Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(193,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 300700 x^{18} + 6140664 x^{17} + 35387063979 x^{16} - 1130222504088 x^{15} + \cdots + 12\!\cdots\!52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{175}\cdot 3^{32} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(255.957 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.10.d.f.193.20 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 81.0000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2358.11i | − 1.68733i | −0.536870 | − | 0.843665i | \(-0.680394\pi\) | ||||
0.536870 | − | 0.843665i | \(-0.319606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1310.82 | −0.206349 | −0.103175 | − | 0.994663i | \(-0.532900\pi\) | ||||
−0.103175 | + | 0.994663i | \(0.532900\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 12659.0i | − 0.260695i | −0.991468 | − | 0.130348i | \(-0.958391\pi\) | ||||
0.991468 | − | 0.130348i | \(-0.0416093\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 149414.i | − 1.45093i | −0.688261 | − | 0.725463i | \(-0.741626\pi\) | ||||
0.688261 | − | 0.725463i | \(-0.258374\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −191007. | −0.974180 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −242843. | −0.705190 | −0.352595 | − | 0.935776i | \(-0.614701\pi\) | ||||
−0.352595 | + | 0.935776i | \(0.614701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 713999.i | − 1.25692i | −0.777844 | − | 0.628458i | \(-0.783686\pi\) | ||||
0.777844 | − | 0.628458i | \(-0.216314\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 106177.i | 0.119136i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −634045. | −0.472438 | −0.236219 | − | 0.971700i | \(-0.575908\pi\) | ||||
−0.236219 | + | 0.971700i | \(0.575908\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.60758e6 | −1.84708 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 919977.i | 0.241538i | 0.992681 | + | 0.120769i | \(0.0385361\pi\) | ||||
−0.992681 | + | 0.120769i | \(0.961464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.06417e6 | 0.984874 | 0.492437 | − | 0.870348i | \(-0.336106\pi\) | ||||
0.492437 | + | 0.870348i | \(0.336106\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.02538e6 | −0.150512 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.09107e6i | 0.348179i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.14011e7i | − 1.00009i | −0.866000 | − | 0.500045i | \(-0.833317\pi\) | ||||
0.866000 | − | 0.500045i | \(-0.166683\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.21025e7 | −0.837693 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.44272e6 | −0.466611 | −0.233306 | − | 0.972403i | \(-0.574954\pi\) | ||||
−0.233306 | + | 0.972403i | \(0.574954\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.27628e7i | − 0.569297i | −0.958632 | − | 0.284649i | \(-0.908123\pi\) | ||||
0.958632 | − | 0.284649i | \(-0.0918769\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.54716e7i | 0.562443i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.08809e6 | −0.0325255 | −0.0162628 | − | 0.999868i | \(-0.505177\pi\) | ||||
−0.0162628 | + | 0.999868i | \(0.505177\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.86353e7 | −0.957420 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.96703e7i | 0.407142i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.16666e6i | 0.159577i | 0.996812 | + | 0.0797884i | \(0.0254245\pi\) | ||||
−0.996812 | + | 0.0797884i | \(0.974576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.98514e7 | −0.439879 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.78339e7 | −0.725681 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.45165e6i | 0.0263406i | 0.999913 | + | 0.0131703i | \(0.00419235\pi\) | ||||
−0.999913 | + | 0.0131703i | \(0.995808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.46880e7i | − 0.413244i | −0.978421 | − | 0.206622i | \(-0.933753\pi\) | ||||
0.978421 | − | 0.206622i | \(-0.0662471\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.60032e6 | 0.0687831 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.52335e8 | −2.44819 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 2.55851e8i | − 1.55114i | −0.631264 | − | 0.775568i | \(-0.717463\pi\) | ||||
0.631264 | − | 0.775568i | \(-0.282537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.13577e7i | 0.272762i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.45406e8 | 0.679079 | 0.339539 | − | 0.940592i | \(-0.389729\pi\) | ||||
0.339539 | + | 0.940592i | \(0.389729\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.89644e8 | −1.60589 | −0.802944 | − | 0.596054i | \(-0.796734\pi\) | ||||
−0.802944 | + | 0.596054i | \(0.796734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.92214e8i | 1.06641i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.65937e7i | 0.0537943i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.65328e8 | −1.92183 | −0.960913 | − | 0.276850i | \(-0.910710\pi\) | ||||
−0.960913 | + | 0.276850i | \(0.910710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.04812e8i | 0.704986i | 0.935814 | + | 0.352493i | \(0.114666\pi\) | ||||
−0.935814 | + | 0.352493i | \(0.885334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.72653e8i | 1.18989i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.45182e7 | 0.139452 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.38397e8 | 0.571705 | 0.285852 | − | 0.958274i | \(-0.407723\pi\) | ||||
0.285852 | + | 0.958274i | \(0.407723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.95855e8i | 0.299398i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.10198e8i | − 0.568617i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.68369e9 | −2.12083 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.28207e9 | 1.47041 | 0.735203 | − | 0.677847i | \(-0.237087\pi\) | ||||
0.735203 | + | 0.677847i | \(0.237087\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.30558e7i | 0.0868984i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.21088e9i | − 1.15786i | −0.815379 | − | 0.578928i | \(-0.803471\pi\) | ||||
0.815379 | − | 0.578928i | \(-0.196529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.71434e9 | 1.50082 | 0.750412 | − | 0.660970i | \(-0.229855\pi\) | ||||
0.750412 | + | 0.660970i | \(0.229855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.50377e8 | 0.201021 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.28518e9i | − 1.68536i | −0.538412 | − | 0.842682i | \(-0.680976\pi\) | ||||
0.538412 | − | 0.842682i | \(-0.319024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.16653e8i | − 0.0791549i | −0.999217 | − | 0.0395774i | \(-0.987399\pi\) | ||||
0.999217 | − | 0.0395774i | \(-0.0126012\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.23489e8 | −0.577402 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.33117e9 | 1.34500 | 0.672499 | − | 0.740098i | \(-0.265221\pi\) | ||||
0.672499 | + | 0.740098i | \(0.265221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.49515e9i | 0.797159i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.80303e8i | 0.483642i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.18325e8 | 0.145516 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.19770e9 | 0.932038 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.83860e8i | 0.269398i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.90140e9i | 1.42931i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.43019e9 | −1.17004 | −0.585021 | − | 0.811018i | \(-0.698914\pi\) | ||||
−0.585021 | + | 0.811018i | \(0.698914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.03379e9 | −0.328684 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 5.02477e9i | − 1.49072i | −0.666664 | − | 0.745358i | \(-0.732279\pi\) | ||||
0.666664 | − | 0.745358i | \(-0.267721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.35926e8i | 0.259364i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.25320e9 | 0.324727 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.35961e9 | −0.329741 | −0.164870 | − | 0.986315i | \(-0.552721\pi\) | ||||
−0.164870 | + | 0.986315i | \(0.552721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.29504e9i | 1.65753i | 0.559597 | + | 0.828765i | \(0.310956\pi\) | ||||
−0.559597 | + | 0.828765i | \(0.689044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.81353e7i | 0.0187786i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.89143e9 | −0.378249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.16941e9 | 0.407555 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.12946e9i | 0.552767i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.34307e8i | 0.105429i | 0.998610 | + | 0.0527146i | \(0.0167874\pi\) | ||||
−0.998610 | + | 0.0527146i | \(0.983213\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.80634e9 | −0.439283 | −0.219642 | − | 0.975581i | \(-0.570489\pi\) | ||||
−0.219642 | + | 0.975581i | \(0.570489\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.59330e9 | 0.235063 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 1.19419e10i | − 1.66181i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.70003e9i | − 0.617380i | −0.951163 | − | 0.308690i | \(-0.900110\pi\) | ||||
0.951163 | − | 0.308690i | \(-0.0998905\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.42500e8 | 0.0921317 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.31122e8 | 0.0974874 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.00023e9i | 0.998641i | 0.866417 | + | 0.499320i | \(0.166417\pi\) | ||||
−0.866417 | + | 0.499320i | \(0.833583\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.41796e9i | 0.253964i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.51957e10 | 1.51181 | 0.755904 | − | 0.654683i | \(-0.227198\pi\) | ||||
0.755904 | + | 0.654683i | \(0.227198\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.17200e10 | −1.10519 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.68454e9i | 0.418972i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.48179e10i | 1.25771i | 0.777524 | + | 0.628853i | \(0.216475\pi\) | ||||
−0.777524 | + | 0.628853i | \(0.783525\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.72890e9 | 0.381144 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.98584e8 | 0.0152077 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2.46574e10i | − 1.79518i | −0.440832 | − | 0.897590i | \(-0.645317\pi\) | ||||
0.440832 | − | 0.897590i | \(-0.354683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.24515e10i | 1.55486i | 0.628969 | + | 0.777430i | \(0.283477\pi\) | ||||
−0.628969 | + | 0.777430i | \(0.716523\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.61973e9 | −0.238587 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.68851e10 | −1.68748 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.07416e9i | 0.183840i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 6.96626e8i | − 0.0397120i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.05951e8 | −0.0329448 | −0.0164724 | − | 0.999864i | \(-0.505244\pi\) | ||||
−0.0164724 | + | 0.999864i | \(0.505244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.24435e10 | −0.645559 | −0.322780 | − | 0.946474i | \(-0.604617\pi\) | ||||
−0.322780 | + | 0.946474i | \(0.604617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.85391e10i | 1.41346i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 6.81666e9i | − 0.322458i | −0.986917 | − | 0.161229i | \(-0.948454\pi\) | ||||
0.986917 | − | 0.161229i | \(-0.0515458\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.91661e10 | 0.866351 | 0.433175 | − | 0.901310i | \(-0.357393\pi\) | ||||
0.433175 | + | 0.901310i | \(0.357393\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.07239e10 | −0.895549 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.20593e9i | − 0.0498413i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.99089e10i | 0.787327i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.15997e9 | 0.157479 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.03852e9 | −0.327672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 9.48425e9i | − 0.329406i | −0.986343 | − | 0.164703i | \(-0.947333\pi\) | ||||
0.986343 | − | 0.164703i | \(-0.0526666\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.17779e10i | − 0.392066i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00962e10 | −0.960592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.63824e9 | −0.203228 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.15612e10i | 0.927160i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.62841e10i | 1.02318i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.82364e10 | 1.30618 | 0.653089 | − | 0.757281i | \(-0.273473\pi\) | ||||
0.653089 | + | 0.757281i | \(0.273473\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.36693e10 | 0.615694 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3.93639e10i | − 0.983970i | −0.870604 | − | 0.491985i | \(-0.836271\pi\) | ||||
0.870604 | − | 0.491985i | \(-0.163729\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.21477e10i | 1.49336i | 0.665182 | + | 0.746681i | \(0.268354\pi\) | ||||
−0.665182 | + | 0.746681i | \(0.731646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.34409e9 | 0.0310581 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.09062e10 | 1.57610 | 0.788048 | − | 0.615614i | \(-0.211092\pi\) | ||||
0.788048 | + | 0.615614i | \(0.211092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.56584e9i | 0.0548813i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.38916e10i | 1.10957i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.01178e10 | 1.39007 | 0.695036 | − | 0.718975i | \(-0.255388\pi\) | ||||
0.695036 | + | 0.718975i | \(0.255388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.33658e10 | 1.40093 | 0.700466 | − | 0.713686i | \(-0.252975\pi\) | ||||
0.700466 | + | 0.713686i | \(0.252975\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 3.48678e9i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.11066e10i | 1.61548i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.06681e11 | −1.82369 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.46898e10 | 0.407024 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 5.19577e10i | − 0.826263i | −0.910671 | − | 0.413132i | \(-0.864435\pi\) | ||||
0.910671 | − | 0.413132i | \(-0.135565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.02639e9i | 0.123162i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.63849e10 | 0.686982 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.06918e11 | 1.52881 | 0.764405 | − | 0.644736i | \(-0.223033\pi\) | ||||
0.764405 | + | 0.644736i | \(0.223033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.49448e10i | 0.206368i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 6.03597e9i | − 0.0805128i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.44592e10 | −0.959660 | −0.479830 | − | 0.877362i | \(-0.659302\pi\) | ||||
−0.479830 | + | 0.877362i | \(0.659302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.16160e10 | 0.269259 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.74102e10i | − 0.330074i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.17901e10i | 0.486618i | 0.969949 | + | 0.243309i | \(0.0782329\pi\) | ||||
−0.969949 | + | 0.243309i | \(0.921767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.20098e10 | −0.473139 | −0.236570 | − | 0.971615i | \(-0.576023\pi\) | ||||
−0.236570 | + | 0.971615i | \(0.576023\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.58643e10 | 0.172857 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.56684e10i | 0.481525i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.22601e11i | 1.25122i | 0.780136 | + | 0.625610i | \(0.215150\pi\) | ||||
−0.780136 | + | 0.625610i | \(0.784850\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.32260e10 | −0.328291 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.14643e11 | −1.09690 | −0.548452 | − | 0.836182i | \(-0.684783\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.15293e11i | 1.06848i | 0.845334 | + | 0.534239i | \(0.179402\pi\) | ||||
−0.845334 | + | 0.534239i | \(0.820598\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.36379e11i | 1.22446i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.10669e10 | 0.0962849 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.96149e10 | −0.502707 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.03847e11i | − 0.848939i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.62732e11i | 1.28994i | 0.764207 | + | 0.644971i | \(0.223130\pi\) | ||||
−0.764207 | + | 0.644971i | \(0.776870\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.78128e9 | 0.0444452 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.72752e9 | 0.0501708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.47351e10i | 0.685473i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.67298e10i | 0.117474i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.80812e10 | −0.668488 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.05380e11 | −0.697280 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 4.86945e10i | − 0.312865i | −0.987689 | − | 0.156433i | \(-0.950001\pi\) | ||||
0.987689 | − | 0.156433i | \(-0.0499994\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.38862e11i | − 0.866501i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.73861e11 | 1.05386 | 0.526928 | − | 0.849910i | \(-0.323344\pi\) | ||||
0.526928 | + | 0.849910i | \(0.323344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.89931e10 | −0.229635 | −0.114818 | − | 0.993387i | \(-0.536628\pi\) | ||||
−0.114818 | + | 0.993387i | \(0.536628\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.02805e10i | − 0.116060i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.07976e11i | 1.15677i | 0.815764 | + | 0.578385i | \(0.196317\pi\) | ||||
−0.815764 | + | 0.578385i | \(0.803683\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.16460e10 | 0.0629679 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.85100e11 | −0.973045 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.73390e11i | 0.886365i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.39022e11i | 2.67998i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.44892e9 | −0.0457001 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.42629e9 | 0.00671163 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1.26118e11i | − 0.577498i | −0.957405 | − | 0.288749i | \(-0.906761\pi\) | ||||
0.957405 | − | 0.288749i | \(-0.0932393\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.48026e10i | 0.333363i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.03325e11 | −2.61728 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.49166e11 | −0.629991 | −0.314996 | − | 0.949093i | \(-0.602003\pi\) | ||||
−0.314996 | + | 0.949093i | \(0.602003\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.88825e11i | − 0.776535i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 6.41074e10i | − 0.256752i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.03541e11 | 0.403912 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.21107e11 | 0.460240 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.56632e11i | 1.32050i | 0.751046 | + | 0.660250i | \(0.229550\pi\) | ||||
−0.751046 | + | 0.660250i | \(0.770450\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.37695e10i | 0.194009i | 0.995284 | + | 0.0970044i | \(0.0309261\pi\) | ||||
−0.995284 | + | 0.0970044i | \(0.969074\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.94046e10 | 0.279231 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.75541e11 | −0.601718 | −0.300859 | − | 0.953669i | \(-0.597273\pi\) | ||||
−0.300859 | + | 0.953669i | \(0.597273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 3.42884e11i | − 1.14583i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2.57843e10i | − 0.0840134i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.70333e11 | 0.858963 | 0.429482 | − | 0.903076i | \(-0.358696\pi\) | ||||
0.429482 | + | 0.903076i | \(0.358696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.87106e11 | −0.579837 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.78013e11i | − 0.538112i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.18826e11i | 2.70966i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.72371e11 | −1.93469 | −0.967345 | − | 0.253463i | \(-0.918431\pi\) | ||||
−0.967345 | + | 0.253463i | \(0.918431\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.53927e10 | 0.155537 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.20159e10i | − 0.0329286i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.33707e11i | 1.42762i | 0.700339 | + | 0.713811i | \(0.253032\pi\) | ||||
−0.700339 | + | 0.713811i | \(0.746968\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.16013e11 | 0.825210 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.37457e11 | 0.350454 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 2.28214e11i | − 0.568155i | −0.958801 | − | 0.284077i | \(-0.908313\pi\) | ||||
0.958801 | − | 0.284077i | \(-0.0916872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.77845e11i | 0.675524i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.21713e11 | 1.71384 | 0.856919 | − | 0.515451i | \(-0.172376\pi\) | ||||
0.856919 | + | 0.515451i | \(0.172376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.91299e10 | 0.0907687 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.37370e10i | 0.189766i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3.78958e11i | − 0.839107i | −0.907731 | − | 0.419554i | \(-0.862187\pi\) | ||||
0.907731 | − | 0.419554i | \(-0.137813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.53974e11 | 0.333159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.07006e11 | −0.860665 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.56892e12i | 3.24275i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 7.33971e11i | − 1.48293i | −0.670989 | − | 0.741467i | \(-0.734130\pi\) | ||||
0.670989 | − | 0.741467i | \(-0.265870\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.58100e10 | 0.149744 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.66124e11 | −0.513967 | −0.256983 | − | 0.966416i | \(-0.582729\pi\) | ||||
−0.256983 | + | 0.966416i | \(0.582729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 7.56657e11i | − 1.42898i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.01509e11i | − 0.187481i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.44327e11 | −0.260718 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.86135e11 | 1.21242 | 0.606212 | − | 0.795303i | \(-0.292688\pi\) | ||||
0.606212 | + | 0.795303i | \(0.292688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10129e11i | 0.190376i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.21369e9i | − 0.00543536i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.18781e11 | 1.18954 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.90898e11 | 0.956975 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 3.83589e11i | − 0.608000i | −0.952672 | − | 0.304000i | \(-0.901678\pi\) | ||||
0.952672 | − | 0.304000i | \(-0.0983223\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.77263e11i | 1.05072i | 0.850879 | + | 0.525361i | \(0.176070\pi\) | ||||
−0.850879 | + | 0.525361i | \(0.823930\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.13896e9 | 0.0108418 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.76077e11 | 1.30254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.85782e10i | 0.0852727i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.53206e11i | 0.218382i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.46217e11 | −0.483282 | −0.241641 | − | 0.970366i | \(-0.577686\pi\) | ||||
−0.241641 | + | 0.970366i | \(0.577686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.60273e11 | 1.03938 | 0.519689 | − | 0.854355i | \(-0.326048\pi\) | ||||
0.519689 | + | 0.854355i | \(0.326048\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.75722e11i | − 0.235302i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.52708e11i | 0.593815i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.35206e11 | −0.173742 | −0.0868710 | − | 0.996220i | \(-0.527687\pi\) | ||||
−0.0868710 | + | 0.996220i | \(0.527687\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.53487e11 | 0.319140 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9.04003e11i | − 1.11520i | −0.830110 | − | 0.557600i | \(-0.811722\pi\) | ||||
0.830110 | − | 0.557600i | \(-0.188278\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 7.97980e11i | − 0.964655i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.13789e10 | 0.0608696 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.50987e11 | 0.639784 | 0.319892 | − | 0.947454i | \(-0.396353\pi\) | ||||
0.319892 | + | 0.947454i | \(0.396353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06877e11i | 0.121643i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.27314e11i | 0.253620i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.61849e11 | 0.505183 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.15885e12 | 1.24281 | 0.621405 | − | 0.783489i | \(-0.286562\pi\) | ||||
0.621405 | + | 0.783489i | \(0.286562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.29057e11i | − 0.135714i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.46065e11i | 0.666227i | 0.942887 | + | 0.333113i | \(0.108099\pi\) | ||||
−0.942887 | + | 0.333113i | \(0.891901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.66388e11 | −0.876189 | −0.438094 | − | 0.898929i | \(-0.644346\pi\) | ||||
−0.438094 | + | 0.898929i | \(0.644346\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.67294e11 | −0.959445 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2.75888e11i | − 0.268415i | −0.990953 | − | 0.134207i | \(-0.957151\pi\) | ||||
0.990953 | − | 0.134207i | \(-0.0428488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.35375e11i | 0.320076i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.80702e11 | −0.356444 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.61565e11 | −0.148413 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.57581e12i | 2.32163i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 6.01425e10i | − 0.0531923i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.20650e12 | 1.91511 | 0.957555 | − | 0.288249i | \(-0.0930732\pi\) | ||||
0.957555 | + | 0.288249i | \(0.0930732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70348e12 | −1.45106 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6.73209e10i | − 0.0562844i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 3.02326e12i | − 2.48106i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.21730e11 | −0.259186 | −0.129593 | − | 0.991567i | \(-0.541367\pi\) | ||||
−0.129593 | + | 0.991567i | \(0.541367\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.29018e11 | 0.576566 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 3.80381e11i | − 0.295360i | −0.989035 | − | 0.147680i | \(-0.952819\pi\) | ||||
0.989035 | − | 0.147680i | \(-0.0471806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.23410e11i | − 0.170330i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.95855e11 | 0.146626 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.90602e11 | −0.140127 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.33496e11i | 0.240790i | 0.992726 | + | 0.120395i | \(0.0384161\pi\) | ||||
−0.992726 | + | 0.120395i | \(0.961584\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.23085e12i | − 0.872843i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.16862e12 | −0.813990 | −0.406995 | − | 0.913430i | \(-0.633423\pi\) | ||||
−0.406995 | + | 0.913430i | \(0.633423\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.85539e12 | −1.95368 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.49317e11i | 0.638080i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.20618e12i | − 0.796494i | −0.917278 | − | 0.398247i | \(-0.869619\pi\) | ||||
0.917278 | − | 0.398247i | \(-0.130381\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.10755e11 | 0.331374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.79448e11 | 0.241894 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.04261e12i | − 2.53238i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.37742e10i | 0.00847925i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.20025e12 | 0.726137 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.06301e12 | −1.82129 | −0.910645 | − | 0.413189i | \(-0.864415\pi\) | ||||
−0.910645 | + | 0.413189i | \(0.864415\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.23351e12i | 1.30536i | 0.757633 | + | 0.652681i | \(0.226356\pi\) | ||||
−0.757633 | + | 0.652681i | \(0.773644\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3.83041e11i | − 0.220054i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.22980e12 | −0.694524 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.39914e12 | −0.776802 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.60853e10i | − 0.00878019i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.26146e12i | 0.677018i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.38872e12 | −2.84376 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.99725e12 | −1.03645 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.89085e11i | 0.249595i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 5.90938e11i | − 0.296588i | −0.988943 | − | 0.148294i | \(-0.952622\pi\) | ||||
0.988943 | − | 0.148294i | \(-0.0473782\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.81857e12 | 0.897699 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.75082e11 | −0.133560 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.09173e12i | − 1.47659i | −0.674479 | − | 0.738294i | \(-0.735632\pi\) | ||||
0.674479 | − | 0.738294i | \(-0.264368\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.93198e11i | 0.137748i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.56862e11 | 0.303593 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.72128e11 | 0.396568 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.17769e12i | 0.974267i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2.94524e12i | − 1.29650i | −0.761428 | − | 0.648249i | \(-0.775501\pi\) | ||||
0.761428 | − | 0.648249i | \(-0.224499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.90694e12 | −0.826009 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.49007e11 | 0.106140 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.62039e12i | − 1.09920i | −0.835427 | − | 0.549602i | \(-0.814779\pi\) | ||||
0.835427 | − | 0.549602i | \(-0.185221\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.49718e12i | − 2.26946i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.64267e10 | −0.0229277 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.57955e11 | 0.383124 | 0.191562 | − | 0.981480i | \(-0.438645\pi\) | ||||
0.191562 | + | 0.981480i | \(0.438645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.78103e12i | 0.701148i | 0.936535 | + | 0.350574i | \(0.114014\pi\) | ||||
−0.936535 | + | 0.350574i | \(0.885986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.90820e10i | 0.0190207i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.28737e12 | 0.872632 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.57175e12 | 1.71708 | 0.858542 | − | 0.512743i | \(-0.171371\pi\) | ||||
0.858542 | + | 0.512743i | \(0.171371\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.00793e12i | 0.372714i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 3.99555e11i | − 0.145473i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.16041e11 | 0.0416009 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.31167e12 | 0.816064 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.32819e12i | − 0.809368i | −0.914456 | − | 0.404684i | \(-0.867381\pi\) | ||||
0.914456 | − | 0.404684i | \(-0.132619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.61581e12i | − 1.23790i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.52149e11 | −0.186171 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.75980e11 | 0.257694 | 0.128847 | − | 0.991664i | \(-0.458872\pi\) | ||||
0.128847 | + | 0.991664i | \(0.458872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 7.50647e11i | − 0.245533i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.55245e12i | − 0.500188i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.58904e12 | −1.13909 | −0.569544 | − | 0.821961i | \(-0.692880\pi\) | ||||
−0.569544 | + | 0.821961i | \(0.692880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.43528e12 | −0.761400 | −0.380700 | − | 0.924699i | \(-0.624317\pi\) | ||||
−0.380700 | + | 0.924699i | \(0.624317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.67864e12i | 0.517045i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 5.18242e12i | − 1.57266i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.16109e11 | −0.0646136 | −0.0323068 | − | 0.999478i | \(-0.510285\pi\) | ||||
−0.0323068 | + | 0.999478i | \(0.510285\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.76802e10 | −0.0287759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.62576e11i | 0.0471922i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.34985e12i | − 1.53028i | −0.643866 | − | 0.765138i | \(-0.722671\pi\) | ||||
0.643866 | − | 0.765138i | \(-0.277329\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.61262e12 | 0.454563 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.02003e12 | 1.11673 | 0.558363 | − | 0.829597i | \(-0.311430\pi\) | ||||
0.558363 | + | 0.829597i | \(0.311430\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.33115e12i | 0.638209i | 0.947720 | + | 0.319104i | \(0.103382\pi\) | ||||
−0.947720 | + | 0.319104i | \(0.896618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 3.36958e11i | − 0.0909208i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.43579e11 | −0.117971 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.15389e12 | 0.564629 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.32120e11i | 0.189181i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.76868e12i | 0.705253i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.60959e12 | 0.404188 | 0.202094 | − | 0.979366i | \(-0.435225\pi\) | ||||
0.202094 | + | 0.979366i | \(0.435225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.68225e11 | −0.190183 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.08878e12i | 1.97425i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.77265e12i | 1.38915i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.54010e11 | −0.226360 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.07113e10 | 0.0212227 | 0.0106113 | − | 0.999944i | \(-0.496622\pi\) | ||||
0.0106113 | + | 0.999944i | \(0.496622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.99830e12i | − 0.922415i | −0.887292 | − | 0.461207i | \(-0.847416\pi\) | ||||
0.887292 | − | 0.461207i | \(-0.152584\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.43780e12i | 0.554598i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.74626e12 | 1.73789 | 0.868946 | − | 0.494907i | \(-0.164798\pi\) | ||||
0.868946 | + | 0.494907i | \(0.164798\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.10355e10 | 0.00686685 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.37697e11i | 0.117334i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3.69315e12i | − 0.794854i | −0.917634 | − | 0.397427i | \(-0.869903\pi\) | ||||
0.917634 | − | 0.397427i | \(-0.130097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.18490e13 | −2.51533 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.55646e12 | 0.535296 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 9.56399e12i | − 1.97540i | −0.156363 | − | 0.987700i | \(-0.549977\pi\) | ||||
0.156363 | − | 0.987700i | \(-0.450023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 5.90211e12i | − 1.20254i | −0.799044 | − | 0.601272i | \(-0.794661\pi\) | ||||
0.799044 | − | 0.601272i | \(-0.205339\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.93902e12 | 0.590733 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.20702e12 | 0.437632 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5.83307e11i | − 0.114112i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 3.90714e12i | − 0.754123i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.65707e11 | −0.107731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.04043e12 | 0.383402 | 0.191701 | − | 0.981453i | \(-0.438600\pi\) | ||||
0.191701 | + | 0.981453i | \(0.438600\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.91722e12i | − 0.355471i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.46220e12i | − 0.999352i | −0.866212 | − | 0.499676i | \(-0.833452\pi\) | ||||
0.866212 | − | 0.499676i | \(-0.166548\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.68056e12 | −0.303417 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.18848e12 | −0.568096 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.00775e13i | 1.77198i | 0.463703 | + | 0.885991i | \(0.346520\pi\) | ||||
−0.463703 | + | 0.885991i | \(0.653480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.20612e12i | 0.556381i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.03396e12 | 0.862193 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.36962e12 | 0.231534 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 4.61451e12i | − 0.769970i | −0.922923 | − | 0.384985i | \(-0.874207\pi\) | ||||
0.922923 | − | 0.384985i | \(-0.125793\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.08872e11i | − 0.0179314i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.72025e13 | 2.79680 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.05026e12 | 0.329050 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 5.74340e12i | − 0.909959i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.75605e12i | − 0.274666i | −0.990525 | − | 0.137333i | \(-0.956147\pi\) | ||||
0.990525 | − | 0.137333i | \(-0.0438531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.14037e12 | −1.25703 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.07833e11 | 0.0316857 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.58725e12i | 0.238923i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.66308e12i | − 0.247175i | −0.992334 | − | 0.123587i | \(-0.960560\pi\) | ||||
0.992334 | − | 0.123587i | \(-0.0394399\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.36522e12 | 0.640609 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.21091e12 | −0.465292 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.46021e12i | 0.638231i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 5.67954e12i | − 0.802559i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.86871e12 | 0.400319 | 0.200160 | − | 0.979763i | \(-0.435854\pi\) | ||||
0.200160 | + | 0.979763i | \(0.435854\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.24720e12 | −0.309694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 5.94263e12i | − 0.808829i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.31889e12i | − 0.446141i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.23515e12 | −0.429526 | −0.214763 | − | 0.976666i | \(-0.568898\pi\) | ||||
−0.214763 | + | 0.976666i | \(0.568898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.09937e12i | 0.401463i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.30921e12i | 0.423405i | 0.977334 | + | 0.211703i | \(0.0679008\pi\) | ||||
−0.977334 | + | 0.211703i | \(0.932099\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.37963e12 | 0.932700 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.23882e12 | −0.404374 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.46011e12i | 0.426766i | 0.976969 | + | 0.213383i | \(0.0684482\pi\) | ||||
−0.976969 | + | 0.213383i | \(0.931552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.64118e12i | 1.05291i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.38595e12 | −0.527976 | −0.263988 | − | 0.964526i | \(-0.585038\pi\) | ||||
−0.263988 | + | 0.964526i | \(0.585038\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.49577e12 | 0.177894 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.99987e12i | − 0.234995i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.99547e12i | 0.347774i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.34891e12 | 0.154741 | 0.0773703 | − | 0.997002i | \(-0.475348\pi\) | ||||
0.0773703 | + | 0.997002i | \(0.475348\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.20858e12 | −0.477043 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.61768e12i | 0.741216i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 8.21137e10i | − 0.00908833i | −0.999990 | − | 0.00454417i | \(-0.998554\pi\) | ||||
0.999990 | − | 0.00454417i | \(-0.00144646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.50138e11 | 0.0711078 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.70402e13 | −1.84180 | −0.920901 | − | 0.389796i | \(-0.872545\pi\) | ||||
−0.920901 | + | 0.389796i | \(0.872545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.52912e11i | 0.0163336i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3.75717e12i | − 0.396629i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.66311e11 | 0.0382182 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.31929e13 | −1.36041 | −0.680206 | − | 0.733021i | \(-0.738109\pi\) | ||||
−0.680206 | + | 0.733021i | \(0.738109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 8.66040e12i | − 0.882659i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.36151e12i | 0.943057i | 0.881851 | + | 0.471529i | \(0.156298\pi\) | ||||
−0.881851 | + | 0.471529i | \(0.843702\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.82694e13 | −1.81914 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.21053e12 | 0.119147 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.02809e12i | 0.586491i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.84070e12i | − 0.177033i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.88914e11 | −0.0464841 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.10832e13 | −1.04172 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.69737e12i | − 0.436484i | −0.975895 | − | 0.218242i | \(-0.929968\pi\) | ||||
0.975895 | − | 0.218242i | \(-0.0700323\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.03119e12i | 0.554060i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.05576e12 | −0.277540 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.67701e12 | −0.599587 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.75090e12i | − 0.155457i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.57832e12i | − 0.138558i | −0.997597 | − | 0.0692791i | \(-0.977930\pi\) | ||||
0.997597 | − | 0.0692791i | \(-0.0220699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.64236e11 | 0.0229367 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.22022e12 | −0.190568 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.93251e12i | 0.418647i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.95988e12i | − 0.164493i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.38500e12 | 0.280949 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.60915e13 | 1.32077 | 0.660387 | − | 0.750925i | \(-0.270392\pi\) | ||||
0.660387 | + | 0.750925i | \(0.270392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.29953e12i | 0.186657i | 0.995635 | + | 0.0933287i | \(0.0297507\pi\) | ||||
−0.995635 | + | 0.0933287i | \(0.970249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.40280e12i | 0.273167i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.12236e13 | 1.68504 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.11265e12 | −0.715559 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.28501e12i | − 0.0997993i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.01265e13i | 0.777887i | 0.921262 | + | 0.388944i | \(0.127160\pi\) | ||||
−0.921262 | + | 0.388944i | \(0.872840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.20614e13 | −0.916426 | −0.458213 | − | 0.888842i | \(-0.651510\pi\) | ||||
−0.458213 | + | 0.888842i | \(0.651510\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.69914e12 | 0.278009 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.44216e13i | 1.07211i | 0.844183 | + | 0.536054i | \(0.180086\pi\) | ||||
−0.844183 | + | 0.536054i | \(0.819914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.01515e13i | 1.48187i | 0.671574 | + | 0.740937i | \(0.265618\pi\) | ||||
−0.671574 | + | 0.740937i | \(0.734382\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.93065e12 | 0.722392 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.38234e12 | 0.675163 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.58332e13i | − 2.55092i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.69131e12i | 0.189539i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.41876e13 | −0.988507 | −0.494253 | − | 0.869318i | \(-0.664558\pi\) | ||||
−0.494253 | + | 0.869318i | \(0.664558\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.36608e13 | 0.941659 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.28607e12i | 0.633298i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.76370e13i | 1.86482i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.88079e12 | −0.192325 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.33877e12 | 0.616886 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.22881e12i | 0.472481i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.03561e13i | 0.669768i | 0.942259 | + | 0.334884i | \(0.108697\pi\) | ||||
−0.942259 | + | 0.334884i | \(0.891303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.10467e13 | 0.706944 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.15824e13 | 0.733476 | 0.366738 | − | 0.930324i | \(-0.380475\pi\) | ||||
0.366738 | + | 0.930324i | \(0.380475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4.06490e12i | − 0.254730i | −0.991856 | − | 0.127365i | \(-0.959348\pi\) | ||||
0.991856 | − | 0.127365i | \(-0.0406520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 8.96421e11i | − 0.0555901i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.08032e12 | 0.189037 | 0.0945186 | − | 0.995523i | \(-0.469869\pi\) | ||||
0.0945186 | + | 0.995523i | \(0.469869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.49423e13 | 2.12217 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.82881e12i | 0.290238i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.42240e12i | 0.501011i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.82276e13 | −2.25058 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.41163e12 | −0.490135 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5.11405e12i | − 0.294936i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.13243e11i | − 0.0121724i | −0.999981 | − | 0.00608620i | \(-0.998063\pi\) | ||||
0.999981 | − | 0.00608620i | \(-0.00193731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.31813e13 | 0.744748 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.30543e10 | −0.00408558 | −0.00204279 | − | 0.999998i | \(-0.500650\pi\) | ||||
−0.00204279 | + | 0.999998i | \(0.500650\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.02997e13i | 0.570164i | 0.958503 | + | 0.285082i | \(0.0920209\pi\) | ||||
−0.958503 | + | 0.285082i | \(0.907979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 4.68284e11i | − 0.0256605i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.79649e13 | 1.51690 | 0.758450 | − | 0.651732i | \(-0.225957\pi\) | ||||
0.758450 | + | 0.651732i | \(0.225957\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.49637e12 | 0.241437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5.44929e11i | − 0.0289661i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.76895e11i | 0.0408819i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.81449e13 | −3.02906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.67354e12 | 0.395758 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.65892e12i | 0.237885i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.22606e12i | − 0.112532i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.35512e12 | 0.0678237 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.29432e13 | 2.62356 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.31646e12i | 0.113656i | 0.998384 | + | 0.0568279i | \(0.0180986\pi\) | ||||
−0.998384 | + | 0.0568279i | \(0.981901\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.94457e12i | 0.385952i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.61506e13 | 0.776883 | 0.388442 | − | 0.921473i | \(-0.373014\pi\) | ||||
0.388442 | + | 0.921473i | \(0.373014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.85862e12 | 0.183786 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.53574e12i | 0.402575i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.58658e12i | 0.307608i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.40206e13 | −1.57334 | −0.786670 | − | 0.617374i | \(-0.788197\pi\) | ||||
−0.786670 | + | 0.617374i | \(0.788197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.94425e12 | −0.180633 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.17257e13i | − 0.985293i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.11304e13i | 1.84725i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.12478e13 | −0.500275 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.99915e13 | −1.32108 | −0.660538 | − | 0.750793i | \(-0.729672\pi\) | ||||
−0.660538 | + | 0.750793i | \(0.729672\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.75856e13i | 1.20340i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.40828e13i | − 0.608444i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.24922e12 | 0.310198 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.38419e13 | −1.01044 | −0.505222 | − | 0.862990i | \(-0.668589\pi\) | ||||
−0.505222 | + | 0.862990i | \(0.668589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.15844e12i | 0.132580i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.93491e12i | 0.163599i | 0.996649 | + | 0.0817996i | \(0.0260667\pi\) | ||||
−0.996649 | + | 0.0817996i | \(0.973933\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.35307e12 | 0.220445 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.64272e12 | −0.0670072 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.29195e13i | − 0.926042i | −0.886347 | − | 0.463021i | \(-0.846765\pi\) | ||||
0.886347 | − | 0.463021i | \(-0.153235\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.82182e13i | 2.33003i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.68461e13 | 0.667862 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.69689e13 | −1.05912 | −0.529561 | − | 0.848272i | \(-0.677643\pi\) | ||||
−0.529561 | + | 0.848272i | \(0.677643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.42890e12i | 0.0555888i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.43326e11i | − 0.0363545i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.78221e12 | 0.0680418 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.93797e11 | −0.0300230 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.49931e13i | 0.561788i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.93433e13i | 1.08927i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.79377e13 | 0.659703 | 0.329852 | − | 0.944033i | \(-0.393001\pi\) | ||||
0.329852 | + | 0.944033i | \(0.393001\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.40446e13 | 0.511743 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 3.36215e13i | − 1.21375i | −0.794796 | − | 0.606876i | \(-0.792422\pi\) | ||||
0.794796 | − | 0.606876i | \(-0.207578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.56252e12i | − 0.342030i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.36608e13 | 1.54729 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.54989e13 | −1.24649 | −0.623245 | − | 0.782026i | \(-0.714186\pi\) | ||||
−0.623245 | + | 0.782026i | \(0.714186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 4.28378e12i | − 0.149041i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.65362e11i | 0.0263850i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.84871e11 | −0.0268107 | −0.0134053 | − | 0.999910i | \(-0.504267\pi\) | ||||
−0.0134053 | + | 0.999910i | \(0.504267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.60745e13 | −0.544093 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.15530e11i | − 0.00387496i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.09222e12i | 0.268958i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.31644e13 | −1.42165 | −0.710827 | − | 0.703367i | \(-0.751679\pi\) | ||||
−0.710827 | + | 0.703367i | \(0.751679\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.02155e13 | −0.333419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 4.51958e13i | − 1.46182i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.72331e12i | − 0.119344i | −0.998218 | − | 0.0596720i | \(-0.980995\pi\) | ||||
0.998218 | − | 0.0596720i | \(-0.0190055\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.05901e12 | 0.192467 |
(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 | 384.10.d.f.193.1 | ✓ | 20 | |
4.3 | odd | 2 | inner | 384.10.d.f.193.11 | yes | 20 | |
8.3 | odd | 2 | inner | 384.10.d.f.193.10 | yes | 20 | |
8.5 | even | 2 | inner | 384.10.d.f.193.20 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.d.f.193.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
384.10.d.f.193.10 | yes | 20 | 8.3 | odd | 2 | inner | |
384.10.d.f.193.11 | yes | 20 | 4.3 | odd | 2 | inner | |
384.10.d.f.193.20 | yes | 20 | 8.5 | even | 2 | inner |