Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,8,Mod(1,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.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: | \(8.43439568807\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 16 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.59339 | −0.671167 | −0.335583 | − | 0.942010i | \(-0.608933\pi\) | ||||
−0.335583 | + | 0.942010i | \(0.608933\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −70.3405 | −0.549535 | ||||||||
\(5\) | 65.8132 | 0.235461 | 0.117730 | − | 0.993046i | \(-0.462438\pi\) | ||||
0.117730 | + | 0.993046i | \(0.462438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −738.405 | −0.813676 | −0.406838 | − | 0.913500i | \(-0.633369\pi\) | ||||
−0.406838 | + | 0.913500i | \(0.633369\pi\) | |||||||
\(8\) | 1506.08 | 1.04000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −499.745 | −0.158033 | ||||||||
\(11\) | 4961.26 | 1.12387 | 0.561937 | − | 0.827180i | \(-0.310056\pi\) | ||||
0.561937 | + | 0.827180i | \(0.310056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5967.24 | 0.753306 | 0.376653 | − | 0.926354i | \(-0.377075\pi\) | ||||
0.376653 | + | 0.926354i | \(0.377075\pi\) | |||||||
\(14\) | 5606.99 | 0.546112 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2432.64 | −0.148476 | ||||||||
\(17\) | 36651.6 | 1.80935 | 0.904674 | − | 0.426104i | \(-0.140114\pi\) | ||||
0.904674 | + | 0.426104i | \(0.140114\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 22378.9 | 0.748518 | 0.374259 | − | 0.927324i | \(-0.377897\pi\) | ||||
0.374259 | + | 0.927324i | \(0.377897\pi\) | |||||||
\(20\) | −4629.33 | −0.129394 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −37672.8 | −0.754308 | ||||||||
\(23\) | −51473.6 | −0.882139 | −0.441069 | − | 0.897473i | \(-0.645401\pi\) | ||||
−0.441069 | + | 0.897473i | \(0.645401\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −73793.6 | −0.944558 | ||||||||
\(26\) | −45311.5 | −0.505594 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 51939.7 | 0.447143 | ||||||||
\(29\) | −68495.7 | −0.521519 | −0.260760 | − | 0.965404i | \(-0.583973\pi\) | ||||
−0.260760 | + | 0.965404i | \(0.583973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 150655. | 0.908275 | 0.454137 | − | 0.890932i | \(-0.349948\pi\) | ||||
0.454137 | + | 0.890932i | \(0.349948\pi\) | |||||||
\(32\) | −174306. | −0.940344 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −278310. | −1.21437 | ||||||||
\(35\) | −48596.8 | −0.191589 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 489027. | 1.58718 | 0.793591 | − | 0.608451i | \(-0.208209\pi\) | ||||
0.793591 | + | 0.608451i | \(0.208209\pi\) | |||||||
\(38\) | −169932. | −0.502380 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 99119.7 | 0.244878 | ||||||||
\(41\) | 590635. | 1.33837 | 0.669184 | − | 0.743096i | \(-0.266644\pi\) | ||||
0.669184 | + | 0.743096i | \(0.266644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −842643. | −1.61623 | −0.808117 | − | 0.589023i | \(-0.799513\pi\) | ||||
−0.808117 | + | 0.589023i | \(0.799513\pi\) | |||||||
\(44\) | −348978. | −0.617609 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 390859. | 0.592062 | ||||||||
\(47\) | 1.22637e6 | 1.72297 | 0.861486 | − | 0.507782i | \(-0.169534\pi\) | ||||
0.861486 | + | 0.507782i | \(0.169534\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −278301. | −0.337932 | ||||||||
\(50\) | 560343. | 0.633956 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −419738. | −0.413968 | ||||||||
\(53\) | 958904. | 0.884727 | 0.442364 | − | 0.896836i | \(-0.354140\pi\) | ||||
0.442364 | + | 0.896836i | \(0.354140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 326517. | 0.264628 | ||||||||
\(56\) | −1.11209e6 | −0.846220 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 520114. | 0.350027 | ||||||||
\(59\) | −316269. | −0.200482 | −0.100241 | − | 0.994963i | \(-0.531961\pi\) | ||||
−0.100241 | + | 0.994963i | \(0.531961\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29722.9 | −0.0167663 | −0.00838315 | − | 0.999965i | \(-0.502668\pi\) | ||||
−0.00838315 | + | 0.999965i | \(0.502668\pi\) | |||||||
\(62\) | −1.14398e6 | −0.609604 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.63495e6 | 0.779604 | ||||||||
\(65\) | 392723. | 0.177374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 293025. | 0.119026 | 0.0595130 | − | 0.998228i | \(-0.481045\pi\) | ||||
0.0595130 | + | 0.998228i | \(0.481045\pi\) | |||||||
\(68\) | −2.57809e6 | −0.994300 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 369014. | 0.128588 | ||||||||
\(71\) | 714537. | 0.236930 | 0.118465 | − | 0.992958i | \(-0.462203\pi\) | ||||
0.118465 | + | 0.992958i | \(0.462203\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.96273e6 | −1.19224 | −0.596121 | − | 0.802894i | \(-0.703292\pi\) | ||||
−0.596121 | + | 0.802894i | \(0.703292\pi\) | |||||||
\(74\) | −3.71337e6 | −1.06526 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.57415e6 | −0.411337 | ||||||||
\(77\) | −3.66342e6 | −0.914470 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.53805e6 | 0.579168 | 0.289584 | − | 0.957153i | \(-0.406483\pi\) | ||||
0.289584 | + | 0.957153i | \(0.406483\pi\) | |||||||
\(80\) | −160100. | −0.0349603 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.48492e6 | −0.898269 | ||||||||
\(83\) | 1.66311e6 | 0.319263 | 0.159631 | − | 0.987177i | \(-0.448969\pi\) | ||||
0.159631 | + | 0.987177i | \(0.448969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.41216e6 | 0.426030 | ||||||||
\(86\) | 6.39851e6 | 1.08476 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.47204e6 | 1.16883 | ||||||||
\(89\) | 4.64819e6 | 0.698906 | 0.349453 | − | 0.936954i | \(-0.386368\pi\) | ||||
0.349453 | + | 0.936954i | \(0.386368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.40624e6 | −0.612947 | ||||||||
\(92\) | 3.62068e6 | 0.484766 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.31228e6 | −1.15640 | ||||||||
\(95\) | 1.47283e6 | 0.176246 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.47010e7 | 1.63548 | 0.817738 | − | 0.575590i | \(-0.195228\pi\) | ||||
0.817738 | + | 0.575590i | \(0.195228\pi\) | |||||||
\(98\) | 2.11325e6 | 0.226809 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.19068e6 | 0.519068 | ||||||||
\(101\) | 9.28380e6 | 0.896604 | 0.448302 | − | 0.893882i | \(-0.352029\pi\) | ||||
0.448302 | + | 0.893882i | \(0.352029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.11049e6 | 0.370650 | 0.185325 | − | 0.982677i | \(-0.440666\pi\) | ||||
0.185325 | + | 0.982677i | \(0.440666\pi\) | |||||||
\(104\) | 8.98711e6 | 0.783436 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.28133e6 | −0.593800 | ||||||||
\(107\) | −1.77931e7 | −1.40414 | −0.702068 | − | 0.712110i | \(-0.747740\pi\) | ||||
−0.702068 | + | 0.712110i | \(0.747740\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.72244e7 | −1.27394 | −0.636972 | − | 0.770887i | \(-0.719813\pi\) | ||||
−0.636972 | + | 0.770887i | \(0.719813\pi\) | |||||||
\(110\) | −2.47937e6 | −0.177610 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.79627e6 | 0.120812 | ||||||||
\(113\) | −2.16751e6 | −0.141315 | −0.0706573 | − | 0.997501i | \(-0.522510\pi\) | ||||
−0.0706573 | + | 0.997501i | \(0.522510\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.38764e6 | −0.207709 | ||||||||
\(116\) | 4.81802e6 | 0.286593 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.40156e6 | 0.134557 | ||||||||
\(119\) | −2.70638e7 | −1.47222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.12697e6 | 0.263095 | ||||||||
\(122\) | 225698. | 0.0112530 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.05971e7 | −0.499129 | ||||||||
\(125\) | −9.99825e6 | −0.457867 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.66827e6 | 0.418828 | 0.209414 | − | 0.977827i | \(-0.432844\pi\) | ||||
0.209414 | + | 0.977827i | \(0.432844\pi\) | |||||||
\(128\) | 9.89634e6 | 0.417100 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.98210e6 | −0.119048 | ||||||||
\(131\) | −4.22431e7 | −1.64175 | −0.820873 | − | 0.571111i | \(-0.806513\pi\) | ||||
−0.820873 | + | 0.571111i | \(0.806513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.65247e7 | −0.609051 | ||||||||
\(134\) | −2.22505e6 | −0.0798864 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.52002e7 | 1.88172 | ||||||||
\(137\) | −8.01451e6 | −0.266290 | −0.133145 | − | 0.991097i | \(-0.542508\pi\) | ||||
−0.133145 | + | 0.991097i | \(0.542508\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.46010e7 | 0.461138 | 0.230569 | − | 0.973056i | \(-0.425941\pi\) | ||||
0.230569 | + | 0.973056i | \(0.425941\pi\) | |||||||
\(140\) | 3.41832e6 | 0.105285 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.42576e6 | −0.159020 | ||||||||
\(143\) | 2.96050e7 | 0.846622 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.50792e6 | −0.122797 | ||||||||
\(146\) | 3.00906e7 | 0.800194 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.43984e7 | −0.872212 | ||||||||
\(149\) | 4.07087e7 | 1.00817 | 0.504086 | − | 0.863653i | \(-0.331829\pi\) | ||||
0.504086 | + | 0.863653i | \(0.331829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.29940e7 | −1.25259 | −0.626293 | − | 0.779588i | \(-0.715428\pi\) | ||||
−0.626293 | + | 0.779588i | \(0.715428\pi\) | |||||||
\(152\) | 3.37044e7 | 0.778456 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.78178e7 | 0.613762 | ||||||||
\(155\) | 9.91508e6 | 0.213863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.10669e7 | 0.846922 | 0.423461 | − | 0.905914i | \(-0.360815\pi\) | ||||
0.423461 | + | 0.905914i | \(0.360815\pi\) | |||||||
\(158\) | −1.92724e7 | −0.388718 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.14716e7 | −0.221414 | ||||||||
\(161\) | 3.80083e7 | 0.717775 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.33772e7 | −0.784522 | −0.392261 | − | 0.919854i | \(-0.628307\pi\) | ||||
−0.392261 | + | 0.919854i | \(0.628307\pi\) | |||||||
\(164\) | −4.15456e7 | −0.735480 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.26287e7 | −0.214279 | ||||||||
\(167\) | 3.86845e7 | 0.642731 | 0.321365 | − | 0.946955i | \(-0.395858\pi\) | ||||
0.321365 | + | 0.946955i | \(0.395858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.71406e7 | −0.432529 | ||||||||
\(170\) | −1.83165e7 | −0.285937 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.92719e7 | 0.888177 | ||||||||
\(173\) | 5.30547e7 | 0.779045 | 0.389523 | − | 0.921017i | \(-0.372640\pi\) | ||||
0.389523 | + | 0.921017i | \(0.372640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.44896e7 | 0.768564 | ||||||||
\(176\) | −1.20689e7 | −0.166869 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.52955e7 | −0.469082 | ||||||||
\(179\) | −1.34132e8 | −1.74802 | −0.874012 | − | 0.485904i | \(-0.838491\pi\) | ||||
−0.874012 | + | 0.485904i | \(0.838491\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.35105e6 | 0.0796105 | 0.0398053 | − | 0.999207i | \(-0.487326\pi\) | ||||
0.0398053 | + | 0.999207i | \(0.487326\pi\) | |||||||
\(182\) | 3.34583e7 | 0.411390 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.75231e7 | −0.917422 | ||||||||
\(185\) | 3.21845e7 | 0.373719 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.81839e8 | 2.03348 | ||||||||
\(188\) | −8.62633e7 | −0.946833 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.11838e7 | −0.118291 | ||||||||
\(191\) | −1.15843e8 | −1.20297 | −0.601483 | − | 0.798885i | \(-0.705423\pi\) | ||||
−0.601483 | + | 0.798885i | \(0.705423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.73856e7 | 0.574582 | 0.287291 | − | 0.957843i | \(-0.407245\pi\) | ||||
0.287291 | + | 0.957843i | \(0.407245\pi\) | |||||||
\(194\) | −1.11630e8 | −1.09768 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.95759e7 | 0.185705 | ||||||||
\(197\) | 1.04846e8 | 0.977059 | 0.488530 | − | 0.872547i | \(-0.337533\pi\) | ||||
0.488530 | + | 0.872547i | \(0.337533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.10623e8 | −1.89461 | −0.947304 | − | 0.320335i | \(-0.896205\pi\) | ||||
−0.947304 | + | 0.320335i | \(0.896205\pi\) | |||||||
\(200\) | −1.11139e8 | −0.982337 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.04955e7 | −0.601771 | ||||||||
\(203\) | 5.05776e7 | 0.424348 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.88716e7 | 0.315133 | ||||||||
\(206\) | −3.12125e7 | −0.248768 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.45161e7 | −0.111848 | ||||||||
\(209\) | 1.11028e8 | 0.841240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.49193e7 | −0.475757 | −0.237878 | − | 0.971295i | \(-0.576452\pi\) | ||||
−0.237878 | + | 0.971295i | \(0.576452\pi\) | |||||||
\(212\) | −6.74497e7 | −0.486189 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.35110e8 | 0.942410 | ||||||||
\(215\) | −5.54570e7 | −0.380559 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.11244e8 | −0.739041 | ||||||||
\(218\) | 1.30791e8 | 0.855030 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.29674e7 | −0.145422 | ||||||||
\(221\) | 2.18709e8 | 1.36299 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.40879e8 | 0.850705 | 0.425352 | − | 0.905028i | \(-0.360150\pi\) | ||||
0.425352 | + | 0.905028i | \(0.360150\pi\) | |||||||
\(224\) | 1.28708e8 | 0.765135 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.64588e7 | 0.0948457 | ||||||||
\(227\) | −3.40163e6 | −0.0193017 | −0.00965086 | − | 0.999953i | \(-0.503072\pi\) | ||||
−0.00965086 | + | 0.999953i | \(0.503072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.76169e7 | −0.151967 | −0.0759836 | − | 0.997109i | \(-0.524210\pi\) | ||||
−0.0759836 | + | 0.997109i | \(0.524210\pi\) | |||||||
\(230\) | 2.57237e7 | 0.139407 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.03160e8 | −0.542378 | ||||||||
\(233\) | 3.51458e8 | 1.82023 | 0.910117 | − | 0.414351i | \(-0.135992\pi\) | ||||
0.910117 | + | 0.414351i | \(0.135992\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.07112e7 | 0.405692 | ||||||||
\(236\) | 2.22465e7 | 0.110172 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.05506e8 | 0.988107 | ||||||||
\(239\) | −3.79195e8 | −1.79668 | −0.898339 | − | 0.439302i | \(-0.855226\pi\) | ||||
−0.898339 | + | 0.439302i | \(0.855226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.99276e7 | 0.137725 | 0.0688624 | − | 0.997626i | \(-0.478063\pi\) | ||||
0.0688624 | + | 0.997626i | \(0.478063\pi\) | |||||||
\(242\) | −3.89311e7 | −0.176581 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.09072e6 | 0.00921367 | ||||||||
\(245\) | −1.83159e7 | −0.0795696 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.33540e8 | 0.563863 | ||||||||
\(248\) | 2.26898e8 | 0.944602 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.59206e7 | 0.307305 | ||||||||
\(251\) | −1.71456e7 | −0.0684374 | −0.0342187 | − | 0.999414i | \(-0.510894\pi\) | ||||
−0.0342187 | + | 0.999414i | \(0.510894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.55374e8 | −0.991414 | ||||||||
\(254\) | −7.34149e7 | −0.281103 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.84420e8 | −1.05955 | ||||||||
\(257\) | −9.79449e7 | −0.359928 | −0.179964 | − | 0.983673i | \(-0.557598\pi\) | ||||
−0.179964 | + | 0.983673i | \(0.557598\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.61100e8 | −1.29145 | ||||||||
\(260\) | −2.76243e7 | −0.0974732 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.20768e8 | 1.10189 | ||||||||
\(263\) | −8.92540e7 | −0.302540 | −0.151270 | − | 0.988492i | \(-0.548336\pi\) | ||||
−0.151270 | + | 0.988492i | \(0.548336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.31085e7 | 0.208318 | ||||||||
\(266\) | 1.25479e8 | 0.408775 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.06115e7 | −0.0654090 | ||||||||
\(269\) | −5.34653e8 | −1.67471 | −0.837354 | − | 0.546662i | \(-0.815898\pi\) | ||||
−0.837354 | + | 0.546662i | \(0.815898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.11501e8 | 0.645535 | 0.322768 | − | 0.946478i | \(-0.395387\pi\) | ||||
0.322768 | + | 0.946478i | \(0.395387\pi\) | |||||||
\(272\) | −8.91601e7 | −0.268645 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.08573e7 | 0.178725 | ||||||||
\(275\) | −3.66110e8 | −1.06157 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.24017e8 | −0.915986 | −0.457993 | − | 0.888956i | \(-0.651432\pi\) | ||||
−0.457993 | + | 0.888956i | \(0.651432\pi\) | |||||||
\(278\) | −1.10871e8 | −0.309501 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.31905e7 | −0.199251 | ||||||||
\(281\) | 4.91210e7 | 0.132067 | 0.0660336 | − | 0.997817i | \(-0.478966\pi\) | ||||
0.0660336 | + | 0.997817i | \(0.478966\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.03017e8 | −1.05699 | −0.528495 | − | 0.848936i | \(-0.677244\pi\) | ||||
−0.528495 | + | 0.848936i | \(0.677244\pi\) | |||||||
\(284\) | −5.02609e7 | −0.130202 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.24803e8 | −0.568225 | ||||||||
\(287\) | −4.36128e8 | −1.08900 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.33004e8 | 2.27374 | ||||||||
\(290\) | 3.42304e7 | 0.0824174 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.78740e8 | 0.655179 | ||||||||
\(293\) | 4.85906e8 | 1.12854 | 0.564268 | − | 0.825592i | \(-0.309159\pi\) | ||||
0.564268 | + | 0.825592i | \(0.309159\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.08147e7 | −0.0472056 | ||||||||
\(296\) | 7.36512e8 | 1.65066 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.09117e8 | −0.676652 | ||||||||
\(299\) | −3.07155e8 | −0.664521 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.22212e8 | 1.31509 | ||||||||
\(302\) | 4.02404e8 | 0.840694 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.44398e7 | −0.111137 | ||||||||
\(305\) | −1.95616e6 | −0.00394780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.82215e8 | 0.556668 | 0.278334 | − | 0.960484i | \(-0.410218\pi\) | ||||
0.278334 | + | 0.960484i | \(0.410218\pi\) | |||||||
\(308\) | 2.57687e8 | 0.502533 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.52890e7 | −0.143538 | ||||||||
\(311\) | 7.04440e7 | 0.132795 | 0.0663977 | − | 0.997793i | \(-0.478849\pi\) | ||||
0.0663977 | + | 0.997793i | \(0.478849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.78096e8 | −0.881273 | −0.440636 | − | 0.897686i | \(-0.645247\pi\) | ||||
−0.440636 | + | 0.897686i | \(0.645247\pi\) | |||||||
\(314\) | −3.11837e8 | −0.568426 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.78527e8 | −0.318273 | ||||||||
\(317\) | 6.89470e8 | 1.21565 | 0.607824 | − | 0.794072i | \(-0.292043\pi\) | ||||
0.607824 | + | 0.794072i | \(0.292043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.39825e8 | −0.586123 | ||||||||
\(320\) | 1.07601e8 | 0.183566 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.88612e8 | −0.481747 | ||||||||
\(323\) | 8.20225e8 | 1.35433 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.40344e8 | −0.711542 | ||||||||
\(326\) | 3.29380e8 | 0.526545 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.89541e8 | 1.39190 | ||||||||
\(329\) | −9.05555e8 | −1.40194 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.36833e8 | 0.813657 | 0.406829 | − | 0.913504i | \(-0.366635\pi\) | ||||
0.406829 | + | 0.913504i | \(0.366635\pi\) | |||||||
\(332\) | −1.16984e8 | −0.175446 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.93746e8 | −0.431379 | ||||||||
\(335\) | 1.92849e7 | 0.0280259 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.24011e9 | −1.76505 | −0.882524 | − | 0.470268i | \(-0.844157\pi\) | ||||
−0.882524 | + | 0.470268i | \(0.844157\pi\) | |||||||
\(338\) | 2.06089e8 | 0.290299 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.69673e8 | −0.234119 | ||||||||
\(341\) | 7.47438e8 | 1.02079 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.13607e8 | 1.08864 | ||||||||
\(344\) | −1.26908e9 | −1.68088 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.02865e8 | −0.522869 | ||||||||
\(347\) | 4.86766e7 | 0.0625413 | 0.0312706 | − | 0.999511i | \(-0.490045\pi\) | ||||
0.0312706 | + | 0.999511i | \(0.490045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.23665e9 | 1.55725 | 0.778626 | − | 0.627488i | \(-0.215917\pi\) | ||||
0.778626 | + | 0.627488i | \(0.215917\pi\) | |||||||
\(350\) | −4.13760e8 | −0.515835 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.64777e8 | −1.05683 | ||||||||
\(353\) | 6.06858e7 | 0.0734304 | 0.0367152 | − | 0.999326i | \(-0.488311\pi\) | ||||
0.0367152 | + | 0.999326i | \(0.488311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.70260e7 | 0.0557878 | ||||||||
\(356\) | −3.26956e8 | −0.384073 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.01852e9 | 1.17322 | ||||||||
\(359\) | −5.36061e8 | −0.611482 | −0.305741 | − | 0.952115i | \(-0.598904\pi\) | ||||
−0.305741 | + | 0.952115i | \(0.598904\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.93055e8 | −0.439722 | ||||||||
\(362\) | −4.82260e7 | −0.0534320 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.09937e8 | 0.336836 | ||||||||
\(365\) | −2.60800e8 | −0.280726 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.31327e8 | −0.455487 | −0.227743 | − | 0.973721i | \(-0.573135\pi\) | ||||
−0.227743 | + | 0.973721i | \(0.573135\pi\) | |||||||
\(368\) | 1.25216e8 | 0.130977 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.44389e8 | −0.250828 | ||||||||
\(371\) | −7.08059e8 | −0.719881 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.69689e8 | 0.269080 | 0.134540 | − | 0.990908i | \(-0.457044\pi\) | ||||
0.134540 | + | 0.990908i | \(0.457044\pi\) | |||||||
\(374\) | −1.38077e9 | −1.36481 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.84700e9 | 1.79188 | ||||||||
\(377\) | −4.08730e8 | −0.392864 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.03807e8 | −0.758429 | −0.379214 | − | 0.925309i | \(-0.623806\pi\) | ||||
−0.379214 | + | 0.925309i | \(0.623806\pi\) | |||||||
\(380\) | −1.03600e8 | −0.0968535 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.79642e8 | 0.807392 | ||||||||
\(383\) | 9.83923e8 | 0.894882 | 0.447441 | − | 0.894314i | \(-0.352336\pi\) | ||||
0.447441 | + | 0.894314i | \(0.352336\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.41102e8 | −0.215322 | ||||||||
\(386\) | −4.35751e8 | −0.385641 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.03407e9 | −0.898752 | ||||||||
\(389\) | −2.16250e8 | −0.186265 | −0.0931326 | − | 0.995654i | \(-0.529688\pi\) | ||||
−0.0931326 | + | 0.995654i | \(0.529688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.88659e9 | −1.59610 | ||||||||
\(392\) | −4.19143e8 | −0.351448 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.96138e8 | −0.655770 | ||||||||
\(395\) | 1.67037e8 | 0.136371 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.33533e8 | 0.347741 | 0.173870 | − | 0.984769i | \(-0.444373\pi\) | ||||
0.173870 | + | 0.984769i | \(0.444373\pi\) | |||||||
\(398\) | 1.59934e9 | 1.27160 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.79513e8 | 0.140245 | ||||||||
\(401\) | 2.42713e9 | 1.87970 | 0.939849 | − | 0.341591i | \(-0.110966\pi\) | ||||
0.939849 | + | 0.341591i | \(0.110966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.98993e8 | 0.684209 | ||||||||
\(404\) | −6.53027e8 | −0.492715 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.84055e8 | −0.284808 | ||||||||
\(407\) | 2.42619e9 | 1.78379 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.18976e8 | 0.664160 | 0.332080 | − | 0.943251i | \(-0.392250\pi\) | ||||
0.332080 | + | 0.943251i | \(0.392250\pi\) | |||||||
\(410\) | −2.95167e8 | −0.211507 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.89134e8 | −0.203685 | ||||||||
\(413\) | 2.33535e8 | 0.163127 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.09455e8 | 0.0751738 | ||||||||
\(416\) | −1.04012e9 | −0.708367 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.43077e8 | −0.564612 | ||||||||
\(419\) | 1.10024e9 | 0.730699 | 0.365349 | − | 0.930870i | \(-0.380950\pi\) | ||||
0.365349 | + | 0.930870i | \(0.380950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.14909e9 | −1.40367 | −0.701837 | − | 0.712337i | \(-0.747637\pi\) | ||||
−0.701837 | + | 0.712337i | \(0.747637\pi\) | |||||||
\(422\) | 4.92957e8 | 0.319312 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.44418e9 | 0.920113 | ||||||||
\(425\) | −2.70466e9 | −1.70904 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.19476e7 | 0.0136423 | ||||||||
\(428\) | 1.25158e9 | 0.771622 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.21107e8 | 0.255419 | ||||||||
\(431\) | 1.61850e9 | 0.973737 | 0.486869 | − | 0.873475i | \(-0.338139\pi\) | ||||
0.486869 | + | 0.873475i | \(0.338139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.16527e9 | 0.689794 | 0.344897 | − | 0.938641i | \(-0.387914\pi\) | ||||
0.344897 | + | 0.938641i | \(0.387914\pi\) | |||||||
\(434\) | 8.44721e8 | 0.496020 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.21157e9 | 0.700077 | ||||||||
\(437\) | −1.15192e9 | −0.660296 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.08096e9 | 1.17392 | 0.586958 | − | 0.809617i | \(-0.300325\pi\) | ||||
0.586958 | + | 0.809617i | \(0.300325\pi\) | |||||||
\(440\) | 4.91759e8 | 0.275212 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.66074e9 | −0.914796 | ||||||||
\(443\) | 2.23100e9 | 1.21923 | 0.609616 | − | 0.792697i | \(-0.291324\pi\) | ||||
0.609616 | + | 0.792697i | \(0.291324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.05912e8 | 0.164565 | ||||||||
\(446\) | −1.06975e9 | −0.570965 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.20725e9 | −0.634345 | ||||||||
\(449\) | −2.52631e9 | −1.31712 | −0.658559 | − | 0.752529i | \(-0.728834\pi\) | ||||
−0.658559 | + | 0.752529i | \(0.728834\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.93030e9 | 1.50416 | ||||||||
\(452\) | 1.52464e8 | 0.0776573 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.58299e7 | 0.0129547 | ||||||||
\(455\) | −2.89989e8 | −0.144325 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.87627e9 | −0.919579 | −0.459790 | − | 0.888028i | \(-0.652075\pi\) | ||||
−0.459790 | + | 0.888028i | \(0.652075\pi\) | |||||||
\(458\) | 2.09705e8 | 0.101995 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.38288e8 | 0.114143 | ||||||||
\(461\) | −1.97321e9 | −0.938036 | −0.469018 | − | 0.883189i | \(-0.655392\pi\) | ||||
−0.469018 | + | 0.883189i | \(0.655392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.60344e9 | −0.750790 | −0.375395 | − | 0.926865i | \(-0.622493\pi\) | ||||
−0.375395 | + | 0.926865i | \(0.622493\pi\) | |||||||
\(464\) | 1.66625e8 | 0.0774333 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.66875e9 | −1.22168 | ||||||||
\(467\) | −1.32390e9 | −0.601515 | −0.300757 | − | 0.953701i | \(-0.597239\pi\) | ||||
−0.300757 | + | 0.953701i | \(0.597239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.16371e8 | −0.0968486 | ||||||||
\(470\) | −6.12871e8 | −0.272287 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.76326e8 | −0.208501 | ||||||||
\(473\) | −4.18057e9 | −1.81644 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.65142e9 | −0.707018 | ||||||||
\(476\) | 1.90368e9 | 0.809038 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.87938e9 | 1.20587 | ||||||||
\(479\) | −2.44225e9 | −1.01535 | −0.507675 | − | 0.861548i | \(-0.669495\pi\) | ||||
−0.507675 | + | 0.861548i | \(0.669495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.91814e9 | 1.19563 | ||||||||
\(482\) | −2.27252e8 | −0.0924363 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.60634e8 | −0.144580 | ||||||||
\(485\) | 9.67517e8 | 0.385090 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.37309e7 | −0.00538701 | −0.00269350 | − | 0.999996i | \(-0.500857\pi\) | ||||
−0.00269350 | + | 0.999996i | \(0.500857\pi\) | |||||||
\(488\) | −4.47650e7 | −0.0174369 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.39080e8 | 0.0534045 | ||||||||
\(491\) | −6.32242e8 | −0.241045 | −0.120522 | − | 0.992711i | \(-0.538457\pi\) | ||||
−0.120522 | + | 0.992711i | \(0.538457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.51048e9 | −0.943610 | ||||||||
\(494\) | −1.01402e9 | −0.378446 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.66488e8 | −0.134857 | ||||||||
\(497\) | −5.27618e8 | −0.192784 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.43365e9 | −0.876812 | −0.438406 | − | 0.898777i | \(-0.644457\pi\) | ||||
−0.438406 | + | 0.898777i | \(0.644457\pi\) | |||||||
\(500\) | 7.03282e8 | 0.251614 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.30193e8 | 0.0459329 | ||||||||
\(503\) | 2.00281e9 | 0.701700 | 0.350850 | − | 0.936432i | \(-0.385893\pi\) | ||||
0.350850 | + | 0.936432i | \(0.385893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.10997e8 | 0.211115 | ||||||||
\(506\) | 1.93915e9 | 0.665404 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.80071e8 | −0.230161 | ||||||||
\(509\) | −5.28309e8 | −0.177573 | −0.0887863 | − | 0.996051i | \(-0.528299\pi\) | ||||
−0.0887863 | + | 0.996051i | \(0.528299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.92610e9 | 0.970099 | ||||||||
\(512\) | 8.92980e8 | 0.294034 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.43734e8 | 0.241572 | ||||||||
\(515\) | 2.70525e8 | 0.0872733 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.08433e9 | 1.93640 | ||||||||
\(518\) | 2.74197e9 | 0.866780 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.91471e8 | 0.184468 | ||||||||
\(521\) | −1.76283e9 | −0.546109 | −0.273055 | − | 0.961999i | \(-0.588034\pi\) | ||||
−0.273055 | + | 0.961999i | \(0.588034\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.39318e9 | −1.03717 | −0.518586 | − | 0.855026i | \(-0.673541\pi\) | ||||
−0.518586 | + | 0.855026i | \(0.673541\pi\) | |||||||
\(524\) | 2.97140e9 | 0.902197 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.77740e8 | 0.203055 | ||||||||
\(527\) | 5.52175e9 | 1.64339 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.55295e8 | −0.221831 | ||||||||
\(530\) | −4.79208e8 | −0.139816 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.16236e9 | 0.334695 | ||||||||
\(533\) | 3.52446e9 | 1.00820 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.17102e9 | −0.330619 | ||||||||
\(536\) | 4.41317e8 | 0.123787 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.05983e9 | 1.12401 | ||||||||
\(539\) | −1.38073e9 | −0.379793 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.83907e9 | −1.04240 | −0.521202 | − | 0.853433i | \(-0.674516\pi\) | ||||
−0.521202 | + | 0.853433i | \(0.674516\pi\) | |||||||
\(542\) | −1.60601e9 | −0.433262 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.38859e9 | −1.70141 | ||||||||
\(545\) | −1.13359e9 | −0.299964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.31235e9 | 1.12657 | 0.563285 | − | 0.826263i | \(-0.309537\pi\) | ||||
0.563285 | + | 0.826263i | \(0.309537\pi\) | |||||||
\(548\) | 5.63744e8 | 0.146336 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.78001e9 | 0.712488 | ||||||||
\(551\) | −1.53286e9 | −0.390366 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.87410e9 | −0.471255 | ||||||||
\(554\) | 2.46039e9 | 0.614779 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.02704e9 | −0.253412 | ||||||||
\(557\) | −1.84109e9 | −0.451421 | −0.225710 | − | 0.974194i | \(-0.572470\pi\) | ||||
−0.225710 | + | 0.974194i | \(0.572470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.02825e9 | −1.21752 | ||||||||
\(560\) | 1.18218e8 | 0.0284464 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.72994e8 | −0.0886391 | ||||||||
\(563\) | −1.16055e9 | −0.274085 | −0.137042 | − | 0.990565i | \(-0.543760\pi\) | ||||
−0.137042 | + | 0.990565i | \(0.543760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.42651e8 | −0.0332740 | ||||||||
\(566\) | 3.06027e9 | 0.709417 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.07615e9 | 0.246407 | ||||||||
\(569\) | 7.02920e8 | 0.159960 | 0.0799802 | − | 0.996796i | \(-0.474514\pi\) | ||||
0.0799802 | + | 0.996796i | \(0.474514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.95929e8 | −0.178915 | −0.0894577 | − | 0.995991i | \(-0.528513\pi\) | ||||
−0.0894577 | + | 0.995991i | \(0.528513\pi\) | |||||||
\(572\) | −2.08243e9 | −0.465249 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.31169e9 | 0.730900 | ||||||||
\(575\) | 3.79842e9 | 0.833232 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.44712e9 | −0.963749 | −0.481874 | − | 0.876240i | \(-0.660044\pi\) | ||||
−0.481874 | + | 0.876240i | \(0.660044\pi\) | |||||||
\(578\) | −7.08466e9 | −1.52606 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.17090e8 | 0.0674814 | ||||||||
\(581\) | −1.22805e9 | −0.259776 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.75737e9 | 0.994323 | ||||||||
\(584\) | −5.96818e9 | −1.23993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.68967e9 | −0.757436 | ||||||||
\(587\) | 5.50846e9 | 1.12408 | 0.562039 | − | 0.827111i | \(-0.310017\pi\) | ||||
0.562039 | + | 0.827111i | \(0.310017\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.37150e9 | 0.679859 | ||||||||
\(590\) | 1.58054e8 | 0.0316828 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.18962e9 | −0.235659 | ||||||||
\(593\) | −8.05850e9 | −1.58695 | −0.793475 | − | 0.608603i | \(-0.791730\pi\) | ||||
−0.793475 | + | 0.608603i | \(0.791730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.78115e9 | −0.346650 | ||||||||
\(596\) | −2.86347e9 | −0.554026 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.33235e9 | 0.446004 | ||||||||
\(599\) | −3.39566e9 | −0.645551 | −0.322775 | − | 0.946476i | \(-0.604616\pi\) | ||||
−0.322775 | + | 0.946476i | \(0.604616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.35177e9 | 0.254005 | 0.127002 | − | 0.991902i | \(-0.459464\pi\) | ||||
0.127002 | + | 0.991902i | \(0.459464\pi\) | |||||||
\(602\) | −4.72469e9 | −0.882645 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.72762e9 | 0.688339 | ||||||||
\(605\) | 3.37423e8 | 0.0619485 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.91297e9 | 0.891627 | 0.445814 | − | 0.895126i | \(-0.352914\pi\) | ||||
0.445814 | + | 0.895126i | \(0.352914\pi\) | |||||||
\(608\) | −3.90078e9 | −0.703864 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.48539e7 | 0.00264963 | ||||||||
\(611\) | 7.31802e9 | 1.29793 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.06110e9 | −0.361399 | −0.180700 | − | 0.983538i | \(-0.557836\pi\) | ||||
−0.180700 | + | 0.983538i | \(0.557836\pi\) | |||||||
\(614\) | −2.14297e9 | −0.373617 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.51739e9 | −0.951045 | ||||||||
\(617\) | −3.72277e9 | −0.638071 | −0.319035 | − | 0.947743i | \(-0.603359\pi\) | ||||
−0.319035 | + | 0.947743i | \(0.603359\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.30066e9 | 0.559349 | 0.279675 | − | 0.960095i | \(-0.409773\pi\) | ||||
0.279675 | + | 0.960095i | \(0.409773\pi\) | |||||||
\(620\) | −6.97432e8 | −0.117525 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.34909e8 | −0.0891278 | ||||||||
\(623\) | −3.43224e9 | −0.568683 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.10711e9 | 0.836749 | ||||||||
\(626\) | 3.63037e9 | 0.591481 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.88867e9 | −0.465413 | ||||||||
\(629\) | 1.79236e10 | 2.87177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.12709e9 | 0.812397 | 0.406199 | − | 0.913785i | \(-0.366854\pi\) | ||||
0.406199 | + | 0.913785i | \(0.366854\pi\) | |||||||
\(632\) | 3.82249e9 | 0.602333 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.23541e9 | −0.815903 | ||||||||
\(635\) | 6.36300e8 | 0.0986174 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.66069e9 | −0.254566 | ||||||||
\(638\) | 2.58043e9 | 0.393386 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.51310e8 | 0.0982105 | ||||||||
\(641\) | −4.51842e9 | −0.677615 | −0.338808 | − | 0.940856i | \(-0.610024\pi\) | ||||
−0.338808 | + | 0.940856i | \(0.610024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.70600e9 | −1.43980 | −0.719900 | − | 0.694078i | \(-0.755812\pi\) | ||||
−0.719900 | + | 0.694078i | \(0.755812\pi\) | |||||||
\(644\) | −2.67353e9 | −0.394443 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.22829e9 | −0.908981 | ||||||||
\(647\) | −6.12536e9 | −0.889132 | −0.444566 | − | 0.895746i | \(-0.646642\pi\) | ||||
−0.444566 | + | 0.895746i | \(0.646642\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.56910e9 | −0.225317 | ||||||||
\(650\) | 3.34370e9 | 0.477563 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.05117e9 | 0.431122 | ||||||||
\(653\) | 1.30103e10 | 1.82849 | 0.914243 | − | 0.405166i | \(-0.132786\pi\) | ||||
0.914243 | + | 0.405166i | \(0.132786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.78015e9 | −0.386566 | ||||||||
\(656\) | −1.43680e9 | −0.198716 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.87623e9 | 0.940936 | ||||||||
\(659\) | 1.23137e10 | 1.67606 | 0.838032 | − | 0.545621i | \(-0.183706\pi\) | ||||
0.838032 | + | 0.545621i | \(0.183706\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.97776e9 | 0.939746 | 0.469873 | − | 0.882734i | \(-0.344300\pi\) | ||||
0.469873 | + | 0.882734i | \(0.344300\pi\) | |||||||
\(662\) | −4.07638e9 | −0.546100 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.50477e9 | 0.332032 | ||||||||
\(665\) | −1.08755e9 | −0.143407 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.52572e9 | 0.460053 | ||||||||
\(668\) | −2.72108e9 | −0.353203 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.46438e8 | −0.0188101 | ||||||||
\(671\) | −1.47463e8 | −0.0188432 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.06462e10 | −1.34630 | −0.673152 | − | 0.739504i | \(-0.735060\pi\) | ||||
−0.673152 | + | 0.739504i | \(0.735060\pi\) | |||||||
\(674\) | 9.41665e9 | 1.18464 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.90908e9 | 0.237690 | ||||||||
\(677\) | 4.33348e9 | 0.536756 | 0.268378 | − | 0.963314i | \(-0.413512\pi\) | ||||
0.268378 | + | 0.963314i | \(0.413512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.08553e10 | −1.33075 | ||||||||
\(680\) | 3.63290e9 | 0.443070 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.67559e9 | −0.685118 | ||||||||
\(683\) | −6.16980e9 | −0.740966 | −0.370483 | − | 0.928839i | \(-0.620808\pi\) | ||||
−0.370483 | + | 0.928839i | \(0.620808\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.27461e8 | −0.0627008 | ||||||||
\(686\) | −6.17803e9 | −0.730661 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.04984e9 | 0.239972 | ||||||||
\(689\) | 5.72201e9 | 0.666471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.57273e9 | 0.873131 | 0.436565 | − | 0.899672i | \(-0.356195\pi\) | ||||
0.436565 | + | 0.899672i | \(0.356195\pi\) | |||||||
\(692\) | −3.73190e9 | −0.428113 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.69620e8 | −0.0419756 | ||||||||
\(695\) | 9.60939e8 | 0.108580 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.16477e10 | 2.42158 | ||||||||
\(698\) | −9.39039e9 | −1.04518 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.83282e9 | −0.422353 | ||||||||
\(701\) | −4.42696e9 | −0.485391 | −0.242696 | − | 0.970102i | \(-0.578032\pi\) | ||||
−0.242696 | + | 0.970102i | \(0.578032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.09439e10 | 1.18803 | ||||||||
\(704\) | 8.11141e9 | 0.876178 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.60811e8 | −0.0492841 | ||||||||
\(707\) | −6.85520e9 | −0.729545 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.13232e10 | −1.19319 | −0.596594 | − | 0.802544i | \(-0.703480\pi\) | ||||
−0.596594 | + | 0.802544i | \(0.703480\pi\) | |||||||
\(710\) | −3.57087e8 | −0.0374429 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.00052e9 | 0.726859 | ||||||||
\(713\) | −7.75474e9 | −0.801224 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.94840e9 | 0.199346 | ||||||||
\(716\) | 9.43492e9 | 0.960601 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.07052e9 | 0.410407 | ||||||||
\(719\) | −1.02156e10 | −1.02497 | −0.512487 | − | 0.858695i | \(-0.671276\pi\) | ||||
−0.512487 | + | 0.858695i | \(0.671276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.03521e9 | −0.301589 | ||||||||
\(722\) | 2.98462e9 | 0.295127 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.46736e8 | −0.0437488 | ||||||||
\(725\) | 5.05455e9 | 0.492605 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.95355e10 | −1.88562 | −0.942811 | − | 0.333329i | \(-0.891828\pi\) | ||||
−0.942811 | + | 0.333329i | \(0.891828\pi\) | |||||||
\(728\) | −6.63613e9 | −0.637463 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.98036e9 | 0.188414 | ||||||||
\(731\) | −3.08842e10 | −2.92433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.32745e10 | −1.24496 | −0.622478 | − | 0.782637i | \(-0.713874\pi\) | ||||
−0.622478 | + | 0.782637i | \(0.713874\pi\) | |||||||
\(734\) | 3.27523e9 | 0.305708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.97214e9 | 0.829514 | ||||||||
\(737\) | 1.45377e9 | 0.133770 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.69495e9 | 0.154490 | 0.0772452 | − | 0.997012i | \(-0.475388\pi\) | ||||
0.0772452 | + | 0.997012i | \(0.475388\pi\) | |||||||
\(740\) | −2.26387e9 | −0.205372 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.37657e9 | 0.483160 | ||||||||
\(743\) | −9.34493e9 | −0.835824 | −0.417912 | − | 0.908487i | \(-0.637238\pi\) | ||||
−0.417912 | + | 0.908487i | \(0.637238\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.67917e9 | 0.237385 | ||||||||
\(746\) | −2.04785e9 | −0.180598 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.27906e10 | −1.11747 | ||||||||
\(749\) | 1.31385e10 | 1.14251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.31194e10 | −1.13025 | −0.565124 | − | 0.825006i | \(-0.691172\pi\) | ||||
−0.565124 | + | 0.825006i | \(0.691172\pi\) | |||||||
\(752\) | −2.98330e9 | −0.255820 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.10365e9 | 0.263677 | ||||||||
\(755\) | −3.48770e9 | −0.294934 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.72593e9 | 0.479745 | 0.239873 | − | 0.970804i | \(-0.422894\pi\) | ||||
0.239873 | + | 0.970804i | \(0.422894\pi\) | |||||||
\(758\) | 6.10362e9 | 0.509032 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.21819e9 | 0.183296 | ||||||||
\(761\) | −1.47621e10 | −1.21423 | −0.607115 | − | 0.794614i | \(-0.707673\pi\) | ||||
−0.607115 | + | 0.794614i | \(0.707673\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.27186e10 | 1.03658 | ||||||||
\(764\) | 8.14847e9 | 0.661072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.47131e9 | −0.600615 | ||||||||
\(767\) | −1.88726e9 | −0.151024 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.63551e9 | 0.446880 | 0.223440 | − | 0.974718i | \(-0.428271\pi\) | ||||
0.223440 | + | 0.974718i | \(0.428271\pi\) | |||||||
\(770\) | 1.83078e9 | 0.144517 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.03653e9 | −0.315753 | ||||||||
\(773\) | 4.65338e9 | 0.362360 | 0.181180 | − | 0.983450i | \(-0.442008\pi\) | ||||
0.181180 | + | 0.983450i | \(0.442008\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.11174e10 | −0.857918 | ||||||||
\(776\) | 2.21408e10 | 1.70089 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.64207e9 | 0.125015 | ||||||||
\(779\) | 1.32178e10 | 1.00179 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.54501e9 | 0.266280 | ||||||||
\(782\) | 1.43256e10 | 1.07125 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.77006e8 | 0.0501749 | ||||||||
\(785\) | 2.70275e9 | 0.199417 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.23587e10 | −0.903780 | −0.451890 | − | 0.892074i | \(-0.649250\pi\) | ||||
−0.451890 | + | 0.892074i | \(0.649250\pi\) | |||||||
\(788\) | −7.37493e9 | −0.536928 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.26838e9 | −0.0915279 | ||||||||
\(791\) | 1.60050e9 | 0.114984 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.77364e8 | −0.0126302 | ||||||||
\(794\) | −3.29198e9 | −0.233392 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.48153e10 | 1.04115 | ||||||||
\(797\) | 1.70444e10 | 1.19256 | 0.596278 | − | 0.802778i | \(-0.296646\pi\) | ||||
0.596278 | + | 0.802778i | \(0.296646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.49484e10 | 3.11746 | ||||||||
\(800\) | 1.28627e10 | 0.888210 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.84301e10 | −1.26159 | ||||||||
\(803\) | −1.96602e10 | −1.33993 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.50145e9 | 0.169008 | ||||||||
\(806\) | −6.82640e9 | −0.459218 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.39821e10 | 0.932465 | ||||||||
\(809\) | 1.00497e10 | 0.667315 | 0.333658 | − | 0.942694i | \(-0.391717\pi\) | ||||
0.333658 | + | 0.942694i | \(0.391717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.26821e9 | 0.346809 | 0.173404 | − | 0.984851i | \(-0.444523\pi\) | ||||
0.173404 | + | 0.984851i | \(0.444523\pi\) | |||||||
\(812\) | −3.55765e9 | −0.233194 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.84230e10 | −1.19722 | ||||||||
\(815\) | −2.85480e9 | −0.184724 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.88575e10 | −1.20978 | ||||||||
\(818\) | −6.97814e9 | −0.445762 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.73425e9 | −0.173177 | ||||||||
\(821\) | 1.82202e10 | 1.14909 | 0.574543 | − | 0.818474i | \(-0.305180\pi\) | ||||
0.574543 | + | 0.818474i | \(0.305180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.35868e9 | −0.0849603 | −0.0424802 | − | 0.999097i | \(-0.513526\pi\) | ||||
−0.0424802 | + | 0.999097i | \(0.513526\pi\) | |||||||
\(824\) | 6.19071e9 | 0.385474 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.77332e9 | −0.109486 | ||||||||
\(827\) | 8.90171e9 | 0.547273 | 0.273637 | − | 0.961833i | \(-0.411773\pi\) | ||||
0.273637 | + | 0.961833i | \(0.411773\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.14205e9 | 0.374432 | 0.187216 | − | 0.982319i | \(-0.440054\pi\) | ||||
0.187216 | + | 0.982319i | \(0.440054\pi\) | |||||||
\(830\) | −8.31133e8 | −0.0504542 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.75613e9 | 0.587281 | ||||||||
\(833\) | −1.02002e10 | −0.611436 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.54595e9 | 0.151338 | ||||||||
\(836\) | −7.80975e9 | −0.462291 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.35455e9 | −0.490421 | ||||||||
\(839\) | 1.05464e10 | 0.616504 | 0.308252 | − | 0.951305i | \(-0.400256\pi\) | ||||
0.308252 | + | 0.951305i | \(0.400256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.25582e10 | −0.728018 | ||||||||
\(842\) | 1.63188e10 | 0.942100 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.56645e9 | 0.261445 | ||||||||
\(845\) | −1.78621e9 | −0.101844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.78578e9 | −0.214074 | ||||||||
\(848\) | −2.33266e9 | −0.131361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.05375e10 | 1.14705 | ||||||||
\(851\) | −2.51720e10 | −1.40012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.41878e9 | 0.188604 | 0.0943018 | − | 0.995544i | \(-0.469938\pi\) | ||||
0.0943018 | + | 0.995544i | \(0.469938\pi\) | |||||||
\(854\) | −1.66656e8 | −0.00915628 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.67978e10 | −1.46030 | ||||||||
\(857\) | −2.17037e10 | −1.17788 | −0.588941 | − | 0.808176i | \(-0.700455\pi\) | ||||
−0.588941 | + | 0.808176i | \(0.700455\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.19211e10 | −1.18001 | −0.590005 | − | 0.807400i | \(-0.700874\pi\) | ||||
−0.590005 | + | 0.807400i | \(0.700874\pi\) | |||||||
\(860\) | 3.90088e9 | 0.209131 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.22899e10 | −0.653540 | ||||||||
\(863\) | −1.35347e10 | −0.716822 | −0.358411 | − | 0.933564i | \(-0.616681\pi\) | ||||
−0.358411 | + | 0.933564i | \(0.616681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.49170e9 | 0.183434 | ||||||||
\(866\) | −8.84836e9 | −0.462967 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.82497e9 | 0.406129 | ||||||||
\(869\) | 1.25919e10 | 0.650912 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.74855e9 | 0.0896631 | ||||||||
\(872\) | −2.59412e10 | −1.32490 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.74701e9 | 0.443169 | ||||||||
\(875\) | 7.38276e9 | 0.372555 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.45197e10 | 1.22749 | 0.613743 | − | 0.789506i | \(-0.289663\pi\) | ||||
0.613743 | + | 0.789506i | \(0.289663\pi\) | |||||||
\(878\) | −1.58015e10 | −0.787894 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.94296e8 | −0.0392910 | ||||||||
\(881\) | −2.13536e10 | −1.05210 | −0.526048 | − | 0.850455i | \(-0.676327\pi\) | ||||
−0.526048 | + | 0.850455i | \(0.676327\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.64504e9 | −0.0804109 | −0.0402054 | − | 0.999191i | \(-0.512801\pi\) | ||||
−0.0402054 | + | 0.999191i | \(0.512801\pi\) | |||||||
\(884\) | −1.53841e10 | −0.749013 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.69408e10 | −0.818309 | ||||||||
\(887\) | 9.65301e9 | 0.464441 | 0.232220 | − | 0.972663i | \(-0.425401\pi\) | ||||
0.232220 | + | 0.972663i | \(0.425401\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.13909e9 | −0.340790 | ||||||||
\(890\) | −2.32291e9 | −0.110450 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.90949e9 | −0.467492 | ||||||||
\(893\) | 2.74448e10 | 1.28967 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.82767e9 | −0.411591 | ||||||||
\(896\) | −7.30751e9 | −0.339384 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.91833e10 | 0.884006 | ||||||||
\(899\) | −1.03192e10 | −0.473683 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.51454e10 | 1.60078 | ||||||||
\(902\) | −2.22509e10 | −1.00954 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.26444e9 | −0.146967 | ||||||||
\(905\) | 4.17983e8 | 0.0187451 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.05417e9 | −0.358423 | −0.179211 | − | 0.983811i | \(-0.557355\pi\) | ||||
−0.179211 | + | 0.983811i | \(0.557355\pi\) | |||||||
\(908\) | 2.39272e8 | 0.0106070 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.20200e9 | 0.0968661 | ||||||||
\(911\) | 5.73799e9 | 0.251446 | 0.125723 | − | 0.992065i | \(-0.459875\pi\) | ||||
0.125723 | + | 0.992065i | \(0.459875\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.25114e9 | 0.358811 | ||||||||
\(914\) | 1.42473e10 | 0.617191 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.94258e9 | 0.0835113 | ||||||||
\(917\) | 3.11925e10 | 1.33585 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.67326e10 | 1.56116 | 0.780579 | − | 0.625057i | \(-0.214924\pi\) | ||||
0.780579 | + | 0.625057i | \(0.214924\pi\) | |||||||
\(920\) | −5.10205e9 | −0.216017 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.49833e10 | 0.629579 | ||||||||
\(923\) | 4.26381e9 | 0.178481 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.60871e10 | −1.49919 | ||||||||
\(926\) | 1.21755e10 | 0.503906 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.19392e10 | 0.490408 | ||||||||
\(929\) | −3.50768e9 | −0.143537 | −0.0717687 | − | 0.997421i | \(-0.522864\pi\) | ||||
−0.0717687 | + | 0.997421i | \(0.522864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.22809e9 | −0.252948 | ||||||||
\(932\) | −2.47217e10 | −1.00028 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.00529e10 | 0.403717 | ||||||||
\(935\) | 1.19674e10 | 0.478805 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.68124e10 | −0.667638 | −0.333819 | − | 0.942637i | \(-0.608337\pi\) | ||||
−0.333819 | + | 0.942637i | \(0.608337\pi\) | |||||||
\(938\) | 1.64299e9 | 0.0650016 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.67726e9 | −0.222942 | ||||||||
\(941\) | 3.51454e10 | 1.37501 | 0.687503 | − | 0.726182i | \(-0.258707\pi\) | ||||
0.687503 | + | 0.726182i | \(0.258707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.04021e10 | −1.18063 | ||||||||
\(944\) | 7.69368e8 | 0.0297668 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.17447e10 | 1.21914 | ||||||||
\(947\) | 3.30590e10 | 1.26493 | 0.632463 | − | 0.774591i | \(-0.282044\pi\) | ||||
0.632463 | + | 0.774591i | \(0.282044\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.36466e10 | −0.898124 | ||||||||
\(950\) | 1.25399e10 | 0.474527 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.07601e10 | −1.53111 | ||||||||
\(953\) | 6.24805e9 | 0.233840 | 0.116920 | − | 0.993141i | \(-0.462698\pi\) | ||||
0.116920 | + | 0.993141i | \(0.462698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.62401e9 | −0.283251 | ||||||||
\(956\) | 2.66728e10 | 0.987338 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.85450e10 | 0.681470 | ||||||||
\(959\) | 5.91795e9 | 0.216674 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.81574e9 | −0.175037 | ||||||||
\(962\) | −2.21586e10 | −0.802471 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.10512e9 | −0.0756846 | ||||||||
\(965\) | 3.77673e9 | 0.135291 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.21264e10 | 0.786899 | 0.393449 | − | 0.919346i | \(-0.371282\pi\) | ||||
0.393449 | + | 0.919346i | \(0.371282\pi\) | |||||||
\(968\) | 7.72161e9 | 0.273618 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.34673e9 | −0.258460 | ||||||||
\(971\) | 5.45446e9 | 0.191199 | 0.0955993 | − | 0.995420i | \(-0.469523\pi\) | ||||
0.0955993 | + | 0.995420i | \(0.469523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.07815e10 | −0.375217 | ||||||||
\(974\) | 1.04264e8 | 0.00361558 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.23050e7 | 0.00248940 | ||||||||
\(977\) | −4.95373e10 | −1.69942 | −0.849711 | − | 0.527248i | \(-0.823224\pi\) | ||||
−0.849711 | + | 0.527248i | \(0.823224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.30609e10 | 0.785482 | ||||||||
\(980\) | 1.28835e9 | 0.0437263 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.80086e9 | 0.161781 | ||||||||
\(983\) | −8.72042e9 | −0.292820 | −0.146410 | − | 0.989224i | \(-0.546772\pi\) | ||||
−0.146410 | + | 0.989224i | \(0.546772\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.90027e9 | 0.230059 | ||||||||
\(986\) | 1.90631e10 | 0.633320 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.39330e9 | −0.309862 | ||||||||
\(989\) | 4.33739e10 | 1.42574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.64359e10 | 0.536458 | 0.268229 | − | 0.963355i | \(-0.413562\pi\) | ||||
0.268229 | + | 0.963355i | \(0.413562\pi\) | |||||||
\(992\) | −2.62600e10 | −0.854091 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.00641e9 | 0.129391 | ||||||||
\(995\) | −1.38618e10 | −0.446106 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.18717e10 | −1.01853 | −0.509264 | − | 0.860611i | \(-0.670082\pi\) | ||||
−0.509264 | + | 0.860611i | \(0.670082\pi\) | |||||||
\(998\) | 1.84797e10 | 0.588487 | ||||||||
\(999\) | 0 | 0 |
(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 | 27.8.a.e.1.1 | yes | 2 | |
3.2 | odd | 2 | 27.8.a.b.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 432.8.a.q.1.1 | 2 | |||
9.2 | odd | 6 | 81.8.c.h.28.1 | 4 | |||
9.4 | even | 3 | 81.8.c.d.55.2 | 4 | |||
9.5 | odd | 6 | 81.8.c.h.55.1 | 4 | |||
9.7 | even | 3 | 81.8.c.d.28.2 | 4 | |||
12.11 | even | 2 | 432.8.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.8.a.b.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
27.8.a.e.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
81.8.c.d.28.2 | 4 | 9.7 | even | 3 | |||
81.8.c.d.55.2 | 4 | 9.4 | even | 3 | |||
81.8.c.h.28.1 | 4 | 9.2 | odd | 6 | |||
81.8.c.h.55.1 | 4 | 9.5 | odd | 6 | |||
432.8.a.j.1.2 | 2 | 12.11 | even | 2 | |||
432.8.a.q.1.1 | 2 | 4.3 | odd | 2 |