Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-17.9442\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 17.9442 | 1.58606 | 0.793028 | − | 0.609185i | \(-0.208503\pi\) | ||||
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 193.993 | 1.51557 | ||||||||
\(5\) | 1.22320 | 0.00437627 | 0.00218813 | − | 0.999998i | \(-0.499303\pi\) | ||||
0.00218813 | + | 0.999998i | \(0.499303\pi\) | |||||||
\(6\) | −484.493 | −0.915710 | ||||||||
\(7\) | −719.259 | −0.792578 | −0.396289 | − | 0.918126i | \(-0.629702\pi\) | ||||
−0.396289 | + | 0.918126i | \(0.629702\pi\) | |||||||
\(8\) | 1184.20 | 0.817727 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 21.9494 | 0.00694101 | ||||||||
\(11\) | 1110.85 | 0.251640 | 0.125820 | − | 0.992053i | \(-0.459844\pi\) | ||||
0.125820 | + | 0.992053i | \(0.459844\pi\) | |||||||
\(12\) | −5237.82 | −0.875016 | ||||||||
\(13\) | 8283.40 | 1.04570 | 0.522850 | − | 0.852425i | \(-0.324869\pi\) | ||||
0.522850 | + | 0.852425i | \(0.324869\pi\) | |||||||
\(14\) | −12906.5 | −1.25707 | ||||||||
\(15\) | −33.0265 | −0.00252664 | ||||||||
\(16\) | −3581.74 | −0.218612 | ||||||||
\(17\) | 4834.97 | 0.238684 | 0.119342 | − | 0.992853i | \(-0.461922\pi\) | ||||
0.119342 | + | 0.992853i | \(0.461922\pi\) | |||||||
\(18\) | 13081.3 | 0.528685 | ||||||||
\(19\) | −31620.9 | −1.05764 | −0.528818 | − | 0.848735i | \(-0.677365\pi\) | ||||
−0.528818 | + | 0.848735i | \(0.677365\pi\) | |||||||
\(20\) | 237.293 | 0.00663255 | ||||||||
\(21\) | 19420.0 | 0.457595 | ||||||||
\(22\) | 19933.3 | 0.399116 | ||||||||
\(23\) | −43588.0 | −0.746997 | −0.373499 | − | 0.927631i | \(-0.621842\pi\) | ||||
−0.373499 | + | 0.927631i | \(0.621842\pi\) | |||||||
\(24\) | −31973.3 | −0.472115 | ||||||||
\(25\) | −78123.5 | −0.999981 | ||||||||
\(26\) | 148639. | 1.65854 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −139531. | −1.20121 | ||||||||
\(29\) | −232502. | −1.77025 | −0.885123 | − | 0.465358i | \(-0.845926\pi\) | ||||
−0.885123 | + | 0.465358i | \(0.845926\pi\) | |||||||
\(30\) | −592.634 | −0.00400739 | ||||||||
\(31\) | −85314.0 | −0.514345 | −0.257172 | − | 0.966366i | \(-0.582791\pi\) | ||||
−0.257172 | + | 0.966366i | \(0.582791\pi\) | |||||||
\(32\) | −215848. | −1.16446 | ||||||||
\(33\) | −29992.9 | −0.145285 | ||||||||
\(34\) | 86759.6 | 0.378566 | ||||||||
\(35\) | −879.800 | −0.00346853 | ||||||||
\(36\) | 141421. | 0.505191 | ||||||||
\(37\) | −52796.8 | −0.171357 | −0.0856784 | − | 0.996323i | \(-0.527306\pi\) | ||||
−0.0856784 | + | 0.996323i | \(0.527306\pi\) | |||||||
\(38\) | −567411. | −1.67747 | ||||||||
\(39\) | −223652. | −0.603735 | ||||||||
\(40\) | 1448.51 | 0.00357859 | ||||||||
\(41\) | −589172. | −1.33505 | −0.667527 | − | 0.744585i | \(-0.732647\pi\) | ||||
−0.667527 | + | 0.744585i | \(0.732647\pi\) | |||||||
\(42\) | 348476. | 0.725771 | ||||||||
\(43\) | 367000. | 0.703926 | 0.351963 | − | 0.936014i | \(-0.385514\pi\) | ||||
0.351963 | + | 0.936014i | \(0.385514\pi\) | |||||||
\(44\) | 215497. | 0.381379 | ||||||||
\(45\) | 891.716 | 0.00145876 | ||||||||
\(46\) | −782150. | −1.18478 | ||||||||
\(47\) | 739433. | 1.03886 | 0.519429 | − | 0.854514i | \(-0.326145\pi\) | ||||
0.519429 | + | 0.854514i | \(0.326145\pi\) | |||||||
\(48\) | 96706.9 | 0.126216 | ||||||||
\(49\) | −306210. | −0.371820 | ||||||||
\(50\) | −1.40186e6 | −1.58603 | ||||||||
\(51\) | −130544. | −0.137804 | ||||||||
\(52\) | 1.60692e6 | 1.58483 | ||||||||
\(53\) | 1.53905e6 | 1.42000 | 0.710000 | − | 0.704201i | \(-0.248695\pi\) | ||||
0.710000 | + | 0.704201i | \(0.248695\pi\) | |||||||
\(54\) | −353195. | −0.305237 | ||||||||
\(55\) | 1358.79 | 0.00110125 | ||||||||
\(56\) | −851743. | −0.648113 | ||||||||
\(57\) | 853764. | 0.610627 | ||||||||
\(58\) | −4.17205e6 | −2.80771 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −6406.92 | −0.00382931 | ||||||||
\(61\) | 325249. | 0.183469 | 0.0917343 | − | 0.995784i | \(-0.470759\pi\) | ||||
0.0917343 | + | 0.995784i | \(0.470759\pi\) | |||||||
\(62\) | −1.53089e6 | −0.815779 | ||||||||
\(63\) | −524340. | −0.264193 | ||||||||
\(64\) | −3.41476e6 | −1.62828 | ||||||||
\(65\) | 10132.3 | 0.00457626 | ||||||||
\(66\) | −538198. | −0.230430 | ||||||||
\(67\) | −1.72338e6 | −0.700035 | −0.350018 | − | 0.936743i | \(-0.613824\pi\) | ||||
−0.350018 | + | 0.936743i | \(0.613824\pi\) | |||||||
\(68\) | 937953. | 0.361743 | ||||||||
\(69\) | 1.17687e6 | 0.431279 | ||||||||
\(70\) | −15787.3 | −0.00550129 | ||||||||
\(71\) | −4.29199e6 | −1.42316 | −0.711582 | − | 0.702603i | \(-0.752021\pi\) | ||||
−0.711582 | + | 0.702603i | \(0.752021\pi\) | |||||||
\(72\) | 863278. | 0.272576 | ||||||||
\(73\) | −1.55847e6 | −0.468888 | −0.234444 | − | 0.972130i | \(-0.575327\pi\) | ||||
−0.234444 | + | 0.972130i | \(0.575327\pi\) | |||||||
\(74\) | −947394. | −0.271781 | ||||||||
\(75\) | 2.10933e6 | 0.577339 | ||||||||
\(76\) | −6.13424e6 | −1.60292 | ||||||||
\(77\) | −798988. | −0.199445 | ||||||||
\(78\) | −4.01324e6 | −0.957557 | ||||||||
\(79\) | −3.39722e6 | −0.775226 | −0.387613 | − | 0.921822i | \(-0.626700\pi\) | ||||
−0.387613 | + | 0.921822i | \(0.626700\pi\) | |||||||
\(80\) | −4381.20 | −0.000956704 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −1.05722e7 | −2.11747 | ||||||||
\(83\) | −7.04945e6 | −1.35326 | −0.676631 | − | 0.736322i | \(-0.736561\pi\) | ||||
−0.676631 | + | 0.736322i | \(0.736561\pi\) | |||||||
\(84\) | 3.76735e6 | 0.693519 | ||||||||
\(85\) | 5914.16 | 0.00104454 | ||||||||
\(86\) | 6.58552e6 | 1.11647 | ||||||||
\(87\) | 6.27755e6 | 1.02205 | ||||||||
\(88\) | 1.31546e6 | 0.205773 | ||||||||
\(89\) | 1.14007e7 | 1.71422 | 0.857109 | − | 0.515136i | \(-0.172259\pi\) | ||||
0.857109 | + | 0.515136i | \(0.172259\pi\) | |||||||
\(90\) | 16001.1 | 0.00231367 | ||||||||
\(91\) | −5.95791e6 | −0.828798 | ||||||||
\(92\) | −8.45577e6 | −1.13213 | ||||||||
\(93\) | 2.30348e6 | 0.296957 | ||||||||
\(94\) | 1.32685e7 | 1.64769 | ||||||||
\(95\) | −38678.8 | −0.00462850 | ||||||||
\(96\) | 5.82790e6 | 0.672300 | ||||||||
\(97\) | 1.36312e7 | 1.51647 | 0.758236 | − | 0.651980i | \(-0.226062\pi\) | ||||
0.758236 | + | 0.651980i | \(0.226062\pi\) | |||||||
\(98\) | −5.49468e6 | −0.589727 | ||||||||
\(99\) | 809809. | 0.0838802 | ||||||||
\(100\) | −1.51554e7 | −1.51554 | ||||||||
\(101\) | −1.39105e7 | −1.34344 | −0.671719 | − | 0.740806i | \(-0.734444\pi\) | ||||
−0.671719 | + | 0.740806i | \(0.734444\pi\) | |||||||
\(102\) | −2.34251e6 | −0.218565 | ||||||||
\(103\) | 5.48771e6 | 0.494835 | 0.247418 | − | 0.968909i | \(-0.420418\pi\) | ||||
0.247418 | + | 0.968909i | \(0.420418\pi\) | |||||||
\(104\) | 9.80916e6 | 0.855097 | ||||||||
\(105\) | 23754.6 | 0.00200256 | ||||||||
\(106\) | 2.76171e7 | 2.25220 | ||||||||
\(107\) | 735470. | 0.0580393 | 0.0290196 | − | 0.999579i | \(-0.490761\pi\) | ||||
0.0290196 | + | 0.999579i | \(0.490761\pi\) | |||||||
\(108\) | −3.81837e6 | −0.291672 | ||||||||
\(109\) | 2.33048e7 | 1.72366 | 0.861831 | − | 0.507196i | \(-0.169318\pi\) | ||||
0.861831 | + | 0.507196i | \(0.169318\pi\) | |||||||
\(110\) | 24382.5 | 0.00174664 | ||||||||
\(111\) | 1.42551e6 | 0.0989329 | ||||||||
\(112\) | 2.57620e6 | 0.173267 | ||||||||
\(113\) | 1.31124e7 | 0.854885 | 0.427442 | − | 0.904043i | \(-0.359415\pi\) | ||||
0.427442 | + | 0.904043i | \(0.359415\pi\) | |||||||
\(114\) | 1.53201e7 | 0.968488 | ||||||||
\(115\) | −53317.0 | −0.00326906 | ||||||||
\(116\) | −4.51038e7 | −2.68294 | ||||||||
\(117\) | 6.03860e6 | 0.348566 | ||||||||
\(118\) | 3.68536e6 | 0.206487 | ||||||||
\(119\) | −3.47760e6 | −0.189176 | ||||||||
\(120\) | −39109.9 | −0.00206610 | ||||||||
\(121\) | −1.82532e7 | −0.936677 | ||||||||
\(122\) | 5.83632e6 | 0.290991 | ||||||||
\(123\) | 1.59077e7 | 0.770794 | ||||||||
\(124\) | −1.65503e7 | −0.779527 | ||||||||
\(125\) | −191124. | −0.00875245 | ||||||||
\(126\) | −9.40884e6 | −0.419024 | ||||||||
\(127\) | 2.57648e7 | 1.11613 | 0.558063 | − | 0.829799i | \(-0.311545\pi\) | ||||
0.558063 | + | 0.829799i | \(0.311545\pi\) | |||||||
\(128\) | −3.36464e7 | −1.41809 | ||||||||
\(129\) | −9.90901e6 | −0.406412 | ||||||||
\(130\) | 181815. | 0.00725820 | ||||||||
\(131\) | −4.04125e7 | −1.57060 | −0.785302 | − | 0.619113i | \(-0.787492\pi\) | ||||
−0.785302 | + | 0.619113i | \(0.787492\pi\) | |||||||
\(132\) | −5.81843e6 | −0.220190 | ||||||||
\(133\) | 2.27436e7 | 0.838259 | ||||||||
\(134\) | −3.09247e7 | −1.11029 | ||||||||
\(135\) | −24076.3 | −0.000842213 0 | ||||||||
\(136\) | 5.72555e6 | 0.195178 | ||||||||
\(137\) | 3.40595e7 | 1.13166 | 0.565830 | − | 0.824522i | \(-0.308556\pi\) | ||||
0.565830 | + | 0.824522i | \(0.308556\pi\) | |||||||
\(138\) | 2.11180e7 | 0.684033 | ||||||||
\(139\) | 3.98464e6 | 0.125845 | 0.0629227 | − | 0.998018i | \(-0.479958\pi\) | ||||
0.0629227 | + | 0.998018i | \(0.479958\pi\) | |||||||
\(140\) | −170675. | −0.00525682 | ||||||||
\(141\) | −1.99647e7 | −0.599785 | ||||||||
\(142\) | −7.70163e7 | −2.25722 | ||||||||
\(143\) | 9.20160e6 | 0.263140 | ||||||||
\(144\) | −2.61109e6 | −0.0728706 | ||||||||
\(145\) | −284397. | −0.00774707 | ||||||||
\(146\) | −2.79655e7 | −0.743682 | ||||||||
\(147\) | 8.26767e6 | 0.214670 | ||||||||
\(148\) | −1.02422e7 | −0.259704 | ||||||||
\(149\) | 5.83891e6 | 0.144604 | 0.0723020 | − | 0.997383i | \(-0.476965\pi\) | ||||
0.0723020 | + | 0.997383i | \(0.476965\pi\) | |||||||
\(150\) | 3.78503e7 | 0.915692 | ||||||||
\(151\) | 5.13811e7 | 1.21446 | 0.607231 | − | 0.794525i | \(-0.292280\pi\) | ||||
0.607231 | + | 0.794525i | \(0.292280\pi\) | |||||||
\(152\) | −3.74453e7 | −0.864858 | ||||||||
\(153\) | 3.52470e6 | 0.0795613 | ||||||||
\(154\) | −1.43372e7 | −0.316330 | ||||||||
\(155\) | −104356. | −0.00225091 | ||||||||
\(156\) | −4.33869e7 | −0.915004 | ||||||||
\(157\) | −1.14443e7 | −0.236016 | −0.118008 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118008 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(158\) | −6.09602e7 | −1.22955 | ||||||||
\(159\) | −4.15545e7 | −0.819838 | ||||||||
\(160\) | −264027. | −0.00509598 | ||||||||
\(161\) | 3.13510e7 | 0.592054 | ||||||||
\(162\) | 9.53627e6 | 0.176228 | ||||||||
\(163\) | 1.25340e7 | 0.226690 | 0.113345 | − | 0.993556i | \(-0.463844\pi\) | ||||
0.113345 | + | 0.993556i | \(0.463844\pi\) | |||||||
\(164\) | −1.14296e8 | −2.02337 | ||||||||
\(165\) | −36687.5 | −0.000635805 0 | ||||||||
\(166\) | −1.26497e8 | −2.14635 | ||||||||
\(167\) | −3.77486e7 | −0.627182 | −0.313591 | − | 0.949558i | \(-0.601532\pi\) | ||||
−0.313591 | + | 0.949558i | \(0.601532\pi\) | |||||||
\(168\) | 2.29971e7 | 0.374188 | ||||||||
\(169\) | 5.86614e6 | 0.0934865 | ||||||||
\(170\) | 106125. | 0.00165671 | ||||||||
\(171\) | −2.30516e7 | −0.352545 | ||||||||
\(172\) | 7.11956e7 | 1.06685 | ||||||||
\(173\) | −2.06219e7 | −0.302808 | −0.151404 | − | 0.988472i | \(-0.548379\pi\) | ||||
−0.151404 | + | 0.988472i | \(0.548379\pi\) | |||||||
\(174\) | 1.12645e8 | 1.62103 | ||||||||
\(175\) | 5.61910e7 | 0.792563 | ||||||||
\(176\) | −3.97877e6 | −0.0550116 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 2.04576e8 | 2.71884 | ||||||||
\(179\) | −1.01937e8 | −1.32845 | −0.664227 | − | 0.747531i | \(-0.731239\pi\) | ||||
−0.664227 | + | 0.747531i | \(0.731239\pi\) | |||||||
\(180\) | 172987. | 0.00221085 | ||||||||
\(181\) | 9.14678e6 | 0.114655 | 0.0573275 | − | 0.998355i | \(-0.481742\pi\) | ||||
0.0573275 | + | 0.998355i | \(0.481742\pi\) | |||||||
\(182\) | −1.06910e8 | −1.31452 | ||||||||
\(183\) | −8.78172e6 | −0.105926 | ||||||||
\(184\) | −5.16167e7 | −0.610840 | ||||||||
\(185\) | −64581.2 | −0.000749903 0 | ||||||||
\(186\) | 4.13340e7 | 0.470990 | ||||||||
\(187\) | 5.37092e6 | 0.0600625 | ||||||||
\(188\) | 1.43445e8 | 1.57447 | ||||||||
\(189\) | 1.41572e7 | 0.152532 | ||||||||
\(190\) | −694059. | −0.00734106 | ||||||||
\(191\) | 1.28136e8 | 1.33062 | 0.665311 | − | 0.746566i | \(-0.268299\pi\) | ||||
0.665311 | + | 0.746566i | \(0.268299\pi\) | |||||||
\(192\) | 9.21984e7 | 0.940090 | ||||||||
\(193\) | 2.97509e7 | 0.297885 | 0.148943 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148943 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(194\) | 2.44601e8 | 2.40521 | ||||||||
\(195\) | −273572. | −0.00264211 | ||||||||
\(196\) | −5.94027e7 | −0.563521 | ||||||||
\(197\) | −1.48736e7 | −0.138607 | −0.0693036 | − | 0.997596i | \(-0.522078\pi\) | ||||
−0.0693036 | + | 0.997596i | \(0.522078\pi\) | |||||||
\(198\) | 1.45313e7 | 0.133039 | ||||||||
\(199\) | −1.07194e8 | −0.964242 | −0.482121 | − | 0.876105i | \(-0.660133\pi\) | ||||
−0.482121 | + | 0.876105i | \(0.660133\pi\) | |||||||
\(200\) | −9.25135e7 | −0.817712 | ||||||||
\(201\) | 4.65313e7 | 0.404166 | ||||||||
\(202\) | −2.49612e8 | −2.13077 | ||||||||
\(203\) | 1.67229e8 | 1.40306 | ||||||||
\(204\) | −2.53247e7 | −0.208852 | ||||||||
\(205\) | −720678. | −0.00584256 | ||||||||
\(206\) | 9.84724e7 | 0.784836 | ||||||||
\(207\) | −3.17756e7 | −0.248999 | ||||||||
\(208\) | −2.96690e7 | −0.228602 | ||||||||
\(209\) | −3.51260e7 | −0.266144 | ||||||||
\(210\) | 426257. | 0.00317617 | ||||||||
\(211\) | 8.62669e7 | 0.632201 | 0.316101 | − | 0.948726i | \(-0.397626\pi\) | ||||
0.316101 | + | 0.948726i | \(0.397626\pi\) | |||||||
\(212\) | 2.98566e8 | 2.15211 | ||||||||
\(213\) | 1.15884e8 | 0.821664 | ||||||||
\(214\) | 1.31974e7 | 0.0920535 | ||||||||
\(215\) | 448917. | 0.00308057 | ||||||||
\(216\) | −2.33085e7 | −0.157372 | ||||||||
\(217\) | 6.13628e7 | 0.407658 | ||||||||
\(218\) | 4.18185e8 | 2.73382 | ||||||||
\(219\) | 4.20787e7 | 0.270712 | ||||||||
\(220\) | 263597. | 0.00166902 | ||||||||
\(221\) | 4.00500e7 | 0.249591 | ||||||||
\(222\) | 2.55797e7 | 0.156913 | ||||||||
\(223\) | 1.22690e8 | 0.740871 | 0.370435 | − | 0.928858i | \(-0.379208\pi\) | ||||
0.370435 | + | 0.928858i | \(0.379208\pi\) | |||||||
\(224\) | 1.55251e8 | 0.922924 | ||||||||
\(225\) | −5.69520e7 | −0.333327 | ||||||||
\(226\) | 2.35291e8 | 1.35590 | ||||||||
\(227\) | 1.12105e8 | 0.636115 | 0.318057 | − | 0.948071i | \(-0.396970\pi\) | ||||
0.318057 | + | 0.948071i | \(0.396970\pi\) | |||||||
\(228\) | 1.65624e8 | 0.925449 | ||||||||
\(229\) | 1.28324e8 | 0.706131 | 0.353066 | − | 0.935599i | \(-0.385139\pi\) | ||||
0.353066 | + | 0.935599i | \(0.385139\pi\) | |||||||
\(230\) | −956729. | −0.00518491 | ||||||||
\(231\) | 2.15727e7 | 0.115149 | ||||||||
\(232\) | −2.75328e8 | −1.44758 | ||||||||
\(233\) | −3.60112e7 | −0.186505 | −0.0932527 | − | 0.995642i | \(-0.529726\pi\) | ||||
−0.0932527 | + | 0.995642i | \(0.529726\pi\) | |||||||
\(234\) | 1.08358e8 | 0.552846 | ||||||||
\(235\) | 904477. | 0.00454632 | ||||||||
\(236\) | 3.98422e7 | 0.197311 | ||||||||
\(237\) | 9.17248e7 | 0.447577 | ||||||||
\(238\) | −6.24026e7 | −0.300043 | ||||||||
\(239\) | −2.30387e8 | −1.09160 | −0.545801 | − | 0.837915i | \(-0.683775\pi\) | ||||
−0.545801 | + | 0.837915i | \(0.683775\pi\) | |||||||
\(240\) | 118292. | 0.000552354 0 | ||||||||
\(241\) | −3.09598e8 | −1.42475 | −0.712376 | − | 0.701798i | \(-0.752381\pi\) | ||||
−0.712376 | + | 0.701798i | \(0.752381\pi\) | |||||||
\(242\) | −3.27538e8 | −1.48562 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 6.30961e7 | 0.278060 | ||||||||
\(245\) | −374557. | −0.00162718 | ||||||||
\(246\) | 2.85450e8 | 1.22252 | ||||||||
\(247\) | −2.61928e8 | −1.10597 | ||||||||
\(248\) | −1.01028e8 | −0.420594 | ||||||||
\(249\) | 1.90335e8 | 0.781307 | ||||||||
\(250\) | −3.42956e6 | −0.0138819 | ||||||||
\(251\) | 1.81483e8 | 0.724399 | 0.362200 | − | 0.932101i | \(-0.382026\pi\) | ||||
0.362200 | + | 0.932101i | \(0.382026\pi\) | |||||||
\(252\) | −1.01718e8 | −0.400403 | ||||||||
\(253\) | −4.84196e7 | −0.187975 | ||||||||
\(254\) | 4.62327e8 | 1.77024 | ||||||||
\(255\) | −159682. | −0.000603068 0 | ||||||||
\(256\) | −1.66668e8 | −0.620887 | ||||||||
\(257\) | 4.15191e8 | 1.52574 | 0.762872 | − | 0.646549i | \(-0.223788\pi\) | ||||
0.762872 | + | 0.646549i | \(0.223788\pi\) | |||||||
\(258\) | −1.77809e8 | −0.644592 | ||||||||
\(259\) | 3.79745e7 | 0.135814 | ||||||||
\(260\) | 1.96560e6 | 0.00693566 | ||||||||
\(261\) | −1.69494e8 | −0.590082 | ||||||||
\(262\) | −7.25169e8 | −2.49106 | ||||||||
\(263\) | −3.81009e8 | −1.29149 | −0.645744 | − | 0.763554i | \(-0.723453\pi\) | ||||
−0.645744 | + | 0.763554i | \(0.723453\pi\) | |||||||
\(264\) | −3.55175e7 | −0.118803 | ||||||||
\(265\) | 1.88258e6 | 0.00621430 | ||||||||
\(266\) | 4.08115e8 | 1.32953 | ||||||||
\(267\) | −3.07818e8 | −0.989704 | ||||||||
\(268\) | −3.34325e8 | −1.06095 | ||||||||
\(269\) | −9.53490e7 | −0.298664 | −0.149332 | − | 0.988787i | \(-0.547712\pi\) | ||||
−0.149332 | + | 0.988787i | \(0.547712\pi\) | |||||||
\(270\) | −432030. | −0.00133580 | ||||||||
\(271\) | −4.17979e8 | −1.27574 | −0.637870 | − | 0.770144i | \(-0.720184\pi\) | ||||
−0.637870 | + | 0.770144i | \(0.720184\pi\) | |||||||
\(272\) | −1.73176e7 | −0.0521791 | ||||||||
\(273\) | 1.60863e8 | 0.478507 | ||||||||
\(274\) | 6.11169e8 | 1.79488 | ||||||||
\(275\) | −8.67834e7 | −0.251636 | ||||||||
\(276\) | 2.28306e8 | 0.653635 | ||||||||
\(277\) | −3.26940e8 | −0.924249 | −0.462125 | − | 0.886815i | \(-0.652913\pi\) | ||||
−0.462125 | + | 0.886815i | \(0.652913\pi\) | |||||||
\(278\) | 7.15011e7 | 0.199598 | ||||||||
\(279\) | −6.21939e7 | −0.171448 | ||||||||
\(280\) | −1.04186e6 | −0.00283631 | ||||||||
\(281\) | 9.47550e7 | 0.254759 | 0.127380 | − | 0.991854i | \(-0.459343\pi\) | ||||
0.127380 | + | 0.991854i | \(0.459343\pi\) | |||||||
\(282\) | −3.58250e8 | −0.951292 | ||||||||
\(283\) | −4.46938e8 | −1.17218 | −0.586091 | − | 0.810246i | \(-0.699334\pi\) | ||||
−0.586091 | + | 0.810246i | \(0.699334\pi\) | |||||||
\(284\) | −8.32618e8 | −2.15691 | ||||||||
\(285\) | 1.04433e6 | 0.00267227 | ||||||||
\(286\) | 1.65115e8 | 0.417355 | ||||||||
\(287\) | 4.23767e8 | 1.05813 | ||||||||
\(288\) | −1.57353e8 | −0.388153 | ||||||||
\(289\) | −3.86962e8 | −0.943030 | ||||||||
\(290\) | −5.10327e6 | −0.0122873 | ||||||||
\(291\) | −3.68044e8 | −0.875535 | ||||||||
\(292\) | −3.02333e8 | −0.710634 | ||||||||
\(293\) | 4.04818e8 | 0.940207 | 0.470103 | − | 0.882611i | \(-0.344217\pi\) | ||||
0.470103 | + | 0.882611i | \(0.344217\pi\) | |||||||
\(294\) | 1.48356e8 | 0.340479 | ||||||||
\(295\) | 251220. | 0.000569742 0 | ||||||||
\(296\) | −6.25217e7 | −0.140123 | ||||||||
\(297\) | −2.18648e7 | −0.0484282 | ||||||||
\(298\) | 1.04774e8 | 0.229350 | ||||||||
\(299\) | −3.61056e8 | −0.781134 | ||||||||
\(300\) | 4.09197e8 | 0.875000 | ||||||||
\(301\) | −2.63968e8 | −0.557916 | ||||||||
\(302\) | 9.21991e8 | 1.92620 | ||||||||
\(303\) | 3.75583e8 | 0.775634 | ||||||||
\(304\) | 1.13258e8 | 0.231212 | ||||||||
\(305\) | 397846. | 0.000802908 0 | ||||||||
\(306\) | 6.32478e7 | 0.126189 | ||||||||
\(307\) | −7.95438e8 | −1.56900 | −0.784498 | − | 0.620131i | \(-0.787079\pi\) | ||||
−0.784498 | + | 0.620131i | \(0.787079\pi\) | |||||||
\(308\) | −1.54998e8 | −0.302273 | ||||||||
\(309\) | −1.48168e8 | −0.285693 | ||||||||
\(310\) | −1.87259e6 | −0.00357007 | ||||||||
\(311\) | 3.49530e8 | 0.658906 | 0.329453 | − | 0.944172i | \(-0.393136\pi\) | ||||
0.329453 | + | 0.944172i | \(0.393136\pi\) | |||||||
\(312\) | −2.64847e8 | −0.493690 | ||||||||
\(313\) | 9.82107e7 | 0.181031 | 0.0905157 | − | 0.995895i | \(-0.471148\pi\) | ||||
0.0905157 | + | 0.995895i | \(0.471148\pi\) | |||||||
\(314\) | −2.05359e8 | −0.374334 | ||||||||
\(315\) | −641374. | −0.00115618 | ||||||||
\(316\) | −6.59037e8 | −1.17491 | ||||||||
\(317\) | 9.11476e8 | 1.60708 | 0.803541 | − | 0.595250i | \(-0.202947\pi\) | ||||
0.803541 | + | 0.595250i | \(0.202947\pi\) | |||||||
\(318\) | −7.45661e8 | −1.30031 | ||||||||
\(319\) | −2.58274e8 | −0.445465 | ||||||||
\(320\) | −4.17695e6 | −0.00712580 | ||||||||
\(321\) | −1.98577e7 | −0.0335090 | ||||||||
\(322\) | 5.62568e8 | 0.939030 | ||||||||
\(323\) | −1.52886e8 | −0.252441 | ||||||||
\(324\) | 1.03096e8 | 0.168397 | ||||||||
\(325\) | −6.47128e8 | −1.04568 | ||||||||
\(326\) | 2.24912e8 | 0.359542 | ||||||||
\(327\) | −6.29229e8 | −0.995157 | ||||||||
\(328\) | −6.97695e8 | −1.09171 | ||||||||
\(329\) | −5.31844e8 | −0.823376 | ||||||||
\(330\) | −658326. | −0.00100842 | ||||||||
\(331\) | 8.69089e8 | 1.31724 | 0.658622 | − | 0.752474i | \(-0.271140\pi\) | ||||
0.658622 | + | 0.752474i | \(0.271140\pi\) | |||||||
\(332\) | −1.36755e9 | −2.05097 | ||||||||
\(333\) | −3.84889e7 | −0.0571189 | ||||||||
\(334\) | −6.77368e8 | −0.994745 | ||||||||
\(335\) | −2.10805e6 | −0.00306354 | ||||||||
\(336\) | −6.95573e7 | −0.100036 | ||||||||
\(337\) | 3.71807e7 | 0.0529192 | 0.0264596 | − | 0.999650i | \(-0.491577\pi\) | ||||
0.0264596 | + | 0.999650i | \(0.491577\pi\) | |||||||
\(338\) | 1.05263e8 | 0.148275 | ||||||||
\(339\) | −3.54035e8 | −0.493568 | ||||||||
\(340\) | 1.14731e6 | 0.00158308 | ||||||||
\(341\) | −9.47709e7 | −0.129430 | ||||||||
\(342\) | −4.13642e8 | −0.559157 | ||||||||
\(343\) | 8.12585e8 | 1.08727 | ||||||||
\(344\) | 4.34600e8 | 0.575619 | ||||||||
\(345\) | 1.43956e6 | 0.00188739 | ||||||||
\(346\) | −3.70043e8 | −0.480270 | ||||||||
\(347\) | −5.17499e8 | −0.664900 | −0.332450 | − | 0.943121i | \(-0.607875\pi\) | ||||
−0.332450 | + | 0.943121i | \(0.607875\pi\) | |||||||
\(348\) | 1.21780e9 | 1.54899 | ||||||||
\(349\) | −7.74296e8 | −0.975030 | −0.487515 | − | 0.873115i | \(-0.662097\pi\) | ||||
−0.487515 | + | 0.873115i | \(0.662097\pi\) | |||||||
\(350\) | 1.00830e9 | 1.25705 | ||||||||
\(351\) | −1.63042e8 | −0.201245 | ||||||||
\(352\) | −2.39775e8 | −0.293025 | ||||||||
\(353\) | −6.61876e8 | −0.800876 | −0.400438 | − | 0.916324i | \(-0.631142\pi\) | ||||
−0.400438 | + | 0.916324i | \(0.631142\pi\) | |||||||
\(354\) | −9.95046e7 | −0.119215 | ||||||||
\(355\) | −5.24998e6 | −0.00622815 | ||||||||
\(356\) | 2.21166e9 | 2.59802 | ||||||||
\(357\) | 9.38951e7 | 0.109221 | ||||||||
\(358\) | −1.82918e9 | −2.10700 | ||||||||
\(359\) | 6.26557e8 | 0.714711 | 0.357355 | − | 0.933968i | \(-0.383679\pi\) | ||||
0.357355 | + | 0.933968i | \(0.383679\pi\) | |||||||
\(360\) | 1.05597e6 | 0.00119286 | ||||||||
\(361\) | 1.06008e8 | 0.118595 | ||||||||
\(362\) | 1.64131e8 | 0.181849 | ||||||||
\(363\) | 4.92836e8 | 0.540791 | ||||||||
\(364\) | −1.15579e9 | −1.25610 | ||||||||
\(365\) | −1.90633e6 | −0.00205198 | ||||||||
\(366\) | −1.57581e8 | −0.168004 | ||||||||
\(367\) | 8.99146e7 | 0.0949509 | 0.0474755 | − | 0.998872i | \(-0.484882\pi\) | ||||
0.0474755 | + | 0.998872i | \(0.484882\pi\) | |||||||
\(368\) | 1.56121e8 | 0.163303 | ||||||||
\(369\) | −4.29507e8 | −0.445018 | ||||||||
\(370\) | −1.15886e6 | −0.00118939 | ||||||||
\(371\) | −1.10698e9 | −1.12546 | ||||||||
\(372\) | 4.46859e8 | 0.450060 | ||||||||
\(373\) | 1.93821e8 | 0.193383 | 0.0966917 | − | 0.995314i | \(-0.469174\pi\) | ||||
0.0966917 | + | 0.995314i | \(0.469174\pi\) | |||||||
\(374\) | 9.63768e7 | 0.0952625 | ||||||||
\(375\) | 5.16034e6 | 0.00505323 | ||||||||
\(376\) | 8.75633e8 | 0.849503 | ||||||||
\(377\) | −1.92591e9 | −1.85114 | ||||||||
\(378\) | 2.54039e8 | 0.241924 | ||||||||
\(379\) | −2.28105e8 | −0.215227 | −0.107614 | − | 0.994193i | \(-0.534321\pi\) | ||||
−0.107614 | + | 0.994193i | \(0.534321\pi\) | |||||||
\(380\) | −7.50343e6 | −0.00701483 | ||||||||
\(381\) | −6.95649e8 | −0.644395 | ||||||||
\(382\) | 2.29930e9 | 2.11044 | ||||||||
\(383\) | −1.16094e8 | −0.105588 | −0.0527938 | − | 0.998605i | \(-0.516813\pi\) | ||||
−0.0527938 | + | 0.998605i | \(0.516813\pi\) | |||||||
\(384\) | 9.08453e8 | 0.818735 | ||||||||
\(385\) | −977325. | −0.000872824 0 | ||||||||
\(386\) | 5.33855e8 | 0.472463 | ||||||||
\(387\) | 2.67543e8 | 0.234642 | ||||||||
\(388\) | 2.64437e9 | 2.29832 | ||||||||
\(389\) | 6.84222e8 | 0.589351 | 0.294675 | − | 0.955597i | \(-0.404789\pi\) | ||||
0.294675 | + | 0.955597i | \(0.404789\pi\) | |||||||
\(390\) | −4.90902e6 | −0.00419053 | ||||||||
\(391\) | −2.10747e8 | −0.178296 | ||||||||
\(392\) | −3.62612e8 | −0.304047 | ||||||||
\(393\) | 1.09114e9 | 0.906788 | ||||||||
\(394\) | −2.66895e8 | −0.219839 | ||||||||
\(395\) | −4.15549e6 | −0.00339260 | ||||||||
\(396\) | 1.57097e8 | 0.127126 | ||||||||
\(397\) | −1.73331e9 | −1.39031 | −0.695153 | − | 0.718862i | \(-0.744663\pi\) | ||||
−0.695153 | + | 0.718862i | \(0.744663\pi\) | |||||||
\(398\) | −1.92351e9 | −1.52934 | ||||||||
\(399\) | −6.14077e8 | −0.483969 | ||||||||
\(400\) | 2.79818e8 | 0.218608 | ||||||||
\(401\) | 1.39266e9 | 1.07855 | 0.539274 | − | 0.842130i | \(-0.318699\pi\) | ||||
0.539274 | + | 0.842130i | \(0.318699\pi\) | |||||||
\(402\) | 8.34966e8 | 0.641029 | ||||||||
\(403\) | −7.06690e8 | −0.537850 | ||||||||
\(404\) | −2.69854e9 | −2.03608 | ||||||||
\(405\) | 650061. | 0.000486252 0 | ||||||||
\(406\) | 3.00079e9 | 2.22533 | ||||||||
\(407\) | −5.86492e7 | −0.0431203 | ||||||||
\(408\) | −1.54590e8 | −0.112686 | ||||||||
\(409\) | −1.48753e9 | −1.07506 | −0.537530 | − | 0.843244i | \(-0.680643\pi\) | ||||
−0.537530 | + | 0.843244i | \(0.680643\pi\) | |||||||
\(410\) | −1.29320e7 | −0.00926662 | ||||||||
\(411\) | −9.19606e8 | −0.653364 | ||||||||
\(412\) | 1.06458e9 | 0.749959 | ||||||||
\(413\) | −1.47721e8 | −0.103185 | ||||||||
\(414\) | −5.70187e8 | −0.394927 | ||||||||
\(415\) | −8.62292e6 | −0.00592224 | ||||||||
\(416\) | −1.78796e9 | −1.21767 | ||||||||
\(417\) | −1.07585e8 | −0.0726569 | ||||||||
\(418\) | −6.30307e8 | −0.422119 | ||||||||
\(419\) | 9.73899e8 | 0.646792 | 0.323396 | − | 0.946264i | \(-0.395175\pi\) | ||||
0.323396 | + | 0.946264i | \(0.395175\pi\) | |||||||
\(420\) | 4.60824e6 | 0.00303502 | ||||||||
\(421\) | 2.01358e9 | 1.31517 | 0.657584 | − | 0.753381i | \(-0.271578\pi\) | ||||
0.657584 | + | 0.753381i | \(0.271578\pi\) | |||||||
\(422\) | 1.54799e9 | 1.00271 | ||||||||
\(423\) | 5.39047e8 | 0.346286 | ||||||||
\(424\) | 1.82254e9 | 1.16117 | ||||||||
\(425\) | −3.77725e8 | −0.238679 | ||||||||
\(426\) | 2.07944e9 | 1.30320 | ||||||||
\(427\) | −2.33938e8 | −0.145413 | ||||||||
\(428\) | 1.42676e8 | 0.0879627 | ||||||||
\(429\) | −2.48443e8 | −0.151924 | ||||||||
\(430\) | 8.05544e6 | 0.00488596 | ||||||||
\(431\) | 2.94920e8 | 0.177433 | 0.0887164 | − | 0.996057i | \(-0.471724\pi\) | ||||
0.0887164 | + | 0.996057i | \(0.471724\pi\) | |||||||
\(432\) | 7.04993e7 | 0.0420719 | ||||||||
\(433\) | −1.42354e9 | −0.842676 | −0.421338 | − | 0.906904i | \(-0.638439\pi\) | ||||
−0.421338 | + | 0.906904i | \(0.638439\pi\) | |||||||
\(434\) | 1.10111e9 | 0.646569 | ||||||||
\(435\) | 7.67873e6 | 0.00447277 | ||||||||
\(436\) | 4.52097e9 | 2.61233 | ||||||||
\(437\) | 1.37829e9 | 0.790052 | ||||||||
\(438\) | 7.55068e8 | 0.429365 | ||||||||
\(439\) | −1.55418e9 | −0.876750 | −0.438375 | − | 0.898792i | \(-0.644446\pi\) | ||||
−0.438375 | + | 0.898792i | \(0.644446\pi\) | |||||||
\(440\) | 1.60908e6 | 0.000900519 0 | ||||||||
\(441\) | −2.23227e8 | −0.123940 | ||||||||
\(442\) | 7.18664e8 | 0.395866 | ||||||||
\(443\) | −6.41286e8 | −0.350460 | −0.175230 | − | 0.984528i | \(-0.556067\pi\) | ||||
−0.175230 | + | 0.984528i | \(0.556067\pi\) | |||||||
\(444\) | 2.76540e8 | 0.149940 | ||||||||
\(445\) | 1.39454e7 | 0.00750187 | ||||||||
\(446\) | 2.20157e9 | 1.17506 | ||||||||
\(447\) | −1.57651e8 | −0.0834871 | ||||||||
\(448\) | 2.45609e9 | 1.29054 | ||||||||
\(449\) | 2.96725e9 | 1.54701 | 0.773503 | − | 0.633793i | \(-0.218503\pi\) | ||||
0.773503 | + | 0.633793i | \(0.218503\pi\) | |||||||
\(450\) | −1.02196e9 | −0.528675 | ||||||||
\(451\) | −6.54481e8 | −0.335954 | ||||||||
\(452\) | 2.54372e9 | 1.29564 | ||||||||
\(453\) | −1.38729e9 | −0.701170 | ||||||||
\(454\) | 2.01164e9 | 1.00891 | ||||||||
\(455\) | −7.28774e6 | −0.00362704 | ||||||||
\(456\) | 1.01102e9 | 0.499326 | ||||||||
\(457\) | −3.31780e9 | −1.62609 | −0.813043 | − | 0.582203i | \(-0.802191\pi\) | ||||
−0.813043 | + | 0.582203i | \(0.802191\pi\) | |||||||
\(458\) | 2.30268e9 | 1.11996 | ||||||||
\(459\) | −9.51668e7 | −0.0459347 | ||||||||
\(460\) | −1.03431e7 | −0.00495450 | ||||||||
\(461\) | 9.48650e8 | 0.450975 | 0.225488 | − | 0.974246i | \(-0.427602\pi\) | ||||
0.225488 | + | 0.974246i | \(0.427602\pi\) | |||||||
\(462\) | 3.87104e8 | 0.182633 | ||||||||
\(463\) | 1.33385e9 | 0.624561 | 0.312281 | − | 0.949990i | \(-0.398907\pi\) | ||||
0.312281 | + | 0.949990i | \(0.398907\pi\) | |||||||
\(464\) | 8.32761e8 | 0.386997 | ||||||||
\(465\) | 2.81762e6 | 0.00129956 | ||||||||
\(466\) | −6.46191e8 | −0.295808 | ||||||||
\(467\) | −3.76180e9 | −1.70918 | −0.854588 | − | 0.519306i | \(-0.826190\pi\) | ||||
−0.854588 | + | 0.519306i | \(0.826190\pi\) | |||||||
\(468\) | 1.17145e9 | 0.528278 | ||||||||
\(469\) | 1.23956e9 | 0.554833 | ||||||||
\(470\) | 1.62301e7 | 0.00721072 | ||||||||
\(471\) | 3.08997e8 | 0.136264 | ||||||||
\(472\) | 2.43209e8 | 0.106459 | ||||||||
\(473\) | 4.07682e8 | 0.177136 | ||||||||
\(474\) | 1.64593e9 | 0.709882 | ||||||||
\(475\) | 2.47033e9 | 1.05762 | ||||||||
\(476\) | −6.74631e8 | −0.286709 | ||||||||
\(477\) | 1.12197e9 | 0.473334 | ||||||||
\(478\) | −4.13410e9 | −1.73134 | ||||||||
\(479\) | −2.93522e9 | −1.22030 | −0.610151 | − | 0.792285i | \(-0.708891\pi\) | ||||
−0.610151 | + | 0.792285i | \(0.708891\pi\) | |||||||
\(480\) | 7.12872e6 | 0.00294217 | ||||||||
\(481\) | −4.37337e8 | −0.179188 | ||||||||
\(482\) | −5.55549e9 | −2.25973 | ||||||||
\(483\) | −8.46478e8 | −0.341822 | ||||||||
\(484\) | −3.54100e9 | −1.41960 | ||||||||
\(485\) | 1.66738e7 | 0.00663649 | ||||||||
\(486\) | −2.57479e8 | −0.101746 | ||||||||
\(487\) | −1.25935e9 | −0.494077 | −0.247038 | − | 0.969006i | \(-0.579457\pi\) | ||||
−0.247038 | + | 0.969006i | \(0.579457\pi\) | |||||||
\(488\) | 3.85158e8 | 0.150027 | ||||||||
\(489\) | −3.38417e8 | −0.130879 | ||||||||
\(490\) | −6.72112e6 | −0.00258081 | ||||||||
\(491\) | 4.20973e8 | 0.160498 | 0.0802489 | − | 0.996775i | \(-0.474428\pi\) | ||||
0.0802489 | + | 0.996775i | \(0.474428\pi\) | |||||||
\(492\) | 3.08598e9 | 1.16819 | ||||||||
\(493\) | −1.12414e9 | −0.422529 | ||||||||
\(494\) | −4.70009e9 | −1.75413 | ||||||||
\(495\) | 990562. | 0.000367082 0 | ||||||||
\(496\) | 3.05572e8 | 0.112442 | ||||||||
\(497\) | 3.08705e9 | 1.12797 | ||||||||
\(498\) | 3.41541e9 | 1.23920 | ||||||||
\(499\) | −4.86604e9 | −1.75317 | −0.876584 | − | 0.481248i | \(-0.840184\pi\) | ||||
−0.876584 | + | 0.481248i | \(0.840184\pi\) | |||||||
\(500\) | −3.70767e7 | −0.0132650 | ||||||||
\(501\) | 1.01921e9 | 0.362104 | ||||||||
\(502\) | 3.25656e9 | 1.14894 | ||||||||
\(503\) | −3.22489e9 | −1.12987 | −0.564933 | − | 0.825137i | \(-0.691098\pi\) | ||||
−0.564933 | + | 0.825137i | \(0.691098\pi\) | |||||||
\(504\) | −6.20921e8 | −0.216038 | ||||||||
\(505\) | −1.70154e7 | −0.00587925 | ||||||||
\(506\) | −8.68850e8 | −0.298138 | ||||||||
\(507\) | −1.58386e8 | −0.0539745 | ||||||||
\(508\) | 4.99819e9 | 1.69157 | ||||||||
\(509\) | 1.08431e8 | 0.0364452 | 0.0182226 | − | 0.999834i | \(-0.494199\pi\) | ||||
0.0182226 | + | 0.999834i | \(0.494199\pi\) | |||||||
\(510\) | −2.86537e6 | −0.000956499 0 | ||||||||
\(511\) | 1.12094e9 | 0.371630 | ||||||||
\(512\) | 1.31602e9 | 0.433329 | ||||||||
\(513\) | 6.22394e8 | 0.203542 | ||||||||
\(514\) | 7.45026e9 | 2.41992 | ||||||||
\(515\) | 6.71259e6 | 0.00216553 | ||||||||
\(516\) | −1.92228e9 | −0.615947 | ||||||||
\(517\) | 8.21398e8 | 0.261419 | ||||||||
\(518\) | 6.81422e8 | 0.215408 | ||||||||
\(519\) | 5.56791e8 | 0.174826 | ||||||||
\(520\) | 1.19986e7 | 0.00374213 | ||||||||
\(521\) | 2.88309e8 | 0.0893152 | 0.0446576 | − | 0.999002i | \(-0.485780\pi\) | ||||
0.0446576 | + | 0.999002i | \(0.485780\pi\) | |||||||
\(522\) | −3.04143e9 | −0.935903 | ||||||||
\(523\) | 8.83228e8 | 0.269971 | 0.134985 | − | 0.990848i | \(-0.456901\pi\) | ||||
0.134985 | + | 0.990848i | \(0.456901\pi\) | |||||||
\(524\) | −7.83976e9 | −2.38036 | ||||||||
\(525\) | −1.51716e9 | −0.457586 | ||||||||
\(526\) | −6.83689e9 | −2.04837 | ||||||||
\(527\) | −4.12491e8 | −0.122766 | ||||||||
\(528\) | 1.07427e8 | 0.0317610 | ||||||||
\(529\) | −1.50492e9 | −0.441995 | ||||||||
\(530\) | 3.37813e7 | 0.00985623 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 4.41211e9 | 1.27044 | ||||||||
\(533\) | −4.88035e9 | −1.39607 | ||||||||
\(534\) | −5.52355e9 | −1.56973 | ||||||||
\(535\) | 899630. | 0.000253995 0 | ||||||||
\(536\) | −2.04082e9 | −0.572438 | ||||||||
\(537\) | 2.75230e9 | 0.766984 | ||||||||
\(538\) | −1.71096e9 | −0.473698 | ||||||||
\(539\) | −3.40153e8 | −0.0935650 | ||||||||
\(540\) | −4.67065e6 | −0.00127644 | ||||||||
\(541\) | −3.92838e9 | −1.06665 | −0.533326 | − | 0.845910i | \(-0.679058\pi\) | ||||
−0.533326 | + | 0.845910i | \(0.679058\pi\) | |||||||
\(542\) | −7.50029e9 | −2.02340 | ||||||||
\(543\) | −2.46963e8 | −0.0661961 | ||||||||
\(544\) | −1.04362e9 | −0.277937 | ||||||||
\(545\) | 2.85065e7 | 0.00754321 | ||||||||
\(546\) | 2.88656e9 | 0.758938 | ||||||||
\(547\) | 1.10099e9 | 0.287624 | 0.143812 | − | 0.989605i | \(-0.454064\pi\) | ||||
0.143812 | + | 0.989605i | \(0.454064\pi\) | |||||||
\(548\) | 6.60731e9 | 1.71511 | ||||||||
\(549\) | 2.37107e8 | 0.0611562 | ||||||||
\(550\) | −1.55726e9 | −0.399108 | ||||||||
\(551\) | 7.35191e9 | 1.87228 | ||||||||
\(552\) | 1.39365e9 | 0.352669 | ||||||||
\(553\) | 2.44348e9 | 0.614427 | ||||||||
\(554\) | −5.86667e9 | −1.46591 | ||||||||
\(555\) | 1.74369e6 | 0.000432957 0 | ||||||||
\(556\) | 7.72994e8 | 0.190728 | ||||||||
\(557\) | −5.42968e9 | −1.33132 | −0.665658 | − | 0.746257i | \(-0.731849\pi\) | ||||
−0.665658 | + | 0.746257i | \(0.731849\pi\) | |||||||
\(558\) | −1.11602e9 | −0.271926 | ||||||||
\(559\) | 3.04001e9 | 0.736095 | ||||||||
\(560\) | 3.15121e6 | 0.000758263 0 | ||||||||
\(561\) | −1.45015e8 | −0.0346771 | ||||||||
\(562\) | 1.70030e9 | 0.404063 | ||||||||
\(563\) | −7.14917e8 | −0.168840 | −0.0844201 | − | 0.996430i | \(-0.526904\pi\) | ||||
−0.0844201 | + | 0.996430i | \(0.526904\pi\) | |||||||
\(564\) | −3.87302e9 | −0.909018 | ||||||||
\(565\) | 1.60391e7 | 0.00374121 | ||||||||
\(566\) | −8.01993e9 | −1.85914 | ||||||||
\(567\) | −3.82244e8 | −0.0880642 | ||||||||
\(568\) | −5.08256e9 | −1.16376 | ||||||||
\(569\) | −1.67905e9 | −0.382094 | −0.191047 | − | 0.981581i | \(-0.561188\pi\) | ||||
−0.191047 | + | 0.981581i | \(0.561188\pi\) | |||||||
\(570\) | 1.87396e7 | 0.00423836 | ||||||||
\(571\) | −9.65128e8 | −0.216950 | −0.108475 | − | 0.994099i | \(-0.534597\pi\) | ||||
−0.108475 | + | 0.994099i | \(0.534597\pi\) | |||||||
\(572\) | 1.78505e9 | 0.398808 | ||||||||
\(573\) | −3.45968e9 | −0.768235 | ||||||||
\(574\) | 7.60416e9 | 1.67826 | ||||||||
\(575\) | 3.40524e9 | 0.746983 | ||||||||
\(576\) | −2.48936e9 | −0.542761 | ||||||||
\(577\) | 2.50966e9 | 0.543875 | 0.271938 | − | 0.962315i | \(-0.412336\pi\) | ||||
0.271938 | + | 0.962315i | \(0.412336\pi\) | |||||||
\(578\) | −6.94371e9 | −1.49570 | ||||||||
\(579\) | −8.03274e8 | −0.171984 | ||||||||
\(580\) | −5.51712e7 | −0.0117412 | ||||||||
\(581\) | 5.07038e9 | 1.07257 | ||||||||
\(582\) | −6.60424e9 | −1.38865 | ||||||||
\(583\) | 1.70966e9 | 0.357330 | ||||||||
\(584\) | −1.84554e9 | −0.383422 | ||||||||
\(585\) | 7.38644e6 | 0.00152542 | ||||||||
\(586\) | 7.26413e9 | 1.49122 | ||||||||
\(587\) | 3.24638e9 | 0.662470 | 0.331235 | − | 0.943548i | \(-0.392535\pi\) | ||||
0.331235 | + | 0.943548i | \(0.392535\pi\) | |||||||
\(588\) | 1.60387e9 | 0.325349 | ||||||||
\(589\) | 2.69770e9 | 0.543990 | ||||||||
\(590\) | 4.50794e6 | 0.000903642 0 | ||||||||
\(591\) | 4.01588e8 | 0.0800249 | ||||||||
\(592\) | 1.89104e8 | 0.0374606 | ||||||||
\(593\) | 7.03607e9 | 1.38560 | 0.692801 | − | 0.721129i | \(-0.256376\pi\) | ||||
0.692801 | + | 0.721129i | \(0.256376\pi\) | |||||||
\(594\) | −3.92346e8 | −0.0768099 | ||||||||
\(595\) | −4.25381e6 | −0.000827883 0 | ||||||||
\(596\) | 1.13271e9 | 0.219158 | ||||||||
\(597\) | 2.89425e9 | 0.556705 | ||||||||
\(598\) | −6.47886e9 | −1.23892 | ||||||||
\(599\) | 9.00254e9 | 1.71148 | 0.855738 | − | 0.517409i | \(-0.173103\pi\) | ||||
0.855738 | + | 0.517409i | \(0.173103\pi\) | |||||||
\(600\) | 2.49786e9 | 0.472106 | ||||||||
\(601\) | 5.40983e9 | 1.01654 | 0.508268 | − | 0.861199i | \(-0.330286\pi\) | ||||
0.508268 | + | 0.861199i | \(0.330286\pi\) | |||||||
\(602\) | −4.73669e9 | −0.884886 | ||||||||
\(603\) | −1.25635e9 | −0.233345 | ||||||||
\(604\) | 9.96758e9 | 1.84061 | ||||||||
\(605\) | −2.23274e7 | −0.00409915 | ||||||||
\(606\) | 6.73953e9 | 1.23020 | ||||||||
\(607\) | −6.20066e9 | −1.12532 | −0.562662 | − | 0.826687i | \(-0.690223\pi\) | ||||
−0.562662 | + | 0.826687i | \(0.690223\pi\) | |||||||
\(608\) | 6.82531e9 | 1.23157 | ||||||||
\(609\) | −4.51518e9 | −0.810056 | ||||||||
\(610\) | 7.13902e6 | 0.00127346 | ||||||||
\(611\) | 6.12502e9 | 1.08633 | ||||||||
\(612\) | 6.83767e8 | 0.120581 | ||||||||
\(613\) | 5.56027e9 | 0.974955 | 0.487477 | − | 0.873136i | \(-0.337917\pi\) | ||||
0.487477 | + | 0.873136i | \(0.337917\pi\) | |||||||
\(614\) | −1.42735e10 | −2.48851 | ||||||||
\(615\) | 1.94583e7 | 0.00337320 | ||||||||
\(616\) | −9.46158e8 | −0.163091 | ||||||||
\(617\) | 8.63571e9 | 1.48013 | 0.740065 | − | 0.672535i | \(-0.234795\pi\) | ||||
0.740065 | + | 0.672535i | \(0.234795\pi\) | |||||||
\(618\) | −2.65875e9 | −0.453125 | ||||||||
\(619\) | 4.62517e9 | 0.783809 | 0.391904 | − | 0.920006i | \(-0.371816\pi\) | ||||
0.391904 | + | 0.920006i | \(0.371816\pi\) | |||||||
\(620\) | −2.02445e7 | −0.00341142 | ||||||||
\(621\) | 8.57942e8 | 0.143760 | ||||||||
\(622\) | 6.27203e9 | 1.04506 | ||||||||
\(623\) | −8.20004e9 | −1.35865 | ||||||||
\(624\) | 8.01062e8 | 0.131984 | ||||||||
\(625\) | 6.10316e9 | 0.999943 | ||||||||
\(626\) | 1.76231e9 | 0.287126 | ||||||||
\(627\) | 9.48402e8 | 0.153658 | ||||||||
\(628\) | −2.22012e9 | −0.357699 | ||||||||
\(629\) | −2.55271e8 | −0.0409001 | ||||||||
\(630\) | −1.15089e7 | −0.00183376 | ||||||||
\(631\) | −4.78738e9 | −0.758568 | −0.379284 | − | 0.925280i | \(-0.623830\pi\) | ||||
−0.379284 | + | 0.925280i | \(0.623830\pi\) | |||||||
\(632\) | −4.02297e9 | −0.633923 | ||||||||
\(633\) | −2.32921e9 | −0.365002 | ||||||||
\(634\) | 1.63557e10 | 2.54892 | ||||||||
\(635\) | 3.15156e7 | 0.00488447 | ||||||||
\(636\) | −8.06129e9 | −1.24252 | ||||||||
\(637\) | −2.53646e9 | −0.388812 | ||||||||
\(638\) | −4.63452e9 | −0.706533 | ||||||||
\(639\) | −3.12886e9 | −0.474388 | ||||||||
\(640\) | −4.11564e7 | −0.00620594 | ||||||||
\(641\) | 1.18477e10 | 1.77676 | 0.888382 | − | 0.459104i | \(-0.151830\pi\) | ||||
0.888382 | + | 0.459104i | \(0.151830\pi\) | |||||||
\(642\) | −3.56330e8 | −0.0531471 | ||||||||
\(643\) | −1.06317e10 | −1.57712 | −0.788562 | − | 0.614956i | \(-0.789174\pi\) | ||||
−0.788562 | + | 0.614956i | \(0.789174\pi\) | |||||||
\(644\) | 6.08189e9 | 0.897300 | ||||||||
\(645\) | −1.21207e7 | −0.00177857 | ||||||||
\(646\) | −2.74342e9 | −0.400385 | ||||||||
\(647\) | −9.21966e9 | −1.33829 | −0.669145 | − | 0.743132i | \(-0.733339\pi\) | ||||
−0.669145 | + | 0.743132i | \(0.733339\pi\) | |||||||
\(648\) | 6.29330e8 | 0.0908586 | ||||||||
\(649\) | 2.28145e8 | 0.0327608 | ||||||||
\(650\) | −1.16122e10 | −1.65851 | ||||||||
\(651\) | −1.65680e9 | −0.235362 | ||||||||
\(652\) | 2.43150e9 | 0.343565 | ||||||||
\(653\) | −1.41112e10 | −1.98321 | −0.991605 | − | 0.129302i | \(-0.958726\pi\) | ||||
−0.991605 | + | 0.129302i | \(0.958726\pi\) | |||||||
\(654\) | −1.12910e10 | −1.57837 | ||||||||
\(655\) | −4.94328e7 | −0.00687338 | ||||||||
\(656\) | 2.11026e9 | 0.291859 | ||||||||
\(657\) | −1.13613e9 | −0.156296 | ||||||||
\(658\) | −9.54349e9 | −1.30592 | ||||||||
\(659\) | 6.80419e9 | 0.926141 | 0.463071 | − | 0.886321i | \(-0.346748\pi\) | ||||
0.463071 | + | 0.886321i | \(0.346748\pi\) | |||||||
\(660\) | −7.11712e6 | −0.000963609 0 | ||||||||
\(661\) | 2.76563e8 | 0.0372468 | 0.0186234 | − | 0.999827i | \(-0.494072\pi\) | ||||
0.0186234 | + | 0.999827i | \(0.494072\pi\) | |||||||
\(662\) | 1.55951e10 | 2.08922 | ||||||||
\(663\) | −1.08135e9 | −0.144102 | ||||||||
\(664\) | −8.34793e9 | −1.10660 | ||||||||
\(665\) | 2.78201e7 | 0.00366845 | ||||||||
\(666\) | −6.90651e8 | −0.0905938 | ||||||||
\(667\) | 1.01343e10 | 1.32237 | ||||||||
\(668\) | −7.32298e9 | −0.950540 | ||||||||
\(669\) | −3.31263e9 | −0.427742 | ||||||||
\(670\) | −3.78272e7 | −0.00485895 | ||||||||
\(671\) | 3.61302e8 | 0.0461681 | ||||||||
\(672\) | −4.19177e9 | −0.532850 | ||||||||
\(673\) | −7.86611e9 | −0.994734 | −0.497367 | − | 0.867540i | \(-0.665700\pi\) | ||||
−0.497367 | + | 0.867540i | \(0.665700\pi\) | |||||||
\(674\) | 6.67178e8 | 0.0839328 | ||||||||
\(675\) | 1.53770e9 | 0.192446 | ||||||||
\(676\) | 1.13799e9 | 0.141686 | ||||||||
\(677\) | 6.11786e8 | 0.0757773 | 0.0378886 | − | 0.999282i | \(-0.487937\pi\) | ||||
0.0378886 | + | 0.999282i | \(0.487937\pi\) | |||||||
\(678\) | −6.35286e9 | −0.782826 | ||||||||
\(679\) | −9.80439e9 | −1.20192 | ||||||||
\(680\) | 7.00352e6 | 0.000854152 0 | ||||||||
\(681\) | −3.02684e9 | −0.367261 | ||||||||
\(682\) | −1.70059e9 | −0.205283 | ||||||||
\(683\) | −1.81400e9 | −0.217854 | −0.108927 | − | 0.994050i | \(-0.534741\pi\) | ||||
−0.108927 | + | 0.994050i | \(0.534741\pi\) | |||||||
\(684\) | −4.47186e9 | −0.534308 | ||||||||
\(685\) | 4.16617e7 | 0.00495245 | ||||||||
\(686\) | 1.45812e10 | 1.72448 | ||||||||
\(687\) | −3.46476e9 | −0.407685 | ||||||||
\(688\) | −1.31450e9 | −0.153887 | ||||||||
\(689\) | 1.27486e10 | 1.48489 | ||||||||
\(690\) | 2.58317e7 | 0.00299351 | ||||||||
\(691\) | 8.17172e9 | 0.942194 | 0.471097 | − | 0.882081i | \(-0.343858\pi\) | ||||
0.471097 | + | 0.882081i | \(0.343858\pi\) | |||||||
\(692\) | −4.00051e9 | −0.458927 | ||||||||
\(693\) | −5.82462e8 | −0.0664816 | ||||||||
\(694\) | −9.28610e9 | −1.05457 | ||||||||
\(695\) | 4.87403e6 | 0.000550734 0 | ||||||||
\(696\) | 7.43385e9 | 0.835759 | ||||||||
\(697\) | −2.84863e9 | −0.318656 | ||||||||
\(698\) | −1.38941e10 | −1.54645 | ||||||||
\(699\) | 9.72302e8 | 0.107679 | ||||||||
\(700\) | 1.09007e10 | 1.20119 | ||||||||
\(701\) | 8.54219e9 | 0.936605 | 0.468302 | − | 0.883568i | \(-0.344866\pi\) | ||||
0.468302 | + | 0.883568i | \(0.344866\pi\) | |||||||
\(702\) | −2.92566e9 | −0.319186 | ||||||||
\(703\) | 1.66948e9 | 0.181233 | ||||||||
\(704\) | −3.79328e9 | −0.409742 | ||||||||
\(705\) | −2.44209e7 | −0.00262482 | ||||||||
\(706\) | −1.18768e10 | −1.27023 | ||||||||
\(707\) | 1.00052e10 | 1.06478 | ||||||||
\(708\) | −1.07574e9 | −0.113917 | ||||||||
\(709\) | −8.20988e9 | −0.865117 | −0.432559 | − | 0.901606i | \(-0.642389\pi\) | ||||
−0.432559 | + | 0.901606i | \(0.642389\pi\) | |||||||
\(710\) | −9.42066e7 | −0.00987819 | ||||||||
\(711\) | −2.47657e9 | −0.258409 | ||||||||
\(712\) | 1.35006e10 | 1.40176 | ||||||||
\(713\) | 3.71866e9 | 0.384214 | ||||||||
\(714\) | 1.68487e9 | 0.173230 | ||||||||
\(715\) | 1.12554e7 | 0.00115157 | ||||||||
\(716\) | −1.97751e10 | −2.01337 | ||||||||
\(717\) | 6.22044e9 | 0.630237 | ||||||||
\(718\) | 1.12431e10 | 1.13357 | ||||||||
\(719\) | −1.72415e9 | −0.172991 | −0.0864957 | − | 0.996252i | \(-0.527567\pi\) | ||||
−0.0864957 | + | 0.996252i | \(0.527567\pi\) | |||||||
\(720\) | −3.19389e6 | −0.000318901 0 | ||||||||
\(721\) | −3.94708e9 | −0.392196 | ||||||||
\(722\) | 1.90223e9 | 0.188098 | ||||||||
\(723\) | 8.35916e9 | 0.822580 | ||||||||
\(724\) | 1.77441e9 | 0.173768 | ||||||||
\(725\) | 1.81639e10 | 1.77021 | ||||||||
\(726\) | 8.84353e9 | 0.857724 | ||||||||
\(727\) | −1.17427e9 | −0.113343 | −0.0566717 | − | 0.998393i | \(-0.518049\pi\) | ||||
−0.0566717 | + | 0.998393i | \(0.518049\pi\) | |||||||
\(728\) | −7.05532e9 | −0.677731 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −3.42075e7 | −0.00325455 | ||||||||
\(731\) | 1.77444e9 | 0.168016 | ||||||||
\(732\) | −1.70360e9 | −0.160538 | ||||||||
\(733\) | 1.78077e10 | 1.67011 | 0.835053 | − | 0.550170i | \(-0.185437\pi\) | ||||
0.835053 | + | 0.550170i | \(0.185437\pi\) | |||||||
\(734\) | 1.61344e9 | 0.150597 | ||||||||
\(735\) | 1.01130e7 | 0.000939456 0 | ||||||||
\(736\) | 9.40839e9 | 0.869847 | ||||||||
\(737\) | −1.91442e9 | −0.176157 | ||||||||
\(738\) | −7.70714e9 | −0.705824 | ||||||||
\(739\) | −1.69312e10 | −1.54324 | −0.771620 | − | 0.636084i | \(-0.780553\pi\) | ||||
−0.771620 | + | 0.636084i | \(0.780553\pi\) | |||||||
\(740\) | −1.25283e7 | −0.00113653 | ||||||||
\(741\) | 7.07206e9 | 0.638532 | ||||||||
\(742\) | −1.98638e10 | −1.78504 | ||||||||
\(743\) | 5.43777e9 | 0.486362 | 0.243181 | − | 0.969981i | \(-0.421809\pi\) | ||||
0.243181 | + | 0.969981i | \(0.421809\pi\) | |||||||
\(744\) | 2.72777e9 | 0.242830 | ||||||||
\(745\) | 7.14219e6 | 0.000632826 0 | ||||||||
\(746\) | 3.47795e9 | 0.306717 | ||||||||
\(747\) | −5.13905e9 | −0.451088 | ||||||||
\(748\) | 1.04192e9 | 0.0910291 | ||||||||
\(749\) | −5.28993e8 | −0.0460006 | ||||||||
\(750\) | 9.25981e7 | 0.00801471 | ||||||||
\(751\) | −1.10319e10 | −0.950406 | −0.475203 | − | 0.879876i | \(-0.657625\pi\) | ||||
−0.475203 | + | 0.879876i | \(0.657625\pi\) | |||||||
\(752\) | −2.64845e9 | −0.227107 | ||||||||
\(753\) | −4.90004e9 | −0.418232 | ||||||||
\(754\) | −3.45588e10 | −2.93602 | ||||||||
\(755\) | 6.28496e7 | 0.00531481 | ||||||||
\(756\) | 2.74640e9 | 0.231173 | ||||||||
\(757\) | 9.41776e9 | 0.789064 | 0.394532 | − | 0.918882i | \(-0.370907\pi\) | ||||
0.394532 | + | 0.918882i | \(0.370907\pi\) | |||||||
\(758\) | −4.09315e9 | −0.341363 | ||||||||
\(759\) | 1.30733e9 | 0.108527 | ||||||||
\(760\) | −4.58033e7 | −0.00378485 | ||||||||
\(761\) | 1.61763e10 | 1.33056 | 0.665278 | − | 0.746596i | \(-0.268313\pi\) | ||||
0.665278 | + | 0.746596i | \(0.268313\pi\) | |||||||
\(762\) | −1.24828e10 | −1.02205 | ||||||||
\(763\) | −1.67622e10 | −1.36614 | ||||||||
\(764\) | 2.48575e10 | 2.01665 | ||||||||
\(765\) | 4.31142e6 | 0.000348181 0 | ||||||||
\(766\) | −2.08321e9 | −0.167468 | ||||||||
\(767\) | 1.70124e9 | 0.136138 | ||||||||
\(768\) | 4.50004e9 | 0.358469 | ||||||||
\(769\) | −1.61743e10 | −1.28257 | −0.641287 | − | 0.767301i | \(-0.721599\pi\) | ||||
−0.641287 | + | 0.767301i | \(0.721599\pi\) | |||||||
\(770\) | −1.75373e7 | −0.00138435 | ||||||||
\(771\) | −1.12102e10 | −0.880889 | ||||||||
\(772\) | 5.77147e9 | 0.451467 | ||||||||
\(773\) | −1.43501e9 | −0.111745 | −0.0558723 | − | 0.998438i | \(-0.517794\pi\) | ||||
−0.0558723 | + | 0.998438i | \(0.517794\pi\) | |||||||
\(774\) | 4.80084e9 | 0.372155 | ||||||||
\(775\) | 6.66503e9 | 0.514335 | ||||||||
\(776\) | 1.61421e10 | 1.24006 | ||||||||
\(777\) | −1.02531e9 | −0.0784120 | ||||||||
\(778\) | 1.22778e10 | 0.934743 | ||||||||
\(779\) | 1.86302e10 | 1.41200 | ||||||||
\(780\) | −5.30711e7 | −0.00400430 | ||||||||
\(781\) | −4.76775e9 | −0.358125 | ||||||||
\(782\) | −3.78167e9 | −0.282788 | ||||||||
\(783\) | 4.57633e9 | 0.340684 | ||||||||
\(784\) | 1.09676e9 | 0.0812843 | ||||||||
\(785\) | −1.39987e7 | −0.00103287 | ||||||||
\(786\) | 1.95796e10 | 1.43822 | ||||||||
\(787\) | −1.73282e10 | −1.26719 | −0.633597 | − | 0.773664i | \(-0.718422\pi\) | ||||
−0.633597 | + | 0.773664i | \(0.718422\pi\) | |||||||
\(788\) | −2.88539e9 | −0.210069 | ||||||||
\(789\) | 1.02872e10 | 0.745641 | ||||||||
\(790\) | −7.45668e7 | −0.00538085 | ||||||||
\(791\) | −9.43121e9 | −0.677563 | ||||||||
\(792\) | 9.58972e8 | 0.0685911 | ||||||||
\(793\) | 2.69417e9 | 0.191853 | ||||||||
\(794\) | −3.11029e10 | −2.20510 | ||||||||
\(795\) | −5.08296e7 | −0.00358783 | ||||||||
\(796\) | −2.07950e10 | −1.46138 | ||||||||
\(797\) | −1.59506e10 | −1.11602 | −0.558012 | − | 0.829833i | \(-0.688436\pi\) | ||||
−0.558012 | + | 0.829833i | \(0.688436\pi\) | |||||||
\(798\) | −1.10191e10 | −0.767602 | ||||||||
\(799\) | 3.57514e9 | 0.247959 | ||||||||
\(800\) | 1.68628e10 | 1.16444 | ||||||||
\(801\) | 8.31110e9 | 0.571406 | ||||||||
\(802\) | 2.49901e10 | 1.71064 | ||||||||
\(803\) | −1.73123e9 | −0.117991 | ||||||||
\(804\) | 9.02677e9 | 0.612542 | ||||||||
\(805\) | 3.83487e7 | 0.00259099 | ||||||||
\(806\) | −1.26810e10 | −0.853060 | ||||||||
\(807\) | 2.57442e9 | 0.172434 | ||||||||
\(808\) | −1.64727e10 | −1.09857 | ||||||||
\(809\) | 1.99696e10 | 1.32602 | 0.663010 | − | 0.748611i | \(-0.269279\pi\) | ||||
0.663010 | + | 0.748611i | \(0.269279\pi\) | |||||||
\(810\) | 1.16648e7 | 0.000771223 0 | ||||||||
\(811\) | 1.94704e10 | 1.28175 | 0.640874 | − | 0.767646i | \(-0.278572\pi\) | ||||
0.640874 | + | 0.767646i | \(0.278572\pi\) | |||||||
\(812\) | 3.24413e10 | 2.12644 | ||||||||
\(813\) | 1.12854e10 | 0.736549 | ||||||||
\(814\) | −1.05241e9 | −0.0683912 | ||||||||
\(815\) | 1.53316e7 | 0.000992055 0 | ||||||||
\(816\) | 4.67575e8 | 0.0301256 | ||||||||
\(817\) | −1.16049e10 | −0.744498 | ||||||||
\(818\) | −2.66924e10 | −1.70511 | ||||||||
\(819\) | −4.34331e9 | −0.276266 | ||||||||
\(820\) | −1.39807e8 | −0.00885482 | ||||||||
\(821\) | −1.65074e10 | −1.04107 | −0.520534 | − | 0.853841i | \(-0.674267\pi\) | ||||
−0.520534 | + | 0.853841i | \(0.674267\pi\) | |||||||
\(822\) | −1.65016e10 | −1.03627 | ||||||||
\(823\) | 1.23795e10 | 0.774113 | 0.387057 | − | 0.922056i | \(-0.373492\pi\) | ||||
0.387057 | + | 0.922056i | \(0.373492\pi\) | |||||||
\(824\) | 6.49852e9 | 0.404640 | ||||||||
\(825\) | 2.34315e9 | 0.145282 | ||||||||
\(826\) | −2.65072e9 | −0.163657 | ||||||||
\(827\) | 7.73227e9 | 0.475376 | 0.237688 | − | 0.971342i | \(-0.423610\pi\) | ||||
0.237688 | + | 0.971342i | \(0.423610\pi\) | |||||||
\(828\) | −6.16426e9 | −0.377376 | ||||||||
\(829\) | 8.83980e9 | 0.538892 | 0.269446 | − | 0.963016i | \(-0.413159\pi\) | ||||
0.269446 | + | 0.963016i | \(0.413159\pi\) | |||||||
\(830\) | −1.54731e8 | −0.00939300 | ||||||||
\(831\) | 8.82738e9 | 0.533615 | ||||||||
\(832\) | −2.82858e10 | −1.70269 | ||||||||
\(833\) | −1.48052e9 | −0.0887474 | ||||||||
\(834\) | −1.93053e9 | −0.115238 | ||||||||
\(835\) | −4.61743e7 | −0.00274472 | ||||||||
\(836\) | −6.81421e9 | −0.403361 | ||||||||
\(837\) | 1.67924e9 | 0.0989857 | ||||||||
\(838\) | 1.74758e10 | 1.02585 | ||||||||
\(839\) | −1.45899e10 | −0.852877 | −0.426439 | − | 0.904516i | \(-0.640232\pi\) | ||||
−0.426439 | + | 0.904516i | \(0.640232\pi\) | |||||||
\(840\) | 2.81301e7 | 0.00163755 | ||||||||
\(841\) | 3.68072e10 | 2.13377 | ||||||||
\(842\) | 3.61320e10 | 2.08593 | ||||||||
\(843\) | −2.55839e9 | −0.147085 | ||||||||
\(844\) | 1.67352e10 | 0.958147 | ||||||||
\(845\) | 7.17549e6 | 0.000409122 0 | ||||||||
\(846\) | 9.67274e9 | 0.549229 | ||||||||
\(847\) | 1.31288e10 | 0.742390 | ||||||||
\(848\) | −5.51249e9 | −0.310429 | ||||||||
\(849\) | 1.20673e10 | 0.676759 | ||||||||
\(850\) | −6.77796e9 | −0.378559 | ||||||||
\(851\) | 2.30130e9 | 0.128003 | ||||||||
\(852\) | 2.24807e10 | 1.24529 | ||||||||
\(853\) | −1.83684e10 | −1.01333 | −0.506665 | − | 0.862143i | \(-0.669122\pi\) | ||||
−0.506665 | + | 0.862143i | \(0.669122\pi\) | |||||||
\(854\) | −4.19783e9 | −0.230633 | ||||||||
\(855\) | −2.81968e7 | −0.00154283 | ||||||||
\(856\) | 8.70941e8 | 0.0474603 | ||||||||
\(857\) | 1.71154e10 | 0.928871 | 0.464436 | − | 0.885607i | \(-0.346257\pi\) | ||||
0.464436 | + | 0.885607i | \(0.346257\pi\) | |||||||
\(858\) | −4.45811e9 | −0.240960 | ||||||||
\(859\) | −1.64262e10 | −0.884220 | −0.442110 | − | 0.896961i | \(-0.645770\pi\) | ||||
−0.442110 | + | 0.896961i | \(0.645770\pi\) | |||||||
\(860\) | 8.70868e7 | 0.00466883 | ||||||||
\(861\) | −1.14417e10 | −0.610914 | ||||||||
\(862\) | 5.29210e9 | 0.281418 | ||||||||
\(863\) | −1.57145e10 | −0.832265 | −0.416132 | − | 0.909304i | \(-0.636615\pi\) | ||||
−0.416132 | + | 0.909304i | \(0.636615\pi\) | |||||||
\(864\) | 4.24854e9 | 0.224100 | ||||||||
\(865\) | −2.52248e7 | −0.00132517 | ||||||||
\(866\) | −2.55442e10 | −1.33653 | ||||||||
\(867\) | 1.04480e10 | 0.544459 | ||||||||
\(868\) | 1.19040e10 | 0.617836 | ||||||||
\(869\) | −3.77379e9 | −0.195078 | ||||||||
\(870\) | 1.37788e8 | 0.00709407 | ||||||||
\(871\) | −1.42755e10 | −0.732026 | ||||||||
\(872\) | 2.75974e10 | 1.40949 | ||||||||
\(873\) | 9.93718e9 | 0.505491 | ||||||||
\(874\) | 2.47323e10 | 1.25307 | ||||||||
\(875\) | 1.37467e8 | 0.00693700 | ||||||||
\(876\) | 8.16299e9 | 0.410284 | ||||||||
\(877\) | 4.28124e9 | 0.214324 | 0.107162 | − | 0.994242i | \(-0.465824\pi\) | ||||
0.107162 | + | 0.994242i | \(0.465824\pi\) | |||||||
\(878\) | −2.78885e10 | −1.39057 | ||||||||
\(879\) | −1.09301e10 | −0.542829 | ||||||||
\(880\) | −4.86685e6 | −0.000240746 0 | ||||||||
\(881\) | 1.71858e10 | 0.846748 | 0.423374 | − | 0.905955i | \(-0.360846\pi\) | ||||
0.423374 | + | 0.905955i | \(0.360846\pi\) | |||||||
\(882\) | −4.00562e9 | −0.196576 | ||||||||
\(883\) | −1.87937e10 | −0.918648 | −0.459324 | − | 0.888269i | \(-0.651908\pi\) | ||||
−0.459324 | + | 0.888269i | \(0.651908\pi\) | |||||||
\(884\) | 7.76943e9 | 0.378274 | ||||||||
\(885\) | −6.78295e6 | −0.000328941 0 | ||||||||
\(886\) | −1.15073e10 | −0.555849 | ||||||||
\(887\) | 1.22073e10 | 0.587339 | 0.293669 | − | 0.955907i | \(-0.405124\pi\) | ||||
0.293669 | + | 0.955907i | \(0.405124\pi\) | |||||||
\(888\) | 1.68809e9 | 0.0809001 | ||||||||
\(889\) | −1.85315e10 | −0.884617 | ||||||||
\(890\) | 2.50238e8 | 0.0118984 | ||||||||
\(891\) | 5.90351e8 | 0.0279601 | ||||||||
\(892\) | 2.38011e10 | 1.12284 | ||||||||
\(893\) | −2.33815e10 | −1.09873 | ||||||||
\(894\) | −2.82891e9 | −0.132415 | ||||||||
\(895\) | −1.24690e8 | −0.00581368 | ||||||||
\(896\) | 2.42005e10 | 1.12395 | ||||||||
\(897\) | 9.74852e9 | 0.450988 | ||||||||
\(898\) | 5.32448e10 | 2.45364 | ||||||||
\(899\) | 1.98357e10 | 0.910516 | ||||||||
\(900\) | −1.10483e10 | −0.505181 | ||||||||
\(901\) | 7.44129e9 | 0.338931 | ||||||||
\(902\) | −1.17441e10 | −0.532841 | ||||||||
\(903\) | 7.12714e9 | 0.322113 | ||||||||
\(904\) | 1.55276e10 | 0.699063 | ||||||||
\(905\) | 1.11884e7 | 0.000501761 0 | ||||||||
\(906\) | −2.48938e10 | −1.11209 | ||||||||
\(907\) | 1.54047e9 | 0.0685534 | 0.0342767 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342767 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(908\) | 2.17477e10 | 0.964078 | ||||||||
\(909\) | −1.01407e10 | −0.447813 | ||||||||
\(910\) | −1.30772e8 | −0.00575269 | ||||||||
\(911\) | 3.19695e10 | 1.40094 | 0.700472 | − | 0.713680i | \(-0.252973\pi\) | ||||
0.700472 | + | 0.713680i | \(0.252973\pi\) | |||||||
\(912\) | −3.05796e9 | −0.133490 | ||||||||
\(913\) | −7.83088e9 | −0.340536 | ||||||||
\(914\) | −5.95352e10 | −2.57906 | ||||||||
\(915\) | −1.07418e7 | −0.000463559 0 | ||||||||
\(916\) | 2.48941e10 | 1.07019 | ||||||||
\(917\) | 2.90671e10 | 1.24483 | ||||||||
\(918\) | −1.70769e9 | −0.0728550 | ||||||||
\(919\) | 2.59602e10 | 1.10333 | 0.551663 | − | 0.834067i | \(-0.313993\pi\) | ||||
0.551663 | + | 0.834067i | \(0.313993\pi\) | |||||||
\(920\) | −6.31377e7 | −0.00267320 | ||||||||
\(921\) | 2.14768e10 | 0.905860 | ||||||||
\(922\) | 1.70227e10 | 0.715272 | ||||||||
\(923\) | −3.55523e10 | −1.48820 | ||||||||
\(924\) | 4.18495e9 | 0.174517 | ||||||||
\(925\) | 4.12467e9 | 0.171354 | ||||||||
\(926\) | 2.39349e10 | 0.990589 | ||||||||
\(927\) | 4.00054e9 | 0.164945 | ||||||||
\(928\) | 5.01851e10 | 2.06138 | ||||||||
\(929\) | −6.20074e9 | −0.253740 | −0.126870 | − | 0.991919i | \(-0.540493\pi\) | ||||
−0.126870 | + | 0.991919i | \(0.540493\pi\) | |||||||
\(930\) | 5.05599e7 | 0.00206118 | ||||||||
\(931\) | 9.68263e9 | 0.393251 | ||||||||
\(932\) | −6.98593e9 | −0.282663 | ||||||||
\(933\) | −9.43732e9 | −0.380419 | ||||||||
\(934\) | −6.75024e10 | −2.71085 | ||||||||
\(935\) | 6.56974e6 | 0.000262850 0 | ||||||||
\(936\) | 7.15088e9 | 0.285032 | ||||||||
\(937\) | −2.50957e10 | −0.996575 | −0.498288 | − | 0.867012i | \(-0.666038\pi\) | ||||
−0.498288 | + | 0.867012i | \(0.666038\pi\) | |||||||
\(938\) | 2.22428e10 | 0.879995 | ||||||||
\(939\) | −2.65169e9 | −0.104518 | ||||||||
\(940\) | 1.75463e8 | 0.00689028 | ||||||||
\(941\) | −8.17848e9 | −0.319970 | −0.159985 | − | 0.987119i | \(-0.551145\pi\) | ||||
−0.159985 | + | 0.987119i | \(0.551145\pi\) | |||||||
\(942\) | 5.54469e9 | 0.216122 | ||||||||
\(943\) | 2.56808e10 | 0.997282 | ||||||||
\(944\) | −7.35614e8 | −0.0284608 | ||||||||
\(945\) | 1.73171e7 | 0.000667520 0 | ||||||||
\(946\) | 7.31552e9 | 0.280948 | ||||||||
\(947\) | 1.81622e10 | 0.694935 | 0.347468 | − | 0.937692i | \(-0.387042\pi\) | ||||
0.347468 | + | 0.937692i | \(0.387042\pi\) | |||||||
\(948\) | 1.77940e10 | 0.678336 | ||||||||
\(949\) | −1.29094e10 | −0.490315 | ||||||||
\(950\) | 4.43281e10 | 1.67744 | ||||||||
\(951\) | −2.46099e10 | −0.927849 | ||||||||
\(952\) | −4.11815e9 | −0.154694 | ||||||||
\(953\) | −4.42866e10 | −1.65748 | −0.828738 | − | 0.559637i | \(-0.810941\pi\) | ||||
−0.828738 | + | 0.559637i | \(0.810941\pi\) | |||||||
\(954\) | 2.01328e10 | 0.750733 | ||||||||
\(955\) | 1.56737e8 | 0.00582316 | ||||||||
\(956\) | −4.46935e10 | −1.65440 | ||||||||
\(957\) | 6.97341e9 | 0.257190 | ||||||||
\(958\) | −5.26702e10 | −1.93547 | ||||||||
\(959\) | −2.44976e10 | −0.896929 | ||||||||
\(960\) | 1.12778e8 | 0.00411409 | ||||||||
\(961\) | −2.02341e10 | −0.735449 | ||||||||
\(962\) | −7.84764e9 | −0.284202 | ||||||||
\(963\) | 5.36158e8 | 0.0193464 | ||||||||
\(964\) | −6.00600e10 | −2.15931 | ||||||||
\(965\) | 3.63914e7 | 0.00130363 | ||||||||
\(966\) | −1.51893e10 | −0.542149 | ||||||||
\(967\) | 3.34893e10 | 1.19101 | 0.595503 | − | 0.803353i | \(-0.296953\pi\) | ||||
0.595503 | + | 0.803353i | \(0.296953\pi\) | |||||||
\(968\) | −2.16153e10 | −0.765946 | ||||||||
\(969\) | 4.12793e9 | 0.145747 | ||||||||
\(970\) | 2.99197e8 | 0.0105258 | ||||||||
\(971\) | −2.53801e10 | −0.889663 | −0.444831 | − | 0.895614i | \(-0.646736\pi\) | ||||
−0.444831 | + | 0.895614i | \(0.646736\pi\) | |||||||
\(972\) | −2.78359e9 | −0.0972240 | ||||||||
\(973\) | −2.86599e9 | −0.0997423 | ||||||||
\(974\) | −2.25980e10 | −0.783633 | ||||||||
\(975\) | 1.74725e10 | 0.603723 | ||||||||
\(976\) | −1.16496e9 | −0.0401084 | ||||||||
\(977\) | −1.10528e10 | −0.379177 | −0.189589 | − | 0.981864i | \(-0.560715\pi\) | ||||
−0.189589 | + | 0.981864i | \(0.560715\pi\) | |||||||
\(978\) | −6.07261e9 | −0.207582 | ||||||||
\(979\) | 1.26644e10 | 0.431366 | ||||||||
\(980\) | −7.26616e7 | −0.00246612 | ||||||||
\(981\) | 1.69892e10 | 0.574554 | ||||||||
\(982\) | 7.55401e9 | 0.254558 | ||||||||
\(983\) | −3.71529e9 | −0.124754 | −0.0623771 | − | 0.998053i | \(-0.519868\pi\) | ||||
−0.0623771 | + | 0.998053i | \(0.519868\pi\) | |||||||
\(984\) | 1.88378e10 | 0.630299 | ||||||||
\(985\) | −1.81935e7 | −0.000606582 0 | ||||||||
\(986\) | −2.01718e10 | −0.670154 | ||||||||
\(987\) | 1.43598e10 | 0.475376 | ||||||||
\(988\) | −5.08123e10 | −1.67618 | ||||||||
\(989\) | −1.59968e10 | −0.525831 | ||||||||
\(990\) | 1.77748e7 | 0.000582213 0 | ||||||||
\(991\) | −3.64285e10 | −1.18901 | −0.594503 | − | 0.804094i | \(-0.702651\pi\) | ||||
−0.594503 | + | 0.804094i | \(0.702651\pi\) | |||||||
\(992\) | 1.84149e10 | 0.598933 | ||||||||
\(993\) | −2.34654e10 | −0.760511 | ||||||||
\(994\) | 5.53946e10 | 1.78902 | ||||||||
\(995\) | −1.31121e8 | −0.00421978 | ||||||||
\(996\) | 3.69238e10 | 1.18413 | ||||||||
\(997\) | 4.94528e10 | 1.58037 | 0.790183 | − | 0.612871i | \(-0.209985\pi\) | ||||
0.790183 | + | 0.612871i | \(0.209985\pi\) | |||||||
\(998\) | −8.73170e10 | −2.78062 | ||||||||
\(999\) | 1.03920e9 | 0.0329776 |
(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 | 177.8.a.a.1.14 | ✓ | 16 | |
3.2 | odd | 2 | 531.8.a.b.1.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.14 | ✓ | 16 | 1.1 | even | 1 | trivial | |
531.8.a.b.1.3 | 16 | 3.2 | odd | 2 |