Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,14,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(3.21692786856\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1969}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 492 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(22.6867\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −160.120 | −1.76910 | −0.884548 | − | 0.466450i | \(-0.845533\pi\) | ||||
−0.884548 | + | 0.466450i | \(0.845533\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 17446.5 | 2.12970 | ||||||||
\(5\) | 3318.61 | 0.0949841 | 0.0474921 | − | 0.998872i | \(-0.484877\pi\) | ||||
0.0474921 | + | 0.998872i | \(0.484877\pi\) | |||||||
\(6\) | −116728. | −1.02139 | ||||||||
\(7\) | 449560. | 1.44428 | 0.722138 | − | 0.691749i | \(-0.243160\pi\) | ||||
0.722138 | + | 0.691749i | \(0.243160\pi\) | |||||||
\(8\) | −1.48183e6 | −1.99855 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −531376. | −0.168036 | ||||||||
\(11\) | 5.20947e6 | 0.886627 | 0.443314 | − | 0.896367i | \(-0.353803\pi\) | ||||
0.443314 | + | 0.896367i | \(0.353803\pi\) | |||||||
\(12\) | 1.27185e7 | 1.22958 | ||||||||
\(13\) | −3.19535e6 | −0.183606 | −0.0918030 | − | 0.995777i | \(-0.529263\pi\) | ||||
−0.0918030 | + | 0.995777i | \(0.529263\pi\) | |||||||
\(14\) | −7.19836e7 | −2.55506 | ||||||||
\(15\) | 2.41927e6 | 0.0548391 | ||||||||
\(16\) | 9.43496e7 | 1.40592 | ||||||||
\(17\) | 3.22068e7 | 0.323616 | 0.161808 | − | 0.986822i | \(-0.448267\pi\) | ||||
0.161808 | + | 0.986822i | \(0.448267\pi\) | |||||||
\(18\) | −8.50945e7 | −0.589699 | ||||||||
\(19\) | 2.60127e7 | 0.126849 | 0.0634244 | − | 0.997987i | \(-0.479798\pi\) | ||||
0.0634244 | + | 0.997987i | \(0.479798\pi\) | |||||||
\(20\) | 5.78981e7 | 0.202288 | ||||||||
\(21\) | 3.27729e8 | 0.833853 | ||||||||
\(22\) | −8.34142e8 | −1.56853 | ||||||||
\(23\) | 9.21991e8 | 1.29866 | 0.649330 | − | 0.760507i | \(-0.275049\pi\) | ||||
0.649330 | + | 0.760507i | \(0.275049\pi\) | |||||||
\(24\) | −1.08026e9 | −1.15386 | ||||||||
\(25\) | −1.20969e9 | −0.990978 | ||||||||
\(26\) | 5.11640e8 | 0.324816 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 7.84324e9 | 3.07587 | ||||||||
\(29\) | −3.17741e9 | −0.991942 | −0.495971 | − | 0.868339i | \(-0.665188\pi\) | ||||
−0.495971 | + | 0.868339i | \(0.665188\pi\) | |||||||
\(30\) | −3.87373e8 | −0.0970156 | ||||||||
\(31\) | −7.65586e9 | −1.54933 | −0.774663 | − | 0.632374i | \(-0.782081\pi\) | ||||
−0.774663 | + | 0.632374i | \(0.782081\pi\) | |||||||
\(32\) | −2.96811e9 | −0.488659 | ||||||||
\(33\) | 3.79770e9 | 0.511894 | ||||||||
\(34\) | −5.15697e9 | −0.572508 | ||||||||
\(35\) | 1.49191e9 | 0.137183 | ||||||||
\(36\) | 9.27178e9 | 0.709900 | ||||||||
\(37\) | 1.60133e10 | 1.02605 | 0.513026 | − | 0.858373i | \(-0.328525\pi\) | ||||
0.513026 | + | 0.858373i | \(0.328525\pi\) | |||||||
\(38\) | −4.16515e9 | −0.224408 | ||||||||
\(39\) | −2.32941e9 | −0.106005 | ||||||||
\(40\) | −4.91762e9 | −0.189830 | ||||||||
\(41\) | −5.42402e9 | −0.178331 | −0.0891653 | − | 0.996017i | \(-0.528420\pi\) | ||||
−0.0891653 | + | 0.996017i | \(0.528420\pi\) | |||||||
\(42\) | −5.24760e10 | −1.47517 | ||||||||
\(43\) | 3.58248e10 | 0.864250 | 0.432125 | − | 0.901814i | \(-0.357764\pi\) | ||||
0.432125 | + | 0.901814i | \(0.357764\pi\) | |||||||
\(44\) | 9.08870e10 | 1.88825 | ||||||||
\(45\) | 1.76364e9 | 0.0316614 | ||||||||
\(46\) | −1.47629e11 | −2.29745 | ||||||||
\(47\) | −1.26460e11 | −1.71127 | −0.855633 | − | 0.517582i | \(-0.826832\pi\) | ||||
−0.855633 | + | 0.517582i | \(0.826832\pi\) | |||||||
\(48\) | 6.87809e10 | 0.811707 | ||||||||
\(49\) | 1.05215e11 | 1.08593 | ||||||||
\(50\) | 1.93696e11 | 1.75313 | ||||||||
\(51\) | 2.34788e10 | 0.186840 | ||||||||
\(52\) | −5.57477e10 | −0.391025 | ||||||||
\(53\) | 6.08596e10 | 0.377169 | 0.188585 | − | 0.982057i | \(-0.439610\pi\) | ||||
0.188585 | + | 0.982057i | \(0.439610\pi\) | |||||||
\(54\) | −6.20339e10 | −0.340463 | ||||||||
\(55\) | 1.72882e10 | 0.0842155 | ||||||||
\(56\) | −6.66172e11 | −2.88645 | ||||||||
\(57\) | 1.89632e10 | 0.0732362 | ||||||||
\(58\) | 5.08767e11 | 1.75484 | ||||||||
\(59\) | −4.10975e11 | −1.26846 | −0.634230 | − | 0.773144i | \(-0.718683\pi\) | ||||
−0.634230 | + | 0.773144i | \(0.718683\pi\) | |||||||
\(60\) | 4.22077e10 | 0.116791 | ||||||||
\(61\) | −1.17141e11 | −0.291116 | −0.145558 | − | 0.989350i | \(-0.546498\pi\) | ||||
−0.145558 | + | 0.989350i | \(0.546498\pi\) | |||||||
\(62\) | 1.22586e12 | 2.74091 | ||||||||
\(63\) | 2.38914e11 | 0.481425 | ||||||||
\(64\) | −2.97657e11 | −0.541434 | ||||||||
\(65\) | −1.06041e10 | −0.0174396 | ||||||||
\(66\) | −6.08089e11 | −0.905590 | ||||||||
\(67\) | −1.16014e12 | −1.56684 | −0.783419 | − | 0.621494i | \(-0.786526\pi\) | ||||
−0.783419 | + | 0.621494i | \(0.786526\pi\) | |||||||
\(68\) | 5.61896e11 | 0.689205 | ||||||||
\(69\) | 6.72131e11 | 0.749782 | ||||||||
\(70\) | −2.38885e11 | −0.242690 | ||||||||
\(71\) | 2.58837e11 | 0.239799 | 0.119899 | − | 0.992786i | \(-0.461743\pi\) | ||||
0.119899 | + | 0.992786i | \(0.461743\pi\) | |||||||
\(72\) | −7.87506e11 | −0.666182 | ||||||||
\(73\) | 1.87421e12 | 1.44950 | 0.724752 | − | 0.689010i | \(-0.241954\pi\) | ||||
0.724752 | + | 0.689010i | \(0.241954\pi\) | |||||||
\(74\) | −2.56405e12 | −1.81518 | ||||||||
\(75\) | −8.81864e11 | −0.572141 | ||||||||
\(76\) | 4.53830e11 | 0.270150 | ||||||||
\(77\) | 2.34197e12 | 1.28053 | ||||||||
\(78\) | 3.72986e11 | 0.187533 | ||||||||
\(79\) | −2.22847e11 | −0.103141 | −0.0515704 | − | 0.998669i | \(-0.516423\pi\) | ||||
−0.0515704 | + | 0.998669i | \(0.516423\pi\) | |||||||
\(80\) | 3.13109e11 | 0.133540 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 8.68495e11 | 0.315484 | ||||||||
\(83\) | −2.08940e12 | −0.701477 | −0.350739 | − | 0.936473i | \(-0.614069\pi\) | ||||
−0.350739 | + | 0.936473i | \(0.614069\pi\) | |||||||
\(84\) | 5.71772e12 | 1.77586 | ||||||||
\(85\) | 1.06882e11 | 0.0307384 | ||||||||
\(86\) | −5.73628e12 | −1.52894 | ||||||||
\(87\) | −2.31633e12 | −0.572698 | ||||||||
\(88\) | −7.71956e12 | −1.77196 | ||||||||
\(89\) | −1.34175e12 | −0.286177 | −0.143089 | − | 0.989710i | \(-0.545703\pi\) | ||||
−0.143089 | + | 0.989710i | \(0.545703\pi\) | |||||||
\(90\) | −2.82395e11 | −0.0560120 | ||||||||
\(91\) | −1.43650e12 | −0.265178 | ||||||||
\(92\) | 1.60855e13 | 2.76576 | ||||||||
\(93\) | −5.58112e12 | −0.894504 | ||||||||
\(94\) | 2.02488e13 | 3.02739 | ||||||||
\(95\) | 8.63258e10 | 0.0120486 | ||||||||
\(96\) | −2.16376e12 | −0.282127 | ||||||||
\(97\) | −3.12485e9 | −0.000380902 0 | −0.000190451 | − | 1.00000i | \(-0.500061\pi\) | ||||
−0.000190451 | 1.00000i | \(0.500061\pi\) | ||||||||
\(98\) | −1.68470e13 | −1.92112 | ||||||||
\(99\) | 2.76853e12 | 0.295542 | ||||||||
\(100\) | −2.11048e13 | −2.11048 | ||||||||
\(101\) | 1.35294e13 | 1.26820 | 0.634102 | − | 0.773249i | \(-0.281370\pi\) | ||||
0.634102 | + | 0.773249i | \(0.281370\pi\) | |||||||
\(102\) | −3.75943e12 | −0.330537 | ||||||||
\(103\) | 3.69605e12 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(104\) | 4.73497e12 | 0.366945 | ||||||||
\(105\) | 1.08760e12 | 0.0792028 | ||||||||
\(106\) | −9.74486e12 | −0.667248 | ||||||||
\(107\) | 7.56519e12 | 0.487332 | 0.243666 | − | 0.969859i | \(-0.421650\pi\) | ||||
0.243666 | + | 0.969859i | \(0.421650\pi\) | |||||||
\(108\) | 6.75913e12 | 0.409861 | ||||||||
\(109\) | −2.05699e13 | −1.17479 | −0.587394 | − | 0.809301i | \(-0.699846\pi\) | ||||
−0.587394 | + | 0.809301i | \(0.699846\pi\) | |||||||
\(110\) | −2.76819e12 | −0.148985 | ||||||||
\(111\) | 1.16737e13 | 0.592391 | ||||||||
\(112\) | 4.24158e13 | 2.03053 | ||||||||
\(113\) | −1.50599e13 | −0.680475 | −0.340238 | − | 0.940340i | \(-0.610507\pi\) | ||||
−0.340238 | + | 0.940340i | \(0.610507\pi\) | |||||||
\(114\) | −3.03640e12 | −0.129562 | ||||||||
\(115\) | 3.05973e12 | 0.123352 | ||||||||
\(116\) | −5.54346e13 | −2.11254 | ||||||||
\(117\) | −1.69814e12 | −0.0612020 | ||||||||
\(118\) | 6.58054e13 | 2.24403 | ||||||||
\(119\) | 1.44789e13 | 0.467391 | ||||||||
\(120\) | −3.58494e12 | −0.109598 | ||||||||
\(121\) | −7.38413e12 | −0.213892 | ||||||||
\(122\) | 1.87567e13 | 0.515012 | ||||||||
\(123\) | −3.95411e12 | −0.102959 | ||||||||
\(124\) | −1.33568e14 | −3.29960 | ||||||||
\(125\) | −8.06552e12 | −0.189111 | ||||||||
\(126\) | −3.82550e13 | −0.851687 | ||||||||
\(127\) | 3.25187e13 | 0.687717 | 0.343858 | − | 0.939022i | \(-0.388266\pi\) | ||||
0.343858 | + | 0.939022i | \(0.388266\pi\) | |||||||
\(128\) | 7.19757e13 | 1.44651 | ||||||||
\(129\) | 2.61163e13 | 0.498975 | ||||||||
\(130\) | 1.69793e12 | 0.0308524 | ||||||||
\(131\) | −4.24335e13 | −0.733577 | −0.366788 | − | 0.930304i | \(-0.619543\pi\) | ||||
−0.366788 | + | 0.930304i | \(0.619543\pi\) | |||||||
\(132\) | 6.62566e13 | 1.09018 | ||||||||
\(133\) | 1.16942e13 | 0.183205 | ||||||||
\(134\) | 1.85762e14 | 2.77188 | ||||||||
\(135\) | 1.28570e12 | 0.0182797 | ||||||||
\(136\) | −4.77251e13 | −0.646761 | ||||||||
\(137\) | −1.38138e14 | −1.78496 | −0.892481 | − | 0.451085i | \(-0.851037\pi\) | ||||
−0.892481 | + | 0.451085i | \(0.851037\pi\) | |||||||
\(138\) | −1.07622e14 | −1.32644 | ||||||||
\(139\) | 6.55318e13 | 0.770648 | 0.385324 | − | 0.922781i | \(-0.374090\pi\) | ||||
0.385324 | + | 0.922781i | \(0.374090\pi\) | |||||||
\(140\) | 2.60286e13 | 0.292159 | ||||||||
\(141\) | −9.21895e13 | −0.988000 | ||||||||
\(142\) | −4.14450e13 | −0.424227 | ||||||||
\(143\) | −1.66461e13 | −0.162790 | ||||||||
\(144\) | 5.01412e13 | 0.468639 | ||||||||
\(145\) | −1.05446e13 | −0.0942187 | ||||||||
\(146\) | −3.00099e14 | −2.56431 | ||||||||
\(147\) | 7.67016e13 | 0.626963 | ||||||||
\(148\) | 2.79376e14 | 2.18518 | ||||||||
\(149\) | 1.62826e14 | 1.21902 | 0.609512 | − | 0.792777i | \(-0.291365\pi\) | ||||
0.609512 | + | 0.792777i | \(0.291365\pi\) | |||||||
\(150\) | 1.41204e14 | 1.01217 | ||||||||
\(151\) | 7.18136e13 | 0.493011 | 0.246505 | − | 0.969141i | \(-0.420718\pi\) | ||||
0.246505 | + | 0.969141i | \(0.420718\pi\) | |||||||
\(152\) | −3.85464e13 | −0.253513 | ||||||||
\(153\) | 1.71160e13 | 0.107872 | ||||||||
\(154\) | −3.74996e14 | −2.26539 | ||||||||
\(155\) | −2.54068e13 | −0.147161 | ||||||||
\(156\) | −4.06400e13 | −0.225759 | ||||||||
\(157\) | −4.46499e13 | −0.237943 | −0.118971 | − | 0.992898i | \(-0.537960\pi\) | ||||
−0.118971 | + | 0.992898i | \(0.537960\pi\) | |||||||
\(158\) | 3.56823e13 | 0.182466 | ||||||||
\(159\) | 4.43667e13 | 0.217759 | ||||||||
\(160\) | −9.85001e12 | −0.0464148 | ||||||||
\(161\) | 4.14490e14 | 1.87562 | ||||||||
\(162\) | −4.52227e13 | −0.196566 | ||||||||
\(163\) | −7.29720e13 | −0.304745 | −0.152373 | − | 0.988323i | \(-0.548691\pi\) | ||||
−0.152373 | + | 0.988323i | \(0.548691\pi\) | |||||||
\(164\) | −9.46301e13 | −0.379790 | ||||||||
\(165\) | 1.26031e13 | 0.0486218 | ||||||||
\(166\) | 3.34555e14 | 1.24098 | ||||||||
\(167\) | −5.24603e14 | −1.87143 | −0.935715 | − | 0.352757i | \(-0.885244\pi\) | ||||
−0.935715 | + | 0.352757i | \(0.885244\pi\) | |||||||
\(168\) | −4.85639e14 | −1.66649 | ||||||||
\(169\) | −2.92665e14 | −0.966289 | ||||||||
\(170\) | −1.71139e13 | −0.0543791 | ||||||||
\(171\) | 1.38242e13 | 0.0422829 | ||||||||
\(172\) | 6.25018e14 | 1.84059 | ||||||||
\(173\) | 3.74739e14 | 1.06275 | 0.531373 | − | 0.847138i | \(-0.321676\pi\) | ||||
0.531373 | + | 0.847138i | \(0.321676\pi\) | |||||||
\(174\) | 3.70891e14 | 1.01316 | ||||||||
\(175\) | −5.43828e14 | −1.43125 | ||||||||
\(176\) | 4.91511e14 | 1.24653 | ||||||||
\(177\) | −2.99601e14 | −0.732346 | ||||||||
\(178\) | 2.14841e14 | 0.506275 | ||||||||
\(179\) | 1.41559e14 | 0.321657 | 0.160828 | − | 0.986982i | \(-0.448583\pi\) | ||||
0.160828 | + | 0.986982i | \(0.448583\pi\) | |||||||
\(180\) | 3.07694e13 | 0.0674292 | ||||||||
\(181\) | 2.66316e14 | 0.562973 | 0.281486 | − | 0.959565i | \(-0.409173\pi\) | ||||
0.281486 | + | 0.959565i | \(0.409173\pi\) | |||||||
\(182\) | 2.30013e14 | 0.469124 | ||||||||
\(183\) | −8.53960e13 | −0.168076 | ||||||||
\(184\) | −1.36624e15 | −2.59543 | ||||||||
\(185\) | 5.31418e13 | 0.0974586 | ||||||||
\(186\) | 8.93651e14 | 1.58246 | ||||||||
\(187\) | 1.67781e14 | 0.286927 | ||||||||
\(188\) | −2.20629e15 | −3.64448 | ||||||||
\(189\) | 1.74169e14 | 0.277951 | ||||||||
\(190\) | −1.38225e13 | −0.0213152 | ||||||||
\(191\) | −1.59059e14 | −0.237051 | −0.118526 | − | 0.992951i | \(-0.537817\pi\) | ||||
−0.118526 | + | 0.992951i | \(0.537817\pi\) | |||||||
\(192\) | −2.16992e14 | −0.312597 | ||||||||
\(193\) | 5.78312e14 | 0.805452 | 0.402726 | − | 0.915320i | \(-0.368063\pi\) | ||||
0.402726 | + | 0.915320i | \(0.368063\pi\) | |||||||
\(194\) | 5.00352e11 | 0.000673852 0 | ||||||||
\(195\) | −7.73040e12 | −0.0100688 | ||||||||
\(196\) | 1.83563e15 | 2.31271 | ||||||||
\(197\) | 7.45344e14 | 0.908503 | 0.454252 | − | 0.890873i | \(-0.349907\pi\) | ||||
0.454252 | + | 0.890873i | \(0.349907\pi\) | |||||||
\(198\) | −4.43297e14 | −0.522843 | ||||||||
\(199\) | 9.14435e14 | 1.04378 | 0.521889 | − | 0.853014i | \(-0.325228\pi\) | ||||
0.521889 | + | 0.853014i | \(0.325228\pi\) | |||||||
\(200\) | 1.79256e15 | 1.98051 | ||||||||
\(201\) | −8.45741e14 | −0.904614 | ||||||||
\(202\) | −2.16633e15 | −2.24358 | ||||||||
\(203\) | −1.42843e15 | −1.43264 | ||||||||
\(204\) | 4.09622e14 | 0.397912 | ||||||||
\(205\) | −1.80002e13 | −0.0169386 | ||||||||
\(206\) | −5.91812e14 | −0.539569 | ||||||||
\(207\) | 4.89984e14 | 0.432887 | ||||||||
\(208\) | −3.01480e14 | −0.258135 | ||||||||
\(209\) | 1.35512e14 | 0.112468 | ||||||||
\(210\) | −1.74147e14 | −0.140117 | ||||||||
\(211\) | 4.28835e14 | 0.334545 | 0.167272 | − | 0.985911i | \(-0.446504\pi\) | ||||
0.167272 | + | 0.985911i | \(0.446504\pi\) | |||||||
\(212\) | 1.06179e15 | 0.803257 | ||||||||
\(213\) | 1.88692e14 | 0.138448 | ||||||||
\(214\) | −1.21134e15 | −0.862137 | ||||||||
\(215\) | 1.18889e14 | 0.0820900 | ||||||||
\(216\) | −5.74092e14 | −0.384620 | ||||||||
\(217\) | −3.44177e15 | −2.23765 | ||||||||
\(218\) | 3.29365e15 | 2.07831 | ||||||||
\(219\) | 1.36630e15 | 0.836871 | ||||||||
\(220\) | 3.01618e14 | 0.179354 | ||||||||
\(221\) | −1.02912e14 | −0.0594178 | ||||||||
\(222\) | −1.86919e15 | −1.04800 | ||||||||
\(223\) | 2.03442e15 | 1.10779 | 0.553897 | − | 0.832585i | \(-0.313140\pi\) | ||||
0.553897 | + | 0.832585i | \(0.313140\pi\) | |||||||
\(224\) | −1.33434e15 | −0.705758 | ||||||||
\(225\) | −6.42879e14 | −0.330326 | ||||||||
\(226\) | 2.41139e15 | 1.20383 | ||||||||
\(227\) | −2.60190e15 | −1.26218 | −0.631091 | − | 0.775708i | \(-0.717393\pi\) | ||||
−0.631091 | + | 0.775708i | \(0.717393\pi\) | |||||||
\(228\) | 3.30842e14 | 0.155971 | ||||||||
\(229\) | 7.15955e14 | 0.328061 | 0.164031 | − | 0.986455i | \(-0.447550\pi\) | ||||
0.164031 | + | 0.986455i | \(0.447550\pi\) | |||||||
\(230\) | −4.89924e14 | −0.218222 | ||||||||
\(231\) | 1.70729e15 | 0.739317 | ||||||||
\(232\) | 4.70838e15 | 1.98244 | ||||||||
\(233\) | 2.42556e15 | 0.993112 | 0.496556 | − | 0.868005i | \(-0.334598\pi\) | ||||
0.496556 | + | 0.868005i | \(0.334598\pi\) | |||||||
\(234\) | 2.71907e14 | 0.108272 | ||||||||
\(235\) | −4.19672e14 | −0.162543 | ||||||||
\(236\) | −7.17007e15 | −2.70144 | ||||||||
\(237\) | −1.62455e14 | −0.0595483 | ||||||||
\(238\) | −2.31836e15 | −0.826859 | ||||||||
\(239\) | −2.17202e15 | −0.753836 | −0.376918 | − | 0.926247i | \(-0.623016\pi\) | ||||
−0.376918 | + | 0.926247i | \(0.623016\pi\) | |||||||
\(240\) | 2.28257e14 | 0.0770993 | ||||||||
\(241\) | −4.62659e15 | −1.52108 | −0.760538 | − | 0.649294i | \(-0.775065\pi\) | ||||
−0.760538 | + | 0.649294i | \(0.775065\pi\) | |||||||
\(242\) | 1.18235e15 | 0.378396 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −2.04371e15 | −0.619990 | ||||||||
\(245\) | 3.49167e14 | 0.103146 | ||||||||
\(246\) | 6.33133e14 | 0.182145 | ||||||||
\(247\) | −8.31196e13 | −0.0232902 | ||||||||
\(248\) | 1.13447e16 | 3.09640 | ||||||||
\(249\) | −1.52317e15 | −0.404998 | ||||||||
\(250\) | 1.29145e15 | 0.334556 | ||||||||
\(251\) | 5.16492e15 | 1.30372 | 0.651860 | − | 0.758339i | \(-0.273989\pi\) | ||||
0.651860 | + | 0.758339i | \(0.273989\pi\) | |||||||
\(252\) | 4.16822e15 | 1.02529 | ||||||||
\(253\) | 4.80308e15 | 1.15143 | ||||||||
\(254\) | −5.20691e15 | −1.21664 | ||||||||
\(255\) | 7.79169e13 | 0.0177468 | ||||||||
\(256\) | −9.08636e15 | −2.01758 | ||||||||
\(257\) | −6.62253e15 | −1.43370 | −0.716851 | − | 0.697227i | \(-0.754417\pi\) | ||||
−0.716851 | + | 0.697227i | \(0.754417\pi\) | |||||||
\(258\) | −4.18175e15 | −0.882734 | ||||||||
\(259\) | 7.19892e15 | 1.48190 | ||||||||
\(260\) | −1.85005e14 | −0.0371412 | ||||||||
\(261\) | −1.68861e15 | −0.330647 | ||||||||
\(262\) | 6.79447e15 | 1.29777 | ||||||||
\(263\) | 8.43203e14 | 0.157116 | 0.0785579 | − | 0.996910i | \(-0.474968\pi\) | ||||
0.0785579 | + | 0.996910i | \(0.474968\pi\) | |||||||
\(264\) | −5.62756e15 | −1.02304 | ||||||||
\(265\) | 2.01969e14 | 0.0358251 | ||||||||
\(266\) | −1.87248e15 | −0.324106 | ||||||||
\(267\) | −9.78133e14 | −0.165225 | ||||||||
\(268\) | −2.02404e16 | −3.33689 | ||||||||
\(269\) | 1.22523e16 | 1.97164 | 0.985821 | − | 0.167803i | \(-0.0536672\pi\) | ||||
0.985821 | + | 0.167803i | \(0.0536672\pi\) | |||||||
\(270\) | −2.05866e14 | −0.0323385 | ||||||||
\(271\) | −2.29585e14 | −0.0352082 | −0.0176041 | − | 0.999845i | \(-0.505604\pi\) | ||||
−0.0176041 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(272\) | 3.03870e15 | 0.454978 | ||||||||
\(273\) | −1.04721e15 | −0.153100 | ||||||||
\(274\) | 2.21187e16 | 3.15777 | ||||||||
\(275\) | −6.30184e15 | −0.878628 | ||||||||
\(276\) | 1.17263e16 | 1.59681 | ||||||||
\(277\) | −2.21417e15 | −0.294505 | −0.147252 | − | 0.989099i | \(-0.547043\pi\) | ||||
−0.147252 | + | 0.989099i | \(0.547043\pi\) | |||||||
\(278\) | −1.04930e16 | −1.36335 | ||||||||
\(279\) | −4.06864e15 | −0.516442 | ||||||||
\(280\) | −2.21076e15 | −0.274167 | ||||||||
\(281\) | −3.89035e15 | −0.471409 | −0.235704 | − | 0.971825i | \(-0.575740\pi\) | ||||
−0.235704 | + | 0.971825i | \(0.575740\pi\) | |||||||
\(282\) | 1.47614e16 | 1.74787 | ||||||||
\(283\) | −1.39198e16 | −1.61072 | −0.805362 | − | 0.592783i | \(-0.798029\pi\) | ||||
−0.805362 | + | 0.592783i | \(0.798029\pi\) | |||||||
\(284\) | 4.51580e15 | 0.510699 | ||||||||
\(285\) | 6.29315e13 | 0.00695627 | ||||||||
\(286\) | 2.66538e15 | 0.287991 | ||||||||
\(287\) | −2.43842e15 | −0.257558 | ||||||||
\(288\) | −1.57738e15 | −0.162886 | ||||||||
\(289\) | −8.86730e15 | −0.895273 | ||||||||
\(290\) | 1.68840e15 | 0.166682 | ||||||||
\(291\) | −2.27802e12 | −0.000219914 0 | ||||||||
\(292\) | 3.26984e16 | 3.08701 | ||||||||
\(293\) | 1.52234e16 | 1.40563 | 0.702817 | − | 0.711371i | \(-0.251925\pi\) | ||||
0.702817 | + | 0.711371i | \(0.251925\pi\) | |||||||
\(294\) | −1.22815e16 | −1.10916 | ||||||||
\(295\) | −1.36386e15 | −0.120484 | ||||||||
\(296\) | −2.37290e16 | −2.05061 | ||||||||
\(297\) | 2.01826e15 | 0.170631 | ||||||||
\(298\) | −2.60717e16 | −2.15657 | ||||||||
\(299\) | −2.94608e15 | −0.238442 | ||||||||
\(300\) | −1.53854e16 | −1.21849 | ||||||||
\(301\) | 1.61054e16 | 1.24821 | ||||||||
\(302\) | −1.14988e16 | −0.872183 | ||||||||
\(303\) | 9.86293e15 | 0.732198 | ||||||||
\(304\) | 2.45428e15 | 0.178339 | ||||||||
\(305\) | −3.88746e14 | −0.0276514 | ||||||||
\(306\) | −2.74062e15 | −0.190836 | ||||||||
\(307\) | −8.48697e14 | −0.0578566 | −0.0289283 | − | 0.999581i | \(-0.509209\pi\) | ||||
−0.0289283 | + | 0.999581i | \(0.509209\pi\) | |||||||
\(308\) | 4.08591e16 | 2.72715 | ||||||||
\(309\) | 2.69442e15 | 0.176090 | ||||||||
\(310\) | 4.06814e15 | 0.260343 | ||||||||
\(311\) | −2.48376e15 | −0.155657 | −0.0778283 | − | 0.996967i | \(-0.524799\pi\) | ||||
−0.0778283 | + | 0.996967i | \(0.524799\pi\) | |||||||
\(312\) | 3.45179e15 | 0.211856 | ||||||||
\(313\) | 4.39913e15 | 0.264441 | 0.132220 | − | 0.991220i | \(-0.457789\pi\) | ||||
0.132220 | + | 0.991220i | \(0.457789\pi\) | |||||||
\(314\) | 7.14935e15 | 0.420944 | ||||||||
\(315\) | 7.92863e14 | 0.0457277 | ||||||||
\(316\) | −3.88789e15 | −0.219659 | ||||||||
\(317\) | 2.19567e16 | 1.21530 | 0.607648 | − | 0.794206i | \(-0.292113\pi\) | ||||
0.607648 | + | 0.794206i | \(0.292113\pi\) | |||||||
\(318\) | −7.10400e15 | −0.385236 | ||||||||
\(319\) | −1.65526e16 | −0.879482 | ||||||||
\(320\) | −9.87806e14 | −0.0514277 | ||||||||
\(321\) | 5.51502e15 | 0.281361 | ||||||||
\(322\) | −6.63682e16 | −3.31816 | ||||||||
\(323\) | 8.37785e14 | 0.0410503 | ||||||||
\(324\) | 4.92741e15 | 0.236633 | ||||||||
\(325\) | 3.86538e15 | 0.181949 | ||||||||
\(326\) | 1.16843e16 | 0.539124 | ||||||||
\(327\) | −1.49954e16 | −0.678264 | ||||||||
\(328\) | 8.03748e15 | 0.356402 | ||||||||
\(329\) | −5.68514e16 | −2.47154 | ||||||||
\(330\) | −2.01801e15 | −0.0860167 | ||||||||
\(331\) | 2.65474e16 | 1.10953 | 0.554767 | − | 0.832006i | \(-0.312808\pi\) | ||||
0.554767 | + | 0.832006i | \(0.312808\pi\) | |||||||
\(332\) | −3.64527e16 | −1.49394 | ||||||||
\(333\) | 8.51011e15 | 0.342017 | ||||||||
\(334\) | 8.39995e16 | 3.31074 | ||||||||
\(335\) | −3.85005e15 | −0.148825 | ||||||||
\(336\) | 3.09211e16 | 1.17233 | ||||||||
\(337\) | 1.40823e16 | 0.523697 | 0.261848 | − | 0.965109i | \(-0.415668\pi\) | ||||
0.261848 | + | 0.965109i | \(0.415668\pi\) | |||||||
\(338\) | 4.68616e16 | 1.70946 | ||||||||
\(339\) | −1.09787e16 | −0.392872 | ||||||||
\(340\) | 1.86471e15 | 0.0654635 | ||||||||
\(341\) | −3.98830e16 | −1.37368 | ||||||||
\(342\) | −2.21353e15 | −0.0748025 | ||||||||
\(343\) | 3.74294e15 | 0.124108 | ||||||||
\(344\) | −5.30864e16 | −1.72724 | ||||||||
\(345\) | 2.23054e15 | 0.0712174 | ||||||||
\(346\) | −6.00033e16 | −1.88010 | ||||||||
\(347\) | 4.85833e16 | 1.49398 | 0.746992 | − | 0.664834i | \(-0.231498\pi\) | ||||
0.746992 | + | 0.664834i | \(0.231498\pi\) | |||||||
\(348\) | −4.04119e16 | −1.21967 | ||||||||
\(349\) | 1.20256e16 | 0.356239 | 0.178119 | − | 0.984009i | \(-0.442999\pi\) | ||||
0.178119 | + | 0.984009i | \(0.442999\pi\) | |||||||
\(350\) | 8.70778e16 | 2.53201 | ||||||||
\(351\) | −1.23794e15 | −0.0353350 | ||||||||
\(352\) | −1.54623e16 | −0.433258 | ||||||||
\(353\) | −3.68917e16 | −1.01483 | −0.507415 | − | 0.861702i | \(-0.669399\pi\) | ||||
−0.507415 | + | 0.861702i | \(0.669399\pi\) | |||||||
\(354\) | 4.79721e16 | 1.29559 | ||||||||
\(355\) | 8.58978e14 | 0.0227771 | ||||||||
\(356\) | −2.34088e16 | −0.609472 | ||||||||
\(357\) | 1.05551e16 | 0.269848 | ||||||||
\(358\) | −2.26664e16 | −0.569041 | ||||||||
\(359\) | 2.30169e16 | 0.567456 | 0.283728 | − | 0.958905i | \(-0.408429\pi\) | ||||
0.283728 | + | 0.958905i | \(0.408429\pi\) | |||||||
\(360\) | −2.61342e15 | −0.0632767 | ||||||||
\(361\) | −4.13763e16 | −0.983909 | ||||||||
\(362\) | −4.26427e16 | −0.995952 | ||||||||
\(363\) | −5.38303e15 | −0.123491 | ||||||||
\(364\) | −2.50619e16 | −0.564748 | ||||||||
\(365\) | 6.21976e15 | 0.137680 | ||||||||
\(366\) | 1.36736e16 | 0.297342 | ||||||||
\(367\) | 6.59133e15 | 0.140813 | 0.0704066 | − | 0.997518i | \(-0.477570\pi\) | ||||
0.0704066 | + | 0.997518i | \(0.477570\pi\) | |||||||
\(368\) | 8.69895e16 | 1.82581 | ||||||||
\(369\) | −2.88254e15 | −0.0594435 | ||||||||
\(370\) | −8.50908e15 | −0.172413 | ||||||||
\(371\) | 2.73600e16 | 0.544736 | ||||||||
\(372\) | −9.73710e16 | −1.90502 | ||||||||
\(373\) | 9.60592e15 | 0.184685 | 0.0923425 | − | 0.995727i | \(-0.470565\pi\) | ||||
0.0923425 | + | 0.995727i | \(0.470565\pi\) | |||||||
\(374\) | −2.68651e16 | −0.507601 | ||||||||
\(375\) | −5.87977e15 | −0.109183 | ||||||||
\(376\) | 1.87393e17 | 3.42004 | ||||||||
\(377\) | 1.01529e16 | 0.182126 | ||||||||
\(378\) | −2.78879e16 | −0.491722 | ||||||||
\(379\) | −8.91020e16 | −1.54430 | −0.772151 | − | 0.635439i | \(-0.780819\pi\) | ||||
−0.772151 | + | 0.635439i | \(0.780819\pi\) | |||||||
\(380\) | 1.50608e15 | 0.0256599 | ||||||||
\(381\) | 2.37062e16 | 0.397053 | ||||||||
\(382\) | 2.54686e16 | 0.419366 | ||||||||
\(383\) | 7.32809e16 | 1.18631 | 0.593156 | − | 0.805088i | \(-0.297882\pi\) | ||||
0.593156 | + | 0.805088i | \(0.297882\pi\) | |||||||
\(384\) | 5.24703e16 | 0.835142 | ||||||||
\(385\) | 7.77207e15 | 0.121630 | ||||||||
\(386\) | −9.25995e16 | −1.42492 | ||||||||
\(387\) | 1.90388e16 | 0.288083 | ||||||||
\(388\) | −5.45177e13 | −0.000811206 0 | ||||||||
\(389\) | −4.08834e16 | −0.598239 | −0.299119 | − | 0.954216i | \(-0.596693\pi\) | ||||
−0.299119 | + | 0.954216i | \(0.596693\pi\) | |||||||
\(390\) | 1.23779e15 | 0.0178126 | ||||||||
\(391\) | 2.96944e16 | 0.420267 | ||||||||
\(392\) | −1.55911e17 | −2.17028 | ||||||||
\(393\) | −3.09340e16 | −0.423531 | ||||||||
\(394\) | −1.19345e17 | −1.60723 | ||||||||
\(395\) | −7.39541e14 | −0.00979673 | ||||||||
\(396\) | 4.83011e16 | 0.629416 | ||||||||
\(397\) | −1.12376e16 | −0.144058 | −0.0720289 | − | 0.997403i | \(-0.522947\pi\) | ||||
−0.0720289 | + | 0.997403i | \(0.522947\pi\) | |||||||
\(398\) | −1.46420e17 | −1.84654 | ||||||||
\(399\) | 8.52510e15 | 0.105773 | ||||||||
\(400\) | −1.14134e17 | −1.39323 | ||||||||
\(401\) | 1.32254e17 | 1.58844 | 0.794219 | − | 0.607632i | \(-0.207880\pi\) | ||||
0.794219 | + | 0.607632i | \(0.207880\pi\) | |||||||
\(402\) | 1.35420e17 | 1.60035 | ||||||||
\(403\) | 2.44632e16 | 0.284466 | ||||||||
\(404\) | 2.36040e17 | 2.70089 | ||||||||
\(405\) | 9.37273e14 | 0.0105538 | ||||||||
\(406\) | 2.28721e17 | 2.53447 | ||||||||
\(407\) | 8.34207e16 | 0.909725 | ||||||||
\(408\) | −3.47916e16 | −0.373408 | ||||||||
\(409\) | −1.13059e17 | −1.19428 | −0.597139 | − | 0.802138i | \(-0.703696\pi\) | ||||
−0.597139 | + | 0.802138i | \(0.703696\pi\) | |||||||
\(410\) | 2.88219e15 | 0.0299660 | ||||||||
\(411\) | −1.00703e17 | −1.03055 | ||||||||
\(412\) | 6.44831e16 | 0.649552 | ||||||||
\(413\) | −1.84758e17 | −1.83201 | ||||||||
\(414\) | −7.84563e16 | −0.765818 | ||||||||
\(415\) | −6.93389e15 | −0.0666292 | ||||||||
\(416\) | 9.48417e15 | 0.0897207 | ||||||||
\(417\) | 4.77727e16 | 0.444934 | ||||||||
\(418\) | −2.16982e16 | −0.198966 | ||||||||
\(419\) | −6.14346e16 | −0.554654 | −0.277327 | − | 0.960776i | \(-0.589448\pi\) | ||||
−0.277327 | + | 0.960776i | \(0.589448\pi\) | |||||||
\(420\) | 1.89749e16 | 0.168678 | ||||||||
\(421\) | 1.62906e17 | 1.42595 | 0.712974 | − | 0.701190i | \(-0.247348\pi\) | ||||
0.712974 | + | 0.701190i | \(0.247348\pi\) | |||||||
\(422\) | −6.86651e16 | −0.591841 | ||||||||
\(423\) | −6.72061e16 | −0.570422 | ||||||||
\(424\) | −9.01838e16 | −0.753790 | ||||||||
\(425\) | −3.89603e16 | −0.320696 | ||||||||
\(426\) | −3.02134e16 | −0.244927 | ||||||||
\(427\) | −5.26620e16 | −0.420452 | ||||||||
\(428\) | 1.31986e17 | 1.03787 | ||||||||
\(429\) | −1.21350e16 | −0.0939869 | ||||||||
\(430\) | −1.90365e16 | −0.145225 | ||||||||
\(431\) | −2.03574e17 | −1.52975 | −0.764875 | − | 0.644179i | \(-0.777199\pi\) | ||||
−0.764875 | + | 0.644179i | \(0.777199\pi\) | |||||||
\(432\) | 3.65530e16 | 0.270569 | ||||||||
\(433\) | 1.73408e17 | 1.26444 | 0.632218 | − | 0.774791i | \(-0.282145\pi\) | ||||
0.632218 | + | 0.774791i | \(0.282145\pi\) | |||||||
\(434\) | 5.51096e17 | 3.95862 | ||||||||
\(435\) | −7.68700e15 | −0.0543972 | ||||||||
\(436\) | −3.58872e17 | −2.50195 | ||||||||
\(437\) | 2.39834e16 | 0.164734 | ||||||||
\(438\) | −2.18772e17 | −1.48050 | ||||||||
\(439\) | −7.14926e16 | −0.476696 | −0.238348 | − | 0.971180i | \(-0.576606\pi\) | ||||
−0.238348 | + | 0.971180i | \(0.576606\pi\) | |||||||
\(440\) | −2.56182e16 | −0.168309 | ||||||||
\(441\) | 5.59155e16 | 0.361977 | ||||||||
\(442\) | 1.64783e16 | 0.105116 | ||||||||
\(443\) | 2.09427e17 | 1.31646 | 0.658231 | − | 0.752816i | \(-0.271305\pi\) | ||||
0.658231 | + | 0.752816i | \(0.271305\pi\) | |||||||
\(444\) | 2.03665e17 | 1.26161 | ||||||||
\(445\) | −4.45273e15 | −0.0271823 | ||||||||
\(446\) | −3.25752e17 | −1.95979 | ||||||||
\(447\) | 1.18700e17 | 0.703804 | ||||||||
\(448\) | −1.33814e17 | −0.781980 | ||||||||
\(449\) | 4.62356e16 | 0.266302 | 0.133151 | − | 0.991096i | \(-0.457490\pi\) | ||||
0.133151 | + | 0.991096i | \(0.457490\pi\) | |||||||
\(450\) | 1.02938e17 | 0.584378 | ||||||||
\(451\) | −2.82562e16 | −0.158113 | ||||||||
\(452\) | −2.62742e17 | −1.44921 | ||||||||
\(453\) | 5.23521e16 | 0.284640 | ||||||||
\(454\) | 4.16617e17 | 2.23292 | ||||||||
\(455\) | −4.76718e15 | −0.0251877 | ||||||||
\(456\) | −2.81003e16 | −0.146366 | ||||||||
\(457\) | 3.28135e17 | 1.68499 | 0.842494 | − | 0.538706i | \(-0.181087\pi\) | ||||
0.842494 | + | 0.538706i | \(0.181087\pi\) | |||||||
\(458\) | −1.14639e17 | −0.580371 | ||||||||
\(459\) | 1.24776e16 | 0.0622799 | ||||||||
\(460\) | 5.33815e16 | 0.262703 | ||||||||
\(461\) | 7.87892e16 | 0.382306 | 0.191153 | − | 0.981560i | \(-0.438777\pi\) | ||||
0.191153 | + | 0.981560i | \(0.438777\pi\) | |||||||
\(462\) | −2.73372e17 | −1.30792 | ||||||||
\(463\) | 6.33656e16 | 0.298935 | 0.149468 | − | 0.988767i | \(-0.452244\pi\) | ||||
0.149468 | + | 0.988767i | \(0.452244\pi\) | |||||||
\(464\) | −2.99787e17 | −1.39459 | ||||||||
\(465\) | −1.85216e16 | −0.0849637 | ||||||||
\(466\) | −3.88381e17 | −1.75691 | ||||||||
\(467\) | −2.32240e17 | −1.03604 | −0.518020 | − | 0.855368i | \(-0.673331\pi\) | ||||
−0.518020 | + | 0.855368i | \(0.673331\pi\) | |||||||
\(468\) | −2.96266e16 | −0.130342 | ||||||||
\(469\) | −5.21552e17 | −2.26294 | ||||||||
\(470\) | 6.71980e16 | 0.287554 | ||||||||
\(471\) | −3.25498e16 | −0.137376 | ||||||||
\(472\) | 6.08995e17 | 2.53508 | ||||||||
\(473\) | 1.86628e17 | 0.766268 | ||||||||
\(474\) | 2.60124e16 | 0.105347 | ||||||||
\(475\) | −3.14673e16 | −0.125704 | ||||||||
\(476\) | 2.52606e17 | 0.995401 | ||||||||
\(477\) | 3.23433e16 | 0.125723 | ||||||||
\(478\) | 3.47784e17 | 1.33361 | ||||||||
\(479\) | −4.79339e17 | −1.81327 | −0.906634 | − | 0.421919i | \(-0.861357\pi\) | ||||
−0.906634 | + | 0.421919i | \(0.861357\pi\) | |||||||
\(480\) | −7.18066e15 | −0.0267976 | ||||||||
\(481\) | −5.11680e16 | −0.188389 | ||||||||
\(482\) | 7.40811e17 | 2.69093 | ||||||||
\(483\) | 3.02163e17 | 1.08289 | ||||||||
\(484\) | −1.28827e17 | −0.455526 | ||||||||
\(485\) | −1.03702e13 | −3.61796e−5 0 | ||||||||
\(486\) | −3.29673e16 | −0.113488 | ||||||||
\(487\) | −2.92692e17 | −0.994197 | −0.497098 | − | 0.867694i | \(-0.665601\pi\) | ||||
−0.497098 | + | 0.867694i | \(0.665601\pi\) | |||||||
\(488\) | 1.73584e17 | 0.581809 | ||||||||
\(489\) | −5.31966e16 | −0.175945 | ||||||||
\(490\) | −5.59087e16 | −0.182476 | ||||||||
\(491\) | 6.92352e16 | 0.222996 | 0.111498 | − | 0.993765i | \(-0.464435\pi\) | ||||
0.111498 | + | 0.993765i | \(0.464435\pi\) | |||||||
\(492\) | −6.89853e16 | −0.219272 | ||||||||
\(493\) | −1.02334e17 | −0.321008 | ||||||||
\(494\) | 1.33091e16 | 0.0412026 | ||||||||
\(495\) | 9.18765e15 | 0.0280718 | ||||||||
\(496\) | −7.22327e17 | −2.17823 | ||||||||
\(497\) | 1.16363e17 | 0.346335 | ||||||||
\(498\) | 2.43891e17 | 0.716480 | ||||||||
\(499\) | 4.50229e17 | 1.30551 | 0.652755 | − | 0.757569i | \(-0.273613\pi\) | ||||
0.652755 | + | 0.757569i | \(0.273613\pi\) | |||||||
\(500\) | −1.40715e17 | −0.402750 | ||||||||
\(501\) | −3.82435e17 | −1.08047 | ||||||||
\(502\) | −8.27008e17 | −2.30641 | ||||||||
\(503\) | 3.62365e17 | 0.997596 | 0.498798 | − | 0.866718i | \(-0.333775\pi\) | ||||
0.498798 | + | 0.866718i | \(0.333775\pi\) | |||||||
\(504\) | −3.54031e17 | −0.962150 | ||||||||
\(505\) | 4.48988e16 | 0.120459 | ||||||||
\(506\) | −7.69071e17 | −2.03699 | ||||||||
\(507\) | −2.13353e17 | −0.557887 | ||||||||
\(508\) | 5.67338e17 | 1.46463 | ||||||||
\(509\) | −4.92663e16 | −0.125569 | −0.0627847 | − | 0.998027i | \(-0.519998\pi\) | ||||
−0.0627847 | + | 0.998027i | \(0.519998\pi\) | |||||||
\(510\) | −1.24761e16 | −0.0313958 | ||||||||
\(511\) | 8.42568e17 | 2.09348 | ||||||||
\(512\) | 8.65285e17 | 2.12278 | ||||||||
\(513\) | 1.00778e16 | 0.0244121 | ||||||||
\(514\) | 1.06040e18 | 2.53636 | ||||||||
\(515\) | 1.22657e16 | 0.0289699 | ||||||||
\(516\) | 4.55638e17 | 1.06267 | ||||||||
\(517\) | −6.58791e17 | −1.51726 | ||||||||
\(518\) | −1.15269e18 | −2.62162 | ||||||||
\(519\) | 2.73185e17 | 0.613576 | ||||||||
\(520\) | 1.57135e16 | 0.0348539 | ||||||||
\(521\) | 8.86374e16 | 0.194165 | 0.0970826 | − | 0.995276i | \(-0.469049\pi\) | ||||
0.0970826 | + | 0.995276i | \(0.469049\pi\) | |||||||
\(522\) | 2.70380e17 | 0.584946 | ||||||||
\(523\) | −8.32000e16 | −0.177772 | −0.0888858 | − | 0.996042i | \(-0.528331\pi\) | ||||
−0.0888858 | + | 0.996042i | \(0.528331\pi\) | |||||||
\(524\) | −7.40316e17 | −1.56230 | ||||||||
\(525\) | −3.96450e17 | −0.826330 | ||||||||
\(526\) | −1.35014e17 | −0.277953 | ||||||||
\(527\) | −2.46571e17 | −0.501387 | ||||||||
\(528\) | 3.58312e17 | 0.719682 | ||||||||
\(529\) | 3.46031e17 | 0.686519 | ||||||||
\(530\) | −3.23394e16 | −0.0633780 | ||||||||
\(531\) | −2.18409e17 | −0.422820 | ||||||||
\(532\) | 2.04023e17 | 0.390171 | ||||||||
\(533\) | 1.73316e16 | 0.0327426 | ||||||||
\(534\) | 1.56619e17 | 0.292298 | ||||||||
\(535\) | 2.51059e16 | 0.0462888 | ||||||||
\(536\) | 1.71913e18 | 3.13140 | ||||||||
\(537\) | 1.03196e17 | 0.185709 | ||||||||
\(538\) | −1.96184e18 | −3.48802 | ||||||||
\(539\) | 5.48113e17 | 0.962816 | ||||||||
\(540\) | 2.24309e16 | 0.0389303 | ||||||||
\(541\) | −4.36899e16 | −0.0749201 | −0.0374601 | − | 0.999298i | \(-0.511927\pi\) | ||||
−0.0374601 | + | 0.999298i | \(0.511927\pi\) | |||||||
\(542\) | 3.67612e16 | 0.0622866 | ||||||||
\(543\) | 1.94145e17 | 0.325032 | ||||||||
\(544\) | −9.55935e16 | −0.158138 | ||||||||
\(545\) | −6.82634e16 | −0.111586 | ||||||||
\(546\) | 1.67679e17 | 0.270849 | ||||||||
\(547\) | −3.78763e17 | −0.604575 | −0.302287 | − | 0.953217i | \(-0.597750\pi\) | ||||
−0.302287 | + | 0.953217i | \(0.597750\pi\) | |||||||
\(548\) | −2.41002e18 | −3.80143 | ||||||||
\(549\) | −6.22537e16 | −0.0970387 | ||||||||
\(550\) | 1.00905e18 | 1.55438 | ||||||||
\(551\) | −8.26528e16 | −0.125827 | ||||||||
\(552\) | −9.95986e17 | −1.49847 | ||||||||
\(553\) | −1.00183e17 | −0.148964 | ||||||||
\(554\) | 3.54534e17 | 0.521007 | ||||||||
\(555\) | 3.87404e16 | 0.0562677 | ||||||||
\(556\) | 1.14330e18 | 1.64125 | ||||||||
\(557\) | 6.88487e17 | 0.976871 | 0.488435 | − | 0.872600i | \(-0.337568\pi\) | ||||
0.488435 | + | 0.872600i | \(0.337568\pi\) | |||||||
\(558\) | 6.51471e17 | 0.913636 | ||||||||
\(559\) | −1.14473e17 | −0.158681 | ||||||||
\(560\) | 1.40761e17 | 0.192868 | ||||||||
\(561\) | 1.22312e17 | 0.165657 | ||||||||
\(562\) | 6.22924e17 | 0.833967 | ||||||||
\(563\) | −2.26569e17 | −0.299844 | −0.149922 | − | 0.988698i | \(-0.547902\pi\) | ||||
−0.149922 | + | 0.988698i | \(0.547902\pi\) | |||||||
\(564\) | −1.60838e18 | −2.10414 | ||||||||
\(565\) | −4.99779e16 | −0.0646343 | ||||||||
\(566\) | 2.22884e18 | 2.84953 | ||||||||
\(567\) | 1.26969e17 | 0.160475 | ||||||||
\(568\) | −3.83553e17 | −0.479249 | ||||||||
\(569\) | 7.35304e17 | 0.908316 | 0.454158 | − | 0.890921i | \(-0.349940\pi\) | ||||
0.454158 | + | 0.890921i | \(0.349940\pi\) | |||||||
\(570\) | −1.00766e16 | −0.0123063 | ||||||||
\(571\) | 4.30093e16 | 0.0519311 | 0.0259655 | − | 0.999663i | \(-0.491734\pi\) | ||||
0.0259655 | + | 0.999663i | \(0.491734\pi\) | |||||||
\(572\) | −2.90416e17 | −0.346694 | ||||||||
\(573\) | −1.15954e17 | −0.136862 | ||||||||
\(574\) | 3.90440e17 | 0.455646 | ||||||||
\(575\) | −1.11532e18 | −1.28694 | ||||||||
\(576\) | −1.58187e17 | −0.180478 | ||||||||
\(577\) | −1.37324e18 | −1.54919 | −0.774594 | − | 0.632458i | \(-0.782046\pi\) | ||||
−0.774594 | + | 0.632458i | \(0.782046\pi\) | |||||||
\(578\) | 1.41983e18 | 1.58382 | ||||||||
\(579\) | 4.21590e17 | 0.465028 | ||||||||
\(580\) | −1.83966e17 | −0.200657 | ||||||||
\(581\) | −9.39309e17 | −1.01313 | ||||||||
\(582\) | 3.64757e14 | 0.000389049 0 | ||||||||
\(583\) | 3.17047e17 | 0.334409 | ||||||||
\(584\) | −2.77726e18 | −2.89690 | ||||||||
\(585\) | −5.63546e15 | −0.00581322 | ||||||||
\(586\) | −2.43758e18 | −2.48670 | ||||||||
\(587\) | −6.95010e17 | −0.701203 | −0.350601 | − | 0.936525i | \(-0.614023\pi\) | ||||
−0.350601 | + | 0.936525i | \(0.614023\pi\) | |||||||
\(588\) | 1.33817e18 | 1.33524 | ||||||||
\(589\) | −1.99149e17 | −0.196530 | ||||||||
\(590\) | 2.18382e17 | 0.213147 | ||||||||
\(591\) | 5.43356e17 | 0.524525 | ||||||||
\(592\) | 1.51085e18 | 1.44254 | ||||||||
\(593\) | 1.10257e18 | 1.04124 | 0.520620 | − | 0.853789i | \(-0.325701\pi\) | ||||
0.520620 | + | 0.853789i | \(0.325701\pi\) | |||||||
\(594\) | −3.23164e17 | −0.301863 | ||||||||
\(595\) | 4.80498e16 | 0.0443947 | ||||||||
\(596\) | 2.84074e18 | 2.59616 | ||||||||
\(597\) | 6.66623e17 | 0.602625 | ||||||||
\(598\) | 4.71728e17 | 0.421826 | ||||||||
\(599\) | −9.09357e17 | −0.804377 | −0.402189 | − | 0.915557i | \(-0.631750\pi\) | ||||
−0.402189 | + | 0.915557i | \(0.631750\pi\) | |||||||
\(600\) | 1.30677e18 | 1.14345 | ||||||||
\(601\) | 1.26383e18 | 1.09397 | 0.546984 | − | 0.837143i | \(-0.315776\pi\) | ||||
0.546984 | + | 0.837143i | \(0.315776\pi\) | |||||||
\(602\) | −2.57880e18 | −2.20821 | ||||||||
\(603\) | −6.16546e17 | −0.522279 | ||||||||
\(604\) | 1.25290e18 | 1.04996 | ||||||||
\(605\) | −2.45051e16 | −0.0203164 | ||||||||
\(606\) | −1.57925e18 | −1.29533 | ||||||||
\(607\) | −2.53124e17 | −0.205403 | −0.102701 | − | 0.994712i | \(-0.532749\pi\) | ||||
−0.102701 | + | 0.994712i | \(0.532749\pi\) | |||||||
\(608\) | −7.72085e16 | −0.0619858 | ||||||||
\(609\) | −1.04133e18 | −0.827133 | ||||||||
\(610\) | 6.22461e16 | 0.0489180 | ||||||||
\(611\) | 4.04085e17 | 0.314199 | ||||||||
\(612\) | 2.98615e17 | 0.229735 | ||||||||
\(613\) | 2.18461e18 | 1.66295 | 0.831476 | − | 0.555560i | \(-0.187496\pi\) | ||||
0.831476 | + | 0.555560i | \(0.187496\pi\) | |||||||
\(614\) | 1.35894e17 | 0.102354 | ||||||||
\(615\) | −1.31221e16 | −0.00977949 | ||||||||
\(616\) | −3.47040e18 | −2.55920 | ||||||||
\(617\) | 1.93526e17 | 0.141217 | 0.0706083 | − | 0.997504i | \(-0.477506\pi\) | ||||
0.0706083 | + | 0.997504i | \(0.477506\pi\) | |||||||
\(618\) | −4.31431e17 | −0.311520 | ||||||||
\(619\) | 1.78009e17 | 0.127190 | 0.0635948 | − | 0.997976i | \(-0.479743\pi\) | ||||
0.0635948 | + | 0.997976i | \(0.479743\pi\) | |||||||
\(620\) | −4.43260e17 | −0.313410 | ||||||||
\(621\) | 3.57198e17 | 0.249927 | ||||||||
\(622\) | 3.97701e17 | 0.275371 | ||||||||
\(623\) | −6.03195e17 | −0.413319 | ||||||||
\(624\) | −2.19779e17 | −0.149034 | ||||||||
\(625\) | 1.44991e18 | 0.973015 | ||||||||
\(626\) | −7.04389e17 | −0.467821 | ||||||||
\(627\) | 9.87884e16 | 0.0649332 | ||||||||
\(628\) | −7.78984e17 | −0.506747 | ||||||||
\(629\) | 5.15737e17 | 0.332047 | ||||||||
\(630\) | −1.26953e17 | −0.0808967 | ||||||||
\(631\) | 1.13174e18 | 0.713769 | 0.356884 | − | 0.934149i | \(-0.383839\pi\) | ||||
0.356884 | + | 0.934149i | \(0.383839\pi\) | |||||||
\(632\) | 3.30221e17 | 0.206131 | ||||||||
\(633\) | 3.12621e17 | 0.193149 | ||||||||
\(634\) | −3.51571e18 | −2.14998 | ||||||||
\(635\) | 1.07917e17 | 0.0653222 | ||||||||
\(636\) | 7.74043e17 | 0.463761 | ||||||||
\(637\) | −3.36198e17 | −0.199383 | ||||||||
\(638\) | 2.65041e18 | 1.55589 | ||||||||
\(639\) | 1.37557e17 | 0.0799329 | ||||||||
\(640\) | 2.38859e17 | 0.137395 | ||||||||
\(641\) | −2.32314e18 | −1.32281 | −0.661406 | − | 0.750028i | \(-0.730040\pi\) | ||||
−0.661406 | + | 0.750028i | \(0.730040\pi\) | |||||||
\(642\) | −8.83067e17 | −0.497755 | ||||||||
\(643\) | −2.63934e18 | −1.47273 | −0.736366 | − | 0.676583i | \(-0.763460\pi\) | ||||
−0.736366 | + | 0.676583i | \(0.763460\pi\) | |||||||
\(644\) | 7.23139e18 | 3.99451 | ||||||||
\(645\) | 8.66698e16 | 0.0473947 | ||||||||
\(646\) | −1.34146e17 | −0.0726219 | ||||||||
\(647\) | 1.32570e18 | 0.710503 | 0.355251 | − | 0.934771i | \(-0.384395\pi\) | ||||
0.355251 | + | 0.934771i | \(0.384395\pi\) | |||||||
\(648\) | −4.18513e17 | −0.222061 | ||||||||
\(649\) | −2.14096e18 | −1.12465 | ||||||||
\(650\) | −6.18926e17 | −0.321886 | ||||||||
\(651\) | −2.50905e18 | −1.29191 | ||||||||
\(652\) | −1.27311e18 | −0.649016 | ||||||||
\(653\) | −2.10774e18 | −1.06385 | −0.531926 | − | 0.846791i | \(-0.678532\pi\) | ||||
−0.531926 | + | 0.846791i | \(0.678532\pi\) | |||||||
\(654\) | 2.40107e18 | 1.19991 | ||||||||
\(655\) | −1.40820e17 | −0.0696781 | ||||||||
\(656\) | −5.11754e17 | −0.250718 | ||||||||
\(657\) | 9.96031e17 | 0.483168 | ||||||||
\(658\) | 9.10306e18 | 4.37239 | ||||||||
\(659\) | 2.06081e18 | 0.980126 | 0.490063 | − | 0.871687i | \(-0.336974\pi\) | ||||
0.490063 | + | 0.871687i | \(0.336974\pi\) | |||||||
\(660\) | 2.19880e17 | 0.103550 | ||||||||
\(661\) | 2.22419e18 | 1.03720 | 0.518600 | − | 0.855017i | \(-0.326453\pi\) | ||||
0.518600 | + | 0.855017i | \(0.326453\pi\) | |||||||
\(662\) | −4.25078e18 | −1.96287 | ||||||||
\(663\) | −7.50229e16 | −0.0343049 | ||||||||
\(664\) | 3.09614e18 | 1.40193 | ||||||||
\(665\) | 3.88086e16 | 0.0174015 | ||||||||
\(666\) | −1.36264e18 | −0.605061 | ||||||||
\(667\) | −2.92954e18 | −1.28820 | ||||||||
\(668\) | −9.15248e18 | −3.98558 | ||||||||
\(669\) | 1.48309e18 | 0.639585 | ||||||||
\(670\) | 6.16471e17 | 0.263285 | ||||||||
\(671\) | −6.10244e17 | −0.258111 | ||||||||
\(672\) | −9.72737e17 | −0.407469 | ||||||||
\(673\) | −3.24859e18 | −1.34771 | −0.673856 | − | 0.738863i | \(-0.735363\pi\) | ||||
−0.673856 | + | 0.738863i | \(0.735363\pi\) | |||||||
\(674\) | −2.25486e18 | −0.926470 | ||||||||
\(675\) | −4.68659e17 | −0.190714 | ||||||||
\(676\) | −5.10598e18 | −2.05790 | ||||||||
\(677\) | 3.36868e18 | 1.34472 | 0.672362 | − | 0.740222i | \(-0.265280\pi\) | ||||
0.672362 | + | 0.740222i | \(0.265280\pi\) | |||||||
\(678\) | 1.75791e18 | 0.695029 | ||||||||
\(679\) | −1.40481e15 | −0.000550127 0 | ||||||||
\(680\) | −1.58381e17 | −0.0614320 | ||||||||
\(681\) | −1.89678e18 | −0.728722 | ||||||||
\(682\) | 6.38607e18 | 2.43016 | ||||||||
\(683\) | 5.02495e18 | 1.89408 | 0.947038 | − | 0.321122i | \(-0.104060\pi\) | ||||
0.947038 | + | 0.321122i | \(0.104060\pi\) | |||||||
\(684\) | 2.41184e17 | 0.0900499 | ||||||||
\(685\) | −4.58425e17 | −0.169543 | ||||||||
\(686\) | −5.99320e17 | −0.219559 | ||||||||
\(687\) | 5.21931e17 | 0.189406 | ||||||||
\(688\) | 3.38006e18 | 1.21506 | ||||||||
\(689\) | −1.94468e17 | −0.0692505 | ||||||||
\(690\) | −3.57155e17 | −0.125990 | ||||||||
\(691\) | 3.84714e18 | 1.34441 | 0.672204 | − | 0.740366i | \(-0.265348\pi\) | ||||
0.672204 | + | 0.740366i | \(0.265348\pi\) | |||||||
\(692\) | 6.53788e18 | 2.26333 | ||||||||
\(693\) | 1.24462e18 | 0.426845 | ||||||||
\(694\) | −7.77917e18 | −2.64300 | ||||||||
\(695\) | 2.17474e17 | 0.0731993 | ||||||||
\(696\) | 3.43241e18 | 1.14456 | ||||||||
\(697\) | −1.74690e17 | −0.0577106 | ||||||||
\(698\) | −1.92554e18 | −0.630220 | ||||||||
\(699\) | 1.76823e18 | 0.573373 | ||||||||
\(700\) | −9.48789e18 | −3.04812 | ||||||||
\(701\) | −3.06033e18 | −0.974095 | −0.487048 | − | 0.873375i | \(-0.661926\pi\) | ||||
−0.487048 | + | 0.873375i | \(0.661926\pi\) | |||||||
\(702\) | 1.98220e17 | 0.0625110 | ||||||||
\(703\) | 4.16548e17 | 0.130153 | ||||||||
\(704\) | −1.55063e18 | −0.480050 | ||||||||
\(705\) | −3.05941e17 | −0.0938443 | ||||||||
\(706\) | 5.90711e18 | 1.79533 | ||||||||
\(707\) | 6.08227e18 | 1.83164 | ||||||||
\(708\) | −5.22698e18 | −1.55968 | ||||||||
\(709\) | −2.08211e18 | −0.615605 | −0.307803 | − | 0.951450i | \(-0.599594\pi\) | ||||
−0.307803 | + | 0.951450i | \(0.599594\pi\) | |||||||
\(710\) | −1.37540e17 | −0.0402948 | ||||||||
\(711\) | −1.18430e17 | −0.0343802 | ||||||||
\(712\) | 1.98824e18 | 0.571938 | ||||||||
\(713\) | −7.05863e18 | −2.01205 | ||||||||
\(714\) | −1.69009e18 | −0.477387 | ||||||||
\(715\) | −5.52418e16 | −0.0154625 | ||||||||
\(716\) | 2.46971e18 | 0.685032 | ||||||||
\(717\) | −1.58340e18 | −0.435227 | ||||||||
\(718\) | −3.68547e18 | −1.00388 | ||||||||
\(719\) | −3.53851e18 | −0.955175 | −0.477588 | − | 0.878584i | \(-0.658489\pi\) | ||||
−0.477588 | + | 0.878584i | \(0.658489\pi\) | |||||||
\(720\) | 1.66399e17 | 0.0445133 | ||||||||
\(721\) | 1.66159e18 | 0.440500 | ||||||||
\(722\) | 6.62519e18 | 1.74063 | ||||||||
\(723\) | −3.37279e18 | −0.878193 | ||||||||
\(724\) | 4.64629e18 | 1.19896 | ||||||||
\(725\) | 3.84368e18 | 0.982992 | ||||||||
\(726\) | 8.61933e17 | 0.218467 | ||||||||
\(727\) | 1.72239e17 | 0.0432671 | 0.0216335 | − | 0.999766i | \(-0.493113\pi\) | ||||
0.0216335 | + | 0.999766i | \(0.493113\pi\) | |||||||
\(728\) | 2.12865e18 | 0.529969 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −9.95910e17 | −0.243569 | ||||||||
\(731\) | 1.15380e18 | 0.279685 | ||||||||
\(732\) | −1.48986e18 | −0.357951 | ||||||||
\(733\) | 4.07961e18 | 0.971501 | 0.485751 | − | 0.874097i | \(-0.338546\pi\) | ||||
0.485751 | + | 0.874097i | \(0.338546\pi\) | |||||||
\(734\) | −1.05541e18 | −0.249112 | ||||||||
\(735\) | 2.54543e17 | 0.0595515 | ||||||||
\(736\) | −2.73657e18 | −0.634602 | ||||||||
\(737\) | −6.04371e18 | −1.38920 | ||||||||
\(738\) | 4.61554e17 | 0.105161 | ||||||||
\(739\) | 2.80600e18 | 0.633722 | 0.316861 | − | 0.948472i | \(-0.397371\pi\) | ||||
0.316861 | + | 0.948472i | \(0.397371\pi\) | |||||||
\(740\) | 9.27138e17 | 0.207557 | ||||||||
\(741\) | −6.05942e16 | −0.0134466 | ||||||||
\(742\) | −4.38090e18 | −0.963690 | ||||||||
\(743\) | −3.51196e18 | −0.765813 | −0.382907 | − | 0.923787i | \(-0.625077\pi\) | ||||
−0.382907 | + | 0.923787i | \(0.625077\pi\) | |||||||
\(744\) | 8.27028e18 | 1.78771 | ||||||||
\(745\) | 5.40355e17 | 0.115788 | ||||||||
\(746\) | −1.53810e18 | −0.326725 | ||||||||
\(747\) | −1.11039e18 | −0.233826 | ||||||||
\(748\) | 2.92718e18 | 0.611068 | ||||||||
\(749\) | 3.40100e18 | 0.703842 | ||||||||
\(750\) | 9.41470e17 | 0.193156 | ||||||||
\(751\) | −1.57963e18 | −0.321289 | −0.160644 | − | 0.987012i | \(-0.551357\pi\) | ||||
−0.160644 | + | 0.987012i | \(0.551357\pi\) | |||||||
\(752\) | −1.19315e19 | −2.40590 | ||||||||
\(753\) | 3.76523e18 | 0.752703 | ||||||||
\(754\) | −1.62569e18 | −0.322199 | ||||||||
\(755\) | 2.38321e17 | 0.0468282 | ||||||||
\(756\) | 3.03863e18 | 0.591952 | ||||||||
\(757\) | 4.57886e18 | 0.884371 | 0.442185 | − | 0.896924i | \(-0.354203\pi\) | ||||
0.442185 | + | 0.896924i | \(0.354203\pi\) | |||||||
\(758\) | 1.42670e19 | 2.73202 | ||||||||
\(759\) | 3.50145e18 | 0.664777 | ||||||||
\(760\) | −1.27920e17 | −0.0240797 | ||||||||
\(761\) | −3.19192e18 | −0.595733 | −0.297867 | − | 0.954608i | \(-0.596275\pi\) | ||||
−0.297867 | + | 0.954608i | \(0.596275\pi\) | |||||||
\(762\) | −3.79584e18 | −0.702425 | ||||||||
\(763\) | −9.24739e18 | −1.69672 | ||||||||
\(764\) | −2.77503e18 | −0.504848 | ||||||||
\(765\) | 5.68014e16 | 0.0102461 | ||||||||
\(766\) | −1.17338e19 | −2.09870 | ||||||||
\(767\) | 1.31321e18 | 0.232897 | ||||||||
\(768\) | −6.62395e18 | −1.16485 | ||||||||
\(769\) | −2.98686e18 | −0.520827 | −0.260414 | − | 0.965497i | \(-0.583859\pi\) | ||||
−0.260414 | + | 0.965497i | \(0.583859\pi\) | |||||||
\(770\) | −1.24447e18 | −0.215176 | ||||||||
\(771\) | −4.82783e18 | −0.827748 | ||||||||
\(772\) | 1.00895e19 | 1.71537 | ||||||||
\(773\) | −6.01573e18 | −1.01420 | −0.507098 | − | 0.861888i | \(-0.669282\pi\) | ||||
−0.507098 | + | 0.861888i | \(0.669282\pi\) | |||||||
\(774\) | −3.04850e18 | −0.509647 | ||||||||
\(775\) | 9.26122e18 | 1.53535 | ||||||||
\(776\) | 4.63050e15 | 0.000761250 0 | ||||||||
\(777\) | 5.24801e18 | 0.855576 | ||||||||
\(778\) | 6.54626e18 | 1.05834 | ||||||||
\(779\) | −1.41093e17 | −0.0226210 | ||||||||
\(780\) | −1.34868e17 | −0.0214435 | ||||||||
\(781\) | 1.34840e18 | 0.212612 | ||||||||
\(782\) | −4.75467e18 | −0.743493 | ||||||||
\(783\) | −1.23099e18 | −0.190899 | ||||||||
\(784\) | 9.92697e18 | 1.52673 | ||||||||
\(785\) | −1.48175e17 | −0.0226008 | ||||||||
\(786\) | 4.95317e18 | 0.749266 | ||||||||
\(787\) | −8.17242e18 | −1.22607 | −0.613034 | − | 0.790056i | \(-0.710051\pi\) | ||||
−0.613034 | + | 0.790056i | \(0.710051\pi\) | |||||||
\(788\) | 1.30036e19 | 1.93484 | ||||||||
\(789\) | 6.14695e17 | 0.0907108 | ||||||||
\(790\) | 1.18415e17 | 0.0173313 | ||||||||
\(791\) | −6.77032e18 | −0.982793 | ||||||||
\(792\) | −4.10249e18 | −0.590655 | ||||||||
\(793\) | 3.74308e17 | 0.0534506 | ||||||||
\(794\) | 1.79937e18 | 0.254852 | ||||||||
\(795\) | 1.47236e17 | 0.0206836 | ||||||||
\(796\) | 1.59537e19 | 2.22293 | ||||||||
\(797\) | 1.06035e19 | 1.46545 | 0.732726 | − | 0.680523i | \(-0.238248\pi\) | ||||
0.732726 | + | 0.680523i | \(0.238248\pi\) | |||||||
\(798\) | −1.36504e18 | −0.187123 | ||||||||
\(799\) | −4.07288e18 | −0.553793 | ||||||||
\(800\) | 3.59050e18 | 0.484250 | ||||||||
\(801\) | −7.13059e17 | −0.0953925 | ||||||||
\(802\) | −2.11765e19 | −2.81010 | ||||||||
\(803\) | 9.76363e18 | 1.28517 | ||||||||
\(804\) | −1.47552e19 | −1.92656 | ||||||||
\(805\) | 1.37553e18 | 0.178154 | ||||||||
\(806\) | −3.91705e18 | −0.503247 | ||||||||
\(807\) | 8.93193e18 | 1.13833 | ||||||||
\(808\) | −2.00483e19 | −2.53456 | ||||||||
\(809\) | 9.68399e18 | 1.21448 | 0.607238 | − | 0.794520i | \(-0.292278\pi\) | ||||
0.607238 | + | 0.794520i | \(0.292278\pi\) | |||||||
\(810\) | −1.50076e17 | −0.0186707 | ||||||||
\(811\) | −5.91477e18 | −0.729966 | −0.364983 | − | 0.931014i | \(-0.618925\pi\) | ||||
−0.364983 | + | 0.931014i | \(0.618925\pi\) | |||||||
\(812\) | −2.49212e19 | −3.05108 | ||||||||
\(813\) | −1.67368e17 | −0.0203275 | ||||||||
\(814\) | −1.33573e19 | −1.60939 | ||||||||
\(815\) | −2.42166e17 | −0.0289460 | ||||||||
\(816\) | 2.21521e18 | 0.262681 | ||||||||
\(817\) | 9.31899e17 | 0.109629 | ||||||||
\(818\) | 1.81031e19 | 2.11279 | ||||||||
\(819\) | −7.63415e17 | −0.0883925 | ||||||||
\(820\) | −3.14040e17 | −0.0360741 | ||||||||
\(821\) | 7.57709e17 | 0.0863519 | 0.0431759 | − | 0.999067i | \(-0.486252\pi\) | ||||
0.0431759 | + | 0.999067i | \(0.486252\pi\) | |||||||
\(822\) | 1.61245e19 | 1.82314 | ||||||||
\(823\) | 1.14913e19 | 1.28905 | 0.644523 | − | 0.764585i | \(-0.277056\pi\) | ||||
0.644523 | + | 0.764585i | \(0.277056\pi\) | |||||||
\(824\) | −5.47692e18 | −0.609551 | ||||||||
\(825\) | −4.59404e18 | −0.507276 | ||||||||
\(826\) | 2.95834e19 | 3.24099 | ||||||||
\(827\) | −1.01647e19 | −1.10486 | −0.552430 | − | 0.833559i | \(-0.686299\pi\) | ||||
−0.552430 | + | 0.833559i | \(0.686299\pi\) | |||||||
\(828\) | 8.54850e18 | 0.921919 | ||||||||
\(829\) | 2.72808e18 | 0.291913 | 0.145956 | − | 0.989291i | \(-0.453374\pi\) | ||||
0.145956 | + | 0.989291i | \(0.453374\pi\) | |||||||
\(830\) | 1.11026e18 | 0.117873 | ||||||||
\(831\) | −1.61413e18 | −0.170033 | ||||||||
\(832\) | 9.51118e17 | 0.0994106 | ||||||||
\(833\) | 3.38863e18 | 0.351425 | ||||||||
\(834\) | −7.64938e18 | −0.787130 | ||||||||
\(835\) | −1.74095e18 | −0.177756 | ||||||||
\(836\) | 2.36421e18 | 0.239522 | ||||||||
\(837\) | −2.96604e18 | −0.298168 | ||||||||
\(838\) | 9.83692e18 | 0.981235 | ||||||||
\(839\) | −1.69983e19 | −1.68249 | −0.841245 | − | 0.540655i | \(-0.818177\pi\) | ||||
−0.841245 | + | 0.540655i | \(0.818177\pi\) | |||||||
\(840\) | −1.61165e18 | −0.158290 | ||||||||
\(841\) | −1.64704e17 | −0.0160520 | ||||||||
\(842\) | −2.60846e19 | −2.52264 | ||||||||
\(843\) | −2.83606e18 | −0.272168 | ||||||||
\(844\) | 7.48166e18 | 0.712479 | ||||||||
\(845\) | −9.71240e17 | −0.0917821 | ||||||||
\(846\) | 1.07611e19 | 1.00913 | ||||||||
\(847\) | −3.31961e18 | −0.308919 | ||||||||
\(848\) | 5.74208e18 | 0.530269 | ||||||||
\(849\) | −1.01475e19 | −0.929952 | ||||||||
\(850\) | 6.23833e18 | 0.567342 | ||||||||
\(851\) | 1.47641e19 | 1.33249 | ||||||||
\(852\) | 3.29201e18 | 0.294852 | ||||||||
\(853\) | −2.07516e19 | −1.84452 | −0.922261 | − | 0.386568i | \(-0.873660\pi\) | ||||
−0.922261 | + | 0.386568i | \(0.873660\pi\) | |||||||
\(854\) | 8.43225e18 | 0.743819 | ||||||||
\(855\) | 4.58771e16 | 0.00401621 | ||||||||
\(856\) | −1.12103e19 | −0.973956 | ||||||||
\(857\) | 8.07408e18 | 0.696174 | 0.348087 | − | 0.937462i | \(-0.386831\pi\) | ||||
0.348087 | + | 0.937462i | \(0.386831\pi\) | |||||||
\(858\) | 1.94306e18 | 0.166272 | ||||||||
\(859\) | 1.35586e19 | 1.15149 | 0.575743 | − | 0.817631i | \(-0.304713\pi\) | ||||
0.575743 | + | 0.817631i | \(0.304713\pi\) | |||||||
\(860\) | 2.07419e18 | 0.174827 | ||||||||
\(861\) | −1.77761e18 | −0.148701 | ||||||||
\(862\) | 3.25964e19 | 2.70627 | ||||||||
\(863\) | −1.19838e19 | −0.987469 | −0.493735 | − | 0.869613i | \(-0.664369\pi\) | ||||
−0.493735 | + | 0.869613i | \(0.664369\pi\) | |||||||
\(864\) | −1.14991e18 | −0.0940424 | ||||||||
\(865\) | 1.24361e18 | 0.100944 | ||||||||
\(866\) | −2.77661e19 | −2.23691 | ||||||||
\(867\) | −6.46426e18 | −0.516886 | ||||||||
\(868\) | −6.00467e19 | −4.76553 | ||||||||
\(869\) | −1.16091e18 | −0.0914474 | ||||||||
\(870\) | 1.23084e18 | 0.0962338 | ||||||||
\(871\) | 3.70705e18 | 0.287681 | ||||||||
\(872\) | 3.04811e19 | 2.34787 | ||||||||
\(873\) | −1.66067e15 | −0.000126967 0 | ||||||||
\(874\) | −3.84023e18 | −0.291429 | ||||||||
\(875\) | −3.62593e18 | −0.273129 | ||||||||
\(876\) | 2.38371e19 | 1.78228 | ||||||||
\(877\) | −6.80753e18 | −0.505234 | −0.252617 | − | 0.967566i | \(-0.581291\pi\) | ||||
−0.252617 | + | 0.967566i | \(0.581291\pi\) | |||||||
\(878\) | 1.14474e19 | 0.843322 | ||||||||
\(879\) | 1.10979e19 | 0.811543 | ||||||||
\(880\) | 1.63113e18 | 0.118400 | ||||||||
\(881\) | 1.23865e19 | 0.892492 | 0.446246 | − | 0.894910i | \(-0.352761\pi\) | ||||
0.446246 | + | 0.894910i | \(0.352761\pi\) | |||||||
\(882\) | −8.95320e18 | −0.640372 | ||||||||
\(883\) | 1.00764e19 | 0.715421 | 0.357711 | − | 0.933832i | \(-0.383557\pi\) | ||||
0.357711 | + | 0.933832i | \(0.383557\pi\) | |||||||
\(884\) | −1.79546e18 | −0.126542 | ||||||||
\(885\) | −9.94257e17 | −0.0695613 | ||||||||
\(886\) | −3.35335e19 | −2.32895 | ||||||||
\(887\) | 1.28943e17 | 0.00888981 | 0.00444491 | − | 0.999990i | \(-0.498585\pi\) | ||||
0.00444491 | + | 0.999990i | \(0.498585\pi\) | |||||||
\(888\) | −1.72984e19 | −1.18392 | ||||||||
\(889\) | 1.46191e19 | 0.993252 | ||||||||
\(890\) | 7.12972e17 | 0.0480881 | ||||||||
\(891\) | 1.47131e18 | 0.0985141 | ||||||||
\(892\) | 3.54935e19 | 2.35927 | ||||||||
\(893\) | −3.28957e18 | −0.217072 | ||||||||
\(894\) | −1.90063e19 | −1.24510 | ||||||||
\(895\) | 4.69779e17 | 0.0305523 | ||||||||
\(896\) | 3.23573e19 | 2.08916 | ||||||||
\(897\) | −2.14770e18 | −0.137664 | ||||||||
\(898\) | −7.40325e18 | −0.471114 | ||||||||
\(899\) | 2.43258e19 | 1.53684 | ||||||||
\(900\) | −1.12160e19 | −0.703495 | ||||||||
\(901\) | 1.96010e18 | 0.122058 | ||||||||
\(902\) | 4.52440e18 | 0.279717 | ||||||||
\(903\) | 1.17408e19 | 0.720657 | ||||||||
\(904\) | 2.23162e19 | 1.35996 | ||||||||
\(905\) | 8.83800e17 | 0.0534735 | ||||||||
\(906\) | −8.38263e18 | −0.503555 | ||||||||
\(907\) | −1.98412e19 | −1.18337 | −0.591685 | − | 0.806169i | \(-0.701537\pi\) | ||||
−0.591685 | + | 0.806169i | \(0.701537\pi\) | |||||||
\(908\) | −4.53940e19 | −2.68807 | ||||||||
\(909\) | 7.19007e18 | 0.422735 | ||||||||
\(910\) | 7.63323e17 | 0.0445594 | ||||||||
\(911\) | −9.94765e18 | −0.576568 | −0.288284 | − | 0.957545i | \(-0.593085\pi\) | ||||
−0.288284 | + | 0.957545i | \(0.593085\pi\) | |||||||
\(912\) | 1.78917e18 | 0.102964 | ||||||||
\(913\) | −1.08847e19 | −0.621949 | ||||||||
\(914\) | −5.25410e19 | −2.98090 | ||||||||
\(915\) | −2.83396e17 | −0.0159645 | ||||||||
\(916\) | 1.24909e19 | 0.698671 | ||||||||
\(917\) | −1.90764e19 | −1.05949 | ||||||||
\(918\) | −1.99791e18 | −0.110179 | ||||||||
\(919\) | 2.38402e19 | 1.30544 | 0.652722 | − | 0.757598i | \(-0.273627\pi\) | ||||
0.652722 | + | 0.757598i | \(0.273627\pi\) | |||||||
\(920\) | −4.53400e18 | −0.246525 | ||||||||
\(921\) | −6.18700e17 | −0.0334035 | ||||||||
\(922\) | −1.26157e19 | −0.676335 | ||||||||
\(923\) | −8.27075e17 | −0.0440285 | ||||||||
\(924\) | 2.97863e19 | 1.57452 | ||||||||
\(925\) | −1.93711e19 | −1.01679 | ||||||||
\(926\) | −1.01461e19 | −0.528845 | ||||||||
\(927\) | 1.96423e18 | 0.101666 | ||||||||
\(928\) | 9.43091e18 | 0.484721 | ||||||||
\(929\) | 1.47875e19 | 0.754731 | 0.377366 | − | 0.926064i | \(-0.376830\pi\) | ||||
0.377366 | + | 0.926064i | \(0.376830\pi\) | |||||||
\(930\) | 2.96568e18 | 0.150309 | ||||||||
\(931\) | 2.73692e18 | 0.137749 | ||||||||
\(932\) | 4.23175e19 | 2.11503 | ||||||||
\(933\) | −1.81066e18 | −0.0898684 | ||||||||
\(934\) | 3.71863e19 | 1.83285 | ||||||||
\(935\) | 5.56798e17 | 0.0272535 | ||||||||
\(936\) | 2.51636e18 | 0.122315 | ||||||||
\(937\) | −2.68119e19 | −1.29425 | −0.647127 | − | 0.762382i | \(-0.724030\pi\) | ||||
−0.647127 | + | 0.762382i | \(0.724030\pi\) | |||||||
\(938\) | 8.35110e19 | 4.00336 | ||||||||
\(939\) | 3.20696e18 | 0.152675 | ||||||||
\(940\) | −7.32180e18 | −0.346168 | ||||||||
\(941\) | −3.43324e19 | −1.61202 | −0.806011 | − | 0.591900i | \(-0.798378\pi\) | ||||
−0.806011 | + | 0.591900i | \(0.798378\pi\) | |||||||
\(942\) | 5.21188e18 | 0.243032 | ||||||||
\(943\) | −5.00089e18 | −0.231591 | ||||||||
\(944\) | −3.87753e19 | −1.78335 | ||||||||
\(945\) | 5.77997e17 | 0.0264009 | ||||||||
\(946\) | −2.98830e19 | −1.35560 | ||||||||
\(947\) | 1.84464e19 | 0.831067 | 0.415534 | − | 0.909578i | \(-0.363595\pi\) | ||||
0.415534 | + | 0.909578i | \(0.363595\pi\) | |||||||
\(948\) | −2.83427e18 | −0.126820 | ||||||||
\(949\) | −5.98875e18 | −0.266137 | ||||||||
\(950\) | 5.03854e18 | 0.222383 | ||||||||
\(951\) | 1.60064e19 | 0.701652 | ||||||||
\(952\) | −2.14553e19 | −0.934101 | ||||||||
\(953\) | 1.31082e19 | 0.566814 | 0.283407 | − | 0.959000i | \(-0.408535\pi\) | ||||
0.283407 | + | 0.959000i | \(0.408535\pi\) | |||||||
\(954\) | −5.17882e18 | −0.222416 | ||||||||
\(955\) | −5.27856e17 | −0.0225161 | ||||||||
\(956\) | −3.78941e19 | −1.60544 | ||||||||
\(957\) | −1.20669e19 | −0.507769 | ||||||||
\(958\) | 7.67519e19 | 3.20784 | ||||||||
\(959\) | −6.21012e19 | −2.57798 | ||||||||
\(960\) | −7.20111e17 | −0.0296918 | ||||||||
\(961\) | 3.41947e19 | 1.40041 | ||||||||
\(962\) | 8.19304e18 | 0.333278 | ||||||||
\(963\) | 4.02045e18 | 0.162444 | ||||||||
\(964\) | −8.07179e19 | −3.23943 | ||||||||
\(965\) | 1.91919e18 | 0.0765052 | ||||||||
\(966\) | −4.83824e19 | −1.91574 | ||||||||
\(967\) | 2.99771e19 | 1.17901 | 0.589505 | − | 0.807765i | \(-0.299323\pi\) | ||||
0.589505 | + | 0.807765i | \(0.299323\pi\) | |||||||
\(968\) | 1.09420e19 | 0.427473 | ||||||||
\(969\) | 6.10745e17 | 0.0237004 | ||||||||
\(970\) | 1.66047e15 | 6.40052e−5 0 | ||||||||
\(971\) | −7.97793e18 | −0.305468 | −0.152734 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152734 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(972\) | 3.59208e18 | 0.136620 | ||||||||
\(973\) | 2.94605e19 | 1.11303 | ||||||||
\(974\) | 4.68659e19 | 1.75883 | ||||||||
\(975\) | 2.81786e18 | 0.105049 | ||||||||
\(976\) | −1.10522e19 | −0.409286 | ||||||||
\(977\) | 2.51869e19 | 0.926530 | 0.463265 | − | 0.886220i | \(-0.346678\pi\) | ||||
0.463265 | + | 0.886220i | \(0.346678\pi\) | |||||||
\(978\) | 8.51786e18 | 0.311263 | ||||||||
\(979\) | −6.98979e18 | −0.253733 | ||||||||
\(980\) | 6.09173e18 | 0.219670 | ||||||||
\(981\) | −1.09317e19 | −0.391596 | ||||||||
\(982\) | −1.10860e19 | −0.394501 | ||||||||
\(983\) | −2.17925e19 | −0.770387 | −0.385193 | − | 0.922836i | \(-0.625865\pi\) | ||||
−0.385193 | + | 0.922836i | \(0.625865\pi\) | |||||||
\(984\) | 5.85932e18 | 0.205769 | ||||||||
\(985\) | 2.47351e18 | 0.0862934 | ||||||||
\(986\) | 1.63858e19 | 0.567894 | ||||||||
\(987\) | −4.14447e19 | −1.42694 | ||||||||
\(988\) | −1.45015e18 | −0.0496011 | ||||||||
\(989\) | 3.30302e19 | 1.12237 | ||||||||
\(990\) | −1.47113e18 | −0.0496618 | ||||||||
\(991\) | −1.55987e18 | −0.0523132 | −0.0261566 | − | 0.999658i | \(-0.508327\pi\) | ||||
−0.0261566 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(992\) | 2.27235e19 | 0.757092 | ||||||||
\(993\) | 1.93531e19 | 0.640589 | ||||||||
\(994\) | −1.86320e19 | −0.612700 | ||||||||
\(995\) | 3.03465e18 | 0.0991422 | ||||||||
\(996\) | −2.65740e19 | −0.862524 | ||||||||
\(997\) | −1.80157e19 | −0.580942 | −0.290471 | − | 0.956884i | \(-0.593812\pi\) | ||||
−0.290471 | + | 0.956884i | \(0.593812\pi\) | |||||||
\(998\) | −7.20908e19 | −2.30957 | ||||||||
\(999\) | 6.20387e18 | 0.197464 |
(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 | 3.14.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 9.14.a.c.1.2 | 2 | |||
4.3 | odd | 2 | 48.14.a.g.1.1 | 2 | |||
5.2 | odd | 4 | 75.14.b.c.49.1 | 4 | |||
5.3 | odd | 4 | 75.14.b.c.49.4 | 4 | |||
5.4 | even | 2 | 75.14.a.e.1.2 | 2 | |||
7.6 | odd | 2 | 147.14.a.b.1.1 | 2 | |||
8.3 | odd | 2 | 192.14.a.o.1.2 | 2 | |||
8.5 | even | 2 | 192.14.a.k.1.2 | 2 | |||
12.11 | even | 2 | 144.14.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.14.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.14.a.c.1.2 | 2 | 3.2 | odd | 2 | |||
48.14.a.g.1.1 | 2 | 4.3 | odd | 2 | |||
75.14.a.e.1.2 | 2 | 5.4 | even | 2 | |||
75.14.b.c.49.1 | 4 | 5.2 | odd | 4 | |||
75.14.b.c.49.4 | 4 | 5.3 | odd | 4 | |||
144.14.a.m.1.2 | 2 | 12.11 | even | 2 | |||
147.14.a.b.1.1 | 2 | 7.6 | odd | 2 | |||
192.14.a.k.1.2 | 2 | 8.5 | even | 2 | |||
192.14.a.o.1.2 | 2 | 8.3 | odd | 2 |