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: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 30) |
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 | ||||||||
\(7\) | −4.00000 | −0.0308542 | −0.0154271 | − | 0.999881i | \(-0.504911\pi\) | ||||
−0.0154271 | + | 0.999881i | \(0.504911\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −500.000 | −1.24591 | −0.622957 | − | 0.782256i | \(-0.714069\pi\) | ||||
−0.622957 | + | 0.782256i | \(0.714069\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −288.000 | −0.472644 | −0.236322 | − | 0.971675i | \(-0.575942\pi\) | ||||
−0.236322 | + | 0.971675i | \(0.575942\pi\) | |||||||
\(14\) | −16.0000 | −0.0218172 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1516.00 | 1.27226 | 0.636132 | − | 0.771581i | \(-0.280534\pi\) | ||||
0.636132 | + | 0.771581i | \(0.280534\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | −1344.00 | −0.854113 | −0.427056 | − | 0.904225i | \(-0.640449\pi\) | ||||
−0.427056 | + | 0.904225i | \(0.640449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 36.0000 | 0.0178137 | ||||||||
\(22\) | −2000.00 | −0.880995 | ||||||||
\(23\) | −4100.00 | −1.61609 | −0.808043 | − | 0.589124i | \(-0.799473\pi\) | ||||
−0.808043 | + | 0.589124i | \(0.799473\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1152.00 | −0.334210 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −64.0000 | −0.0154271 | ||||||||
\(29\) | −2646.00 | −0.584245 | −0.292122 | − | 0.956381i | \(-0.594361\pi\) | ||||
−0.292122 | + | 0.956381i | \(0.594361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5612.00 | −1.04885 | −0.524425 | − | 0.851457i | \(-0.675720\pi\) | ||||
−0.524425 | + | 0.851457i | \(0.675720\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 4500.00 | 0.719329 | ||||||||
\(34\) | 6064.00 | 0.899626 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −7288.00 | −0.875193 | −0.437597 | − | 0.899171i | \(-0.644170\pi\) | ||||
−0.437597 | + | 0.899171i | \(0.644170\pi\) | |||||||
\(38\) | −5376.00 | −0.603949 | ||||||||
\(39\) | 2592.00 | 0.272881 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18986.0 | −1.76390 | −0.881950 | − | 0.471343i | \(-0.843769\pi\) | ||||
−0.881950 | + | 0.471343i | \(0.843769\pi\) | |||||||
\(42\) | 144.000 | 0.0125962 | ||||||||
\(43\) | −2404.00 | −0.198273 | −0.0991364 | − | 0.995074i | \(-0.531608\pi\) | ||||
−0.0991364 | + | 0.995074i | \(0.531608\pi\) | |||||||
\(44\) | −8000.00 | −0.622957 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16400.0 | −1.14274 | ||||||||
\(47\) | 8900.00 | 0.587686 | 0.293843 | − | 0.955854i | \(-0.405066\pi\) | ||||
0.293843 | + | 0.955854i | \(0.405066\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −16791.0 | −0.999048 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13644.0 | −0.734541 | ||||||||
\(52\) | −4608.00 | −0.236322 | ||||||||
\(53\) | 39804.0 | 1.94642 | 0.973211 | − | 0.229913i | \(-0.0738443\pi\) | ||||
0.973211 | + | 0.229913i | \(0.0738443\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −256.000 | −0.0109086 | ||||||||
\(57\) | 12096.0 | 0.493122 | ||||||||
\(58\) | −10584.0 | −0.413123 | ||||||||
\(59\) | −28300.0 | −1.05842 | −0.529208 | − | 0.848492i | \(-0.677511\pi\) | ||||
−0.529208 | + | 0.848492i | \(0.677511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18290.0 | 0.629345 | 0.314673 | − | 0.949200i | \(-0.398105\pi\) | ||||
0.314673 | + | 0.949200i | \(0.398105\pi\) | |||||||
\(62\) | −22448.0 | −0.741649 | ||||||||
\(63\) | −324.000 | −0.0102847 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 18000.0 | 0.508643 | ||||||||
\(67\) | 65956.0 | 1.79501 | 0.897506 | − | 0.441002i | \(-0.145377\pi\) | ||||
0.897506 | + | 0.441002i | \(0.145377\pi\) | |||||||
\(68\) | 24256.0 | 0.636132 | ||||||||
\(69\) | 36900.0 | 0.933047 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −28800.0 | −0.678026 | −0.339013 | − | 0.940782i | \(-0.610093\pi\) | ||||
−0.339013 | + | 0.940782i | \(0.610093\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | −30808.0 | −0.676638 | −0.338319 | − | 0.941031i | \(-0.609858\pi\) | ||||
−0.338319 | + | 0.941031i | \(0.609858\pi\) | |||||||
\(74\) | −29152.0 | −0.618855 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21504.0 | −0.427056 | ||||||||
\(77\) | 2000.00 | 0.0384418 | ||||||||
\(78\) | 10368.0 | 0.192956 | ||||||||
\(79\) | 60228.0 | 1.08575 | 0.542876 | − | 0.839813i | \(-0.317335\pi\) | ||||
0.542876 | + | 0.839813i | \(0.317335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −75944.0 | −1.24727 | ||||||||
\(83\) | −2468.00 | −0.0393233 | −0.0196616 | − | 0.999807i | \(-0.506259\pi\) | ||||
−0.0196616 | + | 0.999807i | \(0.506259\pi\) | |||||||
\(84\) | 576.000 | 0.00890685 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9616.00 | −0.140200 | ||||||||
\(87\) | 23814.0 | 0.337314 | ||||||||
\(88\) | −32000.0 | −0.440497 | ||||||||
\(89\) | 22678.0 | 0.303480 | 0.151740 | − | 0.988420i | \(-0.451512\pi\) | ||||
0.151740 | + | 0.988420i | \(0.451512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1152.00 | 0.0145831 | ||||||||
\(92\) | −65600.0 | −0.808043 | ||||||||
\(93\) | 50508.0 | 0.605554 | ||||||||
\(94\) | 35600.0 | 0.415557 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −36968.0 | −0.398930 | −0.199465 | − | 0.979905i | \(-0.563920\pi\) | ||||
−0.199465 | + | 0.979905i | \(0.563920\pi\) | |||||||
\(98\) | −67164.0 | −0.706434 | ||||||||
\(99\) | −40500.0 | −0.415305 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 167918. | 1.63792 | 0.818962 | − | 0.573848i | \(-0.194550\pi\) | ||||
0.818962 | + | 0.573848i | \(0.194550\pi\) | |||||||
\(102\) | −54576.0 | −0.519399 | ||||||||
\(103\) | −154364. | −1.43368 | −0.716841 | − | 0.697236i | \(-0.754413\pi\) | ||||
−0.716841 | + | 0.697236i | \(0.754413\pi\) | |||||||
\(104\) | −18432.0 | −0.167105 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 159216. | 1.37633 | ||||||||
\(107\) | 136788. | 1.15502 | 0.577509 | − | 0.816385i | \(-0.304025\pi\) | ||||
0.577509 | + | 0.816385i | \(0.304025\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | −53810.0 | −0.433807 | −0.216904 | − | 0.976193i | \(-0.569596\pi\) | ||||
−0.216904 | + | 0.976193i | \(0.569596\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 65592.0 | 0.505293 | ||||||||
\(112\) | −1024.00 | −0.00771356 | ||||||||
\(113\) | 82692.0 | 0.609211 | 0.304605 | − | 0.952479i | \(-0.401475\pi\) | ||||
0.304605 | + | 0.952479i | \(0.401475\pi\) | |||||||
\(114\) | 48384.0 | 0.348690 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −42336.0 | −0.292122 | ||||||||
\(117\) | −23328.0 | −0.157548 | ||||||||
\(118\) | −113200. | −0.748413 | ||||||||
\(119\) | −6064.00 | −0.0392547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 88949.0 | 0.552303 | ||||||||
\(122\) | 73160.0 | 0.445014 | ||||||||
\(123\) | 170874. | 1.01839 | ||||||||
\(124\) | −89792.0 | −0.524425 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1296.00 | −0.00727241 | ||||||||
\(127\) | −211780. | −1.16513 | −0.582567 | − | 0.812783i | \(-0.697952\pi\) | ||||
−0.582567 | + | 0.812783i | \(0.697952\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 21636.0 | 0.114473 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 169500. | 0.862962 | 0.431481 | − | 0.902122i | \(-0.357991\pi\) | ||||
0.431481 | + | 0.902122i | \(0.357991\pi\) | |||||||
\(132\) | 72000.0 | 0.359665 | ||||||||
\(133\) | 5376.00 | 0.0263530 | ||||||||
\(134\) | 263824. | 1.26927 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 97024.0 | 0.449813 | ||||||||
\(137\) | 252036. | 1.14726 | 0.573629 | − | 0.819115i | \(-0.305535\pi\) | ||||
0.573629 | + | 0.819115i | \(0.305535\pi\) | |||||||
\(138\) | 147600. | 0.659764 | ||||||||
\(139\) | 192016. | 0.842947 | 0.421474 | − | 0.906841i | \(-0.361513\pi\) | ||||
0.421474 | + | 0.906841i | \(0.361513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −80100.0 | −0.339301 | ||||||||
\(142\) | −115200. | −0.479437 | ||||||||
\(143\) | 144000. | 0.588874 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −123232. | −0.478455 | ||||||||
\(147\) | 151119. | 0.576801 | ||||||||
\(148\) | −116608. | −0.437597 | ||||||||
\(149\) | 235694. | 0.869727 | 0.434863 | − | 0.900496i | \(-0.356797\pi\) | ||||
0.434863 | + | 0.900496i | \(0.356797\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −371492. | −1.32589 | −0.662944 | − | 0.748669i | \(-0.730693\pi\) | ||||
−0.662944 | + | 0.748669i | \(0.730693\pi\) | |||||||
\(152\) | −86016.0 | −0.301975 | ||||||||
\(153\) | 122796. | 0.424088 | ||||||||
\(154\) | 8000.00 | 0.0271824 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 41472.0 | 0.136441 | ||||||||
\(157\) | 264952. | 0.857863 | 0.428932 | − | 0.903337i | \(-0.358890\pi\) | ||||
0.428932 | + | 0.903337i | \(0.358890\pi\) | |||||||
\(158\) | 240912. | 0.767743 | ||||||||
\(159\) | −358236. | −1.12377 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16400.0 | 0.0498631 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −403124. | −1.18842 | −0.594210 | − | 0.804310i | \(-0.702535\pi\) | ||||
−0.594210 | + | 0.804310i | \(0.702535\pi\) | |||||||
\(164\) | −303776. | −0.881950 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9872.00 | −0.0278058 | ||||||||
\(167\) | −261900. | −0.726682 | −0.363341 | − | 0.931656i | \(-0.618364\pi\) | ||||
−0.363341 | + | 0.931656i | \(0.618364\pi\) | |||||||
\(168\) | 2304.00 | 0.00629810 | ||||||||
\(169\) | −288349. | −0.776608 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −108864. | −0.284704 | ||||||||
\(172\) | −38464.0 | −0.0991364 | ||||||||
\(173\) | 326228. | 0.828716 | 0.414358 | − | 0.910114i | \(-0.364006\pi\) | ||||
0.414358 | + | 0.910114i | \(0.364006\pi\) | |||||||
\(174\) | 95256.0 | 0.238517 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −128000. | −0.311479 | ||||||||
\(177\) | 254700. | 0.611077 | ||||||||
\(178\) | 90712.0 | 0.214593 | ||||||||
\(179\) | −109516. | −0.255473 | −0.127736 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127736 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −53146.0 | −0.120580 | −0.0602898 | − | 0.998181i | \(-0.519202\pi\) | ||||
−0.0602898 | + | 0.998181i | \(0.519202\pi\) | |||||||
\(182\) | 4608.00 | 0.0103118 | ||||||||
\(183\) | −164610. | −0.363353 | ||||||||
\(184\) | −262400. | −0.571372 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 202032. | 0.428191 | ||||||||
\(187\) | −758000. | −1.58513 | ||||||||
\(188\) | 142400. | 0.293843 | ||||||||
\(189\) | 2916.00 | 0.00593790 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 232056. | 0.460267 | 0.230133 | − | 0.973159i | \(-0.426084\pi\) | ||||
0.230133 | + | 0.973159i | \(0.426084\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −1.03067e6 | −1.99172 | −0.995858 | − | 0.0909274i | \(-0.971017\pi\) | ||||
−0.995858 | + | 0.0909274i | \(0.971017\pi\) | |||||||
\(194\) | −147872. | −0.282086 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −268656. | −0.499524 | ||||||||
\(197\) | −522796. | −0.959769 | −0.479884 | − | 0.877332i | \(-0.659321\pi\) | ||||
−0.479884 | + | 0.877332i | \(0.659321\pi\) | |||||||
\(198\) | −162000. | −0.293665 | ||||||||
\(199\) | −215292. | −0.385385 | −0.192693 | − | 0.981259i | \(-0.561722\pi\) | ||||
−0.192693 | + | 0.981259i | \(0.561722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −593604. | −1.03635 | ||||||||
\(202\) | 671672. | 1.15819 | ||||||||
\(203\) | 10584.0 | 0.0180264 | ||||||||
\(204\) | −218304. | −0.367271 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −617456. | −1.01377 | ||||||||
\(207\) | −332100. | −0.538695 | ||||||||
\(208\) | −73728.0 | −0.118161 | ||||||||
\(209\) | 672000. | 1.06415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.03008e6 | −1.59281 | −0.796407 | − | 0.604762i | \(-0.793268\pi\) | ||||
−0.796407 | + | 0.604762i | \(0.793268\pi\) | |||||||
\(212\) | 636864. | 0.973211 | ||||||||
\(213\) | 259200. | 0.391459 | ||||||||
\(214\) | 547152. | 0.816721 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 22448.0 | 0.0323615 | ||||||||
\(218\) | −215240. | −0.306748 | ||||||||
\(219\) | 277272. | 0.390657 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −436608. | −0.601327 | ||||||||
\(222\) | 262368. | 0.357296 | ||||||||
\(223\) | 456020. | 0.614075 | 0.307038 | − | 0.951697i | \(-0.400662\pi\) | ||||
0.307038 | + | 0.951697i | \(0.400662\pi\) | |||||||
\(224\) | −4096.00 | −0.00545431 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 330768. | 0.430777 | ||||||||
\(227\) | −434252. | −0.559342 | −0.279671 | − | 0.960096i | \(-0.590225\pi\) | ||||
−0.279671 | + | 0.960096i | \(0.590225\pi\) | |||||||
\(228\) | 193536. | 0.246561 | ||||||||
\(229\) | −722710. | −0.910700 | −0.455350 | − | 0.890313i | \(-0.650486\pi\) | ||||
−0.455350 | + | 0.890313i | \(0.650486\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18000.0 | −0.0221944 | ||||||||
\(232\) | −169344. | −0.206562 | ||||||||
\(233\) | −565348. | −0.682223 | −0.341111 | − | 0.940023i | \(-0.610803\pi\) | ||||
−0.341111 | + | 0.940023i | \(0.610803\pi\) | |||||||
\(234\) | −93312.0 | −0.111403 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −452800. | −0.529208 | ||||||||
\(237\) | −542052. | −0.626859 | ||||||||
\(238\) | −24256.0 | −0.0277573 | ||||||||
\(239\) | 324904. | 0.367926 | 0.183963 | − | 0.982933i | \(-0.441107\pi\) | ||||
0.183963 | + | 0.982933i | \(0.441107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 915262. | 1.01509 | 0.507543 | − | 0.861626i | \(-0.330554\pi\) | ||||
0.507543 | + | 0.861626i | \(0.330554\pi\) | |||||||
\(242\) | 355796. | 0.390537 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 292640. | 0.314673 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 683496. | 0.720109 | ||||||||
\(247\) | 387072. | 0.403691 | ||||||||
\(248\) | −359168. | −0.370825 | ||||||||
\(249\) | 22212.0 | 0.0227033 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.36708e6 | 1.36965 | 0.684823 | − | 0.728709i | \(-0.259879\pi\) | ||||
0.684823 | + | 0.728709i | \(0.259879\pi\) | |||||||
\(252\) | −5184.00 | −0.00514237 | ||||||||
\(253\) | 2.05000e6 | 2.01350 | ||||||||
\(254\) | −847120. | −0.823874 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 892932. | 0.843307 | 0.421653 | − | 0.906757i | \(-0.361450\pi\) | ||||
0.421653 | + | 0.906757i | \(0.361450\pi\) | |||||||
\(258\) | 86544.0 | 0.0809446 | ||||||||
\(259\) | 29152.0 | 0.0270034 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −214326. | −0.194748 | ||||||||
\(262\) | 678000. | 0.610206 | ||||||||
\(263\) | −1.86650e6 | −1.66394 | −0.831972 | − | 0.554818i | \(-0.812788\pi\) | ||||
−0.831972 | + | 0.554818i | \(0.812788\pi\) | |||||||
\(264\) | 288000. | 0.254321 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21504.0 | 0.0186344 | ||||||||
\(267\) | −204102. | −0.175214 | ||||||||
\(268\) | 1.05530e6 | 0.897506 | ||||||||
\(269\) | −1.37227e6 | −1.15627 | −0.578133 | − | 0.815943i | \(-0.696218\pi\) | ||||
−0.578133 | + | 0.815943i | \(0.696218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 458644. | 0.379361 | 0.189680 | − | 0.981846i | \(-0.439255\pi\) | ||||
0.189680 | + | 0.981846i | \(0.439255\pi\) | |||||||
\(272\) | 388096. | 0.318066 | ||||||||
\(273\) | −10368.0 | −0.00841954 | ||||||||
\(274\) | 1.00814e6 | 0.811234 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 590400. | 0.466524 | ||||||||
\(277\) | −985408. | −0.771643 | −0.385822 | − | 0.922573i | \(-0.626082\pi\) | ||||
−0.385822 | + | 0.922573i | \(0.626082\pi\) | |||||||
\(278\) | 768064. | 0.596054 | ||||||||
\(279\) | −454572. | −0.349617 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 165798. | 0.125260 | 0.0626302 | − | 0.998037i | \(-0.480051\pi\) | ||||
0.0626302 | + | 0.998037i | \(0.480051\pi\) | |||||||
\(282\) | −320400. | −0.239922 | ||||||||
\(283\) | −1.66471e6 | −1.23558 | −0.617792 | − | 0.786342i | \(-0.711972\pi\) | ||||
−0.617792 | + | 0.786342i | \(0.711972\pi\) | |||||||
\(284\) | −460800. | −0.339013 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 576000. | 0.416397 | ||||||||
\(287\) | 75944.0 | 0.0544238 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 878399. | 0.618653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 332712. | 0.230322 | ||||||||
\(292\) | −492928. | −0.338319 | ||||||||
\(293\) | 2.55104e6 | 1.73600 | 0.867998 | − | 0.496567i | \(-0.165406\pi\) | ||||
0.867998 | + | 0.496567i | \(0.165406\pi\) | |||||||
\(294\) | 604476. | 0.407860 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −466432. | −0.309428 | ||||||||
\(297\) | 364500. | 0.239776 | ||||||||
\(298\) | 942776. | 0.614990 | ||||||||
\(299\) | 1.18080e6 | 0.763833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9616.00 | 0.00611756 | ||||||||
\(302\) | −1.48597e6 | −0.937545 | ||||||||
\(303\) | −1.51126e6 | −0.945656 | ||||||||
\(304\) | −344064. | −0.213528 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 491184. | 0.299875 | ||||||||
\(307\) | 736020. | 0.445701 | 0.222851 | − | 0.974853i | \(-0.428464\pi\) | ||||
0.222851 | + | 0.974853i | \(0.428464\pi\) | |||||||
\(308\) | 32000.0 | 0.0192209 | ||||||||
\(309\) | 1.38928e6 | 0.827737 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.71660e6 | 1.00639 | 0.503197 | − | 0.864172i | \(-0.332157\pi\) | ||||
0.503197 | + | 0.864172i | \(0.332157\pi\) | |||||||
\(312\) | 165888. | 0.0964780 | ||||||||
\(313\) | 2.83851e6 | 1.63768 | 0.818842 | − | 0.574020i | \(-0.194617\pi\) | ||||
0.818842 | + | 0.574020i | \(0.194617\pi\) | |||||||
\(314\) | 1.05981e6 | 0.606601 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 963648. | 0.542876 | ||||||||
\(317\) | −1.27605e6 | −0.713215 | −0.356607 | − | 0.934254i | \(-0.616067\pi\) | ||||
−0.356607 | + | 0.934254i | \(0.616067\pi\) | |||||||
\(318\) | −1.43294e6 | −0.794624 | ||||||||
\(319\) | 1.32300e6 | 0.727919 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.23109e6 | −0.666850 | ||||||||
\(322\) | 65600.0 | 0.0352585 | ||||||||
\(323\) | −2.03750e6 | −1.08666 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.61250e6 | −0.840339 | ||||||||
\(327\) | 484290. | 0.250459 | ||||||||
\(328\) | −1.21510e6 | −0.623633 | ||||||||
\(329\) | −35600.0 | −0.0181326 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 443992. | 0.222744 | 0.111372 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111372 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(332\) | −39488.0 | −0.0196616 | ||||||||
\(333\) | −590328. | −0.291731 | ||||||||
\(334\) | −1.04760e6 | −0.513842 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9216.00 | 0.00445343 | ||||||||
\(337\) | 2.71326e6 | 1.30142 | 0.650708 | − | 0.759328i | \(-0.274472\pi\) | ||||
0.650708 | + | 0.759328i | \(0.274472\pi\) | |||||||
\(338\) | −1.15340e6 | −0.549145 | ||||||||
\(339\) | −744228. | −0.351728 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.80600e6 | 1.30678 | ||||||||
\(342\) | −435456. | −0.201316 | ||||||||
\(343\) | 134392. | 0.0616791 | ||||||||
\(344\) | −153856. | −0.0701001 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.30491e6 | 0.585991 | ||||||||
\(347\) | −1.31051e6 | −0.584273 | −0.292137 | − | 0.956377i | \(-0.594366\pi\) | ||||
−0.292137 | + | 0.956377i | \(0.594366\pi\) | |||||||
\(348\) | 381024. | 0.168657 | ||||||||
\(349\) | −298910. | −0.131364 | −0.0656821 | − | 0.997841i | \(-0.520922\pi\) | ||||
−0.0656821 | + | 0.997841i | \(0.520922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 209952. | 0.0909604 | ||||||||
\(352\) | −512000. | −0.220249 | ||||||||
\(353\) | 737996. | 0.315223 | 0.157611 | − | 0.987501i | \(-0.449621\pi\) | ||||
0.157611 | + | 0.987501i | \(0.449621\pi\) | |||||||
\(354\) | 1.01880e6 | 0.432097 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 362848. | 0.151740 | ||||||||
\(357\) | 54576.0 | 0.0226637 | ||||||||
\(358\) | −438064. | −0.180647 | ||||||||
\(359\) | −2.34074e6 | −0.958557 | −0.479278 | − | 0.877663i | \(-0.659102\pi\) | ||||
−0.479278 | + | 0.877663i | \(0.659102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −669763. | −0.270491 | ||||||||
\(362\) | −212584. | −0.0852627 | ||||||||
\(363\) | −800541. | −0.318872 | ||||||||
\(364\) | 18432.0 | 0.00729154 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −658440. | −0.256929 | ||||||||
\(367\) | 127292. | 0.0493328 | 0.0246664 | − | 0.999696i | \(-0.492148\pi\) | ||||
0.0246664 | + | 0.999696i | \(0.492148\pi\) | |||||||
\(368\) | −1.04960e6 | −0.404021 | ||||||||
\(369\) | −1.53787e6 | −0.587966 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −159216. | −0.0600554 | ||||||||
\(372\) | 808128. | 0.302777 | ||||||||
\(373\) | 4.03870e6 | 1.50303 | 0.751517 | − | 0.659713i | \(-0.229322\pi\) | ||||
0.751517 | + | 0.659713i | \(0.229322\pi\) | |||||||
\(374\) | −3.03200e6 | −1.12086 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 569600. | 0.207778 | ||||||||
\(377\) | 762048. | 0.276140 | ||||||||
\(378\) | 11664.0 | 0.00419873 | ||||||||
\(379\) | 1.01214e6 | 0.361944 | 0.180972 | − | 0.983488i | \(-0.442076\pi\) | ||||
0.180972 | + | 0.983488i | \(0.442076\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.90602e6 | 0.672690 | ||||||||
\(382\) | 928224. | 0.325458 | ||||||||
\(383\) | −2.37610e6 | −0.827690 | −0.413845 | − | 0.910347i | \(-0.635814\pi\) | ||||
−0.413845 | + | 0.910347i | \(0.635814\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.12269e6 | −1.40836 | ||||||||
\(387\) | −194724. | −0.0660910 | ||||||||
\(388\) | −591488. | −0.199465 | ||||||||
\(389\) | 1.42497e6 | 0.477456 | 0.238728 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238728 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.21560e6 | −2.05609 | ||||||||
\(392\) | −1.07462e6 | −0.353217 | ||||||||
\(393\) | −1.52550e6 | −0.498231 | ||||||||
\(394\) | −2.09118e6 | −0.678659 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −648000. | −0.207652 | ||||||||
\(397\) | 1.69345e6 | 0.539257 | 0.269628 | − | 0.962964i | \(-0.413099\pi\) | ||||
0.269628 | + | 0.962964i | \(0.413099\pi\) | |||||||
\(398\) | −861168. | −0.272509 | ||||||||
\(399\) | −48384.0 | −0.0152149 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.84501e6 | −0.883532 | −0.441766 | − | 0.897130i | \(-0.645648\pi\) | ||||
−0.441766 | + | 0.897130i | \(0.645648\pi\) | |||||||
\(402\) | −2.37442e6 | −0.732810 | ||||||||
\(403\) | 1.61626e6 | 0.495733 | ||||||||
\(404\) | 2.68669e6 | 0.818962 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 42336.0 | 0.0127466 | ||||||||
\(407\) | 3.64400e6 | 1.09042 | ||||||||
\(408\) | −873216. | −0.259700 | ||||||||
\(409\) | −1.89069e6 | −0.558873 | −0.279436 | − | 0.960164i | \(-0.590148\pi\) | ||||
−0.279436 | + | 0.960164i | \(0.590148\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.26832e6 | −0.662370 | ||||||||
\(412\) | −2.46982e6 | −0.716841 | ||||||||
\(413\) | 113200. | 0.0326566 | ||||||||
\(414\) | −1.32840e6 | −0.380915 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −294912. | −0.0835524 | ||||||||
\(417\) | −1.72814e6 | −0.486676 | ||||||||
\(418\) | 2.68800e6 | 0.752469 | ||||||||
\(419\) | 4.60930e6 | 1.28263 | 0.641313 | − | 0.767280i | \(-0.278390\pi\) | ||||
0.641313 | + | 0.767280i | \(0.278390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.04151e6 | −1.66127 | −0.830635 | − | 0.556817i | \(-0.812022\pi\) | ||||
−0.830635 | + | 0.556817i | \(0.812022\pi\) | |||||||
\(422\) | −4.12032e6 | −1.12629 | ||||||||
\(423\) | 720900. | 0.195895 | ||||||||
\(424\) | 2.54746e6 | 0.688164 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.03680e6 | 0.276803 | ||||||||
\(427\) | −73160.0 | −0.0194180 | ||||||||
\(428\) | 2.18861e6 | 0.577509 | ||||||||
\(429\) | −1.29600e6 | −0.339987 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3800.00 | −0.000985350 0 | −0.000492675 | − | 1.00000i | \(-0.500157\pi\) | ||||
−0.000492675 | 1.00000i | \(0.500157\pi\) | ||||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 250736. | 0.0642683 | 0.0321342 | − | 0.999484i | \(-0.489770\pi\) | ||||
0.0321342 | + | 0.999484i | \(0.489770\pi\) | |||||||
\(434\) | 89792.0 | 0.0228830 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −860960. | −0.216904 | ||||||||
\(437\) | 5.51040e6 | 1.38032 | ||||||||
\(438\) | 1.10909e6 | 0.276236 | ||||||||
\(439\) | −3.58873e6 | −0.888750 | −0.444375 | − | 0.895841i | \(-0.646574\pi\) | ||||
−0.444375 | + | 0.895841i | \(0.646574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.36007e6 | −0.333016 | ||||||||
\(442\) | −1.74643e6 | −0.425203 | ||||||||
\(443\) | −1.41479e6 | −0.342517 | −0.171258 | − | 0.985226i | \(-0.554783\pi\) | ||||
−0.171258 | + | 0.985226i | \(0.554783\pi\) | |||||||
\(444\) | 1.04947e6 | 0.252647 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.82408e6 | 0.434217 | ||||||||
\(447\) | −2.12125e6 | −0.502137 | ||||||||
\(448\) | −16384.0 | −0.00385678 | ||||||||
\(449\) | −829806. | −0.194250 | −0.0971249 | − | 0.995272i | \(-0.530965\pi\) | ||||
−0.0971249 | + | 0.995272i | \(0.530965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.49300e6 | 2.19767 | ||||||||
\(452\) | 1.32307e6 | 0.304605 | ||||||||
\(453\) | 3.34343e6 | 0.765502 | ||||||||
\(454\) | −1.73701e6 | −0.395514 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 774144. | 0.174345 | ||||||||
\(457\) | 4.68198e6 | 1.04867 | 0.524335 | − | 0.851512i | \(-0.324314\pi\) | ||||
0.524335 | + | 0.851512i | \(0.324314\pi\) | |||||||
\(458\) | −2.89084e6 | −0.643962 | ||||||||
\(459\) | −1.10516e6 | −0.244847 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −141930. | −0.0311044 | −0.0155522 | − | 0.999879i | \(-0.504951\pi\) | ||||
−0.0155522 | + | 0.999879i | \(0.504951\pi\) | |||||||
\(462\) | −72000.0 | −0.0156938 | ||||||||
\(463\) | 727476. | 0.157713 | 0.0788563 | − | 0.996886i | \(-0.474873\pi\) | ||||
0.0788563 | + | 0.996886i | \(0.474873\pi\) | |||||||
\(464\) | −677376. | −0.146061 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.26139e6 | −0.482404 | ||||||||
\(467\) | −4.47640e6 | −0.949809 | −0.474905 | − | 0.880037i | \(-0.657517\pi\) | ||||
−0.474905 | + | 0.880037i | \(0.657517\pi\) | |||||||
\(468\) | −373248. | −0.0787740 | ||||||||
\(469\) | −263824. | −0.0553837 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.38457e6 | −0.495288 | ||||||||
\(472\) | −1.81120e6 | −0.374207 | ||||||||
\(473\) | 1.20200e6 | 0.247031 | ||||||||
\(474\) | −2.16821e6 | −0.443256 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −97024.0 | −0.0196274 | ||||||||
\(477\) | 3.22412e6 | 0.648807 | ||||||||
\(478\) | 1.29962e6 | 0.260163 | ||||||||
\(479\) | −1.32718e6 | −0.264297 | −0.132149 | − | 0.991230i | \(-0.542188\pi\) | ||||
−0.132149 | + | 0.991230i | \(0.542188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.09894e6 | 0.413655 | ||||||||
\(482\) | 3.66105e6 | 0.717774 | ||||||||
\(483\) | −147600. | −0.0287885 | ||||||||
\(484\) | 1.42318e6 | 0.276152 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −4.11647e6 | −0.786507 | −0.393253 | − | 0.919430i | \(-0.628650\pi\) | ||||
−0.393253 | + | 0.919430i | \(0.628650\pi\) | |||||||
\(488\) | 1.17056e6 | 0.222507 | ||||||||
\(489\) | 3.62812e6 | 0.686134 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.12316e6 | −1.14623 | −0.573115 | − | 0.819475i | \(-0.694265\pi\) | ||||
−0.573115 | + | 0.819475i | \(0.694265\pi\) | |||||||
\(492\) | 2.73398e6 | 0.509194 | ||||||||
\(493\) | −4.01134e6 | −0.743313 | ||||||||
\(494\) | 1.54829e6 | 0.285453 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.43667e6 | −0.262213 | ||||||||
\(497\) | 115200. | 0.0209200 | ||||||||
\(498\) | 88848.0 | 0.0160537 | ||||||||
\(499\) | −7.90490e6 | −1.42117 | −0.710584 | − | 0.703613i | \(-0.751569\pi\) | ||||
−0.710584 | + | 0.703613i | \(0.751569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.35710e6 | 0.419550 | ||||||||
\(502\) | 5.46830e6 | 0.968486 | ||||||||
\(503\) | 3.97628e6 | 0.700741 | 0.350370 | − | 0.936611i | \(-0.386056\pi\) | ||||
0.350370 | + | 0.936611i | \(0.386056\pi\) | |||||||
\(504\) | −20736.0 | −0.00363621 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.20000e6 | 1.42376 | ||||||||
\(507\) | 2.59514e6 | 0.448375 | ||||||||
\(508\) | −3.38848e6 | −0.582567 | ||||||||
\(509\) | 781914. | 0.133772 | 0.0668859 | − | 0.997761i | \(-0.478694\pi\) | ||||
0.0668859 | + | 0.997761i | \(0.478694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 123232. | 0.0208772 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 979776. | 0.164374 | ||||||||
\(514\) | 3.57173e6 | 0.596308 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 346176. | 0.0572365 | ||||||||
\(517\) | −4.45000e6 | −0.732207 | ||||||||
\(518\) | 116608. | 0.0190943 | ||||||||
\(519\) | −2.93605e6 | −0.478460 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.82694e6 | 0.940472 | 0.470236 | − | 0.882541i | \(-0.344169\pi\) | ||||
0.470236 | + | 0.882541i | \(0.344169\pi\) | |||||||
\(522\) | −857304. | −0.137708 | ||||||||
\(523\) | −9.78938e6 | −1.56495 | −0.782476 | − | 0.622681i | \(-0.786043\pi\) | ||||
−0.782476 | + | 0.622681i | \(0.786043\pi\) | |||||||
\(524\) | 2.71200e6 | 0.431481 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.46600e6 | −1.17659 | ||||||||
\(527\) | −8.50779e6 | −1.33441 | ||||||||
\(528\) | 1.15200e6 | 0.179832 | ||||||||
\(529\) | 1.03737e7 | 1.61173 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.29230e6 | −0.352805 | ||||||||
\(532\) | 86016.0 | 0.0131765 | ||||||||
\(533\) | 5.46797e6 | 0.833696 | ||||||||
\(534\) | −816408. | −0.123895 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.22118e6 | 0.634633 | ||||||||
\(537\) | 985644. | 0.147497 | ||||||||
\(538\) | −5.48906e6 | −0.817603 | ||||||||
\(539\) | 8.39550e6 | 1.24473 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.76059e6 | 0.699307 | 0.349653 | − | 0.936879i | \(-0.386299\pi\) | ||||
0.349653 | + | 0.936879i | \(0.386299\pi\) | |||||||
\(542\) | 1.83458e6 | 0.268249 | ||||||||
\(543\) | 478314. | 0.0696167 | ||||||||
\(544\) | 1.55238e6 | 0.224906 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −41472.0 | −0.00595351 | ||||||||
\(547\) | −1.16595e6 | −0.166614 | −0.0833069 | − | 0.996524i | \(-0.526548\pi\) | ||||
−0.0833069 | + | 0.996524i | \(0.526548\pi\) | |||||||
\(548\) | 4.03258e6 | 0.573629 | ||||||||
\(549\) | 1.48149e6 | 0.209782 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.55622e6 | 0.499011 | ||||||||
\(552\) | 2.36160e6 | 0.329882 | ||||||||
\(553\) | −240912. | −0.0335001 | ||||||||
\(554\) | −3.94163e6 | −0.545634 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.07226e6 | 0.421474 | ||||||||
\(557\) | −1.61293e6 | −0.220282 | −0.110141 | − | 0.993916i | \(-0.535130\pi\) | ||||
−0.110141 | + | 0.993916i | \(0.535130\pi\) | |||||||
\(558\) | −1.81829e6 | −0.247216 | ||||||||
\(559\) | 692352. | 0.0937125 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.82200e6 | 0.915176 | ||||||||
\(562\) | 663192. | 0.0885724 | ||||||||
\(563\) | 3.40603e6 | 0.452874 | 0.226437 | − | 0.974026i | \(-0.427292\pi\) | ||||
0.226437 | + | 0.974026i | \(0.427292\pi\) | |||||||
\(564\) | −1.28160e6 | −0.169650 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.65883e6 | −0.873689 | ||||||||
\(567\) | −26244.0 | −0.00342825 | ||||||||
\(568\) | −1.84320e6 | −0.239719 | ||||||||
\(569\) | −1.44009e7 | −1.86470 | −0.932350 | − | 0.361557i | \(-0.882245\pi\) | ||||
−0.932350 | + | 0.361557i | \(0.882245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.74772e6 | 0.609389 | 0.304695 | − | 0.952450i | \(-0.401446\pi\) | ||||
0.304695 | + | 0.952450i | \(0.401446\pi\) | |||||||
\(572\) | 2.30400e6 | 0.294437 | ||||||||
\(573\) | −2.08850e6 | −0.265735 | ||||||||
\(574\) | 303776. | 0.0384834 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −1.09094e7 | −1.36415 | −0.682074 | − | 0.731283i | \(-0.738922\pi\) | ||||
−0.682074 | + | 0.731283i | \(0.738922\pi\) | |||||||
\(578\) | 3.51360e6 | 0.437454 | ||||||||
\(579\) | 9.27605e6 | 1.14992 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9872.00 | 0.00121329 | ||||||||
\(582\) | 1.33085e6 | 0.162862 | ||||||||
\(583\) | −1.99020e7 | −2.42508 | ||||||||
\(584\) | −1.97171e6 | −0.239228 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.02042e7 | 1.22754 | ||||||||
\(587\) | 8.53223e6 | 1.02204 | 0.511019 | − | 0.859569i | \(-0.329268\pi\) | ||||
0.511019 | + | 0.859569i | \(0.329268\pi\) | |||||||
\(588\) | 2.41790e6 | 0.288400 | ||||||||
\(589\) | 7.54253e6 | 0.895836 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.70516e6 | 0.554123 | ||||||||
\(592\) | −1.86573e6 | −0.218798 | ||||||||
\(593\) | −4.63182e6 | −0.540897 | −0.270449 | − | 0.962734i | \(-0.587172\pi\) | ||||
−0.270449 | + | 0.962734i | \(0.587172\pi\) | |||||||
\(594\) | 1.45800e6 | 0.169548 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.77110e6 | 0.434863 | ||||||||
\(597\) | 1.93763e6 | 0.222502 | ||||||||
\(598\) | 4.72320e6 | 0.540111 | ||||||||
\(599\) | 6.27598e6 | 0.714684 | 0.357342 | − | 0.933974i | \(-0.383683\pi\) | ||||
0.357342 | + | 0.933974i | \(0.383683\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.71988e6 | 0.871815 | 0.435907 | − | 0.899992i | \(-0.356428\pi\) | ||||
0.435907 | + | 0.899992i | \(0.356428\pi\) | |||||||
\(602\) | 38464.0 | 0.00432577 | ||||||||
\(603\) | 5.34244e6 | 0.598337 | ||||||||
\(604\) | −5.94387e6 | −0.662944 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.04505e6 | −0.668680 | ||||||||
\(607\) | −6.06160e6 | −0.667753 | −0.333876 | − | 0.942617i | \(-0.608357\pi\) | ||||
−0.333876 | + | 0.942617i | \(0.608357\pi\) | |||||||
\(608\) | −1.37626e6 | −0.150987 | ||||||||
\(609\) | −95256.0 | −0.0104076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.56320e6 | −0.277766 | ||||||||
\(612\) | 1.96474e6 | 0.212044 | ||||||||
\(613\) | −3.66489e6 | −0.393921 | −0.196961 | − | 0.980411i | \(-0.563107\pi\) | ||||
−0.196961 | + | 0.980411i | \(0.563107\pi\) | |||||||
\(614\) | 2.94408e6 | 0.315158 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 128000. | 0.0135912 | ||||||||
\(617\) | −9.32522e6 | −0.986157 | −0.493079 | − | 0.869985i | \(-0.664129\pi\) | ||||
−0.493079 | + | 0.869985i | \(0.664129\pi\) | |||||||
\(618\) | 5.55710e6 | 0.585298 | ||||||||
\(619\) | −7.40162e6 | −0.776426 | −0.388213 | − | 0.921570i | \(-0.626907\pi\) | ||||
−0.388213 | + | 0.921570i | \(0.626907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.98890e6 | 0.311016 | ||||||||
\(622\) | 6.86640e6 | 0.711628 | ||||||||
\(623\) | −90712.0 | −0.00936364 | ||||||||
\(624\) | 663552. | 0.0682203 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.13540e7 | 1.15802 | ||||||||
\(627\) | −6.04800e6 | −0.614388 | ||||||||
\(628\) | 4.23923e6 | 0.428932 | ||||||||
\(629\) | −1.10486e7 | −1.11348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 160052. | 0.0160025 | 0.00800125 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800125 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(632\) | 3.85459e6 | 0.383871 | ||||||||
\(633\) | 9.27072e6 | 0.919611 | ||||||||
\(634\) | −5.10421e6 | −0.504319 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.73178e6 | −0.561884 | ||||||||
\(637\) | 4.83581e6 | 0.472194 | ||||||||
\(638\) | 5.29200e6 | 0.514717 | ||||||||
\(639\) | −2.33280e6 | −0.226009 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.69565e7 | −1.63002 | −0.815008 | − | 0.579450i | \(-0.803268\pi\) | ||||
−0.815008 | + | 0.579450i | \(0.803268\pi\) | |||||||
\(642\) | −4.92437e6 | −0.471534 | ||||||||
\(643\) | 1.10128e7 | 1.05044 | 0.525219 | − | 0.850967i | \(-0.323984\pi\) | ||||
0.525219 | + | 0.850967i | \(0.323984\pi\) | |||||||
\(644\) | 262400. | 0.0249315 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.15002e6 | −0.768382 | ||||||||
\(647\) | 3.33848e6 | 0.313537 | 0.156768 | − | 0.987635i | \(-0.449892\pi\) | ||||
0.156768 | + | 0.987635i | \(0.449892\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 1.41500e7 | 1.31870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −202032. | −0.0186839 | ||||||||
\(652\) | −6.44998e6 | −0.594210 | ||||||||
\(653\) | −4.76181e6 | −0.437008 | −0.218504 | − | 0.975836i | \(-0.570118\pi\) | ||||
−0.218504 | + | 0.975836i | \(0.570118\pi\) | |||||||
\(654\) | 1.93716e6 | 0.177101 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.86042e6 | −0.440975 | ||||||||
\(657\) | −2.49545e6 | −0.225546 | ||||||||
\(658\) | −142400. | −0.0128217 | ||||||||
\(659\) | 798188. | 0.0715965 | 0.0357982 | − | 0.999359i | \(-0.488603\pi\) | ||||
0.0357982 | + | 0.999359i | \(0.488603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.54048e7 | −1.37136 | −0.685682 | − | 0.727901i | \(-0.740496\pi\) | ||||
−0.685682 | + | 0.727901i | \(0.740496\pi\) | |||||||
\(662\) | 1.77597e6 | 0.157503 | ||||||||
\(663\) | 3.92947e6 | 0.347177 | ||||||||
\(664\) | −157952. | −0.0139029 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.36131e6 | −0.206285 | ||||||||
\(667\) | 1.08486e7 | 0.944189 | ||||||||
\(668\) | −4.19040e6 | −0.363341 | ||||||||
\(669\) | −4.10418e6 | −0.354537 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.14500e6 | −0.784111 | ||||||||
\(672\) | 36864.0 | 0.00314905 | ||||||||
\(673\) | −976704. | −0.0831238 | −0.0415619 | − | 0.999136i | \(-0.513233\pi\) | ||||
−0.0415619 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(674\) | 1.08530e7 | 0.920240 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.61358e6 | −0.388304 | ||||||||
\(677\) | 1.93885e7 | 1.62582 | 0.812911 | − | 0.582388i | \(-0.197881\pi\) | ||||
0.812911 | + | 0.582388i | \(0.197881\pi\) | |||||||
\(678\) | −2.97691e6 | −0.248709 | ||||||||
\(679\) | 147872. | 0.0123087 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.90827e6 | 0.322936 | ||||||||
\(682\) | 1.12240e7 | 0.924031 | ||||||||
\(683\) | −5.25573e6 | −0.431103 | −0.215552 | − | 0.976492i | \(-0.569155\pi\) | ||||
−0.215552 | + | 0.976492i | \(0.569155\pi\) | |||||||
\(684\) | −1.74182e6 | −0.142352 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 537568. | 0.0436137 | ||||||||
\(687\) | 6.50439e6 | 0.525793 | ||||||||
\(688\) | −615424. | −0.0495682 | ||||||||
\(689\) | −1.14636e7 | −0.919965 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.45034e6 | −0.434238 | −0.217119 | − | 0.976145i | \(-0.569666\pi\) | ||||
−0.217119 | + | 0.976145i | \(0.569666\pi\) | |||||||
\(692\) | 5.21965e6 | 0.414358 | ||||||||
\(693\) | 162000. | 0.0128139 | ||||||||
\(694\) | −5.24203e6 | −0.413144 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.52410e6 | 0.119258 | ||||||||
\(697\) | −2.87828e7 | −2.24414 | ||||||||
\(698\) | −1.19564e6 | −0.0928885 | ||||||||
\(699\) | 5.08813e6 | 0.393881 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.43961e6 | −0.341232 | −0.170616 | − | 0.985338i | \(-0.554576\pi\) | ||||
−0.170616 | + | 0.985338i | \(0.554576\pi\) | |||||||
\(702\) | 839808. | 0.0643187 | ||||||||
\(703\) | 9.79507e6 | 0.747514 | ||||||||
\(704\) | −2.04800e6 | −0.155739 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.95198e6 | 0.222896 | ||||||||
\(707\) | −671672. | −0.0505369 | ||||||||
\(708\) | 4.07520e6 | 0.305538 | ||||||||
\(709\) | 4.55918e6 | 0.340621 | 0.170310 | − | 0.985390i | \(-0.445523\pi\) | ||||
0.170310 | + | 0.985390i | \(0.445523\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.87847e6 | 0.361917 | ||||||||
\(712\) | 1.45139e6 | 0.107296 | ||||||||
\(713\) | 2.30092e7 | 1.69503 | ||||||||
\(714\) | 218304. | 0.0160257 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.75226e6 | −0.127736 | ||||||||
\(717\) | −2.92414e6 | −0.212422 | ||||||||
\(718\) | −9.36298e6 | −0.677802 | ||||||||
\(719\) | −2.06630e7 | −1.49063 | −0.745317 | − | 0.666710i | \(-0.767702\pi\) | ||||
−0.745317 | + | 0.666710i | \(0.767702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 617456. | 0.0442352 | ||||||||
\(722\) | −2.67905e6 | −0.191266 | ||||||||
\(723\) | −8.23736e6 | −0.586060 | ||||||||
\(724\) | −850336. | −0.0602898 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.20216e6 | −0.225477 | ||||||||
\(727\) | 5.48161e6 | 0.384656 | 0.192328 | − | 0.981331i | \(-0.438396\pi\) | ||||
0.192328 | + | 0.981331i | \(0.438396\pi\) | |||||||
\(728\) | 73728.0 | 0.00515589 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.64446e6 | −0.252255 | ||||||||
\(732\) | −2.63376e6 | −0.181676 | ||||||||
\(733\) | −8.55579e6 | −0.588166 | −0.294083 | − | 0.955780i | \(-0.595014\pi\) | ||||
−0.294083 | + | 0.955780i | \(0.595014\pi\) | |||||||
\(734\) | 509168. | 0.0348836 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.19840e6 | −0.285686 | ||||||||
\(737\) | −3.29780e7 | −2.23643 | ||||||||
\(738\) | −6.15146e6 | −0.415755 | ||||||||
\(739\) | −5.29119e6 | −0.356404 | −0.178202 | − | 0.983994i | \(-0.557028\pi\) | ||||
−0.178202 | + | 0.983994i | \(0.557028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.48365e6 | −0.233071 | ||||||||
\(742\) | −636864. | −0.0424656 | ||||||||
\(743\) | −2.36432e6 | −0.157121 | −0.0785606 | − | 0.996909i | \(-0.525032\pi\) | ||||
−0.0785606 | + | 0.996909i | \(0.525032\pi\) | |||||||
\(744\) | 3.23251e6 | 0.214096 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.61548e7 | 1.06281 | ||||||||
\(747\) | −199908. | −0.0131078 | ||||||||
\(748\) | −1.21280e7 | −0.792566 | ||||||||
\(749\) | −547152. | −0.0356372 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.79694e6 | −0.569157 | −0.284578 | − | 0.958653i | \(-0.591854\pi\) | ||||
−0.284578 | + | 0.958653i | \(0.591854\pi\) | |||||||
\(752\) | 2.27840e6 | 0.146922 | ||||||||
\(753\) | −1.23037e7 | −0.790766 | ||||||||
\(754\) | 3.04819e6 | 0.195260 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 46656.0 | 0.00296895 | ||||||||
\(757\) | 2.95808e7 | 1.87616 | 0.938079 | − | 0.346421i | \(-0.112603\pi\) | ||||
0.938079 | + | 0.346421i | \(0.112603\pi\) | |||||||
\(758\) | 4.04854e6 | 0.255933 | ||||||||
\(759\) | −1.84500e7 | −1.16250 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.26296e7 | −0.790549 | −0.395274 | − | 0.918563i | \(-0.629351\pi\) | ||||
−0.395274 | + | 0.918563i | \(0.629351\pi\) | |||||||
\(762\) | 7.62408e6 | 0.475664 | ||||||||
\(763\) | 215240. | 0.0133848 | ||||||||
\(764\) | 3.71290e6 | 0.230133 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.50440e6 | −0.585265 | ||||||||
\(767\) | 8.15040e6 | 0.500254 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −2.32186e7 | −1.41586 | −0.707929 | − | 0.706283i | \(-0.750370\pi\) | ||||
−0.707929 | + | 0.706283i | \(0.750370\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.03639e6 | −0.486883 | ||||||||
\(772\) | −1.64908e7 | −0.995858 | ||||||||
\(773\) | −1.73201e7 | −1.04256 | −0.521280 | − | 0.853386i | \(-0.674545\pi\) | ||||
−0.521280 | + | 0.853386i | \(0.674545\pi\) | |||||||
\(774\) | −778896. | −0.0467334 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.36595e6 | −0.141043 | ||||||||
\(777\) | −262368. | −0.0155904 | ||||||||
\(778\) | 5.69990e6 | 0.337612 | ||||||||
\(779\) | 2.55172e7 | 1.50657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.44000e7 | 0.844763 | ||||||||
\(782\) | −2.48624e7 | −1.45387 | ||||||||
\(783\) | 1.92893e6 | 0.112438 | ||||||||
\(784\) | −4.29850e6 | −0.249762 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.10200e6 | −0.352303 | ||||||||
\(787\) | 556676. | 0.0320380 | 0.0160190 | − | 0.999872i | \(-0.494901\pi\) | ||||
0.0160190 | + | 0.999872i | \(0.494901\pi\) | |||||||
\(788\) | −8.36474e6 | −0.479884 | ||||||||
\(789\) | 1.67985e7 | 0.960678 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −330768. | −0.0187967 | ||||||||
\(792\) | −2.59200e6 | −0.146832 | ||||||||
\(793\) | −5.26752e6 | −0.297456 | ||||||||
\(794\) | 6.77379e6 | 0.381312 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.44467e6 | −0.192693 | ||||||||
\(797\) | 3.00562e6 | 0.167606 | 0.0838028 | − | 0.996482i | \(-0.473293\pi\) | ||||
0.0838028 | + | 0.996482i | \(0.473293\pi\) | |||||||
\(798\) | −193536. | −0.0107586 | ||||||||
\(799\) | 1.34924e7 | 0.747691 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.83692e6 | 0.101160 | ||||||||
\(802\) | −1.13800e7 | −0.624751 | ||||||||
\(803\) | 1.54040e7 | 0.843033 | ||||||||
\(804\) | −9.49766e6 | −0.518175 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.46502e6 | 0.350536 | ||||||||
\(807\) | 1.23504e7 | 0.667570 | ||||||||
\(808\) | 1.07468e7 | 0.579094 | ||||||||
\(809\) | 2.23153e6 | 0.119876 | 0.0599378 | − | 0.998202i | \(-0.480910\pi\) | ||||
0.0599378 | + | 0.998202i | \(0.480910\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.24862e7 | 1.20051 | 0.600253 | − | 0.799810i | \(-0.295067\pi\) | ||||
0.600253 | + | 0.799810i | \(0.295067\pi\) | |||||||
\(812\) | 169344. | 0.00901322 | ||||||||
\(813\) | −4.12780e6 | −0.219024 | ||||||||
\(814\) | 1.45760e7 | 0.771041 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.49286e6 | −0.183635 | ||||||||
\(817\) | 3.23098e6 | 0.169347 | ||||||||
\(818\) | −7.56278e6 | −0.395183 | ||||||||
\(819\) | 93312.0 | 0.00486102 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.65921e7 | −0.859098 | −0.429549 | − | 0.903044i | \(-0.641327\pi\) | ||||
−0.429549 | + | 0.903044i | \(0.641327\pi\) | |||||||
\(822\) | −9.07330e6 | −0.468366 | ||||||||
\(823\) | 1.47544e7 | 0.759316 | 0.379658 | − | 0.925127i | \(-0.376042\pi\) | ||||
0.379658 | + | 0.925127i | \(0.376042\pi\) | |||||||
\(824\) | −9.87930e6 | −0.506883 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 452800. | 0.0230917 | ||||||||
\(827\) | −3.39475e6 | −0.172601 | −0.0863006 | − | 0.996269i | \(-0.527505\pi\) | ||||
−0.0863006 | + | 0.996269i | \(0.527505\pi\) | |||||||
\(828\) | −5.31360e6 | −0.269348 | ||||||||
\(829\) | −509442. | −0.0257459 | −0.0128730 | − | 0.999917i | \(-0.504098\pi\) | ||||
−0.0128730 | + | 0.999917i | \(0.504098\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.86867e6 | 0.445509 | ||||||||
\(832\) | −1.17965e6 | −0.0590805 | ||||||||
\(833\) | −2.54552e7 | −1.27105 | ||||||||
\(834\) | −6.91258e6 | −0.344132 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.07520e7 | 0.532076 | ||||||||
\(837\) | 4.09115e6 | 0.201851 | ||||||||
\(838\) | 1.84372e7 | 0.906953 | ||||||||
\(839\) | 4.00609e7 | 1.96479 | 0.982394 | − | 0.186819i | \(-0.0598178\pi\) | ||||
0.982394 | + | 0.186819i | \(0.0598178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.35098e7 | −0.658658 | ||||||||
\(842\) | −2.41660e7 | −1.17470 | ||||||||
\(843\) | −1.49218e6 | −0.0723191 | ||||||||
\(844\) | −1.64813e7 | −0.796407 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.88360e6 | 0.138519 | ||||||||
\(847\) | −355796. | −0.0170409 | ||||||||
\(848\) | 1.01898e7 | 0.486606 | ||||||||
\(849\) | 1.49824e7 | 0.713364 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.98808e7 | 1.41439 | ||||||||
\(852\) | 4.14720e6 | 0.195729 | ||||||||
\(853\) | 9.67506e6 | 0.455283 | 0.227641 | − | 0.973745i | \(-0.426899\pi\) | ||||
0.227641 | + | 0.973745i | \(0.426899\pi\) | |||||||
\(854\) | −292640. | −0.0137306 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.75443e6 | 0.408360 | ||||||||
\(857\) | 3.27535e7 | 1.52337 | 0.761686 | − | 0.647946i | \(-0.224372\pi\) | ||||
0.761686 | + | 0.647946i | \(0.224372\pi\) | |||||||
\(858\) | −5.18400e6 | −0.240407 | ||||||||
\(859\) | −2.17420e7 | −1.00535 | −0.502675 | − | 0.864476i | \(-0.667651\pi\) | ||||
−0.502675 | + | 0.864476i | \(0.667651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −683496. | −0.0314216 | ||||||||
\(862\) | −15200.0 | −0.000696748 0 | ||||||||
\(863\) | 2.08744e7 | 0.954087 | 0.477043 | − | 0.878880i | \(-0.341708\pi\) | ||||
0.477043 | + | 0.878880i | \(0.341708\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.00294e6 | 0.0454446 | ||||||||
\(867\) | −7.90559e6 | −0.357180 | ||||||||
\(868\) | 359168. | 0.0161807 | ||||||||
\(869\) | −3.01140e7 | −1.35275 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.89953e7 | −0.848401 | ||||||||
\(872\) | −3.44384e6 | −0.153374 | ||||||||
\(873\) | −2.99441e6 | −0.132977 | ||||||||
\(874\) | 2.20416e7 | 0.976033 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.43635e6 | 0.195329 | ||||||||
\(877\) | 3.96804e7 | 1.74212 | 0.871058 | − | 0.491181i | \(-0.163434\pi\) | ||||
0.871058 | + | 0.491181i | \(0.163434\pi\) | |||||||
\(878\) | −1.43549e7 | −0.628441 | ||||||||
\(879\) | −2.29594e7 | −1.00228 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.60742e7 | 1.13180 | 0.565902 | − | 0.824472i | \(-0.308528\pi\) | ||||
0.565902 | + | 0.824472i | \(0.308528\pi\) | |||||||
\(882\) | −5.44028e6 | −0.235478 | ||||||||
\(883\) | 4.10486e7 | 1.77172 | 0.885862 | − | 0.463949i | \(-0.153568\pi\) | ||||
0.885862 | + | 0.463949i | \(0.153568\pi\) | |||||||
\(884\) | −6.98573e6 | −0.300664 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.65915e6 | −0.242196 | ||||||||
\(887\) | 1.37553e7 | 0.587031 | 0.293515 | − | 0.955954i | \(-0.405175\pi\) | ||||
0.293515 | + | 0.955954i | \(0.405175\pi\) | |||||||
\(888\) | 4.19789e6 | 0.178648 | ||||||||
\(889\) | 847120. | 0.0359493 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.28050e6 | −0.138435 | ||||||||
\(892\) | 7.29632e6 | 0.307038 | ||||||||
\(893\) | −1.19616e7 | −0.501950 | ||||||||
\(894\) | −8.48498e6 | −0.355064 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −65536.0 | −0.00272716 | ||||||||
\(897\) | −1.06272e7 | −0.440999 | ||||||||
\(898\) | −3.31922e6 | −0.137355 | ||||||||
\(899\) | 1.48494e7 | 0.612785 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.03429e7 | 2.47636 | ||||||||
\(902\) | 3.79720e7 | 1.55399 | ||||||||
\(903\) | −86544.0 | −0.00353197 | ||||||||
\(904\) | 5.29229e6 | 0.215388 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.33737e7 | 0.541292 | ||||||||
\(907\) | −5.86936e6 | −0.236904 | −0.118452 | − | 0.992960i | \(-0.537793\pi\) | ||||
−0.118452 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(908\) | −6.94803e6 | −0.279671 | ||||||||
\(909\) | 1.36014e7 | 0.545975 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.63982e7 | 1.85227 | 0.926137 | − | 0.377188i | \(-0.123109\pi\) | ||||
0.926137 | + | 0.377188i | \(0.123109\pi\) | |||||||
\(912\) | 3.09658e6 | 0.123281 | ||||||||
\(913\) | 1.23400e6 | 0.0489935 | ||||||||
\(914\) | 1.87279e7 | 0.741521 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.15634e7 | −0.455350 | ||||||||
\(917\) | −678000. | −0.0266260 | ||||||||
\(918\) | −4.42066e6 | −0.173133 | ||||||||
\(919\) | 2.27859e7 | 0.889975 | 0.444988 | − | 0.895537i | \(-0.353208\pi\) | ||||
0.444988 | + | 0.895537i | \(0.353208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.62418e6 | −0.257326 | ||||||||
\(922\) | −567720. | −0.0219941 | ||||||||
\(923\) | 8.29440e6 | 0.320465 | ||||||||
\(924\) | −288000. | −0.0110972 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.90990e6 | 0.111520 | ||||||||
\(927\) | −1.25035e7 | −0.477894 | ||||||||
\(928\) | −2.70950e6 | −0.103281 | ||||||||
\(929\) | 2.70352e7 | 1.02775 | 0.513877 | − | 0.857864i | \(-0.328209\pi\) | ||||
0.513877 | + | 0.857864i | \(0.328209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.25671e7 | 0.853300 | ||||||||
\(932\) | −9.04557e6 | −0.341111 | ||||||||
\(933\) | −1.54494e7 | −0.581042 | ||||||||
\(934\) | −1.79056e7 | −0.671616 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.49299e6 | −0.0557016 | ||||||||
\(937\) | −2.86149e7 | −1.06474 | −0.532370 | − | 0.846512i | \(-0.678699\pi\) | ||||
−0.532370 | + | 0.846512i | \(0.678699\pi\) | |||||||
\(938\) | −1.05530e6 | −0.0391622 | ||||||||
\(939\) | −2.55466e7 | −0.945517 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.67892e7 | −1.35440 | −0.677200 | − | 0.735799i | \(-0.736807\pi\) | ||||
−0.677200 | + | 0.735799i | \(0.736807\pi\) | |||||||
\(942\) | −9.53827e6 | −0.350221 | ||||||||
\(943\) | 7.78426e7 | 2.85061 | ||||||||
\(944\) | −7.24480e6 | −0.264604 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.80800e6 | 0.174677 | ||||||||
\(947\) | 7.96828e6 | 0.288728 | 0.144364 | − | 0.989525i | \(-0.453886\pi\) | ||||
0.144364 | + | 0.989525i | \(0.453886\pi\) | |||||||
\(948\) | −8.67283e6 | −0.313430 | ||||||||
\(949\) | 8.87270e6 | 0.319809 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.14845e7 | 0.411775 | ||||||||
\(952\) | −388096. | −0.0138786 | ||||||||
\(953\) | −4.82202e7 | −1.71987 | −0.859937 | − | 0.510400i | \(-0.829497\pi\) | ||||
−0.859937 | + | 0.510400i | \(0.829497\pi\) | |||||||
\(954\) | 1.28965e7 | 0.458776 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.19846e6 | 0.183963 | ||||||||
\(957\) | −1.19070e7 | −0.420264 | ||||||||
\(958\) | −5.30874e6 | −0.186886 | ||||||||
\(959\) | −1.00814e6 | −0.0353978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86539e6 | 0.100087 | ||||||||
\(962\) | 8.39578e6 | 0.292498 | ||||||||
\(963\) | 1.10798e7 | 0.385006 | ||||||||
\(964\) | 1.46442e7 | 0.507543 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −590400. | −0.0203565 | ||||||||
\(967\) | 4.83510e7 | 1.66280 | 0.831398 | − | 0.555678i | \(-0.187541\pi\) | ||||
0.831398 | + | 0.555678i | \(0.187541\pi\) | |||||||
\(968\) | 5.69274e6 | 0.195269 | ||||||||
\(969\) | 1.83375e7 | 0.627381 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.05515e7 | −1.38025 | −0.690127 | − | 0.723688i | \(-0.742445\pi\) | ||||
−0.690127 | + | 0.723688i | \(0.742445\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −768064. | −0.0260085 | ||||||||
\(974\) | −1.64659e7 | −0.556144 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.68224e6 | 0.157336 | ||||||||
\(977\) | −4.34929e7 | −1.45775 | −0.728874 | − | 0.684648i | \(-0.759956\pi\) | ||||
−0.728874 | + | 0.684648i | \(0.759956\pi\) | |||||||
\(978\) | 1.45125e7 | 0.485170 | ||||||||
\(979\) | −1.13390e7 | −0.378110 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.35861e6 | −0.144602 | ||||||||
\(982\) | −2.44926e7 | −0.810507 | ||||||||
\(983\) | −3.34896e6 | −0.110542 | −0.0552709 | − | 0.998471i | \(-0.517602\pi\) | ||||
−0.0552709 | + | 0.998471i | \(0.517602\pi\) | |||||||
\(984\) | 1.09359e7 | 0.360054 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.60453e7 | −0.525602 | ||||||||
\(987\) | 320400. | 0.0104689 | ||||||||
\(988\) | 6.19315e6 | 0.201846 | ||||||||
\(989\) | 9.85640e6 | 0.320426 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.55726e7 | −1.79753 | −0.898766 | − | 0.438429i | \(-0.855535\pi\) | ||||
−0.898766 | + | 0.438429i | \(0.855535\pi\) | |||||||
\(992\) | −5.74669e6 | −0.185412 | ||||||||
\(993\) | −3.99593e6 | −0.128601 | ||||||||
\(994\) | 460800. | 0.0147927 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 355392. | 0.0113517 | ||||||||
\(997\) | −1.27342e7 | −0.405726 | −0.202863 | − | 0.979207i | \(-0.565025\pi\) | ||||
−0.202863 | + | 0.979207i | \(0.565025\pi\) | |||||||
\(998\) | −3.16196e7 | −1.00492 | ||||||||
\(999\) | 5.31295e6 | 0.168431 |
(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.j.1.1 | 1 | ||
3.2 | odd | 2 | 450.6.a.f.1.1 | 1 | |||
5.2 | odd | 4 | 30.6.c.a.19.2 | yes | 2 | ||
5.3 | odd | 4 | 30.6.c.a.19.1 | ✓ | 2 | ||
5.4 | even | 2 | 150.6.a.f.1.1 | 1 | |||
15.2 | even | 4 | 90.6.c.b.19.1 | 2 | |||
15.8 | even | 4 | 90.6.c.b.19.2 | 2 | |||
15.14 | odd | 2 | 450.6.a.s.1.1 | 1 | |||
20.3 | even | 4 | 240.6.f.a.49.2 | 2 | |||
20.7 | even | 4 | 240.6.f.a.49.1 | 2 | |||
60.23 | odd | 4 | 720.6.f.g.289.2 | 2 | |||
60.47 | odd | 4 | 720.6.f.g.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.6.c.a.19.1 | ✓ | 2 | 5.3 | odd | 4 | ||
30.6.c.a.19.2 | yes | 2 | 5.2 | odd | 4 | ||
90.6.c.b.19.1 | 2 | 15.2 | even | 4 | |||
90.6.c.b.19.2 | 2 | 15.8 | even | 4 | |||
150.6.a.f.1.1 | 1 | 5.4 | even | 2 | |||
150.6.a.j.1.1 | 1 | 1.1 | even | 1 | trivial | ||
240.6.f.a.49.1 | 2 | 20.7 | even | 4 | |||
240.6.f.a.49.2 | 2 | 20.3 | even | 4 | |||
450.6.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.a.s.1.1 | 1 | 15.14 | odd | 2 | |||
720.6.f.g.289.1 | 2 | 60.47 | odd | 4 | |||
720.6.f.g.289.2 | 2 | 60.23 | odd | 4 |