Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,8,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, 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("38.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(11.8706309684\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9097x^{2} - 110520x + 10368000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-48.0684\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 51.0684 | 1.09201 | 0.546006 | − | 0.837781i | \(-0.316147\pi\) | ||||
0.546006 | + | 0.837781i | \(0.316147\pi\) | |||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 338.533 | 1.21117 | 0.605587 | − | 0.795779i | \(-0.292938\pi\) | ||||
0.605587 | + | 0.795779i | \(0.292938\pi\) | |||||||
\(6\) | 408.547 | 0.772170 | ||||||||
\(7\) | −143.677 | −0.158323 | −0.0791614 | − | 0.996862i | \(-0.525224\pi\) | ||||
−0.0791614 | + | 0.996862i | \(0.525224\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 420.979 | 0.192492 | ||||||||
\(10\) | 2708.27 | 0.856429 | ||||||||
\(11\) | −2238.40 | −0.507064 | −0.253532 | − | 0.967327i | \(-0.581592\pi\) | ||||
−0.253532 | + | 0.967327i | \(0.581592\pi\) | |||||||
\(12\) | 3268.38 | 0.546006 | ||||||||
\(13\) | 3817.19 | 0.481884 | 0.240942 | − | 0.970540i | \(-0.422544\pi\) | ||||
0.240942 | + | 0.970540i | \(0.422544\pi\) | |||||||
\(14\) | −1149.41 | −0.111951 | ||||||||
\(15\) | 17288.3 | 1.32262 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −19910.7 | −0.982915 | −0.491457 | − | 0.870902i | \(-0.663536\pi\) | ||||
−0.491457 | + | 0.870902i | \(0.663536\pi\) | |||||||
\(18\) | 3367.83 | 0.136112 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | 21666.1 | 0.605587 | ||||||||
\(21\) | −7337.34 | −0.172890 | ||||||||
\(22\) | −17907.2 | −0.358548 | ||||||||
\(23\) | 97702.1 | 1.67439 | 0.837195 | − | 0.546905i | \(-0.184194\pi\) | ||||
0.837195 | + | 0.546905i | \(0.184194\pi\) | |||||||
\(24\) | 26147.0 | 0.386085 | ||||||||
\(25\) | 36479.8 | 0.466942 | ||||||||
\(26\) | 30537.6 | 0.340744 | ||||||||
\(27\) | −90187.8 | −0.881809 | ||||||||
\(28\) | −9195.31 | −0.0791614 | ||||||||
\(29\) | 35917.5 | 0.273472 | 0.136736 | − | 0.990608i | \(-0.456339\pi\) | ||||
0.136736 | + | 0.990608i | \(0.456339\pi\) | |||||||
\(30\) | 138307. | 0.935232 | ||||||||
\(31\) | −135693. | −0.818073 | −0.409037 | − | 0.912518i | \(-0.634135\pi\) | ||||
−0.409037 | + | 0.912518i | \(0.634135\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −114311. | −0.553720 | ||||||||
\(34\) | −159286. | −0.695026 | ||||||||
\(35\) | −48639.4 | −0.191756 | ||||||||
\(36\) | 26942.7 | 0.0962458 | ||||||||
\(37\) | −112724. | −0.365857 | −0.182929 | − | 0.983126i | \(-0.558558\pi\) | ||||
−0.182929 | + | 0.983126i | \(0.558558\pi\) | |||||||
\(38\) | 54872.0 | 0.162221 | ||||||||
\(39\) | 194938. | 0.526224 | ||||||||
\(40\) | 173329. | 0.428215 | ||||||||
\(41\) | −334966. | −0.759027 | −0.379513 | − | 0.925186i | \(-0.623909\pi\) | ||||
−0.379513 | + | 0.925186i | \(0.623909\pi\) | |||||||
\(42\) | −58698.7 | −0.122252 | ||||||||
\(43\) | −789155. | −1.51364 | −0.756820 | − | 0.653623i | \(-0.773248\pi\) | ||||
−0.756820 | + | 0.653623i | \(0.773248\pi\) | |||||||
\(44\) | −143257. | −0.253532 | ||||||||
\(45\) | 142516. | 0.233141 | ||||||||
\(46\) | 781617. | 1.18397 | ||||||||
\(47\) | −345282. | −0.485100 | −0.242550 | − | 0.970139i | \(-0.577984\pi\) | ||||
−0.242550 | + | 0.970139i | \(0.577984\pi\) | |||||||
\(48\) | 209176. | 0.273003 | ||||||||
\(49\) | −802900. | −0.974934 | ||||||||
\(50\) | 291839. | 0.330178 | ||||||||
\(51\) | −1.01681e6 | −1.07336 | ||||||||
\(52\) | 244300. | 0.240942 | ||||||||
\(53\) | −282722. | −0.260852 | −0.130426 | − | 0.991458i | \(-0.541634\pi\) | ||||
−0.130426 | + | 0.991458i | \(0.541634\pi\) | |||||||
\(54\) | −721503. | −0.623533 | ||||||||
\(55\) | −757772. | −0.614142 | ||||||||
\(56\) | −73562.5 | −0.0559755 | ||||||||
\(57\) | 350278. | 0.250525 | ||||||||
\(58\) | 287340. | 0.193374 | ||||||||
\(59\) | 1.08671e6 | 0.688860 | 0.344430 | − | 0.938812i | \(-0.388072\pi\) | ||||
0.344430 | + | 0.938812i | \(0.388072\pi\) | |||||||
\(60\) | 1.10645e6 | 0.661309 | ||||||||
\(61\) | 1.60239e6 | 0.903886 | 0.451943 | − | 0.892047i | \(-0.350731\pi\) | ||||
0.451943 | + | 0.892047i | \(0.350731\pi\) | |||||||
\(62\) | −1.08555e6 | −0.578465 | ||||||||
\(63\) | −60484.9 | −0.0304758 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.29225e6 | 0.583645 | ||||||||
\(66\) | −914490. | −0.391539 | ||||||||
\(67\) | 825216. | 0.335202 | 0.167601 | − | 0.985855i | \(-0.446398\pi\) | ||||
0.167601 | + | 0.985855i | \(0.446398\pi\) | |||||||
\(68\) | −1.27429e6 | −0.491457 | ||||||||
\(69\) | 4.98949e6 | 1.82845 | ||||||||
\(70\) | −389115. | −0.135592 | ||||||||
\(71\) | 1.45443e6 | 0.482269 | 0.241134 | − | 0.970492i | \(-0.422481\pi\) | ||||
0.241134 | + | 0.970492i | \(0.422481\pi\) | |||||||
\(72\) | 215541. | 0.0680561 | ||||||||
\(73\) | 6.35893e6 | 1.91317 | 0.956587 | − | 0.291449i | \(-0.0941372\pi\) | ||||
0.956587 | + | 0.291449i | \(0.0941372\pi\) | |||||||
\(74\) | −901795. | −0.258700 | ||||||||
\(75\) | 1.86297e6 | 0.509906 | ||||||||
\(76\) | 438976. | 0.114708 | ||||||||
\(77\) | 321605. | 0.0802797 | ||||||||
\(78\) | 1.55950e6 | 0.372096 | ||||||||
\(79\) | −3.41609e6 | −0.779533 | −0.389766 | − | 0.920914i | \(-0.627444\pi\) | ||||
−0.389766 | + | 0.920914i | \(0.627444\pi\) | |||||||
\(80\) | 1.38663e6 | 0.302793 | ||||||||
\(81\) | −5.52643e6 | −1.15544 | ||||||||
\(82\) | −2.67973e6 | −0.536713 | ||||||||
\(83\) | 2.76971e6 | 0.531694 | 0.265847 | − | 0.964015i | \(-0.414348\pi\) | ||||
0.265847 | + | 0.964015i | \(0.414348\pi\) | |||||||
\(84\) | −469590. | −0.0864452 | ||||||||
\(85\) | −6.74044e6 | −1.19048 | ||||||||
\(86\) | −6.31324e6 | −1.07031 | ||||||||
\(87\) | 1.83425e6 | 0.298635 | ||||||||
\(88\) | −1.14606e6 | −0.179274 | ||||||||
\(89\) | −1.95057e6 | −0.293290 | −0.146645 | − | 0.989189i | \(-0.546848\pi\) | ||||
−0.146645 | + | 0.989189i | \(0.546848\pi\) | |||||||
\(90\) | 1.14012e6 | 0.164855 | ||||||||
\(91\) | −548442. | −0.0762932 | ||||||||
\(92\) | 6.25293e6 | 0.837195 | ||||||||
\(93\) | −6.92963e6 | −0.893346 | ||||||||
\(94\) | −2.76225e6 | −0.343017 | ||||||||
\(95\) | 2.32200e6 | 0.277862 | ||||||||
\(96\) | 1.67341e6 | 0.193042 | ||||||||
\(97\) | −1.49299e7 | −1.66095 | −0.830473 | − | 0.557059i | \(-0.811930\pi\) | ||||
−0.830473 | + | 0.557059i | \(0.811930\pi\) | |||||||
\(98\) | −6.42320e6 | −0.689382 | ||||||||
\(99\) | −942318. | −0.0976055 | ||||||||
\(100\) | 2.33471e6 | 0.233471 | ||||||||
\(101\) | −3.70396e6 | −0.357719 | −0.178859 | − | 0.983875i | \(-0.557241\pi\) | ||||
−0.178859 | + | 0.983875i | \(0.557241\pi\) | |||||||
\(102\) | −8.13447e6 | −0.758977 | ||||||||
\(103\) | 1.30203e7 | 1.17406 | 0.587030 | − | 0.809565i | \(-0.300297\pi\) | ||||
0.587030 | + | 0.809565i | \(0.300297\pi\) | |||||||
\(104\) | 1.95440e6 | 0.170372 | ||||||||
\(105\) | −2.48393e6 | −0.209400 | ||||||||
\(106\) | −2.26177e6 | −0.184450 | ||||||||
\(107\) | 1.20392e7 | 0.950065 | 0.475032 | − | 0.879968i | \(-0.342436\pi\) | ||||
0.475032 | + | 0.879968i | \(0.342436\pi\) | |||||||
\(108\) | −5.77202e6 | −0.440905 | ||||||||
\(109\) | 1.00573e7 | 0.743852 | 0.371926 | − | 0.928262i | \(-0.378697\pi\) | ||||
0.371926 | + | 0.928262i | \(0.378697\pi\) | |||||||
\(110\) | −6.06217e6 | −0.434264 | ||||||||
\(111\) | −5.75665e6 | −0.399521 | ||||||||
\(112\) | −588500. | −0.0395807 | ||||||||
\(113\) | 695305. | 0.0453316 | 0.0226658 | − | 0.999743i | \(-0.492785\pi\) | ||||
0.0226658 | + | 0.999743i | \(0.492785\pi\) | |||||||
\(114\) | 2.80222e6 | 0.177148 | ||||||||
\(115\) | 3.30754e7 | 2.02798 | ||||||||
\(116\) | 2.29872e6 | 0.136736 | ||||||||
\(117\) | 1.60696e6 | 0.0927587 | ||||||||
\(118\) | 8.69367e6 | 0.487098 | ||||||||
\(119\) | 2.86071e6 | 0.155618 | ||||||||
\(120\) | 8.85163e6 | 0.467616 | ||||||||
\(121\) | −1.44768e7 | −0.742886 | ||||||||
\(122\) | 1.28191e7 | 0.639144 | ||||||||
\(123\) | −1.71062e7 | −0.828867 | ||||||||
\(124\) | −8.68436e6 | −0.409037 | ||||||||
\(125\) | −1.40983e7 | −0.645626 | ||||||||
\(126\) | −483879. | −0.0215497 | ||||||||
\(127\) | −2.58936e6 | −0.112170 | −0.0560852 | − | 0.998426i | \(-0.517862\pi\) | ||||
−0.0560852 | + | 0.998426i | \(0.517862\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −4.03009e7 | −1.65291 | ||||||||
\(130\) | 1.03380e7 | 0.412700 | ||||||||
\(131\) | 4.28721e7 | 1.66619 | 0.833097 | − | 0.553127i | \(-0.186566\pi\) | ||||
0.833097 | + | 0.553127i | \(0.186566\pi\) | |||||||
\(132\) | −7.31592e6 | −0.276860 | ||||||||
\(133\) | −985479. | −0.0363217 | ||||||||
\(134\) | 6.60173e6 | 0.237023 | ||||||||
\(135\) | −3.05316e7 | −1.06802 | ||||||||
\(136\) | −1.01943e7 | −0.347513 | ||||||||
\(137\) | −4.30326e7 | −1.42980 | −0.714900 | − | 0.699227i | \(-0.753528\pi\) | ||||
−0.714900 | + | 0.699227i | \(0.753528\pi\) | |||||||
\(138\) | 3.99159e7 | 1.29291 | ||||||||
\(139\) | 5.90693e7 | 1.86556 | 0.932781 | − | 0.360443i | \(-0.117375\pi\) | ||||
0.932781 | + | 0.360443i | \(0.117375\pi\) | |||||||
\(140\) | −3.11292e6 | −0.0958782 | ||||||||
\(141\) | −1.76330e7 | −0.529735 | ||||||||
\(142\) | 1.16355e7 | 0.341016 | ||||||||
\(143\) | −8.54439e6 | −0.244346 | ||||||||
\(144\) | 1.72433e6 | 0.0481229 | ||||||||
\(145\) | 1.21593e7 | 0.331222 | ||||||||
\(146\) | 5.08715e7 | 1.35282 | ||||||||
\(147\) | −4.10028e7 | −1.06464 | ||||||||
\(148\) | −7.21436e6 | −0.182929 | ||||||||
\(149\) | 6.40098e7 | 1.58524 | 0.792619 | − | 0.609717i | \(-0.208717\pi\) | ||||
0.792619 | + | 0.609717i | \(0.208717\pi\) | |||||||
\(150\) | 1.49037e7 | 0.360558 | ||||||||
\(151\) | 7.98100e7 | 1.88642 | 0.943210 | − | 0.332198i | \(-0.107790\pi\) | ||||
0.943210 | + | 0.332198i | \(0.107790\pi\) | |||||||
\(152\) | 3.51181e6 | 0.0811107 | ||||||||
\(153\) | −8.38200e6 | −0.189203 | ||||||||
\(154\) | 2.57284e6 | 0.0567663 | ||||||||
\(155\) | −4.59367e7 | −0.990829 | ||||||||
\(156\) | 1.24760e7 | 0.263112 | ||||||||
\(157\) | 5.08701e7 | 1.04909 | 0.524547 | − | 0.851382i | \(-0.324235\pi\) | ||||
0.524547 | + | 0.851382i | \(0.324235\pi\) | |||||||
\(158\) | −2.73287e7 | −0.551213 | ||||||||
\(159\) | −1.44381e7 | −0.284853 | ||||||||
\(160\) | 1.10931e7 | 0.214107 | ||||||||
\(161\) | −1.40375e7 | −0.265094 | ||||||||
\(162\) | −4.42114e7 | −0.817018 | ||||||||
\(163\) | 1.46234e7 | 0.264479 | 0.132240 | − | 0.991218i | \(-0.457783\pi\) | ||||
0.132240 | + | 0.991218i | \(0.457783\pi\) | |||||||
\(164\) | −2.14378e7 | −0.379513 | ||||||||
\(165\) | −3.86982e7 | −0.670651 | ||||||||
\(166\) | 2.21577e7 | 0.375964 | ||||||||
\(167\) | −9.36180e7 | −1.55543 | −0.777717 | − | 0.628615i | \(-0.783622\pi\) | ||||
−0.777717 | + | 0.628615i | \(0.783622\pi\) | |||||||
\(168\) | −3.75672e6 | −0.0611260 | ||||||||
\(169\) | −4.81775e7 | −0.767788 | ||||||||
\(170\) | −5.39236e7 | −0.841797 | ||||||||
\(171\) | 2.88750e6 | 0.0441606 | ||||||||
\(172\) | −5.05059e7 | −0.756820 | ||||||||
\(173\) | −1.10488e8 | −1.62239 | −0.811194 | − | 0.584778i | \(-0.801182\pi\) | ||||
−0.811194 | + | 0.584778i | \(0.801182\pi\) | |||||||
\(174\) | 1.46740e7 | 0.211167 | ||||||||
\(175\) | −5.24130e6 | −0.0739275 | ||||||||
\(176\) | −9.16847e6 | −0.126766 | ||||||||
\(177\) | 5.54965e7 | 0.752244 | ||||||||
\(178\) | −1.56046e7 | −0.207387 | ||||||||
\(179\) | −2.53596e7 | −0.330489 | −0.165245 | − | 0.986253i | \(-0.552841\pi\) | ||||
−0.165245 | + | 0.986253i | \(0.552841\pi\) | |||||||
\(180\) | 9.12099e6 | 0.116570 | ||||||||
\(181\) | 6.18364e7 | 0.775121 | 0.387560 | − | 0.921844i | \(-0.373318\pi\) | ||||
0.387560 | + | 0.921844i | \(0.373318\pi\) | |||||||
\(182\) | −4.38754e6 | −0.0539474 | ||||||||
\(183\) | 8.18314e7 | 0.987055 | ||||||||
\(184\) | 5.00235e7 | 0.591986 | ||||||||
\(185\) | −3.81609e7 | −0.443117 | ||||||||
\(186\) | −5.54371e7 | −0.631691 | ||||||||
\(187\) | 4.45681e7 | 0.498400 | ||||||||
\(188\) | −2.20980e7 | −0.242550 | ||||||||
\(189\) | 1.29579e7 | 0.139610 | ||||||||
\(190\) | 1.85760e7 | 0.196478 | ||||||||
\(191\) | −5.55055e7 | −0.576394 | −0.288197 | − | 0.957571i | \(-0.593056\pi\) | ||||
−0.288197 | + | 0.957571i | \(0.593056\pi\) | |||||||
\(192\) | 1.33873e7 | 0.136502 | ||||||||
\(193\) | 8.64074e7 | 0.865168 | 0.432584 | − | 0.901594i | \(-0.357602\pi\) | ||||
0.432584 | + | 0.901594i | \(0.357602\pi\) | |||||||
\(194\) | −1.19439e8 | −1.17447 | ||||||||
\(195\) | 6.59930e7 | 0.637348 | ||||||||
\(196\) | −5.13856e7 | −0.487467 | ||||||||
\(197\) | −5.25048e7 | −0.489291 | −0.244646 | − | 0.969613i | \(-0.578672\pi\) | ||||
−0.244646 | + | 0.969613i | \(0.578672\pi\) | |||||||
\(198\) | −7.53855e6 | −0.0690175 | ||||||||
\(199\) | 1.16838e8 | 1.05099 | 0.525494 | − | 0.850798i | \(-0.323881\pi\) | ||||
0.525494 | + | 0.850798i | \(0.323881\pi\) | |||||||
\(200\) | 1.86777e7 | 0.165089 | ||||||||
\(201\) | 4.21425e7 | 0.366044 | ||||||||
\(202\) | −2.96317e7 | −0.252945 | ||||||||
\(203\) | −5.16051e6 | −0.0432969 | ||||||||
\(204\) | −6.50757e7 | −0.536678 | ||||||||
\(205\) | −1.13397e8 | −0.919314 | ||||||||
\(206\) | 1.04162e8 | 0.830186 | ||||||||
\(207\) | 4.11306e7 | 0.322306 | ||||||||
\(208\) | 1.56352e7 | 0.120471 | ||||||||
\(209\) | −1.53532e7 | −0.116328 | ||||||||
\(210\) | −1.98715e7 | −0.148068 | ||||||||
\(211\) | 1.46668e8 | 1.07484 | 0.537422 | − | 0.843313i | \(-0.319398\pi\) | ||||
0.537422 | + | 0.843313i | \(0.319398\pi\) | |||||||
\(212\) | −1.80942e7 | −0.130426 | ||||||||
\(213\) | 7.42755e7 | 0.526644 | ||||||||
\(214\) | 9.63133e7 | 0.671797 | ||||||||
\(215\) | −2.67155e8 | −1.83328 | ||||||||
\(216\) | −4.61762e7 | −0.311767 | ||||||||
\(217\) | 1.94960e7 | 0.129520 | ||||||||
\(218\) | 8.04580e7 | 0.525983 | ||||||||
\(219\) | 3.24740e8 | 2.08921 | ||||||||
\(220\) | −4.84974e7 | −0.307071 | ||||||||
\(221\) | −7.60031e7 | −0.473651 | ||||||||
\(222\) | −4.60532e7 | −0.282504 | ||||||||
\(223\) | −4.95094e7 | −0.298965 | −0.149482 | − | 0.988764i | \(-0.547761\pi\) | ||||
−0.149482 | + | 0.988764i | \(0.547761\pi\) | |||||||
\(224\) | −4.70800e6 | −0.0279878 | ||||||||
\(225\) | 1.53573e7 | 0.0898824 | ||||||||
\(226\) | 5.56244e6 | 0.0320543 | ||||||||
\(227\) | 2.68314e8 | 1.52249 | 0.761243 | − | 0.648466i | \(-0.224589\pi\) | ||||
0.761243 | + | 0.648466i | \(0.224589\pi\) | |||||||
\(228\) | 2.24178e7 | 0.125262 | ||||||||
\(229\) | 2.31832e8 | 1.27570 | 0.637850 | − | 0.770161i | \(-0.279824\pi\) | ||||
0.637850 | + | 0.770161i | \(0.279824\pi\) | |||||||
\(230\) | 2.64603e8 | 1.43400 | ||||||||
\(231\) | 1.64239e7 | 0.0876665 | ||||||||
\(232\) | 1.83898e7 | 0.0966870 | ||||||||
\(233\) | 1.79360e7 | 0.0928922 | 0.0464461 | − | 0.998921i | \(-0.485210\pi\) | ||||
0.0464461 | + | 0.998921i | \(0.485210\pi\) | |||||||
\(234\) | 1.28557e7 | 0.0655903 | ||||||||
\(235\) | −1.16889e8 | −0.587540 | ||||||||
\(236\) | 6.95494e7 | 0.344430 | ||||||||
\(237\) | −1.74454e8 | −0.851259 | ||||||||
\(238\) | 2.28857e7 | 0.110038 | ||||||||
\(239\) | 1.04930e8 | 0.497170 | 0.248585 | − | 0.968610i | \(-0.420034\pi\) | ||||
0.248585 | + | 0.968610i | \(0.420034\pi\) | |||||||
\(240\) | 7.08131e7 | 0.330654 | ||||||||
\(241\) | −2.84374e8 | −1.30867 | −0.654334 | − | 0.756205i | \(-0.727051\pi\) | ||||
−0.654334 | + | 0.756205i | \(0.727051\pi\) | |||||||
\(242\) | −1.15814e8 | −0.525300 | ||||||||
\(243\) | −8.49849e7 | −0.379944 | ||||||||
\(244\) | 1.02553e8 | 0.451943 | ||||||||
\(245\) | −2.71808e8 | −1.18081 | ||||||||
\(246\) | −1.36849e8 | −0.586098 | ||||||||
\(247\) | 2.61821e7 | 0.110552 | ||||||||
\(248\) | −6.94749e7 | −0.289233 | ||||||||
\(249\) | 1.41445e8 | 0.580616 | ||||||||
\(250\) | −1.12786e8 | −0.456527 | ||||||||
\(251\) | 1.29621e8 | 0.517390 | 0.258695 | − | 0.965959i | \(-0.416708\pi\) | ||||
0.258695 | + | 0.965959i | \(0.416708\pi\) | |||||||
\(252\) | −3.87104e6 | −0.0152379 | ||||||||
\(253\) | −2.18696e8 | −0.849022 | ||||||||
\(254\) | −2.07148e7 | −0.0793165 | ||||||||
\(255\) | −3.44224e8 | −1.30002 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 4.68302e8 | 1.72092 | 0.860458 | − | 0.509521i | \(-0.170177\pi\) | ||||
0.860458 | + | 0.509521i | \(0.170177\pi\) | |||||||
\(258\) | −3.22407e8 | −1.16879 | ||||||||
\(259\) | 1.61959e7 | 0.0579235 | ||||||||
\(260\) | 8.27039e7 | 0.291823 | ||||||||
\(261\) | 1.51205e7 | 0.0526411 | ||||||||
\(262\) | 3.42977e8 | 1.17818 | ||||||||
\(263\) | −4.36231e8 | −1.47867 | −0.739334 | − | 0.673338i | \(-0.764860\pi\) | ||||
−0.739334 | + | 0.673338i | \(0.764860\pi\) | |||||||
\(264\) | −5.85274e7 | −0.195770 | ||||||||
\(265\) | −9.57107e7 | −0.315937 | ||||||||
\(266\) | −7.88383e6 | −0.0256833 | ||||||||
\(267\) | −9.96126e7 | −0.320276 | ||||||||
\(268\) | 5.28139e7 | 0.167601 | ||||||||
\(269\) | −1.57156e8 | −0.492263 | −0.246132 | − | 0.969236i | \(-0.579160\pi\) | ||||
−0.246132 | + | 0.969236i | \(0.579160\pi\) | |||||||
\(270\) | −2.44253e8 | −0.755207 | ||||||||
\(271\) | 3.04557e8 | 0.929558 | 0.464779 | − | 0.885427i | \(-0.346134\pi\) | ||||
0.464779 | + | 0.885427i | \(0.346134\pi\) | |||||||
\(272\) | −8.15543e7 | −0.245729 | ||||||||
\(273\) | −2.80080e7 | −0.0833132 | ||||||||
\(274\) | −3.44261e8 | −1.01102 | ||||||||
\(275\) | −8.16563e7 | −0.236769 | ||||||||
\(276\) | 3.19327e8 | 0.914227 | ||||||||
\(277\) | −2.88662e8 | −0.816038 | −0.408019 | − | 0.912973i | \(-0.633780\pi\) | ||||
−0.408019 | + | 0.912973i | \(0.633780\pi\) | |||||||
\(278\) | 4.72554e8 | 1.31915 | ||||||||
\(279\) | −5.71240e7 | −0.157472 | ||||||||
\(280\) | −2.49034e7 | −0.0677961 | ||||||||
\(281\) | −4.74373e7 | −0.127540 | −0.0637702 | − | 0.997965i | \(-0.520312\pi\) | ||||
−0.0637702 | + | 0.997965i | \(0.520312\pi\) | |||||||
\(282\) | −1.41064e8 | −0.374579 | ||||||||
\(283\) | −5.34448e8 | −1.40169 | −0.700847 | − | 0.713311i | \(-0.747195\pi\) | ||||
−0.700847 | + | 0.713311i | \(0.747195\pi\) | |||||||
\(284\) | 9.30836e7 | 0.241134 | ||||||||
\(285\) | 1.18581e8 | 0.303429 | ||||||||
\(286\) | −6.83551e7 | −0.172779 | ||||||||
\(287\) | 4.81268e7 | 0.120171 | ||||||||
\(288\) | 1.37946e7 | 0.0340280 | ||||||||
\(289\) | −1.39017e7 | −0.0338786 | ||||||||
\(290\) | 9.72742e7 | 0.234209 | ||||||||
\(291\) | −7.62445e8 | −1.81377 | ||||||||
\(292\) | 4.06972e8 | 0.956587 | ||||||||
\(293\) | −5.89495e8 | −1.36913 | −0.684564 | − | 0.728953i | \(-0.740007\pi\) | ||||
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(294\) | −3.28022e8 | −0.752814 | ||||||||
\(295\) | 3.67887e8 | 0.834330 | ||||||||
\(296\) | −5.77149e7 | −0.129350 | ||||||||
\(297\) | 2.01876e8 | 0.447133 | ||||||||
\(298\) | 5.12078e8 | 1.12093 | ||||||||
\(299\) | 3.72948e8 | 0.806862 | ||||||||
\(300\) | 1.19230e8 | 0.254953 | ||||||||
\(301\) | 1.13383e8 | 0.239644 | ||||||||
\(302\) | 6.38480e8 | 1.33390 | ||||||||
\(303\) | −1.89155e8 | −0.390633 | ||||||||
\(304\) | 2.80945e7 | 0.0573539 | ||||||||
\(305\) | 5.42462e8 | 1.09476 | ||||||||
\(306\) | −6.70560e7 | −0.133787 | ||||||||
\(307\) | 8.87031e8 | 1.74966 | 0.874832 | − | 0.484427i | \(-0.160972\pi\) | ||||
0.874832 | + | 0.484427i | \(0.160972\pi\) | |||||||
\(308\) | 2.05827e7 | 0.0401399 | ||||||||
\(309\) | 6.64925e8 | 1.28209 | ||||||||
\(310\) | −3.67493e8 | −0.700622 | ||||||||
\(311\) | −1.05587e9 | −1.99044 | −0.995222 | − | 0.0976359i | \(-0.968872\pi\) | ||||
−0.995222 | + | 0.0976359i | \(0.968872\pi\) | |||||||
\(312\) | 9.98082e7 | 0.186048 | ||||||||
\(313\) | 5.41700e8 | 0.998513 | 0.499257 | − | 0.866454i | \(-0.333606\pi\) | ||||
0.499257 | + | 0.866454i | \(0.333606\pi\) | |||||||
\(314\) | 4.06961e8 | 0.741821 | ||||||||
\(315\) | −2.04762e7 | −0.0369115 | ||||||||
\(316\) | −2.18630e8 | −0.389766 | ||||||||
\(317\) | 2.77536e8 | 0.489341 | 0.244670 | − | 0.969606i | \(-0.421320\pi\) | ||||
0.244670 | + | 0.969606i | \(0.421320\pi\) | |||||||
\(318\) | −1.15505e8 | −0.201422 | ||||||||
\(319\) | −8.03976e7 | −0.138668 | ||||||||
\(320\) | 8.87445e7 | 0.151397 | ||||||||
\(321\) | 6.14821e8 | 1.03748 | ||||||||
\(322\) | −1.12300e8 | −0.187450 | ||||||||
\(323\) | −1.36568e8 | −0.225496 | ||||||||
\(324\) | −3.53691e8 | −0.577719 | ||||||||
\(325\) | 1.39251e8 | 0.225012 | ||||||||
\(326\) | 1.16987e8 | 0.187015 | ||||||||
\(327\) | 5.13608e8 | 0.812296 | ||||||||
\(328\) | −1.71503e8 | −0.268357 | ||||||||
\(329\) | 4.96090e7 | 0.0768023 | ||||||||
\(330\) | −3.09585e8 | −0.474222 | ||||||||
\(331\) | −6.09280e8 | −0.923461 | −0.461731 | − | 0.887020i | \(-0.652771\pi\) | ||||
−0.461731 | + | 0.887020i | \(0.652771\pi\) | |||||||
\(332\) | 1.77262e8 | 0.265847 | ||||||||
\(333\) | −4.74546e7 | −0.0704245 | ||||||||
\(334\) | −7.48944e8 | −1.09986 | ||||||||
\(335\) | 2.79363e8 | 0.405987 | ||||||||
\(336\) | −3.00537e7 | −0.0432226 | ||||||||
\(337\) | −5.98158e7 | −0.0851356 | −0.0425678 | − | 0.999094i | \(-0.513554\pi\) | ||||
−0.0425678 | + | 0.999094i | \(0.513554\pi\) | |||||||
\(338\) | −3.85420e8 | −0.542908 | ||||||||
\(339\) | 3.55081e7 | 0.0495027 | ||||||||
\(340\) | −4.31388e8 | −0.595240 | ||||||||
\(341\) | 3.03735e8 | 0.414815 | ||||||||
\(342\) | 2.31000e7 | 0.0312263 | ||||||||
\(343\) | 2.33682e8 | 0.312677 | ||||||||
\(344\) | −4.04047e8 | −0.535153 | ||||||||
\(345\) | 1.68911e9 | 2.21458 | ||||||||
\(346\) | −8.83906e8 | −1.14720 | ||||||||
\(347\) | 4.10517e8 | 0.527445 | 0.263723 | − | 0.964599i | \(-0.415050\pi\) | ||||
0.263723 | + | 0.964599i | \(0.415050\pi\) | |||||||
\(348\) | 1.17392e8 | 0.149317 | ||||||||
\(349\) | −1.24340e9 | −1.56575 | −0.782877 | − | 0.622177i | \(-0.786249\pi\) | ||||
−0.782877 | + | 0.622177i | \(0.786249\pi\) | |||||||
\(350\) | −4.19304e7 | −0.0522746 | ||||||||
\(351\) | −3.44264e8 | −0.424930 | ||||||||
\(352\) | −7.33477e7 | −0.0896370 | ||||||||
\(353\) | −1.15769e9 | −1.40081 | −0.700407 | − | 0.713743i | \(-0.746998\pi\) | ||||
−0.700407 | + | 0.713743i | \(0.746998\pi\) | |||||||
\(354\) | 4.43972e8 | 0.531917 | ||||||||
\(355\) | 4.92374e8 | 0.584111 | ||||||||
\(356\) | −1.24837e8 | −0.146645 | ||||||||
\(357\) | 1.46092e8 | 0.169937 | ||||||||
\(358\) | −2.02877e8 | −0.233691 | ||||||||
\(359\) | −1.88893e8 | −0.215470 | −0.107735 | − | 0.994180i | \(-0.534360\pi\) | ||||
−0.107735 | + | 0.994180i | \(0.534360\pi\) | |||||||
\(360\) | 7.29680e7 | 0.0824277 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | 4.94691e8 | 0.548093 | ||||||||
\(363\) | −7.39304e8 | −0.811241 | ||||||||
\(364\) | −3.51003e7 | −0.0381466 | ||||||||
\(365\) | 2.15271e9 | 2.31718 | ||||||||
\(366\) | 6.54651e8 | 0.697953 | ||||||||
\(367\) | −2.05858e8 | −0.217389 | −0.108694 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108694 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(368\) | 4.00188e8 | 0.418597 | ||||||||
\(369\) | −1.41014e8 | −0.146106 | ||||||||
\(370\) | −3.05288e8 | −0.313331 | ||||||||
\(371\) | 4.06205e7 | 0.0412988 | ||||||||
\(372\) | −4.43496e8 | −0.446673 | ||||||||
\(373\) | −3.70971e8 | −0.370134 | −0.185067 | − | 0.982726i | \(-0.559250\pi\) | ||||
−0.185067 | + | 0.982726i | \(0.559250\pi\) | |||||||
\(374\) | 3.56545e8 | 0.352422 | ||||||||
\(375\) | −7.19976e8 | −0.705032 | ||||||||
\(376\) | −1.76784e8 | −0.171509 | ||||||||
\(377\) | 1.37104e8 | 0.131782 | ||||||||
\(378\) | 1.03663e8 | 0.0987195 | ||||||||
\(379\) | −1.75116e8 | −0.165230 | −0.0826150 | − | 0.996582i | \(-0.526327\pi\) | ||||
−0.0826150 | + | 0.996582i | \(0.526327\pi\) | |||||||
\(380\) | 1.48608e8 | 0.138931 | ||||||||
\(381\) | −1.32234e8 | −0.122492 | ||||||||
\(382\) | −4.44044e8 | −0.407572 | ||||||||
\(383\) | 6.36056e8 | 0.578495 | 0.289248 | − | 0.957254i | \(-0.406595\pi\) | ||||
0.289248 | + | 0.957254i | \(0.406595\pi\) | |||||||
\(384\) | 1.07098e8 | 0.0965212 | ||||||||
\(385\) | 1.08874e8 | 0.0972327 | ||||||||
\(386\) | 6.91259e8 | 0.611766 | ||||||||
\(387\) | −3.32218e8 | −0.291363 | ||||||||
\(388\) | −9.55512e8 | −0.830473 | ||||||||
\(389\) | −5.13237e8 | −0.442074 | −0.221037 | − | 0.975265i | \(-0.570944\pi\) | ||||
−0.221037 | + | 0.975265i | \(0.570944\pi\) | |||||||
\(390\) | 5.27944e8 | 0.450673 | ||||||||
\(391\) | −1.94532e9 | −1.64578 | ||||||||
\(392\) | −4.11085e8 | −0.344691 | ||||||||
\(393\) | 2.18941e9 | 1.81950 | ||||||||
\(394\) | −4.20039e8 | −0.345981 | ||||||||
\(395\) | −1.15646e9 | −0.944149 | ||||||||
\(396\) | −6.03084e7 | −0.0488028 | ||||||||
\(397\) | 9.24179e8 | 0.741292 | 0.370646 | − | 0.928774i | \(-0.379136\pi\) | ||||
0.370646 | + | 0.928774i | \(0.379136\pi\) | |||||||
\(398\) | 9.34702e8 | 0.743160 | ||||||||
\(399\) | −5.03268e7 | −0.0396638 | ||||||||
\(400\) | 1.49421e8 | 0.116735 | ||||||||
\(401\) | −2.48504e9 | −1.92454 | −0.962272 | − | 0.272091i | \(-0.912285\pi\) | ||||
−0.962272 | + | 0.272091i | \(0.912285\pi\) | |||||||
\(402\) | 3.37140e8 | 0.258832 | ||||||||
\(403\) | −5.17967e8 | −0.394216 | ||||||||
\(404\) | −2.37053e8 | −0.178859 | ||||||||
\(405\) | −1.87088e9 | −1.39944 | ||||||||
\(406\) | −4.12841e7 | −0.0306155 | ||||||||
\(407\) | 2.52322e8 | 0.185513 | ||||||||
\(408\) | −5.20606e8 | −0.379488 | ||||||||
\(409\) | −2.08902e8 | −0.150977 | −0.0754887 | − | 0.997147i | \(-0.524052\pi\) | ||||
−0.0754887 | + | 0.997147i | \(0.524052\pi\) | |||||||
\(410\) | −9.07177e8 | −0.650053 | ||||||||
\(411\) | −2.19760e9 | −1.56136 | ||||||||
\(412\) | 8.33299e8 | 0.587030 | ||||||||
\(413\) | −1.56135e8 | −0.109062 | ||||||||
\(414\) | 3.29045e8 | 0.227905 | ||||||||
\(415\) | 9.37640e8 | 0.643973 | ||||||||
\(416\) | 1.25082e8 | 0.0851859 | ||||||||
\(417\) | 3.01657e9 | 2.03722 | ||||||||
\(418\) | −1.22825e8 | −0.0822566 | ||||||||
\(419\) | 3.34065e7 | 0.0221861 | 0.0110931 | − | 0.999938i | \(-0.496469\pi\) | ||||
0.0110931 | + | 0.999938i | \(0.496469\pi\) | |||||||
\(420\) | −1.58972e8 | −0.104700 | ||||||||
\(421\) | 7.66238e8 | 0.500468 | 0.250234 | − | 0.968185i | \(-0.419492\pi\) | ||||
0.250234 | + | 0.968185i | \(0.419492\pi\) | |||||||
\(422\) | 1.17334e9 | 0.760030 | ||||||||
\(423\) | −1.45356e8 | −0.0933777 | ||||||||
\(424\) | −1.44754e8 | −0.0922250 | ||||||||
\(425\) | −7.26340e8 | −0.458964 | ||||||||
\(426\) | 5.94204e8 | 0.372393 | ||||||||
\(427\) | −2.30226e8 | −0.143106 | ||||||||
\(428\) | 7.70507e8 | 0.475032 | ||||||||
\(429\) | −4.36348e8 | −0.266829 | ||||||||
\(430\) | −2.13724e9 | −1.29633 | ||||||||
\(431\) | 2.21182e9 | 1.33070 | 0.665350 | − | 0.746532i | \(-0.268282\pi\) | ||||
0.665350 | + | 0.746532i | \(0.268282\pi\) | |||||||
\(432\) | −3.69409e8 | −0.220452 | ||||||||
\(433\) | −2.56377e9 | −1.51765 | −0.758825 | − | 0.651295i | \(-0.774226\pi\) | ||||
−0.758825 | + | 0.651295i | \(0.774226\pi\) | |||||||
\(434\) | 1.55968e8 | 0.0915842 | ||||||||
\(435\) | 6.20954e8 | 0.361699 | ||||||||
\(436\) | 6.43664e8 | 0.371926 | ||||||||
\(437\) | 6.70139e8 | 0.384131 | ||||||||
\(438\) | 2.59792e9 | 1.47729 | ||||||||
\(439\) | −3.39319e8 | −0.191418 | −0.0957088 | − | 0.995409i | \(-0.530512\pi\) | ||||
−0.0957088 | + | 0.995409i | \(0.530512\pi\) | |||||||
\(440\) | −3.87979e8 | −0.217132 | ||||||||
\(441\) | −3.38004e8 | −0.187667 | ||||||||
\(442\) | −6.08025e8 | −0.334922 | ||||||||
\(443\) | −1.65782e9 | −0.905993 | −0.452996 | − | 0.891512i | \(-0.649645\pi\) | ||||
−0.452996 | + | 0.891512i | \(0.649645\pi\) | |||||||
\(444\) | −3.68426e8 | −0.199760 | ||||||||
\(445\) | −6.60334e8 | −0.355225 | ||||||||
\(446\) | −3.96075e8 | −0.211400 | ||||||||
\(447\) | 3.26888e9 | 1.73110 | ||||||||
\(448\) | −3.76640e7 | −0.0197903 | ||||||||
\(449\) | 3.56920e9 | 1.86084 | 0.930419 | − | 0.366498i | \(-0.119443\pi\) | ||||
0.930419 | + | 0.366498i | \(0.119443\pi\) | |||||||
\(450\) | 1.22858e8 | 0.0635565 | ||||||||
\(451\) | 7.49786e8 | 0.384875 | ||||||||
\(452\) | 4.44995e7 | 0.0226658 | ||||||||
\(453\) | 4.07577e9 | 2.05999 | ||||||||
\(454\) | 2.14652e9 | 1.07656 | ||||||||
\(455\) | −1.85666e8 | −0.0924043 | ||||||||
\(456\) | 1.79342e8 | 0.0885739 | ||||||||
\(457\) | −8.20267e8 | −0.402021 | −0.201010 | − | 0.979589i | \(-0.564422\pi\) | ||||
−0.201010 | + | 0.979589i | \(0.564422\pi\) | |||||||
\(458\) | 1.85465e9 | 0.902056 | ||||||||
\(459\) | 1.79570e9 | 0.866743 | ||||||||
\(460\) | 2.11683e9 | 1.01399 | ||||||||
\(461\) | −3.74605e9 | −1.78082 | −0.890410 | − | 0.455159i | \(-0.849582\pi\) | ||||
−0.890410 | + | 0.455159i | \(0.849582\pi\) | |||||||
\(462\) | 1.31391e8 | 0.0619895 | ||||||||
\(463\) | 1.62426e9 | 0.760540 | 0.380270 | − | 0.924875i | \(-0.375831\pi\) | ||||
0.380270 | + | 0.924875i | \(0.375831\pi\) | |||||||
\(464\) | 1.47118e8 | 0.0683680 | ||||||||
\(465\) | −2.34591e9 | −1.08200 | ||||||||
\(466\) | 1.43488e8 | 0.0656847 | ||||||||
\(467\) | −2.70276e9 | −1.22800 | −0.613999 | − | 0.789307i | \(-0.710440\pi\) | ||||
−0.613999 | + | 0.789307i | \(0.710440\pi\) | |||||||
\(468\) | 1.02845e8 | 0.0463793 | ||||||||
\(469\) | −1.18564e8 | −0.0530700 | ||||||||
\(470\) | −9.35115e8 | −0.415454 | ||||||||
\(471\) | 2.59785e9 | 1.14562 | ||||||||
\(472\) | 5.56395e8 | 0.243549 | ||||||||
\(473\) | 1.76644e9 | 0.767512 | ||||||||
\(474\) | −1.39563e9 | −0.601931 | ||||||||
\(475\) | 2.50215e8 | 0.107124 | ||||||||
\(476\) | 1.83085e8 | 0.0778089 | ||||||||
\(477\) | −1.19020e8 | −0.0502118 | ||||||||
\(478\) | 8.39436e8 | 0.351552 | ||||||||
\(479\) | −1.16089e9 | −0.482631 | −0.241316 | − | 0.970447i | \(-0.577579\pi\) | ||||
−0.241316 | + | 0.970447i | \(0.577579\pi\) | |||||||
\(480\) | 5.66505e8 | 0.233808 | ||||||||
\(481\) | −4.30291e8 | −0.176301 | ||||||||
\(482\) | −2.27499e9 | −0.925368 | ||||||||
\(483\) | −7.16873e8 | −0.289486 | ||||||||
\(484\) | −9.26512e8 | −0.371443 | ||||||||
\(485\) | −5.05426e9 | −2.01169 | ||||||||
\(486\) | −6.79879e8 | −0.268661 | ||||||||
\(487\) | 2.66603e9 | 1.04596 | 0.522978 | − | 0.852346i | \(-0.324821\pi\) | ||||
0.522978 | + | 0.852346i | \(0.324821\pi\) | |||||||
\(488\) | 8.20423e8 | 0.319572 | ||||||||
\(489\) | 7.46793e8 | 0.288815 | ||||||||
\(490\) | −2.17447e9 | −0.834962 | ||||||||
\(491\) | −7.10777e8 | −0.270987 | −0.135493 | − | 0.990778i | \(-0.543262\pi\) | ||||
−0.135493 | + | 0.990778i | \(0.543262\pi\) | |||||||
\(492\) | −1.09479e9 | −0.414434 | ||||||||
\(493\) | −7.15143e8 | −0.268800 | ||||||||
\(494\) | 2.09457e8 | 0.0781719 | ||||||||
\(495\) | −3.19006e8 | −0.118217 | ||||||||
\(496\) | −5.55799e8 | −0.204518 | ||||||||
\(497\) | −2.08968e8 | −0.0763541 | ||||||||
\(498\) | 1.13156e9 | 0.410558 | ||||||||
\(499\) | 1.23876e9 | 0.446309 | 0.223154 | − | 0.974783i | \(-0.428365\pi\) | ||||
0.223154 | + | 0.974783i | \(0.428365\pi\) | |||||||
\(500\) | −9.02290e8 | −0.322813 | ||||||||
\(501\) | −4.78092e9 | −1.69855 | ||||||||
\(502\) | 1.03697e9 | 0.365850 | ||||||||
\(503\) | 6.01551e8 | 0.210758 | 0.105379 | − | 0.994432i | \(-0.466394\pi\) | ||||
0.105379 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(504\) | −3.09683e7 | −0.0107748 | ||||||||
\(505\) | −1.25391e9 | −0.433259 | ||||||||
\(506\) | −1.74957e9 | −0.600349 | ||||||||
\(507\) | −2.46035e9 | −0.838434 | ||||||||
\(508\) | −1.65719e8 | −0.0560852 | ||||||||
\(509\) | −7.54337e8 | −0.253544 | −0.126772 | − | 0.991932i | \(-0.540462\pi\) | ||||
−0.126772 | + | 0.991932i | \(0.540462\pi\) | |||||||
\(510\) | −2.75379e9 | −0.919253 | ||||||||
\(511\) | −9.13631e8 | −0.302899 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −6.18598e8 | −0.202301 | ||||||||
\(514\) | 3.74641e9 | 1.21687 | ||||||||
\(515\) | 4.40780e9 | 1.42199 | ||||||||
\(516\) | −2.57926e9 | −0.826457 | ||||||||
\(517\) | 7.72877e8 | 0.245976 | ||||||||
\(518\) | 1.29567e8 | 0.0409581 | ||||||||
\(519\) | −5.64245e9 | −1.77167 | ||||||||
\(520\) | 6.61631e8 | 0.206350 | ||||||||
\(521\) | −4.75312e9 | −1.47247 | −0.736236 | − | 0.676725i | \(-0.763399\pi\) | ||||
−0.736236 | + | 0.676725i | \(0.763399\pi\) | |||||||
\(522\) | 1.20964e8 | 0.0372229 | ||||||||
\(523\) | 2.09748e9 | 0.641125 | 0.320563 | − | 0.947227i | \(-0.396128\pi\) | ||||
0.320563 | + | 0.947227i | \(0.396128\pi\) | |||||||
\(524\) | 2.74382e9 | 0.833097 | ||||||||
\(525\) | −2.67665e8 | −0.0807298 | ||||||||
\(526\) | −3.48984e9 | −1.04558 | ||||||||
\(527\) | 2.70175e9 | 0.804096 | ||||||||
\(528\) | −4.68219e8 | −0.138430 | ||||||||
\(529\) | 6.14088e9 | 1.80358 | ||||||||
\(530\) | −7.65686e8 | −0.223401 | ||||||||
\(531\) | 4.57482e8 | 0.132600 | ||||||||
\(532\) | −6.30706e7 | −0.0181609 | ||||||||
\(533\) | −1.27863e9 | −0.365763 | ||||||||
\(534\) | −7.96901e8 | −0.226470 | ||||||||
\(535\) | 4.07566e9 | 1.15069 | ||||||||
\(536\) | 4.22511e8 | 0.118512 | ||||||||
\(537\) | −1.29508e9 | −0.360898 | ||||||||
\(538\) | −1.25725e9 | −0.348083 | ||||||||
\(539\) | 1.79721e9 | 0.494354 | ||||||||
\(540\) | −1.95402e9 | −0.534012 | ||||||||
\(541\) | −5.19805e9 | −1.41140 | −0.705700 | − | 0.708510i | \(-0.749368\pi\) | ||||
−0.705700 | + | 0.708510i | \(0.749368\pi\) | |||||||
\(542\) | 2.43646e9 | 0.657297 | ||||||||
\(543\) | 3.15789e9 | 0.846442 | ||||||||
\(544\) | −6.52435e8 | −0.173756 | ||||||||
\(545\) | 3.40472e9 | 0.900934 | ||||||||
\(546\) | −2.24064e8 | −0.0589113 | ||||||||
\(547\) | 2.13091e9 | 0.556684 | 0.278342 | − | 0.960482i | \(-0.410215\pi\) | ||||
0.278342 | + | 0.960482i | \(0.410215\pi\) | |||||||
\(548\) | −2.75408e9 | −0.714900 | ||||||||
\(549\) | 6.74573e8 | 0.173990 | ||||||||
\(550\) | −6.53250e8 | −0.167421 | ||||||||
\(551\) | 2.46358e8 | 0.0627388 | ||||||||
\(552\) | 2.55462e9 | 0.646456 | ||||||||
\(553\) | 4.90812e8 | 0.123418 | ||||||||
\(554\) | −2.30930e9 | −0.577026 | ||||||||
\(555\) | −1.94882e9 | −0.483889 | ||||||||
\(556\) | 3.78043e9 | 0.932781 | ||||||||
\(557\) | 1.67168e8 | 0.0409884 | 0.0204942 | − | 0.999790i | \(-0.493476\pi\) | ||||
0.0204942 | + | 0.999790i | \(0.493476\pi\) | |||||||
\(558\) | −4.56992e8 | −0.111350 | ||||||||
\(559\) | −3.01236e9 | −0.729399 | ||||||||
\(560\) | −1.99227e8 | −0.0479391 | ||||||||
\(561\) | 2.27602e9 | 0.544259 | ||||||||
\(562\) | −3.79498e8 | −0.0901847 | ||||||||
\(563\) | 7.02257e9 | 1.65850 | 0.829252 | − | 0.558875i | \(-0.188767\pi\) | ||||
0.829252 | + | 0.558875i | \(0.188767\pi\) | |||||||
\(564\) | −1.12851e9 | −0.264868 | ||||||||
\(565\) | 2.35384e8 | 0.0549044 | ||||||||
\(566\) | −4.27559e9 | −0.991148 | ||||||||
\(567\) | 7.94019e8 | 0.182932 | ||||||||
\(568\) | 7.44669e8 | 0.170508 | ||||||||
\(569\) | 2.82902e9 | 0.643789 | 0.321894 | − | 0.946776i | \(-0.395680\pi\) | ||||
0.321894 | + | 0.946776i | \(0.395680\pi\) | |||||||
\(570\) | 9.48646e8 | 0.214557 | ||||||||
\(571\) | −5.85928e9 | −1.31710 | −0.658549 | − | 0.752538i | \(-0.728829\pi\) | ||||
−0.658549 | + | 0.752538i | \(0.728829\pi\) | |||||||
\(572\) | −5.46841e8 | −0.122173 | ||||||||
\(573\) | −2.83458e9 | −0.629429 | ||||||||
\(574\) | 3.85015e8 | 0.0849739 | ||||||||
\(575\) | 3.56416e9 | 0.781843 | ||||||||
\(576\) | 1.10357e8 | 0.0240615 | ||||||||
\(577\) | 5.86369e9 | 1.27074 | 0.635368 | − | 0.772210i | \(-0.280848\pi\) | ||||
0.635368 | + | 0.772210i | \(0.280848\pi\) | |||||||
\(578\) | −1.11214e8 | −0.0239558 | ||||||||
\(579\) | 4.41268e9 | 0.944774 | ||||||||
\(580\) | 7.78193e8 | 0.165611 | ||||||||
\(581\) | −3.97943e8 | −0.0841792 | ||||||||
\(582\) | −6.09956e9 | −1.28253 | ||||||||
\(583\) | 6.32843e8 | 0.132268 | ||||||||
\(584\) | 3.25577e9 | 0.676409 | ||||||||
\(585\) | 5.44010e8 | 0.112347 | ||||||||
\(586\) | −4.71596e9 | −0.968119 | ||||||||
\(587\) | −2.61552e9 | −0.533734 | −0.266867 | − | 0.963733i | \(-0.585988\pi\) | ||||
−0.266867 | + | 0.963733i | \(0.585988\pi\) | |||||||
\(588\) | −2.62418e9 | −0.532320 | ||||||||
\(589\) | −9.30720e8 | −0.187679 | ||||||||
\(590\) | 2.94310e9 | 0.589960 | ||||||||
\(591\) | −2.68134e9 | −0.534312 | ||||||||
\(592\) | −4.61719e8 | −0.0914643 | ||||||||
\(593\) | −2.82844e9 | −0.557001 | −0.278500 | − | 0.960436i | \(-0.589837\pi\) | ||||
−0.278500 | + | 0.960436i | \(0.589837\pi\) | |||||||
\(594\) | 1.61501e9 | 0.316171 | ||||||||
\(595\) | 9.68445e8 | 0.188480 | ||||||||
\(596\) | 4.09663e9 | 0.792619 | ||||||||
\(597\) | 5.96671e9 | 1.14769 | ||||||||
\(598\) | 2.98358e9 | 0.570537 | ||||||||
\(599\) | 1.27951e9 | 0.243248 | 0.121624 | − | 0.992576i | \(-0.461190\pi\) | ||||
0.121624 | + | 0.992576i | \(0.461190\pi\) | |||||||
\(600\) | 9.53839e8 | 0.180279 | ||||||||
\(601\) | 7.46347e9 | 1.40243 | 0.701214 | − | 0.712951i | \(-0.252642\pi\) | ||||
0.701214 | + | 0.712951i | \(0.252642\pi\) | |||||||
\(602\) | 9.07066e8 | 0.169454 | ||||||||
\(603\) | 3.47399e8 | 0.0645235 | ||||||||
\(604\) | 5.10784e9 | 0.943210 | ||||||||
\(605\) | −4.90086e9 | −0.899765 | ||||||||
\(606\) | −1.51324e9 | −0.276219 | ||||||||
\(607\) | −3.57702e9 | −0.649175 | −0.324587 | − | 0.945856i | \(-0.605225\pi\) | ||||
−0.324587 | + | 0.945856i | \(0.605225\pi\) | |||||||
\(608\) | 2.24756e8 | 0.0405554 | ||||||||
\(609\) | −2.63539e8 | −0.0472807 | ||||||||
\(610\) | 4.33970e9 | 0.774114 | ||||||||
\(611\) | −1.31801e9 | −0.233762 | ||||||||
\(612\) | −5.36448e8 | −0.0946015 | ||||||||
\(613\) | 7.37202e9 | 1.29263 | 0.646316 | − | 0.763070i | \(-0.276309\pi\) | ||||
0.646316 | + | 0.763070i | \(0.276309\pi\) | |||||||
\(614\) | 7.09625e9 | 1.23720 | ||||||||
\(615\) | −5.79101e9 | −1.00390 | ||||||||
\(616\) | 1.64662e8 | 0.0283832 | ||||||||
\(617\) | 6.75777e9 | 1.15826 | 0.579129 | − | 0.815236i | \(-0.303393\pi\) | ||||
0.579129 | + | 0.815236i | \(0.303393\pi\) | |||||||
\(618\) | 5.31940e9 | 0.906574 | ||||||||
\(619\) | 3.00161e7 | 0.00508670 | 0.00254335 | − | 0.999997i | \(-0.499190\pi\) | ||||
0.00254335 | + | 0.999997i | \(0.499190\pi\) | |||||||
\(620\) | −2.93995e9 | −0.495414 | ||||||||
\(621\) | −8.81154e9 | −1.47649 | ||||||||
\(622\) | −8.44698e9 | −1.40746 | ||||||||
\(623\) | 2.80252e8 | 0.0464345 | ||||||||
\(624\) | 7.98466e8 | 0.131556 | ||||||||
\(625\) | −7.62272e9 | −1.24891 | ||||||||
\(626\) | 4.33360e9 | 0.706056 | ||||||||
\(627\) | −7.84061e8 | −0.127032 | ||||||||
\(628\) | 3.25569e9 | 0.524547 | ||||||||
\(629\) | 2.24442e9 | 0.359606 | ||||||||
\(630\) | −1.63809e8 | −0.0261004 | ||||||||
\(631\) | −9.20882e9 | −1.45915 | −0.729577 | − | 0.683899i | \(-0.760283\pi\) | ||||
−0.729577 | + | 0.683899i | \(0.760283\pi\) | |||||||
\(632\) | −1.74904e9 | −0.275606 | ||||||||
\(633\) | 7.49008e9 | 1.17374 | ||||||||
\(634\) | 2.22028e9 | 0.346016 | ||||||||
\(635\) | −8.76583e8 | −0.135858 | ||||||||
\(636\) | −9.24041e8 | −0.142427 | ||||||||
\(637\) | −3.06483e9 | −0.469805 | ||||||||
\(638\) | −6.43180e8 | −0.0980529 | ||||||||
\(639\) | 6.12286e8 | 0.0928327 | ||||||||
\(640\) | 7.09956e8 | 0.107054 | ||||||||
\(641\) | −5.16699e9 | −0.774880 | −0.387440 | − | 0.921895i | \(-0.626641\pi\) | ||||
−0.387440 | + | 0.921895i | \(0.626641\pi\) | |||||||
\(642\) | 4.91857e9 | 0.733611 | ||||||||
\(643\) | −7.56140e9 | −1.12167 | −0.560833 | − | 0.827929i | \(-0.689519\pi\) | ||||
−0.560833 | + | 0.827929i | \(0.689519\pi\) | |||||||
\(644\) | −8.98401e8 | −0.132547 | ||||||||
\(645\) | −1.36432e10 | −2.00197 | ||||||||
\(646\) | −1.09254e9 | −0.159450 | ||||||||
\(647\) | −9.89841e9 | −1.43681 | −0.718407 | − | 0.695623i | \(-0.755128\pi\) | ||||
−0.718407 | + | 0.695623i | \(0.755128\pi\) | |||||||
\(648\) | −2.82953e9 | −0.408509 | ||||||||
\(649\) | −2.43248e9 | −0.349296 | ||||||||
\(650\) | 1.11400e9 | 0.159107 | ||||||||
\(651\) | 9.95627e8 | 0.141437 | ||||||||
\(652\) | 9.35897e8 | 0.132240 | ||||||||
\(653\) | −1.11917e10 | −1.57289 | −0.786446 | − | 0.617659i | \(-0.788081\pi\) | ||||
−0.786446 | + | 0.617659i | \(0.788081\pi\) | |||||||
\(654\) | 4.10886e9 | 0.574380 | ||||||||
\(655\) | 1.45136e10 | 2.01805 | ||||||||
\(656\) | −1.37202e9 | −0.189757 | ||||||||
\(657\) | 2.67698e9 | 0.368270 | ||||||||
\(658\) | 3.96872e8 | 0.0543075 | ||||||||
\(659\) | −5.84630e9 | −0.795760 | −0.397880 | − | 0.917438i | \(-0.630254\pi\) | ||||
−0.397880 | + | 0.917438i | \(0.630254\pi\) | |||||||
\(660\) | −2.47668e9 | −0.335326 | ||||||||
\(661\) | −9.70737e8 | −0.130736 | −0.0653682 | − | 0.997861i | \(-0.520822\pi\) | ||||
−0.0653682 | + | 0.997861i | \(0.520822\pi\) | |||||||
\(662\) | −4.87424e9 | −0.652986 | ||||||||
\(663\) | −3.88136e9 | −0.517233 | ||||||||
\(664\) | 1.41809e9 | 0.187982 | ||||||||
\(665\) | −3.33617e8 | −0.0439919 | ||||||||
\(666\) | −3.79637e8 | −0.0497976 | ||||||||
\(667\) | 3.50921e9 | 0.457899 | ||||||||
\(668\) | −5.99155e9 | −0.777717 | ||||||||
\(669\) | −2.52836e9 | −0.326474 | ||||||||
\(670\) | 2.23491e9 | 0.287076 | ||||||||
\(671\) | −3.58678e9 | −0.458328 | ||||||||
\(672\) | −2.40430e8 | −0.0305630 | ||||||||
\(673\) | 1.20547e10 | 1.52442 | 0.762208 | − | 0.647332i | \(-0.224115\pi\) | ||||
0.762208 | + | 0.647332i | \(0.224115\pi\) | |||||||
\(674\) | −4.78526e8 | −0.0602000 | ||||||||
\(675\) | −3.29004e9 | −0.411754 | ||||||||
\(676\) | −3.08336e9 | −0.383894 | ||||||||
\(677\) | −7.29226e9 | −0.903237 | −0.451619 | − | 0.892211i | \(-0.649153\pi\) | ||||
−0.451619 | + | 0.892211i | \(0.649153\pi\) | |||||||
\(678\) | 2.84065e8 | 0.0350037 | ||||||||
\(679\) | 2.14508e9 | 0.262965 | ||||||||
\(680\) | −3.45111e9 | −0.420898 | ||||||||
\(681\) | 1.37024e10 | 1.66257 | ||||||||
\(682\) | 2.42988e9 | 0.293319 | ||||||||
\(683\) | 1.41645e10 | 1.70110 | 0.850548 | − | 0.525897i | \(-0.176270\pi\) | ||||
0.850548 | + | 0.525897i | \(0.176270\pi\) | |||||||
\(684\) | 1.84800e8 | 0.0220803 | ||||||||
\(685\) | −1.45680e10 | −1.73174 | ||||||||
\(686\) | 1.86946e9 | 0.221096 | ||||||||
\(687\) | 1.18393e10 | 1.39308 | ||||||||
\(688\) | −3.23238e9 | −0.378410 | ||||||||
\(689\) | −1.07920e9 | −0.125700 | ||||||||
\(690\) | 1.35129e10 | 1.56594 | ||||||||
\(691\) | 6.15519e9 | 0.709689 | 0.354845 | − | 0.934925i | \(-0.384534\pi\) | ||||
0.354845 | + | 0.934925i | \(0.384534\pi\) | |||||||
\(692\) | −7.07124e9 | −0.811194 | ||||||||
\(693\) | 1.35389e8 | 0.0154532 | ||||||||
\(694\) | 3.28413e9 | 0.372960 | ||||||||
\(695\) | 1.99969e10 | 2.25952 | ||||||||
\(696\) | 9.39135e8 | 0.105583 | ||||||||
\(697\) | 6.66942e9 | 0.746059 | ||||||||
\(698\) | −9.94724e9 | −1.10716 | ||||||||
\(699\) | 9.15961e8 | 0.101439 | ||||||||
\(700\) | −3.35443e8 | −0.0369638 | ||||||||
\(701\) | −3.60428e9 | −0.395189 | −0.197595 | − | 0.980284i | \(-0.563313\pi\) | ||||
−0.197595 | + | 0.980284i | \(0.563313\pi\) | |||||||
\(702\) | −2.75412e9 | −0.300471 | ||||||||
\(703\) | −7.73176e8 | −0.0839334 | ||||||||
\(704\) | −5.86782e8 | −0.0633830 | ||||||||
\(705\) | −5.96935e9 | −0.641601 | ||||||||
\(706\) | −9.26152e9 | −0.990526 | ||||||||
\(707\) | 5.32173e8 | 0.0566350 | ||||||||
\(708\) | 3.55177e9 | 0.376122 | ||||||||
\(709\) | −7.50645e8 | −0.0790993 | −0.0395497 | − | 0.999218i | \(-0.512592\pi\) | ||||
−0.0395497 | + | 0.999218i | \(0.512592\pi\) | |||||||
\(710\) | 3.93899e9 | 0.413029 | ||||||||
\(711\) | −1.43810e9 | −0.150054 | ||||||||
\(712\) | −9.98694e8 | −0.103694 | ||||||||
\(713\) | −1.32575e10 | −1.36977 | ||||||||
\(714\) | 1.16873e9 | 0.120163 | ||||||||
\(715\) | −2.89256e9 | −0.295945 | ||||||||
\(716\) | −1.62302e9 | −0.165245 | ||||||||
\(717\) | 5.35858e9 | 0.542916 | ||||||||
\(718\) | −1.51115e9 | −0.152360 | ||||||||
\(719\) | −1.21392e10 | −1.21798 | −0.608989 | − | 0.793179i | \(-0.708425\pi\) | ||||
−0.608989 | + | 0.793179i | \(0.708425\pi\) | |||||||
\(720\) | 5.83744e8 | 0.0582852 | ||||||||
\(721\) | −1.87071e9 | −0.185881 | ||||||||
\(722\) | 3.76367e8 | 0.0372161 | ||||||||
\(723\) | −1.45225e10 | −1.42908 | ||||||||
\(724\) | 3.95753e9 | 0.387560 | ||||||||
\(725\) | 1.31026e9 | 0.127696 | ||||||||
\(726\) | −5.91444e9 | −0.573634 | ||||||||
\(727\) | −6.81778e9 | −0.658071 | −0.329035 | − | 0.944318i | \(-0.606724\pi\) | ||||
−0.329035 | + | 0.944318i | \(0.606724\pi\) | |||||||
\(728\) | −2.80802e8 | −0.0269737 | ||||||||
\(729\) | 7.74625e9 | 0.740535 | ||||||||
\(730\) | 1.72217e10 | 1.63850 | ||||||||
\(731\) | 1.57127e10 | 1.48778 | ||||||||
\(732\) | 5.23721e9 | 0.493527 | ||||||||
\(733\) | 5.46670e9 | 0.512697 | 0.256349 | − | 0.966584i | \(-0.417480\pi\) | ||||
0.256349 | + | 0.966584i | \(0.417480\pi\) | |||||||
\(734\) | −1.64687e9 | −0.153717 | ||||||||
\(735\) | −1.38808e10 | −1.28946 | ||||||||
\(736\) | 3.20150e9 | 0.295993 | ||||||||
\(737\) | −1.84716e9 | −0.169969 | ||||||||
\(738\) | −1.12811e9 | −0.103313 | ||||||||
\(739\) | −7.76760e9 | −0.707997 | −0.353998 | − | 0.935246i | \(-0.615178\pi\) | ||||
−0.353998 | + | 0.935246i | \(0.615178\pi\) | |||||||
\(740\) | −2.44230e9 | −0.221558 | ||||||||
\(741\) | 1.33708e9 | 0.120724 | ||||||||
\(742\) | 3.24964e8 | 0.0292026 | ||||||||
\(743\) | −6.32109e8 | −0.0565368 | −0.0282684 | − | 0.999600i | \(-0.508999\pi\) | ||||
−0.0282684 | + | 0.999600i | \(0.508999\pi\) | |||||||
\(744\) | −3.54797e9 | −0.315846 | ||||||||
\(745\) | 2.16695e10 | 1.92000 | ||||||||
\(746\) | −2.96777e9 | −0.261724 | ||||||||
\(747\) | 1.16599e9 | 0.102347 | ||||||||
\(748\) | 2.85236e9 | 0.249200 | ||||||||
\(749\) | −1.72975e9 | −0.150417 | ||||||||
\(750\) | −5.75981e9 | −0.498533 | ||||||||
\(751\) | −8.06627e9 | −0.694917 | −0.347458 | − | 0.937695i | \(-0.612955\pi\) | ||||
−0.347458 | + | 0.937695i | \(0.612955\pi\) | |||||||
\(752\) | −1.41427e9 | −0.121275 | ||||||||
\(753\) | 6.61954e9 | 0.564996 | ||||||||
\(754\) | 1.09683e9 | 0.0931838 | ||||||||
\(755\) | 2.70184e10 | 2.28478 | ||||||||
\(756\) | 8.29305e8 | 0.0698052 | ||||||||
\(757\) | 1.82516e10 | 1.52920 | 0.764602 | − | 0.644503i | \(-0.222936\pi\) | ||||
0.764602 | + | 0.644503i | \(0.222936\pi\) | |||||||
\(758\) | −1.40093e9 | −0.116835 | ||||||||
\(759\) | −1.11684e10 | −0.927143 | ||||||||
\(760\) | 1.18886e9 | 0.0982392 | ||||||||
\(761\) | 1.39681e10 | 1.14893 | 0.574463 | − | 0.818531i | \(-0.305211\pi\) | ||||
0.574463 | + | 0.818531i | \(0.305211\pi\) | |||||||
\(762\) | −1.05787e9 | −0.0866146 | ||||||||
\(763\) | −1.44499e9 | −0.117769 | ||||||||
\(764\) | −3.55235e9 | −0.288197 | ||||||||
\(765\) | −2.83759e9 | −0.229158 | ||||||||
\(766\) | 5.08845e9 | 0.409058 | ||||||||
\(767\) | 4.14818e9 | 0.331951 | ||||||||
\(768\) | 8.56785e8 | 0.0682508 | ||||||||
\(769\) | −1.28542e10 | −1.01930 | −0.509650 | − | 0.860382i | \(-0.670225\pi\) | ||||
−0.509650 | + | 0.860382i | \(0.670225\pi\) | |||||||
\(770\) | 8.70993e8 | 0.0687539 | ||||||||
\(771\) | 2.39154e10 | 1.87926 | ||||||||
\(772\) | 5.53007e9 | 0.432584 | ||||||||
\(773\) | −1.22702e10 | −0.955486 | −0.477743 | − | 0.878500i | \(-0.658545\pi\) | ||||
−0.477743 | + | 0.878500i | \(0.658545\pi\) | |||||||
\(774\) | −2.65774e9 | −0.206025 | ||||||||
\(775\) | −4.95006e9 | −0.381993 | ||||||||
\(776\) | −7.64410e9 | −0.587233 | ||||||||
\(777\) | 8.27096e8 | 0.0632532 | ||||||||
\(778\) | −4.10590e9 | −0.312593 | ||||||||
\(779\) | −2.29753e9 | −0.174133 | ||||||||
\(780\) | 4.22355e9 | 0.318674 | ||||||||
\(781\) | −3.25559e9 | −0.244541 | ||||||||
\(782\) | −1.55626e10 | −1.16374 | ||||||||
\(783\) | −3.23932e9 | −0.241150 | ||||||||
\(784\) | −3.28868e9 | −0.243733 | ||||||||
\(785\) | 1.72212e10 | 1.27063 | ||||||||
\(786\) | 1.75153e10 | 1.28658 | ||||||||
\(787\) | 1.40869e10 | 1.03016 | 0.515079 | − | 0.857143i | \(-0.327763\pi\) | ||||
0.515079 | + | 0.857143i | \(0.327763\pi\) | |||||||
\(788\) | −3.36031e9 | −0.244646 | ||||||||
\(789\) | −2.22776e10 | −1.61473 | ||||||||
\(790\) | −9.25168e9 | −0.667614 | ||||||||
\(791\) | −9.98992e7 | −0.00717702 | ||||||||
\(792\) | −4.82467e8 | −0.0345088 | ||||||||
\(793\) | 6.11663e9 | 0.435568 | ||||||||
\(794\) | 7.39343e9 | 0.524172 | ||||||||
\(795\) | −4.88779e9 | −0.345007 | ||||||||
\(796\) | 7.47762e9 | 0.525494 | ||||||||
\(797\) | 2.68842e10 | 1.88102 | 0.940510 | − | 0.339766i | \(-0.110348\pi\) | ||||
0.940510 | + | 0.339766i | \(0.110348\pi\) | |||||||
\(798\) | −4.02614e8 | −0.0280465 | ||||||||
\(799\) | 6.87481e9 | 0.476812 | ||||||||
\(800\) | 1.19537e9 | 0.0825444 | ||||||||
\(801\) | −8.21151e8 | −0.0564559 | ||||||||
\(802\) | −1.98803e10 | −1.36086 | ||||||||
\(803\) | −1.42338e10 | −0.970100 | ||||||||
\(804\) | 2.69712e9 | 0.183022 | ||||||||
\(805\) | −4.75217e9 | −0.321075 | ||||||||
\(806\) | −4.14374e9 | −0.278753 | ||||||||
\(807\) | −8.02569e9 | −0.537558 | ||||||||
\(808\) | −1.89643e9 | −0.126473 | ||||||||
\(809\) | 1.57674e10 | 1.04699 | 0.523493 | − | 0.852030i | \(-0.324629\pi\) | ||||
0.523493 | + | 0.852030i | \(0.324629\pi\) | |||||||
\(810\) | −1.49670e10 | −0.989551 | ||||||||
\(811\) | −2.41951e9 | −0.159277 | −0.0796387 | − | 0.996824i | \(-0.525377\pi\) | ||||
−0.0796387 | + | 0.996824i | \(0.525377\pi\) | |||||||
\(812\) | −3.30273e8 | −0.0216484 | ||||||||
\(813\) | 1.55532e10 | 1.01509 | ||||||||
\(814\) | 2.01857e9 | 0.131177 | ||||||||
\(815\) | 4.95051e9 | 0.320330 | ||||||||
\(816\) | −4.16485e9 | −0.268339 | ||||||||
\(817\) | −5.41282e9 | −0.347253 | ||||||||
\(818\) | −1.67122e9 | −0.106757 | ||||||||
\(819\) | −2.30883e8 | −0.0146858 | ||||||||
\(820\) | −7.25742e9 | −0.459657 | ||||||||
\(821\) | 1.94539e10 | 1.22689 | 0.613445 | − | 0.789737i | \(-0.289783\pi\) | ||||
0.613445 | + | 0.789737i | \(0.289783\pi\) | |||||||
\(822\) | −1.75808e10 | −1.10405 | ||||||||
\(823\) | −9.90466e9 | −0.619356 | −0.309678 | − | 0.950842i | \(-0.600221\pi\) | ||||
−0.309678 | + | 0.950842i | \(0.600221\pi\) | |||||||
\(824\) | 6.66639e9 | 0.415093 | ||||||||
\(825\) | −4.17005e9 | −0.258555 | ||||||||
\(826\) | −1.24908e9 | −0.0771187 | ||||||||
\(827\) | −1.41557e10 | −0.870285 | −0.435143 | − | 0.900362i | \(-0.643302\pi\) | ||||
−0.435143 | + | 0.900362i | \(0.643302\pi\) | |||||||
\(828\) | 2.63236e9 | 0.161153 | ||||||||
\(829\) | 6.77554e8 | 0.0413050 | 0.0206525 | − | 0.999787i | \(-0.493426\pi\) | ||||
0.0206525 | + | 0.999787i | \(0.493426\pi\) | |||||||
\(830\) | 7.50112e9 | 0.455358 | ||||||||
\(831\) | −1.47415e10 | −0.891124 | ||||||||
\(832\) | 1.00065e9 | 0.0602355 | ||||||||
\(833\) | 1.59863e10 | 0.958277 | ||||||||
\(834\) | 2.41326e10 | 1.44053 | ||||||||
\(835\) | −3.16928e10 | −1.88390 | ||||||||
\(836\) | −9.82602e8 | −0.0581642 | ||||||||
\(837\) | 1.22379e10 | 0.721385 | ||||||||
\(838\) | 2.67252e8 | 0.0156880 | ||||||||
\(839\) | −2.55064e10 | −1.49102 | −0.745509 | − | 0.666496i | \(-0.767793\pi\) | ||||
−0.745509 | + | 0.666496i | \(0.767793\pi\) | |||||||
\(840\) | −1.27177e9 | −0.0740342 | ||||||||
\(841\) | −1.59598e10 | −0.925213 | ||||||||
\(842\) | 6.12991e9 | 0.353884 | ||||||||
\(843\) | −2.42255e9 | −0.139276 | ||||||||
\(844\) | 9.38673e9 | 0.537422 | ||||||||
\(845\) | −1.63097e10 | −0.929924 | ||||||||
\(846\) | −1.16285e9 | −0.0660280 | ||||||||
\(847\) | 2.07997e9 | 0.117616 | ||||||||
\(848\) | −1.15803e9 | −0.0652129 | ||||||||
\(849\) | −2.72934e10 | −1.53067 | ||||||||
\(850\) | −5.81072e9 | −0.324537 | ||||||||
\(851\) | −1.10134e10 | −0.612587 | ||||||||
\(852\) | 4.75363e9 | 0.263322 | ||||||||
\(853\) | 1.10942e10 | 0.612034 | 0.306017 | − | 0.952026i | \(-0.401003\pi\) | ||||
0.306017 | + | 0.952026i | \(0.401003\pi\) | |||||||
\(854\) | −1.84181e9 | −0.101191 | ||||||||
\(855\) | 9.77514e8 | 0.0534862 | ||||||||
\(856\) | 6.16405e9 | 0.335899 | ||||||||
\(857\) | 1.65157e10 | 0.896321 | 0.448160 | − | 0.893953i | \(-0.352079\pi\) | ||||
0.448160 | + | 0.893953i | \(0.352079\pi\) | |||||||
\(858\) | −3.49079e9 | −0.188676 | ||||||||
\(859\) | −2.33583e10 | −1.25738 | −0.628688 | − | 0.777657i | \(-0.716408\pi\) | ||||
−0.628688 | + | 0.777657i | \(0.716408\pi\) | |||||||
\(860\) | −1.70979e10 | −0.916641 | ||||||||
\(861\) | 2.45776e9 | 0.131229 | ||||||||
\(862\) | 1.76946e10 | 0.940947 | ||||||||
\(863\) | 2.90901e9 | 0.154066 | 0.0770330 | − | 0.997029i | \(-0.475455\pi\) | ||||
0.0770330 | + | 0.997029i | \(0.475455\pi\) | |||||||
\(864\) | −2.95527e9 | −0.155883 | ||||||||
\(865\) | −3.74039e10 | −1.96499 | ||||||||
\(866\) | −2.05102e10 | −1.07314 | ||||||||
\(867\) | −7.09937e8 | −0.0369959 | ||||||||
\(868\) | 1.24774e9 | 0.0647598 | ||||||||
\(869\) | 7.64656e9 | 0.395273 | ||||||||
\(870\) | 4.96763e9 | 0.255760 | ||||||||
\(871\) | 3.15001e9 | 0.161528 | ||||||||
\(872\) | 5.14931e9 | 0.262991 | ||||||||
\(873\) | −6.28517e9 | −0.319718 | ||||||||
\(874\) | 5.36111e9 | 0.271622 | ||||||||
\(875\) | 2.02559e9 | 0.102217 | ||||||||
\(876\) | 2.07834e10 | 1.04460 | ||||||||
\(877\) | −2.41950e8 | −0.0121123 | −0.00605616 | − | 0.999982i | \(-0.501928\pi\) | ||||
−0.00605616 | + | 0.999982i | \(0.501928\pi\) | |||||||
\(878\) | −2.71455e9 | −0.135353 | ||||||||
\(879\) | −3.01046e10 | −1.49510 | ||||||||
\(880\) | −3.10383e9 | −0.153536 | ||||||||
\(881\) | −6.21423e8 | −0.0306176 | −0.0153088 | − | 0.999883i | \(-0.504873\pi\) | ||||
−0.0153088 | + | 0.999883i | \(0.504873\pi\) | |||||||
\(882\) | −2.70403e9 | −0.132700 | ||||||||
\(883\) | −3.24481e10 | −1.58609 | −0.793044 | − | 0.609164i | \(-0.791505\pi\) | ||||
−0.793044 | + | 0.609164i | \(0.791505\pi\) | |||||||
\(884\) | −4.86420e9 | −0.236825 | ||||||||
\(885\) | 1.87874e10 | 0.911098 | ||||||||
\(886\) | −1.32626e10 | −0.640634 | ||||||||
\(887\) | 1.39588e10 | 0.671609 | 0.335805 | − | 0.941932i | \(-0.390992\pi\) | ||||
0.335805 | + | 0.941932i | \(0.390992\pi\) | |||||||
\(888\) | −2.94740e9 | −0.141252 | ||||||||
\(889\) | 3.72030e8 | 0.0177591 | ||||||||
\(890\) | −5.28267e9 | −0.251182 | ||||||||
\(891\) | 1.23703e10 | 0.585881 | ||||||||
\(892\) | −3.16860e9 | −0.149482 | ||||||||
\(893\) | −2.36829e9 | −0.111290 | ||||||||
\(894\) | 2.61510e10 | 1.22407 | ||||||||
\(895\) | −8.58508e9 | −0.400280 | ||||||||
\(896\) | −3.01312e8 | −0.0139939 | ||||||||
\(897\) | 1.90458e10 | 0.881103 | ||||||||
\(898\) | 2.85536e10 | 1.31581 | ||||||||
\(899\) | −4.87376e9 | −0.223720 | ||||||||
\(900\) | 9.82864e8 | 0.0449412 | ||||||||
\(901\) | 5.62920e9 | 0.256395 | ||||||||
\(902\) | 5.99829e9 | 0.272148 | ||||||||
\(903\) | 5.79030e9 | 0.261694 | ||||||||
\(904\) | 3.55996e8 | 0.0160271 | ||||||||
\(905\) | 2.09337e10 | 0.938806 | ||||||||
\(906\) | 3.26062e10 | 1.45664 | ||||||||
\(907\) | 4.01035e10 | 1.78467 | 0.892334 | − | 0.451377i | \(-0.149067\pi\) | ||||
0.892334 | + | 0.451377i | \(0.149067\pi\) | |||||||
\(908\) | 1.71721e10 | 0.761243 | ||||||||
\(909\) | −1.55929e9 | −0.0688578 | ||||||||
\(910\) | −1.48533e9 | −0.0653397 | ||||||||
\(911\) | 2.42547e10 | 1.06287 | 0.531436 | − | 0.847099i | \(-0.321653\pi\) | ||||
0.531436 | + | 0.847099i | \(0.321653\pi\) | |||||||
\(912\) | 1.43474e9 | 0.0626312 | ||||||||
\(913\) | −6.19971e9 | −0.269603 | ||||||||
\(914\) | −6.56213e9 | −0.284272 | ||||||||
\(915\) | 2.77027e10 | 1.19549 | ||||||||
\(916\) | 1.48372e10 | 0.637850 | ||||||||
\(917\) | −6.15973e9 | −0.263796 | ||||||||
\(918\) | 1.43656e10 | 0.612880 | ||||||||
\(919\) | 1.89321e10 | 0.804626 | 0.402313 | − | 0.915502i | \(-0.368206\pi\) | ||||
0.402313 | + | 0.915502i | \(0.368206\pi\) | |||||||
\(920\) | 1.69346e10 | 0.716998 | ||||||||
\(921\) | 4.52992e10 | 1.91065 | ||||||||
\(922\) | −2.99684e10 | −1.25923 | ||||||||
\(923\) | 5.55185e9 | 0.232398 | ||||||||
\(924\) | 1.05113e9 | 0.0438332 | ||||||||
\(925\) | −4.11216e9 | −0.170834 | ||||||||
\(926\) | 1.29941e10 | 0.537783 | ||||||||
\(927\) | 5.48128e9 | 0.225997 | ||||||||
\(928\) | 1.17694e9 | 0.0483435 | ||||||||
\(929\) | −2.42440e10 | −0.992086 | −0.496043 | − | 0.868298i | \(-0.665214\pi\) | ||||
−0.496043 | + | 0.868298i | \(0.665214\pi\) | |||||||
\(930\) | −1.87673e10 | −0.765088 | ||||||||
\(931\) | −5.50709e9 | −0.223665 | ||||||||
\(932\) | 1.14790e9 | 0.0464461 | ||||||||
\(933\) | −5.39217e10 | −2.17359 | ||||||||
\(934\) | −2.16220e10 | −0.868326 | ||||||||
\(935\) | 1.50878e10 | 0.603649 | ||||||||
\(936\) | 8.22764e8 | 0.0327951 | ||||||||
\(937\) | 1.89408e9 | 0.0752159 | 0.0376080 | − | 0.999293i | \(-0.488026\pi\) | ||||
0.0376080 | + | 0.999293i | \(0.488026\pi\) | |||||||
\(938\) | −9.48515e8 | −0.0375262 | ||||||||
\(939\) | 2.76638e10 | 1.09039 | ||||||||
\(940\) | −7.48092e9 | −0.293770 | ||||||||
\(941\) | −2.02166e10 | −0.790941 | −0.395471 | − | 0.918479i | \(-0.629419\pi\) | ||||
−0.395471 | + | 0.918479i | \(0.629419\pi\) | |||||||
\(942\) | 2.07828e10 | 0.810078 | ||||||||
\(943\) | −3.27269e10 | −1.27091 | ||||||||
\(944\) | 4.45116e9 | 0.172215 | ||||||||
\(945\) | 4.38668e9 | 0.169093 | ||||||||
\(946\) | 1.41315e10 | 0.542713 | ||||||||
\(947\) | −2.28622e10 | −0.874768 | −0.437384 | − | 0.899275i | \(-0.644095\pi\) | ||||
−0.437384 | + | 0.899275i | \(0.644095\pi\) | |||||||
\(948\) | −1.11651e10 | −0.425630 | ||||||||
\(949\) | 2.42733e10 | 0.921928 | ||||||||
\(950\) | 2.00172e9 | 0.0757480 | ||||||||
\(951\) | 1.41733e10 | 0.534366 | ||||||||
\(952\) | 1.46468e9 | 0.0550192 | ||||||||
\(953\) | 4.18466e9 | 0.156616 | 0.0783079 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783079 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(954\) | −9.52160e8 | −0.0355051 | ||||||||
\(955\) | −1.87905e10 | −0.698113 | ||||||||
\(956\) | 6.71549e9 | 0.248585 | ||||||||
\(957\) | −4.10577e9 | −0.151427 | ||||||||
\(958\) | −9.28709e9 | −0.341272 | ||||||||
\(959\) | 6.18278e9 | 0.226370 | ||||||||
\(960\) | 4.53204e9 | 0.165327 | ||||||||
\(961\) | −9.09997e9 | −0.330756 | ||||||||
\(962\) | −3.44233e9 | −0.124663 | ||||||||
\(963\) | 5.06824e9 | 0.182880 | ||||||||
\(964\) | −1.81999e10 | −0.654334 | ||||||||
\(965\) | 2.92518e10 | 1.04787 | ||||||||
\(966\) | −5.73499e9 | −0.204697 | ||||||||
\(967\) | 8.31822e8 | 0.0295827 | 0.0147913 | − | 0.999891i | \(-0.495292\pi\) | ||||
0.0147913 | + | 0.999891i | \(0.495292\pi\) | |||||||
\(968\) | −7.41210e9 | −0.262650 | ||||||||
\(969\) | −6.97429e9 | −0.246245 | ||||||||
\(970\) | −4.04341e10 | −1.42248 | ||||||||
\(971\) | −3.06782e10 | −1.07538 | −0.537690 | − | 0.843143i | \(-0.680703\pi\) | ||||
−0.537690 | + | 0.843143i | \(0.680703\pi\) | |||||||
\(972\) | −5.43904e9 | −0.189972 | ||||||||
\(973\) | −8.48688e9 | −0.295361 | ||||||||
\(974\) | 2.13282e10 | 0.739602 | ||||||||
\(975\) | 7.11130e9 | 0.245716 | ||||||||
\(976\) | 6.56338e9 | 0.225971 | ||||||||
\(977\) | −2.63977e10 | −0.905599 | −0.452799 | − | 0.891612i | \(-0.649575\pi\) | ||||
−0.452799 | + | 0.891612i | \(0.649575\pi\) | |||||||
\(978\) | 5.97434e9 | 0.204223 | ||||||||
\(979\) | 4.36616e9 | 0.148717 | ||||||||
\(980\) | −1.73957e10 | −0.590407 | ||||||||
\(981\) | 4.23390e9 | 0.143185 | ||||||||
\(982\) | −5.68622e9 | −0.191617 | ||||||||
\(983\) | 3.22583e10 | 1.08319 | 0.541595 | − | 0.840640i | \(-0.317821\pi\) | ||||
0.541595 | + | 0.840640i | \(0.317821\pi\) | |||||||
\(984\) | −8.75836e9 | −0.293049 | ||||||||
\(985\) | −1.77746e10 | −0.592617 | ||||||||
\(986\) | −5.72115e9 | −0.190070 | ||||||||
\(987\) | 2.53345e9 | 0.0838691 | ||||||||
\(988\) | 1.67566e9 | 0.0552759 | ||||||||
\(989\) | −7.71021e10 | −2.53442 | ||||||||
\(990\) | −2.55205e9 | −0.0835922 | ||||||||
\(991\) | 5.69036e10 | 1.85730 | 0.928650 | − | 0.370956i | \(-0.120970\pi\) | ||||
0.928650 | + | 0.370956i | \(0.120970\pi\) | |||||||
\(992\) | −4.44639e9 | −0.144616 | ||||||||
\(993\) | −3.11149e10 | −1.00843 | ||||||||
\(994\) | −1.67174e9 | −0.0539905 | ||||||||
\(995\) | 3.95535e10 | 1.27293 | ||||||||
\(996\) | 9.05247e9 | 0.290308 | ||||||||
\(997\) | −5.83019e8 | −0.0186316 | −0.00931579 | − | 0.999957i | \(-0.502965\pi\) | ||||
−0.00931579 | + | 0.999957i | \(0.502965\pi\) | |||||||
\(998\) | 9.91008e9 | 0.315588 | ||||||||
\(999\) | 1.01664e10 | 0.322616 |
(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 | 38.8.a.e.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 342.8.a.o.1.1 | 4 | |||
4.3 | odd | 2 | 304.8.a.e.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.8.a.e.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
304.8.a.e.1.2 | 4 | 4.3 | odd | 2 | |||
342.8.a.o.1.1 | 4 | 3.2 | odd | 2 |