Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 187x^{4} + 9570x^{2} - 135576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(10.6223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.6223 | 1.87778 | 0.938891 | − | 0.344216i | \(-0.111855\pi\) | ||||
0.938891 | + | 0.344216i | \(0.111855\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 80.8340 | 2.52606 | ||||||||
\(5\) | 67.4751 | 1.20703 | 0.603516 | − | 0.797351i | \(-0.293766\pi\) | ||||
0.603516 | + | 0.797351i | \(0.293766\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 518.731 | 2.86561 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 716.743 | 2.26654 | ||||||||
\(11\) | −522.647 | −1.30235 | −0.651173 | − | 0.758929i | \(-0.725723\pi\) | ||||
−0.651173 | + | 0.758929i | \(0.725723\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −76.6331 | −0.125764 | −0.0628822 | − | 0.998021i | \(-0.520029\pi\) | ||||
−0.0628822 | + | 0.998021i | \(0.520029\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2923.45 | 2.85493 | ||||||||
\(17\) | 1269.60 | 1.06548 | 0.532740 | − | 0.846279i | \(-0.321162\pi\) | ||||
0.532740 | + | 0.846279i | \(0.321162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1892.72 | 1.20283 | 0.601414 | − | 0.798938i | \(-0.294604\pi\) | ||||
0.601414 | + | 0.798938i | \(0.294604\pi\) | |||||||
\(20\) | 5454.28 | 3.04904 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5551.73 | −2.44552 | ||||||||
\(23\) | 1150.04 | 0.453310 | 0.226655 | − | 0.973975i | \(-0.427221\pi\) | ||||
0.226655 | + | 0.973975i | \(0.427221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1427.89 | 0.456925 | ||||||||
\(26\) | −814.022 | −0.236158 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3850.03 | 0.850099 | 0.425049 | − | 0.905170i | \(-0.360257\pi\) | ||||
0.425049 | + | 0.905170i | \(0.360257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10413.7 | 1.94626 | 0.973132 | − | 0.230248i | \(-0.0739539\pi\) | ||||
0.973132 | + | 0.230248i | \(0.0739539\pi\) | |||||||
\(32\) | 14454.4 | 2.49532 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13486.1 | 2.00074 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5602.27 | −0.672760 | −0.336380 | − | 0.941726i | \(-0.609203\pi\) | ||||
−0.336380 | + | 0.941726i | \(0.609203\pi\) | |||||||
\(38\) | 20105.2 | 2.25865 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 35001.4 | 3.45888 | ||||||||
\(41\) | −14232.7 | −1.32229 | −0.661147 | − | 0.750256i | \(-0.729930\pi\) | ||||
−0.661147 | + | 0.750256i | \(0.729930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14827.9 | −1.22295 | −0.611475 | − | 0.791264i | \(-0.709424\pi\) | ||||
−0.611475 | + | 0.791264i | \(0.709424\pi\) | |||||||
\(44\) | −42247.6 | −3.28981 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12216.2 | 0.851216 | ||||||||
\(47\) | −11549.8 | −0.762655 | −0.381328 | − | 0.924440i | \(-0.624533\pi\) | ||||
−0.381328 | + | 0.924440i | \(0.624533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 15167.5 | 0.858004 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6194.56 | −0.317689 | ||||||||
\(53\) | 4677.72 | 0.228741 | 0.114371 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114371 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −35265.6 | −1.57197 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 40896.3 | 1.59630 | ||||||||
\(59\) | 29102.0 | 1.08841 | 0.544205 | − | 0.838952i | \(-0.316831\pi\) | ||||
0.544205 | + | 0.838952i | \(0.316831\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11842.9 | −0.407505 | −0.203753 | − | 0.979022i | \(-0.565314\pi\) | ||||
−0.203753 | + | 0.979022i | \(0.565314\pi\) | |||||||
\(62\) | 110618. | 3.65466 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 59989.5 | 1.83073 | ||||||||
\(65\) | −5170.82 | −0.151802 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −36212.6 | −0.985536 | −0.492768 | − | 0.870161i | \(-0.664015\pi\) | ||||
−0.492768 | + | 0.870161i | \(0.664015\pi\) | |||||||
\(68\) | 102627. | 2.69147 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13477.6 | 0.317298 | 0.158649 | − | 0.987335i | \(-0.449286\pi\) | ||||
0.158649 | + | 0.987335i | \(0.449286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2608.45 | −0.0572896 | −0.0286448 | − | 0.999590i | \(-0.509119\pi\) | ||||
−0.0286448 | + | 0.999590i | \(0.509119\pi\) | |||||||
\(74\) | −59509.2 | −1.26330 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 152996. | 3.03842 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78320.3 | −1.41191 | −0.705955 | − | 0.708257i | \(-0.749482\pi\) | ||||
−0.705955 | + | 0.708257i | \(0.749482\pi\) | |||||||
\(80\) | 197260. | 3.44599 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −151185. | −2.48298 | ||||||||
\(83\) | 16746.0 | 0.266819 | 0.133410 | − | 0.991061i | \(-0.457407\pi\) | ||||
0.133410 | + | 0.991061i | \(0.457407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 85666.5 | 1.28607 | ||||||||
\(86\) | −157507. | −2.29643 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −271113. | −3.73202 | ||||||||
\(89\) | 36768.5 | 0.492040 | 0.246020 | − | 0.969265i | \(-0.420877\pi\) | ||||
0.246020 | + | 0.969265i | \(0.420877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 92962.7 | 1.14509 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −122685. | −1.43210 | ||||||||
\(95\) | 127712. | 1.45185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −36133.4 | −0.389924 | −0.194962 | − | 0.980811i | \(-0.562458\pi\) | ||||
−0.194962 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 115422. | 1.15422 | ||||||||
\(101\) | −98675.2 | −0.962509 | −0.481254 | − | 0.876581i | \(-0.659819\pi\) | ||||
−0.481254 | + | 0.876581i | \(0.659819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7273.50 | −0.0675539 | −0.0337769 | − | 0.999429i | \(-0.510754\pi\) | ||||
−0.0337769 | + | 0.999429i | \(0.510754\pi\) | |||||||
\(104\) | −39751.9 | −0.360392 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 49688.3 | 0.429526 | ||||||||
\(107\) | 30953.5 | 0.261367 | 0.130683 | − | 0.991424i | \(-0.458283\pi\) | ||||
0.130683 | + | 0.991424i | \(0.458283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 113831. | 0.917689 | 0.458844 | − | 0.888517i | \(-0.348264\pi\) | ||||
0.458844 | + | 0.888517i | \(0.348264\pi\) | |||||||
\(110\) | −374603. | −2.95182 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 894.559 | 0.00659041 | 0.00329521 | − | 0.999995i | \(-0.498951\pi\) | ||||
0.00329521 | + | 0.999995i | \(0.498951\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 77599.3 | 0.547159 | ||||||||
\(116\) | 311213. | 2.14740 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 309131. | 2.04379 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 112109. | 0.696106 | ||||||||
\(122\) | −125799. | −0.765206 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 841783. | 4.91638 | ||||||||
\(125\) | −114513. | −0.655509 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 72325.9 | 0.397910 | 0.198955 | − | 0.980009i | \(-0.436245\pi\) | ||||
0.198955 | + | 0.980009i | \(0.436245\pi\) | |||||||
\(128\) | 174687. | 0.942399 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −54926.2 | −0.285050 | ||||||||
\(131\) | −70168.1 | −0.357241 | −0.178620 | − | 0.983918i | \(-0.557163\pi\) | ||||
−0.178620 | + | 0.983918i | \(0.557163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −384662. | −1.85062 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 658582. | 3.05325 | ||||||||
\(137\) | −372009. | −1.69337 | −0.846685 | − | 0.532095i | \(-0.821405\pi\) | ||||
−0.846685 | + | 0.532095i | \(0.821405\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5566.26 | −0.0244358 | −0.0122179 | − | 0.999925i | \(-0.503889\pi\) | ||||
−0.0122179 | + | 0.999925i | \(0.503889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 143164. | 0.595816 | ||||||||
\(143\) | 40052.0 | 0.163789 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 259781. | 1.02610 | ||||||||
\(146\) | −27707.8 | −0.107577 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −452854. | −1.69943 | ||||||||
\(149\) | 333914. | 1.23217 | 0.616083 | − | 0.787681i | \(-0.288719\pi\) | ||||
0.616083 | + | 0.787681i | \(0.288719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 75157.3 | 0.268243 | 0.134122 | − | 0.990965i | \(-0.457179\pi\) | ||||
0.134122 | + | 0.990965i | \(0.457179\pi\) | |||||||
\(152\) | 981815. | 3.44684 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 702667. | 2.34920 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −475585. | −1.53985 | −0.769926 | − | 0.638134i | \(-0.779707\pi\) | ||||
−0.769926 | + | 0.638134i | \(0.779707\pi\) | |||||||
\(158\) | −831945. | −2.65126 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 975314. | 3.01193 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 239223. | 0.705234 | 0.352617 | − | 0.935768i | \(-0.385292\pi\) | ||||
0.352617 | + | 0.935768i | \(0.385292\pi\) | |||||||
\(164\) | −1.15049e6 | −3.34020 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 177882. | 0.501028 | ||||||||
\(167\) | −111308. | −0.308842 | −0.154421 | − | 0.988005i | \(-0.549351\pi\) | ||||
−0.154421 | + | 0.988005i | \(0.549351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −365420. | −0.984183 | ||||||||
\(170\) | 909978. | 2.41495 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.19860e6 | −3.08925 | ||||||||
\(173\) | −698994. | −1.77565 | −0.887826 | − | 0.460179i | \(-0.847785\pi\) | ||||
−0.887826 | + | 0.460179i | \(0.847785\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.52793e6 | −3.71810 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 390567. | 0.923944 | ||||||||
\(179\) | −103909. | −0.242393 | −0.121196 | − | 0.992629i | \(-0.538673\pi\) | ||||
−0.121196 | + | 0.992629i | \(0.538673\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 415260. | 0.942159 | 0.471079 | − | 0.882091i | \(-0.343865\pi\) | ||||
0.471079 | + | 0.882091i | \(0.343865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 596563. | 1.29901 | ||||||||
\(185\) | −378014. | −0.812042 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −663553. | −1.38762 | ||||||||
\(188\) | −933613. | −1.92651 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.35660e6 | 2.72626 | ||||||||
\(191\) | −570116. | −1.13078 | −0.565392 | − | 0.824823i | \(-0.691275\pi\) | ||||
−0.565392 | + | 0.824823i | \(0.691275\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 297709. | 0.575305 | 0.287653 | − | 0.957735i | \(-0.407125\pi\) | ||||
0.287653 | + | 0.957735i | \(0.407125\pi\) | |||||||
\(194\) | −383821. | −0.732192 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −410678. | −0.753938 | −0.376969 | − | 0.926226i | \(-0.623034\pi\) | ||||
−0.376969 | + | 0.926226i | \(0.623034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 699345. | 1.25187 | 0.625934 | − | 0.779876i | \(-0.284718\pi\) | ||||
0.625934 | + | 0.779876i | \(0.284718\pi\) | |||||||
\(200\) | 740690. | 1.30937 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.04816e6 | −1.80738 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −960354. | −1.59605 | ||||||||
\(206\) | −77261.5 | −0.126851 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −224033. | −0.359048 | ||||||||
\(209\) | −989226. | −1.56650 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −58292.9 | −0.0901384 | −0.0450692 | − | 0.998984i | \(-0.514351\pi\) | ||||
−0.0450692 | + | 0.998984i | \(0.514351\pi\) | |||||||
\(212\) | 378119. | 0.577815 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 328799. | 0.490790 | ||||||||
\(215\) | −1.00051e6 | −1.47614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.20915e6 | 1.72322 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.85066e6 | −3.97090 | ||||||||
\(221\) | −97293.5 | −0.133999 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25758.5 | −0.0346864 | −0.0173432 | − | 0.999850i | \(-0.505521\pi\) | ||||
−0.0173432 | + | 0.999850i | \(0.505521\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9502.30 | 0.0123754 | ||||||||
\(227\) | −982245. | −1.26519 | −0.632594 | − | 0.774483i | \(-0.718010\pi\) | ||||
−0.632594 | + | 0.774483i | \(0.718010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −519963. | −0.655215 | −0.327607 | − | 0.944814i | \(-0.606242\pi\) | ||||
−0.327607 | + | 0.944814i | \(0.606242\pi\) | |||||||
\(230\) | 824286. | 1.02744 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.99713e6 | 2.43605 | ||||||||
\(233\) | −1.21941e6 | −1.47149 | −0.735747 | − | 0.677257i | \(-0.763169\pi\) | ||||
−0.735747 | + | 0.677257i | \(0.763169\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −779321. | −0.920548 | ||||||||
\(236\) | 2.35243e6 | 2.74939 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 909357. | 1.02977 | 0.514884 | − | 0.857260i | \(-0.327835\pi\) | ||||
0.514884 | + | 0.857260i | \(0.327835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 641596. | 0.711572 | 0.355786 | − | 0.934567i | \(-0.384213\pi\) | ||||
0.355786 | + | 0.934567i | \(0.384213\pi\) | |||||||
\(242\) | 1.19086e6 | 1.30714 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −957308. | −1.02938 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −145045. | −0.151273 | ||||||||
\(248\) | 5.40192e6 | 5.57723 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.21639e6 | −1.23090 | ||||||||
\(251\) | 1.92052e6 | 1.92413 | 0.962066 | − | 0.272816i | \(-0.0879550\pi\) | ||||
0.962066 | + | 0.272816i | \(0.0879550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −601067. | −0.590366 | ||||||||
\(254\) | 768270. | 0.747188 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −64082.7 | −0.0611140 | ||||||||
\(257\) | −986369. | −0.931551 | −0.465775 | − | 0.884903i | \(-0.654225\pi\) | ||||
−0.465775 | + | 0.884903i | \(0.654225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −417978. | −0.383460 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −745349. | −0.670820 | ||||||||
\(263\) | −849019. | −0.756881 | −0.378441 | − | 0.925626i | \(-0.623540\pi\) | ||||
−0.378441 | + | 0.925626i | \(0.623540\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 315630. | 0.276098 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.92721e6 | −2.48952 | ||||||||
\(269\) | −1.73358e6 | −1.46071 | −0.730355 | − | 0.683068i | \(-0.760645\pi\) | ||||
−0.730355 | + | 0.683068i | \(0.760645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.05565e6 | 0.873167 | 0.436583 | − | 0.899664i | \(-0.356188\pi\) | ||||
0.436583 | + | 0.899664i | \(0.356188\pi\) | |||||||
\(272\) | 3.71161e6 | 3.04187 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.95160e6 | −3.17978 | ||||||||
\(275\) | −746282. | −0.595074 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.62493e6 | 1.27243 | 0.636216 | − | 0.771511i | \(-0.280499\pi\) | ||||
0.636216 | + | 0.771511i | \(0.280499\pi\) | |||||||
\(278\) | −59126.7 | −0.0458851 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.56484e6 | 1.18224 | 0.591118 | − | 0.806585i | \(-0.298687\pi\) | ||||
0.591118 | + | 0.806585i | \(0.298687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 694213. | 0.515260 | 0.257630 | − | 0.966244i | \(-0.417058\pi\) | ||||
0.257630 | + | 0.966244i | \(0.417058\pi\) | |||||||
\(284\) | 1.08945e6 | 0.801515 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 425446. | 0.307560 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 192032. | 0.135247 | ||||||||
\(290\) | 2.75948e6 | 1.92678 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −210851. | −0.144717 | ||||||||
\(293\) | 999262. | 0.680002 | 0.340001 | − | 0.940425i | \(-0.389573\pi\) | ||||
0.340001 | + | 0.940425i | \(0.389573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.96366e6 | 1.31374 | ||||||||
\(296\) | −2.90607e6 | −1.92787 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.54695e6 | 2.31374 | ||||||||
\(299\) | −88131.4 | −0.0570102 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 798346. | 0.503702 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.53328e6 | 3.43399 | ||||||||
\(305\) | −799100. | −0.491872 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −800764. | −0.484907 | −0.242453 | − | 0.970163i | \(-0.577952\pi\) | ||||
−0.242453 | + | 0.970163i | \(0.577952\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.46396e6 | 4.41129 | ||||||||
\(311\) | −582944. | −0.341764 | −0.170882 | − | 0.985292i | \(-0.554662\pi\) | ||||
−0.170882 | + | 0.985292i | \(0.554662\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.99909e6 | 1.15338 | 0.576689 | − | 0.816963i | \(-0.304344\pi\) | ||||
0.576689 | + | 0.816963i | \(0.304344\pi\) | |||||||
\(314\) | −5.05182e6 | −2.89150 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.33095e6 | −3.56657 | ||||||||
\(317\) | −1.80208e6 | −1.00722 | −0.503610 | − | 0.863931i | \(-0.667995\pi\) | ||||
−0.503610 | + | 0.863931i | \(0.667995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.01221e6 | −1.10712 | ||||||||
\(320\) | 4.04780e6 | 2.20975 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.40301e6 | 1.28159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −109424. | −0.0574649 | ||||||||
\(326\) | 2.54110e6 | 1.32428 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.38295e6 | −3.78918 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 103771. | 0.0520603 | 0.0260301 | − | 0.999661i | \(-0.491713\pi\) | ||||
0.0260301 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(332\) | 1.35365e6 | 0.674001 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.18235e6 | −0.579937 | ||||||||
\(335\) | −2.44345e6 | −1.18957 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 961978. | 0.461414 | 0.230707 | − | 0.973023i | \(-0.425896\pi\) | ||||
0.230707 | + | 0.973023i | \(0.425896\pi\) | |||||||
\(338\) | −3.88162e6 | −1.84808 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.92476e6 | 3.24869 | ||||||||
\(341\) | −5.44270e6 | −2.53471 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.69169e6 | −3.50450 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.42494e6 | −3.33429 | ||||||||
\(347\) | −2.43348e6 | −1.08494 | −0.542468 | − | 0.840077i | \(-0.682510\pi\) | ||||
−0.542468 | + | 0.840077i | \(0.682510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.42269e6 | 1.50419 | 0.752096 | − | 0.659053i | \(-0.229043\pi\) | ||||
0.752096 | + | 0.659053i | \(0.229043\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.55456e6 | −3.24977 | ||||||||
\(353\) | 3.85497e6 | 1.64658 | 0.823292 | − | 0.567618i | \(-0.192135\pi\) | ||||
0.823292 | + | 0.567618i | \(0.192135\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 909404. | 0.382989 | ||||||||
\(356\) | 2.97214e6 | 1.24292 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.10375e6 | −0.455161 | ||||||||
\(359\) | 2.48369e6 | 1.01709 | 0.508547 | − | 0.861034i | \(-0.330183\pi\) | ||||
0.508547 | + | 0.861034i | \(0.330183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.10631e6 | 0.446795 | ||||||||
\(362\) | 4.41104e6 | 1.76917 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −176005. | −0.0691503 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.07224e6 | 1.57822 | 0.789111 | − | 0.614250i | \(-0.210542\pi\) | ||||
0.789111 | + | 0.614250i | \(0.210542\pi\) | |||||||
\(368\) | 3.36209e6 | 1.29417 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.01539e6 | −1.52484 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.69272e6 | −1.74644 | −0.873218 | − | 0.487329i | \(-0.837971\pi\) | ||||
−0.873218 | + | 0.487329i | \(0.837971\pi\) | |||||||
\(374\) | −7.04848e6 | −2.60565 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.99121e6 | −2.18547 | ||||||||
\(377\) | −295040. | −0.106912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.04599e6 | 1.80446 | 0.902232 | − | 0.431251i | \(-0.141928\pi\) | ||||
0.902232 | + | 0.431251i | \(0.141928\pi\) | |||||||
\(380\) | 1.03235e7 | 3.66747 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.05596e6 | −2.12336 | ||||||||
\(383\) | 1.65284e6 | 0.575749 | 0.287874 | − | 0.957668i | \(-0.407051\pi\) | ||||
0.287874 | + | 0.957668i | \(0.407051\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.16236e6 | 1.08030 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.92081e6 | −0.984972 | ||||||||
\(389\) | −2.91455e6 | −0.976556 | −0.488278 | − | 0.872688i | \(-0.662375\pi\) | ||||
−0.488278 | + | 0.872688i | \(0.662375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.46010e6 | 0.482992 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.36235e6 | −1.41573 | ||||||||
\(395\) | −5.28467e6 | −1.70422 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 474943. | 0.151239 | 0.0756197 | − | 0.997137i | \(-0.475906\pi\) | ||||
0.0756197 | + | 0.997137i | \(0.475906\pi\) | |||||||
\(398\) | 7.42867e6 | 2.35073 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.17436e6 | 1.30449 | ||||||||
\(401\) | −48881.8 | −0.0151805 | −0.00759025 | − | 0.999971i | \(-0.502416\pi\) | ||||
−0.00759025 | + | 0.999971i | \(0.502416\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −798035. | −0.244771 | ||||||||
\(404\) | −7.97631e6 | −2.43136 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.92801e6 | 0.876166 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.73894e6 | −1.10520 | −0.552599 | − | 0.833447i | \(-0.686364\pi\) | ||||
−0.552599 | + | 0.833447i | \(0.686364\pi\) | |||||||
\(410\) | −1.02012e7 | −2.99703 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −587946. | −0.170645 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.12994e6 | 0.322059 | ||||||||
\(416\) | −1.10769e6 | −0.313822 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.05079e7 | −2.94154 | ||||||||
\(419\) | −681425. | −0.189619 | −0.0948097 | − | 0.995495i | \(-0.530224\pi\) | ||||
−0.0948097 | + | 0.995495i | \(0.530224\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.54803e6 | 0.425670 | 0.212835 | − | 0.977088i | \(-0.431730\pi\) | ||||
0.212835 | + | 0.977088i | \(0.431730\pi\) | |||||||
\(422\) | −619207. | −0.169260 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.42648e6 | 0.655483 | ||||||||
\(425\) | 1.81285e6 | 0.486844 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.50210e6 | 0.660229 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.06278e7 | −2.77187 | ||||||||
\(431\) | 6.37710e6 | 1.65360 | 0.826799 | − | 0.562497i | \(-0.190159\pi\) | ||||
0.826799 | + | 0.562497i | \(0.190159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.32669e6 | −0.340056 | −0.170028 | − | 0.985439i | \(-0.554386\pi\) | ||||
−0.170028 | + | 0.985439i | \(0.554386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.20144e6 | 2.31814 | ||||||||
\(437\) | 2.17672e6 | 0.545253 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.85328e6 | −0.954267 | −0.477133 | − | 0.878831i | \(-0.658324\pi\) | ||||
−0.477133 | + | 0.878831i | \(0.658324\pi\) | |||||||
\(440\) | −1.82934e7 | −4.50466 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.03348e6 | −0.251622 | ||||||||
\(443\) | 1.29104e6 | 0.312559 | 0.156279 | − | 0.987713i | \(-0.450050\pi\) | ||||
0.156279 | + | 0.987713i | \(0.450050\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48096e6 | 0.593908 | ||||||||
\(446\) | −273616. | −0.0651334 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.49006e6 | −1.75335 | −0.876677 | − | 0.481080i | \(-0.840245\pi\) | ||||
−0.876677 | + | 0.481080i | \(0.840245\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.43868e6 | 1.72208 | ||||||||
\(452\) | 72310.7 | 0.0166478 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.04337e7 | −2.37575 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 499323. | 0.111839 | 0.0559193 | − | 0.998435i | \(-0.482191\pi\) | ||||
0.0559193 | + | 0.998435i | \(0.482191\pi\) | |||||||
\(458\) | −5.52322e6 | −1.23035 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.27266e6 | 1.38216 | ||||||||
\(461\) | −5.34926e6 | −1.17231 | −0.586153 | − | 0.810200i | \(-0.699358\pi\) | ||||
−0.586153 | + | 0.810200i | \(0.699358\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.52516e6 | −1.41462 | −0.707308 | − | 0.706906i | \(-0.750091\pi\) | ||||
−0.707308 | + | 0.706906i | \(0.750091\pi\) | |||||||
\(464\) | 1.12554e7 | 2.42697 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.29529e7 | −2.76314 | ||||||||
\(467\) | −3.20648e6 | −0.680357 | −0.340179 | − | 0.940361i | \(-0.610488\pi\) | ||||
−0.340179 | + | 0.940361i | \(0.610488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.27821e6 | −1.72859 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.50961e7 | 3.11896 | ||||||||
\(473\) | 7.74976e6 | 1.59270 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.70260e6 | 0.549602 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.65949e6 | 1.93368 | ||||||||
\(479\) | −8.86811e6 | −1.76601 | −0.883003 | − | 0.469367i | \(-0.844482\pi\) | ||||
−0.883003 | + | 0.469367i | \(0.844482\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 429319. | 0.0846092 | ||||||||
\(482\) | 6.81525e6 | 1.33618 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.06218e6 | 1.75841 | ||||||||
\(485\) | −2.43811e6 | −0.470650 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.84722e6 | 1.11719 | 0.558595 | − | 0.829441i | \(-0.311341\pi\) | ||||
0.558595 | + | 0.829441i | \(0.311341\pi\) | |||||||
\(488\) | −6.14327e6 | −1.16775 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 114241. | 0.0213854 | 0.0106927 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106927 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.88801e6 | 0.905763 | ||||||||
\(494\) | −1.54072e6 | −0.284057 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.04439e7 | 5.55644 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.34482e6 | −1.68004 | −0.840020 | − | 0.542556i | \(-0.817457\pi\) | ||||
−0.840020 | + | 0.542556i | \(0.817457\pi\) | |||||||
\(500\) | −9.25652e6 | −1.65586 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.04004e7 | 3.61310 | ||||||||
\(503\) | −892118. | −0.157218 | −0.0786091 | − | 0.996906i | \(-0.525048\pi\) | ||||
−0.0786091 | + | 0.996906i | \(0.525048\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.65812e6 | −1.16178 | ||||||||
\(506\) | −6.38473e6 | −1.10858 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.84639e6 | 1.00515 | ||||||||
\(509\) | 6.84023e6 | 1.17024 | 0.585122 | − | 0.810946i | \(-0.301047\pi\) | ||||
0.585122 | + | 0.810946i | \(0.301047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.27068e6 | −1.05716 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.04775e7 | −1.74925 | ||||||||
\(515\) | −490780. | −0.0815396 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.03644e6 | 0.993241 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.68227e6 | −0.435004 | ||||||||
\(521\) | 8.91887e6 | 1.43951 | 0.719756 | − | 0.694227i | \(-0.244254\pi\) | ||||
0.719756 | + | 0.694227i | \(0.244254\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −611823. | −0.0978073 | −0.0489037 | − | 0.998803i | \(-0.515573\pi\) | ||||
−0.0489037 | + | 0.998803i | \(0.515573\pi\) | |||||||
\(524\) | −5.67196e6 | −0.902413 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.01856e6 | −1.42126 | ||||||||
\(527\) | 1.32213e7 | 2.07370 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.11374e6 | −0.794510 | ||||||||
\(530\) | 3.35272e6 | 0.518451 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.09070e6 | 0.166298 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.08859e6 | 0.315478 | ||||||||
\(536\) | −1.87846e7 | −2.82416 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.84147e7 | −2.74289 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −244343. | −0.0358928 | −0.0179464 | − | 0.999839i | \(-0.505713\pi\) | ||||
−0.0179464 | + | 0.999839i | \(0.505713\pi\) | |||||||
\(542\) | 1.12135e7 | 1.63962 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.83514e7 | 2.65871 | ||||||||
\(545\) | 7.68078e6 | 1.10768 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.55551e6 | −1.07968 | −0.539840 | − | 0.841767i | \(-0.681515\pi\) | ||||
−0.539840 | + | 0.841767i | \(0.681515\pi\) | |||||||
\(548\) | −3.00709e7 | −4.27756 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.92725e6 | −1.11742 | ||||||||
\(551\) | 7.28705e6 | 1.02252 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.72605e7 | 2.38935 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −449943. | −0.0617264 | ||||||||
\(557\) | −2.57276e6 | −0.351368 | −0.175684 | − | 0.984447i | \(-0.556214\pi\) | ||||
−0.175684 | + | 0.984447i | \(0.556214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.13631e6 | 0.153804 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.66223e7 | 2.21998 | ||||||||
\(563\) | 1.10693e7 | 1.47181 | 0.735903 | − | 0.677087i | \(-0.236758\pi\) | ||||
0.735903 | + | 0.677087i | \(0.236758\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 60360.4 | 0.00795484 | ||||||||
\(566\) | 7.37416e6 | 0.967546 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.99126e6 | 0.909253 | ||||||||
\(569\) | −3.11210e6 | −0.402970 | −0.201485 | − | 0.979492i | \(-0.564577\pi\) | ||||
−0.201485 | + | 0.979492i | \(0.564577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.73724e6 | 0.736398 | 0.368199 | − | 0.929747i | \(-0.379975\pi\) | ||||
0.368199 | + | 0.929747i | \(0.379975\pi\) | |||||||
\(572\) | 3.23756e6 | 0.413741 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.64214e6 | 0.207128 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.11306e7 | 1.39180 | 0.695901 | − | 0.718138i | \(-0.255005\pi\) | ||||
0.695901 | + | 0.718138i | \(0.255005\pi\) | |||||||
\(578\) | 2.03982e6 | 0.253964 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.09992e7 | 2.59198 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.44479e6 | −0.297900 | ||||||||
\(584\) | −1.35308e6 | −0.164170 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.06145e7 | 1.27690 | ||||||||
\(587\) | 7.71211e6 | 0.923800 | 0.461900 | − | 0.886932i | \(-0.347168\pi\) | ||||
0.461900 | + | 0.886932i | \(0.347168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.97103e7 | 2.34102 | ||||||||
\(590\) | 2.08586e7 | 2.46692 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.63779e7 | −1.92068 | ||||||||
\(593\) | 8.33301e6 | 0.973117 | 0.486558 | − | 0.873648i | \(-0.338252\pi\) | ||||
0.486558 | + | 0.873648i | \(0.338252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.69916e7 | 3.11253 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −936161. | −0.107053 | ||||||||
\(599\) | −5.33581e6 | −0.607621 | −0.303811 | − | 0.952732i | \(-0.598259\pi\) | ||||
−0.303811 | + | 0.952732i | \(0.598259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.53972e6 | 0.851470 | 0.425735 | − | 0.904848i | \(-0.360016\pi\) | ||||
0.425735 | + | 0.904848i | \(0.360016\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.07526e6 | 0.677599 | ||||||||
\(605\) | 7.56454e6 | 0.840222 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.68565e6 | 1.06698 | 0.533491 | − | 0.845806i | \(-0.320880\pi\) | ||||
0.533491 | + | 0.845806i | \(0.320880\pi\) | |||||||
\(608\) | 2.73582e7 | 3.00144 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.48831e6 | −0.923627 | ||||||||
\(611\) | 885093. | 0.0959149 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.36761e7 | 1.46998 | 0.734989 | − | 0.678079i | \(-0.237187\pi\) | ||||
0.734989 | + | 0.678079i | \(0.237187\pi\) | |||||||
\(614\) | −8.50598e6 | −0.910549 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.53796e7 | −1.62642 | −0.813211 | − | 0.581969i | \(-0.802283\pi\) | ||||
−0.813211 | + | 0.581969i | \(0.802283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.41608e6 | −0.568144 | −0.284072 | − | 0.958803i | \(-0.591685\pi\) | ||||
−0.284072 | + | 0.958803i | \(0.591685\pi\) | |||||||
\(620\) | 5.67994e7 | 5.93423 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.19223e6 | −0.641757 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.21889e7 | −1.24814 | ||||||||
\(626\) | 2.12350e7 | 2.16579 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.84434e7 | −3.88976 | ||||||||
\(629\) | −7.11266e6 | −0.716812 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.44178e7 | 1.44154 | 0.720770 | − | 0.693174i | \(-0.243788\pi\) | ||||
0.720770 | + | 0.693174i | \(0.243788\pi\) | |||||||
\(632\) | −4.06272e7 | −4.04598 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.91422e7 | −1.89134 | ||||||||
\(635\) | 4.88020e6 | 0.480290 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.13743e7 | −2.07893 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.17870e7 | 1.13751 | ||||||||
\(641\) | −6.13817e6 | −0.590057 | −0.295029 | − | 0.955488i | \(-0.595329\pi\) | ||||
−0.295029 | + | 0.955488i | \(0.595329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 402177. | 0.0383610 | 0.0191805 | − | 0.999816i | \(-0.493894\pi\) | ||||
0.0191805 | + | 0.999816i | \(0.493894\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.55255e7 | 2.40654 | ||||||||
\(647\) | 1.32816e7 | 1.24736 | 0.623678 | − | 0.781682i | \(-0.285638\pi\) | ||||
0.623678 | + | 0.781682i | \(0.285638\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.52100e7 | −1.41749 | ||||||||
\(650\) | −1.16233e6 | −0.107906 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.93373e7 | 1.78147 | ||||||||
\(653\) | −1.12731e7 | −1.03457 | −0.517287 | − | 0.855812i | \(-0.673058\pi\) | ||||
−0.517287 | + | 0.855812i | \(0.673058\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.73460e6 | −0.431201 | ||||||||
\(656\) | −4.16086e7 | −3.77505 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.29624e6 | −0.833861 | −0.416930 | − | 0.908938i | \(-0.636894\pi\) | ||||
−0.416930 | + | 0.908938i | \(0.636894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 628772. | 0.0559744 | 0.0279872 | − | 0.999608i | \(-0.491090\pi\) | ||||
0.0279872 | + | 0.999608i | \(0.491090\pi\) | |||||||
\(662\) | 1.10229e6 | 0.0977578 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.68669e6 | 0.764599 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.42771e6 | 0.385358 | ||||||||
\(668\) | −8.99749e6 | −0.780153 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.59551e7 | −2.23376 | ||||||||
\(671\) | 6.18965e6 | 0.530713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.15635e6 | 0.438838 | 0.219419 | − | 0.975631i | \(-0.429584\pi\) | ||||
0.219419 | + | 0.975631i | \(0.429584\pi\) | |||||||
\(674\) | 1.02185e7 | 0.866434 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.95384e7 | −2.48611 | ||||||||
\(677\) | −6.56297e6 | −0.550337 | −0.275169 | − | 0.961396i | \(-0.588734\pi\) | ||||
−0.275169 | + | 0.961396i | \(0.588734\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.44379e7 | 3.68537 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.78141e7 | −4.75963 | ||||||||
\(683\) | 2.01533e7 | 1.65308 | 0.826540 | − | 0.562879i | \(-0.190306\pi\) | ||||
0.826540 | + | 0.562879i | \(0.190306\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.51013e7 | −2.04395 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.33486e7 | −3.49143 | ||||||||
\(689\) | −358468. | −0.0287675 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.01196e7 | 0.806246 | 0.403123 | − | 0.915146i | \(-0.367925\pi\) | ||||
0.403123 | + | 0.915146i | \(0.367925\pi\) | |||||||
\(692\) | −5.65024e7 | −4.48541 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.58492e7 | −2.03727 | ||||||||
\(695\) | −375584. | −0.0294948 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.80699e7 | −1.40888 | ||||||||
\(698\) | 3.63569e7 | 2.82455 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.27446e6 | 0.251678 | 0.125839 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125839 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.06036e7 | −0.809214 | ||||||||
\(704\) | −3.13533e7 | −2.38425 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.09488e7 | 3.09193 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.99446e6 | 0.447852 | 0.223926 | − | 0.974606i | \(-0.428113\pi\) | ||||
0.223926 | + | 0.974606i | \(0.428113\pi\) | |||||||
\(710\) | 9.65999e6 | 0.719169 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.90729e7 | 1.41000 | ||||||||
\(713\) | 1.19762e7 | 0.882260 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.70251e6 | 0.197698 | ||||||||
\(716\) | −8.39936e6 | −0.612299 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.63826e7 | 1.90988 | ||||||||
\(719\) | 2.47737e7 | 1.78718 | 0.893590 | − | 0.448885i | \(-0.148179\pi\) | ||||
0.893590 | + | 0.448885i | \(0.148179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.17516e7 | 0.838983 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.35672e7 | 2.37995 | ||||||||
\(725\) | 5.49742e6 | 0.388431 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.16194e7 | 0.815357 | 0.407678 | − | 0.913126i | \(-0.366338\pi\) | ||||
0.407678 | + | 0.913126i | \(0.366338\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.86959e6 | −0.129849 | ||||||||
\(731\) | −1.88255e7 | −1.30303 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.27434e7 | 0.876041 | 0.438020 | − | 0.898965i | \(-0.355680\pi\) | ||||
0.438020 | + | 0.898965i | \(0.355680\pi\) | |||||||
\(734\) | 4.32567e7 | 2.96356 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.66232e7 | 1.13115 | ||||||||
\(737\) | 1.89264e7 | 1.28351 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.20918e7 | 0.814477 | 0.407238 | − | 0.913322i | \(-0.366492\pi\) | ||||
0.407238 | + | 0.913322i | \(0.366492\pi\) | |||||||
\(740\) | −3.05564e7 | −2.05127 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.79136e6 | −0.650685 | −0.325343 | − | 0.945596i | \(-0.605480\pi\) | ||||
−0.325343 | + | 0.945596i | \(0.605480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.25309e7 | 1.48726 | ||||||||
\(746\) | −4.98477e7 | −3.27943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.36376e7 | −3.50522 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.75303e7 | −1.13420 | −0.567098 | − | 0.823650i | \(-0.691934\pi\) | ||||
−0.567098 | + | 0.823650i | \(0.691934\pi\) | |||||||
\(752\) | −3.37651e7 | −2.17732 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.13401e6 | −0.200758 | ||||||||
\(755\) | 5.07125e6 | 0.323778 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.01558e6 | 0.381538 | 0.190769 | − | 0.981635i | \(-0.438902\pi\) | ||||
0.190769 | + | 0.981635i | \(0.438902\pi\) | |||||||
\(758\) | 5.36002e7 | 3.38839 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.62481e7 | 4.16044 | ||||||||
\(761\) | 1.27680e7 | 0.799214 | 0.399607 | − | 0.916687i | \(-0.369147\pi\) | ||||
0.399607 | + | 0.916687i | \(0.369147\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.60847e7 | −2.85643 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.75570e7 | 1.08113 | ||||||||
\(767\) | −2.23017e6 | −0.136883 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.32718e6 | 0.385829 | 0.192914 | − | 0.981216i | \(-0.438206\pi\) | ||||
0.192914 | + | 0.981216i | \(0.438206\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.40650e7 | 1.45326 | ||||||||
\(773\) | −1.62017e7 | −0.975240 | −0.487620 | − | 0.873056i | \(-0.662135\pi\) | ||||
−0.487620 | + | 0.873056i | \(0.662135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.48696e7 | 0.889296 | ||||||||
\(776\) | −1.87435e7 | −1.11737 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.09593e7 | −1.83376 | ||||||||
\(779\) | −2.69386e7 | −1.59049 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.04404e6 | −0.413232 | ||||||||
\(782\) | 1.55096e7 | 0.906954 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.20901e7 | −1.85865 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.96547e7 | 1.13118 | 0.565588 | − | 0.824688i | \(-0.308649\pi\) | ||||
0.565588 | + | 0.824688i | \(0.308649\pi\) | |||||||
\(788\) | −3.31967e7 | −1.90449 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.61356e7 | −3.20015 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 907557. | 0.0512497 | ||||||||
\(794\) | 5.04500e6 | 0.283995 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.65308e7 | 3.16230 | ||||||||
\(797\) | 6.39709e6 | 0.356728 | 0.178364 | − | 0.983965i | \(-0.442920\pi\) | ||||
0.178364 | + | 0.983965i | \(0.442920\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.46636e7 | −0.812593 | ||||||||
\(800\) | 2.06393e7 | 1.14017 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −519238. | −0.0285056 | ||||||||
\(803\) | 1.36330e6 | 0.0746108 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.47700e6 | −0.459626 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.11859e7 | −2.75817 | ||||||||
\(809\) | 2.38705e7 | 1.28230 | 0.641152 | − | 0.767414i | \(-0.278457\pi\) | ||||
0.641152 | + | 0.767414i | \(0.278457\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.15356e7 | 1.68364 | 0.841819 | − | 0.539759i | \(-0.181485\pi\) | ||||
0.841819 | + | 0.539759i | \(0.181485\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.11023e7 | 1.64525 | ||||||||
\(815\) | 1.61416e7 | 0.851240 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.80651e7 | −1.47100 | ||||||||
\(818\) | −3.97163e7 | −2.07532 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.76292e7 | −4.03172 | ||||||||
\(821\) | 2.34305e7 | 1.21317 | 0.606587 | − | 0.795017i | \(-0.292538\pi\) | ||||
0.606587 | + | 0.795017i | \(0.292538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.71839e7 | 1.91362 | 0.956810 | − | 0.290712i | \(-0.0938923\pi\) | ||||
0.956810 | + | 0.290712i | \(0.0938923\pi\) | |||||||
\(824\) | −3.77299e6 | −0.193583 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 494429. | 0.0251386 | 0.0125693 | − | 0.999921i | \(-0.495999\pi\) | ||||
0.0125693 | + | 0.999921i | \(0.495999\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.33424e7 | 0.674293 | 0.337147 | − | 0.941452i | \(-0.390538\pi\) | ||||
0.337147 | + | 0.941452i | \(0.390538\pi\) | |||||||
\(830\) | 1.20026e7 | 0.604756 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.59718e6 | −0.230241 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.51053e6 | −0.372782 | ||||||||
\(836\) | −7.99631e7 | −3.95707 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.23832e6 | −0.356064 | ||||||||
\(839\) | −1.74957e7 | −0.858075 | −0.429038 | − | 0.903287i | \(-0.641147\pi\) | ||||
−0.429038 | + | 0.903287i | \(0.641147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68840e6 | −0.277332 | ||||||||
\(842\) | 1.64437e7 | 0.799316 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.71205e6 | −0.227695 | ||||||||
\(845\) | −2.46568e7 | −1.18794 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.36751e7 | 0.653040 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.92567e7 | 0.914186 | ||||||||
\(851\) | −6.44286e6 | −0.304968 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.83938e7 | −0.865565 | −0.432782 | − | 0.901498i | \(-0.642468\pi\) | ||||
−0.432782 | + | 0.901498i | \(0.642468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.60565e7 | 0.748975 | ||||||||
\(857\) | 3.65151e6 | 0.169832 | 0.0849161 | − | 0.996388i | \(-0.472938\pi\) | ||||
0.0849161 | + | 0.996388i | \(0.472938\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.12785e6 | 0.237111 | 0.118556 | − | 0.992947i | \(-0.462174\pi\) | ||||
0.118556 | + | 0.992947i | \(0.462174\pi\) | |||||||
\(860\) | −8.08756e7 | −3.72882 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.77397e7 | 3.10510 | ||||||||
\(863\) | −1.96489e7 | −0.898074 | −0.449037 | − | 0.893513i | \(-0.648233\pi\) | ||||
−0.449037 | + | 0.893513i | \(0.648233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.71647e7 | −2.14327 | ||||||||
\(866\) | −1.40926e7 | −0.638551 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.09339e7 | 1.83880 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.77508e6 | 0.123945 | ||||||||
\(872\) | 5.90478e7 | 2.62974 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.31218e7 | 1.02387 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.07559e7 | −1.35030 | −0.675150 | − | 0.737681i | \(-0.735921\pi\) | ||||
−0.675150 | + | 0.737681i | \(0.735921\pi\) | |||||||
\(878\) | −4.09309e7 | −1.79190 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.03097e8 | −4.48787 | ||||||||
\(881\) | −3.34518e7 | −1.45204 | −0.726022 | − | 0.687671i | \(-0.758633\pi\) | ||||
−0.726022 | + | 0.687671i | \(0.758633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.87952e7 | −1.24285 | −0.621425 | − | 0.783474i | \(-0.713446\pi\) | ||||
−0.621425 | + | 0.783474i | \(0.713446\pi\) | |||||||
\(884\) | −7.86462e6 | −0.338491 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.37139e7 | 0.586917 | ||||||||
\(887\) | −1.68365e7 | −0.718527 | −0.359264 | − | 0.933236i | \(-0.616972\pi\) | ||||
−0.359264 | + | 0.933236i | \(0.616972\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.63536e7 | 1.11523 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.08217e6 | −0.0876200 | ||||||||
\(893\) | −2.18605e7 | −0.917343 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.01126e6 | −0.292576 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.95619e7 | −3.29241 | ||||||||
\(899\) | 4.00932e7 | 1.65452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.93884e6 | 0.243719 | ||||||||
\(902\) | 7.90161e7 | 3.23370 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 464035. | 0.0188856 | ||||||||
\(905\) | 2.80197e7 | 1.13722 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.75606e6 | 0.393782 | 0.196891 | − | 0.980425i | \(-0.436915\pi\) | ||||
0.196891 | + | 0.980425i | \(0.436915\pi\) | |||||||
\(908\) | −7.93988e7 | −3.19594 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.67934e7 | −1.46884 | −0.734420 | − | 0.678696i | \(-0.762546\pi\) | ||||
−0.734420 | + | 0.678696i | \(0.762546\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.75226e6 | −0.347491 | ||||||||
\(914\) | 5.30398e6 | 0.210008 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.20307e7 | −1.65511 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.72178e7 | 0.672495 | 0.336248 | − | 0.941774i | \(-0.390842\pi\) | ||||
0.336248 | + | 0.941774i | \(0.390842\pi\) | |||||||
\(920\) | 4.02532e7 | 1.56794 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.68216e7 | −2.20133 | ||||||||
\(923\) | −1.03283e6 | −0.0399048 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.99943e6 | −0.307400 | ||||||||
\(926\) | −6.93124e7 | −2.65634 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.56500e7 | 2.12127 | ||||||||
\(929\) | 4.90559e7 | 1.86489 | 0.932443 | − | 0.361318i | \(-0.117673\pi\) | ||||
0.932443 | + | 0.361318i | \(0.117673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.85694e7 | −3.71708 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.40604e7 | −1.27756 | ||||||||
\(935\) | −4.47733e7 | −1.67491 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.80929e7 | 1.04532 | 0.522658 | − | 0.852542i | \(-0.324940\pi\) | ||||
0.522658 | + | 0.852542i | \(0.324940\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.29956e7 | −2.32536 | ||||||||
\(941\) | −2.28001e7 | −0.839389 | −0.419695 | − | 0.907665i | \(-0.637863\pi\) | ||||
−0.419695 | + | 0.907665i | \(0.637863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.63682e7 | −0.599409 | ||||||||
\(944\) | 8.50780e7 | 3.10733 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.23205e7 | 2.99075 | ||||||||
\(947\) | 4.35503e7 | 1.57803 | 0.789016 | − | 0.614372i | \(-0.210591\pi\) | ||||
0.789016 | + | 0.614372i | \(0.210591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 199894. | 0.00720499 | ||||||||
\(950\) | 2.87079e7 | 1.03203 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.54239e7 | 1.62014 | 0.810069 | − | 0.586335i | \(-0.199430\pi\) | ||||
0.810069 | + | 0.586335i | \(0.199430\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.84686e7 | −1.36489 | ||||||||
\(956\) | 7.35069e7 | 2.60126 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.42000e7 | −3.31617 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.98164e7 | 2.78794 | ||||||||
\(962\) | 4.56037e6 | 0.158878 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.18628e7 | 1.79748 | ||||||||
\(965\) | 2.00879e7 | 0.694411 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.43677e6 | 0.186971 | 0.0934855 | − | 0.995621i | \(-0.470199\pi\) | ||||
0.0934855 | + | 0.995621i | \(0.470199\pi\) | |||||||
\(968\) | 5.81542e7 | 1.99477 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.58984e7 | −0.883779 | ||||||||
\(971\) | −3.62705e7 | −1.23454 | −0.617270 | − | 0.786751i | \(-0.711762\pi\) | ||||
−0.617270 | + | 0.786751i | \(0.711762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.21111e7 | 2.09784 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.46220e7 | −1.16340 | ||||||||
\(977\) | −5.07312e6 | −0.170035 | −0.0850175 | − | 0.996379i | \(-0.527095\pi\) | ||||
−0.0850175 | + | 0.996379i | \(0.527095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.92169e7 | −0.640807 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.21350e6 | 0.0401571 | ||||||||
\(983\) | 915660. | 0.0302239 | 0.0151119 | − | 0.999886i | \(-0.495190\pi\) | ||||
0.0151119 | + | 0.999886i | \(0.495190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.77105e7 | −0.910026 | ||||||||
\(986\) | 5.19220e7 | 1.70082 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.17246e7 | −0.382125 | ||||||||
\(989\) | −1.70527e7 | −0.554375 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.83986e7 | −0.918571 | −0.459285 | − | 0.888289i | \(-0.651894\pi\) | ||||
−0.459285 | + | 0.888289i | \(0.651894\pi\) | |||||||
\(992\) | 1.50524e8 | 4.85655 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.71884e7 | 1.51104 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.44486e7 | −1.73480 | −0.867399 | − | 0.497613i | \(-0.834210\pi\) | ||||
−0.867399 | + | 0.497613i | \(0.834210\pi\) | |||||||
\(998\) | −9.92638e7 | −3.15475 | ||||||||
\(999\) | 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 | 441.6.a.bd.1.6 | 6 | ||
3.2 | odd | 2 | inner | 441.6.a.bd.1.1 | 6 | ||
7.3 | odd | 6 | 63.6.e.f.37.1 | ✓ | 12 | ||
7.5 | odd | 6 | 63.6.e.f.46.1 | yes | 12 | ||
7.6 | odd | 2 | 441.6.a.bc.1.6 | 6 | |||
21.5 | even | 6 | 63.6.e.f.46.6 | yes | 12 | ||
21.17 | even | 6 | 63.6.e.f.37.6 | yes | 12 | ||
21.20 | even | 2 | 441.6.a.bc.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.6.e.f.37.1 | ✓ | 12 | 7.3 | odd | 6 | ||
63.6.e.f.37.6 | yes | 12 | 21.17 | even | 6 | ||
63.6.e.f.46.1 | yes | 12 | 7.5 | odd | 6 | ||
63.6.e.f.46.6 | yes | 12 | 21.5 | even | 6 | ||
441.6.a.bc.1.1 | 6 | 21.20 | even | 2 | |||
441.6.a.bc.1.6 | 6 | 7.6 | odd | 2 | |||
441.6.a.bd.1.1 | 6 | 3.2 | odd | 2 | inner | ||
441.6.a.bd.1.6 | 6 | 1.1 | even | 1 | trivial |