Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,84,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 84, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 84);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 84 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(87.2544256533\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 287609867501924274375802127400x - 41230865304567060522794640394926417995512500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{7}\cdot 5^{3}\cdot 7\cdot 11\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(5.97202e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19902e12 | −0.707107 | ||||||||
\(3\) | 2.32406e18 | 0.0367888 | 0.0183944 | − | 0.999831i | \(-0.494145\pi\) | ||||
0.0183944 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(4\) | 4.83570e24 | 0.500000 | ||||||||
\(5\) | 1.63642e29 | 1.60931 | 0.804656 | − | 0.593742i | \(-0.202350\pi\) | ||||
0.804656 | + | 0.593742i | \(0.202350\pi\) | |||||||
\(6\) | −5.11067e30 | −0.0260136 | ||||||||
\(7\) | −8.77702e33 | −0.0744352 | −0.0372176 | − | 0.999307i | \(-0.511849\pi\) | ||||
−0.0372176 | + | 0.999307i | \(0.511849\pi\) | |||||||
\(8\) | −1.06338e37 | −0.353553 | ||||||||
\(9\) | −3.98544e39 | −0.998647 | ||||||||
\(10\) | −3.59853e41 | −1.13796 | ||||||||
\(11\) | −4.41257e42 | −0.267236 | −0.133618 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133618 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(12\) | 1.12385e43 | 0.0183944 | ||||||||
\(13\) | −1.03328e45 | −0.0610336 | −0.0305168 | − | 0.999534i | \(-0.509715\pi\) | ||||
−0.0305168 | + | 0.999534i | \(0.509715\pi\) | |||||||
\(14\) | 1.93009e46 | 0.0526336 | ||||||||
\(15\) | 3.80315e47 | 0.0592047 | ||||||||
\(16\) | 2.33840e49 | 0.250000 | ||||||||
\(17\) | 7.89598e50 | 0.681987 | 0.340993 | − | 0.940066i | \(-0.389237\pi\) | ||||
0.340993 | + | 0.940066i | \(0.389237\pi\) | |||||||
\(18\) | 8.76407e51 | 0.706150 | ||||||||
\(19\) | 1.66335e53 | 1.42138 | 0.710688 | − | 0.703507i | \(-0.248384\pi\) | ||||
0.710688 | + | 0.703507i | \(0.248384\pi\) | |||||||
\(20\) | 7.91325e53 | 0.804656 | ||||||||
\(21\) | −2.03984e52 | −0.00273838 | ||||||||
\(22\) | 9.70335e54 | 0.188965 | ||||||||
\(23\) | −3.15448e56 | −0.971007 | −0.485504 | − | 0.874235i | \(-0.661364\pi\) | ||||
−0.485504 | + | 0.874235i | \(0.661364\pi\) | |||||||
\(24\) | −2.47137e55 | −0.0130068 | ||||||||
\(25\) | 1.64390e58 | 1.58988 | ||||||||
\(26\) | 2.27221e57 | 0.0431573 | ||||||||
\(27\) | −1.85374e58 | −0.0735279 | ||||||||
\(28\) | −4.24431e58 | −0.0372176 | ||||||||
\(29\) | −7.28891e60 | −1.48986 | −0.744930 | − | 0.667142i | \(-0.767517\pi\) | ||||
−0.744930 | + | 0.667142i | \(0.767517\pi\) | |||||||
\(30\) | −8.36321e59 | −0.0418640 | ||||||||
\(31\) | 1.29840e62 | 1.66685 | 0.833425 | − | 0.552632i | \(-0.186377\pi\) | ||||
0.833425 | + | 0.552632i | \(0.186377\pi\) | |||||||
\(32\) | −5.14220e61 | −0.176777 | ||||||||
\(33\) | −1.02551e61 | −0.00983131 | ||||||||
\(34\) | −1.73635e63 | −0.482238 | ||||||||
\(35\) | −1.43629e63 | −0.119789 | ||||||||
\(36\) | −1.92724e64 | −0.499323 | ||||||||
\(37\) | 1.79886e65 | 1.49495 | 0.747475 | − | 0.664290i | \(-0.231266\pi\) | ||||
0.747475 | + | 0.664290i | \(0.231266\pi\) | |||||||
\(38\) | −3.65774e65 | −1.00506 | ||||||||
\(39\) | −2.40141e63 | −0.00224536 | ||||||||
\(40\) | −1.74014e66 | −0.568978 | ||||||||
\(41\) | 3.38501e66 | 0.397219 | 0.198609 | − | 0.980079i | \(-0.436358\pi\) | ||||
0.198609 | + | 0.980079i | \(0.436358\pi\) | |||||||
\(42\) | 4.48565e64 | 0.00193633 | ||||||||
\(43\) | −3.48336e67 | −0.566315 | −0.283157 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283157 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(44\) | −2.13379e67 | −0.133618 | ||||||||
\(45\) | −6.52186e68 | −1.60713 | ||||||||
\(46\) | 6.93677e68 | 0.686606 | ||||||||
\(47\) | −1.23539e69 | −0.500892 | −0.250446 | − | 0.968131i | \(-0.580577\pi\) | ||||
−0.250446 | + | 0.968131i | \(0.580577\pi\) | |||||||
\(48\) | 5.43460e67 | 0.00919721 | ||||||||
\(49\) | −1.38269e70 | −0.994459 | ||||||||
\(50\) | −3.61498e70 | −1.12422 | ||||||||
\(51\) | 1.83508e69 | 0.0250895 | ||||||||
\(52\) | −4.99664e69 | −0.0305168 | ||||||||
\(53\) | 3.80797e71 | 1.05498 | 0.527491 | − | 0.849560i | \(-0.323133\pi\) | ||||
0.527491 | + | 0.849560i | \(0.323133\pi\) | |||||||
\(54\) | 4.07641e70 | 0.0519921 | ||||||||
\(55\) | −7.22083e71 | −0.430067 | ||||||||
\(56\) | 9.33333e70 | 0.0263168 | ||||||||
\(57\) | 3.86573e71 | 0.0522908 | ||||||||
\(58\) | 1.60285e73 | 1.05349 | ||||||||
\(59\) | 2.39580e73 | 0.774627 | 0.387313 | − | 0.921948i | \(-0.373403\pi\) | ||||
0.387313 | + | 0.921948i | \(0.373403\pi\) | |||||||
\(60\) | 1.83909e72 | 0.0296023 | ||||||||
\(61\) | −3.26424e73 | −0.264602 | −0.132301 | − | 0.991210i | \(-0.542237\pi\) | ||||
−0.132301 | + | 0.991210i | \(0.542237\pi\) | |||||||
\(62\) | −2.85520e74 | −1.17864 | ||||||||
\(63\) | 3.49803e73 | 0.0743345 | ||||||||
\(64\) | 1.13078e74 | 0.125000 | ||||||||
\(65\) | −1.69088e74 | −0.0982221 | ||||||||
\(66\) | 2.25512e73 | 0.00695179 | ||||||||
\(67\) | −5.45591e75 | −0.901079 | −0.450539 | − | 0.892757i | \(-0.648768\pi\) | ||||
−0.450539 | + | 0.892757i | \(0.648768\pi\) | |||||||
\(68\) | 3.81826e75 | 0.340993 | ||||||||
\(69\) | −7.33121e74 | −0.0357222 | ||||||||
\(70\) | 3.15844e75 | 0.0847039 | ||||||||
\(71\) | 6.95274e76 | 1.03499 | 0.517493 | − | 0.855688i | \(-0.326865\pi\) | ||||
0.517493 | + | 0.855688i | \(0.326865\pi\) | |||||||
\(72\) | 4.23804e76 | 0.353075 | ||||||||
\(73\) | 9.48153e76 | 0.445636 | 0.222818 | − | 0.974860i | \(-0.428474\pi\) | ||||
0.222818 | + | 0.974860i | \(0.428474\pi\) | |||||||
\(74\) | −3.95574e77 | −1.05709 | ||||||||
\(75\) | 3.82053e76 | 0.0584900 | ||||||||
\(76\) | 8.04347e77 | 0.710688 | ||||||||
\(77\) | 3.87292e76 | 0.0198918 | ||||||||
\(78\) | 5.28076e75 | 0.00158771 | ||||||||
\(79\) | −8.48354e78 | −1.50333 | −0.751663 | − | 0.659548i | \(-0.770748\pi\) | ||||
−0.751663 | + | 0.659548i | \(0.770748\pi\) | |||||||
\(80\) | 3.82661e78 | 0.402328 | ||||||||
\(81\) | 1.58622e79 | 0.995942 | ||||||||
\(82\) | −7.44371e78 | −0.280876 | ||||||||
\(83\) | 4.88119e79 | 1.11374 | 0.556871 | − | 0.830599i | \(-0.312002\pi\) | ||||
0.556871 | + | 0.830599i | \(0.312002\pi\) | |||||||
\(84\) | −9.86404e76 | −0.00136919 | ||||||||
\(85\) | 1.29212e80 | 1.09753 | ||||||||
\(86\) | 7.66000e79 | 0.400445 | ||||||||
\(87\) | −1.69399e79 | −0.0548102 | ||||||||
\(88\) | 4.69225e79 | 0.0944823 | ||||||||
\(89\) | 1.14577e81 | 1.44348 | 0.721742 | − | 0.692162i | \(-0.243342\pi\) | ||||
0.721742 | + | 0.692162i | \(0.243342\pi\) | |||||||
\(90\) | 1.43417e81 | 1.13642 | ||||||||
\(91\) | 9.06912e78 | 0.00454305 | ||||||||
\(92\) | −1.52541e81 | −0.485504 | ||||||||
\(93\) | 3.01755e80 | 0.0613215 | ||||||||
\(94\) | 2.71666e81 | 0.354184 | ||||||||
\(95\) | 2.72194e82 | 2.28744 | ||||||||
\(96\) | −1.19508e80 | −0.00650341 | ||||||||
\(97\) | 5.10935e82 | 1.80858 | 0.904292 | − | 0.426915i | \(-0.140400\pi\) | ||||
0.904292 | + | 0.426915i | \(0.140400\pi\) | |||||||
\(98\) | 3.04056e82 | 0.703189 | ||||||||
\(99\) | 1.75860e82 | 0.266875 | ||||||||
\(100\) | 7.94942e82 | 0.794942 | ||||||||
\(101\) | −5.73696e82 | −0.379616 | −0.189808 | − | 0.981821i | \(-0.560787\pi\) | ||||
−0.189808 | + | 0.981821i | \(0.560787\pi\) | |||||||
\(102\) | −4.03538e81 | −0.0177410 | ||||||||
\(103\) | 5.15903e83 | 1.51294 | 0.756472 | − | 0.654026i | \(-0.226921\pi\) | ||||
0.756472 | + | 0.654026i | \(0.226921\pi\) | |||||||
\(104\) | 1.09877e82 | 0.0215786 | ||||||||
\(105\) | −3.33803e81 | −0.00440691 | ||||||||
\(106\) | −8.37382e83 | −0.745986 | ||||||||
\(107\) | −1.67750e84 | −1.01213 | −0.506065 | − | 0.862495i | \(-0.668900\pi\) | ||||
−0.506065 | + | 0.862495i | \(0.668900\pi\) | |||||||
\(108\) | −8.96412e82 | −0.0367639 | ||||||||
\(109\) | −7.46931e83 | −0.208969 | −0.104484 | − | 0.994527i | \(-0.533319\pi\) | ||||
−0.104484 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(110\) | 1.58788e84 | 0.304103 | ||||||||
\(111\) | 4.18068e83 | 0.0549975 | ||||||||
\(112\) | −2.05242e83 | −0.0186088 | ||||||||
\(113\) | −1.45069e85 | −0.909534 | −0.454767 | − | 0.890610i | \(-0.650278\pi\) | ||||
−0.454767 | + | 0.890610i | \(0.650278\pi\) | |||||||
\(114\) | −8.50083e83 | −0.0369752 | ||||||||
\(115\) | −5.16206e85 | −1.56265 | ||||||||
\(116\) | −3.52470e85 | −0.744930 | ||||||||
\(117\) | 4.11808e84 | 0.0609510 | ||||||||
\(118\) | −5.26842e85 | −0.547744 | ||||||||
\(119\) | −6.93032e84 | −0.0507638 | ||||||||
\(120\) | −4.04420e84 | −0.0209320 | ||||||||
\(121\) | −2.53171e86 | −0.928585 | ||||||||
\(122\) | 7.17814e85 | 0.187102 | ||||||||
\(123\) | 7.86697e84 | 0.0146132 | ||||||||
\(124\) | 6.27866e86 | 0.833425 | ||||||||
\(125\) | 9.98096e86 | 0.949307 | ||||||||
\(126\) | −7.69224e85 | −0.0525624 | ||||||||
\(127\) | 3.50206e87 | 1.72373 | 0.861865 | − | 0.507137i | \(-0.169296\pi\) | ||||
0.861865 | + | 0.507137i | \(0.169296\pi\) | |||||||
\(128\) | −2.48662e86 | −0.0883883 | ||||||||
\(129\) | −8.09556e85 | −0.0208341 | ||||||||
\(130\) | 3.71829e86 | 0.0694535 | ||||||||
\(131\) | 5.31708e87 | 0.722628 | 0.361314 | − | 0.932444i | \(-0.382328\pi\) | ||||
0.361314 | + | 0.932444i | \(0.382328\pi\) | |||||||
\(132\) | −4.95906e85 | −0.00491566 | ||||||||
\(133\) | −1.45993e87 | −0.105800 | ||||||||
\(134\) | 1.19977e88 | 0.637159 | ||||||||
\(135\) | −3.03350e87 | −0.118329 | ||||||||
\(136\) | −8.39645e87 | −0.241119 | ||||||||
\(137\) | −2.48949e88 | −0.527481 | −0.263741 | − | 0.964594i | \(-0.584956\pi\) | ||||
−0.263741 | + | 0.964594i | \(0.584956\pi\) | |||||||
\(138\) | 1.61215e87 | 0.0252594 | ||||||||
\(139\) | 2.44056e88 | 0.283384 | 0.141692 | − | 0.989911i | \(-0.454746\pi\) | ||||
0.141692 | + | 0.989911i | \(0.454746\pi\) | |||||||
\(140\) | −6.94548e87 | −0.0598947 | ||||||||
\(141\) | −2.87113e87 | −0.0184272 | ||||||||
\(142\) | −1.52892e89 | −0.731845 | ||||||||
\(143\) | 4.55943e87 | 0.0163104 | ||||||||
\(144\) | −9.31956e88 | −0.249662 | ||||||||
\(145\) | −1.19277e90 | −2.39765 | ||||||||
\(146\) | −2.08501e89 | −0.315112 | ||||||||
\(147\) | −3.21346e88 | −0.0365850 | ||||||||
\(148\) | 8.69877e89 | 0.747475 | ||||||||
\(149\) | −4.37137e89 | −0.284045 | −0.142023 | − | 0.989863i | \(-0.545361\pi\) | ||||
−0.142023 | + | 0.989863i | \(0.545361\pi\) | |||||||
\(150\) | −8.40144e88 | −0.0413587 | ||||||||
\(151\) | 3.88960e90 | 1.45332 | 0.726660 | − | 0.686997i | \(-0.241071\pi\) | ||||
0.726660 | + | 0.686997i | \(0.241071\pi\) | |||||||
\(152\) | −1.76878e90 | −0.502532 | ||||||||
\(153\) | −3.14689e90 | −0.681064 | ||||||||
\(154\) | −8.51665e88 | −0.0140656 | ||||||||
\(155\) | 2.12472e91 | 2.68248 | ||||||||
\(156\) | −1.16125e88 | −0.00112268 | ||||||||
\(157\) | 6.56967e89 | 0.0487201 | 0.0243600 | − | 0.999703i | \(-0.492245\pi\) | ||||
0.0243600 | + | 0.999703i | \(0.492245\pi\) | |||||||
\(158\) | 1.86555e91 | 1.06301 | ||||||||
\(159\) | 8.84998e89 | 0.0388116 | ||||||||
\(160\) | −8.41481e90 | −0.284489 | ||||||||
\(161\) | 2.76869e90 | 0.0722771 | ||||||||
\(162\) | −3.48812e91 | −0.704237 | ||||||||
\(163\) | −4.43454e91 | −0.693526 | −0.346763 | − | 0.937953i | \(-0.612719\pi\) | ||||
−0.346763 | + | 0.937953i | \(0.612719\pi\) | |||||||
\(164\) | 1.63689e91 | 0.198609 | ||||||||
\(165\) | −1.67817e90 | −0.0158216 | ||||||||
\(166\) | −1.07338e92 | −0.787535 | ||||||||
\(167\) | 3.11587e92 | 1.78174 | 0.890872 | − | 0.454254i | \(-0.150094\pi\) | ||||
0.890872 | + | 0.454254i | \(0.150094\pi\) | |||||||
\(168\) | 2.16913e89 | 0.000968165 0 | ||||||||
\(169\) | −2.85547e92 | −0.996275 | ||||||||
\(170\) | −2.84139e92 | −0.776070 | ||||||||
\(171\) | −6.62918e92 | −1.41945 | ||||||||
\(172\) | −1.68445e92 | −0.283157 | ||||||||
\(173\) | 6.09613e92 | 0.805639 | 0.402820 | − | 0.915279i | \(-0.368030\pi\) | ||||
0.402820 | + | 0.915279i | \(0.368030\pi\) | |||||||
\(174\) | 3.72512e91 | 0.0387567 | ||||||||
\(175\) | −1.44286e92 | −0.118343 | ||||||||
\(176\) | −1.03184e92 | −0.0668091 | ||||||||
\(177\) | 5.56800e91 | 0.0284976 | ||||||||
\(178\) | −2.51957e93 | −1.02070 | ||||||||
\(179\) | 3.20014e93 | 1.02747 | 0.513734 | − | 0.857950i | \(-0.328262\pi\) | ||||
0.513734 | + | 0.857950i | \(0.328262\pi\) | |||||||
\(180\) | −3.15378e93 | −0.803567 | ||||||||
\(181\) | 9.04366e93 | 1.83098 | 0.915490 | − | 0.402341i | \(-0.131803\pi\) | ||||
0.915490 | + | 0.402341i | \(0.131803\pi\) | |||||||
\(182\) | −1.99432e91 | −0.00321242 | ||||||||
\(183\) | −7.58630e91 | −0.00973441 | ||||||||
\(184\) | 3.35442e93 | 0.343303 | ||||||||
\(185\) | 2.94370e94 | 2.40584 | ||||||||
\(186\) | −6.63567e92 | −0.0433608 | ||||||||
\(187\) | −3.48416e93 | −0.182252 | ||||||||
\(188\) | −5.97400e93 | −0.250446 | ||||||||
\(189\) | 1.62703e92 | 0.00547306 | ||||||||
\(190\) | −5.98561e94 | −1.61746 | ||||||||
\(191\) | 4.54640e92 | 0.00988060 | 0.00494030 | − | 0.999988i | \(-0.498427\pi\) | ||||
0.00494030 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(192\) | 2.62801e92 | 0.00459860 | ||||||||
\(193\) | 5.51356e94 | 0.777685 | 0.388843 | − | 0.921304i | \(-0.372875\pi\) | ||||
0.388843 | + | 0.921304i | \(0.372875\pi\) | |||||||
\(194\) | −1.12356e95 | −1.27886 | ||||||||
\(195\) | −3.92972e92 | −0.00361348 | ||||||||
\(196\) | −6.68627e94 | −0.497230 | ||||||||
\(197\) | −2.03036e95 | −1.22243 | −0.611216 | − | 0.791464i | \(-0.709319\pi\) | ||||
−0.611216 | + | 0.791464i | \(0.709319\pi\) | |||||||
\(198\) | −3.86721e94 | −0.188709 | ||||||||
\(199\) | 3.23506e95 | 1.28079 | 0.640397 | − | 0.768044i | \(-0.278770\pi\) | ||||
0.640397 | + | 0.768044i | \(0.278770\pi\) | |||||||
\(200\) | −1.74810e95 | −0.562109 | ||||||||
\(201\) | −1.26799e94 | −0.0331496 | ||||||||
\(202\) | 1.26157e95 | 0.268429 | ||||||||
\(203\) | 6.39749e94 | 0.110898 | ||||||||
\(204\) | 8.87389e93 | 0.0125447 | ||||||||
\(205\) | 5.53930e95 | 0.639248 | ||||||||
\(206\) | −1.13448e96 | −1.06981 | ||||||||
\(207\) | 1.25720e96 | 0.969693 | ||||||||
\(208\) | −2.41623e94 | −0.0152584 | ||||||||
\(209\) | −7.33965e95 | −0.379843 | ||||||||
\(210\) | 7.34041e93 | 0.00311616 | ||||||||
\(211\) | 4.35054e96 | 1.51643 | 0.758213 | − | 0.652007i | \(-0.226073\pi\) | ||||
0.758213 | + | 0.652007i | \(0.226073\pi\) | |||||||
\(212\) | 1.84142e96 | 0.527491 | ||||||||
\(213\) | 1.61586e95 | 0.0380759 | ||||||||
\(214\) | 3.68887e96 | 0.715684 | ||||||||
\(215\) | −5.70025e96 | −0.911377 | ||||||||
\(216\) | 1.97123e95 | 0.0259960 | ||||||||
\(217\) | −1.13960e96 | −0.124072 | ||||||||
\(218\) | 1.64252e96 | 0.147763 | ||||||||
\(219\) | 2.20357e95 | 0.0163944 | ||||||||
\(220\) | −3.49178e96 | −0.215033 | ||||||||
\(221\) | −8.15877e95 | −0.0416241 | ||||||||
\(222\) | −9.19340e95 | −0.0388891 | ||||||||
\(223\) | −3.78127e97 | −1.32735 | −0.663675 | − | 0.748021i | \(-0.731004\pi\) | ||||
−0.663675 | + | 0.748021i | \(0.731004\pi\) | |||||||
\(224\) | 4.51332e95 | 0.0131584 | ||||||||
\(225\) | −6.55167e97 | −1.58773 | ||||||||
\(226\) | 3.19010e97 | 0.643138 | ||||||||
\(227\) | −8.45647e97 | −1.41944 | −0.709719 | − | 0.704485i | \(-0.751178\pi\) | ||||
−0.709719 | + | 0.704485i | \(0.751178\pi\) | |||||||
\(228\) | 1.86935e96 | 0.0261454 | ||||||||
\(229\) | 2.17497e97 | 0.253677 | 0.126838 | − | 0.991923i | \(-0.459517\pi\) | ||||
0.126838 | + | 0.991923i | \(0.459517\pi\) | |||||||
\(230\) | 1.13515e98 | 1.10496 | ||||||||
\(231\) | 9.00092e94 | 0.000731796 0 | ||||||||
\(232\) | 7.75090e97 | 0.526745 | ||||||||
\(233\) | 2.88665e98 | 1.64106 | 0.820529 | − | 0.571605i | \(-0.193679\pi\) | ||||
0.820529 | + | 0.571605i | \(0.193679\pi\) | |||||||
\(234\) | −9.05574e96 | −0.0430989 | ||||||||
\(235\) | −2.02163e98 | −0.806092 | ||||||||
\(236\) | 1.15854e98 | 0.387313 | ||||||||
\(237\) | −1.97163e97 | −0.0553056 | ||||||||
\(238\) | 1.52399e97 | 0.0358955 | ||||||||
\(239\) | 3.57970e98 | 0.708491 | 0.354245 | − | 0.935152i | \(-0.384738\pi\) | ||||
0.354245 | + | 0.935152i | \(0.384738\pi\) | |||||||
\(240\) | 8.89329e96 | 0.0148012 | ||||||||
\(241\) | 8.81088e97 | 0.123399 | 0.0616996 | − | 0.998095i | \(-0.480348\pi\) | ||||
0.0616996 | + | 0.998095i | \(0.480348\pi\) | |||||||
\(242\) | 5.56729e98 | 0.656609 | ||||||||
\(243\) | 1.10844e98 | 0.110167 | ||||||||
\(244\) | −1.57849e98 | −0.132301 | ||||||||
\(245\) | −2.26266e99 | −1.60040 | ||||||||
\(246\) | −1.72997e97 | −0.0103331 | ||||||||
\(247\) | −1.71871e98 | −0.0867518 | ||||||||
\(248\) | −1.38069e99 | −0.589321 | ||||||||
\(249\) | 1.13442e98 | 0.0409733 | ||||||||
\(250\) | −2.19484e99 | −0.671261 | ||||||||
\(251\) | 4.77542e99 | 1.23752 | 0.618760 | − | 0.785580i | \(-0.287635\pi\) | ||||
0.618760 | + | 0.785580i | \(0.287635\pi\) | |||||||
\(252\) | 1.69154e98 | 0.0371672 | ||||||||
\(253\) | 1.39194e99 | 0.259488 | ||||||||
\(254\) | −7.70112e99 | −1.21886 | ||||||||
\(255\) | 3.00296e98 | 0.0403768 | ||||||||
\(256\) | 5.46813e98 | 0.0625000 | ||||||||
\(257\) | −1.32968e100 | −1.29277 | −0.646385 | − | 0.763011i | \(-0.723720\pi\) | ||||
−0.646385 | + | 0.763011i | \(0.723720\pi\) | |||||||
\(258\) | 1.78023e98 | 0.0147319 | ||||||||
\(259\) | −1.57887e99 | −0.111277 | ||||||||
\(260\) | −8.17661e98 | −0.0491111 | ||||||||
\(261\) | 2.90495e100 | 1.48784 | ||||||||
\(262\) | −1.16924e100 | −0.510975 | ||||||||
\(263\) | 2.32586e100 | 0.867801 | 0.433900 | − | 0.900961i | \(-0.357137\pi\) | ||||
0.433900 | + | 0.900961i | \(0.357137\pi\) | |||||||
\(264\) | 1.09051e98 | 0.00347589 | ||||||||
\(265\) | 6.23145e100 | 1.69780 | ||||||||
\(266\) | 3.21041e99 | 0.0748122 | ||||||||
\(267\) | 2.66284e99 | 0.0531041 | ||||||||
\(268\) | −2.63831e100 | −0.450539 | ||||||||
\(269\) | 2.33635e100 | 0.341836 | 0.170918 | − | 0.985285i | \(-0.445327\pi\) | ||||
0.170918 | + | 0.985285i | \(0.445327\pi\) | |||||||
\(270\) | 6.67073e99 | 0.0836714 | ||||||||
\(271\) | −3.28823e100 | −0.353783 | −0.176892 | − | 0.984230i | \(-0.556604\pi\) | ||||
−0.176892 | + | 0.984230i | \(0.556604\pi\) | |||||||
\(272\) | 1.84640e100 | 0.170497 | ||||||||
\(273\) | 2.10772e97 | 0.000167134 0 | ||||||||
\(274\) | 5.47445e100 | 0.372986 | ||||||||
\(275\) | −7.25384e100 | −0.424875 | ||||||||
\(276\) | −3.54516e99 | −0.0178611 | ||||||||
\(277\) | −3.52673e101 | −1.52919 | −0.764595 | − | 0.644511i | \(-0.777061\pi\) | ||||
−0.764595 | + | 0.644511i | \(0.777061\pi\) | |||||||
\(278\) | −5.36686e100 | −0.200383 | ||||||||
\(279\) | −5.17467e101 | −1.66459 | ||||||||
\(280\) | 1.52733e100 | 0.0423520 | ||||||||
\(281\) | 9.61452e100 | 0.229940 | 0.114970 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114970 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(282\) | 6.31369e99 | 0.0130300 | ||||||||
\(283\) | 2.03952e101 | 0.363405 | 0.181703 | − | 0.983354i | \(-0.441839\pi\) | ||||
0.181703 | + | 0.983354i | \(0.441839\pi\) | |||||||
\(284\) | 3.36214e101 | 0.517493 | ||||||||
\(285\) | 6.32597e100 | 0.0841521 | ||||||||
\(286\) | −1.00263e100 | −0.0115332 | ||||||||
\(287\) | −2.97103e100 | −0.0295670 | ||||||||
\(288\) | 2.04939e101 | 0.176537 | ||||||||
\(289\) | −7.17015e101 | −0.534894 | ||||||||
\(290\) | 2.62294e102 | 1.69539 | ||||||||
\(291\) | 1.18745e101 | 0.0665357 | ||||||||
\(292\) | 4.58499e101 | 0.222818 | ||||||||
\(293\) | −1.49253e102 | −0.629384 | −0.314692 | − | 0.949194i | \(-0.601901\pi\) | ||||
−0.314692 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(294\) | 7.06647e100 | 0.0258695 | ||||||||
\(295\) | 3.92054e102 | 1.24662 | ||||||||
\(296\) | −1.91288e102 | −0.528545 | ||||||||
\(297\) | 8.17975e100 | 0.0196493 | ||||||||
\(298\) | 9.61275e101 | 0.200850 | ||||||||
\(299\) | 3.25946e101 | 0.0592641 | ||||||||
\(300\) | 1.84750e101 | 0.0292450 | ||||||||
\(301\) | 3.05735e101 | 0.0421537 | ||||||||
\(302\) | −8.55332e102 | −1.02765 | ||||||||
\(303\) | −1.33331e101 | −0.0139656 | ||||||||
\(304\) | 3.88958e102 | 0.355344 | ||||||||
\(305\) | −5.34167e102 | −0.425828 | ||||||||
\(306\) | 6.92009e102 | 0.481585 | ||||||||
\(307\) | 8.20573e102 | 0.498740 | 0.249370 | − | 0.968408i | \(-0.419776\pi\) | ||||
0.249370 | + | 0.968408i | \(0.419776\pi\) | |||||||
\(308\) | 1.87283e101 | 0.00994590 | ||||||||
\(309\) | 1.19899e102 | 0.0556595 | ||||||||
\(310\) | −4.67232e103 | −1.89680 | ||||||||
\(311\) | −5.30457e103 | −1.88406 | −0.942028 | − | 0.335534i | \(-0.891083\pi\) | ||||
−0.942028 | + | 0.335534i | \(0.891083\pi\) | |||||||
\(312\) | 2.55362e100 | 0.000793853 0 | ||||||||
\(313\) | 3.55012e103 | 0.966393 | 0.483196 | − | 0.875512i | \(-0.339476\pi\) | ||||
0.483196 | + | 0.875512i | \(0.339476\pi\) | |||||||
\(314\) | −1.44469e102 | −0.0344503 | ||||||||
\(315\) | 5.72425e102 | 0.119627 | ||||||||
\(316\) | −4.10239e103 | −0.751663 | ||||||||
\(317\) | 1.00605e104 | 1.61681 | 0.808403 | − | 0.588629i | \(-0.200332\pi\) | ||||
0.808403 | + | 0.588629i | \(0.200332\pi\) | |||||||
\(318\) | −1.94613e102 | −0.0274439 | ||||||||
\(319\) | 3.21628e103 | 0.398145 | ||||||||
\(320\) | 1.85044e103 | 0.201164 | ||||||||
\(321\) | −3.89862e102 | −0.0372351 | ||||||||
\(322\) | −6.08842e102 | −0.0511076 | ||||||||
\(323\) | 1.31338e104 | 0.969360 | ||||||||
\(324\) | 7.67047e103 | 0.497971 | ||||||||
\(325\) | −1.69861e103 | −0.0970364 | ||||||||
\(326\) | 9.75165e103 | 0.490397 | ||||||||
\(327\) | −1.73592e102 | −0.00768771 | ||||||||
\(328\) | −3.59956e103 | −0.140438 | ||||||||
\(329\) | 1.08431e103 | 0.0372840 | ||||||||
\(330\) | 3.69033e102 | 0.0111876 | ||||||||
\(331\) | 2.95689e104 | 0.790629 | 0.395315 | − | 0.918546i | \(-0.370636\pi\) | ||||
0.395315 | + | 0.918546i | \(0.370636\pi\) | |||||||
\(332\) | 2.36040e104 | 0.556871 | ||||||||
\(333\) | −7.16926e104 | −1.49293 | ||||||||
\(334\) | −6.85186e104 | −1.25988 | ||||||||
\(335\) | −8.92817e104 | −1.45012 | ||||||||
\(336\) | −4.76996e101 | −0.000684596 0 | ||||||||
\(337\) | −7.28916e104 | −0.924777 | −0.462388 | − | 0.886678i | \(-0.653007\pi\) | ||||
−0.462388 | + | 0.886678i | \(0.653007\pi\) | |||||||
\(338\) | 6.27924e104 | 0.704473 | ||||||||
\(339\) | −3.37150e103 | −0.0334607 | ||||||||
\(340\) | 6.24829e104 | 0.548765 | ||||||||
\(341\) | −5.72927e104 | −0.445443 | ||||||||
\(342\) | 1.45777e105 | 1.00370 | ||||||||
\(343\) | 2.43394e104 | 0.148458 | ||||||||
\(344\) | 3.70415e104 | 0.200222 | ||||||||
\(345\) | −1.19970e104 | −0.0574882 | ||||||||
\(346\) | −1.34055e105 | −0.569673 | ||||||||
\(347\) | −1.85493e105 | −0.699284 | −0.349642 | − | 0.936883i | \(-0.613697\pi\) | ||||
−0.349642 | + | 0.936883i | \(0.613697\pi\) | |||||||
\(348\) | −8.19163e103 | −0.0274051 | ||||||||
\(349\) | 4.41796e105 | 1.31210 | 0.656050 | − | 0.754718i | \(-0.272226\pi\) | ||||
0.656050 | + | 0.754718i | \(0.272226\pi\) | |||||||
\(350\) | 3.17287e104 | 0.0836814 | ||||||||
\(351\) | 1.91543e103 | 0.00448767 | ||||||||
\(352\) | 2.26903e104 | 0.0472412 | ||||||||
\(353\) | −6.26064e104 | −0.115869 | −0.0579347 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579347 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(354\) | −1.22442e104 | −0.0201509 | ||||||||
\(355\) | 1.13776e106 | 1.66561 | ||||||||
\(356\) | 5.54060e105 | 0.721742 | ||||||||
\(357\) | −1.61065e103 | −0.00186754 | ||||||||
\(358\) | −7.03718e105 | −0.726529 | ||||||||
\(359\) | −1.70060e106 | −1.56380 | −0.781901 | − | 0.623403i | \(-0.785750\pi\) | ||||
−0.781901 | + | 0.623403i | \(0.785750\pi\) | |||||||
\(360\) | 6.93523e105 | 0.568208 | ||||||||
\(361\) | 1.39727e106 | 1.02031 | ||||||||
\(362\) | −1.98872e106 | −1.29470 | ||||||||
\(363\) | −5.88386e104 | −0.0341615 | ||||||||
\(364\) | 4.38556e103 | 0.00227153 | ||||||||
\(365\) | 1.55158e106 | 0.717167 | ||||||||
\(366\) | 1.66825e104 | 0.00688327 | ||||||||
\(367\) | 8.71124e105 | 0.320951 | 0.160475 | − | 0.987040i | \(-0.448697\pi\) | ||||
0.160475 | + | 0.987040i | \(0.448697\pi\) | |||||||
\(368\) | −7.37644e105 | −0.242752 | ||||||||
\(369\) | −1.34907e106 | −0.396681 | ||||||||
\(370\) | −6.47327e106 | −1.70119 | ||||||||
\(371\) | −3.34227e105 | −0.0785279 | ||||||||
\(372\) | 1.45920e105 | 0.0306607 | ||||||||
\(373\) | −5.98355e106 | −1.12471 | −0.562357 | − | 0.826895i | \(-0.690105\pi\) | ||||
−0.562357 | + | 0.826895i | \(0.690105\pi\) | |||||||
\(374\) | 7.66175e105 | 0.128871 | ||||||||
\(375\) | 2.31964e105 | 0.0349239 | ||||||||
\(376\) | 1.31370e106 | 0.177092 | ||||||||
\(377\) | 7.53149e105 | 0.0909316 | ||||||||
\(378\) | −3.57787e104 | −0.00387004 | ||||||||
\(379\) | 5.56014e106 | 0.538962 | 0.269481 | − | 0.963006i | \(-0.413148\pi\) | ||||
0.269481 | + | 0.963006i | \(0.413148\pi\) | |||||||
\(380\) | 1.31625e107 | 1.14372 | ||||||||
\(381\) | 8.13902e105 | 0.0634140 | ||||||||
\(382\) | −9.99764e104 | −0.00698664 | ||||||||
\(383\) | 2.06271e107 | 1.29327 | 0.646633 | − | 0.762801i | \(-0.276176\pi\) | ||||
0.646633 | + | 0.762801i | \(0.276176\pi\) | |||||||
\(384\) | −5.77905e104 | −0.00325170 | ||||||||
\(385\) | 6.33774e105 | 0.0320121 | ||||||||
\(386\) | −1.21244e107 | −0.549907 | ||||||||
\(387\) | 1.38827e107 | 0.565548 | ||||||||
\(388\) | 2.47073e107 | 0.904292 | ||||||||
\(389\) | −1.05577e107 | −0.347265 | −0.173633 | − | 0.984811i | \(-0.555550\pi\) | ||||
−0.173633 | + | 0.984811i | \(0.555550\pi\) | |||||||
\(390\) | 8.64155e104 | 0.00255511 | ||||||||
\(391\) | −2.49077e107 | −0.662214 | ||||||||
\(392\) | 1.47033e107 | 0.351594 | ||||||||
\(393\) | 1.23572e106 | 0.0265846 | ||||||||
\(394\) | 4.46481e107 | 0.864390 | ||||||||
\(395\) | −1.38827e108 | −2.41932 | ||||||||
\(396\) | 8.50408e106 | 0.133437 | ||||||||
\(397\) | −3.14955e107 | −0.445084 | −0.222542 | − | 0.974923i | \(-0.571436\pi\) | ||||
−0.222542 | + | 0.974923i | \(0.571436\pi\) | |||||||
\(398\) | −7.11397e107 | −0.905658 | ||||||||
\(399\) | −3.39296e105 | −0.00389227 | ||||||||
\(400\) | 3.84410e107 | 0.397471 | ||||||||
\(401\) | −5.76795e107 | −0.537688 | −0.268844 | − | 0.963184i | \(-0.586642\pi\) | ||||
−0.268844 | + | 0.963184i | \(0.586642\pi\) | |||||||
\(402\) | 2.78833e106 | 0.0234403 | ||||||||
\(403\) | −1.34161e107 | −0.101734 | ||||||||
\(404\) | −2.77422e107 | −0.189808 | ||||||||
\(405\) | 2.59572e108 | 1.60278 | ||||||||
\(406\) | −1.40682e107 | −0.0784168 | ||||||||
\(407\) | −7.93762e107 | −0.399505 | ||||||||
\(408\) | −1.95139e106 | −0.00887048 | ||||||||
\(409\) | −1.57211e107 | −0.0645604 | −0.0322802 | − | 0.999479i | \(-0.510277\pi\) | ||||
−0.0322802 | + | 0.999479i | \(0.510277\pi\) | |||||||
\(410\) | −1.21810e108 | −0.452017 | ||||||||
\(411\) | −5.78574e106 | −0.0194054 | ||||||||
\(412\) | 2.49475e108 | 0.756472 | ||||||||
\(413\) | −2.10280e107 | −0.0576595 | ||||||||
\(414\) | −2.76461e108 | −0.685676 | ||||||||
\(415\) | 7.98768e108 | 1.79236 | ||||||||
\(416\) | 5.31334e106 | 0.0107893 | ||||||||
\(417\) | 5.67203e106 | 0.0104254 | ||||||||
\(418\) | 1.61401e108 | 0.268590 | ||||||||
\(419\) | 3.50647e108 | 0.528431 | 0.264216 | − | 0.964464i | \(-0.414887\pi\) | ||||
0.264216 | + | 0.964464i | \(0.414887\pi\) | |||||||
\(420\) | −1.61417e106 | −0.00220346 | ||||||||
\(421\) | −3.11175e108 | −0.384855 | −0.192428 | − | 0.981311i | \(-0.561636\pi\) | ||||
−0.192428 | + | 0.981311i | \(0.561636\pi\) | |||||||
\(422\) | −9.56694e108 | −1.07228 | ||||||||
\(423\) | 4.92358e108 | 0.500214 | ||||||||
\(424\) | −4.04933e108 | −0.372993 | ||||||||
\(425\) | 1.29802e109 | 1.08428 | ||||||||
\(426\) | −3.55331e107 | −0.0269237 | ||||||||
\(427\) | 2.86503e107 | 0.0196957 | ||||||||
\(428\) | −8.11190e108 | −0.506065 | ||||||||
\(429\) | 1.05964e106 | 0.000600041 0 | ||||||||
\(430\) | 1.25350e109 | 0.644441 | ||||||||
\(431\) | −1.53223e109 | −0.715348 | −0.357674 | − | 0.933847i | \(-0.616430\pi\) | ||||
−0.357674 | + | 0.933847i | \(0.616430\pi\) | |||||||
\(432\) | −4.33478e107 | −0.0183820 | ||||||||
\(433\) | −3.51323e109 | −1.35350 | −0.676751 | − | 0.736212i | \(-0.736612\pi\) | ||||
−0.676751 | + | 0.736212i | \(0.736612\pi\) | |||||||
\(434\) | 2.50602e108 | 0.0877324 | ||||||||
\(435\) | −2.77208e108 | −0.0882067 | ||||||||
\(436\) | −3.61194e108 | −0.104484 | ||||||||
\(437\) | −5.24700e109 | −1.38017 | ||||||||
\(438\) | −4.84570e107 | −0.0115926 | ||||||||
\(439\) | −3.24144e109 | −0.705440 | −0.352720 | − | 0.935729i | \(-0.614743\pi\) | ||||
−0.352720 | + | 0.935729i | \(0.614743\pi\) | |||||||
\(440\) | 7.67851e108 | 0.152051 | ||||||||
\(441\) | 5.51062e109 | 0.993113 | ||||||||
\(442\) | 1.79413e108 | 0.0294327 | ||||||||
\(443\) | −6.20791e108 | −0.0927238 | −0.0463619 | − | 0.998925i | \(-0.514763\pi\) | ||||
−0.0463619 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(444\) | 2.02165e108 | 0.0274987 | ||||||||
\(445\) | 1.87496e110 | 2.32302 | ||||||||
\(446\) | 8.31509e109 | 0.938578 | ||||||||
\(447\) | −1.01593e108 | −0.0104497 | ||||||||
\(448\) | −9.92490e107 | −0.00930440 | ||||||||
\(449\) | −1.81811e110 | −1.55380 | −0.776902 | − | 0.629621i | \(-0.783210\pi\) | ||||
−0.776902 | + | 0.629621i | \(0.783210\pi\) | |||||||
\(450\) | 1.44073e110 | 1.12270 | ||||||||
\(451\) | −1.49366e109 | −0.106151 | ||||||||
\(452\) | −7.01511e109 | −0.454767 | ||||||||
\(453\) | 9.03967e108 | 0.0534660 | ||||||||
\(454\) | 1.85960e110 | 1.00369 | ||||||||
\(455\) | 1.48409e108 | 0.00731118 | ||||||||
\(456\) | −4.11075e108 | −0.0184876 | ||||||||
\(457\) | 2.29346e110 | 0.941823 | 0.470912 | − | 0.882180i | \(-0.343925\pi\) | ||||
0.470912 | + | 0.882180i | \(0.343925\pi\) | |||||||
\(458\) | −4.78280e109 | −0.179376 | ||||||||
\(459\) | −1.46371e109 | −0.0501450 | ||||||||
\(460\) | −2.49622e110 | −0.781326 | ||||||||
\(461\) | −5.17823e110 | −1.48113 | −0.740564 | − | 0.671986i | \(-0.765442\pi\) | ||||
−0.740564 | + | 0.671986i | \(0.765442\pi\) | |||||||
\(462\) | −1.97932e107 | −0.000517458 0 | ||||||||
\(463\) | −2.62604e110 | −0.627611 | −0.313806 | − | 0.949487i | \(-0.601604\pi\) | ||||
−0.313806 | + | 0.949487i | \(0.601604\pi\) | |||||||
\(464\) | −1.70444e110 | −0.372465 | ||||||||
\(465\) | 4.93799e109 | 0.0986854 | ||||||||
\(466\) | −6.34782e110 | −1.16040 | ||||||||
\(467\) | 2.46458e110 | 0.412186 | 0.206093 | − | 0.978532i | \(-0.433925\pi\) | ||||
0.206093 | + | 0.978532i | \(0.433925\pi\) | |||||||
\(468\) | 1.99138e109 | 0.0304755 | ||||||||
\(469\) | 4.78866e109 | 0.0670720 | ||||||||
\(470\) | 4.44560e110 | 0.569993 | ||||||||
\(471\) | 1.52683e108 | 0.00179235 | ||||||||
\(472\) | −2.54765e110 | −0.273872 | ||||||||
\(473\) | 1.53706e110 | 0.151340 | ||||||||
\(474\) | 4.33566e109 | 0.0391069 | ||||||||
\(475\) | 2.73438e111 | 2.25982 | ||||||||
\(476\) | −3.35130e109 | −0.0253819 | ||||||||
\(477\) | −1.51764e111 | −1.05356 | ||||||||
\(478\) | −7.87185e110 | −0.500979 | ||||||||
\(479\) | −3.32526e110 | −0.194045 | −0.0970224 | − | 0.995282i | \(-0.530932\pi\) | ||||
−0.0970224 | + | 0.995282i | \(0.530932\pi\) | |||||||
\(480\) | −1.95566e109 | −0.0104660 | ||||||||
\(481\) | −1.85873e110 | −0.0912423 | ||||||||
\(482\) | −1.93753e110 | −0.0872564 | ||||||||
\(483\) | 6.43462e108 | 0.00265899 | ||||||||
\(484\) | −1.22426e111 | −0.464292 | ||||||||
\(485\) | 8.36105e111 | 2.91057 | ||||||||
\(486\) | −2.43749e110 | −0.0779001 | ||||||||
\(487\) | −1.69478e110 | −0.0497349 | −0.0248675 | − | 0.999691i | \(-0.507916\pi\) | ||||
−0.0248675 | + | 0.999691i | \(0.507916\pi\) | |||||||
\(488\) | 3.47113e110 | 0.0935511 | ||||||||
\(489\) | −1.03061e110 | −0.0255140 | ||||||||
\(490\) | 4.97565e111 | 1.13165 | ||||||||
\(491\) | −7.99441e111 | −1.67072 | −0.835362 | − | 0.549701i | \(-0.814742\pi\) | ||||
−0.835362 | + | 0.549701i | \(0.814742\pi\) | |||||||
\(492\) | 3.80423e109 | 0.00730660 | ||||||||
\(493\) | −5.75531e111 | −1.01607 | ||||||||
\(494\) | 3.77948e110 | 0.0613428 | ||||||||
\(495\) | 2.87782e111 | 0.429484 | ||||||||
\(496\) | 3.03617e111 | 0.416713 | ||||||||
\(497\) | −6.10243e110 | −0.0770394 | ||||||||
\(498\) | −2.49461e110 | −0.0289725 | ||||||||
\(499\) | −1.04099e112 | −1.11243 | −0.556215 | − | 0.831038i | \(-0.687747\pi\) | ||||
−0.556215 | + | 0.831038i | \(0.687747\pi\) | |||||||
\(500\) | 4.82649e111 | 0.474653 | ||||||||
\(501\) | 7.24147e110 | 0.0655483 | ||||||||
\(502\) | −1.05013e112 | −0.875058 | ||||||||
\(503\) | −5.69049e111 | −0.436595 | −0.218297 | − | 0.975882i | \(-0.570050\pi\) | ||||
−0.218297 | + | 0.975882i | \(0.570050\pi\) | |||||||
\(504\) | −3.71974e110 | −0.0262812 | ||||||||
\(505\) | −9.38808e111 | −0.610921 | ||||||||
\(506\) | −3.06090e111 | −0.183486 | ||||||||
\(507\) | −6.63629e110 | −0.0366518 | ||||||||
\(508\) | 1.69349e112 | 0.861865 | ||||||||
\(509\) | −1.97206e112 | −0.924980 | −0.462490 | − | 0.886624i | \(-0.653044\pi\) | ||||
−0.462490 | + | 0.886624i | \(0.653044\pi\) | |||||||
\(510\) | −6.60358e110 | −0.0285507 | ||||||||
\(511\) | −8.32196e110 | −0.0331710 | ||||||||
\(512\) | −1.20245e111 | −0.0441942 | ||||||||
\(513\) | −3.08341e111 | −0.104511 | ||||||||
\(514\) | 2.92399e112 | 0.914127 | ||||||||
\(515\) | 8.44234e112 | 2.43480 | ||||||||
\(516\) | −3.91477e110 | −0.0104170 | ||||||||
\(517\) | 5.45127e111 | 0.133857 | ||||||||
\(518\) | 3.47197e111 | 0.0786847 | ||||||||
\(519\) | 1.41678e111 | 0.0296385 | ||||||||
\(520\) | 1.79806e111 | 0.0347268 | ||||||||
\(521\) | 5.86704e112 | 1.04629 | 0.523147 | − | 0.852242i | \(-0.324758\pi\) | ||||
0.523147 | + | 0.852242i | \(0.324758\pi\) | |||||||
\(522\) | −6.38805e112 | −1.05206 | ||||||||
\(523\) | −2.88574e112 | −0.438973 | −0.219486 | − | 0.975616i | \(-0.570438\pi\) | ||||
−0.219486 | + | 0.975616i | \(0.570438\pi\) | |||||||
\(524\) | 2.57118e112 | 0.361314 | ||||||||
\(525\) | −3.35329e110 | −0.00435371 | ||||||||
\(526\) | −5.11462e112 | −0.613628 | ||||||||
\(527\) | 1.02521e113 | 1.13677 | ||||||||
\(528\) | −2.39806e110 | −0.00245783 | ||||||||
\(529\) | −6.03102e111 | −0.0571453 | ||||||||
\(530\) | −1.37031e113 | −1.20052 | ||||||||
\(531\) | −9.54832e112 | −0.773578 | ||||||||
\(532\) | −7.05977e111 | −0.0529002 | ||||||||
\(533\) | −3.49766e111 | −0.0242437 | ||||||||
\(534\) | −5.85565e111 | −0.0375503 | ||||||||
\(535\) | −2.74510e113 | −1.62883 | ||||||||
\(536\) | 5.80172e112 | 0.318579 | ||||||||
\(537\) | 7.43733e111 | 0.0377993 | ||||||||
\(538\) | −5.13768e112 | −0.241715 | ||||||||
\(539\) | 6.10122e112 | 0.265756 | ||||||||
\(540\) | −1.46691e112 | −0.0591646 | ||||||||
\(541\) | 1.42376e113 | 0.531804 | 0.265902 | − | 0.964000i | \(-0.414330\pi\) | ||||
0.265902 | + | 0.964000i | \(0.414330\pi\) | |||||||
\(542\) | 7.23090e112 | 0.250162 | ||||||||
\(543\) | 2.10180e112 | 0.0673596 | ||||||||
\(544\) | −4.06027e112 | −0.120559 | ||||||||
\(545\) | −1.22230e113 | −0.336296 | ||||||||
\(546\) | −4.63493e109 | −0.000118181 0 | ||||||||
\(547\) | 8.30547e113 | 1.96286 | 0.981432 | − | 0.191812i | \(-0.0614364\pi\) | ||||
0.981432 | + | 0.191812i | \(0.0614364\pi\) | |||||||
\(548\) | −1.20384e113 | −0.263741 | ||||||||
\(549\) | 1.30094e113 | 0.264244 | ||||||||
\(550\) | 1.59514e113 | 0.300432 | ||||||||
\(551\) | −1.21240e114 | −2.11765 | ||||||||
\(552\) | 7.79588e111 | 0.0126297 | ||||||||
\(553\) | 7.44602e112 | 0.111900 | ||||||||
\(554\) | 7.75536e113 | 1.08130 | ||||||||
\(555\) | 6.84135e112 | 0.0885081 | ||||||||
\(556\) | 1.18018e113 | 0.141692 | ||||||||
\(557\) | 5.55034e111 | 0.00618485 | 0.00309242 | − | 0.999995i | \(-0.499016\pi\) | ||||
0.00309242 | + | 0.999995i | \(0.499016\pi\) | |||||||
\(558\) | 1.13792e114 | 1.17705 | ||||||||
\(559\) | 3.59929e112 | 0.0345642 | ||||||||
\(560\) | −3.35863e112 | −0.0299474 | ||||||||
\(561\) | −8.09741e111 | −0.00670483 | ||||||||
\(562\) | −2.11425e113 | −0.162592 | ||||||||
\(563\) | 8.02056e113 | 0.572937 | 0.286468 | − | 0.958090i | \(-0.407519\pi\) | ||||
0.286468 | + | 0.958090i | \(0.407519\pi\) | |||||||
\(564\) | −1.38840e112 | −0.00921362 | ||||||||
\(565\) | −2.37394e114 | −1.46372 | ||||||||
\(566\) | −4.48496e113 | −0.256966 | ||||||||
\(567\) | −1.39222e113 | −0.0741331 | ||||||||
\(568\) | −7.39342e113 | −0.365923 | ||||||||
\(569\) | −1.05698e114 | −0.486304 | −0.243152 | − | 0.969988i | \(-0.578181\pi\) | ||||
−0.243152 | + | 0.969988i | \(0.578181\pi\) | |||||||
\(570\) | −1.39109e113 | −0.0595046 | ||||||||
\(571\) | 2.88695e114 | 1.14826 | 0.574131 | − | 0.818763i | \(-0.305340\pi\) | ||||
0.574131 | + | 0.818763i | \(0.305340\pi\) | |||||||
\(572\) | 2.20480e112 | 0.00815520 | ||||||||
\(573\) | 1.05661e111 | 0.000363496 0 | ||||||||
\(574\) | 6.53336e112 | 0.0209071 | ||||||||
\(575\) | −5.18565e114 | −1.54379 | ||||||||
\(576\) | −4.50666e113 | −0.124831 | ||||||||
\(577\) | 1.02956e113 | 0.0265373 | 0.0132687 | − | 0.999912i | \(-0.495776\pi\) | ||||
0.0132687 | + | 0.999912i | \(0.495776\pi\) | |||||||
\(578\) | 1.57673e114 | 0.378227 | ||||||||
\(579\) | 1.28139e113 | 0.0286101 | ||||||||
\(580\) | −5.76790e114 | −1.19882 | ||||||||
\(581\) | −4.28423e113 | −0.0829016 | ||||||||
\(582\) | −2.61122e113 | −0.0470478 | ||||||||
\(583\) | −1.68030e114 | −0.281930 | ||||||||
\(584\) | −1.00825e114 | −0.157556 | ||||||||
\(585\) | 6.73891e113 | 0.0980892 | ||||||||
\(586\) | 3.28210e114 | 0.445042 | ||||||||
\(587\) | 1.38009e115 | 1.74352 | 0.871760 | − | 0.489934i | \(-0.162979\pi\) | ||||
0.871760 | + | 0.489934i | \(0.162979\pi\) | |||||||
\(588\) | −1.55393e113 | −0.0182925 | ||||||||
\(589\) | 2.15969e115 | 2.36922 | ||||||||
\(590\) | −8.62137e114 | −0.881490 | ||||||||
\(591\) | −4.71869e113 | −0.0449719 | ||||||||
\(592\) | 4.20647e114 | 0.373738 | ||||||||
\(593\) | 1.12438e115 | 0.931413 | 0.465706 | − | 0.884939i | \(-0.345800\pi\) | ||||
0.465706 | + | 0.884939i | \(0.345800\pi\) | |||||||
\(594\) | −1.79875e113 | −0.0138942 | ||||||||
\(595\) | −1.13409e114 | −0.0816948 | ||||||||
\(596\) | −2.11387e114 | −0.142023 | ||||||||
\(597\) | 7.51848e113 | 0.0471189 | ||||||||
\(598\) | −7.16763e113 | −0.0419060 | ||||||||
\(599\) | −2.67619e115 | −1.45983 | −0.729917 | − | 0.683536i | \(-0.760441\pi\) | ||||
−0.729917 | + | 0.683536i | \(0.760441\pi\) | |||||||
\(600\) | −4.06269e113 | −0.0206793 | ||||||||
\(601\) | −2.25935e115 | −1.07323 | −0.536616 | − | 0.843827i | \(-0.680297\pi\) | ||||
−0.536616 | + | 0.843827i | \(0.680297\pi\) | |||||||
\(602\) | −6.72319e113 | −0.0298072 | ||||||||
\(603\) | 2.17442e115 | 0.899859 | ||||||||
\(604\) | 1.88089e115 | 0.726660 | ||||||||
\(605\) | −4.14295e115 | −1.49438 | ||||||||
\(606\) | 2.93197e113 | 0.00987519 | ||||||||
\(607\) | −4.44447e114 | −0.139794 | −0.0698971 | − | 0.997554i | \(-0.522267\pi\) | ||||
−0.0698971 | + | 0.997554i | \(0.522267\pi\) | |||||||
\(608\) | −8.55328e114 | −0.251266 | ||||||||
\(609\) | 1.48682e113 | 0.00407981 | ||||||||
\(610\) | 1.17465e115 | 0.301106 | ||||||||
\(611\) | 1.27651e114 | 0.0305713 | ||||||||
\(612\) | −1.52174e115 | −0.340532 | ||||||||
\(613\) | −6.05295e115 | −1.26578 | −0.632889 | − | 0.774243i | \(-0.718131\pi\) | ||||
−0.632889 | + | 0.774243i | \(0.718131\pi\) | |||||||
\(614\) | −1.80446e115 | −0.352663 | ||||||||
\(615\) | 1.28737e114 | 0.0235172 | ||||||||
\(616\) | −4.11840e113 | −0.00703281 | ||||||||
\(617\) | −1.09654e115 | −0.175061 | −0.0875307 | − | 0.996162i | \(-0.527898\pi\) | ||||
−0.0875307 | + | 0.996162i | \(0.527898\pi\) | |||||||
\(618\) | −2.63661e114 | −0.0393572 | ||||||||
\(619\) | 5.85257e115 | 0.816930 | 0.408465 | − | 0.912774i | \(-0.366064\pi\) | ||||
0.408465 | + | 0.912774i | \(0.366064\pi\) | |||||||
\(620\) | 1.02745e116 | 1.34124 | ||||||||
\(621\) | 5.84757e114 | 0.0713961 | ||||||||
\(622\) | 1.16649e116 | 1.33223 | ||||||||
\(623\) | −1.00564e115 | −0.107446 | ||||||||
\(624\) | −5.61546e112 | −0.000561339 0 | ||||||||
\(625\) | −6.64486e114 | −0.0621534 | ||||||||
\(626\) | −7.80681e115 | −0.683343 | ||||||||
\(627\) | −1.70578e114 | −0.0139740 | ||||||||
\(628\) | 3.17690e114 | 0.0243600 | ||||||||
\(629\) | 1.42038e116 | 1.01954 | ||||||||
\(630\) | −1.25878e115 | −0.0845893 | ||||||||
\(631\) | −2.69928e116 | −1.69836 | −0.849178 | − | 0.528106i | \(-0.822902\pi\) | ||||
−0.849178 | + | 0.528106i | \(0.822902\pi\) | |||||||
\(632\) | 9.02125e115 | 0.531506 | ||||||||
\(633\) | 1.01109e115 | 0.0557876 | ||||||||
\(634\) | −2.21232e116 | −1.14325 | ||||||||
\(635\) | 5.73085e116 | 2.77402 | ||||||||
\(636\) | 4.27959e114 | 0.0194058 | ||||||||
\(637\) | 1.42871e115 | 0.0606955 | ||||||||
\(638\) | −7.07268e115 | −0.281531 | ||||||||
\(639\) | −2.77097e116 | −1.03358 | ||||||||
\(640\) | −4.06915e115 | −0.142244 | ||||||||
\(641\) | 9.11084e115 | 0.298504 | 0.149252 | − | 0.988799i | \(-0.452313\pi\) | ||||
0.149252 | + | 0.988799i | \(0.452313\pi\) | |||||||
\(642\) | 8.57316e114 | 0.0263292 | ||||||||
\(643\) | 2.19094e116 | 0.630775 | 0.315387 | − | 0.948963i | \(-0.397866\pi\) | ||||
0.315387 | + | 0.948963i | \(0.397866\pi\) | |||||||
\(644\) | 1.33886e115 | 0.0361386 | ||||||||
\(645\) | −1.32477e115 | −0.0335285 | ||||||||
\(646\) | −2.88815e116 | −0.685441 | ||||||||
\(647\) | −5.61397e116 | −1.24952 | −0.624759 | − | 0.780818i | \(-0.714803\pi\) | ||||
−0.624759 | + | 0.780818i | \(0.714803\pi\) | |||||||
\(648\) | −1.68675e116 | −0.352119 | ||||||||
\(649\) | −1.05717e116 | −0.207008 | ||||||||
\(650\) | 3.73529e115 | 0.0686151 | ||||||||
\(651\) | −2.64851e114 | −0.00456448 | ||||||||
\(652\) | −2.14441e116 | −0.346763 | ||||||||
\(653\) | −4.41466e116 | −0.669885 | −0.334943 | − | 0.942239i | \(-0.608717\pi\) | ||||
−0.334943 | + | 0.942239i | \(0.608717\pi\) | |||||||
\(654\) | 3.81732e114 | 0.00543603 | ||||||||
\(655\) | 8.70099e116 | 1.16293 | ||||||||
\(656\) | 7.91551e115 | 0.0993046 | ||||||||
\(657\) | −3.77881e116 | −0.445032 | ||||||||
\(658\) | −2.38442e115 | −0.0263638 | ||||||||
\(659\) | 4.14669e116 | 0.430484 | 0.215242 | − | 0.976561i | \(-0.430946\pi\) | ||||
0.215242 | + | 0.976561i | \(0.430946\pi\) | |||||||
\(660\) | −8.11512e114 | −0.00791082 | ||||||||
\(661\) | 2.72258e116 | 0.249241 | 0.124621 | − | 0.992204i | \(-0.460229\pi\) | ||||
0.124621 | + | 0.992204i | \(0.460229\pi\) | |||||||
\(662\) | −6.50226e116 | −0.559059 | ||||||||
\(663\) | −1.89615e114 | −0.00153130 | ||||||||
\(664\) | −5.19057e116 | −0.393767 | ||||||||
\(665\) | −2.38905e116 | −0.170266 | ||||||||
\(666\) | 1.57654e117 | 1.05566 | ||||||||
\(667\) | 2.29927e117 | 1.44666 | ||||||||
\(668\) | 1.50674e117 | 0.890872 | ||||||||
\(669\) | −8.78790e115 | −0.0488317 | ||||||||
\(670\) | 1.96332e117 | 1.02539 | ||||||||
\(671\) | 1.44037e116 | 0.0707114 | ||||||||
\(672\) | 1.04892e114 | 0.000484083 0 | ||||||||
\(673\) | −1.70946e117 | −0.741708 | −0.370854 | − | 0.928691i | \(-0.620935\pi\) | ||||
−0.370854 | + | 0.928691i | \(0.620935\pi\) | |||||||
\(674\) | 1.60290e117 | 0.653916 | ||||||||
\(675\) | −3.04736e116 | −0.116901 | ||||||||
\(676\) | −1.38082e117 | −0.498137 | ||||||||
\(677\) | −3.44694e117 | −1.16951 | −0.584755 | − | 0.811210i | \(-0.698809\pi\) | ||||
−0.584755 | + | 0.811210i | \(0.698809\pi\) | |||||||
\(678\) | 7.41400e115 | 0.0236603 | ||||||||
\(679\) | −4.48448e116 | −0.134622 | ||||||||
\(680\) | −1.37401e117 | −0.388035 | ||||||||
\(681\) | −1.96534e116 | −0.0522194 | ||||||||
\(682\) | 1.25988e117 | 0.314976 | ||||||||
\(683\) | −2.63833e116 | −0.0620684 | −0.0310342 | − | 0.999518i | \(-0.509880\pi\) | ||||
−0.0310342 | + | 0.999518i | \(0.509880\pi\) | |||||||
\(684\) | −3.20567e117 | −0.709726 | ||||||||
\(685\) | −4.07386e117 | −0.848882 | ||||||||
\(686\) | −5.35229e116 | −0.104976 | ||||||||
\(687\) | 5.05476e115 | 0.00933246 | ||||||||
\(688\) | −8.14550e116 | −0.141579 | ||||||||
\(689\) | −3.93471e116 | −0.0643894 | ||||||||
\(690\) | 2.63816e116 | 0.0406503 | ||||||||
\(691\) | −6.42856e117 | −0.932771 | −0.466385 | − | 0.884582i | \(-0.654444\pi\) | ||||
−0.466385 | + | 0.884582i | \(0.654444\pi\) | |||||||
\(692\) | 2.94791e117 | 0.402820 | ||||||||
\(693\) | −1.54353e116 | −0.0198649 | ||||||||
\(694\) | 4.07903e117 | 0.494468 | ||||||||
\(695\) | 3.99379e117 | 0.456054 | ||||||||
\(696\) | 1.80136e116 | 0.0193783 | ||||||||
\(697\) | 2.67280e117 | 0.270898 | ||||||||
\(698\) | −9.71520e117 | −0.927794 | ||||||||
\(699\) | 6.70877e116 | 0.0603726 | ||||||||
\(700\) | −6.97722e116 | −0.0591717 | ||||||||
\(701\) | 1.33757e118 | 1.06910 | 0.534551 | − | 0.845136i | \(-0.320481\pi\) | ||||
0.534551 | + | 0.845136i | \(0.320481\pi\) | |||||||
\(702\) | −4.21208e115 | −0.00317326 | ||||||||
\(703\) | 2.99214e118 | 2.12489 | ||||||||
\(704\) | −4.98966e116 | −0.0334045 | ||||||||
\(705\) | −4.69839e116 | −0.0296552 | ||||||||
\(706\) | 1.37673e117 | 0.0819320 | ||||||||
\(707\) | 5.03534e116 | 0.0282568 | ||||||||
\(708\) | 2.69252e116 | 0.0142488 | ||||||||
\(709\) | −8.81862e117 | −0.440131 | −0.220066 | − | 0.975485i | \(-0.570627\pi\) | ||||
−0.220066 | + | 0.975485i | \(0.570627\pi\) | |||||||
\(710\) | −2.50196e118 | −1.17777 | ||||||||
\(711\) | 3.38106e118 | 1.50129 | ||||||||
\(712\) | −1.21839e118 | −0.510349 | ||||||||
\(713\) | −4.09576e118 | −1.61852 | ||||||||
\(714\) | 3.54186e115 | 0.00132055 | ||||||||
\(715\) | 7.46115e116 | 0.0262485 | ||||||||
\(716\) | 1.54749e118 | 0.513734 | ||||||||
\(717\) | 8.31946e116 | 0.0260646 | ||||||||
\(718\) | 3.73965e118 | 1.10577 | ||||||||
\(719\) | 3.27970e118 | 0.915346 | 0.457673 | − | 0.889121i | \(-0.348683\pi\) | ||||
0.457673 | + | 0.889121i | \(0.348683\pi\) | |||||||
\(720\) | −1.52507e118 | −0.401783 | ||||||||
\(721\) | −4.52809e117 | −0.112616 | ||||||||
\(722\) | −3.07264e118 | −0.721469 | ||||||||
\(723\) | 2.04771e116 | 0.00453971 | ||||||||
\(724\) | 4.37325e118 | 0.915490 | ||||||||
\(725\) | −1.19822e119 | −2.36870 | ||||||||
\(726\) | 1.29387e117 | 0.0241559 | ||||||||
\(727\) | 5.04131e118 | 0.888925 | 0.444462 | − | 0.895797i | \(-0.353395\pi\) | ||||
0.444462 | + | 0.895797i | \(0.353395\pi\) | |||||||
\(728\) | −9.64395e115 | −0.00160621 | ||||||||
\(729\) | −6.30457e118 | −0.991889 | ||||||||
\(730\) | −3.41196e118 | −0.507113 | ||||||||
\(731\) | −2.75046e118 | −0.386219 | ||||||||
\(732\) | −3.66851e116 | −0.00486721 | ||||||||
\(733\) | −1.38378e118 | −0.173481 | −0.0867406 | − | 0.996231i | \(-0.527645\pi\) | ||||
−0.0867406 | + | 0.996231i | \(0.527645\pi\) | |||||||
\(734\) | −1.91562e118 | −0.226946 | ||||||||
\(735\) | −5.25857e117 | −0.0588767 | ||||||||
\(736\) | 1.62210e118 | 0.171651 | ||||||||
\(737\) | 2.40746e118 | 0.240801 | ||||||||
\(738\) | 2.96664e118 | 0.280496 | ||||||||
\(739\) | −2.74550e117 | −0.0245401 | −0.0122701 | − | 0.999925i | \(-0.503906\pi\) | ||||
−0.0122701 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(740\) | 1.42349e119 | 1.20292 | ||||||||
\(741\) | −3.99438e116 | −0.00319150 | ||||||||
\(742\) | 7.34972e117 | 0.0555276 | ||||||||
\(743\) | 6.63096e118 | 0.473741 | 0.236870 | − | 0.971541i | \(-0.423878\pi\) | ||||
0.236870 | + | 0.971541i | \(0.423878\pi\) | |||||||
\(744\) | −3.20881e117 | −0.0216804 | ||||||||
\(745\) | −7.15341e118 | −0.457117 | ||||||||
\(746\) | 1.31580e119 | 0.795293 | ||||||||
\(747\) | −1.94537e119 | −1.11223 | ||||||||
\(748\) | −1.68484e118 | −0.0911258 | ||||||||
\(749\) | 1.47235e118 | 0.0753381 | ||||||||
\(750\) | −5.10094e117 | −0.0246949 | ||||||||
\(751\) | 3.75216e119 | 1.71879 | 0.859397 | − | 0.511309i | \(-0.170839\pi\) | ||||
0.859397 | + | 0.511309i | \(0.170839\pi\) | |||||||
\(752\) | −2.88885e118 | −0.125223 | ||||||||
\(753\) | 1.10984e118 | 0.0455269 | ||||||||
\(754\) | −1.65619e118 | −0.0642983 | ||||||||
\(755\) | 6.36502e119 | 2.33885 | ||||||||
\(756\) | 7.86783e116 | 0.00273653 | ||||||||
\(757\) | −1.85616e118 | −0.0611135 | −0.0305567 | − | 0.999533i | \(-0.509728\pi\) | ||||
−0.0305567 | + | 0.999533i | \(0.509728\pi\) | |||||||
\(758\) | −1.22269e119 | −0.381104 | ||||||||
\(759\) | 3.23495e117 | 0.00954627 | ||||||||
\(760\) | −2.89447e119 | −0.808731 | ||||||||
\(761\) | −6.09820e119 | −1.61339 | −0.806693 | − | 0.590971i | \(-0.798745\pi\) | ||||
−0.806693 | + | 0.590971i | \(0.798745\pi\) | |||||||
\(762\) | −1.78979e118 | −0.0448405 | ||||||||
\(763\) | 6.55583e117 | 0.0155546 | ||||||||
\(764\) | 2.19851e117 | 0.00494030 | ||||||||
\(765\) | −5.14965e119 | −1.09604 | ||||||||
\(766\) | −4.53594e119 | −0.914477 | ||||||||
\(767\) | −2.47554e118 | −0.0472783 | ||||||||
\(768\) | 1.27083e117 | 0.00229930 | ||||||||
\(769\) | −2.58891e119 | −0.443787 | −0.221893 | − | 0.975071i | \(-0.571224\pi\) | ||||
−0.221893 | + | 0.975071i | \(0.571224\pi\) | |||||||
\(770\) | −1.39368e118 | −0.0226360 | ||||||||
\(771\) | −3.09025e118 | −0.0475595 | ||||||||
\(772\) | 2.66619e119 | 0.388843 | ||||||||
\(773\) | −7.57770e119 | −1.04734 | −0.523671 | − | 0.851921i | \(-0.675438\pi\) | ||||
−0.523671 | + | 0.851921i | \(0.675438\pi\) | |||||||
\(774\) | −3.05284e119 | −0.399903 | ||||||||
\(775\) | 2.13443e120 | 2.65010 | ||||||||
\(776\) | −5.43319e119 | −0.639431 | ||||||||
\(777\) | −3.66939e117 | −0.00409375 | ||||||||
\(778\) | 2.32166e119 | 0.245553 | ||||||||
\(779\) | 5.63045e119 | 0.564597 | ||||||||
\(780\) | −1.90030e117 | −0.00180674 | ||||||||
\(781\) | −3.06795e119 | −0.276586 | ||||||||
\(782\) | 5.47726e119 | 0.468256 | ||||||||
\(783\) | 1.35117e119 | 0.109546 | ||||||||
\(784\) | −3.23328e119 | −0.248615 | ||||||||
\(785\) | 1.07508e119 | 0.0784058 | ||||||||
\(786\) | −2.71739e118 | −0.0187982 | ||||||||
\(787\) | 9.41181e119 | 0.617620 | 0.308810 | − | 0.951124i | \(-0.400069\pi\) | ||||
0.308810 | + | 0.951124i | \(0.400069\pi\) | |||||||
\(788\) | −9.81822e119 | −0.611216 | ||||||||
\(789\) | 5.40545e118 | 0.0319254 | ||||||||
\(790\) | 3.05283e120 | 1.71072 | ||||||||
\(791\) | 1.27327e119 | 0.0677014 | ||||||||
\(792\) | −1.87007e119 | −0.0943544 | ||||||||
\(793\) | 3.37288e118 | 0.0161496 | ||||||||
\(794\) | 6.92593e119 | 0.314722 | ||||||||
\(795\) | 1.44823e119 | 0.0624599 | ||||||||
\(796\) | 1.56438e120 | 0.640397 | ||||||||
\(797\) | −2.87243e120 | −1.11617 | −0.558083 | − | 0.829785i | \(-0.688463\pi\) | ||||
−0.558083 | + | 0.829785i | \(0.688463\pi\) | |||||||
\(798\) | 7.46120e117 | 0.00275225 | ||||||||
\(799\) | −9.75465e119 | −0.341602 | ||||||||
\(800\) | −8.45327e119 | −0.281054 | ||||||||
\(801\) | −4.56639e120 | −1.44153 | ||||||||
\(802\) | 1.26839e120 | 0.380203 | ||||||||
\(803\) | −4.18380e119 | −0.119090 | ||||||||
\(804\) | −6.13161e118 | −0.0165748 | ||||||||
\(805\) | 4.53075e119 | 0.116316 | ||||||||
\(806\) | 2.95022e119 | 0.0719368 | ||||||||
\(807\) | 5.42982e118 | 0.0125757 | ||||||||
\(808\) | 6.10058e119 | 0.134215 | ||||||||
\(809\) | 1.38339e119 | 0.0289122 | 0.0144561 | − | 0.999896i | \(-0.495398\pi\) | ||||
0.0144561 | + | 0.999896i | \(0.495398\pi\) | |||||||
\(810\) | −5.70804e120 | −1.13334 | ||||||||
\(811\) | 6.68106e120 | 1.26032 | 0.630159 | − | 0.776466i | \(-0.282990\pi\) | ||||
0.630159 | + | 0.776466i | \(0.282990\pi\) | |||||||
\(812\) | 3.09364e119 | 0.0554490 | ||||||||
\(813\) | −7.64207e118 | −0.0130153 | ||||||||
\(814\) | 1.74550e120 | 0.282493 | ||||||||
\(815\) | −7.25677e120 | −1.11610 | ||||||||
\(816\) | 4.29115e118 | 0.00627237 | ||||||||
\(817\) | −5.79405e120 | −0.804946 | ||||||||
\(818\) | 3.45711e119 | 0.0456511 | ||||||||
\(819\) | −3.61444e118 | −0.00453690 | ||||||||
\(820\) | 2.67864e120 | 0.319624 | ||||||||
\(821\) | −7.61545e120 | −0.863883 | −0.431941 | − | 0.901902i | \(-0.642171\pi\) | ||||
−0.431941 | + | 0.901902i | \(0.642171\pi\) | |||||||
\(822\) | 1.27230e119 | 0.0137217 | ||||||||
\(823\) | 6.60553e120 | 0.677352 | 0.338676 | − | 0.940903i | \(-0.390021\pi\) | ||||
0.338676 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(824\) | −5.48602e120 | −0.534907 | ||||||||
\(825\) | −1.68584e119 | −0.0156306 | ||||||||
\(826\) | 4.62411e119 | 0.0407714 | ||||||||
\(827\) | 1.93219e121 | 1.62021 | 0.810106 | − | 0.586283i | \(-0.199409\pi\) | ||||
0.810106 | + | 0.586283i | \(0.199409\pi\) | |||||||
\(828\) | 6.07943e120 | 0.484846 | ||||||||
\(829\) | 1.50158e121 | 1.13903 | 0.569514 | − | 0.821981i | \(-0.307131\pi\) | ||||
0.569514 | + | 0.821981i | \(0.307131\pi\) | |||||||
\(830\) | −1.75651e121 | −1.26739 | ||||||||
\(831\) | −8.19634e119 | −0.0562571 | ||||||||
\(832\) | −1.16842e119 | −0.00762920 | ||||||||
\(833\) | −1.09177e121 | −0.678208 | ||||||||
\(834\) | −1.24729e119 | −0.00737186 | ||||||||
\(835\) | 5.09887e121 | 2.86738 | ||||||||
\(836\) | −3.54924e120 | −0.189922 | ||||||||
\(837\) | −2.40688e120 | −0.122560 | ||||||||
\(838\) | −7.71081e120 | −0.373657 | ||||||||
\(839\) | −2.01927e121 | −0.931265 | −0.465632 | − | 0.884978i | \(-0.654173\pi\) | ||||
−0.465632 | + | 0.884978i | \(0.654173\pi\) | |||||||
\(840\) | 3.54960e118 | 0.00155808 | ||||||||
\(841\) | 2.91932e121 | 1.21968 | ||||||||
\(842\) | 6.84280e120 | 0.272134 | ||||||||
\(843\) | 2.23447e119 | 0.00845924 | ||||||||
\(844\) | 2.10379e121 | 0.758213 | ||||||||
\(845\) | −4.67275e121 | −1.60332 | ||||||||
\(846\) | −1.08271e121 | −0.353705 | ||||||||
\(847\) | 2.22209e120 | 0.0691194 | ||||||||
\(848\) | 8.90458e120 | 0.263746 | ||||||||
\(849\) | 4.73998e119 | 0.0133693 | ||||||||
\(850\) | −2.85438e121 | −0.766702 | ||||||||
\(851\) | −5.67448e121 | −1.45161 | ||||||||
\(852\) | 7.81382e119 | 0.0190380 | ||||||||
\(853\) | 3.30995e121 | 0.768134 | 0.384067 | − | 0.923305i | \(-0.374523\pi\) | ||||
0.384067 | + | 0.923305i | \(0.374523\pi\) | |||||||
\(854\) | −6.30027e119 | −0.0139270 | ||||||||
\(855\) | −1.08481e122 | −2.28434 | ||||||||
\(856\) | 1.78383e121 | 0.357842 | ||||||||
\(857\) | −1.50953e121 | −0.288495 | −0.144248 | − | 0.989542i | \(-0.546076\pi\) | ||||
−0.144248 | + | 0.989542i | \(0.546076\pi\) | |||||||
\(858\) | −2.33017e118 | −0.000424293 0 | ||||||||
\(859\) | −1.83940e121 | −0.319125 | −0.159562 | − | 0.987188i | \(-0.551008\pi\) | ||||
−0.159562 | + | 0.987188i | \(0.551008\pi\) | |||||||
\(860\) | −2.75647e121 | −0.455688 | ||||||||
\(861\) | −6.90486e118 | −0.00108774 | ||||||||
\(862\) | 3.36941e121 | 0.505827 | ||||||||
\(863\) | 4.65398e121 | 0.665851 | 0.332925 | − | 0.942953i | \(-0.391964\pi\) | ||||
0.332925 | + | 0.942953i | \(0.391964\pi\) | |||||||
\(864\) | 9.53229e119 | 0.0129980 | ||||||||
\(865\) | 9.97583e121 | 1.29652 | ||||||||
\(866\) | 7.72567e121 | 0.957070 | ||||||||
\(867\) | −1.66639e120 | −0.0196781 | ||||||||
\(868\) | −5.51079e120 | −0.0620362 | ||||||||
\(869\) | 3.74343e121 | 0.401743 | ||||||||
\(870\) | 6.09587e120 | 0.0623716 | ||||||||
\(871\) | 5.63748e120 | 0.0549961 | ||||||||
\(872\) | 7.94274e120 | 0.0738816 | ||||||||
\(873\) | −2.03630e122 | −1.80614 | ||||||||
\(874\) | 1.15383e122 | 0.975925 | ||||||||
\(875\) | −8.76030e120 | −0.0706618 | ||||||||
\(876\) | 1.06558e120 | 0.00819721 | ||||||||
\(877\) | 1.51593e122 | 1.11223 | 0.556116 | − | 0.831105i | \(-0.312291\pi\) | ||||
0.556116 | + | 0.831105i | \(0.312291\pi\) | |||||||
\(878\) | 7.12800e121 | 0.498822 | ||||||||
\(879\) | −3.46873e120 | −0.0231543 | ||||||||
\(880\) | −1.68852e121 | −0.107517 | ||||||||
\(881\) | 1.43440e122 | 0.871302 | 0.435651 | − | 0.900116i | \(-0.356518\pi\) | ||||
0.435651 | + | 0.900116i | \(0.356518\pi\) | |||||||
\(882\) | −1.21180e122 | −0.702237 | ||||||||
\(883\) | 4.67996e121 | 0.258746 | 0.129373 | − | 0.991596i | \(-0.458704\pi\) | ||||
0.129373 | + | 0.991596i | \(0.458704\pi\) | |||||||
\(884\) | −3.94534e120 | −0.0208121 | ||||||||
\(885\) | 9.11159e120 | 0.0458615 | ||||||||
\(886\) | 1.36513e121 | 0.0655656 | ||||||||
\(887\) | −9.39454e121 | −0.430572 | −0.215286 | − | 0.976551i | \(-0.569068\pi\) | ||||
−0.215286 | + | 0.976551i | \(0.569068\pi\) | |||||||
\(888\) | −4.44566e120 | −0.0194445 | ||||||||
\(889\) | −3.07377e121 | −0.128306 | ||||||||
\(890\) | −4.12309e122 | −1.64262 | ||||||||
\(891\) | −6.99929e121 | −0.266152 | ||||||||
\(892\) | −1.82851e122 | −0.663675 | ||||||||
\(893\) | −2.05489e122 | −0.711956 | ||||||||
\(894\) | 2.23406e120 | 0.00738905 | ||||||||
\(895\) | 5.23678e122 | 1.65352 | ||||||||
\(896\) | 2.18251e120 | 0.00657921 | ||||||||
\(897\) | 7.57520e119 | 0.00218026 | ||||||||
\(898\) | 3.99806e122 | 1.09871 | ||||||||
\(899\) | −9.46389e122 | −2.48337 | ||||||||
\(900\) | −3.16819e122 | −0.793866 | ||||||||
\(901\) | 3.00677e122 | 0.719484 | ||||||||
\(902\) | 3.28459e121 | 0.0750603 | ||||||||
\(903\) | 7.10549e119 | 0.00155079 | ||||||||
\(904\) | 1.54264e122 | 0.321569 | ||||||||
\(905\) | 1.47992e123 | 2.94662 | ||||||||
\(906\) | −1.98785e121 | −0.0378061 | ||||||||
\(907\) | −9.48577e122 | −1.72334 | −0.861668 | − | 0.507472i | \(-0.830580\pi\) | ||||
−0.861668 | + | 0.507472i | \(0.830580\pi\) | |||||||
\(908\) | −4.08930e122 | −0.709719 | ||||||||
\(909\) | 2.28643e122 | 0.379102 | ||||||||
\(910\) | −3.26355e120 | −0.00516979 | ||||||||
\(911\) | −2.38567e122 | −0.361075 | −0.180538 | − | 0.983568i | \(-0.557784\pi\) | ||||
−0.180538 | + | 0.983568i | \(0.557784\pi\) | |||||||
\(912\) | 9.03963e120 | 0.0130727 | ||||||||
\(913\) | −2.15386e122 | −0.297632 | ||||||||
\(914\) | −5.04338e122 | −0.665970 | ||||||||
\(915\) | −1.24144e121 | −0.0156657 | ||||||||
\(916\) | 1.05175e122 | 0.126838 | ||||||||
\(917\) | −4.66682e121 | −0.0537890 | ||||||||
\(918\) | 3.21873e121 | 0.0354579 | ||||||||
\(919\) | 1.14552e123 | 1.20617 | 0.603087 | − | 0.797675i | \(-0.293937\pi\) | ||||
0.603087 | + | 0.797675i | \(0.293937\pi\) | |||||||
\(920\) | 5.48924e122 | 0.552481 | ||||||||
\(921\) | 1.90706e121 | 0.0183481 | ||||||||
\(922\) | 1.13870e123 | 1.04732 | ||||||||
\(923\) | −7.18413e121 | −0.0631689 | ||||||||
\(924\) | 4.35258e119 | 0.000365898 0 | ||||||||
\(925\) | 2.95716e123 | 2.37680 | ||||||||
\(926\) | 5.77473e122 | 0.443788 | ||||||||
\(927\) | −2.05610e123 | −1.51090 | ||||||||
\(928\) | 3.74810e122 | 0.263373 | ||||||||
\(929\) | −1.53091e123 | −1.02872 | −0.514360 | − | 0.857575i | \(-0.671970\pi\) | ||||
−0.514360 | + | 0.857575i | \(0.671970\pi\) | |||||||
\(930\) | −1.08588e122 | −0.0697811 | ||||||||
\(931\) | −2.29989e123 | −1.41350 | ||||||||
\(932\) | 1.39590e123 | 0.820529 | ||||||||
\(933\) | −1.23282e122 | −0.0693122 | ||||||||
\(934\) | −5.41968e122 | −0.291459 | ||||||||
\(935\) | −5.70156e122 | −0.293300 | ||||||||
\(936\) | −4.37909e121 | −0.0215494 | ||||||||
\(937\) | 1.70966e123 | 0.804853 | 0.402427 | − | 0.915452i | \(-0.368167\pi\) | ||||
0.402427 | + | 0.915452i | \(0.368167\pi\) | |||||||
\(938\) | −1.05304e122 | −0.0474270 | ||||||||
\(939\) | 8.25072e121 | 0.0355525 | ||||||||
\(940\) | −9.77598e122 | −0.403046 | ||||||||
\(941\) | −3.30239e123 | −1.30274 | −0.651371 | − | 0.758759i | \(-0.725806\pi\) | ||||
−0.651371 | + | 0.758759i | \(0.725806\pi\) | |||||||
\(942\) | −3.35754e120 | −0.00126739 | ||||||||
\(943\) | −1.06779e123 | −0.385702 | ||||||||
\(944\) | 5.60235e122 | 0.193657 | ||||||||
\(945\) | 2.66251e121 | 0.00880786 | ||||||||
\(946\) | −3.38003e122 | −0.107013 | ||||||||
\(947\) | −1.72331e122 | −0.0522204 | −0.0261102 | − | 0.999659i | \(-0.508312\pi\) | ||||
−0.0261102 | + | 0.999659i | \(0.508312\pi\) | |||||||
\(948\) | −9.53421e121 | −0.0276528 | ||||||||
\(949\) | −9.79708e121 | −0.0271988 | ||||||||
\(950\) | −6.01297e123 | −1.59794 | ||||||||
\(951\) | 2.33811e122 | 0.0594804 | ||||||||
\(952\) | 7.36958e121 | 0.0179477 | ||||||||
\(953\) | −1.68275e123 | −0.392341 | −0.196171 | − | 0.980570i | \(-0.562851\pi\) | ||||
−0.196171 | + | 0.980570i | \(0.562851\pi\) | |||||||
\(954\) | 3.33733e123 | 0.744976 | ||||||||
\(955\) | 7.43983e121 | 0.0159010 | ||||||||
\(956\) | 1.73104e123 | 0.354245 | ||||||||
\(957\) | 7.47485e121 | 0.0146473 | ||||||||
\(958\) | 7.31233e122 | 0.137210 | ||||||||
\(959\) | 2.18503e122 | 0.0392632 | ||||||||
\(960\) | 4.30053e121 | 0.00740059 | ||||||||
\(961\) | 1.07907e124 | 1.77839 | ||||||||
\(962\) | 4.08739e122 | 0.0645180 | ||||||||
\(963\) | 6.68558e123 | 1.01076 | ||||||||
\(964\) | 4.26068e122 | 0.0616996 | ||||||||
\(965\) | 9.02251e123 | 1.25154 | ||||||||
\(966\) | −1.41499e121 | −0.00188019 | ||||||||
\(967\) | 4.62260e123 | 0.588420 | 0.294210 | − | 0.955741i | \(-0.404943\pi\) | ||||
0.294210 | + | 0.955741i | \(0.404943\pi\) | |||||||
\(968\) | 2.69218e123 | 0.328304 | ||||||||
\(969\) | 3.05237e122 | 0.0356616 | ||||||||
\(970\) | −1.83861e124 | −2.05809 | ||||||||
\(971\) | −6.67325e123 | −0.715714 | −0.357857 | − | 0.933776i | \(-0.616492\pi\) | ||||
−0.357857 | + | 0.933776i | \(0.616492\pi\) | |||||||
\(972\) | 5.36010e122 | 0.0550837 | ||||||||
\(973\) | −2.14209e122 | −0.0210938 | ||||||||
\(974\) | 3.72686e122 | 0.0351679 | ||||||||
\(975\) | −3.94768e121 | −0.00356985 | ||||||||
\(976\) | −7.63311e122 | −0.0661506 | ||||||||
\(977\) | 4.91524e123 | 0.408244 | 0.204122 | − | 0.978945i | \(-0.434566\pi\) | ||||
0.204122 | + | 0.978945i | \(0.434566\pi\) | |||||||
\(978\) | 2.26635e122 | 0.0180411 | ||||||||
\(979\) | −5.05579e123 | −0.385752 | ||||||||
\(980\) | −1.09416e124 | −0.800198 | ||||||||
\(981\) | 2.97685e123 | 0.208686 | ||||||||
\(982\) | 1.75799e124 | 1.18138 | ||||||||
\(983\) | −1.36236e124 | −0.877646 | −0.438823 | − | 0.898573i | \(-0.644605\pi\) | ||||
−0.438823 | + | 0.898573i | \(0.644605\pi\) | |||||||
\(984\) | −8.36560e121 | −0.00516655 | ||||||||
\(985\) | −3.32253e124 | −1.96728 | ||||||||
\(986\) | 1.26561e124 | 0.718467 | ||||||||
\(987\) | 2.52000e121 | 0.00137164 | ||||||||
\(988\) | −8.31116e122 | −0.0433759 | ||||||||
\(989\) | 1.09882e124 | 0.549895 | ||||||||
\(990\) | −6.32839e123 | −0.303691 | ||||||||
\(991\) | −2.74505e124 | −1.26326 | −0.631632 | − | 0.775268i | \(-0.717615\pi\) | ||||
−0.631632 | + | 0.775268i | \(0.717615\pi\) | |||||||
\(992\) | −6.67661e123 | −0.294660 | ||||||||
\(993\) | 6.87199e122 | 0.0290863 | ||||||||
\(994\) | 1.34194e123 | 0.0544751 | ||||||||
\(995\) | 5.29392e124 | 2.06120 | ||||||||
\(996\) | 5.48571e122 | 0.0204866 | ||||||||
\(997\) | −4.86577e124 | −1.74302 | −0.871511 | − | 0.490376i | \(-0.836859\pi\) | ||||
−0.871511 | + | 0.490376i | \(0.836859\pi\) | |||||||
\(998\) | 2.28915e124 | 0.786607 | ||||||||
\(999\) | −3.33462e123 | −0.109921 |
(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 | 2.84.a.a.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.84.a.a.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial |