Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,6,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(36.0863594579\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −225.000 | −1.73555 | −0.867776 | − | 0.496956i | \(-0.834451\pi\) | ||||
−0.867776 | + | 0.496956i | \(0.834451\pi\) | |||||||
\(8\) | 192.000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 434.000 | 1.08145 | 0.540727 | − | 0.841198i | \(-0.318149\pi\) | ||||
0.540727 | + | 0.841198i | \(0.318149\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 613.000 | 1.00601 | 0.503005 | − | 0.864284i | \(-0.332228\pi\) | ||||
0.503005 | + | 0.864284i | \(0.332228\pi\) | |||||||
\(14\) | 900.000 | 1.22722 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | 878.000 | 0.736838 | 0.368419 | − | 0.929660i | \(-0.379899\pi\) | ||||
0.368419 | + | 0.929660i | \(0.379899\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −731.000 | −0.464551 | −0.232275 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232275 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1736.00 | −0.764703 | ||||||||
\(23\) | −2850.00 | −1.12338 | −0.561688 | − | 0.827349i | \(-0.689848\pi\) | ||||
−0.561688 | + | 0.827349i | \(0.689848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2452.00 | −0.711356 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3600.00 | 0.867776 | ||||||||
\(29\) | 7582.00 | 1.67413 | 0.837064 | − | 0.547105i | \(-0.184270\pi\) | ||||
0.837064 | + | 0.547105i | \(0.184270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2175.00 | 0.406495 | 0.203247 | − | 0.979127i | \(-0.434850\pi\) | ||||
0.203247 | + | 0.979127i | \(0.434850\pi\) | |||||||
\(32\) | −5120.00 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3512.00 | −0.521023 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9310.00 | −1.11801 | −0.559005 | − | 0.829165i | \(-0.688817\pi\) | ||||
−0.559005 | + | 0.829165i | \(0.688817\pi\) | |||||||
\(38\) | 2924.00 | 0.328487 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12040.0 | 1.11858 | 0.559290 | − | 0.828972i | \(-0.311074\pi\) | ||||
0.559290 | + | 0.828972i | \(0.311074\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1121.00 | −0.0924559 | −0.0462279 | − | 0.998931i | \(-0.514720\pi\) | ||||
−0.0462279 | + | 0.998931i | \(0.514720\pi\) | |||||||
\(44\) | −6944.00 | −0.540727 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11400.0 | 0.794347 | ||||||||
\(47\) | −29878.0 | −1.97291 | −0.986454 | − | 0.164038i | \(-0.947548\pi\) | ||||
−0.986454 | + | 0.164038i | \(0.947548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 33818.0 | 2.01214 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9808.00 | −0.503005 | ||||||||
\(53\) | −5740.00 | −0.280687 | −0.140343 | − | 0.990103i | \(-0.544821\pi\) | ||||
−0.140343 | + | 0.990103i | \(0.544821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −43200.0 | −1.84083 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −30328.0 | −1.18379 | ||||||||
\(59\) | 5174.00 | 0.193507 | 0.0967534 | − | 0.995308i | \(-0.469154\pi\) | ||||
0.0967534 | + | 0.995308i | \(0.469154\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −38717.0 | −1.33222 | −0.666112 | − | 0.745852i | \(-0.732043\pi\) | ||||
−0.666112 | + | 0.745852i | \(0.732043\pi\) | |||||||
\(62\) | −8700.00 | −0.287435 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 28672.0 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31707.0 | 0.862915 | 0.431458 | − | 0.902133i | \(-0.357999\pi\) | ||||
0.431458 | + | 0.902133i | \(0.357999\pi\) | |||||||
\(68\) | −14048.0 | −0.368419 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −64472.0 | −1.51784 | −0.758919 | − | 0.651185i | \(-0.774272\pi\) | ||||
−0.758919 | + | 0.651185i | \(0.774272\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −19790.0 | −0.434649 | −0.217324 | − | 0.976099i | \(-0.569733\pi\) | ||||
−0.217324 | + | 0.976099i | \(0.569733\pi\) | |||||||
\(74\) | 37240.0 | 0.790552 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11696.0 | 0.232275 | ||||||||
\(77\) | −97650.0 | −1.87692 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −105000. | −1.89287 | −0.946437 | − | 0.322889i | \(-0.895346\pi\) | ||||
−0.946437 | + | 0.322889i | \(0.895346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −48160.0 | −0.790955 | ||||||||
\(83\) | 3318.00 | 0.0528666 | 0.0264333 | − | 0.999651i | \(-0.491585\pi\) | ||||
0.0264333 | + | 0.999651i | \(0.491585\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4484.00 | 0.0653762 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 83328.0 | 1.14706 | ||||||||
\(89\) | 65376.0 | 0.874870 | 0.437435 | − | 0.899250i | \(-0.355887\pi\) | ||||
0.437435 | + | 0.899250i | \(0.355887\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −137925. | −1.74598 | ||||||||
\(92\) | 45600.0 | 0.561688 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 119512. | 1.39506 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −89143.0 | −0.961962 | −0.480981 | − | 0.876731i | \(-0.659719\pi\) | ||||
−0.480981 | + | 0.876731i | \(0.659719\pi\) | |||||||
\(98\) | −135272. | −1.42280 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 94644.0 | 0.923187 | 0.461593 | − | 0.887092i | \(-0.347278\pi\) | ||||
0.461593 | + | 0.887092i | \(0.347278\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −113956. | −1.05839 | −0.529193 | − | 0.848501i | \(-0.677505\pi\) | ||||
−0.529193 | + | 0.848501i | \(0.677505\pi\) | |||||||
\(104\) | 117696. | 1.06703 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22960.0 | 0.198476 | ||||||||
\(107\) | 19212.0 | 0.162223 | 0.0811116 | − | 0.996705i | \(-0.474153\pi\) | ||||
0.0811116 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −152791. | −1.23178 | −0.615888 | − | 0.787834i | \(-0.711203\pi\) | ||||
−0.615888 | + | 0.787834i | \(0.711203\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 57600.0 | 0.433888 | ||||||||
\(113\) | −4012.00 | −0.0295573 | −0.0147787 | − | 0.999891i | \(-0.504704\pi\) | ||||
−0.0147787 | + | 0.999891i | \(0.504704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −121312. | −0.837064 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20696.0 | −0.136830 | ||||||||
\(119\) | −197550. | −1.27882 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27305.0 | 0.169543 | ||||||||
\(122\) | 154868. | 0.942024 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −34800.0 | −0.203247 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −36368.0 | −0.200083 | −0.100041 | − | 0.994983i | \(-0.531898\pi\) | ||||
−0.100041 | + | 0.994983i | \(0.531898\pi\) | |||||||
\(128\) | 49152.0 | 0.265165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 43932.0 | 0.223667 | 0.111834 | − | 0.993727i | \(-0.464328\pi\) | ||||
0.111834 | + | 0.993727i | \(0.464328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 164475. | 0.806252 | ||||||||
\(134\) | −126828. | −0.610173 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 168576. | 0.781535 | ||||||||
\(137\) | −185214. | −0.843087 | −0.421544 | − | 0.906808i | \(-0.638512\pi\) | ||||
−0.421544 | + | 0.906808i | \(0.638512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 115916. | 0.508869 | 0.254435 | − | 0.967090i | \(-0.418111\pi\) | ||||
0.254435 | + | 0.967090i | \(0.418111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 257888. | 1.07327 | ||||||||
\(143\) | 266042. | 1.08795 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 79160.0 | 0.307343 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 148960. | 0.559005 | ||||||||
\(149\) | −33122.0 | −0.122222 | −0.0611112 | − | 0.998131i | \(-0.519464\pi\) | ||||
−0.0611112 | + | 0.998131i | \(0.519464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 431317. | 1.53941 | 0.769705 | − | 0.638400i | \(-0.220403\pi\) | ||||
0.769705 | + | 0.638400i | \(0.220403\pi\) | |||||||
\(152\) | −140352. | −0.492731 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 390600. | 1.32718 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 40439.0 | 0.130934 | 0.0654668 | − | 0.997855i | \(-0.479146\pi\) | ||||
0.0654668 | + | 0.997855i | \(0.479146\pi\) | |||||||
\(158\) | 420000. | 1.33846 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 641250. | 1.94968 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −116299. | −0.342852 | −0.171426 | − | 0.985197i | \(-0.554837\pi\) | ||||
−0.171426 | + | 0.985197i | \(0.554837\pi\) | |||||||
\(164\) | −192640. | −0.559290 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13272.0 | −0.0373823 | ||||||||
\(167\) | 632700. | 1.75552 | 0.877762 | − | 0.479097i | \(-0.159036\pi\) | ||||
0.877762 | + | 0.479097i | \(0.159036\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4476.00 | 0.0120552 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17936.0 | 0.0462279 | ||||||||
\(173\) | −108222. | −0.274916 | −0.137458 | − | 0.990508i | \(-0.543893\pi\) | ||||
−0.137458 | + | 0.990508i | \(0.543893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −111104. | −0.270363 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −261504. | −0.618626 | ||||||||
\(179\) | −496570. | −1.15837 | −0.579186 | − | 0.815196i | \(-0.696629\pi\) | ||||
−0.579186 | + | 0.815196i | \(0.696629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 105365. | 0.239056 | 0.119528 | − | 0.992831i | \(-0.461862\pi\) | ||||
0.119528 | + | 0.992831i | \(0.461862\pi\) | |||||||
\(182\) | 551700. | 1.23460 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −547200. | −1.19152 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 381052. | 0.796857 | ||||||||
\(188\) | 478048. | 0.986454 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −427346. | −0.847610 | −0.423805 | − | 0.905753i | \(-0.639306\pi\) | ||||
−0.423805 | + | 0.905753i | \(0.639306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 646427. | 1.24918 | 0.624592 | − | 0.780951i | \(-0.285265\pi\) | ||||
0.624592 | + | 0.780951i | \(0.285265\pi\) | |||||||
\(194\) | 356572. | 0.680210 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −541088. | −1.00607 | ||||||||
\(197\) | 546954. | 1.00412 | 0.502060 | − | 0.864833i | \(-0.332576\pi\) | ||||
0.502060 | + | 0.864833i | \(0.332576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −581783. | −1.04143 | −0.520713 | − | 0.853732i | \(-0.674334\pi\) | ||||
−0.520713 | + | 0.853732i | \(0.674334\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −378576. | −0.652792 | ||||||||
\(203\) | −1.70595e6 | −2.90554 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 455824. | 0.748392 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −156928. | −0.251502 | ||||||||
\(209\) | −317254. | −0.502390 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −441355. | −0.682467 | −0.341234 | − | 0.939978i | \(-0.610845\pi\) | ||||
−0.341234 | + | 0.939978i | \(0.610845\pi\) | |||||||
\(212\) | 91840.0 | 0.140343 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −76848.0 | −0.114709 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −489375. | −0.705493 | ||||||||
\(218\) | 611164. | 0.870997 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 538214. | 0.741266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −330457. | −0.444993 | −0.222496 | − | 0.974934i | \(-0.571421\pi\) | ||||
−0.222496 | + | 0.974934i | \(0.571421\pi\) | |||||||
\(224\) | 1.15200e6 | 1.53402 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16048.0 | 0.0209002 | ||||||||
\(227\) | −1.12508e6 | −1.44917 | −0.724584 | − | 0.689186i | \(-0.757968\pi\) | ||||
−0.724584 | + | 0.689186i | \(0.757968\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −977379. | −1.23161 | −0.615807 | − | 0.787897i | \(-0.711170\pi\) | ||||
−0.615807 | + | 0.787897i | \(0.711170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.45574e6 | 1.77568 | ||||||||
\(233\) | −334584. | −0.403753 | −0.201876 | − | 0.979411i | \(-0.564704\pi\) | ||||
−0.201876 | + | 0.979411i | \(0.564704\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −82784.0 | −0.0967534 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 790200. | 0.904263 | ||||||||
\(239\) | −218764. | −0.247731 | −0.123866 | − | 0.992299i | \(-0.539529\pi\) | ||||
−0.123866 | + | 0.992299i | \(0.539529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 734041. | 0.814100 | 0.407050 | − | 0.913406i | \(-0.366557\pi\) | ||||
0.407050 | + | 0.913406i | \(0.366557\pi\) | |||||||
\(242\) | −109220. | −0.119885 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 619472. | 0.666112 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −448103. | −0.467343 | ||||||||
\(248\) | 417600. | 0.431153 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.18381e6 | −1.18604 | −0.593019 | − | 0.805189i | \(-0.702064\pi\) | ||||
−0.593019 | + | 0.805189i | \(0.702064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.23690e6 | −1.21488 | ||||||||
\(254\) | 145472. | 0.141480 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.11411e6 | −1.06250 | ||||||||
\(257\) | 333732. | 0.315185 | 0.157592 | − | 0.987504i | \(-0.449627\pi\) | ||||
0.157592 | + | 0.987504i | \(0.449627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.09475e6 | 1.94036 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −175728. | −0.158157 | ||||||||
\(263\) | 731104. | 0.651763 | 0.325882 | − | 0.945411i | \(-0.394339\pi\) | ||||
0.325882 | + | 0.945411i | \(0.394339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −657900. | −0.570106 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −507312. | −0.431458 | ||||||||
\(269\) | −734254. | −0.618679 | −0.309340 | − | 0.950952i | \(-0.600108\pi\) | ||||
−0.309340 | + | 0.950952i | \(0.600108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 335056. | 0.277137 | 0.138568 | − | 0.990353i | \(-0.455750\pi\) | ||||
0.138568 | + | 0.990353i | \(0.455750\pi\) | |||||||
\(272\) | −224768. | −0.184210 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 740856. | 0.596153 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.58260e6 | −1.23929 | −0.619643 | − | 0.784884i | \(-0.712723\pi\) | ||||
−0.619643 | + | 0.784884i | \(0.712723\pi\) | |||||||
\(278\) | −463664. | −0.359825 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.08713e6 | −0.821329 | −0.410665 | − | 0.911786i | \(-0.634703\pi\) | ||||
−0.410665 | + | 0.911786i | \(0.634703\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −607407. | −0.450831 | −0.225415 | − | 0.974263i | \(-0.572374\pi\) | ||||
−0.225415 | + | 0.974263i | \(0.572374\pi\) | |||||||
\(284\) | 1.03155e6 | 0.758919 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.06417e6 | −0.769299 | ||||||||
\(287\) | −2.70900e6 | −1.94135 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −648973. | −0.457069 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 316640. | 0.217324 | ||||||||
\(293\) | −1.23301e6 | −0.839066 | −0.419533 | − | 0.907740i | \(-0.637806\pi\) | ||||
−0.419533 | + | 0.907740i | \(0.637806\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.78752e6 | −1.18583 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 132488. | 0.0864243 | ||||||||
\(299\) | −1.74705e6 | −1.13013 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 252225. | 0.160462 | ||||||||
\(302\) | −1.72527e6 | −1.08853 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 187136. | 0.116138 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 562753. | 0.340778 | 0.170389 | − | 0.985377i | \(-0.445498\pi\) | ||||
0.170389 | + | 0.985377i | \(0.445498\pi\) | |||||||
\(308\) | 1.56240e6 | 0.938459 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.39645e6 | 1.40497 | 0.702487 | − | 0.711697i | \(-0.252073\pi\) | ||||
0.702487 | + | 0.711697i | \(0.252073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.52833e6 | 0.881773 | 0.440886 | − | 0.897563i | \(-0.354664\pi\) | ||||
0.440886 | + | 0.897563i | \(0.354664\pi\) | |||||||
\(314\) | −161756. | −0.0925841 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.68000e6 | 0.946437 | ||||||||
\(317\) | −1.00033e6 | −0.559106 | −0.279553 | − | 0.960130i | \(-0.590186\pi\) | ||||
−0.279553 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.29059e6 | 1.81049 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.56500e6 | −1.37863 | ||||||||
\(323\) | −641818. | −0.342299 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 465196. | 0.242433 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.31168e6 | 1.18643 | ||||||||
\(329\) | 6.72255e6 | 3.42408 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.29093e6 | 1.14932 | 0.574662 | − | 0.818391i | \(-0.305134\pi\) | ||||
0.574662 | + | 0.818391i | \(0.305134\pi\) | |||||||
\(332\) | −53088.0 | −0.0264333 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.53080e6 | −1.24134 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.28904e6 | 0.618290 | 0.309145 | − | 0.951015i | \(-0.399957\pi\) | ||||
0.309145 | + | 0.951015i | \(0.399957\pi\) | |||||||
\(338\) | −17904.0 | −0.00852429 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 943950. | 0.439605 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.82748e6 | −1.75662 | ||||||||
\(344\) | −215232. | −0.0980643 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 432888. | 0.194395 | ||||||||
\(347\) | −19102.0 | −0.00851638 | −0.00425819 | − | 0.999991i | \(-0.501355\pi\) | ||||
−0.00425819 | + | 0.999991i | \(0.501355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.24690e6 | −1.42694 | −0.713470 | − | 0.700686i | \(-0.752877\pi\) | ||||
−0.713470 | + | 0.700686i | \(0.752877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.22208e6 | −0.955879 | ||||||||
\(353\) | −4.28804e6 | −1.83156 | −0.915782 | − | 0.401677i | \(-0.868428\pi\) | ||||
−0.915782 | + | 0.401677i | \(0.868428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.04602e6 | −0.437435 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.98628e6 | 0.819092 | ||||||||
\(359\) | −88656.0 | −0.0363055 | −0.0181527 | − | 0.999835i | \(-0.505779\pi\) | ||||
−0.0181527 | + | 0.999835i | \(0.505779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.94174e6 | −0.784192 | ||||||||
\(362\) | −421460. | −0.169038 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.20680e6 | 0.872990 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.04184e6 | −0.791328 | −0.395664 | − | 0.918395i | \(-0.629485\pi\) | ||||
−0.395664 | + | 0.918395i | \(0.629485\pi\) | |||||||
\(368\) | 729600. | 0.280844 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.29150e6 | 0.487147 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −806321. | −0.300079 | −0.150040 | − | 0.988680i | \(-0.547940\pi\) | ||||
−0.150040 | + | 0.988680i | \(0.547940\pi\) | |||||||
\(374\) | −1.52421e6 | −0.563463 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.73658e6 | −2.09259 | ||||||||
\(377\) | 4.64777e6 | 1.68419 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.41314e6 | −0.862950 | −0.431475 | − | 0.902125i | \(-0.642007\pi\) | ||||
−0.431475 | + | 0.902125i | \(0.642007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.70938e6 | 0.599351 | ||||||||
\(383\) | 1.45856e6 | 0.508076 | 0.254038 | − | 0.967194i | \(-0.418241\pi\) | ||||
0.254038 | + | 0.967194i | \(0.418241\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.58571e6 | −0.883306 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.42629e6 | 0.480981 | ||||||||
\(389\) | −2.65618e6 | −0.889985 | −0.444993 | − | 0.895534i | \(-0.646794\pi\) | ||||
−0.444993 | + | 0.895534i | \(0.646794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.50230e6 | −0.827747 | ||||||||
\(392\) | 6.49306e6 | 2.13419 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.18782e6 | −0.710019 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.68664e6 | 0.537090 | 0.268545 | − | 0.963267i | \(-0.413457\pi\) | ||||
0.268545 | + | 0.963267i | \(0.413457\pi\) | |||||||
\(398\) | 2.32713e6 | 0.736399 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.12533e6 | 0.660033 | 0.330017 | − | 0.943975i | \(-0.392946\pi\) | ||||
0.330017 | + | 0.943975i | \(0.392946\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.33328e6 | 0.408938 | ||||||||
\(404\) | −1.51430e6 | −0.461593 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.82380e6 | 2.05452 | ||||||||
\(407\) | −4.04054e6 | −1.20908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.97158e6 | 0.582782 | 0.291391 | − | 0.956604i | \(-0.405882\pi\) | ||||
0.291391 | + | 0.956604i | \(0.405882\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.82330e6 | 0.529193 | ||||||||
\(413\) | −1.16415e6 | −0.335841 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.13856e6 | −0.889195 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.26902e6 | 0.355244 | ||||||||
\(419\) | −1.75744e6 | −0.489042 | −0.244521 | − | 0.969644i | \(-0.578631\pi\) | ||||
−0.244521 | + | 0.969644i | \(0.578631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.83947e6 | −0.780785 | −0.390392 | − | 0.920649i | \(-0.627661\pi\) | ||||
−0.390392 | + | 0.920649i | \(0.627661\pi\) | |||||||
\(422\) | 1.76542e6 | 0.482577 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.10208e6 | −0.297713 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.71132e6 | 2.31214 | ||||||||
\(428\) | −307392. | −0.0811116 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.69335e6 | 1.21700 | 0.608499 | − | 0.793555i | \(-0.291772\pi\) | ||||
0.608499 | + | 0.793555i | \(0.291772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.71343e6 | −1.72078 | −0.860389 | − | 0.509639i | \(-0.829779\pi\) | ||||
−0.860389 | + | 0.509639i | \(0.829779\pi\) | |||||||
\(434\) | 1.95750e6 | 0.498859 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.44466e6 | 0.615888 | ||||||||
\(437\) | 2.08335e6 | 0.521866 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.92022e6 | 0.970842 | 0.485421 | − | 0.874281i | \(-0.338666\pi\) | ||||
0.485421 | + | 0.874281i | \(0.338666\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.15286e6 | −0.524154 | ||||||||
\(443\) | 6.93031e6 | 1.67781 | 0.838906 | − | 0.544276i | \(-0.183195\pi\) | ||||
0.838906 | + | 0.544276i | \(0.183195\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.32183e6 | 0.314657 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.45120e6 | −1.51861 | ||||||||
\(449\) | −4.38605e6 | −1.02673 | −0.513367 | − | 0.858169i | \(-0.671602\pi\) | ||||
−0.513367 | + | 0.858169i | \(0.671602\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.22536e6 | 1.20969 | ||||||||
\(452\) | 64192.0 | 0.0147787 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.50032e6 | 1.02472 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.41951e6 | 0.541922 | 0.270961 | − | 0.962590i | \(-0.412659\pi\) | ||||
0.270961 | + | 0.962590i | \(0.412659\pi\) | |||||||
\(458\) | 3.90952e6 | 0.870882 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 366228. | 0.0802600 | 0.0401300 | − | 0.999194i | \(-0.487223\pi\) | ||||
0.0401300 | + | 0.999194i | \(0.487223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.62534e6 | 1.43634 | 0.718168 | − | 0.695870i | \(-0.244981\pi\) | ||||
0.718168 | + | 0.695870i | \(0.244981\pi\) | |||||||
\(464\) | −1.94099e6 | −0.418532 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.33834e6 | 0.285496 | ||||||||
\(467\) | −3.38476e6 | −0.718183 | −0.359092 | − | 0.933302i | \(-0.616913\pi\) | ||||
−0.359092 | + | 0.933302i | \(0.616913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.13408e6 | −1.49763 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 993408. | 0.205245 | ||||||||
\(473\) | −486514. | −0.0999868 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.16080e6 | 0.639410 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 875056. | 0.175173 | ||||||||
\(479\) | −6.61905e6 | −1.31813 | −0.659063 | − | 0.752088i | \(-0.729047\pi\) | ||||
−0.659063 | + | 0.752088i | \(0.729047\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.70703e6 | −1.12473 | ||||||||
\(482\) | −2.93616e6 | −0.575656 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −436880. | −0.0847713 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −287383. | −0.0549084 | −0.0274542 | − | 0.999623i | \(-0.508740\pi\) | ||||
−0.0274542 | + | 0.999623i | \(0.508740\pi\) | |||||||
\(488\) | −7.43366e6 | −1.41304 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.51337e6 | −1.21928 | −0.609638 | − | 0.792680i | \(-0.708685\pi\) | ||||
−0.609638 | + | 0.792680i | \(0.708685\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.65700e6 | 1.23356 | ||||||||
\(494\) | 1.79241e6 | 0.330461 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −556800. | −0.101624 | ||||||||
\(497\) | 1.45062e7 | 2.63428 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.17037e6 | −0.210413 | −0.105206 | − | 0.994450i | \(-0.533550\pi\) | ||||
−0.105206 | + | 0.994450i | \(0.533550\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.73525e6 | 0.838655 | ||||||||
\(503\) | 1.40651e6 | 0.247870 | 0.123935 | − | 0.992290i | \(-0.460449\pi\) | ||||
0.123935 | + | 0.992290i | \(0.460449\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.94760e6 | 0.859050 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 581888. | 0.100041 | ||||||||
\(509\) | −3.65645e6 | −0.625554 | −0.312777 | − | 0.949827i | \(-0.601259\pi\) | ||||
−0.312777 | + | 0.949827i | \(0.601259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.45275e6 | 0.754356 | ||||||||
\(512\) | 2.88358e6 | 0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.33493e6 | −0.222869 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.29671e7 | −2.13361 | ||||||||
\(518\) | −8.37900e6 | −1.37204 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.70889e6 | 0.437217 | 0.218609 | − | 0.975813i | \(-0.429848\pi\) | ||||
0.218609 | + | 0.975813i | \(0.429848\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.14014e7 | −1.82265 | −0.911326 | − | 0.411686i | \(-0.864940\pi\) | ||||
−0.911326 | + | 0.411686i | \(0.864940\pi\) | |||||||
\(524\) | −702912. | −0.111834 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.92442e6 | −0.460866 | ||||||||
\(527\) | 1.90965e6 | 0.299521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.68616e6 | 0.261974 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.63160e6 | −0.403126 | ||||||||
\(533\) | 7.38052e6 | 1.12530 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.08774e6 | 0.915260 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.93702e6 | 0.437472 | ||||||||
\(539\) | 1.46770e7 | 2.17603 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.95050e6 | 1.02099 | 0.510497 | − | 0.859880i | \(-0.329461\pi\) | ||||
0.510497 | + | 0.859880i | \(0.329461\pi\) | |||||||
\(542\) | −1.34022e6 | −0.195965 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.49536e6 | −0.651279 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.08532e6 | −1.15539 | −0.577695 | − | 0.816252i | \(-0.696048\pi\) | ||||
−0.577695 | + | 0.816252i | \(0.696048\pi\) | |||||||
\(548\) | 2.96342e6 | 0.421544 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.54244e6 | −0.777718 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.36250e7 | 3.28518 | ||||||||
\(554\) | 6.33040e6 | 0.876307 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.85466e6 | −0.254435 | ||||||||
\(557\) | −1.46025e7 | −1.99429 | −0.997146 | − | 0.0754991i | \(-0.975945\pi\) | ||||
−0.997146 | + | 0.0754991i | \(0.975945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −687173. | −0.0930115 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.34854e6 | 0.580767 | ||||||||
\(563\) | −3.54652e6 | −0.471554 | −0.235777 | − | 0.971807i | \(-0.575764\pi\) | ||||
−0.235777 | + | 0.971807i | \(0.575764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.42963e6 | 0.318786 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.23786e7 | −1.60991 | ||||||||
\(569\) | 1.42681e7 | 1.84750 | 0.923750 | − | 0.382996i | \(-0.125108\pi\) | ||||
0.923750 | + | 0.382996i | \(0.125108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.48534e6 | −0.704066 | −0.352033 | − | 0.935988i | \(-0.614509\pi\) | ||||
−0.352033 | + | 0.935988i | \(0.614509\pi\) | |||||||
\(572\) | −4.25667e6 | −0.543976 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.08360e7 | 1.37274 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.13253e6 | −0.266659 | −0.133329 | − | 0.991072i | \(-0.542567\pi\) | ||||
−0.133329 | + | 0.991072i | \(0.542567\pi\) | |||||||
\(578\) | 2.59589e6 | 0.323197 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −746550. | −0.0917526 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.49116e6 | −0.303550 | ||||||||
\(584\) | −3.79968e6 | −0.461015 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.93202e6 | 0.593309 | ||||||||
\(587\) | −2.39303e6 | −0.286650 | −0.143325 | − | 0.989676i | \(-0.545779\pi\) | ||||
−0.143325 | + | 0.989676i | \(0.545779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.58992e6 | −0.188838 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.38336e6 | 0.279502 | ||||||||
\(593\) | −1.83478e6 | −0.214264 | −0.107132 | − | 0.994245i | \(-0.534167\pi\) | ||||
−0.107132 | + | 0.994245i | \(0.534167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 529952. | 0.0611112 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.98820e6 | 0.799121 | ||||||||
\(599\) | 126508. | 0.0144062 | 0.00720312 | − | 0.999974i | \(-0.497707\pi\) | ||||
0.00720312 | + | 0.999974i | \(0.497707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.03791e7 | 1.17212 | 0.586059 | − | 0.810268i | \(-0.300679\pi\) | ||||
0.586059 | + | 0.810268i | \(0.300679\pi\) | |||||||
\(602\) | −1.00890e6 | −0.113464 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.90107e6 | −0.769705 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −366608. | −0.0403859 | −0.0201930 | − | 0.999796i | \(-0.506428\pi\) | ||||
−0.0201930 | + | 0.999796i | \(0.506428\pi\) | |||||||
\(608\) | 3.74272e6 | 0.410609 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.83152e7 | −1.98476 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.49272e6 | −0.805357 | −0.402678 | − | 0.915342i | \(-0.631921\pi\) | ||||
−0.402678 | + | 0.915342i | \(0.631921\pi\) | |||||||
\(614\) | −2.25101e6 | −0.240967 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.87488e7 | −1.99077 | ||||||||
\(617\) | −2.23748e6 | −0.236618 | −0.118309 | − | 0.992977i | \(-0.537747\pi\) | ||||
−0.118309 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.61648e6 | 0.694065 | 0.347033 | − | 0.937853i | \(-0.387189\pi\) | ||||
0.347033 | + | 0.937853i | \(0.387189\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.58582e6 | −0.993466 | ||||||||
\(623\) | −1.47096e7 | −1.51838 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.11332e6 | −0.623507 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −647024. | −0.0654668 | ||||||||
\(629\) | −8.17418e6 | −0.823792 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.16481e6 | −0.616377 | −0.308189 | − | 0.951325i | \(-0.599723\pi\) | ||||
−0.308189 | + | 0.951325i | \(0.599723\pi\) | |||||||
\(632\) | −2.01600e7 | −2.00770 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.00131e6 | 0.395348 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.07304e7 | 2.02423 | ||||||||
\(638\) | −1.31624e7 | −1.28021 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.79502e6 | −0.460941 | −0.230471 | − | 0.973079i | \(-0.574027\pi\) | ||||
−0.230471 | + | 0.973079i | \(0.574027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.20124e6 | −0.114578 | −0.0572890 | − | 0.998358i | \(-0.518246\pi\) | ||||
−0.0572890 | + | 0.998358i | \(0.518246\pi\) | |||||||
\(644\) | −1.02600e7 | −0.974839 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.56727e6 | 0.242042 | ||||||||
\(647\) | 1.01480e7 | 0.953058 | 0.476529 | − | 0.879159i | \(-0.341895\pi\) | ||||
0.476529 | + | 0.879159i | \(0.341895\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.24552e6 | 0.209269 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.86078e6 | 0.171426 | ||||||||
\(653\) | 1.98614e7 | 1.82275 | 0.911375 | − | 0.411576i | \(-0.135022\pi\) | ||||
0.911375 | + | 0.411576i | \(0.135022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.08224e6 | −0.279645 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.68902e7 | −2.42119 | ||||||||
\(659\) | 5.73308e6 | 0.514250 | 0.257125 | − | 0.966378i | \(-0.417225\pi\) | ||||
0.257125 | + | 0.966378i | \(0.417225\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.92244e6 | −0.705270 | −0.352635 | − | 0.935761i | \(-0.614714\pi\) | ||||
−0.352635 | + | 0.935761i | \(0.614714\pi\) | |||||||
\(662\) | −9.16373e6 | −0.812694 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 637056. | 0.0560735 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.16087e7 | −1.88068 | ||||||||
\(668\) | −1.01232e7 | −0.877762 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.68032e7 | −1.44074 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.75353e6 | −0.659875 | −0.329938 | − | 0.944003i | \(-0.607028\pi\) | ||||
−0.329938 | + | 0.944003i | \(0.607028\pi\) | |||||||
\(674\) | −5.15616e6 | −0.437197 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −71616.0 | −0.00602758 | ||||||||
\(677\) | 3.77777e6 | 0.316785 | 0.158392 | − | 0.987376i | \(-0.449369\pi\) | ||||
0.158392 | + | 0.987376i | \(0.449369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.00572e7 | 1.66953 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.77580e6 | −0.310848 | ||||||||
\(683\) | 6.18290e6 | 0.507155 | 0.253578 | − | 0.967315i | \(-0.418393\pi\) | ||||
0.253578 | + | 0.967315i | \(0.418393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.53099e7 | 1.24212 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 286976. | 0.0231140 | ||||||||
\(689\) | −3.51862e6 | −0.282374 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.38475e7 | −1.89997 | −0.949986 | − | 0.312293i | \(-0.898903\pi\) | ||||
−0.949986 | + | 0.312293i | \(0.898903\pi\) | |||||||
\(692\) | 1.73155e6 | 0.137458 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 76408.0 | 0.00602199 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.05711e7 | 0.824212 | ||||||||
\(698\) | 1.29876e7 | 1.00900 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.81240e6 | 0.446746 | 0.223373 | − | 0.974733i | \(-0.428293\pi\) | ||||
0.223373 | + | 0.974733i | \(0.428293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.80561e6 | 0.519372 | ||||||||
\(704\) | 1.24436e7 | 0.946272 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.71522e7 | 1.29511 | ||||||||
\(707\) | −2.12949e7 | −1.60224 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.53133e6 | −0.562673 | −0.281337 | − | 0.959609i | \(-0.590778\pi\) | ||||
−0.281337 | + | 0.959609i | \(0.590778\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.25522e7 | 0.927939 | ||||||||
\(713\) | −6.19875e6 | −0.456647 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.94512e6 | 0.579186 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 354624. | 0.0256718 | ||||||||
\(719\) | 8.66228e6 | 0.624899 | 0.312450 | − | 0.949934i | \(-0.398850\pi\) | ||||
0.312450 | + | 0.949934i | \(0.398850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.56401e7 | 1.83688 | ||||||||
\(722\) | 7.76695e6 | 0.554508 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.68584e6 | −0.119528 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.94444e6 | 0.206617 | 0.103309 | − | 0.994649i | \(-0.467057\pi\) | ||||
0.103309 | + | 0.994649i | \(0.467057\pi\) | |||||||
\(728\) | −2.64816e7 | −1.85189 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −984238. | −0.0681250 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.92363e7 | 1.32239 | 0.661197 | − | 0.750213i | \(-0.270049\pi\) | ||||
0.661197 | + | 0.750213i | \(0.270049\pi\) | |||||||
\(734\) | 8.16736e6 | 0.559553 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.45920e7 | 0.992934 | ||||||||
\(737\) | 1.37608e7 | 0.933203 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.63909e7 | −1.77764 | −0.888819 | − | 0.458258i | \(-0.848474\pi\) | ||||
−0.888819 | + | 0.458258i | \(0.848474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.16600e6 | −0.344465 | ||||||||
\(743\) | 11516.0 | 0.000765296 0 | 0.000382648 | − | 1.00000i | \(-0.499878\pi\) | ||||
0.000382648 | 1.00000i | \(0.499878\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.22528e6 | 0.212188 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.09683e6 | −0.398428 | ||||||||
\(749\) | −4.32270e6 | −0.281547 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.44836e7 | −1.58407 | −0.792036 | − | 0.610474i | \(-0.790979\pi\) | ||||
−0.792036 | + | 0.610474i | \(0.790979\pi\) | |||||||
\(752\) | 7.64877e6 | 0.493227 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.85911e7 | −1.19090 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.01385e7 | −0.643031 | −0.321515 | − | 0.946904i | \(-0.604192\pi\) | ||||
−0.321515 | + | 0.946904i | \(0.604192\pi\) | |||||||
\(758\) | 9.65258e6 | 0.610197 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.34571e7 | 0.842343 | 0.421172 | − | 0.906981i | \(-0.361619\pi\) | ||||
0.421172 | + | 0.906981i | \(0.361619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.43780e7 | 2.13781 | ||||||||
\(764\) | 6.83754e6 | 0.423805 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.83426e6 | −0.359264 | ||||||||
\(767\) | 3.17166e6 | 0.194670 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.13573e7 | 1.30236 | 0.651181 | − | 0.758923i | \(-0.274274\pi\) | ||||
0.651181 | + | 0.758923i | \(0.274274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.03428e7 | −0.624592 | ||||||||
\(773\) | 2.55468e7 | 1.53776 | 0.768879 | − | 0.639394i | \(-0.220815\pi\) | ||||
0.768879 | + | 0.639394i | \(0.220815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.71155e7 | −1.02031 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.06247e7 | 0.629315 | ||||||||
\(779\) | −8.80124e6 | −0.519637 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.79808e7 | −1.64147 | ||||||||
\(782\) | 1.00092e7 | 0.585305 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.65741e6 | −0.503034 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.32668e7 | 0.763535 | 0.381768 | − | 0.924258i | \(-0.375315\pi\) | ||||
0.381768 | + | 0.924258i | \(0.375315\pi\) | |||||||
\(788\) | −8.75126e6 | −0.502060 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 902700. | 0.0512982 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.37335e7 | −1.34023 | ||||||||
\(794\) | −6.74657e6 | −0.379780 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.30853e6 | 0.520713 | ||||||||
\(797\) | 1.24919e7 | 0.696601 | 0.348300 | − | 0.937383i | \(-0.386759\pi\) | ||||
0.348300 | + | 0.937383i | \(0.386759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.62329e7 | −1.45371 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.50133e6 | −0.466714 | ||||||||
\(803\) | −8.58886e6 | −0.470053 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.33310e6 | −0.289163 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.81716e7 | 0.979188 | ||||||||
\(809\) | 7.83514e6 | 0.420897 | 0.210448 | − | 0.977605i | \(-0.432508\pi\) | ||||
0.210448 | + | 0.977605i | \(0.432508\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.04751e7 | 1.62702 | 0.813510 | − | 0.581551i | \(-0.197554\pi\) | ||||
0.813510 | + | 0.581551i | \(0.197554\pi\) | |||||||
\(812\) | 2.72952e7 | 1.45277 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.61622e7 | 0.854945 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 819451. | 0.0429505 | ||||||||
\(818\) | −7.88632e6 | −0.412089 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.90330e7 | 1.50326 | 0.751629 | − | 0.659586i | \(-0.229268\pi\) | ||||
0.751629 | + | 0.659586i | \(0.229268\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.99935e7 | −1.02894 | −0.514468 | − | 0.857510i | \(-0.672011\pi\) | ||||
−0.514468 | + | 0.857510i | \(0.672011\pi\) | |||||||
\(824\) | −2.18796e7 | −1.12259 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.65660e6 | 0.237476 | ||||||||
\(827\) | 196388. | 0.00998507 | 0.00499254 | − | 0.999988i | \(-0.498411\pi\) | ||||
0.00499254 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.05093e6 | 0.356336 | 0.178168 | − | 0.984000i | \(-0.442983\pi\) | ||||
0.178168 | + | 0.984000i | \(0.442983\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.75759e7 | 0.880258 | ||||||||
\(833\) | 2.96922e7 | 1.48262 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.07606e6 | 0.251195 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.02978e6 | 0.345805 | ||||||||
\(839\) | 3.26118e7 | 1.59945 | 0.799724 | − | 0.600368i | \(-0.204979\pi\) | ||||
0.799724 | + | 0.600368i | \(0.204979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.69756e7 | 1.80271 | ||||||||
\(842\) | 1.13579e7 | 0.552098 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.06168e6 | 0.341234 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.14362e6 | −0.294250 | ||||||||
\(848\) | 1.46944e6 | 0.0701717 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.65335e7 | 1.25595 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.84687e7 | −0.869089 | −0.434545 | − | 0.900650i | \(-0.643091\pi\) | ||||
−0.434545 | + | 0.900650i | \(0.643091\pi\) | |||||||
\(854\) | −3.48453e7 | −1.63493 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.68870e6 | 0.172064 | ||||||||
\(857\) | 3.14310e7 | 1.46186 | 0.730930 | − | 0.682452i | \(-0.239087\pi\) | ||||
0.730930 | + | 0.682452i | \(0.239087\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.80767e7 | 1.29826 | 0.649132 | − | 0.760676i | \(-0.275132\pi\) | ||||
0.649132 | + | 0.760676i | \(0.275132\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.87734e7 | −0.860547 | ||||||||
\(863\) | 2.11951e7 | 0.968744 | 0.484372 | − | 0.874862i | \(-0.339048\pi\) | ||||
0.484372 | + | 0.874862i | \(0.339048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.68537e7 | 1.21677 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.83000e6 | 0.352746 | ||||||||
\(869\) | −4.55700e7 | −2.04706 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.94364e7 | 0.868101 | ||||||||
\(872\) | −2.93359e7 | −1.30650 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.33340e6 | −0.369015 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.70911e7 | 1.62843 | 0.814217 | − | 0.580561i | \(-0.197167\pi\) | ||||
0.814217 | + | 0.580561i | \(0.197167\pi\) | |||||||
\(878\) | −1.56809e7 | −0.686489 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.16386e6 | 0.397776 | 0.198888 | − | 0.980022i | \(-0.436267\pi\) | ||||
0.198888 | + | 0.980022i | \(0.436267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.36396e7 | 0.588706 | 0.294353 | − | 0.955697i | \(-0.404896\pi\) | ||||
0.294353 | + | 0.955697i | \(0.404896\pi\) | |||||||
\(884\) | −8.61142e6 | −0.370633 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.77212e7 | −1.18639 | ||||||||
\(887\) | −2.90401e7 | −1.23934 | −0.619669 | − | 0.784863i | \(-0.712733\pi\) | ||||
−0.619669 | + | 0.784863i | \(0.712733\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.18280e6 | 0.347254 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.28731e6 | 0.222496 | ||||||||
\(893\) | 2.18408e7 | 0.916516 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.10592e7 | −0.460207 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.75442e7 | 0.726011 | ||||||||
\(899\) | 1.64908e7 | 0.680525 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.03972e6 | −0.206821 | ||||||||
\(902\) | −2.09014e7 | −0.855382 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −770304. | −0.0313503 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.12100e7 | 0.856095 | 0.428048 | − | 0.903756i | \(-0.359202\pi\) | ||||
0.428048 | + | 0.903756i | \(0.359202\pi\) | |||||||
\(908\) | 1.80013e7 | 0.724584 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.95267e7 | −0.779531 | −0.389766 | − | 0.920914i | \(-0.627444\pi\) | ||||
−0.389766 | + | 0.920914i | \(0.627444\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.44001e6 | 0.0571728 | ||||||||
\(914\) | −9.67804e6 | −0.383197 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.56381e7 | 0.615807 | ||||||||
\(917\) | −9.88470e6 | −0.388186 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.85930e7 | −1.11679 | −0.558395 | − | 0.829575i | \(-0.688583\pi\) | ||||
−0.558395 | + | 0.829575i | \(0.688583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.46491e6 | −0.0567524 | ||||||||
\(923\) | −3.95213e7 | −1.52696 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.65014e7 | −1.01564 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.88198e7 | −1.47973 | ||||||||
\(929\) | −2.38769e7 | −0.907692 | −0.453846 | − | 0.891080i | \(-0.649948\pi\) | ||||
−0.453846 | + | 0.891080i | \(0.649948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.47210e7 | −0.934741 | ||||||||
\(932\) | 5.35334e6 | 0.201876 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.35390e7 | 0.507832 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.46672e7 | 1.28994 | 0.644970 | − | 0.764208i | \(-0.276870\pi\) | ||||
0.644970 | + | 0.764208i | \(0.276870\pi\) | |||||||
\(938\) | 2.85363e7 | 1.05899 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.64188e7 | −1.70891 | −0.854455 | − | 0.519525i | \(-0.826109\pi\) | ||||
−0.854455 | + | 0.519525i | \(0.826109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.43140e7 | −1.25659 | ||||||||
\(944\) | −1.32454e6 | −0.0483767 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.94606e6 | 0.0707013 | ||||||||
\(947\) | 2.10829e7 | 0.763934 | 0.381967 | − | 0.924176i | \(-0.375247\pi\) | ||||
0.381967 | + | 0.924176i | \(0.375247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.21313e7 | −0.437261 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.79296e7 | −1.35639 | ||||||||
\(953\) | −3.67438e7 | −1.31055 | −0.655273 | − | 0.755392i | \(-0.727446\pi\) | ||||
−0.655273 | + | 0.755392i | \(0.727446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.50022e6 | 0.123866 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.64762e7 | 0.932056 | ||||||||
\(959\) | 4.16732e7 | 1.46322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.38985e7 | −0.834762 | ||||||||
\(962\) | 2.28281e7 | 0.795303 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.17447e7 | −0.407050 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.76234e7 | −1.29388 | −0.646938 | − | 0.762543i | \(-0.723951\pi\) | ||||
−0.646938 | + | 0.762543i | \(0.723951\pi\) | |||||||
\(968\) | 5.24256e6 | 0.179827 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.89205e7 | 1.66511 | 0.832555 | − | 0.553943i | \(-0.186877\pi\) | ||||
0.832555 | + | 0.553943i | \(0.186877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.60811e7 | −0.883169 | ||||||||
\(974\) | 1.14953e6 | 0.0388261 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.91155e6 | 0.333056 | ||||||||
\(977\) | 2.84450e7 | 0.953386 | 0.476693 | − | 0.879070i | \(-0.341835\pi\) | ||||
0.476693 | + | 0.879070i | \(0.341835\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.83732e7 | 0.946131 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.60535e7 | 0.862158 | ||||||||
\(983\) | −4.51611e7 | −1.49067 | −0.745334 | − | 0.666692i | \(-0.767710\pi\) | ||||
−0.745334 | + | 0.666692i | \(0.767710\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.66280e7 | −0.872260 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.16965e6 | 0.233671 | ||||||||
\(989\) | 3.19485e6 | 0.103863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.85517e7 | −0.923524 | −0.461762 | − | 0.887004i | \(-0.652783\pi\) | ||||
−0.461762 | + | 0.887004i | \(0.652783\pi\) | |||||||
\(992\) | −1.11360e7 | −0.359294 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.80248e7 | −1.86272 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.26527e7 | 1.04035 | 0.520177 | − | 0.854058i | \(-0.325866\pi\) | ||||
0.520177 | + | 0.854058i | \(0.325866\pi\) | |||||||
\(998\) | 4.68148e6 | 0.148784 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.6.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 75.6.a.d.1.1 | yes | 1 | ||
5.2 | odd | 4 | 225.6.b.c.199.1 | 2 | |||
5.3 | odd | 4 | 225.6.b.c.199.2 | 2 | |||
5.4 | even | 2 | 225.6.a.g.1.1 | 1 | |||
15.2 | even | 4 | 75.6.b.c.49.2 | 2 | |||
15.8 | even | 4 | 75.6.b.c.49.1 | 2 | |||
15.14 | odd | 2 | 75.6.a.b.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.6.a.b.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
75.6.a.d.1.1 | yes | 1 | 3.2 | odd | 2 | ||
75.6.b.c.49.1 | 2 | 15.8 | even | 4 | |||
75.6.b.c.49.2 | 2 | 15.2 | even | 4 | |||
225.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.6.a.g.1.1 | 1 | 5.4 | even | 2 | |||
225.6.b.c.199.1 | 2 | 5.2 | odd | 4 | |||
225.6.b.c.199.2 | 2 | 5.3 | odd | 4 |