.472832 | + | 0.881153i | \(0.343232\pi\) | ||||
−0.472832 | + | 0.881153i | \(0.656768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 700.000 | 0.719424 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 820.183 | − | 438.406i | 0.841213 | − | 0.449647i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 598.665i | 0.612759i | 0.951910 | + | 0.306379i | \(0.0991176\pi\) | ||||
−0.951910 | + | 0.306379i | \(0.900882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1058.30 | −1.08100 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 350.000 | − | 523.832i | 0.356779 | − | 0.533978i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1544.32i | 1.57103i | 0.618843 | + | 0.785514i | \(0.287602\pi\) | ||||
−0.618843 | + | 0.785514i | \(0.712398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1400.00 | −1.42132 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −84.6640 | − | 158.392i | −0.0857792 | − | 0.160478i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 987.798i | 0.998784i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −608.523 | −0.614049 | −0.307025 | − | 0.951702i | \(-0.599333\pi\) | ||||
−0.307025 | + | 0.951702i | \(0.599333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 350.000 | − | 187.083i | 0.352467 | − | 0.188402i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2573.87i | 2.58680i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −810.000 | −0.812437 | −0.406219 | − | 0.913776i | \(-0.633153\pi\) | ||||
−0.406219 | + | 0.913776i | \(0.633153\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.4575 | + | 268.701i | −0.0264840 | + | 0.268970i |
(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 | 192.3.e.f.65.3 | 4 | ||
3.2 | odd | 2 | inner | 192.3.e.f.65.4 | 4 | ||
4.3 | odd | 2 | inner | 192.3.e.f.65.2 | 4 | ||
8.3 | odd | 2 | 96.3.e.b.65.3 | yes | 4 | ||
8.5 | even | 2 | 96.3.e.b.65.2 | yes | 4 | ||
12.11 | even | 2 | inner | 192.3.e.f.65.1 | 4 | ||
16.3 | odd | 4 | 768.3.h.e.641.2 | 8 | |||
16.5 | even | 4 | 768.3.h.e.641.1 | 8 | |||
16.11 | odd | 4 | 768.3.h.e.641.7 | 8 | |||
16.13 | even | 4 | 768.3.h.e.641.8 | 8 | |||
24.5 | odd | 2 | 96.3.e.b.65.1 | ✓ | 4 | ||
24.11 | even | 2 | 96.3.e.b.65.4 | yes | 4 | ||
48.5 | odd | 4 | 768.3.h.e.641.6 | 8 | |||
48.11 | even | 4 | 768.3.h.e.641.4 | 8 | |||
48.29 | odd | 4 | 768.3.h.e.641.3 | 8 | |||
48.35 | even | 4 | 768.3.h.e.641.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.3.e.b.65.1 | ✓ | 4 | 24.5 | odd | 2 | ||
96.3.e.b.65.2 | yes | 4 | 8.5 | even | 2 | ||
96.3.e.b.65.3 | yes | 4 | 8.3 | odd | 2 | ||
96.3.e.b.65.4 | yes | 4 | 24.11 | even | 2 | ||
192.3.e.f.65.1 | 4 | 12.11 | even | 2 | inner | ||
192.3.e.f.65.2 | 4 | 4.3 | odd | 2 | inner | ||
192.3.e.f.65.3 | 4 | 1.1 | even | 1 | trivial | ||
192.3.e.f.65.4 | 4 | 3.2 | odd | 2 | inner | ||
768.3.h.e.641.1 | 8 | 16.5 | even | 4 | |||
768.3.h.e.641.2 | 8 | 16.3 | odd | 4 | |||
768.3.h.e.641.3 | 8 | 48.29 | odd | 4 | |||
768.3.h.e.641.4 | 8 | 48.11 | even | 4 | |||
768.3.h.e.641.5 | 8 | 48.35 | even | 4 | |||
768.3.h.e.641.6 | 8 | 48.5 | odd | 4 | |||
768.3.h.e.641.7 | 8 | 16.11 | odd | 4 | |||
768.3.h.e.641.8 | 8 | 16.13 | even | 4 |