Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,6,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("225.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(36.0863594579\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −28.0000 | −0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 132.000 | 1.01819 | 0.509095 | − | 0.860710i | \(-0.329980\pi\) | ||||
0.509095 | + | 0.860710i | \(0.329980\pi\) | |||||||
\(8\) | 120.000 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −472.000 | −1.17614 | −0.588072 | − | 0.808809i | \(-0.700113\pi\) | ||||
−0.588072 | + | 0.808809i | \(0.700113\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 686.000 | 1.12581 | 0.562906 | − | 0.826521i | \(-0.309683\pi\) | ||||
0.562906 | + | 0.826521i | \(0.309683\pi\) | |||||||
\(14\) | −264.000 | −0.359985 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 656.000 | 0.640625 | ||||||||
\(17\) | −1562.00 | −1.31087 | −0.655434 | − | 0.755253i | \(-0.727514\pi\) | ||||
−0.655434 | + | 0.755253i | \(0.727514\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2180.00 | −1.38539 | −0.692696 | − | 0.721230i | \(-0.743577\pi\) | ||||
−0.692696 | + | 0.721230i | \(0.743577\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 944.000 | 0.415829 | ||||||||
\(23\) | 264.000 | 0.104060 | 0.0520301 | − | 0.998646i | \(-0.483431\pi\) | ||||
0.0520301 | + | 0.998646i | \(0.483431\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1372.00 | −0.398035 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3696.00 | −0.890916 | ||||||||
\(29\) | −170.000 | −0.0375365 | −0.0187683 | − | 0.999824i | \(-0.505974\pi\) | ||||
−0.0187683 | + | 0.999824i | \(0.505974\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7272.00 | 1.35909 | 0.679547 | − | 0.733632i | \(-0.262176\pi\) | ||||
0.679547 | + | 0.733632i | \(0.262176\pi\) | |||||||
\(32\) | −5152.00 | −0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3124.00 | 0.463462 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 142.000 | 0.0170523 | 0.00852617 | − | 0.999964i | \(-0.497286\pi\) | ||||
0.00852617 | + | 0.999964i | \(0.497286\pi\) | |||||||
\(38\) | 4360.00 | 0.489810 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16198.0 | 1.50488 | 0.752440 | − | 0.658661i | \(-0.228877\pi\) | ||||
0.752440 | + | 0.658661i | \(0.228877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10316.0 | 0.850825 | 0.425412 | − | 0.905000i | \(-0.360129\pi\) | ||||
0.425412 | + | 0.905000i | \(0.360129\pi\) | |||||||
\(44\) | 13216.0 | 1.02913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −528.000 | −0.0367908 | ||||||||
\(47\) | 18568.0 | 1.22608 | 0.613042 | − | 0.790050i | \(-0.289945\pi\) | ||||
0.613042 | + | 0.790050i | \(0.289945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 617.000 | 0.0367109 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19208.0 | −0.985085 | ||||||||
\(53\) | 21514.0 | 1.05204 | 0.526019 | − | 0.850473i | \(-0.323684\pi\) | ||||
0.526019 | + | 0.850473i | \(0.323684\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 15840.0 | 0.674971 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 340.000 | 0.0132712 | ||||||||
\(59\) | −34600.0 | −1.29404 | −0.647018 | − | 0.762475i | \(-0.723984\pi\) | ||||
−0.647018 | + | 0.762475i | \(0.723984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −35738.0 | −1.22972 | −0.614859 | − | 0.788637i | \(-0.710787\pi\) | ||||
−0.614859 | + | 0.788637i | \(0.710787\pi\) | |||||||
\(62\) | −14544.0 | −0.480512 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5772.00 | 0.157087 | 0.0785433 | − | 0.996911i | \(-0.474973\pi\) | ||||
0.0785433 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(68\) | 43736.0 | 1.14701 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 69088.0 | 1.62651 | 0.813255 | − | 0.581907i | \(-0.197693\pi\) | ||||
0.813255 | + | 0.581907i | \(0.197693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70526.0 | 1.54897 | 0.774483 | − | 0.632594i | \(-0.218010\pi\) | ||||
0.774483 | + | 0.632594i | \(0.218010\pi\) | |||||||
\(74\) | −284.000 | −0.00602891 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 61040.0 | 1.21222 | ||||||||
\(77\) | −62304.0 | −1.19754 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 47640.0 | 0.858824 | 0.429412 | − | 0.903109i | \(-0.358721\pi\) | ||||
0.429412 | + | 0.903109i | \(0.358721\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −32396.0 | −0.532055 | ||||||||
\(83\) | 74004.0 | 1.17913 | 0.589563 | − | 0.807723i | \(-0.299300\pi\) | ||||
0.589563 | + | 0.807723i | \(0.299300\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −20632.0 | −0.300812 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −56640.0 | −0.779680 | ||||||||
\(89\) | 90030.0 | 1.20479 | 0.602396 | − | 0.798197i | \(-0.294213\pi\) | ||||
0.602396 | + | 0.798197i | \(0.294213\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 90552.0 | 1.14629 | ||||||||
\(92\) | −7392.00 | −0.0910526 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −37136.0 | −0.433486 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 33502.0 | 0.361528 | 0.180764 | − | 0.983527i | \(-0.442143\pi\) | ||||
0.180764 | + | 0.983527i | \(0.442143\pi\) | |||||||
\(98\) | −1234.00 | −0.0129793 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −78882.0 | −0.769440 | −0.384720 | − | 0.923033i | \(-0.625702\pi\) | ||||
−0.384720 | + | 0.923033i | \(0.625702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 82036.0 | 0.761924 | 0.380962 | − | 0.924591i | \(-0.375593\pi\) | ||||
0.380962 | + | 0.924591i | \(0.375593\pi\) | |||||||
\(104\) | 82320.0 | 0.746315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −43028.0 | −0.371952 | ||||||||
\(107\) | −41652.0 | −0.351703 | −0.175852 | − | 0.984417i | \(-0.556268\pi\) | ||||
−0.175852 | + | 0.984417i | \(0.556268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 104870. | 0.845444 | 0.422722 | − | 0.906259i | \(-0.361075\pi\) | ||||
0.422722 | + | 0.906259i | \(0.361075\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 86592.0 | 0.652278 | ||||||||
\(113\) | −153746. | −1.13268 | −0.566341 | − | 0.824171i | \(-0.691641\pi\) | ||||
−0.566341 | + | 0.824171i | \(0.691641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4760.00 | 0.0328444 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 69200.0 | 0.457511 | ||||||||
\(119\) | −206184. | −1.33471 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 61733.0 | 0.383313 | ||||||||
\(122\) | 71476.0 | 0.434771 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −203616. | −1.18921 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 59372.0 | 0.326642 | 0.163321 | − | 0.986573i | \(-0.447779\pi\) | ||||
0.163321 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(128\) | 186240. | 1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 98808.0 | 0.503053 | 0.251527 | − | 0.967850i | \(-0.419067\pi\) | ||||
0.251527 | + | 0.967850i | \(0.419067\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −287760. | −1.41059 | ||||||||
\(134\) | −11544.0 | −0.0555385 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −187440. | −0.868990 | ||||||||
\(137\) | 306918. | 1.39708 | 0.698539 | − | 0.715572i | \(-0.253834\pi\) | ||||
0.698539 | + | 0.715572i | \(0.253834\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −36820.0 | −0.161639 | −0.0808196 | − | 0.996729i | \(-0.525754\pi\) | ||||
−0.0808196 | + | 0.996729i | \(0.525754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −138176. | −0.575058 | ||||||||
\(143\) | −323792. | −1.32412 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −141052. | −0.547642 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3976.00 | −0.0149208 | ||||||||
\(149\) | 138070. | 0.509488 | 0.254744 | − | 0.967009i | \(-0.418009\pi\) | ||||
0.254744 | + | 0.967009i | \(0.418009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −362408. | −1.29347 | −0.646734 | − | 0.762716i | \(-0.723865\pi\) | ||||
−0.646734 | + | 0.762716i | \(0.723865\pi\) | |||||||
\(152\) | −261600. | −0.918393 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 124608. | 0.423393 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −246098. | −0.796818 | −0.398409 | − | 0.917208i | \(-0.630437\pi\) | ||||
−0.398409 | + | 0.917208i | \(0.630437\pi\) | |||||||
\(158\) | −95280.0 | −0.303640 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 34848.0 | 0.105953 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −170084. | −0.501412 | −0.250706 | − | 0.968063i | \(-0.580663\pi\) | ||||
−0.250706 | + | 0.968063i | \(0.580663\pi\) | |||||||
\(164\) | −453544. | −1.31677 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −148008. | −0.416884 | ||||||||
\(167\) | 274008. | 0.760277 | 0.380139 | − | 0.924929i | \(-0.375876\pi\) | ||||
0.380139 | + | 0.924929i | \(0.375876\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 99303.0 | 0.267452 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −288848. | −0.744472 | ||||||||
\(173\) | −281886. | −0.716075 | −0.358037 | − | 0.933707i | \(-0.616554\pi\) | ||||
−0.358037 | + | 0.933707i | \(0.616554\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −309632. | −0.753467 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −180060. | −0.425958 | ||||||||
\(179\) | 110240. | 0.257162 | 0.128581 | − | 0.991699i | \(-0.458958\pi\) | ||||
0.128581 | + | 0.991699i | \(0.458958\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 693182. | 1.57272 | 0.786359 | − | 0.617770i | \(-0.211964\pi\) | ||||
0.786359 | + | 0.617770i | \(0.211964\pi\) | |||||||
\(182\) | −181104. | −0.405275 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 31680.0 | 0.0689828 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 737264. | 1.54177 | ||||||||
\(188\) | −519904. | −1.07282 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −374792. | −0.743373 | −0.371687 | − | 0.928358i | \(-0.621220\pi\) | ||||
−0.371687 | + | 0.928358i | \(0.621220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −247754. | −0.478771 | −0.239385 | − | 0.970925i | \(-0.576946\pi\) | ||||
−0.239385 | + | 0.970925i | \(0.576946\pi\) | |||||||
\(194\) | −67004.0 | −0.127819 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17276.0 | −0.0321220 | ||||||||
\(197\) | 373578. | 0.685829 | 0.342914 | − | 0.939367i | \(-0.388586\pi\) | ||||
0.342914 | + | 0.939367i | \(0.388586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −482840. | −0.864312 | −0.432156 | − | 0.901799i | \(-0.642247\pi\) | ||||
−0.432156 | + | 0.901799i | \(0.642247\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 157764. | 0.272038 | ||||||||
\(203\) | −22440.0 | −0.0382193 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −164072. | −0.269381 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 450016. | 0.721223 | ||||||||
\(209\) | 1.02896e6 | 1.62942 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −708748. | −1.09594 | −0.547969 | − | 0.836499i | \(-0.684599\pi\) | ||||
−0.547969 | + | 0.836499i | \(0.684599\pi\) | |||||||
\(212\) | −602392. | −0.920533 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 83304.0 | 0.124346 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 959904. | 1.38382 | ||||||||
\(218\) | −209740. | −0.298910 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.07153e6 | −1.47579 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 211036. | 0.284181 | 0.142090 | − | 0.989854i | \(-0.454618\pi\) | ||||
0.142090 | + | 0.989854i | \(0.454618\pi\) | |||||||
\(224\) | −680064. | −0.905586 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 307492. | 0.400463 | ||||||||
\(227\) | 920828. | 1.18608 | 0.593040 | − | 0.805173i | \(-0.297928\pi\) | ||||
0.593040 | + | 0.805173i | \(0.297928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −71130.0 | −0.0896322 | −0.0448161 | − | 0.998995i | \(-0.514270\pi\) | ||||
−0.0448161 | + | 0.998995i | \(0.514270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −20400.0 | −0.0248834 | ||||||||
\(233\) | 1.00049e6 | 1.20733 | 0.603663 | − | 0.797239i | \(-0.293707\pi\) | ||||
0.603663 | + | 0.797239i | \(0.293707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 968800. | 1.13228 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 412368. | 0.471892 | ||||||||
\(239\) | 550520. | 0.623417 | 0.311708 | − | 0.950178i | \(-0.399099\pi\) | ||||
0.311708 | + | 0.950178i | \(0.399099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 543682. | 0.602979 | 0.301490 | − | 0.953469i | \(-0.402516\pi\) | ||||
0.301490 | + | 0.953469i | \(0.402516\pi\) | |||||||
\(242\) | −123466. | −0.135522 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.00066e6 | 1.07600 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.49548e6 | −1.55969 | ||||||||
\(248\) | 872640. | 0.900961 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 659568. | 0.660808 | 0.330404 | − | 0.943840i | \(-0.392815\pi\) | ||||
0.330404 | + | 0.943840i | \(0.392815\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −124608. | −0.122390 | ||||||||
\(254\) | −118744. | −0.115485 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30464.0 | −0.0290527 | ||||||||
\(257\) | −1.54600e6 | −1.46008 | −0.730041 | − | 0.683403i | \(-0.760499\pi\) | ||||
−0.730041 | + | 0.683403i | \(0.760499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18744.0 | 0.0173625 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −197616. | −0.177856 | ||||||||
\(263\) | −96856.0 | −0.0863450 | −0.0431725 | − | 0.999068i | \(-0.513747\pi\) | ||||
−0.0431725 | + | 0.999068i | \(0.513747\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 575520. | 0.498719 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −161616. | −0.137451 | ||||||||
\(269\) | −83530.0 | −0.0703820 | −0.0351910 | − | 0.999381i | \(-0.511204\pi\) | ||||
−0.0351910 | + | 0.999381i | \(0.511204\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −857888. | −0.709590 | −0.354795 | − | 0.934944i | \(-0.615449\pi\) | ||||
−0.354795 | + | 0.934944i | \(0.615449\pi\) | |||||||
\(272\) | −1.02467e6 | −0.839774 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −613836. | −0.493942 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −647538. | −0.507068 | −0.253534 | − | 0.967327i | \(-0.581593\pi\) | ||||
−0.253534 | + | 0.967327i | \(0.581593\pi\) | |||||||
\(278\) | 73640.0 | 0.0571481 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.21480e6 | 1.67328 | 0.836639 | − | 0.547754i | \(-0.184517\pi\) | ||||
0.836639 | + | 0.547754i | \(0.184517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 156276. | 0.115992 | 0.0579958 | − | 0.998317i | \(-0.481529\pi\) | ||||
0.0579958 | + | 0.998317i | \(0.481529\pi\) | |||||||
\(284\) | −1.93446e6 | −1.42320 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 647584. | 0.468146 | ||||||||
\(287\) | 2.13814e6 | 1.53225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.01999e6 | 0.718373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.97473e6 | −1.35535 | ||||||||
\(293\) | −56406.0 | −0.0383845 | −0.0191923 | − | 0.999816i | \(-0.506109\pi\) | ||||
−0.0191923 | + | 0.999816i | \(0.506109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17040.0 | 0.0113042 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −276140. | −0.180131 | ||||||||
\(299\) | 181104. | 0.117152 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.36171e6 | 0.866301 | ||||||||
\(302\) | 724816. | 0.457310 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.43008e6 | −0.887516 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.76061e6 | 1.06615 | 0.533074 | − | 0.846068i | \(-0.321037\pi\) | ||||
0.533074 | + | 0.846068i | \(0.321037\pi\) | |||||||
\(308\) | 1.74451e6 | 1.04785 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.71389e6 | 1.00480 | 0.502402 | − | 0.864634i | \(-0.332450\pi\) | ||||
0.502402 | + | 0.864634i | \(0.332450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.42877e6 | 0.824328 | 0.412164 | − | 0.911110i | \(-0.364773\pi\) | ||||
0.412164 | + | 0.911110i | \(0.364773\pi\) | |||||||
\(314\) | 492196. | 0.281718 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.33392e6 | −0.751471 | ||||||||
\(317\) | −744382. | −0.416052 | −0.208026 | − | 0.978123i | \(-0.566704\pi\) | ||||
−0.208026 | + | 0.978123i | \(0.566704\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 80240.0 | 0.0441483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −69696.0 | −0.0374600 | ||||||||
\(323\) | 3.40516e6 | 1.81606 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 340168. | 0.177276 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.94376e6 | 0.997604 | ||||||||
\(329\) | 2.45098e6 | 1.24839 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −136908. | −0.0686845 | −0.0343423 | − | 0.999410i | \(-0.510934\pi\) | ||||
−0.0343423 | + | 0.999410i | \(0.510934\pi\) | |||||||
\(332\) | −2.07211e6 | −1.03173 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −548016. | −0.268799 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.43594e6 | 1.16840 | 0.584201 | − | 0.811609i | \(-0.301408\pi\) | ||||
0.584201 | + | 0.811609i | \(0.301408\pi\) | |||||||
\(338\) | −198606. | −0.0945585 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.43238e6 | −1.59849 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.13708e6 | −0.980811 | ||||||||
\(344\) | 1.23792e6 | 0.564023 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 563772. | 0.253171 | ||||||||
\(347\) | 1.16127e6 | 0.517736 | 0.258868 | − | 0.965913i | \(-0.416650\pi\) | ||||
0.258868 | + | 0.965913i | \(0.416650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 725830. | 0.318986 | 0.159493 | − | 0.987199i | \(-0.449014\pi\) | ||||
0.159493 | + | 0.987199i | \(0.449014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.43174e6 | 1.04607 | ||||||||
\(353\) | −3.94867e6 | −1.68661 | −0.843303 | − | 0.537438i | \(-0.819392\pi\) | ||||
−0.843303 | + | 0.537438i | \(0.819392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.52084e6 | −1.05419 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −220480. | −0.0909205 | ||||||||
\(359\) | −1.21188e6 | −0.496276 | −0.248138 | − | 0.968725i | \(-0.579819\pi\) | ||||
−0.248138 | + | 0.968725i | \(0.579819\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.27630e6 | 0.919309 | ||||||||
\(362\) | −1.38636e6 | −0.556040 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.53546e6 | −1.00300 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.92999e6 | −1.52309 | −0.761546 | − | 0.648111i | \(-0.775559\pi\) | ||||
−0.761546 | + | 0.648111i | \(0.775559\pi\) | |||||||
\(368\) | 173184. | 0.0666635 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.83985e6 | 1.07117 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.08519e6 | −0.403864 | −0.201932 | − | 0.979400i | \(-0.564722\pi\) | ||||
−0.201932 | + | 0.979400i | \(0.564722\pi\) | |||||||
\(374\) | −1.47453e6 | −0.545097 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.22816e6 | 0.812787 | ||||||||
\(377\) | −116620. | −0.0422590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.06654e6 | 1.45421 | 0.727105 | − | 0.686526i | \(-0.240865\pi\) | ||||
0.727105 | + | 0.686526i | \(0.240865\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 749584. | 0.262822 | ||||||||
\(383\) | −1.53454e6 | −0.534540 | −0.267270 | − | 0.963622i | \(-0.586122\pi\) | ||||
−0.267270 | + | 0.963622i | \(0.586122\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 495508. | 0.169271 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −938056. | −0.316337 | ||||||||
\(389\) | −1.90737e6 | −0.639088 | −0.319544 | − | 0.947571i | \(-0.603530\pi\) | ||||
−0.319544 | + | 0.947571i | \(0.603530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −412368. | −0.136409 | ||||||||
\(392\) | 74040.0 | 0.0243361 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −747156. | −0.242477 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.71162e6 | 0.545044 | 0.272522 | − | 0.962150i | \(-0.412142\pi\) | ||||
0.272522 | + | 0.962150i | \(0.412142\pi\) | |||||||
\(398\) | 965680. | 0.305580 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.46268e6 | −0.764799 | −0.382400 | − | 0.923997i | \(-0.624902\pi\) | ||||
−0.382400 | + | 0.923997i | \(0.624902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.98859e6 | 1.53008 | ||||||||
\(404\) | 2.20870e6 | 0.673260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 44880.0 | 0.0135126 | ||||||||
\(407\) | −67024.0 | −0.0200560 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.69703e6 | −1.09281 | −0.546405 | − | 0.837521i | \(-0.684004\pi\) | ||||
−0.546405 | + | 0.837521i | \(0.684004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.29701e6 | −0.666683 | ||||||||
\(413\) | −4.56720e6 | −1.31757 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.53427e6 | −1.00131 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.05792e6 | −0.576087 | ||||||||
\(419\) | 1.93060e6 | 0.537226 | 0.268613 | − | 0.963248i | \(-0.413435\pi\) | ||||
0.268613 | + | 0.963248i | \(0.413435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.83910e6 | −1.33064 | −0.665318 | − | 0.746560i | \(-0.731704\pi\) | ||||
−0.665318 | + | 0.746560i | \(0.731704\pi\) | |||||||
\(422\) | 1.41750e6 | 0.387472 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.58168e6 | 0.697409 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.71742e6 | −1.25209 | ||||||||
\(428\) | 1.16626e6 | 0.307740 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.74325e6 | 0.711331 | 0.355666 | − | 0.934613i | \(-0.384254\pi\) | ||||
0.355666 | + | 0.934613i | \(0.384254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.05823e6 | −1.55284 | −0.776419 | − | 0.630217i | \(-0.782966\pi\) | ||||
−0.776419 | + | 0.630217i | \(0.782966\pi\) | |||||||
\(434\) | −1.91981e6 | −0.489253 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.93636e6 | −0.739764 | ||||||||
\(437\) | −575520. | −0.144164 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.21044e6 | 1.29037 | 0.645183 | − | 0.764028i | \(-0.276781\pi\) | ||||
0.645183 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.14306e6 | 0.521770 | ||||||||
\(443\) | 1.17248e6 | 0.283856 | 0.141928 | − | 0.989877i | \(-0.454670\pi\) | ||||
0.141928 | + | 0.989877i | \(0.454670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −422072. | −0.100473 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.41082e6 | −0.332105 | ||||||||
\(449\) | −4.14361e6 | −0.969981 | −0.484990 | − | 0.874520i | \(-0.661177\pi\) | ||||
−0.484990 | + | 0.874520i | \(0.661177\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.64546e6 | −1.76995 | ||||||||
\(452\) | 4.30489e6 | 0.991096 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.84166e6 | −0.419343 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.41338e6 | 1.21249 | 0.606245 | − | 0.795278i | \(-0.292675\pi\) | ||||
0.606245 | + | 0.795278i | \(0.292675\pi\) | |||||||
\(458\) | 142260. | 0.0316898 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.36680e6 | −1.17615 | −0.588076 | − | 0.808806i | \(-0.700114\pi\) | ||||
−0.588076 | + | 0.808806i | \(0.700114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.33284e6 | 1.15613 | 0.578064 | − | 0.815992i | \(-0.303808\pi\) | ||||
0.578064 | + | 0.815992i | \(0.303808\pi\) | |||||||
\(464\) | −111520. | −0.0240468 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.00099e6 | −0.426854 | ||||||||
\(467\) | 5.56831e6 | 1.18149 | 0.590746 | − | 0.806857i | \(-0.298833\pi\) | ||||
0.590746 | + | 0.806857i | \(0.298833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 761904. | 0.159944 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.15200e6 | −0.857832 | ||||||||
\(473\) | −4.86915e6 | −1.00069 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.77315e6 | 1.16787 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.10104e6 | −0.220411 | ||||||||
\(479\) | 1.57092e6 | 0.312835 | 0.156417 | − | 0.987691i | \(-0.450005\pi\) | ||||
0.156417 | + | 0.987691i | \(0.450005\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 97412.0 | 0.0191977 | ||||||||
\(482\) | −1.08736e6 | −0.213185 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.72852e6 | −0.335399 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.74497e6 | 1.47978 | 0.739891 | − | 0.672727i | \(-0.234877\pi\) | ||||
0.739891 | + | 0.672727i | \(0.234877\pi\) | |||||||
\(488\) | −4.28856e6 | −0.815196 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.97715e6 | −0.370115 | −0.185057 | − | 0.982728i | \(-0.559247\pi\) | ||||
−0.185057 | + | 0.982728i | \(0.559247\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 265540. | 0.0492054 | ||||||||
\(494\) | 2.99096e6 | 0.551434 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.77043e6 | 0.870670 | ||||||||
\(497\) | 9.11962e6 | 1.65610 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.55994e6 | −1.17937 | −0.589683 | − | 0.807635i | \(-0.700747\pi\) | ||||
−0.589683 | + | 0.807635i | \(0.700747\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.31914e6 | −0.233631 | ||||||||
\(503\) | −5.92850e6 | −1.04478 | −0.522390 | − | 0.852707i | \(-0.674959\pi\) | ||||
−0.522390 | + | 0.852707i | \(0.674959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 249216. | 0.0432713 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.66242e6 | −0.285812 | ||||||||
\(509\) | 1.03055e6 | 0.176309 | 0.0881545 | − | 0.996107i | \(-0.471903\pi\) | ||||
0.0881545 | + | 0.996107i | \(0.471903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.30943e6 | 1.57714 | ||||||||
\(512\) | −5.89875e6 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.09200e6 | 0.516217 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.76410e6 | −1.44205 | ||||||||
\(518\) | −37488.0 | −0.00613858 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.48280e6 | −1.36913 | −0.684566 | − | 0.728951i | \(-0.740008\pi\) | ||||
−0.684566 | + | 0.728951i | \(0.740008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.93676e6 | −1.42865 | −0.714325 | − | 0.699814i | \(-0.753266\pi\) | ||||
−0.714325 | + | 0.699814i | \(0.753266\pi\) | |||||||
\(524\) | −2.76662e6 | −0.440172 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 193712. | 0.0305276 | ||||||||
\(527\) | −1.13589e7 | −1.78159 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.36665e6 | −0.989171 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.05728e6 | 1.23427 | ||||||||
\(533\) | 1.11118e7 | 1.69421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 692640. | 0.104135 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 167060. | 0.0248838 | ||||||||
\(539\) | −291224. | −0.0431773 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.14394e6 | 0.608724 | 0.304362 | − | 0.952556i | \(-0.401557\pi\) | ||||
0.304362 | + | 0.952556i | \(0.401557\pi\) | |||||||
\(542\) | 1.71578e6 | 0.250878 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.04742e6 | 1.16590 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.63115e6 | −0.375991 | −0.187995 | − | 0.982170i | \(-0.560199\pi\) | ||||
−0.187995 | + | 0.982170i | \(0.560199\pi\) | |||||||
\(548\) | −8.59370e6 | −1.22244 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 370600. | 0.0520028 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.28848e6 | 0.874446 | ||||||||
\(554\) | 1.29508e6 | 0.179275 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.03096e6 | 0.141434 | ||||||||
\(557\) | −1.24917e7 | −1.70602 | −0.853012 | − | 0.521892i | \(-0.825227\pi\) | ||||
−0.853012 | + | 0.521892i | \(0.825227\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.07678e6 | 0.957869 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.42960e6 | −0.591593 | ||||||||
\(563\) | 7.63892e6 | 1.01569 | 0.507845 | − | 0.861448i | \(-0.330442\pi\) | ||||
0.507845 | + | 0.861448i | \(0.330442\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −312552. | −0.0410092 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.29056e6 | 1.07823 | ||||||||
\(569\) | −455250. | −0.0589480 | −0.0294740 | − | 0.999566i | \(-0.509383\pi\) | ||||
−0.0294740 | + | 0.999566i | \(0.509383\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −259228. | −0.0332730 | −0.0166365 | − | 0.999862i | \(-0.505296\pi\) | ||||
−0.0166365 | + | 0.999862i | \(0.505296\pi\) | |||||||
\(572\) | 9.06618e6 | 1.15860 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.27627e6 | −0.541733 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.33636e7 | 1.67103 | 0.835513 | − | 0.549470i | \(-0.185170\pi\) | ||||
0.835513 | + | 0.549470i | \(0.185170\pi\) | |||||||
\(578\) | −2.03997e6 | −0.253983 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.76853e6 | 1.20057 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.01546e7 | −1.23735 | ||||||||
\(584\) | 8.46312e6 | 1.02683 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 112812. | 0.0135710 | ||||||||
\(587\) | −1.22332e7 | −1.46536 | −0.732679 | − | 0.680574i | \(-0.761730\pi\) | ||||
−0.732679 | + | 0.680574i | \(0.761730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.58530e7 | −1.88288 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 93152.0 | 0.0109242 | ||||||||
\(593\) | 1.17588e7 | 1.37318 | 0.686589 | − | 0.727046i | \(-0.259107\pi\) | ||||
0.686589 | + | 0.727046i | \(0.259107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.86596e6 | −0.445802 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −362208. | −0.0414195 | ||||||||
\(599\) | −8.58404e6 | −0.977518 | −0.488759 | − | 0.872419i | \(-0.662550\pi\) | ||||
−0.488759 | + | 0.872419i | \(0.662550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.59372e6 | −0.179980 | −0.0899902 | − | 0.995943i | \(-0.528684\pi\) | ||||
−0.0899902 | + | 0.995943i | \(0.528684\pi\) | |||||||
\(602\) | −2.72342e6 | −0.306284 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.01474e7 | 1.13178 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.52801e7 | −1.68327 | −0.841637 | − | 0.540044i | \(-0.818408\pi\) | ||||
−0.841637 | + | 0.540044i | \(0.818408\pi\) | |||||||
\(608\) | 1.12314e7 | 1.23218 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.27376e7 | 1.38034 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.67004e7 | 1.79504 | 0.897521 | − | 0.440971i | \(-0.145366\pi\) | ||||
0.897521 | + | 0.440971i | \(0.145366\pi\) | |||||||
\(614\) | −3.52122e6 | −0.376940 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.47648e6 | −0.793863 | ||||||||
\(617\) | 1.03986e7 | 1.09966 | 0.549832 | − | 0.835275i | \(-0.314692\pi\) | ||||
0.549832 | + | 0.835275i | \(0.314692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.22631e7 | −1.28640 | −0.643199 | − | 0.765699i | \(-0.722393\pi\) | ||||
−0.643199 | + | 0.765699i | \(0.722393\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.42778e6 | −0.355252 | ||||||||
\(623\) | 1.18840e7 | 1.22671 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.85753e6 | −0.291444 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.89074e6 | 0.697215 | ||||||||
\(629\) | −221804. | −0.0223534 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.22509e7 | 1.22488 | 0.612442 | − | 0.790515i | \(-0.290187\pi\) | ||||
0.612442 | + | 0.790515i | \(0.290187\pi\) | |||||||
\(632\) | 5.71680e6 | 0.569325 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.48876e6 | 0.147097 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 423262. | 0.0413296 | ||||||||
\(638\) | −160480. | −0.0156088 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.85904e6 | 0.659353 | 0.329677 | − | 0.944094i | \(-0.393060\pi\) | ||||
0.329677 | + | 0.944094i | \(0.393060\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.31120e6 | 0.315833 | 0.157916 | − | 0.987452i | \(-0.449522\pi\) | ||||
0.157916 | + | 0.987452i | \(0.449522\pi\) | |||||||
\(644\) | −975744. | −0.0927089 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.81032e6 | −0.642076 | ||||||||
\(647\) | 9.91821e6 | 0.931478 | 0.465739 | − | 0.884922i | \(-0.345789\pi\) | ||||
0.465739 | + | 0.884922i | \(0.345789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.63312e7 | 1.52197 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.76235e6 | 0.438735 | ||||||||
\(653\) | −1.39102e7 | −1.27659 | −0.638294 | − | 0.769793i | \(-0.720359\pi\) | ||||
−0.638294 | + | 0.769793i | \(0.720359\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.06259e7 | 0.964063 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.90195e6 | −0.441372 | ||||||||
\(659\) | 3.27884e6 | 0.294108 | 0.147054 | − | 0.989128i | \(-0.453021\pi\) | ||||
0.147054 | + | 0.989128i | \(0.453021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00330e6 | −0.623446 | −0.311723 | − | 0.950173i | \(-0.600906\pi\) | ||||
−0.311723 | + | 0.950173i | \(0.600906\pi\) | |||||||
\(662\) | 273816. | 0.0242836 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.88048e6 | 0.781657 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44880.0 | −0.00390605 | ||||||||
\(668\) | −7.67222e6 | −0.665243 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.68683e7 | 1.44633 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.09747e7 | −0.934019 | −0.467009 | − | 0.884252i | \(-0.654669\pi\) | ||||
−0.467009 | + | 0.884252i | \(0.654669\pi\) | |||||||
\(674\) | −4.87188e6 | −0.413092 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.78048e6 | −0.234020 | ||||||||
\(677\) | −8.90482e6 | −0.746713 | −0.373356 | − | 0.927688i | \(-0.621793\pi\) | ||||
−0.373356 | + | 0.927688i | \(0.621793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.42226e6 | 0.368104 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.86477e6 | 0.565152 | ||||||||
\(683\) | 1.61956e7 | 1.32845 | 0.664227 | − | 0.747531i | \(-0.268761\pi\) | ||||
0.664227 | + | 0.747531i | \(0.268761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.27416e6 | 0.346769 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.76730e6 | 0.545060 | ||||||||
\(689\) | 1.47586e7 | 1.18440 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.51015e6 | −0.120316 | −0.0601581 | − | 0.998189i | \(-0.519160\pi\) | ||||
−0.0601581 | + | 0.998189i | \(0.519160\pi\) | |||||||
\(692\) | 7.89281e6 | 0.626565 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.32254e6 | −0.183047 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.53013e7 | −1.97270 | ||||||||
\(698\) | −1.45166e6 | −0.112779 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.80508e7 | −1.38740 | −0.693698 | − | 0.720266i | \(-0.744020\pi\) | ||||
−0.693698 | + | 0.720266i | \(0.744020\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −309560. | −0.0236242 | ||||||||
\(704\) | 5.04474e6 | 0.383625 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.89733e6 | 0.596305 | ||||||||
\(707\) | −1.04124e7 | −0.783436 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.57918e7 | 1.17982 | 0.589912 | − | 0.807468i | \(-0.299163\pi\) | ||||
0.589912 | + | 0.807468i | \(0.299163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.08036e7 | 0.798672 | ||||||||
\(713\) | 1.91981e6 | 0.141428 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.08672e6 | −0.225017 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.42376e6 | 0.175460 | ||||||||
\(719\) | −897600. | −0.0647531 | −0.0323766 | − | 0.999476i | \(-0.510308\pi\) | ||||
−0.0323766 | + | 0.999476i | \(0.510308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.08288e7 | 0.775783 | ||||||||
\(722\) | −4.55260e6 | −0.325025 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.94091e7 | −1.37613 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.33311e6 | −0.584751 | −0.292376 | − | 0.956304i | \(-0.594446\pi\) | ||||
−0.292376 | + | 0.956304i | \(0.594446\pi\) | |||||||
\(728\) | 1.08662e7 | 0.759890 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.61136e7 | −1.11532 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.05633e6 | 0.416341 | 0.208171 | − | 0.978093i | \(-0.433249\pi\) | ||||
0.208171 | + | 0.978093i | \(0.433249\pi\) | |||||||
\(734\) | 7.85998e6 | 0.538494 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.36013e6 | −0.0925519 | ||||||||
\(737\) | −2.72438e6 | −0.184756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.19646e6 | 0.350023 | 0.175011 | − | 0.984566i | \(-0.444004\pi\) | ||||
0.175011 | + | 0.984566i | \(0.444004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.67970e6 | −0.378717 | ||||||||
\(743\) | 2.67222e6 | 0.177583 | 0.0887914 | − | 0.996050i | \(-0.471700\pi\) | ||||
0.0887914 | + | 0.996050i | \(0.471700\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.17039e6 | 0.142788 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.06434e7 | −1.34905 | ||||||||
\(749\) | −5.49806e6 | −0.358101 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.49981e7 | 0.970366 | 0.485183 | − | 0.874413i | \(-0.338753\pi\) | ||||
0.485183 | + | 0.874413i | \(0.338753\pi\) | |||||||
\(752\) | 1.21806e7 | 0.785461 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 233240. | 0.0149408 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.56846e7 | 1.62905 | 0.814523 | − | 0.580131i | \(-0.196999\pi\) | ||||
0.814523 | + | 0.580131i | \(0.196999\pi\) | |||||||
\(758\) | −8.13308e6 | −0.514141 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.07960e6 | −0.380552 | −0.190276 | − | 0.981731i | \(-0.560938\pi\) | ||||
−0.190276 | + | 0.981731i | \(0.560938\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.38428e7 | 0.860823 | ||||||||
\(764\) | 1.04942e7 | 0.650452 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.06907e6 | 0.188988 | ||||||||
\(767\) | −2.37356e7 | −1.45684 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.82501e7 | −1.72268 | −0.861339 | − | 0.508030i | \(-0.830374\pi\) | ||||
−0.861339 | + | 0.508030i | \(0.830374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.93711e6 | 0.418924 | ||||||||
\(773\) | −2.11430e7 | −1.27268 | −0.636339 | − | 0.771409i | \(-0.719552\pi\) | ||||
−0.636339 | + | 0.771409i | \(0.719552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.02024e6 | 0.239661 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.81474e6 | 0.225952 | ||||||||
\(779\) | −3.53116e7 | −2.08485 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.26095e7 | −1.91301 | ||||||||
\(782\) | 824736. | 0.0482279 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 404752. | 0.0235179 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.42307e7 | 1.39454 | 0.697268 | − | 0.716811i | \(-0.254399\pi\) | ||||
0.697268 | + | 0.716811i | \(0.254399\pi\) | |||||||
\(788\) | −1.04602e7 | −0.600100 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.02945e7 | −1.15328 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.45163e7 | −1.38443 | ||||||||
\(794\) | −3.42324e6 | −0.192702 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.35195e7 | 0.756273 | ||||||||
\(797\) | 1.44322e6 | 0.0804797 | 0.0402398 | − | 0.999190i | \(-0.487188\pi\) | ||||
0.0402398 | + | 0.999190i | \(0.487188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.90032e7 | −1.60723 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.92536e6 | 0.270397 | ||||||||
\(803\) | −3.32883e7 | −1.82181 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.97718e6 | −0.540967 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.46584e6 | −0.510071 | ||||||||
\(809\) | −2.99186e7 | −1.60720 | −0.803599 | − | 0.595171i | \(-0.797084\pi\) | ||||
−0.803599 | + | 0.595171i | \(0.797084\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.30183e6 | −0.283057 | −0.141528 | − | 0.989934i | \(-0.545202\pi\) | ||||
−0.141528 | + | 0.989934i | \(0.545202\pi\) | |||||||
\(812\) | 628320. | 0.0334419 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 134048. | 0.00709087 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.24889e7 | −1.17873 | ||||||||
\(818\) | 7.39406e6 | 0.386367 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.55008e6 | −0.235592 | −0.117796 | − | 0.993038i | \(-0.537583\pi\) | ||||
−0.117796 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.42775e7 | 1.24941 | 0.624705 | − | 0.780861i | \(-0.285219\pi\) | ||||
0.624705 | + | 0.780861i | \(0.285219\pi\) | |||||||
\(824\) | 9.84432e6 | 0.505089 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.13440e6 | 0.465833 | ||||||||
\(827\) | 3.63999e6 | 0.185070 | 0.0925350 | − | 0.995709i | \(-0.470503\pi\) | ||||
0.0925350 | + | 0.995709i | \(0.470503\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.98674e7 | 1.00405 | 0.502023 | − | 0.864854i | \(-0.332589\pi\) | ||||
0.502023 | + | 0.864854i | \(0.332589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.33197e6 | −0.367208 | ||||||||
\(833\) | −963754. | −0.0481231 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.88109e7 | −1.42574 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.86120e6 | −0.189938 | ||||||||
\(839\) | 3.58666e7 | 1.75908 | 0.879539 | − | 0.475826i | \(-0.157851\pi\) | ||||
0.879539 | + | 0.475826i | \(0.157851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04822e7 | −0.998591 | ||||||||
\(842\) | 9.67820e6 | 0.470451 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.98449e7 | 0.958945 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.14876e6 | 0.390286 | ||||||||
\(848\) | 1.41132e7 | 0.673962 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37488.0 | 0.00177447 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.25791e7 | −1.06251 | −0.531256 | − | 0.847212i | \(-0.678280\pi\) | ||||
−0.531256 | + | 0.847212i | \(0.678280\pi\) | |||||||
\(854\) | 9.43483e6 | 0.442680 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.99824e6 | −0.233149 | ||||||||
\(857\) | 1.78039e7 | 0.828063 | 0.414032 | − | 0.910262i | \(-0.364120\pi\) | ||||
0.414032 | + | 0.910262i | \(0.364120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −302900. | −0.0140061 | −0.00700304 | − | 0.999975i | \(-0.502229\pi\) | ||||
−0.00700304 | + | 0.999975i | \(0.502229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.48650e6 | −0.251494 | ||||||||
\(863\) | −4.37306e6 | −0.199875 | −0.0999374 | − | 0.994994i | \(-0.531864\pi\) | ||||
−0.0999374 | + | 0.994994i | \(0.531864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.21165e7 | 0.549011 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.68773e7 | −1.21084 | ||||||||
\(869\) | −2.24861e7 | −1.01010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.95959e6 | 0.176850 | ||||||||
\(872\) | 1.25844e7 | 0.560456 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.15104e6 | 0.0509697 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.24189e7 | −0.984272 | −0.492136 | − | 0.870518i | \(-0.663784\pi\) | ||||
−0.492136 | + | 0.870518i | \(0.663784\pi\) | |||||||
\(878\) | −1.04209e7 | −0.456213 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.40470e7 | 0.609739 | 0.304869 | − | 0.952394i | \(-0.401387\pi\) | ||||
0.304869 | + | 0.952394i | \(0.401387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.41189e7 | 1.04101 | 0.520505 | − | 0.853858i | \(-0.325744\pi\) | ||||
0.520505 | + | 0.853858i | \(0.325744\pi\) | |||||||
\(884\) | 3.00029e7 | 1.29132 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.34497e6 | −0.100358 | ||||||||
\(887\) | 2.05454e7 | 0.876809 | 0.438404 | − | 0.898778i | \(-0.355544\pi\) | ||||
0.438404 | + | 0.898778i | \(0.355544\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.83710e6 | 0.332584 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.90901e6 | −0.248658 | ||||||||
\(893\) | −4.04782e7 | −1.69861 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.45837e7 | 1.02300 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.28722e6 | 0.342940 | ||||||||
\(899\) | −1.23624e6 | −0.0510157 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.36049e7 | −1.37908 | ||||||||
\(902\) | 1.52909e7 | 0.625773 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.84495e7 | −0.750869 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.37425e6 | 0.297646 | 0.148823 | − | 0.988864i | \(-0.452452\pi\) | ||||
0.148823 | + | 0.988864i | \(0.452452\pi\) | |||||||
\(908\) | −2.57832e7 | −1.03782 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.23806e7 | 0.893462 | 0.446731 | − | 0.894668i | \(-0.352588\pi\) | ||||
0.446731 | + | 0.894668i | \(0.352588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.49299e7 | −1.38682 | ||||||||
\(914\) | −1.08268e7 | −0.428680 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.99164e6 | 0.0784282 | ||||||||
\(917\) | 1.30427e7 | 0.512204 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.04744e7 | 1.19027 | 0.595136 | − | 0.803625i | \(-0.297098\pi\) | ||||
0.595136 | + | 0.803625i | \(0.297098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.07336e7 | 0.415832 | ||||||||
\(923\) | 4.73944e7 | 1.83114 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.06657e7 | −0.408753 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 875840. | 0.0333853 | ||||||||
\(929\) | −1.87929e7 | −0.714421 | −0.357211 | − | 0.934024i | \(-0.616272\pi\) | ||||
−0.357211 | + | 0.934024i | \(0.616272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.34506e6 | −0.0508590 | ||||||||
\(932\) | −2.80138e7 | −1.05641 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.11366e7 | −0.417721 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.77386e6 | 0.363678 | 0.181839 | − | 0.983328i | \(-0.441795\pi\) | ||||
0.181839 | + | 0.983328i | \(0.441795\pi\) | |||||||
\(938\) | −1.52381e6 | −0.0565488 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.24022e7 | −0.456590 | −0.228295 | − | 0.973592i | \(-0.573315\pi\) | ||||
−0.228295 | + | 0.973592i | \(0.573315\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.27627e6 | 0.156598 | ||||||||
\(944\) | −2.26976e7 | −0.828991 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.73830e6 | 0.353798 | ||||||||
\(947\) | −1.77052e7 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.83808e7 | 1.74384 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.47421e7 | −0.884797 | ||||||||
\(953\) | 2.37213e6 | 0.0846071 | 0.0423036 | − | 0.999105i | \(-0.486530\pi\) | ||||
0.0423036 | + | 0.999105i | \(0.486530\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.54146e7 | −0.545490 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.14184e6 | −0.110604 | ||||||||
\(959\) | 4.05132e7 | 1.42249 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.42528e7 | 0.847138 | ||||||||
\(962\) | −194824. | −0.00678742 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.52231e7 | −0.527607 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −567548. | −0.0195180 | −0.00975902 | − | 0.999952i | \(-0.503106\pi\) | ||||
−0.00975902 | + | 0.999952i | \(0.503106\pi\) | |||||||
\(968\) | 7.40796e6 | 0.254103 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.33139e7 | 0.793536 | 0.396768 | − | 0.917919i | \(-0.370132\pi\) | ||||
0.396768 | + | 0.917919i | \(0.370132\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.86024e6 | −0.164579 | ||||||||
\(974\) | −1.54899e7 | −0.523182 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.34441e7 | −0.787788 | ||||||||
\(977\) | 3.94860e6 | 0.132345 | 0.0661723 | − | 0.997808i | \(-0.478921\pi\) | ||||
0.0661723 | + | 0.997808i | \(0.478921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.24942e7 | −1.41701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.95430e6 | 0.130855 | ||||||||
\(983\) | 5.01417e7 | 1.65506 | 0.827532 | − | 0.561418i | \(-0.189744\pi\) | ||||
0.827532 | + | 0.561418i | \(0.189744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −531080. | −0.0173967 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.18734e7 | 1.36473 | ||||||||
\(989\) | 2.72342e6 | 0.0885369 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.48675e6 | 0.112781 | 0.0563906 | − | 0.998409i | \(-0.482041\pi\) | ||||
0.0563906 | + | 0.998409i | \(0.482041\pi\) | |||||||
\(992\) | −3.74653e7 | −1.20879 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.82392e7 | −0.585518 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.32373e7 | 0.421756 | 0.210878 | − | 0.977512i | \(-0.432368\pi\) | ||||
0.210878 | + | 0.977512i | \(0.432368\pi\) | |||||||
\(998\) | 1.31199e7 | 0.416969 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.6.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 75.6.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 225.6.b.d.199.1 | 2 | |||
5.3 | odd | 4 | 225.6.b.d.199.2 | 2 | |||
5.4 | even | 2 | 45.6.a.c.1.1 | 1 | |||
15.2 | even | 4 | 75.6.b.d.49.2 | 2 | |||
15.8 | even | 4 | 75.6.b.d.49.1 | 2 | |||
15.14 | odd | 2 | 15.6.a.a.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 720.6.a.w.1.1 | 1 | |||
60.59 | even | 2 | 240.6.a.k.1.1 | 1 | |||
105.104 | even | 2 | 735.6.a.a.1.1 | 1 | |||
120.29 | odd | 2 | 960.6.a.v.1.1 | 1 | |||
120.59 | even | 2 | 960.6.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.6.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
45.6.a.c.1.1 | 1 | 5.4 | even | 2 | |||
75.6.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
75.6.b.d.49.1 | 2 | 15.8 | even | 4 | |||
75.6.b.d.49.2 | 2 | 15.2 | even | 4 | |||
225.6.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.6.b.d.199.1 | 2 | 5.2 | odd | 4 | |||
225.6.b.d.199.2 | 2 | 5.3 | odd | 4 | |||
240.6.a.k.1.1 | 1 | 60.59 | even | 2 | |||
720.6.a.w.1.1 | 1 | 20.19 | odd | 2 | |||
735.6.a.a.1.1 | 1 | 105.104 | even | 2 | |||
960.6.a.m.1.1 | 1 | 120.59 | even | 2 | |||
960.6.a.v.1.1 | 1 | 120.29 | odd | 2 |