Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1028,6,Mod(1,1028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1028, 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("1028.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1028 = 2^{2} \cdot 257 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1028.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: | \(164.874566768\) |
Analytic rank: | \(0\) |
Dimension: | \(57\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 1028.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −25.3624 | −1.62700 | −0.813498 | − | 0.581568i | \(-0.802440\pi\) | ||||
−0.813498 | + | 0.581568i | \(0.802440\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 63.2925 | 1.13221 | 0.566105 | − | 0.824333i | \(-0.308450\pi\) | ||||
0.566105 | + | 0.824333i | \(0.308450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −82.1666 | −0.633797 | −0.316898 | − | 0.948459i | \(-0.602641\pi\) | ||||
−0.316898 | + | 0.948459i | \(0.602641\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 400.249 | 1.64712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −607.299 | −1.51329 | −0.756643 | − | 0.653828i | \(-0.773162\pi\) | ||||
−0.756643 | + | 0.653828i | \(0.773162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −208.834 | −0.342723 | −0.171362 | − | 0.985208i | \(-0.554817\pi\) | ||||
−0.171362 | + | 0.985208i | \(0.554817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1605.25 | −1.84210 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −298.599 | −0.250591 | −0.125295 | − | 0.992119i | \(-0.539988\pi\) | ||||
−0.125295 | + | 0.992119i | \(0.539988\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2221.86 | −1.41199 | −0.705995 | − | 0.708217i | \(-0.749500\pi\) | ||||
−0.705995 | + | 0.708217i | \(0.749500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2083.94 | 1.03118 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3798.31 | −1.49717 | −0.748584 | − | 0.663040i | \(-0.769266\pi\) | ||||
−0.748584 | + | 0.663040i | \(0.769266\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 880.939 | 0.281901 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3988.22 | −1.05286 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4877.74 | −1.07702 | −0.538510 | − | 0.842619i | \(-0.681013\pi\) | ||||
−0.538510 | + | 0.842619i | \(0.681013\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8125.40 | 1.51859 | 0.759295 | − | 0.650746i | \(-0.225544\pi\) | ||||
0.759295 | + | 0.650746i | \(0.225544\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15402.5 | 2.46211 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5200.53 | −0.717591 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3013.99 | −0.361940 | −0.180970 | − | 0.983489i | \(-0.557924\pi\) | ||||
−0.180970 | + | 0.983489i | \(0.557924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5296.53 | 0.557610 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7995.44 | −0.742819 | −0.371409 | − | 0.928469i | \(-0.621125\pi\) | ||||
−0.371409 | + | 0.928469i | \(0.621125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13199.3 | 1.08863 | 0.544313 | − | 0.838882i | \(-0.316791\pi\) | ||||
0.544313 | + | 0.838882i | \(0.316791\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 25332.8 | 1.86488 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2267.38 | 0.149720 | 0.0748600 | − | 0.997194i | \(-0.476149\pi\) | ||||
0.0748600 | + | 0.997194i | \(0.476149\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10055.7 | −0.598302 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7573.16 | 0.407710 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14726.3 | −0.720118 | −0.360059 | − | 0.932929i | \(-0.617243\pi\) | ||||
−0.360059 | + | 0.932929i | \(0.617243\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −38437.5 | −1.71336 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 56351.5 | 2.29730 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −41642.5 | −1.55742 | −0.778711 | − | 0.627382i | \(-0.784126\pi\) | ||||
−0.778711 | + | 0.627382i | \(0.784126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 46768.5 | 1.60927 | 0.804635 | − | 0.593769i | \(-0.202361\pi\) | ||||
0.804635 | + | 0.593769i | \(0.202361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −32887.1 | −1.04394 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13217.7 | −0.388035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25327.5 | 0.689297 | 0.344648 | − | 0.938732i | \(-0.387998\pi\) | ||||
0.344648 | + | 0.938732i | \(0.387998\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 96334.0 | 2.43589 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −69245.9 | −1.63023 | −0.815114 | − | 0.579301i | \(-0.803326\pi\) | ||||
−0.815114 | + | 0.579301i | \(0.803326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −61734.1 | −1.35587 | −0.677935 | − | 0.735121i | \(-0.737125\pi\) | ||||
−0.677935 | + | 0.735121i | \(0.737125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −22342.7 | −0.458651 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 49899.7 | 0.959116 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −72310.5 | −1.30357 | −0.651784 | − | 0.758405i | \(-0.725979\pi\) | ||||
−0.651784 | + | 0.758405i | \(0.725979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3889.98 | 0.0658772 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −93951.4 | −1.49695 | −0.748476 | − | 0.663162i | \(-0.769214\pi\) | ||||
−0.748476 | + | 0.663162i | \(0.769214\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18899.0 | −0.283722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 123711. | 1.75231 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 101944. | 1.36422 | 0.682110 | − | 0.731249i | \(-0.261062\pi\) | ||||
0.682110 | + | 0.731249i | \(0.261062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17159.2 | 0.217217 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −206079. | −2.47074 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −140627. | −1.59867 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 182943. | 1.97418 | 0.987089 | − | 0.160172i | \(-0.0512048\pi\) | ||||
0.987089 | + | 0.160172i | \(0.0512048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −243071. | −2.49256 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −112186. | −1.09430 | −0.547151 | − | 0.837034i | \(-0.684288\pi\) | ||||
−0.547151 | + | 0.837034i | \(0.684288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −162481. | −1.50907 | −0.754536 | − | 0.656259i | \(-0.772138\pi\) | ||||
−0.754536 | + | 0.656259i | \(0.772138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 131898. | 1.16752 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −125621. | −1.06073 | −0.530364 | − | 0.847770i | \(-0.677945\pi\) | ||||
−0.530364 | + | 0.847770i | \(0.677945\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 167703. | 1.35200 | 0.675998 | − | 0.736904i | \(-0.263713\pi\) | ||||
0.675998 | + | 0.736904i | \(0.263713\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 76441.8 | 0.588875 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −36562.4 | −0.269364 | −0.134682 | − | 0.990889i | \(-0.543001\pi\) | ||||
−0.134682 | + | 0.990889i | \(0.543001\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −240404. | −1.69511 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −83585.9 | −0.564505 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24534.8 | 0.158824 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 207762. | 1.29004 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 202783. | 1.20856 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −142032. | −0.813040 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 52866.4 | 0.290851 | 0.145426 | − | 0.989369i | \(-0.453545\pi\) | ||||
0.145426 | + | 0.989369i | \(0.453545\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −334764. | −1.77119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 30684.5 | 0.156222 | 0.0781108 | − | 0.996945i | \(-0.475111\pi\) | ||||
0.0781108 | + | 0.996945i | \(0.475111\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 182562. | 0.894915 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −252424. | −1.19206 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −230918. | −1.05113 | −0.525565 | − | 0.850754i | \(-0.676146\pi\) | ||||
−0.525565 | + | 0.850754i | \(0.676146\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −46789.9 | −0.205407 | −0.102703 | − | 0.994712i | \(-0.532749\pi\) | ||||
−0.102703 | + | 0.994712i | \(0.532749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −57506.1 | −0.243594 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 126825. | 0.518639 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −308724. | −1.21941 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 255035. | 0.973435 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 414691. | 1.53024 | 0.765119 | − | 0.643889i | \(-0.222680\pi\) | ||||
0.765119 | + | 0.643889i | \(0.222680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 287009. | 1.02436 | 0.512180 | − | 0.858878i | \(-0.328838\pi\) | ||||
0.512180 | + | 0.858878i | \(0.328838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −119514. | −0.412753 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 514277. | 1.71936 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −42288.0 | −0.136921 | −0.0684603 | − | 0.997654i | \(-0.521809\pi\) | ||||
−0.0684603 | + | 0.997654i | \(0.521809\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 373494. | 1.17163 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 312094. | 0.948900 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −346287. | −1.02086 | −0.510431 | − | 0.859919i | \(-0.670514\pi\) | ||||
−0.510431 | + | 0.859919i | \(0.670514\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 974866. | 2.78763 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −598136. | −1.65962 | −0.829810 | − | 0.558047i | \(-0.811551\pi\) | ||||
−0.829810 | + | 0.558047i | \(0.811551\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −327681. | −0.882541 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −889296. | −2.32571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 364744. | 0.926559 | 0.463280 | − | 0.886212i | \(-0.346673\pi\) | ||||
0.463280 | + | 0.886212i | \(0.346673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −72383.7 | −0.178668 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.05615e6 | 2.53392 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −212773. | −0.496346 | −0.248173 | − | 0.968716i | \(-0.579830\pi\) | ||||
−0.248173 | + | 0.968716i | \(0.579830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 62180.1 | 0.141077 | 0.0705383 | − | 0.997509i | \(-0.477528\pi\) | ||||
0.0705383 | + | 0.997509i | \(0.477528\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.18616e6 | −2.61828 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −190763. | −0.409793 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 181339. | 0.379216 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 327698. | 0.667297 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −709486. | −1.40721 | −0.703607 | − | 0.710589i | \(-0.748428\pi\) | ||||
−0.703607 | + | 0.710589i | \(0.748428\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −200287. | −0.387044 | −0.193522 | − | 0.981096i | \(-0.561991\pi\) | ||||
−0.193522 | + | 0.981096i | \(0.561991\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 335231. | 0.631331 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −485050. | −0.890473 | −0.445237 | − | 0.895413i | \(-0.646880\pi\) | ||||
−0.445237 | + | 0.895413i | \(0.646880\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 252763. | 0.452460 | 0.226230 | − | 0.974074i | \(-0.427360\pi\) | ||||
0.226230 | + | 0.974074i | \(0.427360\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −642366. | −1.12148 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 400787. | 0.682612 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −506052. | −0.841027 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.52027e6 | −2.46601 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.34933e6 | 2.13675 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 919403. | 1.42167 | 0.710837 | − | 0.703357i | \(-0.248316\pi\) | ||||
0.710837 | + | 0.703357i | \(0.248316\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.75624e6 | 2.65237 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 835414. | 1.23255 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −667636. | −0.962478 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.56572e6 | 2.20600 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 62357.6 | 0.0858834 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 425712. | 0.573263 | 0.286631 | − | 0.958041i | \(-0.407465\pi\) | ||||
0.286631 | + | 0.958041i | \(0.407465\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 352595. | 0.464323 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 435571. | 0.561041 | 0.280520 | − | 0.959848i | \(-0.409493\pi\) | ||||
0.280520 | + | 0.959848i | \(0.409493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23898.9 | −0.0301154 | −0.0150577 | − | 0.999887i | \(-0.504793\pi\) | ||||
−0.0150577 | + | 0.999887i | \(0.504793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.26557e6 | −1.56048 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 615057. | 0.742208 | 0.371104 | − | 0.928591i | \(-0.378979\pi\) | ||||
0.371104 | + | 0.928591i | \(0.378979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 143508. | 0.169514 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.83396e6 | 2.12090 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.63380e6 | −1.85013 | −0.925067 | − | 0.379805i | \(-0.875991\pi\) | ||||
−0.925067 | + | 0.379805i | \(0.875991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21467.7 | −0.0238090 | −0.0119045 | − | 0.999929i | \(-0.503789\pi\) | ||||
−0.0119045 | + | 0.999929i | \(0.503789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 870477. | 0.945675 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −636447. | −0.677403 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 464000. | 0.483922 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.38283e6 | 2.43554 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.76133e6 | 1.76464 | 0.882322 | − | 0.470646i | \(-0.155979\pi\) | ||||
0.882322 | + | 0.470646i | \(0.155979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.30671e6 | 2.26564 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 479324. | 0.461614 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −66049.0 | −0.0623783 | ||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 247649. | 0.229397 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.95231e6 | −1.77398 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 656233. | 0.585018 | 0.292509 | − | 0.956263i | \(-0.405510\pi\) | ||||
0.292509 | + | 0.956263i | \(0.405510\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −932064. | −0.815325 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.58553e6 | −2.21958 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.02706e6 | 1.70799 | 0.853996 | − | 0.520279i | \(-0.174172\pi\) | ||||
0.853996 | + | 0.520279i | \(0.174172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.13734e6 | 0.940737 | 0.470369 | − | 0.882470i | \(-0.344121\pi\) | ||||
0.470369 | + | 0.882470i | \(0.344121\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −435198. | −0.353411 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −534994. | −0.426596 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.23270e6 | −0.965294 | −0.482647 | − | 0.875815i | \(-0.660325\pi\) | ||||
−0.482647 | + | 0.875815i | \(0.660325\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.25219e6 | 2.50130 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −193406. | −0.146118 | −0.0730592 | − | 0.997328i | \(-0.523276\pi\) | ||||
−0.0730592 | + | 0.997328i | \(0.523276\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 951891. | 0.706514 | 0.353257 | − | 0.935526i | \(-0.385074\pi\) | ||||
0.353257 | + | 0.935526i | \(0.385074\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.56663e6 | 2.60103 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 656958. | 0.470796 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.33070e6 | −0.937204 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.63987e6 | −3.21198 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −148771. | −0.101239 | −0.0506197 | − | 0.998718i | \(-0.516120\pi\) | ||||
−0.0506197 | + | 0.998718i | \(0.516120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.63566e6 | −1.76333 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.42204e6 | 1.59327 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 793217. | 0.513114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.08454e6 | −0.689967 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.84531e6 | 1.78042 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.96010e6 | 1.82203 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.36271e6 | 0.825196 | 0.412598 | − | 0.910913i | \(-0.364621\pi\) | ||||
0.412598 | + | 0.910913i | \(0.364621\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.12091e6 | 2.45525 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.24022e6 | 1.89965 | 0.949825 | − | 0.312781i | \(-0.101260\pi\) | ||||
0.949825 | + | 0.312781i | \(0.101260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.79034e6 | 1.60989 | 0.804946 | − | 0.593348i | \(-0.202194\pi\) | ||||
0.804946 | + | 0.593348i | \(0.202194\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.08151e6 | −1.18196 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.89174e6 | 1.61626 | 0.808129 | − | 0.589005i | \(-0.200480\pi\) | ||||
0.808129 | + | 0.589005i | \(0.200480\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.96225e6 | 1.62984 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.18606e6 | 1.72580 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 663443. | 0.353832 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −183970. | −0.0966139 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.25335e6 | −2.19969 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −186303. | −0.0948920 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.61923e6 | 0.812342 | 0.406171 | − | 0.913797i | \(-0.366864\pi\) | ||||
0.406171 | + | 0.913797i | \(0.366864\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.20635e6 | −0.596158 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.60304e6 | 0.780429 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 87783.9 | 0.0421056 | 0.0210528 | − | 0.999778i | \(-0.493298\pi\) | ||||
0.0210528 | + | 0.999778i | \(0.493298\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 927309. | 0.438253 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.93455e6 | −2.29806 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.20721e6 | 1.01300 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.09722e6 | 2.75794 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.32234e6 | 1.48123 | 0.740613 | − | 0.671932i | \(-0.234535\pi\) | ||||
0.740613 | + | 0.671932i | \(0.234535\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.75607e6 | −0.771754 | −0.385877 | − | 0.922550i | \(-0.626101\pi\) | ||||
−0.385877 | + | 0.922550i | \(0.626101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 832877. | 0.360839 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.36787e6 | −0.584263 | −0.292132 | − | 0.956378i | \(-0.594365\pi\) | ||||
−0.292132 | + | 0.956378i | \(0.594365\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.38275e6 | −1.84576 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −622261. | −0.258406 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.66092e6 | −1.08967 | −0.544836 | − | 0.838543i | \(-0.683408\pi\) | ||||
−0.544836 | + | 0.838543i | \(0.683408\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.46054e6 | 0.993717 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.26933e6 | −2.09888 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.90731e6 | −1.53513 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.90557e6 | 1.12607 | 0.563036 | − | 0.826432i | \(-0.309633\pi\) | ||||
0.563036 | + | 0.826432i | \(0.309633\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.20017e6 | −1.22351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.21001e6 | 0.456409 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.73675e6 | 1.01850 | 0.509252 | − | 0.860618i | \(-0.329922\pi\) | ||||
0.509252 | + | 0.860618i | \(0.329922\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.60227e6 | 1.32281 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.01864e6 | 0.369120 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.40613e6 | −1.57565 | −0.787825 | − | 0.615899i | \(-0.788793\pi\) | ||||
−0.787825 | + | 0.615899i | \(0.788793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.34082e6 | −0.473214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.35009e6 | −1.51531 | −0.757654 | − | 0.652656i | \(-0.773655\pi\) | ||||
−0.757654 | + | 0.652656i | \(0.773655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.15828e6 | 1.08592 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.28300e6 | 1.79309 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.93124e6 | −0.647086 | −0.323543 | − | 0.946213i | \(-0.604874\pi\) | ||||
−0.323543 | + | 0.946213i | \(0.604874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.13417e6 | 0.375177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −778232. | −0.254172 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.57671e6 | −1.47591 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.57031e6 | −0.818481 | −0.409240 | − | 0.912427i | \(-0.634206\pi\) | ||||
−0.409240 | + | 0.912427i | \(0.634206\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.63021e6 | −1.45602 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.13571e6 | −1.59492 | −0.797461 | − | 0.603370i | \(-0.793824\pi\) | ||||
−0.797461 | + | 0.603370i | \(0.793824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.69686e6 | −0.520456 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 246207. | 0.0745868 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.83039e6 | 0.547719 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −106740. | −0.0315514 | −0.0157757 | − | 0.999876i | \(-0.505022\pi\) | ||||
−0.0157757 | + | 0.999876i | \(0.505022\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.85662e6 | 1.71018 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.42162e6 | 0.987089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.94642e6 | −1.69487 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.18670e6 | 0.334196 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.05926e6 | −1.12957 | −0.564783 | − | 0.825239i | \(-0.691040\pi\) | ||||
−0.564783 | + | 0.825239i | \(0.691040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.66663e6 | −0.733259 | −0.366630 | − | 0.930367i | \(-0.619488\pi\) | ||||
−0.366630 | + | 0.930367i | \(0.619488\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 907518. | 0.246606 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −263047. | −0.0706417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.84281e6 | −1.01995 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.21658e6 | −0.843823 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −315413. | −0.0817873 | −0.0408937 | − | 0.999164i | \(-0.513020\pi\) | ||||
−0.0408937 | + | 0.999164i | \(0.513020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −775798. | −0.198852 | −0.0994258 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994258 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.82998e6 | 1.98398 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.43929e6 | 2.11399 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.94359e6 | −1.47193 | −0.735966 | − | 0.677019i | \(-0.763272\pi\) | ||||
−0.735966 | + | 0.677019i | \(0.763272\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.02477e6 | −0.985473 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.86038e6 | −1.17669 | −0.588344 | − | 0.808611i | \(-0.700220\pi\) | ||||
−0.588344 | + | 0.808611i | \(0.700220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.45226e6 | 1.54458 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.05175e7 | −2.48969 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.82060e6 | −0.660276 | −0.330138 | − | 0.943933i | \(-0.607095\pi\) | ||||
−0.330138 | + | 0.943933i | \(0.607095\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.85563e6 | 1.12410 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.27922e6 | −1.66663 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.08605e6 | 0.245935 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.15540e6 | 0.706747 | 0.353374 | − | 0.935482i | \(-0.385034\pi\) | ||||
0.353374 | + | 0.935482i | \(0.385034\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.19088e6 | 0.263836 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.38267e6 | −0.960476 | −0.480238 | − | 0.877138i | \(-0.659450\pi\) | ||||
−0.480238 | + | 0.877138i | \(0.659450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.27328e6 | 0.276040 | 0.138020 | − | 0.990429i | \(-0.455926\pi\) | ||||
0.138020 | + | 0.990429i | \(0.455926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.30433e7 | −2.79740 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.74440e6 | 1.64322 | 0.821610 | − | 0.570050i | \(-0.193076\pi\) | ||||
0.821610 | + | 0.570050i | \(0.193076\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.08108e6 | −0.436874 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.07252e6 | 0.222769 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.01590e6 | −1.64740 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.95732e6 | −0.398041 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.89419e6 | −1.18612 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −469201. | −0.0934372 | −0.0467186 | − | 0.998908i | \(-0.514876\pi\) | ||||
−0.0467186 | + | 0.998908i | \(0.514876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 629424. | 0.124045 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.91544e6 | −1.54386 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.15789e7 | 2.23519 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.56737e6 | −0.681595 | −0.340797 | − | 0.940137i | \(-0.610697\pi\) | ||||
−0.340797 | + | 0.940137i | \(0.610697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.78266e6 | 1.66094 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.44437e6 | −0.270381 | −0.135190 | − | 0.990820i | \(-0.543165\pi\) | ||||
−0.135190 | + | 0.990820i | \(0.543165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.45649e6 | 0.269891 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.53846e7 | −2.82210 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.68970e6 | 1.03323 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.67300e6 | 0.300776 | 0.150388 | − | 0.988627i | \(-0.451948\pi\) | ||||
0.150388 | + | 0.988627i | \(0.451948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.51701e7 | 2.70019 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.59839e6 | 1.16283 | 0.581417 | − | 0.813606i | \(-0.302498\pi\) | ||||
0.581417 | + | 0.813606i | \(0.302498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.10056e6 | −1.23898 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.31077e6 | 1.43589 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.45608e6 | −1.10452 | −0.552261 | − | 0.833671i | \(-0.686235\pi\) | ||||
−0.552261 | + | 0.833671i | \(0.686235\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.07248e6 | 0.859347 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.86124e6 | 1.48662 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.02838e7 | −1.70859 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.37698e6 | −0.226569 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.25077e6 | −1.50751 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.93220e6 | 1.28026 | 0.640132 | − | 0.768265i | \(-0.278880\pi\) | ||||
0.640132 | + | 0.768265i | \(0.278880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.63673e6 | 0.741238 | 0.370619 | − | 0.928785i | \(-0.379146\pi\) | ||||
0.370619 | + | 0.928785i | \(0.379146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.83582e6 | 0.290692 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.42623e6 | −0.380545 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.99079e6 | 1.24151 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.66674e7 | −2.56526 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.66972e6 | 0.254581 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.95089e6 | −1.20097 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.39643e6 | 0.807553 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.10679e6 | 0.905402 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.97650e6 | −1.31860 | −0.659301 | − | 0.751879i | \(-0.729148\pi\) | ||||
−0.659301 | + | 0.751879i | \(0.729148\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.57703e6 | −0.229531 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.06144e7 | 1.53074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.21337e6 | 0.459191 | 0.229595 | − | 0.973286i | \(-0.426260\pi\) | ||||
0.229595 | + | 0.973286i | \(0.426260\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.87191e7 | 2.65066 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.08376e7 | 1.52074 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.94150e6 | 0.826197 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.83819e6 | 0.666731 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.38454e7 | 1.89089 | 0.945445 | − | 0.325782i | \(-0.105627\pi\) | ||||
0.945445 | + | 0.325782i | \(0.105627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.75646e6 | −0.373097 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.59918e6 | −0.616983 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.89486e6 | −0.650832 | −0.325416 | − | 0.945571i | \(-0.605504\pi\) | ||||
−0.325416 | + | 0.945571i | \(0.605504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.31413e6 | −0.304976 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −319626. | −0.0417527 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.22650e6 | 0.417783 | 0.208891 | − | 0.977939i | \(-0.433014\pi\) | ||||
0.208891 | + | 0.977939i | \(0.433014\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.95775e6 | −1.14976 | −0.574882 | − | 0.818236i | \(-0.694952\pi\) | ||||
−0.574882 | + | 0.818236i | \(0.694952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.79942e7 | 2.28953 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.34608e6 | −0.422052 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.72902e6 | −0.591333 | −0.295666 | − | 0.955291i | \(-0.595542\pi\) | ||||
−0.295666 | + | 0.955291i | \(0.595542\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.07976e6 | 0.629719 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.71966e6 | 0.948764 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.94327e6 | 1.08975 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.29036e6 | −0.639139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.36901e7 | 1.63987 | 0.819936 | − | 0.572456i | \(-0.194009\pi\) | ||||
0.819936 | + | 0.572456i | \(0.194009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.80535e7 | −2.14423 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.23020e7 | 1.44880 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.19933e7 | 1.40056 | 0.700281 | − | 0.713868i | \(-0.253058\pi\) | ||||
0.700281 | + | 0.713868i | \(0.253058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.55287e6 | 0.179822 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.41065e6 | −0.736150 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.68612e6 | 0.647514 | 0.323757 | − | 0.946140i | \(-0.395054\pi\) | ||||
0.323757 | + | 0.946140i | \(0.395054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.42690e7 | −1.61142 | −0.805710 | − | 0.592310i | \(-0.798216\pi\) | ||||
−0.805710 | + | 0.592310i | \(0.798216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.01373e7 | 1.13535 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.31498e7 | 1.46059 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.52702e6 | 0.168219 | 0.0841093 | − | 0.996457i | \(-0.473196\pi\) | ||||
0.0841093 | + | 0.996457i | \(0.473196\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.01649e7 | −1.11061 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −473507. | −0.0513125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.39418e6 | −0.149854 | −0.0749268 | − | 0.997189i | \(-0.523872\pi\) | ||||
−0.0749268 | + | 0.997189i | \(0.523872\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.28347e7 | 1.36835 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −501546. | −0.0530393 | −0.0265196 | − | 0.999648i | \(-0.508442\pi\) | ||||
−0.0265196 | + | 0.999648i | \(0.508442\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.85188e6 | −0.823658 | −0.411829 | − | 0.911261i | \(-0.635110\pi\) | ||||
−0.411829 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.51485e7 | 1.57630 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.37635e6 | −0.864639 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.17425e7 | −1.20243 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.42222e7 | −3.47648 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 899972. | 0.0906989 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.61935e7 | 1.61908 | 0.809539 | − | 0.587067i | \(-0.199717\pi\) | ||||
0.809539 | + | 0.587067i | \(0.199717\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.33182e7 | −2.31306 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.34605e6 | 0.329305 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.09997e6 | 0.205052 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.77156e7 | −2.68518 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.33189e7 | 1.28034 | 0.640169 | − | 0.768234i | \(-0.278864\pi\) | ||||
0.640169 | + | 0.768234i | \(0.278864\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.01202e6 | −0.859597 | −0.429799 | − | 0.902925i | \(-0.641415\pi\) | ||||
−0.429799 | + | 0.902925i | \(0.641415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.11881e7 | −2.00536 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.25046e6 | −0.211355 | −0.105677 | − | 0.994400i | \(-0.533701\pi\) | ||||
−0.105677 | + | 0.994400i | \(0.533701\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.52895e7 | 2.35683 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.69328e7 | 1.56595 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.14532e7 | −1.05110 | −0.525552 | − | 0.850761i | \(-0.676141\pi\) | ||||
−0.525552 | + | 0.850761i | \(0.676141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.94210e6 | 0.176876 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.47091e7 | −2.23328 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −951649. | −0.0853617 | −0.0426808 | − | 0.999089i | \(-0.513590\pi\) | ||||
−0.0426808 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.35290e7 | 1.20438 | 0.602189 | − | 0.798354i | \(-0.294296\pi\) | ||||
0.602189 | + | 0.798354i | \(0.294296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.58154e6 | −0.139732 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.15548e7 | 1.01323 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.85271e7 | 1.61248 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.07971e7 | −0.932696 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.84025e7 | −2.43529 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.94873e6 | 0.761594 | 0.380797 | − | 0.924659i | \(-0.375650\pi\) | ||||
0.380797 | + | 0.924659i | \(0.375650\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.51338e6 | −0.296801 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −176169. | −0.0147726 | −0.00738632 | − | 0.999973i | \(-0.502351\pi\) | ||||
−0.00738632 | + | 0.999973i | \(0.502351\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.50318e7 | −1.25123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.10471e7 | −0.912811 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.37532e6 | 0.440912 | 0.220456 | − | 0.975397i | \(-0.429245\pi\) | ||||
0.220456 | + | 0.975397i | \(0.429245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.46154e7 | −1.19010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 606131. | 0.0489976 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.07536e6 | 0.246801 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.06270e7 | 0.846669 | 0.423335 | − | 0.905973i | \(-0.360859\pi\) | ||||
0.423335 | + | 0.905973i | \(0.360859\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.99723e7 | 1.57978 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.96145e6 | −0.232564 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.38743e6 | 0.186144 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.55993e7 | −1.20757 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.35541e7 | 1.04178 | 0.520888 | − | 0.853625i | \(-0.325601\pi\) | ||||
0.520888 | + | 0.853625i | \(0.325601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.69664e6 | 0.511056 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.63971e6 | −0.275799 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.21798e6 | 0.693565 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.34298e7 | −1.75046 | −0.875232 | − | 0.483704i | \(-0.839291\pi\) | ||||
−0.875232 | + | 0.483704i | \(0.839291\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.89422e7 | −2.14713 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.08628e7 | −2.27358 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.02707e6 | 0.587208 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.14369e7 | 3.01016 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.56342e7 | 1.84926 | 0.924628 | − | 0.380872i | \(-0.124376\pi\) | ||||
0.924628 | + | 0.380872i | \(0.124376\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.33505e7 | 0.956445 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 544470. | 0.0387372 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.29699e6 | −0.303612 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.64123e6 | 0.255513 | 0.127756 | − | 0.991806i | \(-0.459222\pi\) | ||||
0.127756 | + | 0.991806i | \(0.459222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.30226e7 | −1.60449 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.94128e6 | −0.272800 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.64472e7 | −1.13066 | −0.565331 | − | 0.824864i | \(-0.691252\pi\) | ||||
−0.565331 | + | 0.824864i | \(0.691252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.61418e7 | 1.10213 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.53814e7 | −1.04310 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.00621e6 | −0.471924 | −0.235962 | − | 0.971762i | \(-0.575824\pi\) | ||||
−0.235962 | + | 0.971762i | \(0.575824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.17681e7 | −0.787339 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.23231e7 | −0.818930 | −0.409465 | − | 0.912326i | \(-0.634285\pi\) | ||||
−0.409465 | + | 0.912326i | \(0.634285\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.62468e7 | 1.73255 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.76040e7 | −2.46566 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.03219e7 | 0.672286 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.73690e6 | −0.629972 | −0.314986 | − | 0.949096i | \(-0.602000\pi\) | ||||
−0.314986 | + | 0.949096i | \(0.602000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.46716e7 | −2.87107 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.81655e7 | 1.15979 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.09834e7 | −1.33087 | −0.665437 | − | 0.746454i | \(-0.731755\pi\) | ||||
−0.665437 | + | 0.746454i | \(0.731755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.85036e7 | −3.68619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.02169e6 | −0.0639527 | −0.0319763 | − | 0.999489i | \(-0.510180\pi\) | ||||
−0.0319763 | + | 0.999489i | \(0.510180\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.37796e7 | −0.856890 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.56433e6 | −0.467323 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.69638e6 | 0.533765 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.44093e6 | 0.148847 | 0.0744235 | − | 0.997227i | \(-0.476288\pi\) | ||||
0.0744235 | + | 0.997227i | \(0.476288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.67516e6 | 0.101489 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.46489e7 | 1.48371 | 0.741855 | − | 0.670560i | \(-0.233946\pi\) | ||||
0.741855 | + | 0.670560i | \(0.233946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.15798e6 | 0.428091 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.28096e6 | −0.373227 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.77647e7 | 1.04885 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.20530e7 | 2.46700 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.94535e7 | 1.13395 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.67652e6 | −0.155023 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.02955e7 | 0.592531 | 0.296266 | − | 0.955106i | \(-0.404259\pi\) | ||||
0.296266 | + | 0.955106i | \(0.404259\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.66436e7 | −0.951822 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.00421e6 | 0.170722 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.76688e6 | −0.551535 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.36393e7 | 1.32653 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.22117e6 | 0.514210 | 0.257105 | − | 0.966384i | \(-0.417231\pi\) | ||||
0.257105 | + | 0.966384i | \(0.417231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −677036. | −0.0375185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.08028e7 | 2.24703 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.74911e7 | 2.05182 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.97532e7 | 1.07435 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.14110e7 | −2.77890 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.40070e7 | −1.28963 | −0.644816 | − | 0.764337i | \(-0.723066\pi\) | ||||
−0.644816 | + | 0.764337i | \(0.723066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.91778e7 | −1.02388 | −0.511938 | − | 0.859022i | \(-0.671072\pi\) | ||||
−0.511938 | + | 0.859022i | \(0.671072\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.88457e7 | −1.53058 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.19174e7 | −1.15583 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.93268e7 | −1.53713 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.86796e6 | 0.357782 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.75497e7 | 0.908680 | 0.454340 | − | 0.890828i | \(-0.349875\pi\) | ||||
0.454340 | + | 0.890828i | \(0.349875\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.42818e7 | 1.24963 | 0.624814 | − | 0.780774i | \(-0.285175\pi\) | ||||
0.624814 | + | 0.780774i | \(0.285175\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.35687e7 | 0.694071 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.95813e6 | 0.506307 | 0.253154 | − | 0.967426i | \(-0.418532\pi\) | ||||
0.253154 | + | 0.967426i | \(0.418532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.49600e7 | −1.76679 | −0.883395 | − | 0.468629i | \(-0.844748\pi\) | ||||
−0.883395 | + | 0.468629i | \(0.844748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.12643e7 | 1.57053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.00260e6 | 0.149929 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.78575e7 | −1.87904 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.24059e7 | −1.59886 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.85270e7 | 1.39911 | 0.699553 | − | 0.714581i | \(-0.253383\pi\) | ||||
0.699553 | + | 0.714581i | \(0.253383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.28119e6 | 0.159971 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.90524e6 | 0.237734 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.07398e7 | −0.999222 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.70711e7 | −0.817621 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.41422e7 | −1.14950 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.14480e7 | 0.541885 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.01259e7 | 0.947071 | 0.473535 | − | 0.880775i | \(-0.342978\pi\) | ||||
0.473535 | + | 0.880775i | \(0.342978\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.62858e7 | −2.63320 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.79660e7 | −1.76580 | −0.882902 | − | 0.469556i | \(-0.844414\pi\) | ||||
−0.882902 | + | 0.469556i | \(0.844414\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.92107e7 | 0.888299 | 0.444150 | − | 0.895953i | \(-0.353506\pi\) | ||||
0.444150 | + | 0.895953i | \(0.353506\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.66620e7 | −0.765984 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.26470e6 | 0.286334 | 0.143167 | − | 0.989699i | \(-0.454271\pi\) | ||||
0.143167 | + | 0.989699i | \(0.454271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.30856e7 | 1.04906 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.37496e7 | 1.52483 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.39141e7 | 1.97267 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.28926e6 | −0.236238 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.32228e7 | 3.25170 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.16703e7 | 0.515302 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.91154e7 | 0.839238 | 0.419619 | − | 0.907700i | \(-0.362164\pi\) | ||||
0.419619 | + | 0.907700i | \(0.362164\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.77319e6 | 0.164716 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.41850e7 | 1.48387 | 0.741935 | − | 0.670472i | \(-0.233908\pi\) | ||||
0.741935 | + | 0.670472i | \(0.233908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.42154e7 | 0.613560 | 0.306780 | − | 0.951780i | \(-0.400748\pi\) | ||||
0.306780 | + | 0.951780i | \(0.400748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.68464e7 | 2.86893 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.80799e7 | 0.771590 | 0.385795 | − | 0.922584i | \(-0.373927\pi\) | ||||
0.385795 | + | 0.922584i | \(0.373927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.34385e6 | −0.184340 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.36238e6 | −0.0996910 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.03779e6 | −0.211403 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.34669e7 | −0.561968 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.01179e7 | −0.834835 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.96336e7 | −1.63555 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.39725e6 | 0.180455 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.75064e7 | 1.12257 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.93553e6 | 0.159728 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.38869e7 | 0.964142 | 0.482071 | − | 0.876132i | \(-0.339885\pi\) | ||||
0.482071 | + | 0.876132i | \(0.339885\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.49026e7 | −1.80244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.99135e7 | −1.19419 | −0.597093 | − | 0.802172i | \(-0.703678\pi\) | ||||
−0.597093 | + | 0.802172i | \(0.703678\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.70566e7 | 2.26532 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.50750e7 | −2.96444 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.52124e6 | −0.0990127 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.75882e7 | 0.686961 | 0.343481 | − | 0.939160i | \(-0.388394\pi\) | ||||
0.343481 | + | 0.939160i | \(0.388394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.45615e7 | −1.34259 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.44609e7 | 0.558717 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.65514e6 | −0.102031 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.50330e7 | −2.48562 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.61148e7 | −1.37292 | −0.686461 | − | 0.727166i | \(-0.740837\pi\) | ||||
−0.686461 | + | 0.727166i | \(0.740837\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.23422e7 | 0.844796 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.21797e7 | −3.09072 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.14774e7 | 0.429352 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.82298e7 | −1.79460 | −0.897298 | − | 0.441426i | \(-0.854473\pi\) | ||||
−0.897298 | + | 0.441426i | \(0.854473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.07697e7 | −2.61929 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.05808e7 | −0.389533 | −0.194766 | − | 0.980850i | \(-0.562395\pi\) | ||||
−0.194766 | + | 0.980850i | \(0.562395\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.03691e7 | 1.11212 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.07408e7 | 0.755521 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.00847e7 | −1.81481 | −0.907403 | − | 0.420262i | \(-0.861938\pi\) | ||||
−0.907403 | + | 0.420262i | \(0.861938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.28922e7 | 0.464689 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.33413e7 | −2.62965 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.28166e6 | 0.152714 | 0.0763571 | − | 0.997081i | \(-0.475671\pi\) | ||||
0.0763571 | + | 0.997081i | \(0.475671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.49051e7 | −1.59326 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.51296e7 | −2.65174 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.89737e7 | 0.666203 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.73930e7 | 1.30612 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.02799e7 | −1.74714 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.26767e7 | −0.438215 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.82231e6 | 0.234620 | 0.117310 | − | 0.993095i | \(-0.462573\pi\) | ||||
0.117310 | + | 0.993095i | \(0.462573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.68265e7 | −0.575683 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.32428e7 | −1.47186 | −0.735929 | − | 0.677059i | \(-0.763254\pi\) | ||||
−0.735929 | + | 0.677059i | \(0.763254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.84457e6 | 0.130186 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.66592e6 | 0.157190 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.63654e7 | −1.21885 | −0.609427 | − | 0.792842i | \(-0.708600\pi\) | ||||
−0.609427 | + | 0.792842i | \(0.708600\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.19103e7 | −2.06446 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.71231e7 | 2.22689 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.36478e7 | −0.780561 | −0.390280 | − | 0.920696i | \(-0.627622\pi\) | ||||
−0.390280 | + | 0.920696i | \(0.627622\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.07000e7 | −1.00820 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.72508e6 | 0.154389 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.01348e7 | −1.62985 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.34096e7 | 1.40411 | 0.702056 | − | 0.712122i | \(-0.252266\pi\) | ||||
0.702056 | + | 0.712122i | \(0.252266\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.10675e7 | −1.32168 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.59980e7 | 0.512280 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.15601e7 | 0.686931 | 0.343465 | − | 0.939165i | \(-0.388399\pi\) | ||||
0.343465 | + | 0.939165i | \(0.388399\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.20204e7 | 0.381071 |
(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 | 1028.6.a.b.1.5 | ✓ | 57 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1028.6.a.b.1.5 | ✓ | 57 | 1.1 | even | 1 | trivial |