Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,6,Mod(1,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, 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("150.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(24.0575729719\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 150.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 233.000 | 1.79726 | 0.898630 | − | 0.438708i | \(-0.144564\pi\) | ||||
0.898630 | + | 0.438708i | \(0.144564\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −498.000 | −1.24093 | −0.620465 | − | 0.784234i | \(-0.713056\pi\) | ||||
−0.620465 | + | 0.784234i | \(0.713056\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 809.000 | 1.32767 | 0.663835 | − | 0.747879i | \(-0.268928\pi\) | ||||
0.663835 | + | 0.747879i | \(0.268928\pi\) | |||||||
\(14\) | −932.000 | −1.27085 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1002.00 | −0.840902 | −0.420451 | − | 0.907315i | \(-0.638128\pi\) | ||||
−0.420451 | + | 0.907315i | \(0.638128\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −1705.00 | −1.08353 | −0.541764 | − | 0.840530i | \(-0.682243\pi\) | ||||
−0.541764 | + | 0.840530i | \(0.682243\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2097.00 | −1.03765 | ||||||||
\(22\) | 1992.00 | 0.877471 | ||||||||
\(23\) | 1554.00 | 0.612536 | 0.306268 | − | 0.951945i | \(-0.400920\pi\) | ||||
0.306268 | + | 0.951945i | \(0.400920\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3236.00 | −0.938804 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 3728.00 | 0.898630 | ||||||||
\(29\) | 7830.00 | 1.72889 | 0.864444 | − | 0.502729i | \(-0.167671\pi\) | ||||
0.864444 | + | 0.502729i | \(0.167671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 977.000 | 0.182596 | 0.0912978 | − | 0.995824i | \(-0.470898\pi\) | ||||
0.0912978 | + | 0.995824i | \(0.470898\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 4482.00 | 0.716452 | ||||||||
\(34\) | 4008.00 | 0.594608 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −4822.00 | −0.579059 | −0.289530 | − | 0.957169i | \(-0.593499\pi\) | ||||
−0.289530 | + | 0.957169i | \(0.593499\pi\) | |||||||
\(38\) | 6820.00 | 0.766170 | ||||||||
\(39\) | −7281.00 | −0.766531 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8148.00 | −0.756992 | −0.378496 | − | 0.925603i | \(-0.623559\pi\) | ||||
−0.378496 | + | 0.925603i | \(0.623559\pi\) | |||||||
\(42\) | 8388.00 | 0.733728 | ||||||||
\(43\) | 19469.0 | 1.60573 | 0.802865 | − | 0.596161i | \(-0.203308\pi\) | ||||
0.802865 | + | 0.596161i | \(0.203308\pi\) | |||||||
\(44\) | −7968.00 | −0.620465 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6216.00 | −0.433128 | ||||||||
\(47\) | 8418.00 | 0.555859 | 0.277929 | − | 0.960602i | \(-0.410352\pi\) | ||||
0.277929 | + | 0.960602i | \(0.410352\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 37482.0 | 2.23014 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9018.00 | 0.485495 | ||||||||
\(52\) | 12944.0 | 0.663835 | ||||||||
\(53\) | 17664.0 | 0.863773 | 0.431886 | − | 0.901928i | \(-0.357848\pi\) | ||||
0.431886 | + | 0.901928i | \(0.357848\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14912.0 | −0.635427 | ||||||||
\(57\) | 15345.0 | 0.625576 | ||||||||
\(58\) | −31320.0 | −1.22251 | ||||||||
\(59\) | 35910.0 | 1.34303 | 0.671514 | − | 0.740991i | \(-0.265644\pi\) | ||||
0.671514 | + | 0.740991i | \(0.265644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3527.00 | 0.121361 | 0.0606807 | − | 0.998157i | \(-0.480673\pi\) | ||||
0.0606807 | + | 0.998157i | \(0.480673\pi\) | |||||||
\(62\) | −3908.00 | −0.129115 | ||||||||
\(63\) | 18873.0 | 0.599087 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −17928.0 | −0.506608 | ||||||||
\(67\) | 57473.0 | 1.56414 | 0.782072 | − | 0.623188i | \(-0.214163\pi\) | ||||
0.782072 | + | 0.623188i | \(0.214163\pi\) | |||||||
\(68\) | −16032.0 | −0.420451 | ||||||||
\(69\) | −13986.0 | −0.353648 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7548.00 | −0.177699 | −0.0888497 | − | 0.996045i | \(-0.528319\pi\) | ||||
−0.0888497 | + | 0.996045i | \(0.528319\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | −646.000 | −0.0141881 | −0.00709407 | − | 0.999975i | \(-0.502258\pi\) | ||||
−0.00709407 | + | 0.999975i | \(0.502258\pi\) | |||||||
\(74\) | 19288.0 | 0.409457 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −27280.0 | −0.541764 | ||||||||
\(77\) | −116034. | −2.23028 | ||||||||
\(78\) | 29124.0 | 0.542019 | ||||||||
\(79\) | −22720.0 | −0.409582 | −0.204791 | − | 0.978806i | \(-0.565651\pi\) | ||||
−0.204791 | + | 0.978806i | \(0.565651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 32592.0 | 0.535274 | ||||||||
\(83\) | 11574.0 | 0.184412 | 0.0922058 | − | 0.995740i | \(-0.470608\pi\) | ||||
0.0922058 | + | 0.995740i | \(0.470608\pi\) | |||||||
\(84\) | −33552.0 | −0.518824 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −77876.0 | −1.13542 | ||||||||
\(87\) | −70470.0 | −0.998174 | ||||||||
\(88\) | 31872.0 | 0.438735 | ||||||||
\(89\) | −78960.0 | −1.05665 | −0.528326 | − | 0.849041i | \(-0.677180\pi\) | ||||
−0.528326 | + | 0.849041i | \(0.677180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 188497. | 2.38617 | ||||||||
\(92\) | 24864.0 | 0.306268 | ||||||||
\(93\) | −8793.00 | −0.105422 | ||||||||
\(94\) | −33672.0 | −0.393051 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 54593.0 | 0.589125 | 0.294563 | − | 0.955632i | \(-0.404826\pi\) | ||||
0.294563 | + | 0.955632i | \(0.404826\pi\) | |||||||
\(98\) | −149928. | −1.57695 | ||||||||
\(99\) | −40338.0 | −0.413644 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 105552. | 1.02959 | 0.514793 | − | 0.857314i | \(-0.327869\pi\) | ||||
0.514793 | + | 0.857314i | \(0.327869\pi\) | |||||||
\(102\) | −36072.0 | −0.343297 | ||||||||
\(103\) | −177436. | −1.64797 | −0.823984 | − | 0.566613i | \(-0.808253\pi\) | ||||
−0.823984 | + | 0.566613i | \(0.808253\pi\) | |||||||
\(104\) | −51776.0 | −0.469402 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −70656.0 | −0.610779 | ||||||||
\(107\) | −183792. | −1.55191 | −0.775956 | − | 0.630787i | \(-0.782732\pi\) | ||||
−0.775956 | + | 0.630787i | \(0.782732\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 169685. | 1.36797 | 0.683986 | − | 0.729495i | \(-0.260245\pi\) | ||||
0.683986 | + | 0.729495i | \(0.260245\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 43398.0 | 0.334320 | ||||||||
\(112\) | 59648.0 | 0.449315 | ||||||||
\(113\) | 263484. | 1.94115 | 0.970573 | − | 0.240808i | \(-0.0774123\pi\) | ||||
0.970573 | + | 0.240808i | \(0.0774123\pi\) | |||||||
\(114\) | −61380.0 | −0.442349 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 125280. | 0.864444 | ||||||||
\(117\) | 65529.0 | 0.442557 | ||||||||
\(118\) | −143640. | −0.949665 | ||||||||
\(119\) | −233466. | −1.51132 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 86953.0 | 0.539910 | ||||||||
\(122\) | −14108.0 | −0.0858155 | ||||||||
\(123\) | 73332.0 | 0.437050 | ||||||||
\(124\) | 15632.0 | 0.0912978 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −75492.0 | −0.423618 | ||||||||
\(127\) | −256912. | −1.41343 | −0.706716 | − | 0.707497i | \(-0.749824\pi\) | ||||
−0.706716 | + | 0.707497i | \(0.749824\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −175221. | −0.927069 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −219048. | −1.11522 | −0.557611 | − | 0.830103i | \(-0.688282\pi\) | ||||
−0.557611 | + | 0.830103i | \(0.688282\pi\) | |||||||
\(132\) | 71712.0 | 0.358226 | ||||||||
\(133\) | −397265. | −1.94738 | ||||||||
\(134\) | −229892. | −1.10602 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 64128.0 | 0.297304 | ||||||||
\(137\) | 228678. | 1.04093 | 0.520467 | − | 0.853882i | \(-0.325758\pi\) | ||||
0.520467 | + | 0.853882i | \(0.325758\pi\) | |||||||
\(138\) | 55944.0 | 0.250067 | ||||||||
\(139\) | 339740. | 1.49145 | 0.745727 | − | 0.666252i | \(-0.232102\pi\) | ||||
0.745727 | + | 0.666252i | \(0.232102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −75762.0 | −0.320925 | ||||||||
\(142\) | 30192.0 | 0.125652 | ||||||||
\(143\) | −402882. | −1.64755 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2584.00 | 0.0100325 | ||||||||
\(147\) | −337338. | −1.28757 | ||||||||
\(148\) | −77152.0 | −0.289530 | ||||||||
\(149\) | 306450. | 1.13082 | 0.565411 | − | 0.824810i | \(-0.308718\pi\) | ||||
0.565411 | + | 0.824810i | \(0.308718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 198827. | 0.709632 | 0.354816 | − | 0.934936i | \(-0.384544\pi\) | ||||
0.354816 | + | 0.934936i | \(0.384544\pi\) | |||||||
\(152\) | 109120. | 0.383085 | ||||||||
\(153\) | −81162.0 | −0.280301 | ||||||||
\(154\) | 464136. | 1.57704 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −116496. | −0.383265 | ||||||||
\(157\) | 361283. | 1.16976 | 0.584882 | − | 0.811118i | \(-0.301141\pi\) | ||||
0.584882 | + | 0.811118i | \(0.301141\pi\) | |||||||
\(158\) | 90880.0 | 0.289618 | ||||||||
\(159\) | −158976. | −0.498699 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 362082. | 1.10089 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | 338159. | 0.996901 | 0.498450 | − | 0.866918i | \(-0.333903\pi\) | ||||
0.498450 | + | 0.866918i | \(0.333903\pi\) | |||||||
\(164\) | −130368. | −0.378496 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −46296.0 | −0.130399 | ||||||||
\(167\) | 430248. | 1.19379 | 0.596895 | − | 0.802320i | \(-0.296401\pi\) | ||||
0.596895 | + | 0.802320i | \(0.296401\pi\) | |||||||
\(168\) | 134208. | 0.366864 | ||||||||
\(169\) | 283188. | 0.762708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −138105. | −0.361176 | ||||||||
\(172\) | 311504. | 0.802865 | ||||||||
\(173\) | 603354. | 1.53270 | 0.766350 | − | 0.642424i | \(-0.222071\pi\) | ||||
0.766350 | + | 0.642424i | \(0.222071\pi\) | |||||||
\(174\) | 281880. | 0.705815 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −127488. | −0.310233 | ||||||||
\(177\) | −323190. | −0.775398 | ||||||||
\(178\) | 315840. | 0.747166 | ||||||||
\(179\) | −374370. | −0.873310 | −0.436655 | − | 0.899629i | \(-0.643837\pi\) | ||||
−0.436655 | + | 0.899629i | \(0.643837\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −232423. | −0.527330 | −0.263665 | − | 0.964614i | \(-0.584931\pi\) | ||||
−0.263665 | + | 0.964614i | \(0.584931\pi\) | |||||||
\(182\) | −753988. | −1.68728 | ||||||||
\(183\) | −31743.0 | −0.0700681 | ||||||||
\(184\) | −99456.0 | −0.216564 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 35172.0 | 0.0745443 | ||||||||
\(187\) | 498996. | 1.04350 | ||||||||
\(188\) | 134688. | 0.277929 | ||||||||
\(189\) | −169857. | −0.345883 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −846198. | −1.67837 | −0.839187 | − | 0.543843i | \(-0.816969\pi\) | ||||
−0.839187 | + | 0.543843i | \(0.816969\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −155581. | −0.300651 | −0.150326 | − | 0.988637i | \(-0.548032\pi\) | ||||
−0.150326 | + | 0.988637i | \(0.548032\pi\) | |||||||
\(194\) | −218372. | −0.416574 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 599712. | 1.11507 | ||||||||
\(197\) | −103482. | −0.189976 | −0.0949881 | − | 0.995478i | \(-0.530281\pi\) | ||||
−0.0949881 | + | 0.995478i | \(0.530281\pi\) | |||||||
\(198\) | 161352. | 0.292490 | ||||||||
\(199\) | −140425. | −0.251369 | −0.125685 | − | 0.992070i | \(-0.540113\pi\) | ||||
−0.125685 | + | 0.992070i | \(0.540113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −517257. | −0.903059 | ||||||||
\(202\) | −422208. | −0.728028 | ||||||||
\(203\) | 1.82439e6 | 3.10726 | ||||||||
\(204\) | 144288. | 0.242748 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 709744. | 1.16529 | ||||||||
\(207\) | 125874. | 0.204179 | ||||||||
\(208\) | 207104. | 0.331917 | ||||||||
\(209\) | 849090. | 1.34458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −462673. | −0.715431 | −0.357716 | − | 0.933831i | \(-0.616444\pi\) | ||||
−0.357716 | + | 0.933831i | \(0.616444\pi\) | |||||||
\(212\) | 282624. | 0.431886 | ||||||||
\(213\) | 67932.0 | 0.102595 | ||||||||
\(214\) | 735168. | 1.09737 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 227641. | 0.328172 | ||||||||
\(218\) | −678740. | −0.967302 | ||||||||
\(219\) | 5814.00 | 0.00819152 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −810618. | −1.11644 | ||||||||
\(222\) | −173592. | −0.236400 | ||||||||
\(223\) | −735271. | −0.990114 | −0.495057 | − | 0.868860i | \(-0.664853\pi\) | ||||
−0.495057 | + | 0.868860i | \(0.664853\pi\) | |||||||
\(224\) | −238592. | −0.317714 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.05394e6 | −1.37260 | ||||||||
\(227\) | 967188. | 1.24579 | 0.622897 | − | 0.782304i | \(-0.285956\pi\) | ||||
0.622897 | + | 0.782304i | \(0.285956\pi\) | |||||||
\(228\) | 245520. | 0.312788 | ||||||||
\(229\) | −83695.0 | −0.105466 | −0.0527328 | − | 0.998609i | \(-0.516793\pi\) | ||||
−0.0527328 | + | 0.998609i | \(0.516793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.04431e6 | 1.28765 | ||||||||
\(232\) | −501120. | −0.611254 | ||||||||
\(233\) | −873876. | −1.05453 | −0.527266 | − | 0.849700i | \(-0.676783\pi\) | ||||
−0.527266 | + | 0.849700i | \(0.676783\pi\) | |||||||
\(234\) | −262116. | −0.312935 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 574560. | 0.671514 | ||||||||
\(237\) | 204480. | 0.236472 | ||||||||
\(238\) | 933864. | 1.06866 | ||||||||
\(239\) | −1.06056e6 | −1.20099 | −0.600497 | − | 0.799627i | \(-0.705030\pi\) | ||||
−0.600497 | + | 0.799627i | \(0.705030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −756823. | −0.839367 | −0.419683 | − | 0.907671i | \(-0.637859\pi\) | ||||
−0.419683 | + | 0.907671i | \(0.637859\pi\) | |||||||
\(242\) | −347812. | −0.381774 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 56432.0 | 0.0606807 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −293328. | −0.309041 | ||||||||
\(247\) | −1.37934e6 | −1.43857 | ||||||||
\(248\) | −62528.0 | −0.0645573 | ||||||||
\(249\) | −104166. | −0.106470 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −635148. | −0.636342 | −0.318171 | − | 0.948033i | \(-0.603069\pi\) | ||||
−0.318171 | + | 0.948033i | \(0.603069\pi\) | |||||||
\(252\) | 301968. | 0.299543 | ||||||||
\(253\) | −773892. | −0.760115 | ||||||||
\(254\) | 1.02765e6 | 0.999448 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 30708.0 | 0.0290014 | 0.0145007 | − | 0.999895i | \(-0.495384\pi\) | ||||
0.0145007 | + | 0.999895i | \(0.495384\pi\) | |||||||
\(258\) | 700884. | 0.655537 | ||||||||
\(259\) | −1.12353e6 | −1.04072 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 634230. | 0.576296 | ||||||||
\(262\) | 876192. | 0.788581 | ||||||||
\(263\) | −189516. | −0.168949 | −0.0844747 | − | 0.996426i | \(-0.526921\pi\) | ||||
−0.0844747 | + | 0.996426i | \(0.526921\pi\) | |||||||
\(264\) | −286848. | −0.253304 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.58906e6 | 1.37701 | ||||||||
\(267\) | 710640. | 0.610059 | ||||||||
\(268\) | 919568. | 0.782072 | ||||||||
\(269\) | 1.10997e6 | 0.935256 | 0.467628 | − | 0.883925i | \(-0.345109\pi\) | ||||
0.467628 | + | 0.883925i | \(0.345109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 211952. | 0.175313 | 0.0876565 | − | 0.996151i | \(-0.472062\pi\) | ||||
0.0876565 | + | 0.996151i | \(0.472062\pi\) | |||||||
\(272\) | −256512. | −0.210226 | ||||||||
\(273\) | −1.69647e6 | −1.37765 | ||||||||
\(274\) | −914712. | −0.736051 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −223776. | −0.176824 | ||||||||
\(277\) | 1.04741e6 | 0.820198 | 0.410099 | − | 0.912041i | \(-0.365494\pi\) | ||||
0.410099 | + | 0.912041i | \(0.365494\pi\) | |||||||
\(278\) | −1.35896e6 | −1.05462 | ||||||||
\(279\) | 79137.0 | 0.0608652 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 34002.0 | 0.0256885 | 0.0128442 | − | 0.999918i | \(-0.495911\pi\) | ||||
0.0128442 | + | 0.999918i | \(0.495911\pi\) | |||||||
\(282\) | 303048. | 0.226928 | ||||||||
\(283\) | −281101. | −0.208639 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(284\) | −120768. | −0.0888497 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.61153e6 | 1.16499 | ||||||||
\(287\) | −1.89848e6 | −1.36051 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −415853. | −0.292884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −491337. | −0.340132 | ||||||||
\(292\) | −10336.0 | −0.00709407 | ||||||||
\(293\) | −1.55851e6 | −1.06057 | −0.530285 | − | 0.847819i | \(-0.677915\pi\) | ||||
−0.530285 | + | 0.847819i | \(0.677915\pi\) | |||||||
\(294\) | 1.34935e6 | 0.910452 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 308608. | 0.204728 | ||||||||
\(297\) | 363042. | 0.238817 | ||||||||
\(298\) | −1.22580e6 | −0.799611 | ||||||||
\(299\) | 1.25719e6 | 0.813245 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.53628e6 | 2.88591 | ||||||||
\(302\) | −795308. | −0.501785 | ||||||||
\(303\) | −949968. | −0.594432 | ||||||||
\(304\) | −436480. | −0.270882 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 324648. | 0.198203 | ||||||||
\(307\) | −839917. | −0.508616 | −0.254308 | − | 0.967123i | \(-0.581848\pi\) | ||||
−0.254308 | + | 0.967123i | \(0.581848\pi\) | |||||||
\(308\) | −1.85654e6 | −1.11514 | ||||||||
\(309\) | 1.59692e6 | 0.951455 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −292698. | −0.171601 | −0.0858003 | − | 0.996312i | \(-0.527345\pi\) | ||||
−0.0858003 | + | 0.996312i | \(0.527345\pi\) | |||||||
\(312\) | 465984. | 0.271010 | ||||||||
\(313\) | 127859. | 0.0737684 | 0.0368842 | − | 0.999320i | \(-0.488257\pi\) | ||||
0.0368842 | + | 0.999320i | \(0.488257\pi\) | |||||||
\(314\) | −1.44513e6 | −0.827148 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −363520. | −0.204791 | ||||||||
\(317\) | 648048. | 0.362209 | 0.181104 | − | 0.983464i | \(-0.442033\pi\) | ||||
0.181104 | + | 0.983464i | \(0.442033\pi\) | |||||||
\(318\) | 635904. | 0.352634 | ||||||||
\(319\) | −3.89934e6 | −2.14543 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.65413e6 | 0.895997 | ||||||||
\(322\) | −1.44833e6 | −0.778444 | ||||||||
\(323\) | 1.70841e6 | 0.911141 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.35264e6 | −0.704915 | ||||||||
\(327\) | −1.52716e6 | −0.789799 | ||||||||
\(328\) | 521472. | 0.267637 | ||||||||
\(329\) | 1.96139e6 | 0.999022 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.39315e6 | −1.70229 | −0.851144 | − | 0.524933i | \(-0.824090\pi\) | ||||
−0.851144 | + | 0.524933i | \(0.824090\pi\) | |||||||
\(332\) | 185184. | 0.0922058 | ||||||||
\(333\) | −390582. | −0.193020 | ||||||||
\(334\) | −1.72099e6 | −0.844137 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −536832. | −0.259412 | ||||||||
\(337\) | −1.62085e6 | −0.777441 | −0.388720 | − | 0.921356i | \(-0.627083\pi\) | ||||
−0.388720 | + | 0.921356i | \(0.627083\pi\) | |||||||
\(338\) | −1.13275e6 | −0.539316 | ||||||||
\(339\) | −2.37136e6 | −1.12072 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −486546. | −0.226589 | ||||||||
\(342\) | 552420. | 0.255390 | ||||||||
\(343\) | 4.81728e6 | 2.21088 | ||||||||
\(344\) | −1.24602e6 | −0.567711 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.41342e6 | −1.08378 | ||||||||
\(347\) | −1.28638e6 | −0.573517 | −0.286758 | − | 0.958003i | \(-0.592578\pi\) | ||||
−0.286758 | + | 0.958003i | \(0.592578\pi\) | |||||||
\(348\) | −1.12752e6 | −0.499087 | ||||||||
\(349\) | −2.73055e6 | −1.20001 | −0.600007 | − | 0.799994i | \(-0.704836\pi\) | ||||
−0.600007 | + | 0.799994i | \(0.704836\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −589761. | −0.255510 | ||||||||
\(352\) | 509952. | 0.219368 | ||||||||
\(353\) | −2.13649e6 | −0.912564 | −0.456282 | − | 0.889835i | \(-0.650819\pi\) | ||||
−0.456282 | + | 0.889835i | \(0.650819\pi\) | |||||||
\(354\) | 1.29276e6 | 0.548289 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.26336e6 | −0.528326 | ||||||||
\(357\) | 2.10119e6 | 0.872561 | ||||||||
\(358\) | 1.49748e6 | 0.617523 | ||||||||
\(359\) | 3.26406e6 | 1.33666 | 0.668332 | − | 0.743863i | \(-0.267009\pi\) | ||||
0.668332 | + | 0.743863i | \(0.267009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 430926. | 0.174034 | ||||||||
\(362\) | 929692. | 0.372879 | ||||||||
\(363\) | −782577. | −0.311717 | ||||||||
\(364\) | 3.01595e6 | 1.19308 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 126972. | 0.0495456 | ||||||||
\(367\) | −4.15078e6 | −1.60866 | −0.804330 | − | 0.594183i | \(-0.797476\pi\) | ||||
−0.804330 | + | 0.594183i | \(0.797476\pi\) | |||||||
\(368\) | 397824. | 0.153134 | ||||||||
\(369\) | −659988. | −0.252331 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.11571e6 | 1.55242 | ||||||||
\(372\) | −140688. | −0.0527108 | ||||||||
\(373\) | −2.14242e6 | −0.797320 | −0.398660 | − | 0.917099i | \(-0.630525\pi\) | ||||
−0.398660 | + | 0.917099i | \(0.630525\pi\) | |||||||
\(374\) | −1.99598e6 | −0.737867 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −538752. | −0.196526 | ||||||||
\(377\) | 6.33447e6 | 2.29539 | ||||||||
\(378\) | 679428. | 0.244576 | ||||||||
\(379\) | −1.94699e6 | −0.696253 | −0.348126 | − | 0.937448i | \(-0.613182\pi\) | ||||
−0.348126 | + | 0.937448i | \(0.613182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.31221e6 | 0.816046 | ||||||||
\(382\) | 3.38479e6 | 1.18679 | ||||||||
\(383\) | 2.65052e6 | 0.923283 | 0.461641 | − | 0.887067i | \(-0.347261\pi\) | ||||
0.461641 | + | 0.887067i | \(0.347261\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 622324. | 0.212593 | ||||||||
\(387\) | 1.57699e6 | 0.535243 | ||||||||
\(388\) | 873488. | 0.294563 | ||||||||
\(389\) | 282540. | 0.0946686 | 0.0473343 | − | 0.998879i | \(-0.484927\pi\) | ||||
0.0473343 | + | 0.998879i | \(0.484927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.55711e6 | −0.515083 | ||||||||
\(392\) | −2.39885e6 | −0.788474 | ||||||||
\(393\) | 1.97143e6 | 0.643873 | ||||||||
\(394\) | 413928. | 0.134333 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −645408. | −0.206822 | ||||||||
\(397\) | −2.62066e6 | −0.834515 | −0.417257 | − | 0.908788i | \(-0.637009\pi\) | ||||
−0.417257 | + | 0.908788i | \(0.637009\pi\) | |||||||
\(398\) | 561700. | 0.177745 | ||||||||
\(399\) | 3.57538e6 | 1.12432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −286248. | −0.0888959 | −0.0444479 | − | 0.999012i | \(-0.514153\pi\) | ||||
−0.0444479 | + | 0.999012i | \(0.514153\pi\) | |||||||
\(402\) | 2.06903e6 | 0.638559 | ||||||||
\(403\) | 790393. | 0.242427 | ||||||||
\(404\) | 1.68883e6 | 0.514793 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.29756e6 | −2.19716 | ||||||||
\(407\) | 2.40136e6 | 0.718572 | ||||||||
\(408\) | −577152. | −0.171648 | ||||||||
\(409\) | 4.12069e6 | 1.21804 | 0.609019 | − | 0.793155i | \(-0.291563\pi\) | ||||
0.609019 | + | 0.793155i | \(0.291563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.05810e6 | −0.600983 | ||||||||
\(412\) | −2.83898e6 | −0.823984 | ||||||||
\(413\) | 8.36703e6 | 2.41377 | ||||||||
\(414\) | −503496. | −0.144376 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −828416. | −0.234701 | ||||||||
\(417\) | −3.05766e6 | −0.861091 | ||||||||
\(418\) | −3.39636e6 | −0.950765 | ||||||||
\(419\) | −2.37948e6 | −0.662136 | −0.331068 | − | 0.943607i | \(-0.607409\pi\) | ||||
−0.331068 | + | 0.943607i | \(0.607409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −741298. | −0.203839 | −0.101920 | − | 0.994793i | \(-0.532498\pi\) | ||||
−0.101920 | + | 0.994793i | \(0.532498\pi\) | |||||||
\(422\) | 1.85069e6 | 0.505886 | ||||||||
\(423\) | 681858. | 0.185286 | ||||||||
\(424\) | −1.13050e6 | −0.305390 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −271728. | −0.0725455 | ||||||||
\(427\) | 821791. | 0.218118 | ||||||||
\(428\) | −2.94067e6 | −0.775956 | ||||||||
\(429\) | 3.62594e6 | 0.951212 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −187398. | −0.0485928 | −0.0242964 | − | 0.999705i | \(-0.507735\pi\) | ||||
−0.0242964 | + | 0.999705i | \(0.507735\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 6.55110e6 | 1.67917 | 0.839585 | − | 0.543229i | \(-0.182798\pi\) | ||||
0.839585 | + | 0.543229i | \(0.182798\pi\) | |||||||
\(434\) | −910564. | −0.232052 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.71496e6 | 0.683986 | ||||||||
\(437\) | −2.64957e6 | −0.663700 | ||||||||
\(438\) | −23256.0 | −0.00579228 | ||||||||
\(439\) | 270065. | 0.0668817 | 0.0334408 | − | 0.999441i | \(-0.489353\pi\) | ||||
0.0334408 | + | 0.999441i | \(0.489353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.03604e6 | 0.743381 | ||||||||
\(442\) | 3.24247e6 | 0.789443 | ||||||||
\(443\) | 2.77934e6 | 0.672873 | 0.336436 | − | 0.941706i | \(-0.390778\pi\) | ||||
0.336436 | + | 0.941706i | \(0.390778\pi\) | |||||||
\(444\) | 694368. | 0.167160 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.94108e6 | 0.700116 | ||||||||
\(447\) | −2.75805e6 | −0.652880 | ||||||||
\(448\) | 954368. | 0.224657 | ||||||||
\(449\) | 7.86630e6 | 1.84143 | 0.920714 | − | 0.390238i | \(-0.127607\pi\) | ||||
0.920714 | + | 0.390238i | \(0.127607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.05770e6 | 0.939375 | ||||||||
\(452\) | 4.21574e6 | 0.970573 | ||||||||
\(453\) | −1.78944e6 | −0.409706 | ||||||||
\(454\) | −3.86875e6 | −0.880909 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −982080. | −0.221174 | ||||||||
\(457\) | 6.23356e6 | 1.39619 | 0.698097 | − | 0.716004i | \(-0.254031\pi\) | ||||
0.698097 | + | 0.716004i | \(0.254031\pi\) | |||||||
\(458\) | 334780. | 0.0745754 | ||||||||
\(459\) | 730458. | 0.161832 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.68305e6 | −1.02630 | −0.513152 | − | 0.858298i | \(-0.671522\pi\) | ||||
−0.513152 | + | 0.858298i | \(0.671522\pi\) | |||||||
\(462\) | −4.17722e6 | −0.910506 | ||||||||
\(463\) | −382816. | −0.0829923 | −0.0414961 | − | 0.999139i | \(-0.513212\pi\) | ||||
−0.0414961 | + | 0.999139i | \(0.513212\pi\) | |||||||
\(464\) | 2.00448e6 | 0.432222 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.49550e6 | 0.745667 | ||||||||
\(467\) | −1.93540e6 | −0.410657 | −0.205328 | − | 0.978693i | \(-0.565826\pi\) | ||||
−0.205328 | + | 0.978693i | \(0.565826\pi\) | |||||||
\(468\) | 1.04846e6 | 0.221278 | ||||||||
\(469\) | 1.33912e7 | 2.81117 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.25155e6 | −0.675364 | ||||||||
\(472\) | −2.29824e6 | −0.474832 | ||||||||
\(473\) | −9.69556e6 | −1.99260 | ||||||||
\(474\) | −817920. | −0.167211 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.73546e6 | −0.755660 | ||||||||
\(477\) | 1.43078e6 | 0.287924 | ||||||||
\(478\) | 4.24224e6 | 0.849230 | ||||||||
\(479\) | −5.56917e6 | −1.10905 | −0.554526 | − | 0.832167i | \(-0.687100\pi\) | ||||
−0.554526 | + | 0.832167i | \(0.687100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.90100e6 | −0.768799 | ||||||||
\(482\) | 3.02729e6 | 0.593522 | ||||||||
\(483\) | −3.25874e6 | −0.635597 | ||||||||
\(484\) | 1.39125e6 | 0.269955 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 4.22450e6 | 0.807148 | 0.403574 | − | 0.914947i | \(-0.367768\pi\) | ||||
0.403574 | + | 0.914947i | \(0.367768\pi\) | |||||||
\(488\) | −225728. | −0.0429078 | ||||||||
\(489\) | −3.04343e6 | −0.575561 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.96295e6 | 1.30344 | 0.651718 | − | 0.758461i | \(-0.274049\pi\) | ||||
0.651718 | + | 0.758461i | \(0.274049\pi\) | |||||||
\(492\) | 1.17331e6 | 0.218525 | ||||||||
\(493\) | −7.84566e6 | −1.45383 | ||||||||
\(494\) | 5.51738e6 | 1.01722 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 250112. | 0.0456489 | ||||||||
\(497\) | −1.75868e6 | −0.319372 | ||||||||
\(498\) | 416664. | 0.0752857 | ||||||||
\(499\) | −9.29582e6 | −1.67123 | −0.835616 | − | 0.549315i | \(-0.814889\pi\) | ||||
−0.835616 | + | 0.549315i | \(0.814889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.87223e6 | −0.689235 | ||||||||
\(502\) | 2.54059e6 | 0.449962 | ||||||||
\(503\) | 6.34136e6 | 1.11754 | 0.558770 | − | 0.829323i | \(-0.311274\pi\) | ||||
0.558770 | + | 0.829323i | \(0.311274\pi\) | |||||||
\(504\) | −1.20787e6 | −0.211809 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.09557e6 | 0.537482 | ||||||||
\(507\) | −2.54869e6 | −0.440349 | ||||||||
\(508\) | −4.11059e6 | −0.706716 | ||||||||
\(509\) | −7.38309e6 | −1.26312 | −0.631559 | − | 0.775328i | \(-0.717585\pi\) | ||||
−0.631559 | + | 0.775328i | \(0.717585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −150518. | −0.0254998 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 1.24294e6 | 0.208525 | ||||||||
\(514\) | −122832. | −0.0205071 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.80354e6 | −0.463534 | ||||||||
\(517\) | −4.19216e6 | −0.689782 | ||||||||
\(518\) | 4.49410e6 | 0.735900 | ||||||||
\(519\) | −5.43019e6 | −0.884904 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.19620e6 | 0.677270 | 0.338635 | − | 0.940918i | \(-0.390035\pi\) | ||||
0.338635 | + | 0.940918i | \(0.390035\pi\) | |||||||
\(522\) | −2.53692e6 | −0.407503 | ||||||||
\(523\) | −3.57942e6 | −0.572214 | −0.286107 | − | 0.958198i | \(-0.592361\pi\) | ||||
−0.286107 | + | 0.958198i | \(0.592361\pi\) | |||||||
\(524\) | −3.50477e6 | −0.557611 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 758064. | 0.119465 | ||||||||
\(527\) | −978954. | −0.153545 | ||||||||
\(528\) | 1.14739e6 | 0.179113 | ||||||||
\(529\) | −4.02143e6 | −0.624800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.90871e6 | 0.447676 | ||||||||
\(532\) | −6.35624e6 | −0.973691 | ||||||||
\(533\) | −6.59173e6 | −1.00504 | ||||||||
\(534\) | −2.84256e6 | −0.431377 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.67827e6 | −0.553009 | ||||||||
\(537\) | 3.36933e6 | 0.504206 | ||||||||
\(538\) | −4.43988e6 | −0.661326 | ||||||||
\(539\) | −1.86660e7 | −2.76745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.95548e6 | 0.727934 | 0.363967 | − | 0.931412i | \(-0.381422\pi\) | ||||
0.363967 | + | 0.931412i | \(0.381422\pi\) | |||||||
\(542\) | −847808. | −0.123965 | ||||||||
\(543\) | 2.09181e6 | 0.304454 | ||||||||
\(544\) | 1.02605e6 | 0.148652 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.78589e6 | 0.974149 | ||||||||
\(547\) | −5.31803e6 | −0.759946 | −0.379973 | − | 0.924998i | \(-0.624067\pi\) | ||||
−0.379973 | + | 0.924998i | \(0.624067\pi\) | |||||||
\(548\) | 3.65885e6 | 0.520467 | ||||||||
\(549\) | 285687. | 0.0404538 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.33502e7 | −1.87330 | ||||||||
\(552\) | 895104. | 0.125033 | ||||||||
\(553\) | −5.29376e6 | −0.736125 | ||||||||
\(554\) | −4.18965e6 | −0.579967 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.43584e6 | 0.745727 | ||||||||
\(557\) | −4.25794e6 | −0.581516 | −0.290758 | − | 0.956797i | \(-0.593907\pi\) | ||||
−0.290758 | + | 0.956797i | \(0.593907\pi\) | |||||||
\(558\) | −316548. | −0.0430382 | ||||||||
\(559\) | 1.57504e7 | 2.13188 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.49096e6 | −0.602466 | ||||||||
\(562\) | −136008. | −0.0181645 | ||||||||
\(563\) | −4.37617e6 | −0.581866 | −0.290933 | − | 0.956743i | \(-0.593966\pi\) | ||||
−0.290933 | + | 0.956743i | \(0.593966\pi\) | |||||||
\(564\) | −1.21219e6 | −0.160463 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.12440e6 | 0.147530 | ||||||||
\(567\) | 1.52871e6 | 0.199696 | ||||||||
\(568\) | 483072. | 0.0628262 | ||||||||
\(569\) | 3.57717e6 | 0.463190 | 0.231595 | − | 0.972812i | \(-0.425606\pi\) | ||||
0.231595 | + | 0.972812i | \(0.425606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.94693e6 | 0.249896 | 0.124948 | − | 0.992163i | \(-0.460124\pi\) | ||||
0.124948 | + | 0.992163i | \(0.460124\pi\) | |||||||
\(572\) | −6.44611e6 | −0.823773 | ||||||||
\(573\) | 7.61578e6 | 0.969009 | ||||||||
\(574\) | 7.59394e6 | 0.962027 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 6.95576e6 | 0.869772 | 0.434886 | − | 0.900486i | \(-0.356789\pi\) | ||||
0.434886 | + | 0.900486i | \(0.356789\pi\) | |||||||
\(578\) | 1.66341e6 | 0.207100 | ||||||||
\(579\) | 1.40023e6 | 0.173581 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.69674e6 | 0.331436 | ||||||||
\(582\) | 1.96535e6 | 0.240509 | ||||||||
\(583\) | −8.79667e6 | −1.07188 | ||||||||
\(584\) | 41344.0 | 0.00501626 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.23402e6 | 0.749936 | ||||||||
\(587\) | 2.41853e6 | 0.289705 | 0.144852 | − | 0.989453i | \(-0.453729\pi\) | ||||
0.144852 | + | 0.989453i | \(0.453729\pi\) | |||||||
\(588\) | −5.39741e6 | −0.643787 | ||||||||
\(589\) | −1.66578e6 | −0.197848 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 931338. | 0.109683 | ||||||||
\(592\) | −1.23443e6 | −0.144765 | ||||||||
\(593\) | −9.58396e6 | −1.11920 | −0.559600 | − | 0.828763i | \(-0.689045\pi\) | ||||
−0.559600 | + | 0.828763i | \(0.689045\pi\) | |||||||
\(594\) | −1.45217e6 | −0.168869 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.90320e6 | 0.565411 | ||||||||
\(597\) | 1.26382e6 | 0.145128 | ||||||||
\(598\) | −5.02874e6 | −0.575051 | ||||||||
\(599\) | −1.52070e6 | −0.173172 | −0.0865858 | − | 0.996244i | \(-0.527596\pi\) | ||||
−0.0865858 | + | 0.996244i | \(0.527596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.88283e6 | 0.438492 | 0.219246 | − | 0.975670i | \(-0.429640\pi\) | ||||
0.219246 | + | 0.975670i | \(0.429640\pi\) | |||||||
\(602\) | −1.81451e7 | −2.04065 | ||||||||
\(603\) | 4.65531e6 | 0.521381 | ||||||||
\(604\) | 3.18123e6 | 0.354816 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.79987e6 | 0.420327 | ||||||||
\(607\) | −107992. | −0.0118965 | −0.00594826 | − | 0.999982i | \(-0.501893\pi\) | ||||
−0.00594826 | + | 0.999982i | \(0.501893\pi\) | |||||||
\(608\) | 1.74592e6 | 0.191543 | ||||||||
\(609\) | −1.64195e7 | −1.79398 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.81016e6 | 0.737997 | ||||||||
\(612\) | −1.29859e6 | −0.140150 | ||||||||
\(613\) | 7.49923e6 | 0.806057 | 0.403028 | − | 0.915187i | \(-0.367958\pi\) | ||||
0.403028 | + | 0.915187i | \(0.367958\pi\) | |||||||
\(614\) | 3.35967e6 | 0.359646 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.42618e6 | 0.788521 | ||||||||
\(617\) | −1.22695e6 | −0.129752 | −0.0648761 | − | 0.997893i | \(-0.520665\pi\) | ||||
−0.0648761 | + | 0.997893i | \(0.520665\pi\) | |||||||
\(618\) | −6.38770e6 | −0.672780 | ||||||||
\(619\) | 9.51340e6 | 0.997950 | 0.498975 | − | 0.866616i | \(-0.333710\pi\) | ||||
0.498975 | + | 0.866616i | \(0.333710\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.13287e6 | −0.117883 | ||||||||
\(622\) | 1.17079e6 | 0.121340 | ||||||||
\(623\) | −1.83977e7 | −1.89908 | ||||||||
\(624\) | −1.86394e6 | −0.191633 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −511436. | −0.0521621 | ||||||||
\(627\) | −7.64181e6 | −0.776296 | ||||||||
\(628\) | 5.78053e6 | 0.584882 | ||||||||
\(629\) | 4.83164e6 | 0.486932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.56449e7 | −1.56423 | −0.782114 | − | 0.623135i | \(-0.785859\pi\) | ||||
−0.782114 | + | 0.623135i | \(0.785859\pi\) | |||||||
\(632\) | 1.45408e6 | 0.144809 | ||||||||
\(633\) | 4.16406e6 | 0.413055 | ||||||||
\(634\) | −2.59219e6 | −0.256120 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.54362e6 | −0.249350 | ||||||||
\(637\) | 3.03229e7 | 2.96089 | ||||||||
\(638\) | 1.55974e7 | 1.51705 | ||||||||
\(639\) | −611388. | −0.0592331 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.60395e6 | −0.923219 | −0.461609 | − | 0.887083i | \(-0.652728\pi\) | ||||
−0.461609 | + | 0.887083i | \(0.652728\pi\) | |||||||
\(642\) | −6.61651e6 | −0.633566 | ||||||||
\(643\) | −8.24396e6 | −0.786336 | −0.393168 | − | 0.919467i | \(-0.628621\pi\) | ||||
−0.393168 | + | 0.919467i | \(0.628621\pi\) | |||||||
\(644\) | 5.79331e6 | 0.550443 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.83364e6 | −0.644274 | ||||||||
\(647\) | −4.07353e6 | −0.382570 | −0.191285 | − | 0.981535i | \(-0.561265\pi\) | ||||
−0.191285 | + | 0.981535i | \(0.561265\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | −1.78832e7 | −1.66661 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.04877e6 | −0.189470 | ||||||||
\(652\) | 5.41054e6 | 0.498450 | ||||||||
\(653\) | 1.68193e7 | 1.54357 | 0.771783 | − | 0.635886i | \(-0.219365\pi\) | ||||
0.771783 | + | 0.635886i | \(0.219365\pi\) | |||||||
\(654\) | 6.10866e6 | 0.558472 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.08589e6 | −0.189248 | ||||||||
\(657\) | −52326.0 | −0.00472938 | ||||||||
\(658\) | −7.84558e6 | −0.706415 | ||||||||
\(659\) | 2.87826e6 | 0.258176 | 0.129088 | − | 0.991633i | \(-0.458795\pi\) | ||||
0.129088 | + | 0.991633i | \(0.458795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.33386e7 | 1.18743 | 0.593713 | − | 0.804677i | \(-0.297661\pi\) | ||||
0.593713 | + | 0.804677i | \(0.297661\pi\) | |||||||
\(662\) | 1.35726e7 | 1.20370 | ||||||||
\(663\) | 7.29556e6 | 0.644577 | ||||||||
\(664\) | −740736. | −0.0651993 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.56233e6 | 0.136486 | ||||||||
\(667\) | 1.21678e7 | 1.05901 | ||||||||
\(668\) | 6.88397e6 | 0.596895 | ||||||||
\(669\) | 6.61744e6 | 0.571643 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.75645e6 | −0.150601 | ||||||||
\(672\) | 2.14733e6 | 0.183432 | ||||||||
\(673\) | 6.37345e6 | 0.542422 | 0.271211 | − | 0.962520i | \(-0.412576\pi\) | ||||
0.271211 | + | 0.962520i | \(0.412576\pi\) | |||||||
\(674\) | 6.48339e6 | 0.549734 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.53101e6 | 0.381354 | ||||||||
\(677\) | −2.27210e7 | −1.90526 | −0.952632 | − | 0.304126i | \(-0.901636\pi\) | ||||
−0.952632 | + | 0.304126i | \(0.901636\pi\) | |||||||
\(678\) | 9.48542e6 | 0.792469 | ||||||||
\(679\) | 1.27202e7 | 1.05881 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.70469e6 | −0.719260 | ||||||||
\(682\) | 1.94618e6 | 0.160222 | ||||||||
\(683\) | −1.53612e7 | −1.26001 | −0.630003 | − | 0.776593i | \(-0.716946\pi\) | ||||
−0.630003 | + | 0.776593i | \(0.716946\pi\) | |||||||
\(684\) | −2.20968e6 | −0.180588 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.92691e7 | −1.56333 | ||||||||
\(687\) | 753255. | 0.0608906 | ||||||||
\(688\) | 4.98406e6 | 0.401432 | ||||||||
\(689\) | 1.42902e7 | 1.14680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.05035e6 | 0.641386 | 0.320693 | − | 0.947183i | \(-0.396084\pi\) | ||||
0.320693 | + | 0.947183i | \(0.396084\pi\) | |||||||
\(692\) | 9.65366e6 | 0.766350 | ||||||||
\(693\) | −9.39875e6 | −0.743425 | ||||||||
\(694\) | 5.14553e6 | 0.405538 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.51008e6 | 0.352908 | ||||||||
\(697\) | 8.16430e6 | 0.636556 | ||||||||
\(698\) | 1.09222e7 | 0.848539 | ||||||||
\(699\) | 7.86488e6 | 0.608835 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.27840e6 | 0.559424 | 0.279712 | − | 0.960084i | \(-0.409761\pi\) | ||||
0.279712 | + | 0.960084i | \(0.409761\pi\) | |||||||
\(702\) | 2.35904e6 | 0.180673 | ||||||||
\(703\) | 8.22151e6 | 0.627427 | ||||||||
\(704\) | −2.03981e6 | −0.155116 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.54594e6 | 0.645280 | ||||||||
\(707\) | 2.45936e7 | 1.85044 | ||||||||
\(708\) | −5.17104e6 | −0.387699 | ||||||||
\(709\) | 1.37498e7 | 1.02726 | 0.513630 | − | 0.858012i | \(-0.328300\pi\) | ||||
0.513630 | + | 0.858012i | \(0.328300\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.84032e6 | −0.136527 | ||||||||
\(712\) | 5.05344e6 | 0.373583 | ||||||||
\(713\) | 1.51826e6 | 0.111846 | ||||||||
\(714\) | −8.40478e6 | −0.616994 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.98992e6 | −0.436655 | ||||||||
\(717\) | 9.54504e6 | 0.693394 | ||||||||
\(718\) | −1.30562e7 | −0.945164 | ||||||||
\(719\) | −9.05583e6 | −0.653290 | −0.326645 | − | 0.945147i | \(-0.605918\pi\) | ||||
−0.326645 | + | 0.945147i | \(0.605918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.13426e7 | −2.96183 | ||||||||
\(722\) | −1.72370e6 | −0.123061 | ||||||||
\(723\) | 6.81141e6 | 0.484609 | ||||||||
\(724\) | −3.71877e6 | −0.263665 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.13031e6 | 0.220417 | ||||||||
\(727\) | −2.20979e7 | −1.55065 | −0.775327 | − | 0.631560i | \(-0.782415\pi\) | ||||
−0.775327 | + | 0.631560i | \(0.782415\pi\) | |||||||
\(728\) | −1.20638e7 | −0.843638 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.95079e7 | −1.35026 | ||||||||
\(732\) | −507888. | −0.0350340 | ||||||||
\(733\) | 2.07337e6 | 0.142534 | 0.0712669 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712669 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(734\) | 1.66031e7 | 1.13749 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.59130e6 | −0.108282 | ||||||||
\(737\) | −2.86216e7 | −1.94100 | ||||||||
\(738\) | 2.63995e6 | 0.178425 | ||||||||
\(739\) | 1.48849e7 | 1.00262 | 0.501310 | − | 0.865268i | \(-0.332852\pi\) | ||||
0.501310 | + | 0.865268i | \(0.332852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.24141e7 | 0.830558 | ||||||||
\(742\) | −1.64628e7 | −1.09773 | ||||||||
\(743\) | 2.58856e7 | 1.72023 | 0.860116 | − | 0.510099i | \(-0.170391\pi\) | ||||
0.860116 | + | 0.510099i | \(0.170391\pi\) | |||||||
\(744\) | 562752. | 0.0372722 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.56968e6 | 0.563790 | ||||||||
\(747\) | 937494. | 0.0614705 | ||||||||
\(748\) | 7.98394e6 | 0.521751 | ||||||||
\(749\) | −4.28235e7 | −2.78919 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.98645e6 | −0.516718 | −0.258359 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258359 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(752\) | 2.15501e6 | 0.138965 | ||||||||
\(753\) | 5.71633e6 | 0.367392 | ||||||||
\(754\) | −2.53379e7 | −1.62309 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.71771e6 | −0.172941 | ||||||||
\(757\) | −1.15570e7 | −0.733000 | −0.366500 | − | 0.930418i | \(-0.619444\pi\) | ||||
−0.366500 | + | 0.930418i | \(0.619444\pi\) | |||||||
\(758\) | 7.78798e6 | 0.492325 | ||||||||
\(759\) | 6.96503e6 | 0.438852 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.16705e6 | 0.198241 | 0.0991205 | − | 0.995075i | \(-0.468397\pi\) | ||||
0.0991205 | + | 0.995075i | \(0.468397\pi\) | |||||||
\(762\) | −9.24883e6 | −0.577031 | ||||||||
\(763\) | 3.95366e7 | 2.45860 | ||||||||
\(764\) | −1.35392e7 | −0.839187 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.06021e7 | −0.652860 | ||||||||
\(767\) | 2.90512e7 | 1.78310 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 8.21560e6 | 0.500983 | 0.250492 | − | 0.968119i | \(-0.419408\pi\) | ||||
0.250492 | + | 0.968119i | \(0.419408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −276372. | −0.0167440 | ||||||||
\(772\) | −2.48930e6 | −0.150326 | ||||||||
\(773\) | 1.19708e7 | 0.720567 | 0.360284 | − | 0.932843i | \(-0.382680\pi\) | ||||
0.360284 | + | 0.932843i | \(0.382680\pi\) | |||||||
\(774\) | −6.30796e6 | −0.378474 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.49395e6 | −0.208287 | ||||||||
\(777\) | 1.01117e7 | 0.600860 | ||||||||
\(778\) | −1.13016e6 | −0.0669408 | ||||||||
\(779\) | 1.38923e7 | 0.820223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.75890e6 | 0.220513 | ||||||||
\(782\) | 6.22843e6 | 0.364218 | ||||||||
\(783\) | −5.70807e6 | −0.332725 | ||||||||
\(784\) | 9.59539e6 | 0.557536 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.88573e6 | −0.455287 | ||||||||
\(787\) | −1.71154e7 | −0.985032 | −0.492516 | − | 0.870304i | \(-0.663923\pi\) | ||||
−0.492516 | + | 0.870304i | \(0.663923\pi\) | |||||||
\(788\) | −1.65571e6 | −0.0949881 | ||||||||
\(789\) | 1.70564e6 | 0.0975429 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.13918e7 | 3.48874 | ||||||||
\(792\) | 2.58163e6 | 0.146245 | ||||||||
\(793\) | 2.85334e6 | 0.161128 | ||||||||
\(794\) | 1.04826e7 | 0.590091 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.24680e6 | −0.125685 | ||||||||
\(797\) | −2.80753e7 | −1.56559 | −0.782797 | − | 0.622277i | \(-0.786208\pi\) | ||||
−0.782797 | + | 0.622277i | \(0.786208\pi\) | |||||||
\(798\) | −1.43015e7 | −0.795015 | ||||||||
\(799\) | −8.43484e6 | −0.467423 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.39576e6 | −0.352217 | ||||||||
\(802\) | 1.14499e6 | 0.0628589 | ||||||||
\(803\) | 321708. | 0.0176065 | ||||||||
\(804\) | −8.27611e6 | −0.451530 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.16157e6 | −0.171422 | ||||||||
\(807\) | −9.98973e6 | −0.539970 | ||||||||
\(808\) | −6.75533e6 | −0.364014 | ||||||||
\(809\) | 9.90816e6 | 0.532257 | 0.266129 | − | 0.963938i | \(-0.414255\pi\) | ||||
0.266129 | + | 0.963938i | \(0.414255\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.72573e6 | 0.305688 | 0.152844 | − | 0.988250i | \(-0.451157\pi\) | ||||
0.152844 | + | 0.988250i | \(0.451157\pi\) | |||||||
\(812\) | 2.91902e7 | 1.55363 | ||||||||
\(813\) | −1.90757e6 | −0.101217 | ||||||||
\(814\) | −9.60542e6 | −0.508107 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.30861e6 | 0.121374 | ||||||||
\(817\) | −3.31946e7 | −1.73985 | ||||||||
\(818\) | −1.64827e7 | −0.861284 | ||||||||
\(819\) | 1.52683e7 | 0.795389 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.96570e6 | −0.308890 | −0.154445 | − | 0.988001i | \(-0.549359\pi\) | ||||
−0.154445 | + | 0.988001i | \(0.549359\pi\) | |||||||
\(822\) | 8.23241e6 | 0.424959 | ||||||||
\(823\) | −1.97778e7 | −1.01784 | −0.508918 | − | 0.860815i | \(-0.669954\pi\) | ||||
−0.508918 | + | 0.860815i | \(0.669954\pi\) | |||||||
\(824\) | 1.13559e7 | 0.582645 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.34681e7 | −1.70679 | ||||||||
\(827\) | 2.04045e7 | 1.03744 | 0.518719 | − | 0.854945i | \(-0.326409\pi\) | ||||
0.518719 | + | 0.854945i | \(0.326409\pi\) | |||||||
\(828\) | 2.01398e6 | 0.102089 | ||||||||
\(829\) | −2.77183e7 | −1.40081 | −0.700406 | − | 0.713745i | \(-0.746998\pi\) | ||||
−0.700406 | + | 0.713745i | \(0.746998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.42672e6 | −0.473541 | ||||||||
\(832\) | 3.31366e6 | 0.165959 | ||||||||
\(833\) | −3.75570e7 | −1.87533 | ||||||||
\(834\) | 1.22306e7 | 0.608883 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.35854e7 | 0.672292 | ||||||||
\(837\) | −712233. | −0.0351405 | ||||||||
\(838\) | 9.51792e6 | 0.468201 | ||||||||
\(839\) | −7.79841e6 | −0.382473 | −0.191237 | − | 0.981544i | \(-0.561250\pi\) | ||||
−0.191237 | + | 0.981544i | \(0.561250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.07978e7 | 1.98905 | ||||||||
\(842\) | 2.96519e6 | 0.144136 | ||||||||
\(843\) | −306018. | −0.0148313 | ||||||||
\(844\) | −7.40277e6 | −0.357716 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.72743e6 | −0.131017 | ||||||||
\(847\) | 2.02600e7 | 0.970358 | ||||||||
\(848\) | 4.52198e6 | 0.215943 | ||||||||
\(849\) | 2.52991e6 | 0.120458 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.49339e6 | −0.354694 | ||||||||
\(852\) | 1.08691e6 | 0.0512974 | ||||||||
\(853\) | 6.22554e6 | 0.292957 | 0.146479 | − | 0.989214i | \(-0.453206\pi\) | ||||
0.146479 | + | 0.989214i | \(0.453206\pi\) | |||||||
\(854\) | −3.28716e6 | −0.154233 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.17627e7 | 0.548684 | ||||||||
\(857\) | 3.39757e7 | 1.58022 | 0.790108 | − | 0.612968i | \(-0.210024\pi\) | ||||
0.790108 | + | 0.612968i | \(0.210024\pi\) | |||||||
\(858\) | −1.45038e7 | −0.672608 | ||||||||
\(859\) | −1.47282e7 | −0.681033 | −0.340516 | − | 0.940239i | \(-0.610602\pi\) | ||||
−0.340516 | + | 0.940239i | \(0.610602\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.70864e7 | 0.785492 | ||||||||
\(862\) | 749592. | 0.0343603 | ||||||||
\(863\) | −1.88594e7 | −0.861988 | −0.430994 | − | 0.902355i | \(-0.641837\pi\) | ||||
−0.430994 | + | 0.902355i | \(0.641837\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.62044e7 | −1.18735 | ||||||||
\(867\) | 3.74268e6 | 0.169096 | ||||||||
\(868\) | 3.64226e6 | 0.164086 | ||||||||
\(869\) | 1.13146e7 | 0.508263 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.64957e7 | 2.07667 | ||||||||
\(872\) | −1.08598e7 | −0.483651 | ||||||||
\(873\) | 4.42203e6 | 0.196375 | ||||||||
\(874\) | 1.05983e7 | 0.469307 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 93024.0 | 0.00409576 | ||||||||
\(877\) | −1.82112e7 | −0.799540 | −0.399770 | − | 0.916615i | \(-0.630910\pi\) | ||||
−0.399770 | + | 0.916615i | \(0.630910\pi\) | |||||||
\(878\) | −1.08026e6 | −0.0472925 | ||||||||
\(879\) | 1.40266e7 | 0.612321 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.65425e6 | −0.332248 | −0.166124 | − | 0.986105i | \(-0.553125\pi\) | ||||
−0.166124 | + | 0.986105i | \(0.553125\pi\) | |||||||
\(882\) | −1.21442e7 | −0.525650 | ||||||||
\(883\) | −597451. | −0.0257870 | −0.0128935 | − | 0.999917i | \(-0.504104\pi\) | ||||
−0.0128935 | + | 0.999917i | \(0.504104\pi\) | |||||||
\(884\) | −1.29699e7 | −0.558220 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.11174e7 | −0.475793 | ||||||||
\(887\) | 2.06888e6 | 0.0882929 | 0.0441465 | − | 0.999025i | \(-0.485943\pi\) | ||||
0.0441465 | + | 0.999025i | \(0.485943\pi\) | |||||||
\(888\) | −2.77747e6 | −0.118200 | ||||||||
\(889\) | −5.98605e7 | −2.54031 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.26738e6 | −0.137881 | ||||||||
\(892\) | −1.17643e7 | −0.495057 | ||||||||
\(893\) | −1.43527e7 | −0.602289 | ||||||||
\(894\) | 1.10322e7 | 0.461656 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.81747e6 | −0.158857 | ||||||||
\(897\) | −1.13147e7 | −0.469527 | ||||||||
\(898\) | −3.14652e7 | −1.30209 | ||||||||
\(899\) | 7.64991e6 | 0.315687 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.76993e7 | −0.726348 | ||||||||
\(902\) | −1.62308e7 | −0.664238 | ||||||||
\(903\) | −4.08265e7 | −1.66618 | ||||||||
\(904\) | −1.68630e7 | −0.686299 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.15777e6 | 0.289706 | ||||||||
\(907\) | 7.83331e6 | 0.316175 | 0.158087 | − | 0.987425i | \(-0.449467\pi\) | ||||
0.158087 | + | 0.987425i | \(0.449467\pi\) | |||||||
\(908\) | 1.54750e7 | 0.622897 | ||||||||
\(909\) | 8.54971e6 | 0.343196 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.08133e7 | 1.62932 | 0.814659 | − | 0.579940i | \(-0.196924\pi\) | ||||
0.814659 | + | 0.579940i | \(0.196924\pi\) | |||||||
\(912\) | 3.92832e6 | 0.156394 | ||||||||
\(913\) | −5.76385e6 | −0.228842 | ||||||||
\(914\) | −2.49342e7 | −0.987258 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.33912e6 | −0.0527328 | ||||||||
\(917\) | −5.10382e7 | −2.00434 | ||||||||
\(918\) | −2.92183e6 | −0.114432 | ||||||||
\(919\) | 6.21579e6 | 0.242777 | 0.121389 | − | 0.992605i | \(-0.461265\pi\) | ||||
0.121389 | + | 0.992605i | \(0.461265\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.55925e6 | 0.293650 | ||||||||
\(922\) | 1.87322e7 | 0.725707 | ||||||||
\(923\) | −6.10633e6 | −0.235926 | ||||||||
\(924\) | 1.67089e7 | 0.643825 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.53126e6 | 0.0586844 | ||||||||
\(927\) | −1.43723e7 | −0.549323 | ||||||||
\(928\) | −8.01792e6 | −0.305627 | ||||||||
\(929\) | −4.64847e6 | −0.176714 | −0.0883570 | − | 0.996089i | \(-0.528162\pi\) | ||||
−0.0883570 | + | 0.996089i | \(0.528162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.39068e7 | −2.41642 | ||||||||
\(932\) | −1.39820e7 | −0.527266 | ||||||||
\(933\) | 2.63428e6 | 0.0990736 | ||||||||
\(934\) | 7.74161e6 | 0.290378 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.19386e6 | −0.156467 | ||||||||
\(937\) | −1.33603e7 | −0.497127 | −0.248563 | − | 0.968616i | \(-0.579958\pi\) | ||||
−0.248563 | + | 0.968616i | \(0.579958\pi\) | |||||||
\(938\) | −5.35648e7 | −1.98780 | ||||||||
\(939\) | −1.15073e6 | −0.0425902 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.32569e7 | 1.22436 | 0.612178 | − | 0.790720i | \(-0.290294\pi\) | ||||
0.612178 | + | 0.790720i | \(0.290294\pi\) | |||||||
\(942\) | 1.30062e7 | 0.477554 | ||||||||
\(943\) | −1.26620e7 | −0.463685 | ||||||||
\(944\) | 9.19296e6 | 0.335757 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.87822e7 | 1.40898 | ||||||||
\(947\) | 4.21530e7 | 1.52740 | 0.763702 | − | 0.645569i | \(-0.223380\pi\) | ||||
0.763702 | + | 0.645569i | \(0.223380\pi\) | |||||||
\(948\) | 3.27168e6 | 0.118236 | ||||||||
\(949\) | −522614. | −0.0188372 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.83243e6 | −0.209121 | ||||||||
\(952\) | 1.49418e7 | 0.534332 | ||||||||
\(953\) | 2.24691e7 | 0.801406 | 0.400703 | − | 0.916208i | \(-0.368766\pi\) | ||||
0.400703 | + | 0.916208i | \(0.368766\pi\) | |||||||
\(954\) | −5.72314e6 | −0.203593 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.69690e7 | −0.600497 | ||||||||
\(957\) | 3.50941e7 | 1.23866 | ||||||||
\(958\) | 2.22767e7 | 0.784218 | ||||||||
\(959\) | 5.32820e7 | 1.87083 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.76746e7 | −0.966659 | ||||||||
\(962\) | 1.56040e7 | 0.543623 | ||||||||
\(963\) | −1.48872e7 | −0.517304 | ||||||||
\(964\) | −1.21092e7 | −0.419683 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.30350e7 | 0.449435 | ||||||||
\(967\) | −1.75000e7 | −0.601826 | −0.300913 | − | 0.953652i | \(-0.597291\pi\) | ||||
−0.300913 | + | 0.953652i | \(0.597291\pi\) | |||||||
\(968\) | −5.56499e6 | −0.190887 | ||||||||
\(969\) | −1.53757e7 | −0.526048 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.42920e7 | 1.84794 | 0.923970 | − | 0.382465i | \(-0.124925\pi\) | ||||
0.923970 | + | 0.382465i | \(0.124925\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 7.91594e7 | 2.68053 | ||||||||
\(974\) | −1.68980e7 | −0.570740 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 902912. | 0.0303404 | ||||||||
\(977\) | 2.55925e7 | 0.857782 | 0.428891 | − | 0.903356i | \(-0.358904\pi\) | ||||
0.428891 | + | 0.903356i | \(0.358904\pi\) | |||||||
\(978\) | 1.21737e7 | 0.406983 | ||||||||
\(979\) | 3.93221e7 | 1.31123 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.37445e7 | 0.455991 | ||||||||
\(982\) | −2.78518e7 | −0.921668 | ||||||||
\(983\) | −4.82488e6 | −0.159258 | −0.0796292 | − | 0.996825i | \(-0.525374\pi\) | ||||
−0.0796292 | + | 0.996825i | \(0.525374\pi\) | |||||||
\(984\) | −4.69325e6 | −0.154520 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.13826e7 | 1.02801 | ||||||||
\(987\) | −1.76525e7 | −0.576786 | ||||||||
\(988\) | −2.20695e7 | −0.719284 | ||||||||
\(989\) | 3.02548e7 | 0.983567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.18448e6 | 0.0383127 | 0.0191563 | − | 0.999817i | \(-0.493902\pi\) | ||||
0.0191563 | + | 0.999817i | \(0.493902\pi\) | |||||||
\(992\) | −1.00045e6 | −0.0322786 | ||||||||
\(993\) | 3.05383e7 | 0.982816 | ||||||||
\(994\) | 7.03474e6 | 0.225830 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.66666e6 | −0.0532350 | ||||||||
\(997\) | −2.58178e7 | −0.822585 | −0.411293 | − | 0.911503i | \(-0.634923\pi\) | ||||
−0.411293 | + | 0.911503i | \(0.634923\pi\) | |||||||
\(998\) | 3.71833e7 | 1.18174 | ||||||||
\(999\) | 3.51524e6 | 0.111440 |
(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 | 150.6.a.c.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 450.6.a.x.1.1 | 1 | |||
5.2 | odd | 4 | 150.6.c.e.49.1 | 2 | |||
5.3 | odd | 4 | 150.6.c.e.49.2 | 2 | |||
5.4 | even | 2 | 150.6.a.l.1.1 | yes | 1 | ||
15.2 | even | 4 | 450.6.c.n.199.2 | 2 | |||
15.8 | even | 4 | 450.6.c.n.199.1 | 2 | |||
15.14 | odd | 2 | 450.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.6.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
150.6.a.l.1.1 | yes | 1 | 5.4 | even | 2 | ||
150.6.c.e.49.1 | 2 | 5.2 | odd | 4 | |||
150.6.c.e.49.2 | 2 | 5.3 | odd | 4 | |||
450.6.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
450.6.a.x.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.c.n.199.1 | 2 | 15.8 | even | 4 | |||
450.6.c.n.199.2 | 2 | 15.2 | even | 4 |