Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,18,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(53.1344053299\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −275.201 | −0.760142 | −0.380071 | − | 0.924957i | \(-0.624100\pi\) | ||||
−0.380071 | + | 0.924957i | \(0.624100\pi\) | |||||||
\(3\) | 7065.32 | 0.621729 | 0.310864 | − | 0.950454i | \(-0.399382\pi\) | ||||
0.310864 | + | 0.950454i | \(0.399382\pi\) | |||||||
\(4\) | −55336.6 | −0.422184 | ||||||||
\(5\) | −620891. | −0.710837 | −0.355419 | − | 0.934707i | \(-0.615662\pi\) | ||||
−0.355419 | + | 0.934707i | \(0.615662\pi\) | |||||||
\(6\) | −1.94438e6 | −0.472602 | ||||||||
\(7\) | 2.72618e7 | 1.78740 | 0.893698 | − | 0.448668i | \(-0.148102\pi\) | ||||
0.893698 | + | 0.448668i | \(0.148102\pi\) | |||||||
\(8\) | 5.12998e7 | 1.08106 | ||||||||
\(9\) | −7.92215e7 | −0.613454 | ||||||||
\(10\) | 1.70870e8 | 0.540337 | ||||||||
\(11\) | 6.43661e7 | 0.0905357 | 0.0452678 | − | 0.998975i | \(-0.485586\pi\) | ||||
0.0452678 | + | 0.998975i | \(0.485586\pi\) | |||||||
\(12\) | −3.90970e8 | −0.262484 | ||||||||
\(13\) | 5.86404e8 | 0.199379 | 0.0996893 | − | 0.995019i | \(-0.468215\pi\) | ||||
0.0996893 | + | 0.995019i | \(0.468215\pi\) | |||||||
\(14\) | −7.50246e9 | −1.35867 | ||||||||
\(15\) | −4.38679e9 | −0.441948 | ||||||||
\(16\) | −6.86466e9 | −0.399576 | ||||||||
\(17\) | −3.10293e10 | −1.07884 | −0.539419 | − | 0.842037i | \(-0.681356\pi\) | ||||
−0.539419 | + | 0.842037i | \(0.681356\pi\) | |||||||
\(18\) | 2.18018e10 | 0.466312 | ||||||||
\(19\) | 5.29680e10 | 0.715497 | 0.357749 | − | 0.933818i | \(-0.383544\pi\) | ||||
0.357749 | + | 0.933818i | \(0.383544\pi\) | |||||||
\(20\) | 3.43580e10 | 0.300104 | ||||||||
\(21\) | 1.92613e11 | 1.11128 | ||||||||
\(22\) | −1.77136e10 | −0.0688199 | ||||||||
\(23\) | 1.60419e11 | 0.427138 | 0.213569 | − | 0.976928i | \(-0.431491\pi\) | ||||
0.213569 | + | 0.976928i | \(0.431491\pi\) | |||||||
\(24\) | 3.62449e11 | 0.672127 | ||||||||
\(25\) | −3.77434e11 | −0.494711 | ||||||||
\(26\) | −1.61379e11 | −0.151556 | ||||||||
\(27\) | −1.47214e12 | −1.00313 | ||||||||
\(28\) | −1.50857e12 | −0.754611 | ||||||||
\(29\) | 5.00246e11 | 0.185695 | ||||||||
\(30\) | 1.20725e12 | 0.335943 | ||||||||
\(31\) | 7.27024e11 | 0.153100 | 0.0765498 | − | 0.997066i | \(-0.475610\pi\) | ||||
0.0765498 | + | 0.997066i | \(0.475610\pi\) | |||||||
\(32\) | −4.83480e12 | −0.777328 | ||||||||
\(33\) | 4.54767e11 | 0.0562886 | ||||||||
\(34\) | 8.53929e12 | 0.820070 | ||||||||
\(35\) | −1.69266e13 | −1.27055 | ||||||||
\(36\) | 4.38384e12 | 0.258991 | ||||||||
\(37\) | −9.77502e12 | −0.457513 | −0.228756 | − | 0.973484i | \(-0.573466\pi\) | ||||
−0.228756 | + | 0.973484i | \(0.573466\pi\) | |||||||
\(38\) | −1.45768e13 | −0.543879 | ||||||||
\(39\) | 4.14313e12 | 0.123959 | ||||||||
\(40\) | −3.18515e13 | −0.768459 | ||||||||
\(41\) | −6.44608e13 | −1.26076 | −0.630380 | − | 0.776286i | \(-0.717101\pi\) | ||||
−0.630380 | + | 0.776286i | \(0.717101\pi\) | |||||||
\(42\) | −5.30073e13 | −0.844727 | ||||||||
\(43\) | 1.42883e14 | 1.86422 | 0.932110 | − | 0.362175i | \(-0.117966\pi\) | ||||
0.932110 | + | 0.362175i | \(0.117966\pi\) | |||||||
\(44\) | −3.56180e12 | −0.0382227 | ||||||||
\(45\) | 4.91879e13 | 0.436066 | ||||||||
\(46\) | −4.41474e13 | −0.324686 | ||||||||
\(47\) | 1.73045e14 | 1.06005 | 0.530027 | − | 0.847981i | \(-0.322182\pi\) | ||||
0.530027 | + | 0.847981i | \(0.322182\pi\) | |||||||
\(48\) | −4.85010e13 | −0.248428 | ||||||||
\(49\) | 5.10574e14 | 2.19479 | ||||||||
\(50\) | 1.03870e14 | 0.376050 | ||||||||
\(51\) | −2.19232e14 | −0.670745 | ||||||||
\(52\) | −3.24496e13 | −0.0841745 | ||||||||
\(53\) | −8.85198e13 | −0.195297 | −0.0976485 | − | 0.995221i | \(-0.531132\pi\) | ||||
−0.0976485 | + | 0.995221i | \(0.531132\pi\) | |||||||
\(54\) | 4.05134e14 | 0.762521 | ||||||||
\(55\) | −3.99643e13 | −0.0643561 | ||||||||
\(56\) | 1.39852e15 | 1.93229 | ||||||||
\(57\) | 3.74236e14 | 0.444845 | ||||||||
\(58\) | −1.37668e14 | −0.141155 | ||||||||
\(59\) | 4.51204e14 | 0.400065 | 0.200033 | − | 0.979789i | \(-0.435895\pi\) | ||||
0.200033 | + | 0.979789i | \(0.435895\pi\) | |||||||
\(60\) | 2.42750e14 | 0.186583 | ||||||||
\(61\) | 1.64260e15 | 1.09705 | 0.548526 | − | 0.836133i | \(-0.315189\pi\) | ||||
0.548526 | + | 0.836133i | \(0.315189\pi\) | |||||||
\(62\) | −2.00078e14 | −0.116377 | ||||||||
\(63\) | −2.15972e15 | −1.09648 | ||||||||
\(64\) | 2.23031e15 | 0.990455 | ||||||||
\(65\) | −3.64093e14 | −0.141726 | ||||||||
\(66\) | −1.25152e14 | −0.0427873 | ||||||||
\(67\) | 7.01809e14 | 0.211146 | 0.105573 | − | 0.994412i | \(-0.466332\pi\) | ||||
0.105573 | + | 0.994412i | \(0.466332\pi\) | |||||||
\(68\) | 1.71706e15 | 0.455469 | ||||||||
\(69\) | 1.13341e15 | 0.265564 | ||||||||
\(70\) | 4.65821e15 | 0.965797 | ||||||||
\(71\) | 4.44430e15 | 0.816784 | 0.408392 | − | 0.912807i | \(-0.366090\pi\) | ||||
0.408392 | + | 0.912807i | \(0.366090\pi\) | |||||||
\(72\) | −4.06404e15 | −0.663181 | ||||||||
\(73\) | −8.65761e14 | −0.125648 | −0.0628238 | − | 0.998025i | \(-0.520011\pi\) | ||||
−0.0628238 | + | 0.998025i | \(0.520011\pi\) | |||||||
\(74\) | 2.69009e15 | 0.347775 | ||||||||
\(75\) | −2.66669e15 | −0.307576 | ||||||||
\(76\) | −2.93107e15 | −0.302072 | ||||||||
\(77\) | 1.75474e15 | 0.161823 | ||||||||
\(78\) | −1.14019e15 | −0.0942267 | ||||||||
\(79\) | 1.17326e16 | 0.870090 | 0.435045 | − | 0.900409i | \(-0.356732\pi\) | ||||
0.435045 | + | 0.900409i | \(0.356732\pi\) | |||||||
\(80\) | 4.26220e15 | 0.284033 | ||||||||
\(81\) | −1.70462e14 | −0.0102213 | ||||||||
\(82\) | 1.77397e16 | 0.958357 | ||||||||
\(83\) | 1.52260e16 | 0.742032 | 0.371016 | − | 0.928626i | \(-0.379009\pi\) | ||||
0.371016 | + | 0.928626i | \(0.379009\pi\) | |||||||
\(84\) | −1.06585e16 | −0.469163 | ||||||||
\(85\) | 1.92658e16 | 0.766879 | ||||||||
\(86\) | −3.93214e16 | −1.41707 | ||||||||
\(87\) | 3.53440e15 | 0.115452 | ||||||||
\(88\) | 3.30197e15 | 0.0978747 | ||||||||
\(89\) | 5.11031e16 | 1.37604 | 0.688022 | − | 0.725690i | \(-0.258479\pi\) | ||||
0.688022 | + | 0.725690i | \(0.258479\pi\) | |||||||
\(90\) | −1.35365e16 | −0.331472 | ||||||||
\(91\) | 1.59864e16 | 0.356368 | ||||||||
\(92\) | −8.87702e15 | −0.180331 | ||||||||
\(93\) | 5.13665e15 | 0.0951865 | ||||||||
\(94\) | −4.76222e16 | −0.805792 | ||||||||
\(95\) | −3.28873e16 | −0.508602 | ||||||||
\(96\) | −3.41594e16 | −0.483287 | ||||||||
\(97\) | 7.79795e16 | 1.01023 | 0.505116 | − | 0.863052i | \(-0.331450\pi\) | ||||
0.505116 | + | 0.863052i | \(0.331450\pi\) | |||||||
\(98\) | −1.40510e17 | −1.66835 | ||||||||
\(99\) | −5.09918e15 | −0.0555394 | ||||||||
\(100\) | 2.08859e16 | 0.208859 | ||||||||
\(101\) | −1.75244e16 | −0.161031 | −0.0805157 | − | 0.996753i | \(-0.525657\pi\) | ||||
−0.0805157 | + | 0.996753i | \(0.525657\pi\) | |||||||
\(102\) | 6.03328e16 | 0.509861 | ||||||||
\(103\) | 1.53601e16 | 0.119475 | 0.0597375 | − | 0.998214i | \(-0.480974\pi\) | ||||
0.0597375 | + | 0.998214i | \(0.480974\pi\) | |||||||
\(104\) | 3.00824e16 | 0.215540 | ||||||||
\(105\) | −1.19592e17 | −0.789936 | ||||||||
\(106\) | 2.43607e16 | 0.148453 | ||||||||
\(107\) | 8.04122e16 | 0.452439 | 0.226219 | − | 0.974076i | \(-0.427363\pi\) | ||||
0.226219 | + | 0.974076i | \(0.427363\pi\) | |||||||
\(108\) | 8.14632e16 | 0.423506 | ||||||||
\(109\) | 1.20639e17 | 0.579914 | 0.289957 | − | 0.957040i | \(-0.406359\pi\) | ||||
0.289957 | + | 0.957040i | \(0.406359\pi\) | |||||||
\(110\) | 1.09982e16 | 0.0489198 | ||||||||
\(111\) | −6.90636e16 | −0.284449 | ||||||||
\(112\) | −1.87143e17 | −0.714201 | ||||||||
\(113\) | −3.07891e17 | −1.08951 | −0.544753 | − | 0.838596i | \(-0.683377\pi\) | ||||
−0.544753 | + | 0.838596i | \(0.683377\pi\) | |||||||
\(114\) | −1.02990e17 | −0.338145 | ||||||||
\(115\) | −9.96025e16 | −0.303626 | ||||||||
\(116\) | −2.76819e16 | −0.0783977 | ||||||||
\(117\) | −4.64558e16 | −0.122309 | ||||||||
\(118\) | −1.24172e17 | −0.304106 | ||||||||
\(119\) | −8.45915e17 | −1.92831 | ||||||||
\(120\) | −2.25041e17 | −0.477773 | ||||||||
\(121\) | −5.01304e17 | −0.991803 | ||||||||
\(122\) | −4.52044e17 | −0.833916 | ||||||||
\(123\) | −4.55436e17 | −0.783851 | ||||||||
\(124\) | −4.02310e16 | −0.0646363 | ||||||||
\(125\) | 7.08047e17 | 1.06250 | ||||||||
\(126\) | 5.94356e17 | 0.833484 | ||||||||
\(127\) | 7.36322e17 | 0.965464 | 0.482732 | − | 0.875768i | \(-0.339645\pi\) | ||||
0.482732 | + | 0.875768i | \(0.339645\pi\) | |||||||
\(128\) | 1.99254e16 | 0.0244412 | ||||||||
\(129\) | 1.00951e18 | 1.15904 | ||||||||
\(130\) | 1.00199e17 | 0.107732 | ||||||||
\(131\) | −1.55798e18 | −1.56948 | −0.784739 | − | 0.619827i | \(-0.787203\pi\) | ||||
−0.784739 | + | 0.619827i | \(0.787203\pi\) | |||||||
\(132\) | −2.51652e16 | −0.0237642 | ||||||||
\(133\) | 1.44400e18 | 1.27888 | ||||||||
\(134\) | −1.93138e17 | −0.160501 | ||||||||
\(135\) | 9.14038e17 | 0.713062 | ||||||||
\(136\) | −1.59180e18 | −1.16629 | ||||||||
\(137\) | 2.05599e18 | 1.41546 | 0.707728 | − | 0.706485i | \(-0.249720\pi\) | ||||
0.707728 | + | 0.706485i | \(0.249720\pi\) | |||||||
\(138\) | −3.11915e17 | −0.201866 | ||||||||
\(139\) | −3.10190e18 | −1.88800 | −0.943999 | − | 0.329948i | \(-0.892969\pi\) | ||||
−0.943999 | + | 0.329948i | \(0.892969\pi\) | |||||||
\(140\) | 9.36659e17 | 0.536406 | ||||||||
\(141\) | 1.22262e18 | 0.659066 | ||||||||
\(142\) | −1.22307e18 | −0.620872 | ||||||||
\(143\) | 3.77446e16 | 0.0180509 | ||||||||
\(144\) | 5.43829e17 | 0.245121 | ||||||||
\(145\) | −3.10598e17 | −0.131999 | ||||||||
\(146\) | 2.38258e17 | 0.0955099 | ||||||||
\(147\) | 3.60737e18 | 1.36456 | ||||||||
\(148\) | 5.40916e17 | 0.193155 | ||||||||
\(149\) | 1.10187e18 | 0.371577 | 0.185789 | − | 0.982590i | \(-0.440516\pi\) | ||||
0.185789 | + | 0.982590i | \(0.440516\pi\) | |||||||
\(150\) | 7.33876e17 | 0.233801 | ||||||||
\(151\) | 3.18251e18 | 0.958221 | 0.479111 | − | 0.877754i | \(-0.340959\pi\) | ||||
0.479111 | + | 0.877754i | \(0.340959\pi\) | |||||||
\(152\) | 2.71725e18 | 0.773497 | ||||||||
\(153\) | 2.45819e18 | 0.661817 | ||||||||
\(154\) | −4.82905e17 | −0.123009 | ||||||||
\(155\) | −4.51402e17 | −0.108829 | ||||||||
\(156\) | −2.29266e17 | −0.0523337 | ||||||||
\(157\) | 7.15203e18 | 1.54626 | 0.773129 | − | 0.634248i | \(-0.218690\pi\) | ||||
0.773129 | + | 0.634248i | \(0.218690\pi\) | |||||||
\(158\) | −3.22882e18 | −0.661392 | ||||||||
\(159\) | −6.25420e17 | −0.121422 | ||||||||
\(160\) | 3.00188e18 | 0.552553 | ||||||||
\(161\) | 4.37330e18 | 0.763465 | ||||||||
\(162\) | 4.69113e16 | 0.00776963 | ||||||||
\(163\) | −3.36022e18 | −0.528169 | −0.264084 | − | 0.964500i | \(-0.585070\pi\) | ||||
−0.264084 | + | 0.964500i | \(0.585070\pi\) | |||||||
\(164\) | 3.56704e18 | 0.532274 | ||||||||
\(165\) | −2.82361e17 | −0.0400120 | ||||||||
\(166\) | −4.19021e18 | −0.564050 | ||||||||
\(167\) | −5.61683e18 | −0.718457 | −0.359229 | − | 0.933250i | \(-0.616960\pi\) | ||||
−0.359229 | + | 0.933250i | \(0.616960\pi\) | |||||||
\(168\) | 9.88101e18 | 1.20136 | ||||||||
\(169\) | −8.30655e18 | −0.960248 | ||||||||
\(170\) | −5.30197e18 | −0.582937 | ||||||||
\(171\) | −4.19620e18 | −0.438924 | ||||||||
\(172\) | −7.90663e18 | −0.787045 | ||||||||
\(173\) | 1.01326e19 | 0.960129 | 0.480065 | − | 0.877233i | \(-0.340613\pi\) | ||||
0.480065 | + | 0.877233i | \(0.340613\pi\) | |||||||
\(174\) | −9.72669e17 | −0.0877600 | ||||||||
\(175\) | −1.02895e19 | −0.884244 | ||||||||
\(176\) | −4.41852e17 | −0.0361759 | ||||||||
\(177\) | 3.18790e18 | 0.248732 | ||||||||
\(178\) | −1.40636e19 | −1.04599 | ||||||||
\(179\) | −9.96774e18 | −0.706880 | −0.353440 | − | 0.935457i | \(-0.614988\pi\) | ||||
−0.353440 | + | 0.935457i | \(0.614988\pi\) | |||||||
\(180\) | −2.72189e18 | −0.184100 | ||||||||
\(181\) | 4.00045e18 | 0.258132 | 0.129066 | − | 0.991636i | \(-0.458802\pi\) | ||||
0.129066 | + | 0.991636i | \(0.458802\pi\) | |||||||
\(182\) | −4.39947e18 | −0.270891 | ||||||||
\(183\) | 1.16055e19 | 0.682069 | ||||||||
\(184\) | 8.22944e18 | 0.461763 | ||||||||
\(185\) | 6.06922e18 | 0.325217 | ||||||||
\(186\) | −1.41361e18 | −0.0723552 | ||||||||
\(187\) | −1.99724e18 | −0.0976734 | ||||||||
\(188\) | −9.57574e18 | −0.447539 | ||||||||
\(189\) | −4.01332e19 | −1.79299 | ||||||||
\(190\) | 9.05062e18 | 0.386610 | ||||||||
\(191\) | 3.18928e18 | 0.130289 | 0.0651447 | − | 0.997876i | \(-0.479249\pi\) | ||||
0.0651447 | + | 0.997876i | \(0.479249\pi\) | |||||||
\(192\) | 1.57578e19 | 0.615794 | ||||||||
\(193\) | −1.21602e19 | −0.454679 | −0.227340 | − | 0.973816i | \(-0.573003\pi\) | ||||
−0.227340 | + | 0.973816i | \(0.573003\pi\) | |||||||
\(194\) | −2.14600e19 | −0.767919 | ||||||||
\(195\) | −2.57243e18 | −0.0881149 | ||||||||
\(196\) | −2.82534e19 | −0.926605 | ||||||||
\(197\) | 2.52396e19 | 0.792721 | 0.396360 | − | 0.918095i | \(-0.370273\pi\) | ||||
0.396360 | + | 0.918095i | \(0.370273\pi\) | |||||||
\(198\) | 1.40330e18 | 0.0422178 | ||||||||
\(199\) | 4.17039e19 | 1.20206 | 0.601029 | − | 0.799228i | \(-0.294758\pi\) | ||||
0.601029 | + | 0.799228i | \(0.294758\pi\) | |||||||
\(200\) | −1.93623e19 | −0.534813 | ||||||||
\(201\) | 4.95850e18 | 0.131276 | ||||||||
\(202\) | 4.82272e18 | 0.122407 | ||||||||
\(203\) | 1.36376e19 | 0.331911 | ||||||||
\(204\) | 1.21315e19 | 0.283178 | ||||||||
\(205\) | 4.00231e19 | 0.896196 | ||||||||
\(206\) | −4.22710e18 | −0.0908179 | ||||||||
\(207\) | −1.27086e19 | −0.262029 | ||||||||
\(208\) | −4.02546e18 | −0.0796668 | ||||||||
\(209\) | 3.40935e18 | 0.0647780 | ||||||||
\(210\) | 3.29117e19 | 0.600463 | ||||||||
\(211\) | −6.21552e19 | −1.08912 | −0.544561 | − | 0.838721i | \(-0.683304\pi\) | ||||
−0.544561 | + | 0.838721i | \(0.683304\pi\) | |||||||
\(212\) | 4.89838e18 | 0.0824513 | ||||||||
\(213\) | 3.14004e19 | 0.507818 | ||||||||
\(214\) | −2.21295e19 | −0.343918 | ||||||||
\(215\) | −8.87144e19 | −1.32516 | ||||||||
\(216\) | −7.55205e19 | −1.08445 | ||||||||
\(217\) | 1.98200e19 | 0.273650 | ||||||||
\(218\) | −3.32000e19 | −0.440817 | ||||||||
\(219\) | −6.11688e18 | −0.0781187 | ||||||||
\(220\) | 2.21149e18 | 0.0271701 | ||||||||
\(221\) | −1.81957e19 | −0.215097 | ||||||||
\(222\) | 1.90064e19 | 0.216221 | ||||||||
\(223\) | 1.25750e20 | 1.37694 | 0.688472 | − | 0.725263i | \(-0.258282\pi\) | ||||
0.688472 | + | 0.725263i | \(0.258282\pi\) | |||||||
\(224\) | −1.31805e20 | −1.38939 | ||||||||
\(225\) | 2.99009e19 | 0.303482 | ||||||||
\(226\) | 8.47318e19 | 0.828180 | ||||||||
\(227\) | −1.65848e20 | −1.56131 | −0.780657 | − | 0.624960i | \(-0.785115\pi\) | ||||
−0.780657 | + | 0.624960i | \(0.785115\pi\) | |||||||
\(228\) | −2.07089e19 | −0.187807 | ||||||||
\(229\) | −8.34006e19 | −0.728731 | −0.364366 | − | 0.931256i | \(-0.618714\pi\) | ||||
−0.364366 | + | 0.931256i | \(0.618714\pi\) | |||||||
\(230\) | 2.74107e19 | 0.230799 | ||||||||
\(231\) | 1.23978e19 | 0.100610 | ||||||||
\(232\) | 2.56625e19 | 0.200748 | ||||||||
\(233\) | 1.93098e20 | 1.45631 | 0.728154 | − | 0.685414i | \(-0.240379\pi\) | ||||
0.728154 | + | 0.685414i | \(0.240379\pi\) | |||||||
\(234\) | 1.27847e19 | 0.0929725 | ||||||||
\(235\) | −1.07442e20 | −0.753526 | ||||||||
\(236\) | −2.49681e19 | −0.168901 | ||||||||
\(237\) | 8.28946e19 | 0.540960 | ||||||||
\(238\) | 2.32796e20 | 1.46579 | ||||||||
\(239\) | 2.27368e20 | 1.38149 | 0.690745 | − | 0.723098i | \(-0.257283\pi\) | ||||
0.690745 | + | 0.723098i | \(0.257283\pi\) | |||||||
\(240\) | 3.01138e19 | 0.176592 | ||||||||
\(241\) | 1.33894e20 | 0.757909 | 0.378955 | − | 0.925415i | \(-0.376284\pi\) | ||||
0.378955 | + | 0.925415i | \(0.376284\pi\) | |||||||
\(242\) | 1.37959e20 | 0.753911 | ||||||||
\(243\) | 1.88908e20 | 0.996775 | ||||||||
\(244\) | −9.08957e19 | −0.463159 | ||||||||
\(245\) | −3.17011e20 | −1.56014 | ||||||||
\(246\) | 1.25336e20 | 0.595838 | ||||||||
\(247\) | 3.10606e19 | 0.142655 | ||||||||
\(248\) | 3.72962e19 | 0.165510 | ||||||||
\(249\) | 1.07577e20 | 0.461343 | ||||||||
\(250\) | −1.94855e20 | −0.807647 | ||||||||
\(251\) | 2.46785e19 | 0.0988762 | 0.0494381 | − | 0.998777i | \(-0.484257\pi\) | ||||
0.0494381 | + | 0.998777i | \(0.484257\pi\) | |||||||
\(252\) | 1.19511e20 | 0.462919 | ||||||||
\(253\) | 1.03255e19 | 0.0386712 | ||||||||
\(254\) | −2.02636e20 | −0.733889 | ||||||||
\(255\) | 1.36119e20 | 0.476790 | ||||||||
\(256\) | −2.97814e20 | −1.00903 | ||||||||
\(257\) | 3.37458e20 | 1.10608 | 0.553042 | − | 0.833153i | \(-0.313467\pi\) | ||||
0.553042 | + | 0.833153i | \(0.313467\pi\) | |||||||
\(258\) | −2.77818e20 | −0.881034 | ||||||||
\(259\) | −2.66485e20 | −0.817757 | ||||||||
\(260\) | 2.01476e19 | 0.0598344 | ||||||||
\(261\) | −3.96303e19 | −0.113915 | ||||||||
\(262\) | 4.28756e20 | 1.19303 | ||||||||
\(263\) | 6.61383e20 | 1.78168 | 0.890839 | − | 0.454319i | \(-0.150117\pi\) | ||||
0.890839 | + | 0.454319i | \(0.150117\pi\) | |||||||
\(264\) | 2.33294e19 | 0.0608515 | ||||||||
\(265\) | 5.49611e19 | 0.138824 | ||||||||
\(266\) | −3.97391e20 | −0.972128 | ||||||||
\(267\) | 3.61060e20 | 0.855526 | ||||||||
\(268\) | −3.88357e19 | −0.0891426 | ||||||||
\(269\) | −5.57024e20 | −1.23874 | −0.619369 | − | 0.785100i | \(-0.712612\pi\) | ||||
−0.619369 | + | 0.785100i | \(0.712612\pi\) | |||||||
\(270\) | −2.51544e20 | −0.542028 | ||||||||
\(271\) | 6.76253e20 | 1.41212 | 0.706058 | − | 0.708154i | \(-0.250472\pi\) | ||||
0.706058 | + | 0.708154i | \(0.250472\pi\) | |||||||
\(272\) | 2.13006e20 | 0.431078 | ||||||||
\(273\) | 1.12949e20 | 0.221564 | ||||||||
\(274\) | −5.65810e20 | −1.07595 | ||||||||
\(275\) | −2.42940e19 | −0.0447890 | ||||||||
\(276\) | −6.27189e19 | −0.112117 | ||||||||
\(277\) | 5.65903e20 | 0.980989 | 0.490494 | − | 0.871444i | \(-0.336816\pi\) | ||||
0.490494 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(278\) | 8.53644e20 | 1.43515 | ||||||||
\(279\) | −5.75959e19 | −0.0939195 | ||||||||
\(280\) | −8.68330e20 | −1.37354 | ||||||||
\(281\) | −1.15115e21 | −1.76656 | −0.883282 | − | 0.468842i | \(-0.844671\pi\) | ||||
−0.883282 | + | 0.468842i | \(0.844671\pi\) | |||||||
\(282\) | −3.36466e20 | −0.500984 | ||||||||
\(283\) | −6.78475e20 | −0.980278 | −0.490139 | − | 0.871644i | \(-0.663054\pi\) | ||||
−0.490139 | + | 0.871644i | \(0.663054\pi\) | |||||||
\(284\) | −2.45932e20 | −0.344834 | ||||||||
\(285\) | −2.32359e20 | −0.316212 | ||||||||
\(286\) | −1.03873e19 | −0.0137212 | ||||||||
\(287\) | −1.75732e21 | −2.25348 | ||||||||
\(288\) | 3.83020e20 | 0.476854 | ||||||||
\(289\) | 1.35579e20 | 0.163893 | ||||||||
\(290\) | 8.54769e19 | 0.100338 | ||||||||
\(291\) | 5.50950e20 | 0.628090 | ||||||||
\(292\) | 4.79083e19 | 0.0530464 | ||||||||
\(293\) | −3.70959e20 | −0.398980 | −0.199490 | − | 0.979900i | \(-0.563929\pi\) | ||||
−0.199490 | + | 0.979900i | \(0.563929\pi\) | |||||||
\(294\) | −9.92751e20 | −1.03726 | ||||||||
\(295\) | −2.80148e20 | −0.284381 | ||||||||
\(296\) | −5.01457e20 | −0.494600 | ||||||||
\(297\) | −9.47560e19 | −0.0908191 | ||||||||
\(298\) | −3.03237e20 | −0.282451 | ||||||||
\(299\) | 9.40702e19 | 0.0851622 | ||||||||
\(300\) | 1.47566e20 | 0.129854 | ||||||||
\(301\) | 3.89523e21 | 3.33210 | ||||||||
\(302\) | −8.75829e20 | −0.728384 | ||||||||
\(303\) | −1.23815e20 | −0.100118 | ||||||||
\(304\) | −3.63607e20 | −0.285896 | ||||||||
\(305\) | −1.01987e21 | −0.779826 | ||||||||
\(306\) | −6.76496e20 | −0.503075 | ||||||||
\(307\) | 5.52511e20 | 0.399636 | 0.199818 | − | 0.979833i | \(-0.435965\pi\) | ||||
0.199818 | + | 0.979833i | \(0.435965\pi\) | |||||||
\(308\) | −9.71011e19 | −0.0683192 | ||||||||
\(309\) | 1.08524e20 | 0.0742810 | ||||||||
\(310\) | 1.24226e20 | 0.0827254 | ||||||||
\(311\) | −9.29008e20 | −0.601944 | −0.300972 | − | 0.953633i | \(-0.597311\pi\) | ||||
−0.300972 | + | 0.953633i | \(0.597311\pi\) | |||||||
\(312\) | 2.12542e20 | 0.134008 | ||||||||
\(313\) | 3.11081e21 | 1.90874 | 0.954371 | − | 0.298625i | \(-0.0965278\pi\) | ||||
0.954371 | + | 0.298625i | \(0.0965278\pi\) | |||||||
\(314\) | −1.96824e21 | −1.17538 | ||||||||
\(315\) | 1.34095e21 | 0.779422 | ||||||||
\(316\) | −6.49242e20 | −0.367339 | ||||||||
\(317\) | −3.94921e20 | −0.217524 | −0.108762 | − | 0.994068i | \(-0.534689\pi\) | ||||
−0.108762 | + | 0.994068i | \(0.534689\pi\) | |||||||
\(318\) | 1.72116e20 | 0.0922977 | ||||||||
\(319\) | 3.21989e19 | 0.0168121 | ||||||||
\(320\) | −1.38478e21 | −0.704052 | ||||||||
\(321\) | 5.68137e20 | 0.281294 | ||||||||
\(322\) | −1.20354e21 | −0.580342 | ||||||||
\(323\) | −1.64356e21 | −0.771906 | ||||||||
\(324\) | 9.43279e18 | 0.00431527 | ||||||||
\(325\) | −2.21329e20 | −0.0986347 | ||||||||
\(326\) | 9.24734e20 | 0.401483 | ||||||||
\(327\) | 8.52355e20 | 0.360549 | ||||||||
\(328\) | −3.30682e21 | −1.36296 | ||||||||
\(329\) | 4.71753e21 | 1.89474 | ||||||||
\(330\) | 7.77059e19 | 0.0304148 | ||||||||
\(331\) | 3.35691e21 | 1.28056 | 0.640282 | − | 0.768140i | \(-0.278817\pi\) | ||||
0.640282 | + | 0.768140i | \(0.278817\pi\) | |||||||
\(332\) | −8.42556e20 | −0.313274 | ||||||||
\(333\) | 7.74392e20 | 0.280663 | ||||||||
\(334\) | 1.54575e21 | 0.546129 | ||||||||
\(335\) | −4.35747e20 | −0.150091 | ||||||||
\(336\) | −1.32222e21 | −0.444039 | ||||||||
\(337\) | 8.44884e20 | 0.276658 | 0.138329 | − | 0.990386i | \(-0.455827\pi\) | ||||
0.138329 | + | 0.990386i | \(0.455827\pi\) | |||||||
\(338\) | 2.28597e21 | 0.729925 | ||||||||
\(339\) | −2.17535e21 | −0.677378 | ||||||||
\(340\) | −1.06610e21 | −0.323764 | ||||||||
\(341\) | 4.67957e19 | 0.0138610 | ||||||||
\(342\) | 1.15480e21 | 0.333645 | ||||||||
\(343\) | 7.57725e21 | 2.13556 | ||||||||
\(344\) | 7.32984e21 | 2.01534 | ||||||||
\(345\) | −7.03723e20 | −0.188773 | ||||||||
\(346\) | −2.78850e21 | −0.729834 | ||||||||
\(347\) | 3.04981e21 | 0.778883 | 0.389441 | − | 0.921051i | \(-0.372668\pi\) | ||||
0.389441 | + | 0.921051i | \(0.372668\pi\) | |||||||
\(348\) | −1.95581e20 | −0.0487421 | ||||||||
\(349\) | 6.01583e21 | 1.46312 | 0.731559 | − | 0.681778i | \(-0.238793\pi\) | ||||
0.731559 | + | 0.681778i | \(0.238793\pi\) | |||||||
\(350\) | 2.83169e21 | 0.672151 | ||||||||
\(351\) | −8.63269e20 | −0.200003 | ||||||||
\(352\) | −3.11198e20 | −0.0703759 | ||||||||
\(353\) | −2.35616e21 | −0.520139 | −0.260070 | − | 0.965590i | \(-0.583745\pi\) | ||||
−0.260070 | + | 0.965590i | \(0.583745\pi\) | |||||||
\(354\) | −8.77312e20 | −0.189072 | ||||||||
\(355\) | −2.75942e21 | −0.580601 | ||||||||
\(356\) | −2.82787e21 | −0.580945 | ||||||||
\(357\) | −5.97666e21 | −1.19889 | ||||||||
\(358\) | 2.74313e21 | 0.537329 | ||||||||
\(359\) | 3.40797e21 | 0.651918 | 0.325959 | − | 0.945384i | \(-0.394313\pi\) | ||||
0.325959 | + | 0.945384i | \(0.394313\pi\) | |||||||
\(360\) | 2.52333e21 | 0.471414 | ||||||||
\(361\) | −2.67478e21 | −0.488063 | ||||||||
\(362\) | −1.10093e21 | −0.196217 | ||||||||
\(363\) | −3.54187e21 | −0.616633 | ||||||||
\(364\) | −8.84633e20 | −0.150453 | ||||||||
\(365\) | 5.37543e20 | 0.0893149 | ||||||||
\(366\) | −3.19383e21 | −0.518469 | ||||||||
\(367\) | −8.06166e21 | −1.27868 | −0.639342 | − | 0.768923i | \(-0.720793\pi\) | ||||
−0.639342 | + | 0.768923i | \(0.720793\pi\) | |||||||
\(368\) | −1.10122e21 | −0.170674 | ||||||||
\(369\) | 5.10668e21 | 0.773418 | ||||||||
\(370\) | −1.67025e21 | −0.247211 | ||||||||
\(371\) | −2.41321e21 | −0.349073 | ||||||||
\(372\) | −2.84245e20 | −0.0401862 | ||||||||
\(373\) | −6.29484e21 | −0.869880 | −0.434940 | − | 0.900459i | \(-0.643230\pi\) | ||||
−0.434940 | + | 0.900459i | \(0.643230\pi\) | |||||||
\(374\) | 5.49641e20 | 0.0742456 | ||||||||
\(375\) | 5.00258e21 | 0.660584 | ||||||||
\(376\) | 8.87719e21 | 1.14598 | ||||||||
\(377\) | 2.93346e20 | 0.0370237 | ||||||||
\(378\) | 1.10447e22 | 1.36293 | ||||||||
\(379\) | −8.95460e21 | −1.08047 | −0.540235 | − | 0.841514i | \(-0.681665\pi\) | ||||
−0.540235 | + | 0.841514i | \(0.681665\pi\) | |||||||
\(380\) | 1.81987e21 | 0.214724 | ||||||||
\(381\) | 5.20234e21 | 0.600256 | ||||||||
\(382\) | −8.77693e20 | −0.0990385 | ||||||||
\(383\) | −1.43335e22 | −1.58185 | −0.790923 | − | 0.611916i | \(-0.790399\pi\) | ||||
−0.790923 | + | 0.611916i | \(0.790399\pi\) | |||||||
\(384\) | 1.40779e20 | 0.0151958 | ||||||||
\(385\) | −1.08950e21 | −0.115030 | ||||||||
\(386\) | 3.34651e21 | 0.345621 | ||||||||
\(387\) | −1.13194e22 | −1.14361 | ||||||||
\(388\) | −4.31512e21 | −0.426504 | ||||||||
\(389\) | −1.73259e22 | −1.67542 | −0.837712 | − | 0.546113i | \(-0.816107\pi\) | ||||
−0.837712 | + | 0.546113i | \(0.816107\pi\) | |||||||
\(390\) | 7.07935e20 | 0.0669798 | ||||||||
\(391\) | −4.97769e21 | −0.460813 | ||||||||
\(392\) | 2.61923e22 | 2.37270 | ||||||||
\(393\) | −1.10076e22 | −0.975789 | ||||||||
\(394\) | −6.94597e21 | −0.602580 | ||||||||
\(395\) | −7.28467e21 | −0.618492 | ||||||||
\(396\) | 2.82171e20 | 0.0234479 | ||||||||
\(397\) | 1.60638e22 | 1.30656 | 0.653280 | − | 0.757116i | \(-0.273392\pi\) | ||||
0.653280 | + | 0.757116i | \(0.273392\pi\) | |||||||
\(398\) | −1.14769e22 | −0.913734 | ||||||||
\(399\) | 1.02023e22 | 0.795115 | ||||||||
\(400\) | 2.59096e21 | 0.197674 | ||||||||
\(401\) | −6.15988e21 | −0.460092 | −0.230046 | − | 0.973180i | \(-0.573888\pi\) | ||||
−0.230046 | + | 0.973180i | \(0.573888\pi\) | |||||||
\(402\) | −1.36458e21 | −0.0997881 | ||||||||
\(403\) | 4.26330e20 | 0.0305248 | ||||||||
\(404\) | 9.69738e20 | 0.0679849 | ||||||||
\(405\) | 1.05838e20 | 0.00726567 | ||||||||
\(406\) | −3.75308e21 | −0.252300 | ||||||||
\(407\) | −6.29181e20 | −0.0414212 | ||||||||
\(408\) | −1.12466e22 | −0.725117 | ||||||||
\(409\) | 6.89638e21 | 0.435485 | 0.217743 | − | 0.976006i | \(-0.430131\pi\) | ||||
0.217743 | + | 0.976006i | \(0.430131\pi\) | |||||||
\(410\) | −1.10144e22 | −0.681236 | ||||||||
\(411\) | 1.45262e22 | 0.880029 | ||||||||
\(412\) | −8.49974e20 | −0.0504405 | ||||||||
\(413\) | 1.23006e22 | 0.715075 | ||||||||
\(414\) | 3.49742e21 | 0.199180 | ||||||||
\(415\) | −9.45370e21 | −0.527464 | ||||||||
\(416\) | −2.83515e21 | −0.154982 | ||||||||
\(417\) | −2.19159e22 | −1.17382 | ||||||||
\(418\) | −9.38255e20 | −0.0492405 | ||||||||
\(419\) | −5.13587e21 | −0.264116 | −0.132058 | − | 0.991242i | \(-0.542158\pi\) | ||||
−0.132058 | + | 0.991242i | \(0.542158\pi\) | |||||||
\(420\) | 6.61779e21 | 0.333499 | ||||||||
\(421\) | 2.49739e22 | 1.23336 | 0.616678 | − | 0.787216i | \(-0.288478\pi\) | ||||
0.616678 | + | 0.787216i | \(0.288478\pi\) | |||||||
\(422\) | 1.71052e22 | 0.827888 | ||||||||
\(423\) | −1.37089e22 | −0.650294 | ||||||||
\(424\) | −4.54104e21 | −0.211128 | ||||||||
\(425\) | 1.17115e22 | 0.533713 | ||||||||
\(426\) | −8.64141e21 | −0.386014 | ||||||||
\(427\) | 4.47801e22 | 1.96087 | ||||||||
\(428\) | −4.44973e21 | −0.191013 | ||||||||
\(429\) | 2.66677e20 | 0.0112227 | ||||||||
\(430\) | 2.44143e22 | 1.00731 | ||||||||
\(431\) | −2.73222e22 | −1.10525 | −0.552623 | − | 0.833432i | \(-0.686373\pi\) | ||||
−0.552623 | + | 0.833432i | \(0.686373\pi\) | |||||||
\(432\) | 1.01057e22 | 0.400827 | ||||||||
\(433\) | −3.23696e22 | −1.25890 | −0.629449 | − | 0.777041i | \(-0.716720\pi\) | ||||
−0.629449 | + | 0.777041i | \(0.716720\pi\) | |||||||
\(434\) | −5.45447e21 | −0.208013 | ||||||||
\(435\) | −2.19448e21 | −0.0820676 | ||||||||
\(436\) | −6.67577e21 | −0.244831 | ||||||||
\(437\) | 8.49706e21 | 0.305616 | ||||||||
\(438\) | 1.68337e21 | 0.0593813 | ||||||||
\(439\) | 2.52322e22 | 0.872986 | 0.436493 | − | 0.899708i | \(-0.356220\pi\) | ||||
0.436493 | + | 0.899708i | \(0.356220\pi\) | |||||||
\(440\) | −2.05016e21 | −0.0695729 | ||||||||
\(441\) | −4.04485e22 | −1.34640 | ||||||||
\(442\) | 5.00748e21 | 0.163504 | ||||||||
\(443\) | −5.07854e22 | −1.62670 | −0.813350 | − | 0.581775i | \(-0.802358\pi\) | ||||
−0.813350 | + | 0.581775i | \(0.802358\pi\) | |||||||
\(444\) | 3.82174e21 | 0.120090 | ||||||||
\(445\) | −3.17295e22 | −0.978143 | ||||||||
\(446\) | −3.46065e22 | −1.04667 | ||||||||
\(447\) | 7.78509e21 | 0.231020 | ||||||||
\(448\) | 6.08021e22 | 1.77034 | ||||||||
\(449\) | −3.71727e22 | −1.06201 | −0.531007 | − | 0.847367i | \(-0.678186\pi\) | ||||
−0.531007 | + | 0.847367i | \(0.678186\pi\) | |||||||
\(450\) | −8.22875e21 | −0.230689 | ||||||||
\(451\) | −4.14909e21 | −0.114144 | ||||||||
\(452\) | 1.70376e22 | 0.459973 | ||||||||
\(453\) | 2.24854e22 | 0.595754 | ||||||||
\(454\) | 4.56415e22 | 1.18682 | ||||||||
\(455\) | −9.92582e21 | −0.253320 | ||||||||
\(456\) | 1.91982e22 | 0.480905 | ||||||||
\(457\) | 4.84965e22 | 1.19240 | 0.596201 | − | 0.802835i | \(-0.296676\pi\) | ||||
0.596201 | + | 0.802835i | \(0.296676\pi\) | |||||||
\(458\) | 2.29519e22 | 0.553939 | ||||||||
\(459\) | 4.56795e22 | 1.08222 | ||||||||
\(460\) | 5.51166e21 | 0.128186 | ||||||||
\(461\) | 1.78431e22 | 0.407393 | 0.203697 | − | 0.979034i | \(-0.434704\pi\) | ||||
0.203697 | + | 0.979034i | \(0.434704\pi\) | |||||||
\(462\) | −3.41187e21 | −0.0764779 | ||||||||
\(463\) | −4.48460e21 | −0.0986928 | −0.0493464 | − | 0.998782i | \(-0.515714\pi\) | ||||
−0.0493464 | + | 0.998782i | \(0.515714\pi\) | |||||||
\(464\) | −3.43402e21 | −0.0741994 | ||||||||
\(465\) | −3.18930e21 | −0.0676621 | ||||||||
\(466\) | −5.31408e22 | −1.10700 | ||||||||
\(467\) | −1.51961e22 | −0.310841 | −0.155420 | − | 0.987848i | \(-0.549673\pi\) | ||||
−0.155420 | + | 0.987848i | \(0.549673\pi\) | |||||||
\(468\) | 2.57070e21 | 0.0516371 | ||||||||
\(469\) | 1.91326e22 | 0.377402 | ||||||||
\(470\) | 2.95682e22 | 0.572787 | ||||||||
\(471\) | 5.05313e22 | 0.961353 | ||||||||
\(472\) | 2.31467e22 | 0.432495 | ||||||||
\(473\) | 9.19680e21 | 0.168778 | ||||||||
\(474\) | −2.28126e22 | −0.411206 | ||||||||
\(475\) | −1.99919e22 | −0.353964 | ||||||||
\(476\) | 4.68100e22 | 0.814104 | ||||||||
\(477\) | 7.01267e21 | 0.119806 | ||||||||
\(478\) | −6.25720e22 | −1.05013 | ||||||||
\(479\) | −1.74935e22 | −0.288419 | −0.144210 | − | 0.989547i | \(-0.546064\pi\) | ||||
−0.144210 | + | 0.989547i | \(0.546064\pi\) | |||||||
\(480\) | 2.12093e22 | 0.343538 | ||||||||
\(481\) | −5.73211e21 | −0.0912182 | ||||||||
\(482\) | −3.68478e22 | −0.576118 | ||||||||
\(483\) | 3.08987e22 | 0.474668 | ||||||||
\(484\) | 2.77404e22 | 0.418724 | ||||||||
\(485\) | −4.84167e22 | −0.718110 | ||||||||
\(486\) | −5.19877e22 | −0.757691 | ||||||||
\(487\) | 3.73949e22 | 0.535570 | 0.267785 | − | 0.963479i | \(-0.413708\pi\) | ||||
0.267785 | + | 0.963479i | \(0.413708\pi\) | |||||||
\(488\) | 8.42649e22 | 1.18598 | ||||||||
\(489\) | −2.37410e22 | −0.328378 | ||||||||
\(490\) | 8.72416e22 | 1.18592 | ||||||||
\(491\) | −3.88156e22 | −0.518577 | −0.259289 | − | 0.965800i | \(-0.583488\pi\) | ||||
−0.259289 | + | 0.965800i | \(0.583488\pi\) | |||||||
\(492\) | 2.52022e22 | 0.330930 | ||||||||
\(493\) | −1.55223e22 | −0.200335 | ||||||||
\(494\) | −8.54791e21 | −0.108438 | ||||||||
\(495\) | 3.16603e21 | 0.0394795 | ||||||||
\(496\) | −4.99077e21 | −0.0611749 | ||||||||
\(497\) | 1.21160e23 | 1.45992 | ||||||||
\(498\) | −2.96052e22 | −0.350686 | ||||||||
\(499\) | 2.72246e22 | 0.317034 | 0.158517 | − | 0.987356i | \(-0.449329\pi\) | ||||
0.158517 | + | 0.987356i | \(0.449329\pi\) | |||||||
\(500\) | −3.91809e22 | −0.448569 | ||||||||
\(501\) | −3.96846e22 | −0.446685 | ||||||||
\(502\) | −6.79154e21 | −0.0751600 | ||||||||
\(503\) | 9.46361e21 | 0.102974 | 0.0514872 | − | 0.998674i | \(-0.483604\pi\) | ||||
0.0514872 | + | 0.998674i | \(0.483604\pi\) | |||||||
\(504\) | −1.10793e23 | −1.18537 | ||||||||
\(505\) | 1.08807e22 | 0.114467 | ||||||||
\(506\) | −2.84159e21 | −0.0293956 | ||||||||
\(507\) | −5.86884e22 | −0.597014 | ||||||||
\(508\) | −4.07455e22 | −0.407604 | ||||||||
\(509\) | 1.55676e23 | 1.53152 | 0.765758 | − | 0.643128i | \(-0.222364\pi\) | ||||
0.765758 | + | 0.643128i | \(0.222364\pi\) | |||||||
\(510\) | −3.74601e22 | −0.362428 | ||||||||
\(511\) | −2.36022e22 | −0.224582 | ||||||||
\(512\) | 7.93470e22 | 0.742568 | ||||||||
\(513\) | −7.79764e22 | −0.717737 | ||||||||
\(514\) | −9.28687e22 | −0.840781 | ||||||||
\(515\) | −9.53693e21 | −0.0849272 | ||||||||
\(516\) | −5.58628e22 | −0.489328 | ||||||||
\(517\) | 1.11383e22 | 0.0959727 | ||||||||
\(518\) | 7.33368e22 | 0.621611 | ||||||||
\(519\) | 7.15901e22 | 0.596940 | ||||||||
\(520\) | −1.86779e22 | −0.153214 | ||||||||
\(521\) | −3.31513e22 | −0.267534 | −0.133767 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133767 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(522\) | 1.09063e22 | 0.0865919 | ||||||||
\(523\) | −1.91253e23 | −1.49397 | −0.746987 | − | 0.664838i | \(-0.768500\pi\) | ||||
−0.746987 | + | 0.664838i | \(0.768500\pi\) | |||||||
\(524\) | 8.62131e22 | 0.662609 | ||||||||
\(525\) | −7.26988e22 | −0.549760 | ||||||||
\(526\) | −1.82013e23 | −1.35433 | ||||||||
\(527\) | −2.25591e22 | −0.165170 | ||||||||
\(528\) | −3.12182e21 | −0.0224916 | ||||||||
\(529\) | −1.15316e23 | −0.817553 | ||||||||
\(530\) | −1.51253e22 | −0.105526 | ||||||||
\(531\) | −3.57451e22 | −0.245421 | ||||||||
\(532\) | −7.99061e22 | −0.539922 | ||||||||
\(533\) | −3.78000e22 | −0.251369 | ||||||||
\(534\) | −9.93639e22 | −0.650321 | ||||||||
\(535\) | −4.99272e22 | −0.321610 | ||||||||
\(536\) | 3.60027e22 | 0.228262 | ||||||||
\(537\) | −7.04252e22 | −0.439488 | ||||||||
\(538\) | 1.53294e23 | 0.941617 | ||||||||
\(539\) | 3.28637e22 | 0.198706 | ||||||||
\(540\) | −5.05797e22 | −0.301044 | ||||||||
\(541\) | −1.68705e22 | −0.0988445 | −0.0494222 | − | 0.998778i | \(-0.515738\pi\) | ||||
−0.0494222 | + | 0.998778i | \(0.515738\pi\) | |||||||
\(542\) | −1.86105e23 | −1.07341 | ||||||||
\(543\) | 2.82645e22 | 0.160488 | ||||||||
\(544\) | 1.50021e23 | 0.838611 | ||||||||
\(545\) | −7.49038e22 | −0.412225 | ||||||||
\(546\) | −3.10837e22 | −0.168420 | ||||||||
\(547\) | −3.33920e23 | −1.78135 | −0.890677 | − | 0.454637i | \(-0.849769\pi\) | ||||
−0.890677 | + | 0.454637i | \(0.849769\pi\) | |||||||
\(548\) | −1.13771e23 | −0.597583 | ||||||||
\(549\) | −1.30129e23 | −0.672991 | ||||||||
\(550\) | 6.68572e21 | 0.0340460 | ||||||||
\(551\) | 2.64971e22 | 0.132865 | ||||||||
\(552\) | 5.81436e22 | 0.287091 | ||||||||
\(553\) | 3.19852e23 | 1.55520 | ||||||||
\(554\) | −1.55737e23 | −0.745691 | ||||||||
\(555\) | 4.28810e22 | 0.202197 | ||||||||
\(556\) | 1.71648e23 | 0.797084 | ||||||||
\(557\) | 1.74292e23 | 0.797094 | 0.398547 | − | 0.917148i | \(-0.369515\pi\) | ||||
0.398547 | + | 0.917148i | \(0.369515\pi\) | |||||||
\(558\) | 1.58504e22 | 0.0713922 | ||||||||
\(559\) | 8.37869e22 | 0.371685 | ||||||||
\(560\) | 1.16195e23 | 0.507680 | ||||||||
\(561\) | −1.41111e22 | −0.0607263 | ||||||||
\(562\) | 3.16798e23 | 1.34284 | ||||||||
\(563\) | 1.22487e23 | 0.511409 | 0.255704 | − | 0.966755i | \(-0.417693\pi\) | ||||
0.255704 | + | 0.966755i | \(0.417693\pi\) | |||||||
\(564\) | −6.76556e22 | −0.278248 | ||||||||
\(565\) | 1.91167e23 | 0.774462 | ||||||||
\(566\) | 1.86717e23 | 0.745151 | ||||||||
\(567\) | −4.64711e21 | −0.0182695 | ||||||||
\(568\) | 2.27992e23 | 0.882994 | ||||||||
\(569\) | −4.32759e23 | −1.65117 | −0.825584 | − | 0.564279i | \(-0.809154\pi\) | ||||
−0.825584 | + | 0.564279i | \(0.809154\pi\) | |||||||
\(570\) | 6.39455e22 | 0.240366 | ||||||||
\(571\) | 2.54448e23 | 0.942305 | 0.471153 | − | 0.882052i | \(-0.343838\pi\) | ||||
0.471153 | + | 0.882052i | \(0.343838\pi\) | |||||||
\(572\) | −2.08865e21 | −0.00762079 | ||||||||
\(573\) | 2.25333e22 | 0.0810047 | ||||||||
\(574\) | 4.83615e23 | 1.71296 | ||||||||
\(575\) | −6.05475e22 | −0.211310 | ||||||||
\(576\) | −1.76688e23 | −0.607598 | ||||||||
\(577\) | 2.06031e23 | 0.698134 | 0.349067 | − | 0.937098i | \(-0.386499\pi\) | ||||
0.349067 | + | 0.937098i | \(0.386499\pi\) | |||||||
\(578\) | −3.73114e22 | −0.124582 | ||||||||
\(579\) | −8.59159e22 | −0.282687 | ||||||||
\(580\) | 1.71874e22 | 0.0557280 | ||||||||
\(581\) | 4.15089e23 | 1.32631 | ||||||||
\(582\) | −1.51622e23 | −0.477437 | ||||||||
\(583\) | −5.69768e21 | −0.0176813 | ||||||||
\(584\) | −4.44134e22 | −0.135833 | ||||||||
\(585\) | 2.88440e22 | 0.0869421 | ||||||||
\(586\) | 1.02088e23 | 0.303281 | ||||||||
\(587\) | 1.82842e23 | 0.535368 | 0.267684 | − | 0.963507i | \(-0.413742\pi\) | ||||
0.267684 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(588\) | −1.99619e23 | −0.576097 | ||||||||
\(589\) | 3.85090e22 | 0.109542 | ||||||||
\(590\) | 7.70970e22 | 0.216170 | ||||||||
\(591\) | 1.78326e23 | 0.492857 | ||||||||
\(592\) | 6.71022e22 | 0.182811 | ||||||||
\(593\) | −1.91371e23 | −0.513940 | −0.256970 | − | 0.966419i | \(-0.582724\pi\) | ||||
−0.256970 | + | 0.966419i | \(0.582724\pi\) | |||||||
\(594\) | 2.60769e22 | 0.0690354 | ||||||||
\(595\) | 5.25221e23 | 1.37072 | ||||||||
\(596\) | −6.09740e22 | −0.156874 | ||||||||
\(597\) | 2.94651e23 | 0.747353 | ||||||||
\(598\) | −2.58882e22 | −0.0647353 | ||||||||
\(599\) | −7.84490e23 | −1.93401 | −0.967007 | − | 0.254750i | \(-0.918007\pi\) | ||||
−0.967007 | + | 0.254750i | \(0.918007\pi\) | |||||||
\(600\) | −1.36801e23 | −0.332508 | ||||||||
\(601\) | −8.14238e23 | −1.95127 | −0.975637 | − | 0.219391i | \(-0.929593\pi\) | ||||
−0.975637 | + | 0.219391i | \(0.929593\pi\) | |||||||
\(602\) | −1.07197e24 | −2.53287 | ||||||||
\(603\) | −5.55984e22 | −0.129528 | ||||||||
\(604\) | −1.76109e23 | −0.404546 | ||||||||
\(605\) | 3.11255e23 | 0.705011 | ||||||||
\(606\) | 3.40740e22 | 0.0761037 | ||||||||
\(607\) | 6.62130e23 | 1.45828 | 0.729138 | − | 0.684367i | \(-0.239921\pi\) | ||||
0.729138 | + | 0.684367i | \(0.239921\pi\) | |||||||
\(608\) | −2.56090e23 | −0.556176 | ||||||||
\(609\) | 9.63540e22 | 0.206359 | ||||||||
\(610\) | 2.80670e23 | 0.592778 | ||||||||
\(611\) | 1.01474e23 | 0.211352 | ||||||||
\(612\) | −1.36028e23 | −0.279409 | ||||||||
\(613\) | 7.28838e23 | 1.47644 | 0.738222 | − | 0.674557i | \(-0.235665\pi\) | ||||
0.738222 | + | 0.674557i | \(0.235665\pi\) | |||||||
\(614\) | −1.52052e23 | −0.303780 | ||||||||
\(615\) | 2.82776e23 | 0.557190 | ||||||||
\(616\) | 9.00176e22 | 0.174941 | ||||||||
\(617\) | −1.98266e23 | −0.380035 | −0.190017 | − | 0.981781i | \(-0.560854\pi\) | ||||
−0.190017 | + | 0.981781i | \(0.560854\pi\) | |||||||
\(618\) | −2.98658e22 | −0.0564641 | ||||||||
\(619\) | 1.01053e24 | 1.88442 | 0.942212 | − | 0.335017i | \(-0.108742\pi\) | ||||
0.942212 | + | 0.335017i | \(0.108742\pi\) | |||||||
\(620\) | 2.49791e22 | 0.0459459 | ||||||||
\(621\) | −2.36159e23 | −0.428475 | ||||||||
\(622\) | 2.55664e23 | 0.457563 | ||||||||
\(623\) | 1.39316e24 | 2.45954 | ||||||||
\(624\) | −2.84412e22 | −0.0495312 | ||||||||
\(625\) | −1.51661e23 | −0.260551 | ||||||||
\(626\) | −8.56098e23 | −1.45091 | ||||||||
\(627\) | 2.40881e22 | 0.0402744 | ||||||||
\(628\) | −3.95769e23 | −0.652806 | ||||||||
\(629\) | 3.03312e23 | 0.493583 | ||||||||
\(630\) | −3.69030e23 | −0.592471 | ||||||||
\(631\) | −7.58913e23 | −1.20210 | −0.601052 | − | 0.799210i | \(-0.705252\pi\) | ||||
−0.601052 | + | 0.799210i | \(0.705252\pi\) | |||||||
\(632\) | 6.01880e23 | 0.940621 | ||||||||
\(633\) | −4.39146e23 | −0.677139 | ||||||||
\(634\) | 1.08683e23 | 0.165349 | ||||||||
\(635\) | −4.57175e23 | −0.686287 | ||||||||
\(636\) | 3.46086e22 | 0.0512624 | ||||||||
\(637\) | 2.99403e23 | 0.437593 | ||||||||
\(638\) | −8.86117e21 | −0.0127795 | ||||||||
\(639\) | −3.52084e23 | −0.501059 | ||||||||
\(640\) | −1.23715e22 | −0.0173737 | ||||||||
\(641\) | −8.99920e23 | −1.24713 | −0.623564 | − | 0.781772i | \(-0.714316\pi\) | ||||
−0.623564 | + | 0.781772i | \(0.714316\pi\) | |||||||
\(642\) | −1.56352e23 | −0.213823 | ||||||||
\(643\) | −1.74644e23 | −0.235700 | −0.117850 | − | 0.993031i | \(-0.537600\pi\) | ||||
−0.117850 | + | 0.993031i | \(0.537600\pi\) | |||||||
\(644\) | −2.42003e23 | −0.322323 | ||||||||
\(645\) | −6.26795e23 | −0.823888 | ||||||||
\(646\) | 4.52309e23 | 0.586758 | ||||||||
\(647\) | −1.05814e24 | −1.35474 | −0.677372 | − | 0.735641i | \(-0.736881\pi\) | ||||
−0.677372 | + | 0.735641i | \(0.736881\pi\) | |||||||
\(648\) | −8.74467e21 | −0.0110498 | ||||||||
\(649\) | 2.90423e22 | 0.0362202 | ||||||||
\(650\) | 6.09099e22 | 0.0749763 | ||||||||
\(651\) | 1.40034e23 | 0.170136 | ||||||||
\(652\) | 1.85943e23 | 0.222985 | ||||||||
\(653\) | −9.92357e23 | −1.17464 | −0.587321 | − | 0.809354i | \(-0.699817\pi\) | ||||
−0.587321 | + | 0.809354i | \(0.699817\pi\) | |||||||
\(654\) | −2.34569e23 | −0.274069 | ||||||||
\(655\) | 9.67333e23 | 1.11564 | ||||||||
\(656\) | 4.42501e23 | 0.503770 | ||||||||
\(657\) | 6.85869e22 | 0.0770789 | ||||||||
\(658\) | −1.29827e24 | −1.44027 | ||||||||
\(659\) | 7.39660e23 | 0.810039 | 0.405020 | − | 0.914308i | \(-0.367265\pi\) | ||||
0.405020 | + | 0.914308i | \(0.367265\pi\) | |||||||
\(660\) | 1.56249e22 | 0.0168925 | ||||||||
\(661\) | 1.28597e23 | 0.137252 | 0.0686258 | − | 0.997642i | \(-0.478139\pi\) | ||||
0.0686258 | + | 0.997642i | \(0.478139\pi\) | |||||||
\(662\) | −9.23824e23 | −0.973411 | ||||||||
\(663\) | −1.28558e23 | −0.133732 | ||||||||
\(664\) | 7.81092e23 | 0.802183 | ||||||||
\(665\) | −8.96568e23 | −0.909074 | ||||||||
\(666\) | −2.13113e23 | −0.213344 | ||||||||
\(667\) | 8.02489e22 | 0.0793176 | ||||||||
\(668\) | 3.10816e23 | 0.303321 | ||||||||
\(669\) | 8.88463e23 | 0.856086 | ||||||||
\(670\) | 1.19918e23 | 0.114090 | ||||||||
\(671\) | 1.05728e23 | 0.0993224 | ||||||||
\(672\) | −9.31247e23 | −0.863825 | ||||||||
\(673\) | −1.05495e24 | −0.966283 | −0.483142 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483142 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(674\) | −2.32513e23 | −0.210299 | ||||||||
\(675\) | 5.55636e23 | 0.496259 | ||||||||
\(676\) | 4.59656e23 | 0.405402 | ||||||||
\(677\) | 5.37510e23 | 0.468147 | 0.234074 | − | 0.972219i | \(-0.424794\pi\) | ||||
0.234074 | + | 0.972219i | \(0.424794\pi\) | |||||||
\(678\) | 5.98657e23 | 0.514903 | ||||||||
\(679\) | 2.12586e24 | 1.80568 | ||||||||
\(680\) | 9.88332e23 | 0.829043 | ||||||||
\(681\) | −1.17177e24 | −0.970714 | ||||||||
\(682\) | −1.28782e22 | −0.0105363 | ||||||||
\(683\) | −2.85014e23 | −0.230298 | −0.115149 | − | 0.993348i | \(-0.536735\pi\) | ||||
−0.115149 | + | 0.993348i | \(0.536735\pi\) | |||||||
\(684\) | 2.32204e23 | 0.185307 | ||||||||
\(685\) | −1.27655e24 | −1.00616 | ||||||||
\(686\) | −2.08526e24 | −1.62333 | ||||||||
\(687\) | −5.89251e23 | −0.453073 | ||||||||
\(688\) | −9.80840e23 | −0.744898 | ||||||||
\(689\) | −5.19083e22 | −0.0389380 | ||||||||
\(690\) | 1.93665e23 | 0.143494 | ||||||||
\(691\) | 5.09992e23 | 0.373250 | 0.186625 | − | 0.982431i | \(-0.440245\pi\) | ||||
0.186625 | + | 0.982431i | \(0.440245\pi\) | |||||||
\(692\) | −5.60704e23 | −0.405352 | ||||||||
\(693\) | −1.39013e23 | −0.0992710 | ||||||||
\(694\) | −8.39310e23 | −0.592061 | ||||||||
\(695\) | 1.92594e24 | 1.34206 | ||||||||
\(696\) | 1.81314e23 | 0.124811 | ||||||||
\(697\) | 2.00017e24 | 1.36016 | ||||||||
\(698\) | −1.65556e24 | −1.11218 | ||||||||
\(699\) | 1.36430e24 | 0.905428 | ||||||||
\(700\) | 5.69387e23 | 0.373314 | ||||||||
\(701\) | −1.64225e24 | −1.06374 | −0.531869 | − | 0.846826i | \(-0.678510\pi\) | ||||
−0.531869 | + | 0.846826i | \(0.678510\pi\) | |||||||
\(702\) | 2.37572e23 | 0.152030 | ||||||||
\(703\) | −5.17764e23 | −0.327349 | ||||||||
\(704\) | 1.43556e23 | 0.0896715 | ||||||||
\(705\) | −7.59113e23 | −0.468489 | ||||||||
\(706\) | 6.48417e23 | 0.395379 | ||||||||
\(707\) | −4.77745e23 | −0.287827 | ||||||||
\(708\) | −1.76407e23 | −0.105011 | ||||||||
\(709\) | 1.30885e24 | 0.769831 | 0.384916 | − | 0.922952i | \(-0.374231\pi\) | ||||
0.384916 | + | 0.922952i | \(0.374231\pi\) | |||||||
\(710\) | 7.59396e23 | 0.441339 | ||||||||
\(711\) | −9.29475e23 | −0.533760 | ||||||||
\(712\) | 2.62158e24 | 1.48759 | ||||||||
\(713\) | 1.16628e23 | 0.0653947 | ||||||||
\(714\) | 1.64478e24 | 0.911324 | ||||||||
\(715\) | −2.34352e22 | −0.0128312 | ||||||||
\(716\) | 5.51580e23 | 0.298434 | ||||||||
\(717\) | 1.60643e24 | 0.858912 | ||||||||
\(718\) | −9.37876e23 | −0.495550 | ||||||||
\(719\) | 8.51530e23 | 0.444636 | 0.222318 | − | 0.974974i | \(-0.428638\pi\) | ||||
0.222318 | + | 0.974974i | \(0.428638\pi\) | |||||||
\(720\) | −3.37658e23 | −0.174241 | ||||||||
\(721\) | 4.18743e23 | 0.213549 | ||||||||
\(722\) | 7.36101e23 | 0.370997 | ||||||||
\(723\) | 9.46005e23 | 0.471214 | ||||||||
\(724\) | −2.21371e23 | −0.108979 | ||||||||
\(725\) | −1.88810e23 | −0.0918655 | ||||||||
\(726\) | 9.74725e23 | 0.468728 | ||||||||
\(727\) | −2.16935e24 | −1.03107 | −0.515533 | − | 0.856870i | \(-0.672406\pi\) | ||||
−0.515533 | + | 0.856870i | \(0.672406\pi\) | |||||||
\(728\) | 8.20099e23 | 0.385256 | ||||||||
\(729\) | 1.35671e24 | 0.629945 | ||||||||
\(730\) | −1.47932e23 | −0.0678920 | ||||||||
\(731\) | −4.43355e24 | −2.01119 | ||||||||
\(732\) | −6.42207e23 | −0.287959 | ||||||||
\(733\) | 4.75782e23 | 0.210874 | 0.105437 | − | 0.994426i | \(-0.466376\pi\) | ||||
0.105437 | + | 0.994426i | \(0.466376\pi\) | |||||||
\(734\) | 2.21858e24 | 0.971981 | ||||||||
\(735\) | −2.23978e24 | −0.969981 | ||||||||
\(736\) | −7.75593e23 | −0.332026 | ||||||||
\(737\) | 4.51728e22 | 0.0191163 | ||||||||
\(738\) | −1.40536e24 | −0.587908 | ||||||||
\(739\) | 4.65308e24 | 1.92426 | 0.962128 | − | 0.272598i | \(-0.0878828\pi\) | ||||
0.962128 | + | 0.272598i | \(0.0878828\pi\) | |||||||
\(740\) | −3.35850e23 | −0.137302 | ||||||||
\(741\) | 2.19453e23 | 0.0886926 | ||||||||
\(742\) | 6.64116e23 | 0.265345 | ||||||||
\(743\) | −2.38022e24 | −0.940181 | −0.470091 | − | 0.882618i | \(-0.655779\pi\) | ||||
−0.470091 | + | 0.882618i | \(0.655779\pi\) | |||||||
\(744\) | 2.63509e23 | 0.102902 | ||||||||
\(745\) | −6.84144e23 | −0.264131 | ||||||||
\(746\) | 1.73234e24 | 0.661232 | ||||||||
\(747\) | −1.20623e24 | −0.455202 | ||||||||
\(748\) | 1.10520e23 | 0.0412362 | ||||||||
\(749\) | 2.19218e24 | 0.808687 | ||||||||
\(750\) | −1.37671e24 | −0.502138 | ||||||||
\(751\) | 1.21739e24 | 0.439025 | 0.219512 | − | 0.975610i | \(-0.429553\pi\) | ||||
0.219512 | + | 0.975610i | \(0.429553\pi\) | |||||||
\(752\) | −1.18790e24 | −0.423572 | ||||||||
\(753\) | 1.74361e23 | 0.0614742 | ||||||||
\(754\) | −8.07292e22 | −0.0281432 | ||||||||
\(755\) | −1.97599e24 | −0.681139 | ||||||||
\(756\) | 2.22083e24 | 0.756973 | ||||||||
\(757\) | −1.14951e24 | −0.387434 | −0.193717 | − | 0.981057i | \(-0.562054\pi\) | ||||
−0.193717 | + | 0.981057i | \(0.562054\pi\) | |||||||
\(758\) | 2.46431e24 | 0.821310 | ||||||||
\(759\) | 7.29532e22 | 0.0240430 | ||||||||
\(760\) | −1.68711e24 | −0.549830 | ||||||||
\(761\) | −4.49008e24 | −1.44705 | −0.723527 | − | 0.690296i | \(-0.757480\pi\) | ||||
−0.723527 | + | 0.690296i | \(0.757480\pi\) | |||||||
\(762\) | −1.43169e24 | −0.456280 | ||||||||
\(763\) | 3.28884e24 | 1.03654 | ||||||||
\(764\) | −1.76484e23 | −0.0550062 | ||||||||
\(765\) | −1.52627e24 | −0.470444 | ||||||||
\(766\) | 3.94460e24 | 1.20243 | ||||||||
\(767\) | 2.64588e23 | 0.0797644 | ||||||||
\(768\) | −2.10415e24 | −0.627345 | ||||||||
\(769\) | 1.28099e24 | 0.377720 | 0.188860 | − | 0.982004i | \(-0.439521\pi\) | ||||
0.188860 | + | 0.982004i | \(0.439521\pi\) | |||||||
\(770\) | 2.99831e23 | 0.0874390 | ||||||||
\(771\) | 2.38425e24 | 0.687684 | ||||||||
\(772\) | 6.72906e23 | 0.191958 | ||||||||
\(773\) | 2.30942e24 | 0.651594 | 0.325797 | − | 0.945440i | \(-0.394367\pi\) | ||||
0.325797 | + | 0.945440i | \(0.394367\pi\) | |||||||
\(774\) | 3.11510e24 | 0.869308 | ||||||||
\(775\) | −2.74404e23 | −0.0757400 | ||||||||
\(776\) | 4.00033e24 | 1.09212 | ||||||||
\(777\) | −1.88280e24 | −0.508423 | ||||||||
\(778\) | 4.76810e24 | 1.27356 | ||||||||
\(779\) | −3.41436e24 | −0.902071 | ||||||||
\(780\) | 1.42349e23 | 0.0372007 | ||||||||
\(781\) | 2.86063e23 | 0.0739481 | ||||||||
\(782\) | 1.36986e24 | 0.350283 | ||||||||
\(783\) | −7.36433e23 | −0.186277 | ||||||||
\(784\) | −3.50492e24 | −0.876984 | ||||||||
\(785\) | −4.44063e24 | −1.09914 | ||||||||
\(786\) | 3.02930e24 | 0.741738 | ||||||||
\(787\) | 3.75479e24 | 0.909495 | 0.454747 | − | 0.890620i | \(-0.349730\pi\) | ||||
0.454747 | + | 0.890620i | \(0.349730\pi\) | |||||||
\(788\) | −1.39667e24 | −0.334674 | ||||||||
\(789\) | 4.67288e24 | 1.10772 | ||||||||
\(790\) | 2.00475e24 | 0.470142 | ||||||||
\(791\) | −8.39365e24 | −1.94738 | ||||||||
\(792\) | −2.61587e23 | −0.0600415 | ||||||||
\(793\) | 9.63225e23 | 0.218729 | ||||||||
\(794\) | −4.42077e24 | −0.993171 | ||||||||
\(795\) | 3.88318e23 | 0.0863111 | ||||||||
\(796\) | −2.30775e24 | −0.507490 | ||||||||
\(797\) | −2.11929e24 | −0.461099 | −0.230550 | − | 0.973061i | \(-0.574052\pi\) | ||||
−0.230550 | + | 0.973061i | \(0.574052\pi\) | |||||||
\(798\) | −2.80769e24 | −0.604400 | ||||||||
\(799\) | −5.36948e24 | −1.14363 | ||||||||
\(800\) | 1.82482e24 | 0.384552 | ||||||||
\(801\) | −4.04847e24 | −0.844139 | ||||||||
\(802\) | 1.69520e24 | 0.349735 | ||||||||
\(803\) | −5.57257e22 | −0.0113756 | ||||||||
\(804\) | −2.74386e23 | −0.0554225 | ||||||||
\(805\) | −2.71534e24 | −0.542700 | ||||||||
\(806\) | −1.17326e23 | −0.0232032 | ||||||||
\(807\) | −3.93555e24 | −0.770159 | ||||||||
\(808\) | −8.98996e23 | −0.174085 | ||||||||
\(809\) | 6.41483e24 | 1.22920 | 0.614601 | − | 0.788838i | \(-0.289317\pi\) | ||||
0.614601 | + | 0.788838i | \(0.289317\pi\) | |||||||
\(810\) | −2.91268e22 | −0.00552294 | ||||||||
\(811\) | −7.63671e24 | −1.43294 | −0.716472 | − | 0.697616i | \(-0.754244\pi\) | ||||
−0.716472 | + | 0.697616i | \(0.754244\pi\) | |||||||
\(812\) | −7.54658e23 | −0.140128 | ||||||||
\(813\) | 4.77794e24 | 0.877953 | ||||||||
\(814\) | 1.73151e23 | 0.0314860 | ||||||||
\(815\) | 2.08633e24 | 0.375442 | ||||||||
\(816\) | 1.50495e24 | 0.268014 | ||||||||
\(817\) | 7.56820e24 | 1.33384 | ||||||||
\(818\) | −1.89789e24 | −0.331030 | ||||||||
\(819\) | −1.26647e24 | −0.218615 | ||||||||
\(820\) | −2.21474e24 | −0.378360 | ||||||||
\(821\) | 9.91280e24 | 1.67602 | 0.838010 | − | 0.545654i | \(-0.183719\pi\) | ||||
0.838010 | + | 0.545654i | \(0.183719\pi\) | |||||||
\(822\) | −3.99763e24 | −0.668947 | ||||||||
\(823\) | −9.37680e24 | −1.55295 | −0.776473 | − | 0.630151i | \(-0.782993\pi\) | ||||
−0.776473 | + | 0.630151i | \(0.782993\pi\) | |||||||
\(824\) | 7.87968e23 | 0.129160 | ||||||||
\(825\) | −1.71645e23 | −0.0278466 | ||||||||
\(826\) | −3.38514e24 | −0.543559 | ||||||||
\(827\) | 6.91719e24 | 1.09934 | 0.549671 | − | 0.835381i | \(-0.314753\pi\) | ||||
0.549671 | + | 0.835381i | \(0.314753\pi\) | |||||||
\(828\) | 7.03251e23 | 0.110625 | ||||||||
\(829\) | −9.17167e24 | −1.42802 | −0.714011 | − | 0.700135i | \(-0.753123\pi\) | ||||
−0.714011 | + | 0.700135i | \(0.753123\pi\) | |||||||
\(830\) | 2.60166e24 | 0.400948 | ||||||||
\(831\) | 3.99828e24 | 0.609909 | ||||||||
\(832\) | 1.30786e24 | 0.197475 | ||||||||
\(833\) | −1.58428e25 | −2.36782 | ||||||||
\(834\) | 6.03127e24 | 0.892272 | ||||||||
\(835\) | 3.48743e24 | 0.510706 | ||||||||
\(836\) | −1.88662e23 | −0.0273483 | ||||||||
\(837\) | −1.07028e24 | −0.153579 | ||||||||
\(838\) | 1.41339e24 | 0.200766 | ||||||||
\(839\) | 2.44624e24 | 0.343972 | 0.171986 | − | 0.985099i | \(-0.444982\pi\) | ||||
0.171986 | + | 0.985099i | \(0.444982\pi\) | |||||||
\(840\) | −6.13503e24 | −0.853970 | ||||||||
\(841\) | 2.50246e23 | 0.0344828 | ||||||||
\(842\) | −6.87283e24 | −0.937525 | ||||||||
\(843\) | −8.13326e24 | −1.09832 | ||||||||
\(844\) | 3.43946e24 | 0.459811 | ||||||||
\(845\) | 5.15746e24 | 0.682580 | ||||||||
\(846\) | 3.77270e24 | 0.494316 | ||||||||
\(847\) | −1.36664e25 | −1.77275 | ||||||||
\(848\) | 6.07658e23 | 0.0780360 | ||||||||
\(849\) | −4.79364e24 | −0.609467 | ||||||||
\(850\) | −3.22302e24 | −0.405698 | ||||||||
\(851\) | −1.56810e24 | −0.195421 | ||||||||
\(852\) | −1.73759e24 | −0.214393 | ||||||||
\(853\) | −1.00896e25 | −1.23256 | −0.616281 | − | 0.787526i | \(-0.711361\pi\) | ||||
−0.616281 | + | 0.787526i | \(0.711361\pi\) | |||||||
\(854\) | −1.23235e25 | −1.49054 | ||||||||
\(855\) | 2.60538e24 | 0.312004 | ||||||||
\(856\) | 4.12513e24 | 0.489114 | ||||||||
\(857\) | 9.30465e24 | 1.09235 | 0.546177 | − | 0.837670i | \(-0.316083\pi\) | ||||
0.546177 | + | 0.837670i | \(0.316083\pi\) | |||||||
\(858\) | −7.33898e22 | −0.00853087 | ||||||||
\(859\) | 2.35972e24 | 0.271593 | 0.135796 | − | 0.990737i | \(-0.456641\pi\) | ||||
0.135796 | + | 0.990737i | \(0.456641\pi\) | |||||||
\(860\) | 4.90915e24 | 0.559461 | ||||||||
\(861\) | −1.24160e25 | −1.40105 | ||||||||
\(862\) | 7.51909e24 | 0.840143 | ||||||||
\(863\) | 1.26821e25 | 1.40313 | 0.701567 | − | 0.712603i | \(-0.252484\pi\) | ||||
0.701567 | + | 0.712603i | \(0.252484\pi\) | |||||||
\(864\) | 7.11751e24 | 0.779761 | ||||||||
\(865\) | −6.29125e24 | −0.682495 | ||||||||
\(866\) | 8.90815e24 | 0.956942 | ||||||||
\(867\) | 9.57908e23 | 0.101897 | ||||||||
\(868\) | −1.09677e24 | −0.115531 | ||||||||
\(869\) | 7.55183e23 | 0.0787742 | ||||||||
\(870\) | 6.03921e23 | 0.0623830 | ||||||||
\(871\) | 4.11544e23 | 0.0420980 | ||||||||
\(872\) | 6.18877e24 | 0.626923 | ||||||||
\(873\) | −6.17765e24 | −0.619730 | ||||||||
\(874\) | −2.33840e24 | −0.232312 | ||||||||
\(875\) | 1.93026e25 | 1.89910 | ||||||||
\(876\) | 3.38487e23 | 0.0329805 | ||||||||
\(877\) | −6.95139e24 | −0.670772 | −0.335386 | − | 0.942081i | \(-0.608867\pi\) | ||||
−0.335386 | + | 0.942081i | \(0.608867\pi\) | |||||||
\(878\) | −6.94393e24 | −0.663593 | ||||||||
\(879\) | −2.62094e24 | −0.248057 | ||||||||
\(880\) | 2.74342e23 | 0.0257151 | ||||||||
\(881\) | 1.17883e25 | 1.09435 | 0.547175 | − | 0.837018i | \(-0.315703\pi\) | ||||
0.547175 | + | 0.837018i | \(0.315703\pi\) | |||||||
\(882\) | 1.11314e25 | 1.02345 | ||||||||
\(883\) | −1.85904e24 | −0.169286 | −0.0846432 | − | 0.996411i | \(-0.526975\pi\) | ||||
−0.0846432 | + | 0.996411i | \(0.526975\pi\) | |||||||
\(884\) | 1.00689e24 | 0.0908107 | ||||||||
\(885\) | −1.97934e24 | −0.176808 | ||||||||
\(886\) | 1.39762e25 | 1.23652 | ||||||||
\(887\) | 5.22940e24 | 0.458249 | 0.229124 | − | 0.973397i | \(-0.426414\pi\) | ||||
0.229124 | + | 0.973397i | \(0.426414\pi\) | |||||||
\(888\) | −3.54295e24 | −0.307507 | ||||||||
\(889\) | 2.00734e25 | 1.72567 | ||||||||
\(890\) | 8.73197e24 | 0.743528 | ||||||||
\(891\) | −1.09720e22 | −0.000925391 0 | ||||||||
\(892\) | −6.95857e24 | −0.581325 | ||||||||
\(893\) | 9.16587e24 | 0.758466 | ||||||||
\(894\) | −2.14246e24 | −0.175608 | ||||||||
\(895\) | 6.18888e24 | 0.502477 | ||||||||
\(896\) | 5.43203e23 | 0.0436862 | ||||||||
\(897\) | 6.64635e23 | 0.0529478 | ||||||||
\(898\) | 1.02300e25 | 0.807281 | ||||||||
\(899\) | 3.63691e23 | 0.0284299 | ||||||||
\(900\) | −1.65461e24 | −0.128125 | ||||||||
\(901\) | 2.74671e24 | 0.210694 | ||||||||
\(902\) | 1.14183e24 | 0.0867655 | ||||||||
\(903\) | 2.75210e25 | 2.07166 | ||||||||
\(904\) | −1.57947e25 | −1.17782 | ||||||||
\(905\) | −2.48385e24 | −0.183490 | ||||||||
\(906\) | −6.18801e24 | −0.452857 | ||||||||
\(907\) | 1.94030e25 | 1.40672 | 0.703358 | − | 0.710835i | \(-0.251683\pi\) | ||||
0.703358 | + | 0.710835i | \(0.251683\pi\) | |||||||
\(908\) | 9.17745e24 | 0.659163 | ||||||||
\(909\) | 1.38831e24 | 0.0987853 | ||||||||
\(910\) | 2.73159e24 | 0.192559 | ||||||||
\(911\) | 1.64184e25 | 1.14664 | 0.573318 | − | 0.819333i | \(-0.305656\pi\) | ||||
0.573318 | + | 0.819333i | \(0.305656\pi\) | |||||||
\(912\) | −2.56900e24 | −0.177749 | ||||||||
\(913\) | 9.80041e23 | 0.0671804 | ||||||||
\(914\) | −1.33463e25 | −0.906395 | ||||||||
\(915\) | −7.20573e24 | −0.484840 | ||||||||
\(916\) | 4.61510e24 | 0.307659 | ||||||||
\(917\) | −4.24732e25 | −2.80528 | ||||||||
\(918\) | −1.25710e25 | −0.822637 | ||||||||
\(919\) | −1.78581e25 | −1.15785 | −0.578927 | − | 0.815380i | \(-0.696528\pi\) | ||||
−0.578927 | + | 0.815380i | \(0.696528\pi\) | |||||||
\(920\) | −5.10958e24 | −0.328238 | ||||||||
\(921\) | 3.90367e24 | 0.248465 | ||||||||
\(922\) | −4.91045e24 | −0.309676 | ||||||||
\(923\) | 2.60616e24 | 0.162849 | ||||||||
\(924\) | −6.86050e23 | −0.0424760 | ||||||||
\(925\) | 3.68943e24 | 0.226336 | ||||||||
\(926\) | 1.23417e24 | 0.0750205 | ||||||||
\(927\) | −1.21685e24 | −0.0732923 | ||||||||
\(928\) | −2.41859e24 | −0.144346 | ||||||||
\(929\) | −5.31955e24 | −0.314588 | −0.157294 | − | 0.987552i | \(-0.550277\pi\) | ||||
−0.157294 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(930\) | 8.77698e23 | 0.0514328 | ||||||||
\(931\) | 2.70441e25 | 1.57036 | ||||||||
\(932\) | −1.06854e25 | −0.614830 | ||||||||
\(933\) | −6.56374e24 | −0.374246 | ||||||||
\(934\) | 4.18197e24 | 0.236283 | ||||||||
\(935\) | 1.24007e24 | 0.0694299 | ||||||||
\(936\) | −2.38317e24 | −0.132224 | ||||||||
\(937\) | −2.50045e25 | −1.37478 | −0.687388 | − | 0.726290i | \(-0.741243\pi\) | ||||
−0.687388 | + | 0.726290i | \(0.741243\pi\) | |||||||
\(938\) | −5.26530e24 | −0.286879 | ||||||||
\(939\) | 2.19789e25 | 1.18672 | ||||||||
\(940\) | 5.94548e24 | 0.318127 | ||||||||
\(941\) | −1.25452e25 | −0.665220 | −0.332610 | − | 0.943065i | \(-0.607929\pi\) | ||||
−0.332610 | + | 0.943065i | \(0.607929\pi\) | |||||||
\(942\) | −1.39063e25 | −0.730765 | ||||||||
\(943\) | −1.03407e25 | −0.538519 | ||||||||
\(944\) | −3.09736e24 | −0.159856 | ||||||||
\(945\) | 2.49183e25 | 1.27452 | ||||||||
\(946\) | −2.53097e24 | −0.128296 | ||||||||
\(947\) | 2.41151e25 | 1.21148 | 0.605738 | − | 0.795664i | \(-0.292878\pi\) | ||||
0.605738 | + | 0.795664i | \(0.292878\pi\) | |||||||
\(948\) | −4.58710e24 | −0.228385 | ||||||||
\(949\) | −5.07686e23 | −0.0250514 | ||||||||
\(950\) | 5.50180e24 | 0.269063 | ||||||||
\(951\) | −2.79024e24 | −0.135241 | ||||||||
\(952\) | −4.33952e25 | −2.08463 | ||||||||
\(953\) | 1.36562e25 | 0.650190 | 0.325095 | − | 0.945681i | \(-0.394604\pi\) | ||||
0.325095 | + | 0.945681i | \(0.394604\pi\) | |||||||
\(954\) | −1.92989e24 | −0.0910692 | ||||||||
\(955\) | −1.98020e24 | −0.0926146 | ||||||||
\(956\) | −1.25818e25 | −0.583244 | ||||||||
\(957\) | 2.27496e23 | 0.0104525 | ||||||||
\(958\) | 4.81422e24 | 0.219240 | ||||||||
\(959\) | 5.60500e25 | 2.52998 | ||||||||
\(960\) | −9.78388e24 | −0.437729 | ||||||||
\(961\) | −2.20216e25 | −0.976560 | ||||||||
\(962\) | 1.57748e24 | 0.0693388 | ||||||||
\(963\) | −6.37037e24 | −0.277550 | ||||||||
\(964\) | −7.40925e24 | −0.319977 | ||||||||
\(965\) | 7.55018e24 | 0.323203 | ||||||||
\(966\) | −8.50336e24 | −0.360815 | ||||||||
\(967\) | 2.51961e25 | 1.05976 | 0.529881 | − | 0.848072i | \(-0.322237\pi\) | ||||
0.529881 | + | 0.848072i | \(0.322237\pi\) | |||||||
\(968\) | −2.57168e25 | −1.07220 | ||||||||
\(969\) | −1.16123e25 | −0.479916 | ||||||||
\(970\) | 1.33243e25 | 0.545865 | ||||||||
\(971\) | 1.28706e25 | 0.522678 | 0.261339 | − | 0.965247i | \(-0.415836\pi\) | ||||
0.261339 | + | 0.965247i | \(0.415836\pi\) | |||||||
\(972\) | −1.04535e25 | −0.420823 | ||||||||
\(973\) | −8.45633e25 | −3.37460 | ||||||||
\(974\) | −1.02911e25 | −0.407109 | ||||||||
\(975\) | −1.56376e24 | −0.0613240 | ||||||||
\(976\) | −1.12759e25 | −0.438356 | ||||||||
\(977\) | −3.80187e25 | −1.46519 | −0.732594 | − | 0.680666i | \(-0.761691\pi\) | ||||
−0.732594 | + | 0.680666i | \(0.761691\pi\) | |||||||
\(978\) | 6.53354e24 | 0.249613 | ||||||||
\(979\) | 3.28931e24 | 0.124581 | ||||||||
\(980\) | 1.75423e25 | 0.658665 | ||||||||
\(981\) | −9.55723e24 | −0.355750 | ||||||||
\(982\) | 1.06821e25 | 0.394192 | ||||||||
\(983\) | −1.73844e25 | −0.635997 | −0.317998 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317998 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(984\) | −2.33637e25 | −0.847392 | ||||||||
\(985\) | −1.56711e25 | −0.563495 | ||||||||
\(986\) | 4.27175e24 | 0.152283 | ||||||||
\(987\) | 3.33308e25 | 1.17801 | ||||||||
\(988\) | −1.71879e24 | −0.0602266 | ||||||||
\(989\) | 2.29210e25 | 0.796280 | ||||||||
\(990\) | −8.71295e23 | −0.0300100 | ||||||||
\(991\) | −9.50191e24 | −0.324478 | −0.162239 | − | 0.986752i | \(-0.551871\pi\) | ||||
−0.162239 | + | 0.986752i | \(0.551871\pi\) | |||||||
\(992\) | −3.51502e24 | −0.119009 | ||||||||
\(993\) | 2.37176e25 | 0.796164 | ||||||||
\(994\) | −3.33432e25 | −1.10974 | ||||||||
\(995\) | −2.58935e25 | −0.854467 | ||||||||
\(996\) | −5.95292e24 | −0.194772 | ||||||||
\(997\) | 1.19972e25 | 0.389198 | 0.194599 | − | 0.980883i | \(-0.437659\pi\) | ||||
0.194599 | + | 0.980883i | \(0.437659\pi\) | |||||||
\(998\) | −7.49222e24 | −0.240991 | ||||||||
\(999\) | 1.43902e25 | 0.458945 |
(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 | 29.18.a.b.1.7 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.18.a.b.1.7 | ✓ | 21 | 1.1 | even | 1 | trivial |