Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,18,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, 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("10.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(18.3222087345\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{83281}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 20820 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(144.792\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −256.000 | −0.707107 | ||||||||
\(3\) | −9311.53 | −0.819390 | −0.409695 | − | 0.912223i | \(-0.634365\pi\) | ||||
−0.409695 | + | 0.912223i | \(0.634365\pi\) | |||||||
\(4\) | 65536.0 | 0.500000 | ||||||||
\(5\) | 390625. | 0.447214 | ||||||||
\(6\) | 2.38375e6 | 0.579396 | ||||||||
\(7\) | −2.48655e7 | −1.63029 | −0.815144 | − | 0.579258i | \(-0.803342\pi\) | ||||
−0.815144 | + | 0.579258i | \(0.803342\pi\) | |||||||
\(8\) | −1.67772e7 | −0.353553 | ||||||||
\(9\) | −4.24355e7 | −0.328600 | ||||||||
\(10\) | −1.00000e8 | −0.316228 | ||||||||
\(11\) | −1.90392e8 | −0.267801 | −0.133900 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133900 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(12\) | −6.10241e8 | −0.409695 | ||||||||
\(13\) | −1.57377e7 | −0.00535085 | −0.00267543 | − | 0.999996i | \(-0.500852\pi\) | ||||
−0.00267543 | + | 0.999996i | \(0.500852\pi\) | |||||||
\(14\) | 6.36558e9 | 1.15279 | ||||||||
\(15\) | −3.63732e9 | −0.366442 | ||||||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | −2.25502e10 | −0.784032 | −0.392016 | − | 0.919958i | \(-0.628222\pi\) | ||||
−0.392016 | + | 0.919958i | \(0.628222\pi\) | |||||||
\(18\) | 1.08635e10 | 0.232355 | ||||||||
\(19\) | 1.27984e11 | 1.72882 | 0.864408 | − | 0.502791i | \(-0.167694\pi\) | ||||
0.864408 | + | 0.502791i | \(0.167694\pi\) | |||||||
\(20\) | 2.56000e10 | 0.223607 | ||||||||
\(21\) | 2.31536e11 | 1.33584 | ||||||||
\(22\) | 4.87405e10 | 0.189364 | ||||||||
\(23\) | 2.59325e11 | 0.690490 | 0.345245 | − | 0.938513i | \(-0.387796\pi\) | ||||
0.345245 | + | 0.938513i | \(0.387796\pi\) | |||||||
\(24\) | 1.56222e11 | 0.289698 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | 4.02885e9 | 0.00378363 | ||||||||
\(27\) | 1.59763e12 | 1.08864 | ||||||||
\(28\) | −1.62959e12 | −0.815144 | ||||||||
\(29\) | −2.57953e12 | −0.957542 | −0.478771 | − | 0.877940i | \(-0.658918\pi\) | ||||
−0.478771 | + | 0.877940i | \(0.658918\pi\) | |||||||
\(30\) | 9.31153e11 | 0.259114 | ||||||||
\(31\) | 7.91253e12 | 1.66625 | 0.833126 | − | 0.553083i | \(-0.186549\pi\) | ||||
0.833126 | + | 0.553083i | \(0.186549\pi\) | |||||||
\(32\) | −1.09951e12 | −0.176777 | ||||||||
\(33\) | 1.77285e12 | 0.219433 | ||||||||
\(34\) | 5.77284e12 | 0.554395 | ||||||||
\(35\) | −9.71310e12 | −0.729087 | ||||||||
\(36\) | −2.78105e12 | −0.164300 | ||||||||
\(37\) | −2.09888e13 | −0.982367 | −0.491184 | − | 0.871056i | \(-0.663436\pi\) | ||||
−0.491184 | + | 0.871056i | \(0.663436\pi\) | |||||||
\(38\) | −3.27638e13 | −1.22246 | ||||||||
\(39\) | 1.46542e11 | 0.00438444 | ||||||||
\(40\) | −6.55360e12 | −0.158114 | ||||||||
\(41\) | 1.98123e13 | 0.387499 | 0.193750 | − | 0.981051i | \(-0.437935\pi\) | ||||
0.193750 | + | 0.981051i | \(0.437935\pi\) | |||||||
\(42\) | −5.92733e13 | −0.944583 | ||||||||
\(43\) | −4.60777e13 | −0.601186 | −0.300593 | − | 0.953753i | \(-0.597185\pi\) | ||||
−0.300593 | + | 0.953753i | \(0.597185\pi\) | |||||||
\(44\) | −1.24776e13 | −0.133900 | ||||||||
\(45\) | −1.65764e13 | −0.146955 | ||||||||
\(46\) | −6.63871e13 | −0.488250 | ||||||||
\(47\) | 2.66827e14 | 1.63455 | 0.817274 | − | 0.576250i | \(-0.195484\pi\) | ||||
0.817274 | + | 0.576250i | \(0.195484\pi\) | |||||||
\(48\) | −3.99927e13 | −0.204847 | ||||||||
\(49\) | 3.85664e14 | 1.65784 | ||||||||
\(50\) | −3.90625e13 | −0.141421 | ||||||||
\(51\) | 2.09977e14 | 0.642428 | ||||||||
\(52\) | −1.03139e12 | −0.00267543 | ||||||||
\(53\) | 4.00045e14 | 0.882599 | 0.441300 | − | 0.897360i | \(-0.354518\pi\) | ||||
0.441300 | + | 0.897360i | \(0.354518\pi\) | |||||||
\(54\) | −4.08994e14 | −0.769786 | ||||||||
\(55\) | −7.43721e13 | −0.119764 | ||||||||
\(56\) | 4.17174e14 | 0.576394 | ||||||||
\(57\) | −1.19172e15 | −1.41657 | ||||||||
\(58\) | 6.60360e14 | 0.677084 | ||||||||
\(59\) | 1.82611e15 | 1.61914 | 0.809570 | − | 0.587024i | \(-0.199701\pi\) | ||||
0.809570 | + | 0.587024i | \(0.199701\pi\) | |||||||
\(60\) | −2.38375e14 | −0.183221 | ||||||||
\(61\) | −1.48236e15 | −0.990035 | −0.495017 | − | 0.868883i | \(-0.664838\pi\) | ||||
−0.495017 | + | 0.868883i | \(0.664838\pi\) | |||||||
\(62\) | −2.02561e15 | −1.17822 | ||||||||
\(63\) | 1.05518e15 | 0.535713 | ||||||||
\(64\) | 2.81475e14 | 0.125000 | ||||||||
\(65\) | −6.14754e12 | −0.00239297 | ||||||||
\(66\) | −4.53849e14 | −0.155163 | ||||||||
\(67\) | −2.71410e15 | −0.816563 | −0.408282 | − | 0.912856i | \(-0.633872\pi\) | ||||
−0.408282 | + | 0.912856i | \(0.633872\pi\) | |||||||
\(68\) | −1.47785e15 | −0.392016 | ||||||||
\(69\) | −2.41471e15 | −0.565780 | ||||||||
\(70\) | 2.48655e15 | 0.515542 | ||||||||
\(71\) | −3.87337e15 | −0.711858 | −0.355929 | − | 0.934513i | \(-0.615836\pi\) | ||||
−0.355929 | + | 0.934513i | \(0.615836\pi\) | |||||||
\(72\) | 7.11949e14 | 0.116178 | ||||||||
\(73\) | −2.85786e15 | −0.414759 | −0.207380 | − | 0.978261i | \(-0.566494\pi\) | ||||
−0.207380 | + | 0.978261i | \(0.566494\pi\) | |||||||
\(74\) | 5.37314e15 | 0.694638 | ||||||||
\(75\) | −1.42083e15 | −0.163878 | ||||||||
\(76\) | 8.38753e15 | 0.864408 | ||||||||
\(77\) | 4.73421e15 | 0.436593 | ||||||||
\(78\) | −3.75148e13 | −0.00310026 | ||||||||
\(79\) | 2.80988e15 | 0.208381 | 0.104190 | − | 0.994557i | \(-0.466775\pi\) | ||||
0.104190 | + | 0.994557i | \(0.466775\pi\) | |||||||
\(80\) | 1.67772e15 | 0.111803 | ||||||||
\(81\) | −9.39628e15 | −0.563422 | ||||||||
\(82\) | −5.07194e15 | −0.274003 | ||||||||
\(83\) | −7.04230e15 | −0.343203 | −0.171601 | − | 0.985166i | \(-0.554894\pi\) | ||||
−0.171601 | + | 0.985166i | \(0.554894\pi\) | |||||||
\(84\) | 1.51740e16 | 0.667921 | ||||||||
\(85\) | −8.80866e15 | −0.350630 | ||||||||
\(86\) | 1.17959e16 | 0.425103 | ||||||||
\(87\) | 2.40194e16 | 0.784600 | ||||||||
\(88\) | 3.19426e15 | 0.0946819 | ||||||||
\(89\) | 5.51966e16 | 1.48627 | 0.743135 | − | 0.669142i | \(-0.233338\pi\) | ||||
0.743135 | + | 0.669142i | \(0.233338\pi\) | |||||||
\(90\) | 4.24355e15 | 0.103913 | ||||||||
\(91\) | 3.91327e14 | 0.00872343 | ||||||||
\(92\) | 1.69951e16 | 0.345245 | ||||||||
\(93\) | −7.36778e16 | −1.36531 | ||||||||
\(94\) | −6.83076e16 | −1.15580 | ||||||||
\(95\) | 4.99936e16 | 0.773150 | ||||||||
\(96\) | 1.02381e16 | 0.144849 | ||||||||
\(97\) | 6.42662e16 | 0.832574 | 0.416287 | − | 0.909233i | \(-0.363331\pi\) | ||||
0.416287 | + | 0.909233i | \(0.363331\pi\) | |||||||
\(98\) | −9.87300e16 | −1.17227 | ||||||||
\(99\) | 8.07940e15 | 0.0879994 | ||||||||
\(100\) | 1.00000e16 | 0.100000 | ||||||||
\(101\) | −1.56405e17 | −1.43721 | −0.718603 | − | 0.695421i | \(-0.755218\pi\) | ||||
−0.718603 | + | 0.695421i | \(0.755218\pi\) | |||||||
\(102\) | −5.37540e16 | −0.454265 | ||||||||
\(103\) | −2.33166e17 | −1.81363 | −0.906816 | − | 0.421527i | \(-0.861494\pi\) | ||||
−0.906816 | + | 0.421527i | \(0.861494\pi\) | |||||||
\(104\) | 2.64035e14 | 0.00189181 | ||||||||
\(105\) | 9.04438e16 | 0.597407 | ||||||||
\(106\) | −1.02411e17 | −0.624092 | ||||||||
\(107\) | −1.05397e17 | −0.593017 | −0.296509 | − | 0.955030i | \(-0.595822\pi\) | ||||
−0.296509 | + | 0.955030i | \(0.595822\pi\) | |||||||
\(108\) | 1.04702e17 | 0.544321 | ||||||||
\(109\) | 2.51895e17 | 1.21086 | 0.605431 | − | 0.795898i | \(-0.293001\pi\) | ||||
0.605431 | + | 0.795898i | \(0.293001\pi\) | |||||||
\(110\) | 1.90392e16 | 0.0846861 | ||||||||
\(111\) | 1.95438e17 | 0.804942 | ||||||||
\(112\) | −1.06797e17 | −0.407572 | ||||||||
\(113\) | 4.09395e17 | 1.44869 | 0.724346 | − | 0.689436i | \(-0.242142\pi\) | ||||
0.724346 | + | 0.689436i | \(0.242142\pi\) | |||||||
\(114\) | 3.05081e17 | 1.00167 | ||||||||
\(115\) | 1.01299e17 | 0.308796 | ||||||||
\(116\) | −1.69052e17 | −0.478771 | ||||||||
\(117\) | 6.67838e14 | 0.00175829 | ||||||||
\(118\) | −4.67483e17 | −1.14490 | ||||||||
\(119\) | 5.60722e17 | 1.27820 | ||||||||
\(120\) | 6.10241e16 | 0.129557 | ||||||||
\(121\) | −4.69198e17 | −0.928283 | ||||||||
\(122\) | 3.79484e17 | 0.700060 | ||||||||
\(123\) | −1.84482e17 | −0.317513 | ||||||||
\(124\) | 5.18555e17 | 0.833126 | ||||||||
\(125\) | 5.96046e16 | 0.0894427 | ||||||||
\(126\) | −2.70126e17 | −0.378806 | ||||||||
\(127\) | −6.42410e17 | −0.842327 | −0.421164 | − | 0.906985i | \(-0.638378\pi\) | ||||
−0.421164 | + | 0.906985i | \(0.638378\pi\) | |||||||
\(128\) | −7.20576e16 | −0.0883883 | ||||||||
\(129\) | 4.29054e17 | 0.492606 | ||||||||
\(130\) | 1.57377e15 | 0.00169209 | ||||||||
\(131\) | 3.57323e17 | 0.359961 | 0.179980 | − | 0.983670i | \(-0.442397\pi\) | ||||
0.179980 | + | 0.983670i | \(0.442397\pi\) | |||||||
\(132\) | 1.16185e17 | 0.109717 | ||||||||
\(133\) | −3.18238e18 | −2.81847 | ||||||||
\(134\) | 6.94809e17 | 0.577397 | ||||||||
\(135\) | 6.24075e17 | 0.486855 | ||||||||
\(136\) | 3.78329e17 | 0.277197 | ||||||||
\(137\) | −1.23821e18 | −0.852454 | −0.426227 | − | 0.904616i | \(-0.640158\pi\) | ||||
−0.426227 | + | 0.904616i | \(0.640158\pi\) | |||||||
\(138\) | 6.18166e17 | 0.400067 | ||||||||
\(139\) | 1.95129e18 | 1.18767 | 0.593836 | − | 0.804586i | \(-0.297613\pi\) | ||||
0.593836 | + | 0.804586i | \(0.297613\pi\) | |||||||
\(140\) | −6.36558e17 | −0.364544 | ||||||||
\(141\) | −2.48457e18 | −1.33933 | ||||||||
\(142\) | 9.91584e17 | 0.503360 | ||||||||
\(143\) | 2.99634e15 | 0.00143296 | ||||||||
\(144\) | −1.82259e17 | −0.0821501 | ||||||||
\(145\) | −1.00763e18 | −0.428226 | ||||||||
\(146\) | 7.31611e17 | 0.293279 | ||||||||
\(147\) | −3.59112e18 | −1.35842 | ||||||||
\(148\) | −1.37552e18 | −0.491184 | ||||||||
\(149\) | 1.86793e18 | 0.629908 | 0.314954 | − | 0.949107i | \(-0.398011\pi\) | ||||
0.314954 | + | 0.949107i | \(0.398011\pi\) | |||||||
\(150\) | 3.63732e17 | 0.115879 | ||||||||
\(151\) | 5.18884e18 | 1.56231 | 0.781154 | − | 0.624339i | \(-0.214632\pi\) | ||||
0.781154 | + | 0.624339i | \(0.214632\pi\) | |||||||
\(152\) | −2.14721e18 | −0.611229 | ||||||||
\(153\) | 9.56927e17 | 0.257633 | ||||||||
\(154\) | −1.21196e18 | −0.308718 | ||||||||
\(155\) | 3.09083e18 | 0.745171 | ||||||||
\(156\) | 9.60379e15 | 0.00219222 | ||||||||
\(157\) | 7.78987e18 | 1.68416 | 0.842080 | − | 0.539353i | \(-0.181331\pi\) | ||||
0.842080 | + | 0.539353i | \(0.181331\pi\) | |||||||
\(158\) | −7.19330e17 | −0.147347 | ||||||||
\(159\) | −3.72503e18 | −0.723193 | ||||||||
\(160\) | −4.29497e17 | −0.0790569 | ||||||||
\(161\) | −6.44825e18 | −1.12570 | ||||||||
\(162\) | 2.40545e18 | 0.398399 | ||||||||
\(163\) | 6.16891e18 | 0.969647 | 0.484824 | − | 0.874612i | \(-0.338884\pi\) | ||||
0.484824 | + | 0.874612i | \(0.338884\pi\) | |||||||
\(164\) | 1.29842e18 | 0.193750 | ||||||||
\(165\) | 6.92518e17 | 0.0981336 | ||||||||
\(166\) | 1.80283e18 | 0.242681 | ||||||||
\(167\) | 1.24726e19 | 1.59539 | 0.797693 | − | 0.603064i | \(-0.206054\pi\) | ||||
0.797693 | + | 0.603064i | \(0.206054\pi\) | |||||||
\(168\) | −3.88453e18 | −0.472291 | ||||||||
\(169\) | −8.65017e18 | −0.999971 | ||||||||
\(170\) | 2.25502e18 | 0.247933 | ||||||||
\(171\) | −5.43105e18 | −0.568089 | ||||||||
\(172\) | −3.01975e18 | −0.300593 | ||||||||
\(173\) | 1.64494e19 | 1.55869 | 0.779344 | − | 0.626596i | \(-0.215552\pi\) | ||||
0.779344 | + | 0.626596i | \(0.215552\pi\) | |||||||
\(174\) | −6.14896e18 | −0.554796 | ||||||||
\(175\) | −3.79418e18 | −0.326058 | ||||||||
\(176\) | −8.17729e17 | −0.0669502 | ||||||||
\(177\) | −1.70039e19 | −1.32671 | ||||||||
\(178\) | −1.41303e19 | −1.05095 | ||||||||
\(179\) | −1.53067e18 | −0.108550 | −0.0542751 | − | 0.998526i | \(-0.517285\pi\) | ||||
−0.0542751 | + | 0.998526i | \(0.517285\pi\) | |||||||
\(180\) | −1.08635e18 | −0.0734773 | ||||||||
\(181\) | −8.51444e18 | −0.549399 | −0.274700 | − | 0.961530i | \(-0.588578\pi\) | ||||
−0.274700 | + | 0.961530i | \(0.588578\pi\) | |||||||
\(182\) | −1.00180e17 | −0.00616840 | ||||||||
\(183\) | 1.38031e19 | 0.811224 | ||||||||
\(184\) | −4.35075e18 | −0.244125 | ||||||||
\(185\) | −8.19877e18 | −0.439328 | ||||||||
\(186\) | 1.88615e19 | 0.965420 | ||||||||
\(187\) | 4.29338e18 | 0.209965 | ||||||||
\(188\) | 1.74868e19 | 0.817274 | ||||||||
\(189\) | −3.97260e19 | −1.77480 | ||||||||
\(190\) | −1.27984e19 | −0.546699 | ||||||||
\(191\) | 1.05921e19 | 0.432710 | 0.216355 | − | 0.976315i | \(-0.430583\pi\) | ||||
0.216355 | + | 0.976315i | \(0.430583\pi\) | |||||||
\(192\) | −2.62096e18 | −0.102424 | ||||||||
\(193\) | −1.55768e19 | −0.582425 | −0.291213 | − | 0.956658i | \(-0.594059\pi\) | ||||
−0.291213 | + | 0.956658i | \(0.594059\pi\) | |||||||
\(194\) | −1.64521e19 | −0.588719 | ||||||||
\(195\) | 5.72431e16 | 0.00196078 | ||||||||
\(196\) | 2.52749e19 | 0.828920 | ||||||||
\(197\) | 8.47320e18 | 0.266124 | 0.133062 | − | 0.991108i | \(-0.457519\pi\) | ||||
0.133062 | + | 0.991108i | \(0.457519\pi\) | |||||||
\(198\) | −2.06833e18 | −0.0622250 | ||||||||
\(199\) | 9.48640e18 | 0.273433 | 0.136716 | − | 0.990610i | \(-0.456345\pi\) | ||||
0.136716 | + | 0.990610i | \(0.456345\pi\) | |||||||
\(200\) | −2.56000e18 | −0.0707107 | ||||||||
\(201\) | 2.52724e19 | 0.669083 | ||||||||
\(202\) | 4.00397e19 | 1.01626 | ||||||||
\(203\) | 6.41414e19 | 1.56107 | ||||||||
\(204\) | 1.37610e19 | 0.321214 | ||||||||
\(205\) | 7.73916e18 | 0.173295 | ||||||||
\(206\) | 5.96905e19 | 1.28243 | ||||||||
\(207\) | −1.10046e19 | −0.226895 | ||||||||
\(208\) | −6.75930e16 | −0.00133771 | ||||||||
\(209\) | −2.43671e19 | −0.462978 | ||||||||
\(210\) | −2.31536e19 | −0.422430 | ||||||||
\(211\) | −5.06102e19 | −0.886824 | −0.443412 | − | 0.896318i | \(-0.646232\pi\) | ||||
−0.443412 | + | 0.896318i | \(0.646232\pi\) | |||||||
\(212\) | 2.62173e19 | 0.441300 | ||||||||
\(213\) | 3.60671e19 | 0.583289 | ||||||||
\(214\) | 2.69817e19 | 0.419327 | ||||||||
\(215\) | −1.79991e19 | −0.268858 | ||||||||
\(216\) | −2.68038e19 | −0.384893 | ||||||||
\(217\) | −1.96749e20 | −2.71647 | ||||||||
\(218\) | −6.44851e19 | −0.856208 | ||||||||
\(219\) | 2.66110e19 | 0.339849 | ||||||||
\(220\) | −4.87405e18 | −0.0598821 | ||||||||
\(221\) | 3.54888e17 | 0.00419524 | ||||||||
\(222\) | −5.00322e19 | −0.569180 | ||||||||
\(223\) | 1.13017e20 | 1.23752 | 0.618759 | − | 0.785581i | \(-0.287636\pi\) | ||||
0.618759 | + | 0.785581i | \(0.287636\pi\) | |||||||
\(224\) | 2.73399e19 | 0.288197 | ||||||||
\(225\) | −6.47514e18 | −0.0657201 | ||||||||
\(226\) | −1.04805e20 | −1.02438 | ||||||||
\(227\) | 1.34057e20 | 1.26203 | 0.631016 | − | 0.775770i | \(-0.282638\pi\) | ||||
0.631016 | + | 0.775770i | \(0.282638\pi\) | |||||||
\(228\) | −7.81008e19 | −0.708287 | ||||||||
\(229\) | −1.53092e20 | −1.33768 | −0.668840 | − | 0.743406i | \(-0.733209\pi\) | ||||
−0.668840 | + | 0.743406i | \(0.733209\pi\) | |||||||
\(230\) | −2.59325e19 | −0.218352 | ||||||||
\(231\) | −4.40828e19 | −0.357740 | ||||||||
\(232\) | 4.32773e19 | 0.338542 | ||||||||
\(233\) | 1.54095e20 | 1.16215 | 0.581076 | − | 0.813849i | \(-0.302632\pi\) | ||||
0.581076 | + | 0.813849i | \(0.302632\pi\) | |||||||
\(234\) | −1.70966e17 | −0.00124330 | ||||||||
\(235\) | 1.04229e20 | 0.730992 | ||||||||
\(236\) | 1.19676e20 | 0.809570 | ||||||||
\(237\) | −2.61643e19 | −0.170745 | ||||||||
\(238\) | −1.43545e20 | −0.903823 | ||||||||
\(239\) | 1.10626e20 | 0.672161 | 0.336081 | − | 0.941833i | \(-0.390899\pi\) | ||||
0.336081 | + | 0.941833i | \(0.390899\pi\) | |||||||
\(240\) | −1.56222e19 | −0.0916106 | ||||||||
\(241\) | −1.68590e20 | −0.954303 | −0.477152 | − | 0.878821i | \(-0.658331\pi\) | ||||
−0.477152 | + | 0.878821i | \(0.658331\pi\) | |||||||
\(242\) | 1.20115e20 | 0.656395 | ||||||||
\(243\) | −1.18825e20 | −0.626980 | ||||||||
\(244\) | −9.71480e19 | −0.495017 | ||||||||
\(245\) | 1.50650e20 | 0.741408 | ||||||||
\(246\) | 4.72275e19 | 0.224516 | ||||||||
\(247\) | −2.01417e18 | −0.00925064 | ||||||||
\(248\) | −1.32750e20 | −0.589109 | ||||||||
\(249\) | 6.55746e19 | 0.281217 | ||||||||
\(250\) | −1.52588e19 | −0.0632456 | ||||||||
\(251\) | −8.71684e19 | −0.349247 | −0.174623 | − | 0.984635i | \(-0.555871\pi\) | ||||
−0.174623 | + | 0.984635i | \(0.555871\pi\) | |||||||
\(252\) | 6.91523e19 | 0.267857 | ||||||||
\(253\) | −4.93735e19 | −0.184914 | ||||||||
\(254\) | 1.64457e20 | 0.595615 | ||||||||
\(255\) | 8.20221e19 | 0.287303 | ||||||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | 2.57989e20 | 0.845610 | 0.422805 | − | 0.906221i | \(-0.361046\pi\) | ||||
0.422805 | + | 0.906221i | \(0.361046\pi\) | |||||||
\(258\) | −1.09838e20 | −0.348325 | ||||||||
\(259\) | 5.21899e20 | 1.60154 | ||||||||
\(260\) | −4.02885e17 | −0.00119649 | ||||||||
\(261\) | 1.09464e20 | 0.314648 | ||||||||
\(262\) | −9.14747e19 | −0.254531 | ||||||||
\(263\) | −4.12838e20 | −1.11213 | −0.556065 | − | 0.831139i | \(-0.687689\pi\) | ||||
−0.556065 | + | 0.831139i | \(0.687689\pi\) | |||||||
\(264\) | −2.97434e19 | −0.0775814 | ||||||||
\(265\) | 1.56267e20 | 0.394710 | ||||||||
\(266\) | 8.14689e20 | 1.99296 | ||||||||
\(267\) | −5.13965e20 | −1.21783 | ||||||||
\(268\) | −1.77871e20 | −0.408282 | ||||||||
\(269\) | 3.61622e20 | 0.804194 | 0.402097 | − | 0.915597i | \(-0.368282\pi\) | ||||
0.402097 | + | 0.915597i | \(0.368282\pi\) | |||||||
\(270\) | −1.59763e20 | −0.344259 | ||||||||
\(271\) | −6.61685e20 | −1.38170 | −0.690848 | − | 0.723000i | \(-0.742762\pi\) | ||||
−0.690848 | + | 0.723000i | \(0.742762\pi\) | |||||||
\(272\) | −9.68522e19 | −0.196008 | ||||||||
\(273\) | −3.64385e18 | −0.00714789 | ||||||||
\(274\) | 3.16983e20 | 0.602776 | ||||||||
\(275\) | −2.90516e19 | −0.0535602 | ||||||||
\(276\) | −1.58250e20 | −0.282890 | ||||||||
\(277\) | 2.43700e20 | 0.422452 | 0.211226 | − | 0.977437i | \(-0.432254\pi\) | ||||
0.211226 | + | 0.977437i | \(0.432254\pi\) | |||||||
\(278\) | −4.99531e20 | −0.839812 | ||||||||
\(279\) | −3.35772e20 | −0.547531 | ||||||||
\(280\) | 1.62959e20 | 0.257771 | ||||||||
\(281\) | −9.47052e20 | −1.45335 | −0.726675 | − | 0.686981i | \(-0.758935\pi\) | ||||
−0.726675 | + | 0.686981i | \(0.758935\pi\) | |||||||
\(282\) | 6.36049e20 | 0.947050 | ||||||||
\(283\) | −3.67504e20 | −0.530979 | −0.265489 | − | 0.964114i | \(-0.585534\pi\) | ||||
−0.265489 | + | 0.964114i | \(0.585534\pi\) | |||||||
\(284\) | −2.53845e20 | −0.355929 | ||||||||
\(285\) | −4.65517e20 | −0.633511 | ||||||||
\(286\) | −7.67064e17 | −0.00101326 | ||||||||
\(287\) | −4.92642e20 | −0.631736 | ||||||||
\(288\) | 4.66583e19 | 0.0580889 | ||||||||
\(289\) | −3.18730e20 | −0.385293 | ||||||||
\(290\) | 2.57953e20 | 0.302801 | ||||||||
\(291\) | −5.98417e20 | −0.682203 | ||||||||
\(292\) | −1.87292e20 | −0.207380 | ||||||||
\(293\) | 1.20904e21 | 1.30037 | 0.650183 | − | 0.759778i | \(-0.274692\pi\) | ||||
0.650183 | + | 0.759778i | \(0.274692\pi\) | |||||||
\(294\) | 9.19328e20 | 0.960546 | ||||||||
\(295\) | 7.13323e20 | 0.724101 | ||||||||
\(296\) | 3.52134e20 | 0.347319 | ||||||||
\(297\) | −3.04177e20 | −0.291539 | ||||||||
\(298\) | −4.78190e20 | −0.445412 | ||||||||
\(299\) | −4.08118e18 | −0.00369471 | ||||||||
\(300\) | −9.31153e19 | −0.0819390 | ||||||||
\(301\) | 1.14575e21 | 0.980106 | ||||||||
\(302\) | −1.32834e21 | −1.10472 | ||||||||
\(303\) | 1.45637e21 | 1.17763 | ||||||||
\(304\) | 5.49685e20 | 0.432204 | ||||||||
\(305\) | −5.79047e20 | −0.442757 | ||||||||
\(306\) | −2.44973e20 | −0.182174 | ||||||||
\(307\) | −4.76931e20 | −0.344969 | −0.172484 | − | 0.985012i | \(-0.555179\pi\) | ||||
−0.172484 | + | 0.985012i | \(0.555179\pi\) | |||||||
\(308\) | 3.10261e20 | 0.218296 | ||||||||
\(309\) | 2.17114e21 | 1.48607 | ||||||||
\(310\) | −7.91253e20 | −0.526915 | ||||||||
\(311\) | 3.50418e20 | 0.227051 | 0.113525 | − | 0.993535i | \(-0.463786\pi\) | ||||
0.113525 | + | 0.993535i | \(0.463786\pi\) | |||||||
\(312\) | −2.45857e18 | −0.00155013 | ||||||||
\(313\) | 2.04751e21 | 1.25631 | 0.628157 | − | 0.778087i | \(-0.283810\pi\) | ||||
0.628157 | + | 0.778087i | \(0.283810\pi\) | |||||||
\(314\) | −1.99421e21 | −1.19088 | ||||||||
\(315\) | 4.12180e20 | 0.239578 | ||||||||
\(316\) | 1.84148e20 | 0.104190 | ||||||||
\(317\) | 1.31663e21 | 0.725205 | 0.362602 | − | 0.931944i | \(-0.381888\pi\) | ||||
0.362602 | + | 0.931944i | \(0.381888\pi\) | |||||||
\(318\) | 9.53607e20 | 0.511375 | ||||||||
\(319\) | 4.91123e20 | 0.256430 | ||||||||
\(320\) | 1.09951e20 | 0.0559017 | ||||||||
\(321\) | 9.81411e20 | 0.485912 | ||||||||
\(322\) | 1.65075e21 | 0.795988 | ||||||||
\(323\) | −2.88605e21 | −1.35545 | ||||||||
\(324\) | −6.15795e20 | −0.281711 | ||||||||
\(325\) | −2.40138e18 | −0.00107017 | ||||||||
\(326\) | −1.57924e21 | −0.685644 | ||||||||
\(327\) | −2.34553e21 | −0.992167 | ||||||||
\(328\) | −3.32394e20 | −0.137002 | ||||||||
\(329\) | −6.63479e21 | −2.66478 | ||||||||
\(330\) | −1.77285e20 | −0.0693909 | ||||||||
\(331\) | 3.85862e21 | 1.47195 | 0.735977 | − | 0.677007i | \(-0.236723\pi\) | ||||
0.735977 | + | 0.677007i | \(0.236723\pi\) | |||||||
\(332\) | −4.61524e20 | −0.171601 | ||||||||
\(333\) | 8.90672e20 | 0.322806 | ||||||||
\(334\) | −3.19298e21 | −1.12811 | ||||||||
\(335\) | −1.06019e21 | −0.365178 | ||||||||
\(336\) | 9.94441e20 | 0.333960 | ||||||||
\(337\) | 4.69149e21 | 1.53623 | 0.768115 | − | 0.640312i | \(-0.221195\pi\) | ||||
0.768115 | + | 0.640312i | \(0.221195\pi\) | |||||||
\(338\) | 2.21444e21 | 0.707087 | ||||||||
\(339\) | −3.81210e21 | −1.18704 | ||||||||
\(340\) | −5.77284e20 | −0.175315 | ||||||||
\(341\) | −1.50649e21 | −0.446224 | ||||||||
\(342\) | 1.39035e21 | 0.401700 | ||||||||
\(343\) | −3.80526e21 | −1.07247 | ||||||||
\(344\) | 7.73055e20 | 0.212551 | ||||||||
\(345\) | −9.43246e20 | −0.253025 | ||||||||
\(346\) | −4.21106e21 | −1.10216 | ||||||||
\(347\) | 2.51637e21 | 0.642648 | 0.321324 | − | 0.946969i | \(-0.395872\pi\) | ||||
0.321324 | + | 0.946969i | \(0.395872\pi\) | |||||||
\(348\) | 1.57413e21 | 0.392300 | ||||||||
\(349\) | −2.20222e21 | −0.535606 | −0.267803 | − | 0.963474i | \(-0.586298\pi\) | ||||
−0.267803 | + | 0.963474i | \(0.586298\pi\) | |||||||
\(350\) | 9.71310e20 | 0.230558 | ||||||||
\(351\) | −2.51431e19 | −0.00582516 | ||||||||
\(352\) | 2.09339e20 | 0.0473410 | ||||||||
\(353\) | 1.30214e21 | 0.287456 | 0.143728 | − | 0.989617i | \(-0.454091\pi\) | ||||
0.143728 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(354\) | 4.35299e21 | 0.938123 | ||||||||
\(355\) | −1.51304e21 | −0.318353 | ||||||||
\(356\) | 3.61737e21 | 0.743135 | ||||||||
\(357\) | −5.22118e21 | −1.04734 | ||||||||
\(358\) | 3.91851e20 | 0.0767566 | ||||||||
\(359\) | 2.07162e21 | 0.396285 | 0.198143 | − | 0.980173i | \(-0.436509\pi\) | ||||
0.198143 | + | 0.980173i | \(0.436509\pi\) | |||||||
\(360\) | 2.78105e20 | 0.0519563 | ||||||||
\(361\) | 1.08994e22 | 1.98880 | ||||||||
\(362\) | 2.17970e21 | 0.388484 | ||||||||
\(363\) | 4.36895e21 | 0.760625 | ||||||||
\(364\) | 2.56460e19 | 0.00436172 | ||||||||
\(365\) | −1.11635e21 | −0.185486 | ||||||||
\(366\) | −3.53358e21 | −0.573622 | ||||||||
\(367\) | 4.69137e21 | 0.744111 | 0.372056 | − | 0.928210i | \(-0.378653\pi\) | ||||
0.372056 | + | 0.928210i | \(0.378653\pi\) | |||||||
\(368\) | 1.11379e21 | 0.172622 | ||||||||
\(369\) | −8.40743e20 | −0.127332 | ||||||||
\(370\) | 2.09888e21 | 0.310652 | ||||||||
\(371\) | −9.94732e21 | −1.43889 | ||||||||
\(372\) | −4.82855e21 | −0.682655 | ||||||||
\(373\) | −7.77652e20 | −0.107463 | −0.0537317 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537317 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(374\) | −1.09911e21 | −0.148467 | ||||||||
\(375\) | −5.55011e20 | −0.0732885 | ||||||||
\(376\) | −4.47661e21 | −0.577900 | ||||||||
\(377\) | 4.05959e19 | 0.00512367 | ||||||||
\(378\) | 1.01699e22 | 1.25497 | ||||||||
\(379\) | 3.50054e20 | 0.0422379 | 0.0211189 | − | 0.999777i | \(-0.493277\pi\) | ||||
0.0211189 | + | 0.999777i | \(0.493277\pi\) | |||||||
\(380\) | 3.27638e21 | 0.386575 | ||||||||
\(381\) | 5.98183e21 | 0.690194 | ||||||||
\(382\) | −2.71157e21 | −0.305972 | ||||||||
\(383\) | −1.02315e22 | −1.12914 | −0.564570 | − | 0.825385i | \(-0.690958\pi\) | ||||
−0.564570 | + | 0.825385i | \(0.690958\pi\) | |||||||
\(384\) | 6.70967e20 | 0.0724245 | ||||||||
\(385\) | 1.84930e21 | 0.195250 | ||||||||
\(386\) | 3.98765e21 | 0.411837 | ||||||||
\(387\) | 1.95533e21 | 0.197550 | ||||||||
\(388\) | 4.21175e21 | 0.416287 | ||||||||
\(389\) | −4.13104e21 | −0.399473 | −0.199737 | − | 0.979850i | \(-0.564009\pi\) | ||||
−0.199737 | + | 0.979850i | \(0.564009\pi\) | |||||||
\(390\) | −1.46542e19 | −0.00138648 | ||||||||
\(391\) | −5.84781e21 | −0.541366 | ||||||||
\(392\) | −6.47037e21 | −0.586135 | ||||||||
\(393\) | −3.32723e21 | −0.294948 | ||||||||
\(394\) | −2.16914e21 | −0.188178 | ||||||||
\(395\) | 1.09761e21 | 0.0931907 | ||||||||
\(396\) | 5.29491e20 | 0.0439997 | ||||||||
\(397\) | −7.65334e21 | −0.622489 | −0.311244 | − | 0.950330i | \(-0.600746\pi\) | ||||
−0.311244 | + | 0.950330i | \(0.600746\pi\) | |||||||
\(398\) | −2.42852e21 | −0.193346 | ||||||||
\(399\) | 2.96328e22 | 2.30942 | ||||||||
\(400\) | 6.55360e20 | 0.0500000 | ||||||||
\(401\) | −4.08273e20 | −0.0304947 | −0.0152473 | − | 0.999884i | \(-0.504854\pi\) | ||||
−0.0152473 | + | 0.999884i | \(0.504854\pi\) | |||||||
\(402\) | −6.46974e21 | −0.473113 | ||||||||
\(403\) | −1.24525e20 | −0.00891588 | ||||||||
\(404\) | −1.02502e22 | −0.718603 | ||||||||
\(405\) | −3.67042e21 | −0.251970 | ||||||||
\(406\) | −1.64202e22 | −1.10384 | ||||||||
\(407\) | 3.99612e21 | 0.263079 | ||||||||
\(408\) | −3.52282e21 | −0.227133 | ||||||||
\(409\) | 2.00923e22 | 1.26877 | 0.634383 | − | 0.773019i | \(-0.281254\pi\) | ||||
0.634383 | + | 0.773019i | \(0.281254\pi\) | |||||||
\(410\) | −1.98123e21 | −0.122538 | ||||||||
\(411\) | 1.15297e22 | 0.698493 | ||||||||
\(412\) | −1.52808e22 | −0.906816 | ||||||||
\(413\) | −4.54071e22 | −2.63966 | ||||||||
\(414\) | 2.81717e21 | 0.160439 | ||||||||
\(415\) | −2.75090e21 | −0.153485 | ||||||||
\(416\) | 1.73038e19 | 0.000945906 0 | ||||||||
\(417\) | −1.81695e22 | −0.973167 | ||||||||
\(418\) | 6.23798e21 | 0.327375 | ||||||||
\(419\) | 3.31114e22 | 1.70278 | 0.851390 | − | 0.524533i | \(-0.175760\pi\) | ||||
0.851390 | + | 0.524533i | \(0.175760\pi\) | |||||||
\(420\) | 5.92733e21 | 0.298703 | ||||||||
\(421\) | −2.31325e22 | −1.14242 | −0.571208 | − | 0.820805i | \(-0.693525\pi\) | ||||
−0.571208 | + | 0.820805i | \(0.693525\pi\) | |||||||
\(422\) | 1.29562e22 | 0.627079 | ||||||||
\(423\) | −1.13229e22 | −0.537113 | ||||||||
\(424\) | −6.71163e21 | −0.312046 | ||||||||
\(425\) | −3.44088e21 | −0.156806 | ||||||||
\(426\) | −9.23317e21 | −0.412448 | ||||||||
\(427\) | 3.68597e22 | 1.61404 | ||||||||
\(428\) | −6.90732e21 | −0.296509 | ||||||||
\(429\) | −2.79005e19 | −0.00117416 | ||||||||
\(430\) | 4.60777e21 | 0.190112 | ||||||||
\(431\) | 4.44596e22 | 1.79849 | 0.899247 | − | 0.437440i | \(-0.144115\pi\) | ||||
0.899247 | + | 0.437440i | \(0.144115\pi\) | |||||||
\(432\) | 6.86178e21 | 0.272160 | ||||||||
\(433\) | 2.85304e22 | 1.10959 | 0.554793 | − | 0.831989i | \(-0.312798\pi\) | ||||
0.554793 | + | 0.831989i | \(0.312798\pi\) | |||||||
\(434\) | 5.03678e22 | 1.92084 | ||||||||
\(435\) | 9.38257e21 | 0.350884 | ||||||||
\(436\) | 1.65082e22 | 0.605431 | ||||||||
\(437\) | 3.31893e22 | 1.19373 | ||||||||
\(438\) | −6.81242e21 | −0.240310 | ||||||||
\(439\) | −4.28578e22 | −1.48279 | −0.741397 | − | 0.671066i | \(-0.765837\pi\) | ||||
−0.741397 | + | 0.671066i | \(0.765837\pi\) | |||||||
\(440\) | 1.24776e21 | 0.0423430 | ||||||||
\(441\) | −1.63658e22 | −0.544767 | ||||||||
\(442\) | −9.08513e19 | −0.00296648 | ||||||||
\(443\) | −1.40464e22 | −0.449919 | −0.224959 | − | 0.974368i | \(-0.572225\pi\) | ||||
−0.224959 | + | 0.974368i | \(0.572225\pi\) | |||||||
\(444\) | 1.28082e22 | 0.402471 | ||||||||
\(445\) | 2.15612e22 | 0.664680 | ||||||||
\(446\) | −2.89323e22 | −0.875057 | ||||||||
\(447\) | −1.73933e22 | −0.516140 | ||||||||
\(448\) | −6.99902e21 | −0.203786 | ||||||||
\(449\) | −3.88401e22 | −1.10965 | −0.554826 | − | 0.831966i | \(-0.687215\pi\) | ||||
−0.554826 | + | 0.831966i | \(0.687215\pi\) | |||||||
\(450\) | 1.65764e21 | 0.0464711 | ||||||||
\(451\) | −3.77210e21 | −0.103773 | ||||||||
\(452\) | 2.68301e22 | 0.724346 | ||||||||
\(453\) | −4.83161e22 | −1.28014 | ||||||||
\(454\) | −3.43186e22 | −0.892391 | ||||||||
\(455\) | 1.52862e20 | 0.00390124 | ||||||||
\(456\) | 1.99938e22 | 0.500835 | ||||||||
\(457\) | −2.21160e22 | −0.543774 | −0.271887 | − | 0.962329i | \(-0.587648\pi\) | ||||
−0.271887 | + | 0.962329i | \(0.587648\pi\) | |||||||
\(458\) | 3.91917e22 | 0.945883 | ||||||||
\(459\) | −3.60269e22 | −0.853530 | ||||||||
\(460\) | 6.63871e21 | 0.154398 | ||||||||
\(461\) | 1.69257e22 | 0.386446 | 0.193223 | − | 0.981155i | \(-0.438106\pi\) | ||||
0.193223 | + | 0.981155i | \(0.438106\pi\) | |||||||
\(462\) | 1.12852e22 | 0.252960 | ||||||||
\(463\) | 5.00810e22 | 1.10213 | 0.551067 | − | 0.834461i | \(-0.314221\pi\) | ||||
0.551067 | + | 0.834461i | \(0.314221\pi\) | |||||||
\(464\) | −1.10790e22 | −0.239385 | ||||||||
\(465\) | −2.87804e22 | −0.610585 | ||||||||
\(466\) | −3.94483e22 | −0.821765 | ||||||||
\(467\) | −6.87611e22 | −1.40653 | −0.703266 | − | 0.710927i | \(-0.748276\pi\) | ||||
−0.703266 | + | 0.710927i | \(0.748276\pi\) | |||||||
\(468\) | 4.37674e19 | 0.000879146 0 | ||||||||
\(469\) | 6.74875e22 | 1.33123 | ||||||||
\(470\) | −2.66827e22 | −0.516889 | ||||||||
\(471\) | −7.25357e22 | −1.37998 | ||||||||
\(472\) | −3.06370e22 | −0.572452 | ||||||||
\(473\) | 8.77284e21 | 0.160998 | ||||||||
\(474\) | 6.69806e21 | 0.120735 | ||||||||
\(475\) | 1.95287e22 | 0.345763 | ||||||||
\(476\) | 3.67475e22 | 0.639099 | ||||||||
\(477\) | −1.69761e22 | −0.290022 | ||||||||
\(478\) | −2.83201e22 | −0.475290 | ||||||||
\(479\) | −3.44291e22 | −0.567641 | −0.283821 | − | 0.958877i | \(-0.591602\pi\) | ||||
−0.283821 | + | 0.958877i | \(0.591602\pi\) | |||||||
\(480\) | 3.99927e21 | 0.0647785 | ||||||||
\(481\) | 3.30316e20 | 0.00525650 | ||||||||
\(482\) | 4.31590e22 | 0.674794 | ||||||||
\(483\) | 6.00431e22 | 0.922385 | ||||||||
\(484\) | −3.07493e22 | −0.464141 | ||||||||
\(485\) | 2.51040e22 | 0.372338 | ||||||||
\(486\) | 3.04191e22 | 0.443342 | ||||||||
\(487\) | 8.83844e20 | 0.0126584 | 0.00632921 | − | 0.999980i | \(-0.497985\pi\) | ||||
0.00632921 | + | 0.999980i | \(0.497985\pi\) | |||||||
\(488\) | 2.48699e22 | 0.350030 | ||||||||
\(489\) | −5.74420e22 | −0.794519 | ||||||||
\(490\) | −3.85664e22 | −0.524255 | ||||||||
\(491\) | 1.04515e23 | 1.39632 | 0.698158 | − | 0.715943i | \(-0.254003\pi\) | ||||
0.698158 | + | 0.715943i | \(0.254003\pi\) | |||||||
\(492\) | −1.20902e22 | −0.158757 | ||||||||
\(493\) | 5.81688e22 | 0.750744 | ||||||||
\(494\) | 5.15627e20 | 0.00654119 | ||||||||
\(495\) | 3.15602e21 | 0.0393545 | ||||||||
\(496\) | 3.39841e22 | 0.416563 | ||||||||
\(497\) | 9.63135e22 | 1.16053 | ||||||||
\(498\) | −1.67871e22 | −0.198850 | ||||||||
\(499\) | −5.12067e22 | −0.596310 | −0.298155 | − | 0.954518i | \(-0.596371\pi\) | ||||
−0.298155 | + | 0.954518i | \(0.596371\pi\) | |||||||
\(500\) | 3.90625e21 | 0.0447214 | ||||||||
\(501\) | −1.16139e23 | −1.30724 | ||||||||
\(502\) | 2.23151e22 | 0.246955 | ||||||||
\(503\) | 5.06660e22 | 0.551301 | 0.275650 | − | 0.961258i | \(-0.411107\pi\) | ||||
0.275650 | + | 0.961258i | \(0.411107\pi\) | |||||||
\(504\) | −1.77030e22 | −0.189403 | ||||||||
\(505\) | −6.10957e22 | −0.642738 | ||||||||
\(506\) | 1.26396e22 | 0.130754 | ||||||||
\(507\) | 8.05463e22 | 0.819366 | ||||||||
\(508\) | −4.21010e22 | −0.421164 | ||||||||
\(509\) | 1.68111e23 | 1.65385 | 0.826923 | − | 0.562316i | \(-0.190089\pi\) | ||||
0.826923 | + | 0.562316i | \(0.190089\pi\) | |||||||
\(510\) | −2.09977e22 | −0.203154 | ||||||||
\(511\) | 7.10621e22 | 0.676177 | ||||||||
\(512\) | −4.72237e21 | −0.0441942 | ||||||||
\(513\) | 2.04471e23 | 1.88206 | ||||||||
\(514\) | −6.60452e22 | −0.597936 | ||||||||
\(515\) | −9.10805e22 | −0.811081 | ||||||||
\(516\) | 2.81185e22 | 0.246303 | ||||||||
\(517\) | −5.08018e22 | −0.437733 | ||||||||
\(518\) | −1.33606e23 | −1.13246 | ||||||||
\(519\) | −1.53170e23 | −1.27717 | ||||||||
\(520\) | 1.03139e20 | 0.000846044 0 | ||||||||
\(521\) | 1.13516e23 | 0.916085 | 0.458042 | − | 0.888930i | \(-0.348551\pi\) | ||||
0.458042 | + | 0.888930i | \(0.348551\pi\) | |||||||
\(522\) | −2.80227e22 | −0.222490 | ||||||||
\(523\) | 3.13139e22 | 0.244609 | 0.122305 | − | 0.992493i | \(-0.460972\pi\) | ||||
0.122305 | + | 0.992493i | \(0.460972\pi\) | |||||||
\(524\) | 2.34175e22 | 0.179980 | ||||||||
\(525\) | 3.53296e22 | 0.267168 | ||||||||
\(526\) | 1.05686e23 | 0.786394 | ||||||||
\(527\) | −1.78429e23 | −1.30640 | ||||||||
\(528\) | 7.61432e21 | 0.0548583 | ||||||||
\(529\) | −7.38008e22 | −0.523224 | ||||||||
\(530\) | −4.00045e22 | −0.279102 | ||||||||
\(531\) | −7.74918e22 | −0.532050 | ||||||||
\(532\) | −2.08560e23 | −1.40923 | ||||||||
\(533\) | −3.11800e20 | −0.00207345 | ||||||||
\(534\) | 1.31575e23 | 0.861139 | ||||||||
\(535\) | −4.11708e22 | −0.265205 | ||||||||
\(536\) | 4.55350e22 | 0.288699 | ||||||||
\(537\) | 1.42529e22 | 0.0889449 | ||||||||
\(538\) | −9.25753e22 | −0.568651 | ||||||||
\(539\) | −7.34275e22 | −0.443971 | ||||||||
\(540\) | 4.08994e22 | 0.243428 | ||||||||
\(541\) | −1.32903e23 | −0.778680 | −0.389340 | − | 0.921094i | \(-0.627297\pi\) | ||||
−0.389340 | + | 0.921094i | \(0.627297\pi\) | |||||||
\(542\) | 1.69391e23 | 0.977006 | ||||||||
\(543\) | 7.92825e22 | 0.450172 | ||||||||
\(544\) | 2.47942e22 | 0.138599 | ||||||||
\(545\) | 9.83965e22 | 0.541514 | ||||||||
\(546\) | 9.32826e20 | 0.00505432 | ||||||||
\(547\) | 3.86923e22 | 0.206411 | 0.103205 | − | 0.994660i | \(-0.467090\pi\) | ||||
0.103205 | + | 0.994660i | \(0.467090\pi\) | |||||||
\(548\) | −8.11477e22 | −0.426227 | ||||||||
\(549\) | 6.29047e22 | 0.325326 | ||||||||
\(550\) | 7.43721e21 | 0.0378728 | ||||||||
\(551\) | −3.30138e23 | −1.65541 | ||||||||
\(552\) | 4.05121e22 | 0.200034 | ||||||||
\(553\) | −6.98692e22 | −0.339721 | ||||||||
\(554\) | −6.23872e22 | −0.298719 | ||||||||
\(555\) | 7.63431e22 | 0.359981 | ||||||||
\(556\) | 1.27880e23 | 0.593836 | ||||||||
\(557\) | −1.53384e23 | −0.701475 | −0.350737 | − | 0.936474i | \(-0.614069\pi\) | ||||
−0.350737 | + | 0.936474i | \(0.614069\pi\) | |||||||
\(558\) | 8.59576e22 | 0.387163 | ||||||||
\(559\) | 7.25157e20 | 0.00321686 | ||||||||
\(560\) | −4.17174e22 | −0.182272 | ||||||||
\(561\) | −3.99780e22 | −0.172043 | ||||||||
\(562\) | 2.42445e23 | 1.02767 | ||||||||
\(563\) | −1.19252e23 | −0.497904 | −0.248952 | − | 0.968516i | \(-0.580086\pi\) | ||||
−0.248952 | + | 0.968516i | \(0.580086\pi\) | |||||||
\(564\) | −1.62829e23 | −0.669666 | ||||||||
\(565\) | 1.59920e23 | 0.647875 | ||||||||
\(566\) | 9.40810e22 | 0.375459 | ||||||||
\(567\) | 2.33644e23 | 0.918540 | ||||||||
\(568\) | 6.49844e22 | 0.251680 | ||||||||
\(569\) | −1.07363e23 | −0.409638 | −0.204819 | − | 0.978800i | \(-0.565661\pi\) | ||||
−0.204819 | + | 0.978800i | \(0.565661\pi\) | |||||||
\(570\) | 1.19172e23 | 0.447960 | ||||||||
\(571\) | −2.25644e23 | −0.835634 | −0.417817 | − | 0.908531i | \(-0.637205\pi\) | ||||
−0.417817 | + | 0.908531i | \(0.637205\pi\) | |||||||
\(572\) | 1.96368e20 | 0.000716482 0 | ||||||||
\(573\) | −9.86284e22 | −0.354558 | ||||||||
\(574\) | 1.26116e23 | 0.446705 | ||||||||
\(575\) | 3.95698e22 | 0.138098 | ||||||||
\(576\) | −1.19445e22 | −0.0410750 | ||||||||
\(577\) | −1.29594e23 | −0.439127 | −0.219563 | − | 0.975598i | \(-0.570463\pi\) | ||||
−0.219563 | + | 0.975598i | \(0.570463\pi\) | |||||||
\(578\) | 8.15949e22 | 0.272444 | ||||||||
\(579\) | 1.45044e23 | 0.477233 | ||||||||
\(580\) | −6.60360e22 | −0.214113 | ||||||||
\(581\) | 1.75111e23 | 0.559519 | ||||||||
\(582\) | 1.53195e23 | 0.482390 | ||||||||
\(583\) | −7.61655e22 | −0.236361 | ||||||||
\(584\) | 4.79469e22 | 0.146640 | ||||||||
\(585\) | 2.60874e20 | 0.000786332 0 | ||||||||
\(586\) | −3.09514e23 | −0.919498 | ||||||||
\(587\) | 3.21537e23 | 0.941471 | 0.470735 | − | 0.882274i | \(-0.343989\pi\) | ||||
0.470735 | + | 0.882274i | \(0.343989\pi\) | |||||||
\(588\) | −2.35348e23 | −0.679208 | ||||||||
\(589\) | 1.01267e24 | 2.88064 | ||||||||
\(590\) | −1.82611e23 | −0.512017 | ||||||||
\(591\) | −7.88985e22 | −0.218060 | ||||||||
\(592\) | −9.01464e22 | −0.245592 | ||||||||
\(593\) | −8.23836e22 | −0.221246 | −0.110623 | − | 0.993862i | \(-0.535285\pi\) | ||||
−0.110623 | + | 0.993862i | \(0.535285\pi\) | |||||||
\(594\) | 7.78694e22 | 0.206149 | ||||||||
\(595\) | 2.19032e23 | 0.571628 | ||||||||
\(596\) | 1.22417e23 | 0.314954 | ||||||||
\(597\) | −8.83330e22 | −0.224048 | ||||||||
\(598\) | 1.04478e21 | 0.00261255 | ||||||||
\(599\) | −7.29015e22 | −0.179725 | −0.0898625 | − | 0.995954i | \(-0.528643\pi\) | ||||
−0.0898625 | + | 0.995954i | \(0.528643\pi\) | |||||||
\(600\) | 2.38375e22 | 0.0579396 | ||||||||
\(601\) | 3.79880e23 | 0.910361 | 0.455180 | − | 0.890399i | \(-0.349575\pi\) | ||||
0.455180 | + | 0.890399i | \(0.349575\pi\) | |||||||
\(602\) | −2.93311e23 | −0.693040 | ||||||||
\(603\) | 1.15174e23 | 0.268323 | ||||||||
\(604\) | 3.40056e23 | 0.781154 | ||||||||
\(605\) | −1.83280e23 | −0.415141 | ||||||||
\(606\) | −3.72831e23 | −0.832711 | ||||||||
\(607\) | −3.76245e23 | −0.828641 | −0.414321 | − | 0.910131i | \(-0.635981\pi\) | ||||
−0.414321 | + | 0.910131i | \(0.635981\pi\) | |||||||
\(608\) | −1.40719e23 | −0.305614 | ||||||||
\(609\) | −5.97255e23 | −1.27912 | ||||||||
\(610\) | 1.48236e23 | 0.313076 | ||||||||
\(611\) | −4.19924e21 | −0.00874623 | ||||||||
\(612\) | 6.27132e22 | 0.128817 | ||||||||
\(613\) | −4.60370e23 | −0.932595 | −0.466298 | − | 0.884628i | \(-0.654412\pi\) | ||||
−0.466298 | + | 0.884628i | \(0.654412\pi\) | |||||||
\(614\) | 1.22094e23 | 0.243930 | ||||||||
\(615\) | −7.20635e22 | −0.141996 | ||||||||
\(616\) | −7.94269e22 | −0.154359 | ||||||||
\(617\) | −3.36863e23 | −0.645698 | −0.322849 | − | 0.946451i | \(-0.604641\pi\) | ||||
−0.322849 | + | 0.946451i | \(0.604641\pi\) | |||||||
\(618\) | −5.55811e23 | −1.05081 | ||||||||
\(619\) | 1.49640e23 | 0.279047 | 0.139523 | − | 0.990219i | \(-0.455443\pi\) | ||||
0.139523 | + | 0.990219i | \(0.455443\pi\) | |||||||
\(620\) | 2.02561e23 | 0.372585 | ||||||||
\(621\) | 4.14306e23 | 0.751696 | ||||||||
\(622\) | −8.97070e22 | −0.160549 | ||||||||
\(623\) | −1.37249e24 | −2.42305 | ||||||||
\(624\) | 6.29394e20 | 0.00109611 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | −5.24161e23 | −0.888348 | ||||||||
\(627\) | 2.26895e23 | 0.379360 | ||||||||
\(628\) | 5.10517e23 | 0.842080 | ||||||||
\(629\) | 4.73302e23 | 0.770208 | ||||||||
\(630\) | −1.05518e23 | −0.169407 | ||||||||
\(631\) | −6.17252e21 | −0.00977717 | −0.00488858 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488858 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(632\) | −4.71420e22 | −0.0736737 | ||||||||
\(633\) | 4.71259e23 | 0.726654 | ||||||||
\(634\) | −3.37058e23 | −0.512797 | ||||||||
\(635\) | −2.50942e23 | −0.376700 | ||||||||
\(636\) | −2.44124e23 | −0.361596 | ||||||||
\(637\) | −6.06947e21 | −0.00887086 | ||||||||
\(638\) | −1.25728e23 | −0.181324 | ||||||||
\(639\) | 1.64369e23 | 0.233917 | ||||||||
\(640\) | −2.81475e22 | −0.0395285 | ||||||||
\(641\) | −1.59514e23 | −0.221057 | −0.110529 | − | 0.993873i | \(-0.535254\pi\) | ||||
−0.110529 | + | 0.993873i | \(0.535254\pi\) | |||||||
\(642\) | −2.51241e23 | −0.343592 | ||||||||
\(643\) | 1.37854e24 | 1.86049 | 0.930244 | − | 0.366941i | \(-0.119595\pi\) | ||||
0.930244 | + | 0.366941i | \(0.119595\pi\) | |||||||
\(644\) | −4.22592e23 | −0.562849 | ||||||||
\(645\) | 1.67599e23 | 0.220300 | ||||||||
\(646\) | 7.38829e23 | 0.958446 | ||||||||
\(647\) | 3.15056e23 | 0.403369 | 0.201684 | − | 0.979451i | \(-0.435359\pi\) | ||||
0.201684 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(648\) | 1.57643e23 | 0.199200 | ||||||||
\(649\) | −3.47677e23 | −0.433607 | ||||||||
\(650\) | 6.14754e20 | 0.000756725 0 | ||||||||
\(651\) | 1.83204e24 | 2.22585 | ||||||||
\(652\) | 4.04286e23 | 0.484824 | ||||||||
\(653\) | −2.27963e23 | −0.269838 | −0.134919 | − | 0.990857i | \(-0.543077\pi\) | ||||
−0.134919 | + | 0.990857i | \(0.543077\pi\) | |||||||
\(654\) | 6.00455e23 | 0.701568 | ||||||||
\(655\) | 1.39579e23 | 0.160979 | ||||||||
\(656\) | 8.50930e22 | 0.0968749 | ||||||||
\(657\) | 1.21275e23 | 0.136290 | ||||||||
\(658\) | 1.69851e24 | 1.88429 | ||||||||
\(659\) | 1.18670e24 | 1.29961 | 0.649806 | − | 0.760100i | \(-0.274850\pi\) | ||||
0.649806 | + | 0.760100i | \(0.274850\pi\) | |||||||
\(660\) | 4.53849e22 | 0.0490668 | ||||||||
\(661\) | −1.50237e24 | −1.60348 | −0.801741 | − | 0.597672i | \(-0.796092\pi\) | ||||
−0.801741 | + | 0.597672i | \(0.796092\pi\) | |||||||
\(662\) | −9.87806e23 | −1.04083 | ||||||||
\(663\) | −3.30455e21 | −0.00343754 | ||||||||
\(664\) | 1.18150e23 | 0.121340 | ||||||||
\(665\) | −1.24312e24 | −1.26046 | ||||||||
\(666\) | −2.28012e23 | −0.228258 | ||||||||
\(667\) | −6.68936e23 | −0.661173 | ||||||||
\(668\) | 8.17402e23 | 0.797693 | ||||||||
\(669\) | −1.05236e24 | −1.01401 | ||||||||
\(670\) | 2.71410e23 | 0.258220 | ||||||||
\(671\) | 2.82230e23 | 0.265132 | ||||||||
\(672\) | −2.54577e23 | −0.236146 | ||||||||
\(673\) | 2.53432e23 | 0.232131 | 0.116065 | − | 0.993242i | \(-0.462972\pi\) | ||||
0.116065 | + | 0.993242i | \(0.462972\pi\) | |||||||
\(674\) | −1.20102e24 | −1.08628 | ||||||||
\(675\) | 2.43779e23 | 0.217728 | ||||||||
\(676\) | −5.66897e23 | −0.499986 | ||||||||
\(677\) | 4.60323e23 | 0.400921 | 0.200460 | − | 0.979702i | \(-0.435756\pi\) | ||||
0.200460 | + | 0.979702i | \(0.435756\pi\) | |||||||
\(678\) | 9.75897e23 | 0.839367 | ||||||||
\(679\) | −1.59801e24 | −1.35734 | ||||||||
\(680\) | 1.47785e23 | 0.123966 | ||||||||
\(681\) | −1.24828e24 | −1.03410 | ||||||||
\(682\) | 3.85660e23 | 0.315528 | ||||||||
\(683\) | −6.27345e23 | −0.506910 | −0.253455 | − | 0.967347i | \(-0.581567\pi\) | ||||
−0.253455 | + | 0.967347i | \(0.581567\pi\) | |||||||
\(684\) | −3.55929e23 | −0.284045 | ||||||||
\(685\) | −4.83678e23 | −0.381229 | ||||||||
\(686\) | 9.74147e23 | 0.758349 | ||||||||
\(687\) | 1.42553e24 | 1.09608 | ||||||||
\(688\) | −1.97902e23 | −0.150296 | ||||||||
\(689\) | −6.29579e21 | −0.00472266 | ||||||||
\(690\) | 2.41471e23 | 0.178915 | ||||||||
\(691\) | 4.11645e23 | 0.301272 | 0.150636 | − | 0.988589i | \(-0.451868\pi\) | ||||
0.150636 | + | 0.988589i | \(0.451868\pi\) | |||||||
\(692\) | 1.07803e24 | 0.779344 | ||||||||
\(693\) | −2.00899e23 | −0.143464 | ||||||||
\(694\) | −6.44190e23 | −0.454421 | ||||||||
\(695\) | 7.62224e23 | 0.531144 | ||||||||
\(696\) | −4.02978e23 | −0.277398 | ||||||||
\(697\) | −4.46770e23 | −0.303812 | ||||||||
\(698\) | 5.63770e23 | 0.378731 | ||||||||
\(699\) | −1.43486e24 | −0.952255 | ||||||||
\(700\) | −2.48655e23 | −0.163029 | ||||||||
\(701\) | 2.88292e23 | 0.186737 | 0.0933683 | − | 0.995632i | \(-0.470237\pi\) | ||||
0.0933683 | + | 0.995632i | \(0.470237\pi\) | |||||||
\(702\) | 6.43663e21 | 0.00411901 | ||||||||
\(703\) | −2.68623e24 | −1.69833 | ||||||||
\(704\) | −5.35907e22 | −0.0334751 | ||||||||
\(705\) | −9.70534e23 | −0.598967 | ||||||||
\(706\) | −3.33347e23 | −0.203262 | ||||||||
\(707\) | 3.88909e24 | 2.34306 | ||||||||
\(708\) | −1.11436e24 | −0.663353 | ||||||||
\(709\) | −2.85869e24 | −1.68141 | −0.840707 | − | 0.541491i | \(-0.817860\pi\) | ||||
−0.840707 | + | 0.541491i | \(0.817860\pi\) | |||||||
\(710\) | 3.87337e23 | 0.225109 | ||||||||
\(711\) | −1.19239e23 | −0.0684740 | ||||||||
\(712\) | −9.26046e23 | −0.525475 | ||||||||
\(713\) | 2.05191e24 | 1.15053 | ||||||||
\(714\) | 1.33662e24 | 0.740583 | ||||||||
\(715\) | 1.17045e21 | 0.000640841 0 | ||||||||
\(716\) | −1.00314e23 | −0.0542751 | ||||||||
\(717\) | −1.03009e24 | −0.550762 | ||||||||
\(718\) | −5.30336e23 | −0.280216 | ||||||||
\(719\) | −1.21983e24 | −0.636946 | −0.318473 | − | 0.947932i | \(-0.603170\pi\) | ||||
−0.318473 | + | 0.947932i | \(0.603170\pi\) | |||||||
\(720\) | −7.11949e22 | −0.0367386 | ||||||||
\(721\) | 5.79780e24 | 2.95674 | ||||||||
\(722\) | −2.79025e24 | −1.40630 | ||||||||
\(723\) | 1.56983e24 | 0.781947 | ||||||||
\(724\) | −5.58002e23 | −0.274700 | ||||||||
\(725\) | −3.93605e23 | −0.191508 | ||||||||
\(726\) | −1.11845e24 | −0.537843 | ||||||||
\(727\) | −2.28060e24 | −1.08394 | −0.541972 | − | 0.840396i | \(-0.682322\pi\) | ||||
−0.541972 | + | 0.840396i | \(0.682322\pi\) | |||||||
\(728\) | −6.56537e21 | −0.00308420 | ||||||||
\(729\) | 2.31988e24 | 1.07716 | ||||||||
\(730\) | 2.85786e23 | 0.131158 | ||||||||
\(731\) | 1.03906e24 | 0.471349 | ||||||||
\(732\) | 9.04597e23 | 0.405612 | ||||||||
\(733\) | −8.50533e23 | −0.376970 | −0.188485 | − | 0.982076i | \(-0.560358\pi\) | ||||
−0.188485 | + | 0.982076i | \(0.560358\pi\) | |||||||
\(734\) | −1.20099e24 | −0.526166 | ||||||||
\(735\) | −1.40278e24 | −0.607503 | ||||||||
\(736\) | −2.85130e23 | −0.122062 | ||||||||
\(737\) | 5.16744e23 | 0.218676 | ||||||||
\(738\) | 2.15230e23 | 0.0900376 | ||||||||
\(739\) | 2.14385e24 | 0.886578 | 0.443289 | − | 0.896379i | \(-0.353812\pi\) | ||||
0.443289 | + | 0.896379i | \(0.353812\pi\) | |||||||
\(740\) | −5.37314e23 | −0.219664 | ||||||||
\(741\) | 1.87550e22 | 0.00757988 | ||||||||
\(742\) | 2.54651e24 | 1.01745 | ||||||||
\(743\) | 2.23446e24 | 0.882606 | 0.441303 | − | 0.897358i | \(-0.354516\pi\) | ||||
0.441303 | + | 0.897358i | \(0.354516\pi\) | |||||||
\(744\) | 1.23611e24 | 0.482710 | ||||||||
\(745\) | 7.29660e23 | 0.281703 | ||||||||
\(746\) | 1.99079e23 | 0.0759880 | ||||||||
\(747\) | 2.98843e23 | 0.112777 | ||||||||
\(748\) | 2.81371e23 | 0.104982 | ||||||||
\(749\) | 2.62076e24 | 0.966789 | ||||||||
\(750\) | 1.42083e23 | 0.0518228 | ||||||||
\(751\) | −1.71798e24 | −0.619555 | −0.309778 | − | 0.950809i | \(-0.600255\pi\) | ||||
−0.309778 | + | 0.950809i | \(0.600255\pi\) | |||||||
\(752\) | 1.14601e24 | 0.408637 | ||||||||
\(753\) | 8.11671e23 | 0.286169 | ||||||||
\(754\) | −1.03926e22 | −0.00362298 | ||||||||
\(755\) | 2.02689e24 | 0.698685 | ||||||||
\(756\) | −2.60348e24 | −0.887400 | ||||||||
\(757\) | −1.09729e24 | −0.369832 | −0.184916 | − | 0.982754i | \(-0.559201\pi\) | ||||
−0.184916 | + | 0.982754i | \(0.559201\pi\) | |||||||
\(758\) | −8.96138e22 | −0.0298667 | ||||||||
\(759\) | 4.59743e23 | 0.151516 | ||||||||
\(760\) | −8.38753e23 | −0.273350 | ||||||||
\(761\) | −1.70967e24 | −0.550990 | −0.275495 | − | 0.961302i | \(-0.588842\pi\) | ||||
−0.275495 | + | 0.961302i | \(0.588842\pi\) | |||||||
\(762\) | −1.53135e24 | −0.488041 | ||||||||
\(763\) | −6.26350e24 | −1.97405 | ||||||||
\(764\) | 6.94162e23 | 0.216355 | ||||||||
\(765\) | 3.73800e23 | 0.115217 | ||||||||
\(766\) | 2.61925e24 | 0.798423 | ||||||||
\(767\) | −2.87388e22 | −0.00866378 | ||||||||
\(768\) | −1.71767e23 | −0.0512119 | ||||||||
\(769\) | 1.22119e24 | 0.360090 | 0.180045 | − | 0.983658i | \(-0.442376\pi\) | ||||
0.180045 | + | 0.983658i | \(0.442376\pi\) | |||||||
\(770\) | −4.73421e23 | −0.138063 | ||||||||
\(771\) | −2.40228e24 | −0.692884 | ||||||||
\(772\) | −1.02084e24 | −0.291213 | ||||||||
\(773\) | 2.59069e24 | 0.730952 | 0.365476 | − | 0.930821i | \(-0.380906\pi\) | ||||
0.365476 | + | 0.930821i | \(0.380906\pi\) | |||||||
\(774\) | −5.00564e23 | −0.139689 | ||||||||
\(775\) | 1.20736e24 | 0.333251 | ||||||||
\(776\) | −1.07821e24 | −0.294359 | ||||||||
\(777\) | −4.85968e24 | −1.31229 | ||||||||
\(778\) | 1.05755e24 | 0.282470 | ||||||||
\(779\) | 2.53564e24 | 0.669915 | ||||||||
\(780\) | 3.75148e21 | 0.000980390 0 | ||||||||
\(781\) | 7.37461e23 | 0.190636 | ||||||||
\(782\) | 1.49704e24 | 0.382804 | ||||||||
\(783\) | −4.12114e24 | −1.04242 | ||||||||
\(784\) | 1.65641e24 | 0.414460 | ||||||||
\(785\) | 3.04292e24 | 0.753179 | ||||||||
\(786\) | 8.51770e23 | 0.208560 | ||||||||
\(787\) | 2.64413e24 | 0.640467 | 0.320234 | − | 0.947339i | \(-0.396239\pi\) | ||||
0.320234 | + | 0.947339i | \(0.396239\pi\) | |||||||
\(788\) | 5.55300e23 | 0.133062 | ||||||||
\(789\) | 3.84415e24 | 0.911268 | ||||||||
\(790\) | −2.80988e23 | −0.0658958 | ||||||||
\(791\) | −1.01798e25 | −2.36179 | ||||||||
\(792\) | −1.35550e23 | −0.0311125 | ||||||||
\(793\) | 2.33290e22 | 0.00529753 | ||||||||
\(794\) | 1.95925e24 | 0.440166 | ||||||||
\(795\) | −1.45509e24 | −0.323422 | ||||||||
\(796\) | 6.21701e23 | 0.136716 | ||||||||
\(797\) | −6.24909e24 | −1.35963 | −0.679815 | − | 0.733383i | \(-0.737940\pi\) | ||||
−0.679815 | + | 0.733383i | \(0.737940\pi\) | |||||||
\(798\) | −7.58601e24 | −1.63301 | ||||||||
\(799\) | −6.01699e24 | −1.28154 | ||||||||
\(800\) | −1.67772e23 | −0.0353553 | ||||||||
\(801\) | −2.34230e24 | −0.488388 | ||||||||
\(802\) | 1.04518e23 | 0.0215630 | ||||||||
\(803\) | 5.44114e23 | 0.111073 | ||||||||
\(804\) | 1.65625e24 | 0.334542 | ||||||||
\(805\) | −2.51885e24 | −0.503427 | ||||||||
\(806\) | 3.18784e22 | 0.00630448 | ||||||||
\(807\) | −3.36726e24 | −0.658948 | ||||||||
\(808\) | 2.62404e24 | 0.508129 | ||||||||
\(809\) | 5.76985e24 | 1.10561 | 0.552805 | − | 0.833311i | \(-0.313557\pi\) | ||||
0.552805 | + | 0.833311i | \(0.313557\pi\) | |||||||
\(810\) | 9.39628e23 | 0.178170 | ||||||||
\(811\) | 3.03433e24 | 0.569359 | 0.284679 | − | 0.958623i | \(-0.408113\pi\) | ||||
0.284679 | + | 0.958623i | \(0.408113\pi\) | |||||||
\(812\) | 4.20357e24 | 0.780534 | ||||||||
\(813\) | 6.16130e24 | 1.13215 | ||||||||
\(814\) | −1.02301e24 | −0.186025 | ||||||||
\(815\) | 2.40973e24 | 0.433639 | ||||||||
\(816\) | 9.01843e23 | 0.160607 | ||||||||
\(817\) | −5.89719e24 | −1.03934 | ||||||||
\(818\) | −5.14363e24 | −0.897153 | ||||||||
\(819\) | −1.66061e22 | −0.00286652 | ||||||||
\(820\) | 5.07194e23 | 0.0866475 | ||||||||
\(821\) | 4.15299e24 | 0.702172 | 0.351086 | − | 0.936343i | \(-0.385812\pi\) | ||||
0.351086 | + | 0.936343i | \(0.385812\pi\) | |||||||
\(822\) | −2.95160e24 | −0.493909 | ||||||||
\(823\) | 9.22848e23 | 0.152838 | 0.0764191 | − | 0.997076i | \(-0.475651\pi\) | ||||
0.0764191 | + | 0.997076i | \(0.475651\pi\) | |||||||
\(824\) | 3.91188e24 | 0.641216 | ||||||||
\(825\) | 2.70515e23 | 0.0438867 | ||||||||
\(826\) | 1.16242e25 | 1.86652 | ||||||||
\(827\) | 7.67636e24 | 1.22000 | 0.609998 | − | 0.792403i | \(-0.291170\pi\) | ||||
0.609998 | + | 0.792403i | \(0.291170\pi\) | |||||||
\(828\) | −7.21195e23 | −0.113448 | ||||||||
\(829\) | 8.23009e23 | 0.128142 | 0.0640709 | − | 0.997945i | \(-0.479592\pi\) | ||||
0.0640709 | + | 0.997945i | \(0.479592\pi\) | |||||||
\(830\) | 7.04230e23 | 0.108530 | ||||||||
\(831\) | −2.26922e24 | −0.346153 | ||||||||
\(832\) | −4.42977e21 | −0.000668857 0 | ||||||||
\(833\) | −8.69679e24 | −1.29980 | ||||||||
\(834\) | 4.65140e24 | 0.688133 | ||||||||
\(835\) | 4.87209e24 | 0.713478 | ||||||||
\(836\) | −1.59692e24 | −0.231489 | ||||||||
\(837\) | 1.26413e25 | 1.81395 | ||||||||
\(838\) | −8.47652e24 | −1.20405 | ||||||||
\(839\) | −9.57083e24 | −1.34578 | −0.672888 | − | 0.739744i | \(-0.734947\pi\) | ||||
−0.672888 | + | 0.739744i | \(0.734947\pi\) | |||||||
\(840\) | −1.51740e24 | −0.211215 | ||||||||
\(841\) | −6.03171e23 | −0.0831140 | ||||||||
\(842\) | 5.92192e24 | 0.807811 | ||||||||
\(843\) | 8.81851e24 | 1.19086 | ||||||||
\(844\) | −3.31679e24 | −0.443412 | ||||||||
\(845\) | −3.37897e24 | −0.447201 | ||||||||
\(846\) | 2.89867e24 | 0.379796 | ||||||||
\(847\) | 1.16669e25 | 1.51337 | ||||||||
\(848\) | 1.71818e24 | 0.220650 | ||||||||
\(849\) | 3.42203e24 | 0.435079 | ||||||||
\(850\) | 8.80866e23 | 0.110879 | ||||||||
\(851\) | −5.44292e24 | −0.678314 | ||||||||
\(852\) | 2.36369e24 | 0.291645 | ||||||||
\(853\) | 2.48597e24 | 0.303690 | 0.151845 | − | 0.988404i | \(-0.451479\pi\) | ||||
0.151845 | + | 0.988404i | \(0.451479\pi\) | |||||||
\(854\) | −9.43608e24 | −1.14130 | ||||||||
\(855\) | −2.12150e24 | −0.254057 | ||||||||
\(856\) | 1.76827e24 | 0.209663 | ||||||||
\(857\) | −2.10495e24 | −0.247118 | −0.123559 | − | 0.992337i | \(-0.539431\pi\) | ||||
−0.123559 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(858\) | 7.14254e21 | 0.000830253 0 | ||||||||
\(859\) | −7.58565e23 | −0.0873074 | −0.0436537 | − | 0.999047i | \(-0.513900\pi\) | ||||
−0.0436537 | + | 0.999047i | \(0.513900\pi\) | |||||||
\(860\) | −1.17959e24 | −0.134429 | ||||||||
\(861\) | 4.58725e24 | 0.517638 | ||||||||
\(862\) | −1.13817e25 | −1.27173 | ||||||||
\(863\) | −5.83299e24 | −0.645356 | −0.322678 | − | 0.946509i | \(-0.604583\pi\) | ||||
−0.322678 | + | 0.946509i | \(0.604583\pi\) | |||||||
\(864\) | −1.75662e24 | −0.192446 | ||||||||
\(865\) | 6.42556e24 | 0.697067 | ||||||||
\(866\) | −7.30378e24 | −0.784595 | ||||||||
\(867\) | 2.96787e24 | 0.315706 | ||||||||
\(868\) | −1.28942e25 | −1.35824 | ||||||||
\(869\) | −5.34980e23 | −0.0558046 | ||||||||
\(870\) | −2.40194e24 | −0.248112 | ||||||||
\(871\) | 4.27137e22 | 0.00436931 | ||||||||
\(872\) | −4.22610e24 | −0.428104 | ||||||||
\(873\) | −2.72717e24 | −0.273584 | ||||||||
\(874\) | −8.49646e24 | −0.844094 | ||||||||
\(875\) | −1.48210e24 | −0.145817 | ||||||||
\(876\) | 1.74398e24 | 0.169925 | ||||||||
\(877\) | −1.53835e25 | −1.48443 | −0.742214 | − | 0.670163i | \(-0.766224\pi\) | ||||
−0.742214 | + | 0.670163i | \(0.766224\pi\) | |||||||
\(878\) | 1.09716e25 | 1.04849 | ||||||||
\(879\) | −1.12580e25 | −1.06551 | ||||||||
\(880\) | −3.19426e23 | −0.0299410 | ||||||||
\(881\) | −1.57727e25 | −1.46424 | −0.732118 | − | 0.681178i | \(-0.761468\pi\) | ||||
−0.732118 | + | 0.681178i | \(0.761468\pi\) | |||||||
\(882\) | 4.18966e24 | 0.385208 | ||||||||
\(883\) | 1.75208e25 | 1.59547 | 0.797734 | − | 0.603009i | \(-0.206032\pi\) | ||||
0.797734 | + | 0.603009i | \(0.206032\pi\) | |||||||
\(884\) | 2.32579e22 | 0.00209762 | ||||||||
\(885\) | −6.64213e24 | −0.593321 | ||||||||
\(886\) | 3.59588e24 | 0.318140 | ||||||||
\(887\) | −1.05988e25 | −0.928764 | −0.464382 | − | 0.885635i | \(-0.653724\pi\) | ||||
−0.464382 | + | 0.885635i | \(0.653724\pi\) | |||||||
\(888\) | −3.27891e24 | −0.284590 | ||||||||
\(889\) | 1.59739e25 | 1.37324 | ||||||||
\(890\) | −5.51966e24 | −0.470000 | ||||||||
\(891\) | 1.78898e24 | 0.150885 | ||||||||
\(892\) | 7.40667e24 | 0.618759 | ||||||||
\(893\) | 3.41494e25 | 2.82583 | ||||||||
\(894\) | 4.45268e24 | 0.364966 | ||||||||
\(895\) | −5.97918e23 | −0.0485451 | ||||||||
\(896\) | 1.79175e24 | 0.144098 | ||||||||
\(897\) | 3.80020e22 | 0.00302741 | ||||||||
\(898\) | 9.94307e24 | 0.784643 | ||||||||
\(899\) | −2.04106e25 | −1.59551 | ||||||||
\(900\) | −4.24355e23 | −0.0328600 | ||||||||
\(901\) | −9.02107e24 | −0.691986 | ||||||||
\(902\) | 9.65659e23 | 0.0733784 | ||||||||
\(903\) | −1.06687e25 | −0.803089 | ||||||||
\(904\) | −6.86852e24 | −0.512190 | ||||||||
\(905\) | −3.32595e24 | −0.245699 | ||||||||
\(906\) | 1.23689e25 | 0.905195 | ||||||||
\(907\) | 6.72762e24 | 0.487753 | 0.243876 | − | 0.969806i | \(-0.421581\pi\) | ||||
0.243876 | + | 0.969806i | \(0.421581\pi\) | |||||||
\(908\) | 8.78557e24 | 0.631016 | ||||||||
\(909\) | 6.63712e24 | 0.472266 | ||||||||
\(910\) | −3.91327e22 | −0.00275859 | ||||||||
\(911\) | 1.90734e25 | 1.33205 | 0.666027 | − | 0.745928i | \(-0.267994\pi\) | ||||
0.666027 | + | 0.745928i | \(0.267994\pi\) | |||||||
\(912\) | −5.11841e24 | −0.354143 | ||||||||
\(913\) | 1.34080e24 | 0.0919100 | ||||||||
\(914\) | 5.66169e24 | 0.384506 | ||||||||
\(915\) | 5.39182e24 | 0.362791 | ||||||||
\(916\) | −1.00331e25 | −0.668840 | ||||||||
\(917\) | −8.88503e24 | −0.586840 | ||||||||
\(918\) | 9.22288e24 | 0.603537 | ||||||||
\(919\) | −1.73304e25 | −1.12364 | −0.561818 | − | 0.827261i | \(-0.689898\pi\) | ||||
−0.561818 | + | 0.827261i | \(0.689898\pi\) | |||||||
\(920\) | −1.69951e24 | −0.109176 | ||||||||
\(921\) | 4.44096e24 | 0.282664 | ||||||||
\(922\) | −4.33297e24 | −0.273258 | ||||||||
\(923\) | 6.09580e22 | 0.00380905 | ||||||||
\(924\) | −2.88901e24 | −0.178870 | ||||||||
\(925\) | −3.20264e24 | −0.196473 | ||||||||
\(926\) | −1.28207e25 | −0.779326 | ||||||||
\(927\) | 9.89452e24 | 0.595960 | ||||||||
\(928\) | 2.83622e24 | 0.169271 | ||||||||
\(929\) | −6.38514e24 | −0.377605 | −0.188802 | − | 0.982015i | \(-0.560461\pi\) | ||||
−0.188802 | + | 0.982015i | \(0.560461\pi\) | |||||||
\(930\) | 7.36778e24 | 0.431749 | ||||||||
\(931\) | 4.93587e25 | 2.86610 | ||||||||
\(932\) | 1.00988e25 | 0.581076 | ||||||||
\(933\) | −3.26293e24 | −0.186043 | ||||||||
\(934\) | 1.76029e25 | 0.994568 | ||||||||
\(935\) | 1.67710e24 | 0.0938990 | ||||||||
\(936\) | −1.12045e22 | −0.000621650 0 | ||||||||
\(937\) | −2.87864e25 | −1.58271 | −0.791354 | − | 0.611358i | \(-0.790624\pi\) | ||||
−0.791354 | + | 0.611358i | \(0.790624\pi\) | |||||||
\(938\) | −1.72768e25 | −0.941324 | ||||||||
\(939\) | −1.90654e25 | −1.02941 | ||||||||
\(940\) | 6.83076e24 | 0.365496 | ||||||||
\(941\) | −2.31234e25 | −1.22614 | −0.613071 | − | 0.790028i | \(-0.710066\pi\) | ||||
−0.613071 | + | 0.790028i | \(0.710066\pi\) | |||||||
\(942\) | 1.85691e25 | 0.975796 | ||||||||
\(943\) | 5.13781e24 | 0.267564 | ||||||||
\(944\) | 7.84307e24 | 0.404785 | ||||||||
\(945\) | −1.55180e25 | −0.793714 | ||||||||
\(946\) | −2.24585e24 | −0.113843 | ||||||||
\(947\) | 1.60999e25 | 0.808816 | 0.404408 | − | 0.914579i | \(-0.367478\pi\) | ||||
0.404408 | + | 0.914579i | \(0.367478\pi\) | |||||||
\(948\) | −1.71470e24 | −0.0853725 | ||||||||
\(949\) | 4.49761e22 | 0.00221932 | ||||||||
\(950\) | −4.99936e24 | −0.244491 | ||||||||
\(951\) | −1.22599e25 | −0.594225 | ||||||||
\(952\) | −9.40735e24 | −0.451911 | ||||||||
\(953\) | −1.12344e25 | −0.534883 | −0.267441 | − | 0.963574i | \(-0.586178\pi\) | ||||
−0.267441 | + | 0.963574i | \(0.586178\pi\) | |||||||
\(954\) | 4.34588e24 | 0.205077 | ||||||||
\(955\) | 4.13753e24 | 0.193514 | ||||||||
\(956\) | 7.24996e24 | 0.336081 | ||||||||
\(957\) | −4.57311e24 | −0.210117 | ||||||||
\(958\) | 8.81385e24 | 0.401383 | ||||||||
\(959\) | 3.07889e25 | 1.38975 | ||||||||
\(960\) | −1.02381e24 | −0.0458053 | ||||||||
\(961\) | 4.00580e25 | 1.77640 | ||||||||
\(962\) | −8.45610e22 | −0.00371691 | ||||||||
\(963\) | 4.47259e24 | 0.194866 | ||||||||
\(964\) | −1.10487e25 | −0.477152 | ||||||||
\(965\) | −6.08468e24 | −0.260469 | ||||||||
\(966\) | −1.53710e25 | −0.652225 | ||||||||
\(967\) | 2.40854e24 | 0.101305 | 0.0506524 | − | 0.998716i | \(-0.483870\pi\) | ||||
0.0506524 | + | 0.998716i | \(0.483870\pi\) | |||||||
\(968\) | 7.87183e24 | 0.328197 | ||||||||
\(969\) | 2.68736e25 | 1.11064 | ||||||||
\(970\) | −6.42662e24 | −0.263283 | ||||||||
\(971\) | −2.55647e25 | −1.03819 | −0.519095 | − | 0.854716i | \(-0.673731\pi\) | ||||
−0.519095 | + | 0.854716i | \(0.673731\pi\) | |||||||
\(972\) | −7.78730e24 | −0.313490 | ||||||||
\(973\) | −4.85200e25 | −1.93625 | ||||||||
\(974\) | −2.26264e23 | −0.00895085 | ||||||||
\(975\) | 2.23606e22 | 0.000876887 0 | ||||||||
\(976\) | −6.36669e24 | −0.247509 | ||||||||
\(977\) | −2.30301e25 | −0.887547 | −0.443774 | − | 0.896139i | \(-0.646361\pi\) | ||||
−0.443774 | + | 0.896139i | \(0.646361\pi\) | |||||||
\(978\) | 1.47052e25 | 0.561810 | ||||||||
\(979\) | −1.05090e25 | −0.398024 | ||||||||
\(980\) | 9.87300e24 | 0.370704 | ||||||||
\(981\) | −1.06893e25 | −0.397889 | ||||||||
\(982\) | −2.67557e25 | −0.987345 | ||||||||
\(983\) | −2.04718e25 | −0.748949 | −0.374474 | − | 0.927237i | \(-0.622177\pi\) | ||||
−0.374474 | + | 0.927237i | \(0.622177\pi\) | |||||||
\(984\) | 3.09510e24 | 0.112258 | ||||||||
\(985\) | 3.30984e24 | 0.119014 | ||||||||
\(986\) | −1.48912e25 | −0.530856 | ||||||||
\(987\) | 6.17801e25 | 2.18350 | ||||||||
\(988\) | −1.32001e23 | −0.00462532 | ||||||||
\(989\) | −1.19491e25 | −0.415113 | ||||||||
\(990\) | −8.07940e23 | −0.0278279 | ||||||||
\(991\) | 1.20622e25 | 0.411907 | 0.205954 | − | 0.978562i | \(-0.433970\pi\) | ||||
0.205954 | + | 0.978562i | \(0.433970\pi\) | |||||||
\(992\) | −8.69992e24 | −0.294555 | ||||||||
\(993\) | −3.59297e25 | −1.20610 | ||||||||
\(994\) | −2.46563e25 | −0.820621 | ||||||||
\(995\) | 3.70563e24 | 0.122283 | ||||||||
\(996\) | 4.29750e24 | 0.140608 | ||||||||
\(997\) | −1.73789e23 | −0.00563786 | −0.00281893 | − | 0.999996i | \(-0.500897\pi\) | ||||
−0.00281893 | + | 0.999996i | \(0.500897\pi\) | |||||||
\(998\) | 1.31089e25 | 0.421655 | ||||||||
\(999\) | −3.35325e25 | −1.06945 |
(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 | 10.18.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 90.18.a.k.1.1 | 2 | |||
4.3 | odd | 2 | 80.18.a.d.1.2 | 2 | |||
5.2 | odd | 4 | 50.18.b.d.49.2 | 4 | |||
5.3 | odd | 4 | 50.18.b.d.49.3 | 4 | |||
5.4 | even | 2 | 50.18.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.18.a.f.1.2 | 2 | 5.4 | even | 2 | |||
50.18.b.d.49.2 | 4 | 5.2 | odd | 4 | |||
50.18.b.d.49.3 | 4 | 5.3 | odd | 4 | |||
80.18.a.d.1.2 | 2 | 4.3 | odd | 2 | |||
90.18.a.k.1.1 | 2 | 3.2 | odd | 2 |