Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{79}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 79 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.88819\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −10.7764 | −0.691306 | −0.345653 | − | 0.938362i | \(-0.612343\pi\) | ||||
−0.345653 | + | 0.938362i | \(0.612343\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −106.106 | −1.89807 | −0.949037 | − | 0.315165i | \(-0.897940\pi\) | ||||
−0.949037 | + | 0.315165i | \(0.897940\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −126.869 | −0.522096 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 93.4347 | 0.232823 | 0.116412 | − | 0.993201i | \(-0.462861\pi\) | ||||
0.116412 | + | 0.993201i | \(0.462861\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −661.131 | −1.08500 | −0.542499 | − | 0.840057i | \(-0.682522\pi\) | ||||
−0.542499 | + | 0.840057i | \(0.682522\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1143.43 | 1.31215 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −455.919 | −0.382618 | −0.191309 | − | 0.981530i | \(-0.561273\pi\) | ||||
−0.191309 | + | 0.981530i | \(0.561273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1106.28 | 0.703041 | 0.351521 | − | 0.936180i | \(-0.385665\pi\) | ||||
0.351521 | + | 0.936180i | \(0.385665\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −748.390 | −0.294991 | −0.147495 | − | 0.989063i | \(-0.547121\pi\) | ||||
−0.147495 | + | 0.989063i | \(0.547121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8133.39 | 2.60268 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3985.86 | 1.05223 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2804.78 | 0.619304 | 0.309652 | − | 0.950850i | \(-0.399787\pi\) | ||||
0.309652 | + | 0.950850i | \(0.399787\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −359.299 | −0.0671508 | −0.0335754 | − | 0.999436i | \(-0.510689\pi\) | ||||
−0.0335754 | + | 0.999436i | \(0.510689\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1006.89 | −0.160952 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6812.82 | −0.818131 | −0.409066 | − | 0.912505i | \(-0.634145\pi\) | ||||
−0.409066 | + | 0.912505i | \(0.634145\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7124.60 | 0.750065 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2319.39 | −0.215484 | −0.107742 | − | 0.994179i | \(-0.534362\pi\) | ||||
−0.107742 | + | 0.994179i | \(0.534362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19965.7 | 1.64670 | 0.823349 | − | 0.567535i | \(-0.192103\pi\) | ||||
0.823349 | + | 0.567535i | \(0.192103\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13461.6 | 0.990978 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −14209.5 | −0.938287 | −0.469143 | − | 0.883122i | \(-0.655437\pi\) | ||||
−0.469143 | + | 0.883122i | \(0.655437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4913.17 | 0.264506 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26144.2 | 1.27846 | 0.639228 | − | 0.769017i | \(-0.279254\pi\) | ||||
0.639228 | + | 0.769017i | \(0.279254\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9913.94 | −0.441916 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11921.7 | −0.486016 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4904.35 | 0.183422 | 0.0917110 | − | 0.995786i | \(-0.470766\pi\) | ||||
0.0917110 | + | 0.995786i | \(0.470766\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13203.3 | 0.454315 | 0.227158 | − | 0.973858i | \(-0.427057\pi\) | ||||
0.227158 | + | 0.973858i | \(0.427057\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 70149.6 | 2.05941 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 59658.1 | 1.62361 | 0.811807 | − | 0.583926i | \(-0.198484\pi\) | ||||
0.811807 | + | 0.583926i | \(0.198484\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8064.94 | 0.203929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8906.43 | −0.209680 | −0.104840 | − | 0.994489i | \(-0.533433\pi\) | ||||
−0.104840 | + | 0.994489i | \(0.533433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10480.6 | 0.230186 | 0.115093 | − | 0.993355i | \(-0.463283\pi\) | ||||
0.115093 | + | 0.993355i | \(0.463283\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −87648.6 | −1.79925 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7230.02 | 0.130338 | 0.0651691 | − | 0.997874i | \(-0.479241\pi\) | ||||
0.0651691 | + | 0.997874i | \(0.479241\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12123.9 | −0.205319 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −100461. | −1.60067 | −0.800336 | − | 0.599552i | \(-0.795345\pi\) | ||||
−0.800336 | + | 0.599552i | \(0.795345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 48375.6 | 0.726238 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −30225.4 | −0.428128 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −20071.8 | −0.268603 | −0.134302 | − | 0.990940i | \(-0.542879\pi\) | ||||
−0.134302 | + | 0.990940i | \(0.542879\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3871.94 | 0.0464217 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −117382. | −1.33442 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23320.9 | 0.251662 | 0.125831 | − | 0.992052i | \(-0.459840\pi\) | ||||
0.125831 | + | 0.992052i | \(0.459840\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11854.0 | −0.121556 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 68974.1 | 0.672795 | 0.336398 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336398 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 113725. | 1.05624 | 0.528121 | − | 0.849169i | \(-0.322897\pi\) | ||||
0.528121 | + | 0.849169i | \(0.322897\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 121287. | 1.02413 | 0.512066 | − | 0.858946i | \(-0.328880\pi\) | ||||
0.512066 | + | 0.858946i | \(0.328880\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −61373.9 | −0.494786 | −0.247393 | − | 0.968915i | \(-0.579574\pi\) | ||||
−0.247393 | + | 0.968915i | \(0.579574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 73417.7 | 0.565579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −242939. | −1.78979 | −0.894893 | − | 0.446281i | \(-0.852748\pi\) | ||||
−0.894893 | + | 0.446281i | \(0.852748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 79408.4 | 0.559914 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 83877.3 | 0.566474 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −152321. | −0.945793 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24994.7 | 0.148965 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −531418. | −3.04201 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −201922. | −1.11090 | −0.555448 | − | 0.831551i | \(-0.687453\pi\) | ||||
−0.555448 | + | 0.831551i | \(0.687453\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −215159. | −1.13837 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 283521. | 1.44347 | 0.721734 | − | 0.692171i | \(-0.243345\pi\) | ||||
0.721734 | + | 0.692171i | \(0.243345\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −422922. | −1.99722 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 188471. | 0.857911 | 0.428955 | − | 0.903326i | \(-0.358882\pi\) | ||||
0.428955 | + | 0.903326i | \(0.358882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −211579. | −0.928830 | −0.464415 | − | 0.885618i | \(-0.653735\pi\) | ||||
−0.464415 | + | 0.885618i | \(0.653735\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 153128. | 0.648643 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −61772.5 | −0.252613 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −297603. | −1.17548 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −293324. | −1.08238 | −0.541192 | − | 0.840899i | \(-0.682027\pi\) | ||||
−0.541192 | + | 0.840899i | \(0.682027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 204476. | 0.729794 | 0.364897 | − | 0.931048i | \(-0.381104\pi\) | ||||
0.364897 | + | 0.931048i | \(0.381104\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 57842.2 | 0.199764 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 38123.6 | 0.127457 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −505915. | −1.63805 | −0.819027 | − | 0.573755i | \(-0.805486\pi\) | ||||
−0.819027 | + | 0.573755i | \(0.805486\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −281740. | −0.883804 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 284200. | 0.837829 | 0.418914 | − | 0.908026i | \(-0.362411\pi\) | ||||
0.418914 | + | 0.908026i | \(0.362411\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 106837. | 0.305499 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13145.7 | −0.0364747 | −0.0182373 | − | 0.999834i | \(-0.505805\pi\) | ||||
−0.0182373 | + | 0.999834i | \(0.505805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 65800.6 | 0.177220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −140353. | −0.367055 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −51453.0 | −0.130706 | −0.0653530 | − | 0.997862i | \(-0.520817\pi\) | ||||
−0.0653530 | + | 0.997862i | \(0.520817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −52851.2 | −0.126801 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 497735. | 1.16109 | 0.580544 | − | 0.814229i | \(-0.302840\pi\) | ||||
0.580544 | + | 0.814229i | \(0.302840\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 227120. | 0.515299 | 0.257650 | − | 0.966238i | \(-0.417052\pi\) | ||||
0.257650 | + | 0.966238i | \(0.417052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −142284. | −0.314071 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 722879. | 1.55287 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −42598.7 | −0.0890825 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −502778. | −0.997225 | −0.498612 | − | 0.866825i | \(-0.666157\pi\) | ||||
−0.498612 | + | 0.866825i | \(0.666157\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 140322. | 0.271165 | 0.135582 | − | 0.990766i | \(-0.456709\pi\) | ||||
0.135582 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −755960. | −1.42368 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 378993. | 0.695769 | 0.347885 | − | 0.937537i | \(-0.386900\pi\) | ||||
0.347885 | + | 0.937537i | \(0.386900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −461022. | −0.825256 | −0.412628 | − | 0.910900i | \(-0.635389\pi\) | ||||
−0.412628 | + | 0.910900i | \(0.635389\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −642899. | −1.12241 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 246100. | 0.409004 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 94947.9 | 0.154014 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 103365. | 0.163684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −202139. | −0.312567 | −0.156284 | − | 0.987712i | \(-0.549951\pi\) | ||||
−0.156284 | + | 0.987712i | \(0.549951\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 95979.1 | 0.144953 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.11848e6 | −3.12556 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −112943. | −0.159129 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 301422. | 0.415140 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 694340. | 0.934997 | 0.467498 | − | 0.883994i | \(-0.345155\pi\) | ||||
0.467498 | + | 0.883994i | \(0.345155\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.03188e6 | −1.35885 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.26697e6 | 1.63194 | 0.815968 | − | 0.578096i | \(-0.196204\pi\) | ||||
0.815968 | + | 0.578096i | \(0.196204\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −856477. | −1.07926 | −0.539631 | − | 0.841902i | \(-0.681436\pi\) | ||||
−0.539631 | + | 0.841902i | \(0.681436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −284358. | −0.343143 | −0.171571 | − | 0.985172i | \(-0.554884\pi\) | ||||
−0.171571 | + | 0.985172i | \(0.554884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.50771e6 | 1.78094 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −77913.5 | −0.0901035 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 427941. | 0.484606 | 0.242303 | − | 0.970201i | \(-0.422097\pi\) | ||||
0.242303 | + | 0.970201i | \(0.422097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −809581. | −0.897879 | −0.448940 | − | 0.893562i | \(-0.648198\pi\) | ||||
−0.448940 | + | 0.893562i | \(0.648198\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −837912. | −0.910296 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −731395. | −0.762798 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.08261e6 | 1.10655 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.26305e6 | −1.26542 | −0.632711 | − | 0.774388i | \(-0.718058\pi\) | ||||
−0.632711 | + | 0.774388i | \(0.718058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −69925.6 | −0.0686808 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −521314. | −0.502052 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −56138.2 | −0.0530183 | −0.0265091 | − | 0.999649i | \(-0.508439\pi\) | ||||
−0.0265091 | + | 0.999649i | \(0.508439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −355841. | −0.323336 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.54275e6 | −1.37533 | −0.687664 | − | 0.726029i | \(-0.741364\pi\) | ||||
−0.687664 | + | 0.726029i | \(0.741364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.77405e6 | −2.42660 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 216302. | 0.185687 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.20535e6 | 1.01563 | 0.507813 | − | 0.861467i | \(-0.330454\pi\) | ||||
0.507813 | + | 0.861467i | \(0.330454\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.76489e6 | 1.45980 | 0.729900 | − | 0.683554i | \(-0.239567\pi\) | ||||
0.729900 | + | 0.683554i | \(0.239567\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 759941. | 0.605966 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.48319e6 | 1.16144 | 0.580719 | − | 0.814104i | \(-0.302771\pi\) | ||||
0.580719 | + | 0.814104i | \(0.302771\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 45584.0 | 0.0350592 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.26812e6 | −0.958061 | −0.479031 | − | 0.877798i | \(-0.659012\pi\) | ||||
−0.479031 | + | 0.877798i | \(0.659012\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.44657e6 | −1.07368 | −0.536838 | − | 0.843685i | \(-0.680381\pi\) | ||||
−0.536838 | + | 0.843685i | \(0.680381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.26496e6 | 0.922495 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.21199e6 | −0.853603 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −251316. | −0.173975 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −367016. | −0.249756 | −0.124878 | − | 0.992172i | \(-0.539854\pi\) | ||||
−0.124878 | + | 0.992172i | \(0.539854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −520379. | −0.348149 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 372417. | 0.244985 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 494784. | 0.320064 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −743292. | −0.465107 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.40094e6 | −0.862324 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −131281. | −0.0794979 | −0.0397490 | − | 0.999210i | \(-0.512656\pi\) | ||||
−0.0397490 | + | 0.999210i | \(0.512656\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.22555e6 | −0.730186 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.33471e6 | −1.36878 | −0.684389 | − | 0.729118i | \(-0.739931\pi\) | ||||
−0.684389 | + | 0.729118i | \(0.739931\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 772801. | 0.445869 | 0.222934 | − | 0.974833i | \(-0.428436\pi\) | ||||
0.222934 | + | 0.974833i | \(0.428436\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 524336. | 0.293063 | 0.146532 | − | 0.989206i | \(-0.453189\pi\) | ||||
0.146532 | + | 0.989206i | \(0.453189\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 262064. | 0.144188 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.30704e6 | −0.707988 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −504374. | −0.268996 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.37723e6 | −2.82391 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 661389. | 0.342048 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −631635. | −0.316881 | −0.158440 | − | 0.987369i | \(-0.550647\pi\) | ||||
−0.158440 | + | 0.987369i | \(0.550647\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 864339. | 0.427143 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.33006e6 | −3.08174 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.33479e6 | 1.59954 | 0.799768 | − | 0.600309i | \(-0.204956\pi\) | ||||
0.799768 | + | 0.600309i | \(0.204956\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.61800e6 | 1.23729 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33571.0 | −0.0156343 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −855735. | −0.387072 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 650351. | 0.289951 | 0.144975 | − | 0.989435i | \(-0.453690\pi\) | ||||
0.144975 | + | 0.989435i | \(0.453690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 601041. | 0.264144 | 0.132072 | − | 0.991240i | \(-0.457837\pi\) | ||||
0.132072 | + | 0.991240i | \(0.457837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.63517e6 | −1.14167 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.88889e6 | 1.23394 | 0.616970 | − | 0.786987i | \(-0.288360\pi\) | ||||
0.616970 | + | 0.786987i | \(0.288360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 945021. | 0.397989 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 97830.5 | 0.0400625 | 0.0200313 | − | 0.999799i | \(-0.493623\pi\) | ||||
0.0200313 | + | 0.999799i | \(0.493623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.25225e6 | −0.505733 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.64147e6 | 0.653832 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.11205e6 | −0.436910 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.14775e6 | 0.832374 | 0.416187 | − | 0.909279i | \(-0.363366\pi\) | ||||
0.416187 | + | 0.909279i | \(0.363366\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 294260. | 0.112503 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.20458e6 | 1.56477 | 0.782386 | − | 0.622794i | \(-0.214003\pi\) | ||||
0.782386 | + | 0.622794i | \(0.214003\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.72677e6 | 2.10296 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.85433e6 | −0.671943 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 535586. | 0.191527 | 0.0957637 | − | 0.995404i | \(-0.469471\pi\) | ||||
0.0957637 | + | 0.995404i | \(0.469471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.17599e6 | 0.767969 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.84697e6 | −1.34005 | −0.670027 | − | 0.742337i | \(-0.733717\pi\) | ||||
−0.670027 | + | 0.742337i | \(0.733717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.53304e6 | −0.859736 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.69833e6 | −0.569045 | −0.284523 | − | 0.958669i | \(-0.591835\pi\) | ||||
−0.284523 | + | 0.958669i | \(0.591835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 341206. | 0.112869 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.05533e6 | −0.997877 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −767145. | −0.247391 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.62378e6 | −1.15394 | −0.576972 | − | 0.816764i | \(-0.695766\pi\) | ||||
−0.576972 | + | 0.816764i | \(0.695766\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.79801e6 | −0.868937 | −0.434469 | − | 0.900687i | \(-0.643064\pi\) | ||||
−0.434469 | + | 0.900687i | \(0.643064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 237543. | 0.0728585 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.28641e6 | 0.389710 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −636554. | −0.190480 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 666281. | 0.196947 | 0.0984735 | − | 0.995140i | \(-0.468604\pi\) | ||||
0.0984735 | + | 0.995140i | \(0.468604\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.03103e6 | −0.593078 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.06595e7 | 3.03819 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.28006e6 | 0.642105 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.89203e6 | 0.804762 | 0.402381 | − | 0.915472i | \(-0.368183\pi\) | ||||
0.402381 | + | 0.915472i | \(0.368183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.72027e6 | 1.84791 | 0.923956 | − | 0.382498i | \(-0.124936\pi\) | ||||
0.923956 | + | 0.382498i | \(0.124936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.80276e6 | 0.489876 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.70817e6 | −0.995835 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 665685. | 0.174633 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.72298e6 | −1.22468 | −0.612341 | − | 0.790594i | \(-0.709772\pi\) | ||||
−0.612341 | + | 0.790594i | \(0.709772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.78136e6 | 1.48187 | 0.740935 | − | 0.671577i | \(-0.234383\pi\) | ||||
0.740935 | + | 0.671577i | \(0.234383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.20708e6 | 0.812619 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −827929. | −0.207391 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.36873e6 | 1.32957 | 0.664784 | − | 0.747036i | \(-0.268524\pi\) | ||||
0.664784 | + | 0.747036i | \(0.268524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.31511e6 | −1.04468 | −0.522339 | − | 0.852738i | \(-0.674941\pi\) | ||||
−0.522339 | + | 0.852738i | \(0.674941\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.12973e6 | 0.509829 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.16097e6 | 0.748259 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.75292e6 | 1.11261 | 0.556307 | − | 0.830977i | \(-0.312218\pi\) | ||||
0.556307 | + | 0.830977i | \(0.312218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −216712. | −0.0501696 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.20352e6 | −0.504511 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.13728e6 | 0.478707 | 0.239354 | − | 0.970932i | \(-0.423064\pi\) | ||||
0.239354 | + | 0.970932i | \(0.423064\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.81723e6 | −0.402604 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.72920e6 | 0.378959 | 0.189479 | − | 0.981885i | \(-0.439320\pi\) | ||||
0.189479 | + | 0.981885i | \(0.439320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.54367e6 | 1.41863 | 0.709315 | − | 0.704892i | \(-0.249004\pi\) | ||||
0.709315 | + | 0.704892i | \(0.249004\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −410835. | −0.0881119 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.79419e6 | −0.380694 | −0.190347 | − | 0.981717i | \(-0.560961\pi\) | ||||
−0.190347 | + | 0.981717i | \(0.560961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.45194e6 | 1.13240 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.86549e6 | 0.383390 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.99780e6 | 1.82979 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.31690e6 | −0.667477 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.09403e6 | 0.815289 | 0.407645 | − | 0.913141i | \(-0.366350\pi\) | ||||
0.407645 | + | 0.913141i | \(0.366350\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50417e6 | 0.887670 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.47448e6 | −0.477672 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.45210e6 | 0.850634 | 0.425317 | − | 0.905045i | \(-0.360163\pi\) | ||||
0.425317 | + | 0.905045i | \(0.360163\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.06265e6 | −0.579196 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.09674e6 | −1.32848 | −0.664240 | − | 0.747519i | \(-0.731245\pi\) | ||||
−0.664240 | + | 0.747519i | \(0.731245\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.27875e6 | −0.236957 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.25778e6 | 0.230723 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.41903e6 | −1.69338 | −0.846691 | − | 0.532085i | \(-0.821409\pi\) | ||||
−0.846691 | + | 0.532085i | \(0.821409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 141663. | 0.0252152 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 957258. | 0.168698 | 0.0843489 | − | 0.996436i | \(-0.473119\pi\) | ||||
0.0843489 | + | 0.996436i | \(0.473119\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.31854e6 | −1.27702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −709093. | −0.122513 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.01453e6 | 0.686816 | 0.343408 | − | 0.939186i | \(-0.388419\pi\) | ||||
0.343408 | + | 0.939186i | \(0.388419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.40947e6 | 0.739764 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.20669e7 | −2.00483 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.32766e6 | −0.218455 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 554478. | 0.0903578 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.31820e6 | 0.696960 | 0.348480 | − | 0.937316i | \(-0.386698\pi\) | ||||
0.348480 | + | 0.937316i | \(0.386698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.34501e6 | 0.215017 | 0.107508 | − | 0.994204i | \(-0.465713\pi\) | ||||
0.107508 | + | 0.994204i | \(0.465713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 163811. | 0.0256931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.87626e6 | −0.912980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −622212. | −0.0957640 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.53342e6 | 0.233799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.28692e7 | −1.94388 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.36378e6 | −0.802667 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.06006e6 | −1.03709 | −0.518543 | − | 0.855051i | \(-0.673526\pi\) | ||||
−0.518543 | + | 0.855051i | \(0.673526\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.44754e6 | −0.356229 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.51211e6 | 0.939140 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.23520e7 | 1.76510 | 0.882549 | − | 0.470221i | \(-0.155826\pi\) | ||||
0.882549 | + | 0.470221i | \(0.155826\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.67509e6 | −0.237196 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.10287e6 | 0.435396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.79002e6 | −1.07351 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.22251e7 | −1.66961 | −0.834803 | − | 0.550549i | \(-0.814418\pi\) | ||||
−0.834803 | + | 0.550549i | \(0.814418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.32000e7 | −1.78666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 459060. | 0.0615832 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −812527. | −0.108036 | −0.0540178 | − | 0.998540i | \(-0.517203\pi\) | ||||
−0.0540178 | + | 0.998540i | \(0.517203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.57772e7 | 3.39715 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.43881e6 | −1.09270 | −0.546350 | − | 0.837557i | \(-0.683983\pi\) | ||||
−0.546350 | + | 0.837557i | \(0.683983\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.71511e6 | −0.476849 | −0.238425 | − | 0.971161i | \(-0.576631\pi\) | ||||
−0.238425 | + | 0.971161i | \(0.576631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.41813e6 | 0.689387 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.08695e6 | −0.767768 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.30375e7 | −1.63025 | −0.815126 | − | 0.579284i | \(-0.803332\pi\) | ||||
−0.815126 | + | 0.579284i | \(0.803332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.51217e6 | −0.187458 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.44278e6 | 0.297654 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.89984e6 | −1.07521 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.15227e7 | 1.38026 | 0.690128 | − | 0.723687i | \(-0.257554\pi\) | ||||
0.690128 | + | 0.723687i | \(0.257554\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −397485. | −0.0472098 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.08417e6 | −0.480989 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.20103e7 | 1.40254 | 0.701271 | − | 0.712895i | \(-0.252616\pi\) | ||||
0.701271 | + | 0.712895i | \(0.252616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.96815e6 | 0.570504 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.17460e6 | 0.133759 | 0.0668794 | − | 0.997761i | \(-0.478696\pi\) | ||||
0.0668794 | + | 0.997761i | \(0.478696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.62934e7 | 1.84003 | 0.920014 | − | 0.391886i | \(-0.128177\pi\) | ||||
0.920014 | + | 0.391886i | \(0.128177\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.56879e6 | −0.847683 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.61621e7 | 1.79519 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.82629e6 | −0.201186 | −0.100593 | − | 0.994928i | \(-0.532074\pi\) | ||||
−0.100593 | + | 0.994928i | \(0.532074\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.39436e6 | 1.01804 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.10271e6 | −0.548466 | −0.274233 | − | 0.961663i | \(-0.588424\pi\) | ||||
−0.274233 | + | 0.961663i | \(0.588424\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.65207e6 | −0.282747 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.03920e6 | −0.850158 | −0.425079 | − | 0.905156i | \(-0.639754\pi\) | ||||
−0.425079 | + | 0.905156i | \(0.639754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.60132e6 | 0.902274 | 0.451137 | − | 0.892455i | \(-0.351019\pi\) | ||||
0.451137 | + | 0.892455i | \(0.351019\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.98298e6 | −0.310399 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.09695e7 | 3.17128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.11390e6 | −0.113156 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.10610e6 | 0.313032 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.21151e6 | −0.621046 | −0.310523 | − | 0.950566i | \(-0.600504\pi\) | ||||
−0.310523 | + | 0.950566i | \(0.600504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.17833e6 | 0.216080 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.14250e7 | 2.10856 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.12995e6 | 0.109473 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.45143e6 | 0.427912 | 0.213956 | − | 0.976843i | \(-0.431365\pi\) | ||||
0.213956 | + | 0.976843i | \(0.431365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.58708e7 | 1.51381 | 0.756907 | − | 0.653523i | \(-0.226710\pi\) | ||||
0.756907 | + | 0.653523i | \(0.226710\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.28295e7 | 2.16071 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.65619e6 | −0.343375 | −0.171687 | − | 0.985151i | \(-0.554922\pi\) | ||||
−0.171687 | + | 0.985151i | \(0.554922\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 458237. | 0.0427049 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.15039e6 | −0.380896 | −0.190448 | − | 0.981697i | \(-0.560994\pi\) | ||||
−0.190448 | + | 0.981697i | \(0.560994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00832e7 | −2.73981 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.32967e6 | −0.120179 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.33739e7 | 1.19962 | 0.599810 | − | 0.800143i | \(-0.295243\pi\) | ||||
0.599810 | + | 0.800143i | \(0.295243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.82641e6 | 0.874764 | 0.437382 | − | 0.899276i | \(-0.355906\pi\) | ||||
0.437382 | + | 0.899276i | \(0.355906\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.24824e6 | −0.286989 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.09907e6 | −0.182689 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.48248e6 | −0.646369 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.23365e6 | 0.105775 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 401148. | 0.0341403 | 0.0170702 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170702 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.24185e7 | 2.73863 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.07302e7 | −1.73833 | −0.869164 | − | 0.494524i | \(-0.835343\pi\) | ||||
−0.869164 | + | 0.494524i | \(0.835343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.36534e7 | −1.12817 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.91996e7 | 1.57485 | 0.787427 | − | 0.616409i | \(-0.211413\pi\) | ||||
0.787427 | + | 0.616409i | \(0.211413\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.99978e7 | −1.62838 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.22972e6 | 0.746100 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.72847e7 | −1.38712 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.13093e7 | −0.901033 | −0.450517 | − | 0.892768i | \(-0.648760\pi\) | ||||
−0.450517 | + | 0.892768i | \(0.648760\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.24497e7 | 1.76299 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.05746e6 | 0.0824480 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.06435e6 | 0.237217 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.92159e7 | −1.47695 | −0.738473 | − | 0.674283i | \(-0.764453\pi\) | ||||
−0.738473 | + | 0.674283i | \(0.764453\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.53689e6 | −0.575180 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.62477e7 | −1.23117 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.64480e6 | 0.421729 | 0.210864 | − | 0.977515i | \(-0.432372\pi\) | ||||
0.210864 | + | 0.977515i | \(0.432372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −917268. | −0.0680491 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 268896. | 0.0198089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.55441e6 | 0.479478 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.61166e6 | −0.335011 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.42077e6 | 0.318916 | 0.159458 | − | 0.987205i | \(-0.449025\pi\) | ||||
0.159458 | + | 0.987205i | \(0.449025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.72436e6 | 0.620709 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.28124e7 | 1.61185 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.92503e7 | 1.35083 | 0.675416 | − | 0.737437i | \(-0.263964\pi\) | ||||
0.675416 | + | 0.737437i | \(0.263964\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.19758e7 | 0.834611 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.10277e6 | −0.630057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.30187e7 | −0.894966 | −0.447483 | − | 0.894292i | \(-0.647680\pi\) | ||||
−0.447483 | + | 0.894292i | \(0.647680\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.57414e6 | 0.378015 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.70955e7 | 1.15152 | 0.575758 | − | 0.817620i | \(-0.304707\pi\) | ||||
0.575758 | + | 0.817620i | \(0.304707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.88180e6 | 0.527327 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.36546e7 | −1.57197 | −0.785984 | − | 0.618247i | \(-0.787843\pi\) | ||||
−0.785984 | + | 0.618247i | \(0.787843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.11233e7 | 2.05445 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.27454e7 | 0.835705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 166564. | 0.0107766 | 0.00538828 | − | 0.999985i | \(-0.498285\pi\) | ||||
0.00538828 | + | 0.999985i | \(0.498285\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.36111e7 | 0.874794 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.16961e7 | −1.38520 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.63842e6 | −0.294192 | −0.147096 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147096 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 753546. | 0.0474794 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.96999e6 | 0.436285 | 0.218143 | − | 0.975917i | \(-0.430000\pi\) | ||||
0.218143 | + | 0.975917i | \(0.430000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.13738e6 | −0.379166 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.24242e6 | −0.199013 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.02590e6 | −0.184518 | −0.0922590 | − | 0.995735i | \(-0.529409\pi\) | ||||
−0.0922590 | + | 0.995735i | \(0.529409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 604967. | 0.0366518 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.78539e7 | −1.67663 | −0.838314 | − | 0.545188i | \(-0.816458\pi\) | ||||
−0.838314 | + | 0.545188i | \(0.816458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.92232e6 | −0.174772 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.56589e6 | −0.151494 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −832170. | −0.0488185 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.11795e7 | 0.651653 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.36804e7 | 3.10915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.87913e7 | 1.65701 | 0.828503 | − | 0.559985i | \(-0.189193\pi\) | ||||
0.828503 | + | 0.559985i | \(0.189193\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.66253e7 | 0.950773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.72910e6 | −0.492931 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.98942e7 | 1.67753 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.67489e6 | 0.204927 | 0.102463 | − | 0.994737i | \(-0.467328\pi\) | ||||
0.102463 | + | 0.994737i | \(0.467328\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.47841e6 | 0.359006 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.54650e6 | 0.140237 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 979251. | 0.0535926 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.29894e7 | −0.702108 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.04012e7 | −0.558744 | −0.279372 | − | 0.960183i | \(-0.590126\pi\) | ||||
−0.279372 | + | 0.960183i | \(0.590126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.53749e7 | −0.820844 | −0.410422 | − | 0.911896i | \(-0.634619\pi\) | ||||
−0.410422 | + | 0.911896i | \(0.634619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.90191e7 | −1.00917 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.01552e7 | −1.59026 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.20877e7 | 1.15770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.91243e7 | 0.990209 | 0.495104 | − | 0.868834i | \(-0.335130\pi\) | ||||
0.495104 | + | 0.868834i | \(0.335130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.88895e6 | −0.148676 | −0.0743381 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743381 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.18942e6 | −0.418908 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.99201e7 | 1.01281 | 0.506406 | − | 0.862295i | \(-0.330974\pi\) | ||||
0.506406 | + | 0.862295i | \(0.330974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.19726e7 | 0.605065 | 0.302532 | − | 0.953139i | \(-0.402168\pi\) | ||||
0.302532 | + | 0.953139i | \(0.402168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.59834e7 | −0.802909 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.39483e6 | 0.0692316 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.43211e6 | −0.0706584 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.43453e7 | −0.703568 | −0.351784 | − | 0.936081i | \(-0.614425\pi\) | ||||
−0.351784 | + | 0.936081i | \(0.614425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.26444e7 | −0.616463 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.36657e7 | 0.662313 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.98181e6 | −0.336377 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.55888e7 | 0.742239 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.09865e6 | 0.241341 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.41859e7 | 0.667551 | 0.333776 | − | 0.942653i | \(-0.391677\pi\) | ||||
0.333776 | + | 0.942653i | \(0.391677\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.48922e7 | 0.696698 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.41394e7 | −1.12273 | −0.561363 | − | 0.827570i | \(-0.689723\pi\) | ||||
−0.561363 | + | 0.827570i | \(0.689723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.37343e7 | 0.635071 | 0.317536 | − | 0.948246i | \(-0.397145\pi\) | ||||
0.317536 | + | 0.948246i | \(0.397145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.74905e7 | −0.799419 | −0.399709 | − | 0.916642i | \(-0.630889\pi\) | ||||
−0.399709 | + | 0.916642i | \(0.630889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.45945e6 | 0.248090 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.30609e7 | 0.590101 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 675534. | 0.0303458 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.94418e7 | −1.76162 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.95872e6 | −0.131392 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.51221e7 | −1.54199 | −0.770995 | − | 0.636842i | \(-0.780241\pi\) | ||||
−0.770995 | + | 0.636842i | \(0.780241\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.95510e6 | 0.172658 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.78528e6 | 0.381343 | 0.190672 | − | 0.981654i | \(-0.438933\pi\) | ||||
0.190672 | + | 0.981654i | \(0.438933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.87501e7 | −0.809287 | −0.404643 | − | 0.914475i | \(-0.632604\pi\) | ||||
−0.404643 | + | 0.914475i | \(0.632604\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.60781e6 | 0.240677 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.72434e7 | −1.16266 | −0.581330 | − | 0.813668i | \(-0.697468\pi\) | ||||
−0.581330 | + | 0.813668i | \(0.697468\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.13279e6 | −0.0478030 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.57197e7 | −0.659654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.28124e7 | −2.20383 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.33198e6 | −0.221262 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00775e6 | −0.0415868 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.19197e7 | −0.489161 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.40987e7 | −0.978076 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.90420e7 | −1.17222 | −0.586110 | − | 0.810232i | \(-0.699341\pi\) | ||||
−0.586110 | + | 0.810232i | \(0.699341\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.75071e6 | −0.351264 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.12057e7 | −1.64498 | −0.822491 | − | 0.568778i | \(-0.807417\pi\) | ||||
−0.822491 | + | 0.568778i | \(0.807417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.38655e6 | −0.372674 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.50971e7 | 0.596130 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.04768e7 | −1.19037 | −0.595184 | − | 0.803589i | \(-0.702921\pi\) | ||||
−0.595184 | + | 0.803589i | \(0.702921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.41473e6 | 0.0549574 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.88831e6 | 0.227503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.54114e7 | −2.12934 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.44283e7 | −0.551460 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.60640e7 | 1.37099 | 0.685495 | − | 0.728077i | \(-0.259586\pi\) | ||||
0.685495 | + | 0.728077i | \(0.259586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.51598e7 | 0.946243 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.51996e6 | 0.169085 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.80602e7 | −1.78828 | −0.894141 | − | 0.447785i | \(-0.852213\pi\) | ||||
−0.894141 | + | 0.447785i | \(0.852213\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.32800e6 | −0.308231 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.28577e7 | 1.57781 | 0.788906 | − | 0.614514i | \(-0.210648\pi\) | ||||
0.788906 | + | 0.614514i | \(0.210648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.73581e6 | 0.0635657 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.32432e7 | −1.56690 | −0.783452 | − | 0.621452i | \(-0.786543\pi\) | ||||
−0.783452 | + | 0.621452i | \(0.786543\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.92904e6 | −0.249751 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.65045e6 | −0.202596 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.81115e7 | −1.00265 | −0.501327 | − | 0.865258i | \(-0.667155\pi\) | ||||
−0.501327 | + | 0.865258i | \(0.667155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.33476e7 | 1.89281 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.82410e6 | −0.0996783 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.85001e7 | −0.995491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.53876e7 | −0.534695 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.48890e7 | −0.514691 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.70437e7 | −1.27394 | −0.636968 | − | 0.770890i | \(-0.719812\pi\) | ||||
−0.636968 | + | 0.770890i | \(0.719812\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.43533e6 | 0.185959 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.58140e7 | −1.55937 | −0.779686 | − | 0.626170i | \(-0.784621\pi\) | ||||
−0.779686 | + | 0.626170i | \(0.784621\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.79471e7 | 1.95218 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.17497e6 | 0.0393812 | 0.0196906 | − | 0.999806i | \(-0.493732\pi\) | ||||
0.0196906 | + | 0.999806i | \(0.493732\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.87540e6 | −0.0625372 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.78647e6 | 0.258326 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.63520e7 | −0.869822 | −0.434911 | − | 0.900474i | \(-0.643220\pi\) | ||||
−0.434911 | + | 0.900474i | \(0.643220\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.02132e7 | −1.32062 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.49422e7 | −0.485761 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.82424e7 | −1.23697 | −0.618487 | − | 0.785795i | \(-0.712254\pi\) | ||||
−0.618487 | + | 0.785795i | \(0.712254\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.80674e6 | 0.219062 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.89170e7 | 1.56640 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.36919e7 | −1.39208 | −0.696038 | − | 0.718005i | \(-0.745055\pi\) | ||||
−0.696038 | + | 0.718005i | \(0.745055\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.71549e7 | −0.860865 |
(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 | 784.6.a.bb.1.1 | 2 | ||
4.3 | odd | 2 | 98.6.a.g.1.2 | 2 | |||
7.3 | odd | 6 | 112.6.i.d.65.1 | 4 | |||
7.5 | odd | 6 | 112.6.i.d.81.1 | 4 | |||
7.6 | odd | 2 | 784.6.a.s.1.2 | 2 | |||
12.11 | even | 2 | 882.6.a.bi.1.2 | 2 | |||
28.3 | even | 6 | 14.6.c.a.9.2 | ✓ | 4 | ||
28.11 | odd | 6 | 98.6.c.e.79.1 | 4 | |||
28.19 | even | 6 | 14.6.c.a.11.2 | yes | 4 | ||
28.23 | odd | 6 | 98.6.c.e.67.1 | 4 | |||
28.27 | even | 2 | 98.6.a.h.1.1 | 2 | |||
84.47 | odd | 6 | 126.6.g.j.109.2 | 4 | |||
84.59 | odd | 6 | 126.6.g.j.37.2 | 4 | |||
84.83 | odd | 2 | 882.6.a.ba.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.a.9.2 | ✓ | 4 | 28.3 | even | 6 | ||
14.6.c.a.11.2 | yes | 4 | 28.19 | even | 6 | ||
98.6.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
98.6.a.h.1.1 | 2 | 28.27 | even | 2 | |||
98.6.c.e.67.1 | 4 | 28.23 | odd | 6 | |||
98.6.c.e.79.1 | 4 | 28.11 | odd | 6 | |||
112.6.i.d.65.1 | 4 | 7.3 | odd | 6 | |||
112.6.i.d.81.1 | 4 | 7.5 | odd | 6 | |||
126.6.g.j.37.2 | 4 | 84.59 | odd | 6 | |||
126.6.g.j.109.2 | 4 | 84.47 | odd | 6 | |||
784.6.a.s.1.2 | 2 | 7.6 | odd | 2 | |||
784.6.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial | ||
882.6.a.ba.1.1 | 2 | 84.83 | odd | 2 | |||
882.6.a.bi.1.2 | 2 | 12.11 | even | 2 |