Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −14.0000 | −0.898100 | −0.449050 | − | 0.893507i | \(-0.648238\pi\) | ||||
−0.449050 | + | 0.893507i | \(0.648238\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 64.0000 | 1.14487 | 0.572433 | − | 0.819951i | \(-0.306000\pi\) | ||||
0.572433 | + | 0.819951i | \(0.306000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −47.0000 | −0.193416 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 420.000 | 1.04657 | 0.523284 | − | 0.852158i | \(-0.324707\pi\) | ||||
0.523284 | + | 0.852158i | \(0.324707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −860.000 | −1.41137 | −0.705684 | − | 0.708527i | \(-0.749360\pi\) | ||||
−0.705684 | + | 0.708527i | \(0.749360\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −896.000 | −1.02821 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 830.000 | 0.696556 | 0.348278 | − | 0.937391i | \(-0.386767\pi\) | ||||
0.348278 | + | 0.937391i | \(0.386767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −490.000 | −0.311395 | −0.155698 | − | 0.987805i | \(-0.549763\pi\) | ||||
−0.155698 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 686.000 | 0.339450 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4872.00 | 1.92038 | 0.960191 | − | 0.279344i | \(-0.0901169\pi\) | ||||
0.960191 | + | 0.279344i | \(0.0901169\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 971.000 | 0.310720 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4060.00 | 1.07181 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8754.00 | −1.93291 | −0.966455 | − | 0.256837i | \(-0.917320\pi\) | ||||
−0.966455 | + | 0.256837i | \(0.917320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5628.00 | 1.05184 | 0.525920 | − | 0.850534i | \(-0.323721\pi\) | ||||
0.525920 | + | 0.850534i | \(0.323721\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5880.00 | −0.939923 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3136.00 | −0.432719 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1434.00 | −0.172205 | −0.0861023 | − | 0.996286i | \(-0.527441\pi\) | ||||
−0.0861023 | + | 0.996286i | \(0.527441\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12040.0 | 1.26755 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9258.00 | −0.860117 | −0.430059 | − | 0.902801i | \(-0.641507\pi\) | ||||
−0.430059 | + | 0.902801i | \(0.641507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14756.0 | −1.21702 | −0.608510 | − | 0.793546i | \(-0.708232\pi\) | ||||
−0.608510 | + | 0.793546i | \(0.708232\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3008.00 | −0.221435 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10108.0 | −0.667453 | −0.333726 | − | 0.942670i | \(-0.608306\pi\) | ||||
−0.333726 | + | 0.942670i | \(0.608306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11620.0 | −0.625577 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23058.0 | 1.12754 | 0.563770 | − | 0.825932i | \(-0.309350\pi\) | ||||
0.563770 | + | 0.825932i | \(0.309350\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26880.0 | 1.19818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6860.00 | 0.279664 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13734.0 | 0.513650 | 0.256825 | − | 0.966458i | \(-0.417324\pi\) | ||||
0.256825 | + | 0.966458i | \(0.417324\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25352.0 | 0.872344 | 0.436172 | − | 0.899863i | \(-0.356334\pi\) | ||||
0.436172 | + | 0.899863i | \(0.356334\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2303.00 | 0.0731042 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −55040.0 | −1.61583 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −19768.0 | −0.537992 | −0.268996 | − | 0.963141i | \(-0.586692\pi\) | ||||
−0.268996 | + | 0.963141i | \(0.586692\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −68208.0 | −1.72470 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1792.00 | 0.0421883 | 0.0210942 | − | 0.999777i | \(-0.493285\pi\) | ||||
0.0210942 | + | 0.999777i | \(0.493285\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37914.0 | 0.832707 | 0.416354 | − | 0.909203i | \(-0.363308\pi\) | ||||
0.416354 | + | 0.909203i | \(0.363308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13594.0 | −0.279058 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −20580.0 | −0.395566 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 95984.0 | 1.73034 | 0.865169 | − | 0.501480i | \(-0.167211\pi\) | ||||
0.865169 | + | 0.501480i | \(0.167211\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −45419.0 | −0.769175 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −88242.0 | −1.40598 | −0.702992 | − | 0.711198i | \(-0.748153\pi\) | ||||
−0.702992 | + | 0.711198i | \(0.748153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 53120.0 | 0.797463 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 122556. | 1.73595 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 43762.0 | 0.585628 | 0.292814 | − | 0.956169i | \(-0.405408\pi\) | ||||
0.292814 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 42140.0 | 0.533447 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −78792.0 | −0.944658 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −31360.0 | −0.356506 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 65790.0 | 0.709955 | 0.354977 | − | 0.934875i | \(-0.384489\pi\) | ||||
0.354977 | + | 0.934875i | \(0.384489\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19740.0 | −0.202423 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17728.0 | 0.172924 | 0.0864622 | − | 0.996255i | \(-0.472444\pi\) | ||||
0.0864622 | + | 0.996255i | \(0.472444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 121660. | 1.12994 | 0.564969 | − | 0.825112i | \(-0.308888\pi\) | ||||
0.564969 | + | 0.825112i | \(0.308888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 43904.0 | 0.388625 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 48272.0 | 0.407602 | 0.203801 | − | 0.979012i | \(-0.434671\pi\) | ||||
0.203801 | + | 0.979012i | \(0.434671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 177606. | 1.43183 | 0.715915 | − | 0.698188i | \(-0.246010\pi\) | ||||
0.715915 | + | 0.698188i | \(0.246010\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20076.0 | 0.154657 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 128198. | 0.944463 | 0.472232 | − | 0.881474i | \(-0.343449\pi\) | ||||
0.472232 | + | 0.881474i | \(0.343449\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 311808. | 2.19858 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 40420.0 | 0.272981 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −40670.0 | −0.263273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15349.0 | 0.0953052 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 129612. | 0.772471 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −137856. | −0.789134 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 302960. | 1.66677 | 0.833386 | − | 0.552692i | \(-0.186399\pi\) | ||||
0.833386 | + | 0.552692i | \(0.186399\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 206584. | 1.09301 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 295638. | 1.50516 | 0.752579 | − | 0.658502i | \(-0.228810\pi\) | ||||
0.752579 | + | 0.658502i | \(0.228810\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24010.0 | 0.117696 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 259840. | 1.22708 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −78318.0 | −0.356501 | −0.178250 | − | 0.983985i | \(-0.557044\pi\) | ||||
−0.178250 | + | 0.983985i | \(0.557044\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 234010. | 1.02730 | 0.513650 | − | 0.858000i | \(-0.328293\pi\) | ||||
0.513650 | + | 0.858000i | \(0.328293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 141512. | 0.599440 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −361200. | −1.47709 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −560256. | −2.21292 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −33614.0 | −0.128300 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 397642. | 1.46733 | 0.733663 | − | 0.679514i | \(-0.237809\pi\) | ||||
0.733663 | + | 0.679514i | \(0.237809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −236432. | −0.843847 | −0.421924 | − | 0.906631i | \(-0.638645\pi\) | ||||
−0.421924 | + | 0.906631i | \(0.638645\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −39010.0 | −0.134725 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 360192. | 1.20422 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31852.0 | −0.103131 | −0.0515653 | − | 0.998670i | \(-0.516421\pi\) | ||||
−0.0515653 | + | 0.998670i | \(0.516421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −322812. | −1.01264 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −238728. | −0.725836 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −403172. | −1.18856 | −0.594280 | − | 0.804258i | \(-0.702563\pi\) | ||||
−0.594280 | + | 0.804258i | \(0.702563\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −376320. | −1.07609 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 569044. | 1.57890 | 0.789450 | − | 0.613815i | \(-0.210366\pi\) | ||||
0.789450 | + | 0.613815i | \(0.210366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 368307. | 0.991958 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23030.0 | 0.0602287 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −500116. | −1.27044 | −0.635222 | − | 0.772330i | \(-0.719091\pi\) | ||||
−0.635222 | + | 0.772330i | \(0.719091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −47579.0 | −0.117441 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −192276. | −0.461309 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 112896. | 0.263358 | 0.131679 | − | 0.991292i | \(-0.457963\pi\) | ||||
0.131679 | + | 0.991292i | \(0.457963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20780.0 | 0.0471465 | 0.0235732 | − | 0.999722i | \(-0.492496\pi\) | ||||
0.0235732 | + | 0.999722i | \(0.492496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −354928. | −0.783452 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −91776.0 | −0.197151 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 348600. | 0.728993 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −198940. | −0.405105 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −215040. | −0.426516 | −0.213258 | − | 0.976996i | \(-0.568408\pi\) | ||||
−0.213258 | + | 0.976996i | \(0.568408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 408590. | 0.789577 | 0.394788 | − | 0.918772i | \(-0.370818\pi\) | ||||
0.394788 | + | 0.918772i | \(0.370818\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 770560. | 1.45118 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 721674. | 1.32488 | 0.662438 | − | 0.749116i | \(-0.269522\pi\) | ||||
0.662438 | + | 0.749116i | \(0.269522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 378308. | 0.677194 | 0.338597 | − | 0.940932i | \(-0.390048\pi\) | ||||
0.338597 | + | 0.940932i | \(0.390048\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 276752. | 0.483171 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 428946. | 0.730571 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −592512. | −0.984719 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −228984. | −0.371432 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −205800. | −0.325896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 265272. | 0.410190 | 0.205095 | − | 0.978742i | \(-0.434250\pi\) | ||||
0.205095 | + | 0.978742i | \(0.434250\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25088.0 | −0.0378893 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −944384. | −1.39333 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −275772. | −0.397558 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −530796. | −0.747855 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −713800. | −0.983096 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 419608. | 0.565043 | 0.282522 | − | 0.959261i | \(-0.408829\pi\) | ||||
0.282522 | + | 0.959261i | \(0.408829\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −45637.0 | −0.0600981 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 776678. | 1.00041 | 0.500203 | − | 0.865908i | \(-0.333259\pi\) | ||||
0.500203 | + | 0.865908i | \(0.333259\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 71924.0 | 0.0906327 | 0.0453164 | − | 0.998973i | \(-0.485570\pi\) | ||||
0.0453164 | + | 0.998973i | \(0.485570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 288120. | 0.355258 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −356966. | −0.430762 | −0.215381 | − | 0.976530i | \(-0.569099\pi\) | ||||
−0.215381 | + | 0.976530i | \(0.569099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −646912. | −0.764145 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.34378e6 | −1.55402 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.06383e6 | 1.20470 | 0.602349 | − | 0.798233i | \(-0.294232\pi\) | ||||
0.602349 | + | 0.798233i | \(0.294232\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −834866. | −0.925921 | −0.462961 | − | 0.886379i | \(-0.653213\pi\) | ||||
−0.462961 | + | 0.886379i | \(0.653213\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −350714. | −0.381011 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 153664. | 0.163552 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 421400. | 0.439493 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.23539e6 | 1.26271 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.59069e6 | −1.59368 | −0.796842 | − | 0.604187i | \(-0.793498\pi\) | ||||
−0.796842 | + | 0.604187i | \(0.793498\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.04624e6 | 2.00981 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −743680. | −0.716202 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 74754.0 | 0.0705995 | 0.0352998 | − | 0.999377i | \(-0.488761\pi\) | ||||
0.0352998 | + | 0.999377i | \(0.488761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 70266.0 | 0.0650872 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 411438. | 0.373855 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9744.00 | −0.00868656 | −0.00434328 | − | 0.999991i | \(-0.501383\pi\) | ||||
−0.00434328 | + | 0.999991i | \(0.501383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.47571e6 | 1.29088 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −612668. | −0.525953 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.24555e6 | 1.04949 | 0.524747 | − | 0.851258i | \(-0.324160\pi\) | ||||
0.524747 | + | 0.851258i | \(0.324160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.62635e6 | 1.34521 | 0.672607 | − | 0.740000i | \(-0.265175\pi\) | ||||
0.672607 | + | 0.740000i | \(0.265175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −589960. | −0.479089 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 407820. | 0.325190 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −99070.0 | −0.0775787 | −0.0387894 | − | 0.999247i | \(-0.512350\pi\) | ||||
−0.0387894 | + | 0.999247i | \(0.512350\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −264516. | −0.203442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.79165e6 | −1.35359 | −0.676797 | − | 0.736170i | \(-0.736632\pi\) | ||||
−0.676797 | + | 0.736170i | \(0.736632\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.07132e6 | −0.795159 | −0.397579 | − | 0.917568i | \(-0.630150\pi\) | ||||
−0.397579 | + | 0.917568i | \(0.630150\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 439040. | 0.320178 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 453642. | 0.325094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −730957. | −0.514810 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −921060. | −0.637610 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 396024. | 0.269496 | 0.134748 | − | 0.990880i | \(-0.456977\pi\) | ||||
0.134748 | + | 0.990880i | \(0.456977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 878976. | 0.588060 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.70520e6 | 1.12172 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.18992e6 | −2.71036 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 723044. | 0.459990 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −248192. | −0.155303 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.62253e6 | 0.998717 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.26209e6 | 0.764263 | 0.382132 | − | 0.924108i | \(-0.375190\pi\) | ||||
0.382132 | + | 0.924108i | \(0.375190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.70324e6 | −1.01480 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.71018e6 | 1.00263 | 0.501316 | − | 0.865264i | \(-0.332849\pi\) | ||||
0.501316 | + | 0.865264i | \(0.332849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −640634. | −0.369615 | −0.184807 | − | 0.982775i | \(-0.559166\pi\) | ||||
−0.184807 | + | 0.982775i | \(0.559166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 147392. | 0.0836946 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 518738. | 0.289935 | 0.144967 | − | 0.989436i | \(-0.453692\pi\) | ||||
0.144967 | + | 0.989436i | \(0.453692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.67668e6 | −2.02292 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −675808. | −0.366067 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −406700. | −0.216904 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −835060. | −0.438540 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.48648e6 | −1.28593 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 495292. | 0.252273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −699412. | −0.350884 | −0.175442 | − | 0.984490i | \(-0.556135\pi\) | ||||
−0.175442 | + | 0.984490i | \(0.556135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 67398.0 | 0.0333071 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.26515e6 | −0.615929 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.51064e6 | 1.20423 | 0.602115 | − | 0.798409i | \(-0.294325\pi\) | ||||
0.602115 | + | 0.798409i | \(0.294325\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.79477e6 | −0.848223 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.36376e6 | 1.10082 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.36531e6 | −1.97455 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.16604e6 | −1.85737 | −0.928687 | − | 0.370865i | \(-0.879061\pi\) | ||||
−0.928687 | + | 0.370865i | \(0.879061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.12754e6 | −1.81396 | −0.906980 | − | 0.421174i | \(-0.861618\pi\) | ||||
−0.906980 | + | 0.421174i | \(0.861618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.49160e6 | −1.51271 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.54063e6 | 1.51232 | 0.756159 | − | 0.654388i | \(-0.227074\pi\) | ||||
0.756159 | + | 0.654388i | \(0.227074\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 114688. | 0.0483000 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 569380. | 0.236446 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.27029e6 | −1.33921 | −0.669607 | − | 0.742716i | \(-0.733537\pi\) | ||||
−0.669607 | + | 0.742716i | \(0.733537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.23600e6 | −0.903033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −214886. | −0.0855937 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.42650e6 | 0.953339 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.34337e6 | 1.29574 | 0.647872 | − | 0.761749i | \(-0.275659\pi\) | ||||
0.647872 | + | 0.761749i | \(0.275659\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 435126. | 0.166360 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.12984e6 | −0.426170 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 127946. | 0.0476162 | 0.0238081 | − | 0.999717i | \(-0.492421\pi\) | ||||
0.0238081 | + | 0.999717i | \(0.492421\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.92998e6 | 0.708721 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.52844e6 | 2.72805 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.40339e6 | −0.501857 | −0.250928 | − | 0.968006i | \(-0.580736\pi\) | ||||
−0.250928 | + | 0.968006i | \(0.580736\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.24144e6 | −1.49693 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.55134e6 | −0.540393 | −0.270197 | − | 0.962805i | \(-0.587089\pi\) | ||||
−0.270197 | + | 0.962805i | \(0.587089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.31712e6 | −0.452870 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 693532. | 0.235391 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.23841e6 | −1.75520 | −0.877598 | − | 0.479398i | \(-0.840855\pi\) | ||||
−0.877598 | + | 0.479398i | \(0.840855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.04376e6 | 1.33765 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.13893e6 | −1.35178 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.14298e6 | 1.98101 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.66579e6 | 1.80420 | 0.902099 | − | 0.431530i | \(-0.142026\pi\) | ||||
0.902099 | + | 0.431530i | \(0.142026\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −336140. | −0.105703 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.22010e6 | −0.689463 | −0.344732 | − | 0.938701i | \(-0.612030\pi\) | ||||
−0.344732 | + | 0.938701i | \(0.612030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.84008e6 | −1.48453 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.90682e6 | −0.880603 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −602280. | −0.180224 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.89847e6 | −1.15235 | −0.576176 | − | 0.817325i | \(-0.695456\pi\) | ||||
−0.576176 | + | 0.817325i | \(0.695456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.09645e6 | 0.320173 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −672966. | −0.194141 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.64749e6 | −1.60966 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.27614e6 | −0.922619 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.78551e6 | 1.60993 | 0.804965 | − | 0.593323i | \(-0.202184\pi\) | ||||
0.804965 | + | 0.593323i | \(0.202184\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 563554. | 0.154964 | 0.0774819 | − | 0.996994i | \(-0.475312\pi\) | ||||
0.0774819 | + | 0.996994i | \(0.475312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 475076. | 0.129096 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 805930. | 0.216434 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.24225e6 | −0.329715 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.05680e6 | 1.32658 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.61036e6 | −1.45478 | −0.727390 | − | 0.686224i | \(-0.759267\pi\) | ||||
−0.727390 | + | 0.686224i | \(0.759267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.27497e6 | 1.86471 | 0.932355 | − | 0.361545i | \(-0.117750\pi\) | ||||
0.932355 | + | 0.361545i | \(0.117750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.84358e6 | 1.98743 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.38728e6 | −0.597998 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.46326e6 | 1.10533 | 0.552663 | − | 0.833405i | \(-0.313612\pi\) | ||||
0.552663 | + | 0.833405i | \(0.313612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −112847. | −0.0276308 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.78006e6 | 0.915143 | 0.457571 | − | 0.889173i | \(-0.348719\pi\) | ||||
0.457571 | + | 0.889173i | \(0.348719\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.80077e6 | 0.670467 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.56699e6 | −1.31781 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.95465e6 | −1.62802 | −0.814010 | − | 0.580851i | \(-0.802720\pi\) | ||||
−0.814010 | + | 0.580851i | \(0.802720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.88836e6 | −0.900171 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.31005e6 | 0.757860 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.69696e6 | 0.610725 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.25765e6 | 0.505670 | 0.252835 | − | 0.967509i | \(-0.418637\pi\) | ||||
0.252835 | + | 0.967509i | \(0.418637\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.36980e6 | 0.746573 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.56697e6 | −0.781713 | −0.390857 | − | 0.920452i | \(-0.627821\pi\) | ||||
−0.390857 | + | 0.920452i | \(0.627821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.06417e6 | −0.230705 | −0.115353 | − | 0.993325i | \(-0.536800\pi\) | ||||
−0.115353 | + | 0.993325i | \(0.536800\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.04269e6 | −1.08151 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.83622e6 | 1.23834 | 0.619170 | − | 0.785257i | \(-0.287469\pi\) | ||||
0.619170 | + | 0.785257i | \(0.287469\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 968632. | 0.203342 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 445928. | 0.0926216 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.19752e6 | −1.27369 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −475790. | −0.0967568 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.08373e6 | −0.218084 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.71199e6 | −0.739210 | −0.369605 | − | 0.929189i | \(-0.620507\pi\) | ||||
−0.369605 | + | 0.929189i | \(0.620507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.23324e6 | 0.243044 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.34219e6 | 0.651874 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.21056e6 | 0.812803 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.64175e6 | 0.313679 | 0.156839 | − | 0.987624i | \(-0.449869\pi\) | ||||
0.156839 | + | 0.987624i | \(0.449869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.64441e6 | 1.06745 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.18164e6 | −0.595590 | −0.297795 | − | 0.954630i | \(-0.596251\pi\) | ||||
−0.297795 | + | 0.954630i | \(0.596251\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.26582e6 | −1.34638 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.26336e6 | −0.231747 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −87808.0 | −0.0159457 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 274120. | 0.0492821 | 0.0246411 | − | 0.999696i | \(-0.492156\pi\) | ||||
0.0246411 | + | 0.999696i | \(0.492156\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.96662e6 | −1.41801 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.34274e6 | −0.941551 | −0.470775 | − | 0.882253i | \(-0.656026\pi\) | ||||
−0.470775 | + | 0.882253i | \(0.656026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.13459e6 | 0.197975 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.15630e6 | −0.890878 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.82107e6 | 0.482635 | 0.241318 | − | 0.970446i | \(-0.422420\pi\) | ||||
0.241318 | + | 0.970446i | \(0.422420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.85779e6 | −0.314734 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.98940e6 | −0.333756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.78624e6 | 1.29363 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.24536e6 | −0.698535 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.00162e6 | 1.14099 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.67233e6 | 0.269915 | 0.134957 | − | 0.990851i | \(-0.456910\pi\) | ||||
0.134957 | + | 0.990851i | \(0.456910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.85991e6 | −1.57623 | −0.788113 | − | 0.615530i | \(-0.788942\pi\) | ||||
−0.788113 | + | 0.615530i | \(0.788942\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 666106. | 0.105474 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.67124e6 | 0.732665 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.73000e7 | 2.68787 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −645498. | −0.0993479 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.96188e6 | 1.21394 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.08941e6 | 0.466650 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.58054e6 | −0.236522 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00842e6 | 0.149510 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.36207e6 | 1.37524 | 0.687620 | − | 0.726071i | \(-0.258655\pi\) | ||||
0.687620 | + | 0.726071i | \(0.258655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −290920. | −0.0423423 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.13668e7 | 1.63925 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 539252. | 0.0770590 | 0.0385295 | − | 0.999257i | \(-0.487733\pi\) | ||||
0.0385295 | + | 0.999257i | \(0.487733\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.19154e6 | −0.168725 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.28946e6 | 0.601899 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.70322e6 | −0.654007 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.28486e6 | 0.177062 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.74443e6 | −0.784529 | −0.392264 | − | 0.919852i | \(-0.628308\pi\) | ||||
−0.392264 | + | 0.919852i | \(0.628308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.26902e7 | 1.71766 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.88040e6 | −0.654709 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.14723e7 | 1.52538 | 0.762690 | − | 0.646764i | \(-0.223878\pi\) | ||||
0.762690 | + | 0.646764i | \(0.223878\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.20467e6 | 1.08128 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.22553e6 | 0.290721 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.71119e6 | −0.998484 | −0.499242 | − | 0.866463i | \(-0.666388\pi\) | ||||
−0.499242 | + | 0.866463i | \(0.666388\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.86588e6 | −0.367848 | −0.183924 | − | 0.982940i | \(-0.558880\pi\) | ||||
−0.183924 | + | 0.982940i | \(0.558880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.01056e6 | 0.383055 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.73071e6 | 0.596701 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.12357e6 | 0.640668 | 0.320334 | − | 0.947305i | \(-0.396205\pi\) | ||||
0.320334 | + | 0.947305i | \(0.396205\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.72026e6 | −0.709119 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.32386e6 | 0.531412 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.68436e6 | 1.18005 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.58688e6 | 0.312526 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.63952e6 | −0.316176 | −0.158088 | − | 0.987425i | \(-0.550533\pi\) | ||||
−0.158088 | + | 0.987425i | \(0.550533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.75772e6 | −0.327538 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.01034e7 | −1.18987 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.59576e7 | 1.86350 | 0.931751 | − | 0.363098i | \(-0.118281\pi\) | ||||
0.931751 | + | 0.363098i | \(0.118281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.60288e6 | −0.301413 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.29631e6 | −0.608188 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.16868e7 | 1.33085 | 0.665425 | − | 0.746465i | \(-0.268251\pi\) | ||||
0.665425 | + | 0.746465i | \(0.268251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.10344e6 | −0.576337 | −0.288169 | − | 0.957580i | \(-0.593046\pi\) | ||||
−0.288169 | + | 0.957580i | \(0.593046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 929096. | 0.104056 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 982336. | 0.109112 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.91995e6 | −1.09279 | −0.546396 | − | 0.837527i | \(-0.684001\pi\) | ||||
−0.546396 | + | 0.837527i | \(0.684001\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.00524e6 | −0.656126 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.69288e6 | 0.942021 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.70881e7 | −1.83672 | −0.918360 | − | 0.395745i | \(-0.870486\pi\) | ||||
−0.918360 | + | 0.395745i | \(0.870486\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.29517e6 | 0.884377 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.80959e6 | 0.720125 | 0.360063 | − | 0.932928i | \(-0.382755\pi\) | ||||
0.360063 | + | 0.932928i | \(0.382755\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.56275e6 | −0.583529 | −0.291765 | − | 0.956490i | \(-0.594242\pi\) | ||||
−0.291765 | + | 0.956490i | \(0.594242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.97803e7 | 2.05828 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.14434e6 | −0.221347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.18572e7 | −1.21417 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.88120e6 | 0.292688 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.19022e6 | −0.119950 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.11026e6 | 0.111007 | 0.0555034 | − | 0.998458i | \(-0.482324\pi\) | ||||
0.0555034 | + | 0.998458i | \(0.482324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.71381e6 | −0.368392 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.93894e7 | 1.90823 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.06486e6 | −0.201624 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −84224.0 | −0.00815988 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00885e7 | −0.969797 | −0.484898 | − | 0.874570i | \(-0.661143\pi\) | ||||
−0.484898 | + | 0.874570i | \(0.661143\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.87096e6 | −0.369225 | −0.184612 | − | 0.982811i | \(-0.559103\pi\) | ||||
−0.184612 | + | 0.982811i | \(0.559103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.32214e7 | 1.25135 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.51508e7 | 1.42290 | 0.711449 | − | 0.702737i | \(-0.248039\pi\) | ||||
0.711449 | + | 0.702737i | \(0.248039\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.76828e6 | 0.537569 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.86081e6 | 0.357047 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.86286e7 | −1.70961 | −0.854806 | − | 0.518947i | \(-0.826324\pi\) | ||||
−0.854806 | + | 0.518947i | \(0.826324\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.89208e7 | 1.72321 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.78196e6 | −0.161059 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.23368e6 | 0.379756 | 0.189878 | − | 0.981808i | \(-0.439191\pi\) | ||||
0.189878 | + | 0.981808i | \(0.439191\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.91690e6 | 0.704777 | 0.352389 | − | 0.935854i | \(-0.385370\pi\) | ||||
0.352389 | + | 0.935854i | \(0.385370\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.99320e6 | 0.882919 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.53664e6 | 0.134747 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.26495e7 | −3.71193 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.87451e6 | −0.507465 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.06478e7 | 0.912967 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.50142e7 | −1.27780 | −0.638900 | − | 0.769290i | \(-0.720610\pi\) | ||||
−0.638900 | + | 0.769290i | \(0.720610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.94226e6 | 0.333032 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.52404e6 | −0.379362 | −0.189681 | − | 0.981846i | \(-0.560745\pi\) | ||||
−0.189681 | + | 0.981846i | \(0.560745\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.22371e6 | −0.268338 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.08735e7 | −0.898465 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.79046e7 | 1.46863 | 0.734316 | − | 0.678808i | \(-0.237503\pi\) | ||||
0.734316 | + | 0.678808i | \(0.237503\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.01235e6 | −0.408146 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.00694e6 | −0.0813973 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.98299e7 | −1.59137 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.15754e6 | 0.570255 | 0.285127 | − | 0.958490i | \(-0.407964\pi\) | ||||
0.285127 | + | 0.958490i | \(0.407964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 967260. | 0.0765086 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.49766e7 | 1.17612 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.68414e6 | −0.599119 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.99752e6 | 0.386867 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.95052e7 | 1.49918 | 0.749592 | − | 0.661900i | \(-0.230250\pi\) | ||||
0.749592 | + | 0.661900i | \(0.230250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 702660. | 0.0536237 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.05677e6 | 0.686279 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −868672. | −0.0653593 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.18187e6 | −0.685986 | −0.342993 | − | 0.939338i | \(-0.611441\pi\) | ||||
−0.342993 | + | 0.939338i | \(0.611441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.51125e6 | −0.334675 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.74196e7 | 2.01994 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.31168e7 | −1.69107 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.48936e7 | −1.08194 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.64528e6 | −0.335112 | −0.167556 | − | 0.985863i | \(-0.553588\pi\) | ||||
−0.167556 | + | 0.985863i | \(0.553588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.96134e6 | −0.427077 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.16881e7 | 0.831570 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.50013e6 | −0.600594 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.67153e7 | −1.17295 | −0.586473 | − | 0.809969i | \(-0.699484\pi\) | ||||
−0.586473 | + | 0.809969i | \(0.699484\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.59468e7 | 1.11136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.22475e7 | −0.847722 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.55366e6 | 0.244295 | 0.122148 | − | 0.992512i | \(-0.461022\pi\) | ||||
0.122148 | + | 0.992512i | \(0.461022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.15130e6 | −0.146886 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.30256e6 | −0.563045 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.34812e7 | 0.908069 | 0.454035 | − | 0.890984i | \(-0.349984\pi\) | ||||
0.454035 | + | 0.890984i | \(0.349984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.89960e6 | −0.394709 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.04869e7 | −0.696907 | −0.348454 | − | 0.937326i | \(-0.613293\pi\) | ||||
−0.348454 | + | 0.937326i | \(0.613293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.54491e7 | 1.67989 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.14737e6 | 0.271939 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.36533e6 | −0.154059 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15094e7 | 0.744651 | 0.372326 | − | 0.928102i | \(-0.378560\pi\) | ||||
0.372326 | + | 0.928102i | \(0.378560\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.22697e7 | 1.43129 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.51316e7 | −0.966093 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.45928e7 | 0.925548 | 0.462774 | − | 0.886476i | \(-0.346854\pi\) | ||||
0.462774 | + | 0.886476i | \(0.346854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.86474e7 | −1.80501 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.33690e6 | −0.208873 | −0.104436 | − | 0.994532i | \(-0.533304\pi\) | ||||
−0.104436 | + | 0.994532i | \(0.533304\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.70269e6 | −0.541181 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.49664e6 | −0.154242 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.18112e7 | −0.724948 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.49953e7 | −0.914408 | −0.457204 | − | 0.889362i | \(-0.651149\pi\) | ||||
−0.457204 | + | 0.889362i | \(0.651149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.04656e6 | −0.0634054 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.89084e7 | 1.13817 | 0.569085 | − | 0.822279i | \(-0.307298\pi\) | ||||
0.569085 | + | 0.822279i | \(0.307298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.46479e6 | 0.326828 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −983724. | −0.0584549 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.53642e6 | 0.267836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 752640. | 0.0441529 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.55412e7 | −2.07171 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.03853e6 | −0.118071 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.28586e7 | 0.740044 | 0.370022 | − | 0.929023i | \(-0.379350\pi\) | ||||
0.370022 | + | 0.929023i | \(0.379350\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 136416. | 0.00780140 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.28170e6 | −0.356974 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.18027e7 | −1.23120 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.06600e7 | −1.15934 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.38505e7 | −1.33000 | −0.665001 | − | 0.746842i | \(-0.731569\pi\) | ||||
−0.665001 | + | 0.746842i | \(0.731569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.38964e6 | −0.464918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.05681e6 | −0.113270 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.59239e7 | 0.871485 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.52786e7 | −0.830986 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.74377e7 | −0.942551 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.95899e7 | −1.58955 | −0.794773 | − | 0.606907i | \(-0.792410\pi\) | ||||
−0.794773 | + | 0.606907i | \(0.792410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.73826e7 | −1.46192 | −0.730959 | − | 0.682421i | \(-0.760927\pi\) | ||||
−0.730959 | + | 0.682421i | \(0.760927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.27689e7 | −1.20814 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.58030e7 | −1.36074 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.23044e6 | 0.378974 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.98058e6 | −0.103177 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.62427e7 | −0.841007 | −0.420503 | − | 0.907291i | \(-0.638147\pi\) | ||||
−0.420503 | + | 0.907291i | \(0.638147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.13459e7 | −1.09854 | −0.549269 | − | 0.835646i | \(-0.685094\pi\) | ||||
−0.549269 | + | 0.835646i | \(0.685094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.70948e6 | −0.292053 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.88590e7 | 0.958860 | 0.479430 | − | 0.877580i | \(-0.340843\pi\) | ||||
0.479430 | + | 0.877580i | \(0.340843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.50128e7 | −1.26408 | −0.632041 | − | 0.774935i | \(-0.717783\pi\) | ||||
−0.632041 | + | 0.774935i | \(0.717783\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.38698e6 | 0.0696735 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.99283e6 | 0.0995079 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.64188e7 | 1.80763 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.28497e7 | 1.12737 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.34469e6 | −0.114996 | −0.0574978 | − | 0.998346i | \(-0.518312\pi\) | ||||
−0.0574978 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.61214e7 | 2.73614 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.50832e7 | 1.21566 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.35716e7 | 1.13566 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −752101. | −0.0360220 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.49985e7 | 0.714133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.98645e6 | −0.330699 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.96869e7 | 1.86756 | 0.933780 | − | 0.357846i | \(-0.116489\pi\) | ||||
0.933780 | + | 0.357846i | \(0.116489\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.47392e6 | 0.0689539 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.61557e6 | 0.214671 | 0.107335 | − | 0.994223i | \(-0.465768\pi\) | ||||
0.107335 | + | 0.994223i | \(0.465768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.95701e6 | −0.275452 | −0.137726 | − | 0.990470i | \(-0.543979\pi\) | ||||
−0.137726 | + | 0.990470i | \(0.543979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.35099e6 | −0.291967 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.36222e6 | 0.245086 | 0.122543 | − | 0.992463i | \(-0.460895\pi\) | ||||
0.122543 | + | 0.992463i | \(0.460895\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.20074e7 | −1.45449 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.02334e7 | 0.462351 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.03133e7 | 1.81092 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.70005e7 | 0.759304 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.09213e6 | −0.137316 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.75494e6 | 0.298265 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.19646e7 | 1.84240 | 0.921200 | − | 0.389090i | \(-0.127210\pi\) | ||||
0.921200 | + | 0.389090i | \(0.127210\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.54434e6 | −0.242035 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.03589e7 | −0.449649 | −0.224824 | − | 0.974399i | \(-0.572181\pi\) | ||||
−0.224824 | + | 0.974399i | \(0.572181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.46323e7 | −1.49479 | −0.747394 | − | 0.664381i | \(-0.768695\pi\) | ||||
−0.747394 | + | 0.664381i | \(0.768695\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.23057e7 | −0.528137 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.43735e7 | 1.04018 | 0.520090 | − | 0.854112i | \(-0.325898\pi\) | ||||
0.520090 | + | 0.854112i | \(0.325898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.48450e7 | −0.629980 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.90760e7 | −0.804994 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.95292e6 | 0.207842 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.22534e6 | 0.301509 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.86589e7 | 2.43418 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.92675e7 | −2.03311 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.91381e7 | 0.785394 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.01226e7 | −0.413117 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.32992e6 | 0.0539764 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.84124e7 | 1.14680 | 0.573402 | − | 0.819274i | \(-0.305623\pi\) | ||||
0.573402 | + | 0.819274i | \(0.305623\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −833216. | −0.0334463 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.72159e7 | −0.687278 | −0.343639 | − | 0.939102i | \(-0.611660\pi\) | ||||
−0.343639 | + | 0.939102i | \(0.611660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.70616e7 | −1.47146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.27154e7 | −0.896948 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.44863e7 | −0.568896 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.23398e7 | −1.65371 | −0.826855 | − | 0.562415i | \(-0.809872\pi\) | ||||
−0.826855 | + | 0.562415i | \(0.809872\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.76692e7 | −0.686385 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.54112e6 | −0.0595432 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.39241e6 | −0.0535074 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.71802e6 | −0.218548 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.05248e7 | 0.780260 | 0.390130 | − | 0.920760i | \(-0.372430\pi\) | ||||
0.390130 | + | 0.920760i | \(0.372430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.17649e6 | −0.0444850 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.39426e7 | −0.900465 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.23104e7 | 0.834600 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.86579e7 | 0.694248 | 0.347124 | − | 0.937819i | \(-0.387158\pi\) | ||||
0.347124 | + | 0.937819i | \(0.387158\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.96888e6 | 0.331951 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.42313e6 | −0.162838 | −0.0814189 | − | 0.996680i | \(-0.525945\pi\) | ||||
−0.0814189 | + | 0.996680i | \(0.525945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.51050e7 | −1.65175 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.27322e7 | −0.463791 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.46116e6 | 0.161649 | 0.0808244 | − | 0.996728i | \(-0.474245\pi\) | ||||
0.0808244 | + | 0.996728i | \(0.474245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.26060e7 | −1.17526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.26233e6 | −0.260390 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.95591e7 | −0.697616 | −0.348808 | − | 0.937194i | \(-0.613413\pi\) | ||||
−0.348808 | + | 0.937194i | \(0.613413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.37626e7 | −0.488305 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.14735e7 | 1.81679 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.83758e6 | 0.134745 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.04523e6 | 0.106368 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.26878e6 | −0.0788365 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.61498e7 | 0.903960 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.70289e7 | −0.585625 | −0.292813 | − | 0.956170i | \(-0.594591\pi\) | ||||
−0.292813 | + | 0.956170i | \(0.594591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.69380e6 | 0.194802 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.10092e7 | 0.374721 | 0.187361 | − | 0.982291i | \(-0.440007\pi\) | ||||
0.187361 | + | 0.982291i | \(0.440007\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.14665e7 | −0.388283 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.16908e7 | 0.393853 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.84999e7 | −0.620058 | −0.310029 | − | 0.950727i | \(-0.600339\pi\) | ||||
−0.310029 | + | 0.950727i | \(0.600339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.83800e7 | 0.612900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.34748e6 | −0.276938 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.19756e7 | 1.05544 | 0.527721 | − | 0.849418i | \(-0.323047\pi\) | ||||
0.527721 | + | 0.849418i | \(0.323047\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.61871e7 | 1.51681 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.93409e6 | −0.226567 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.18912e7 | −2.33714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.23128e7 | 1.69209 | 0.846046 | − | 0.533111i | \(-0.178977\pi\) | ||||
0.846046 | + | 0.533111i | \(0.178977\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.79177e6 | 0.315129 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.42117e7 | 0.775296 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.60757e7 | −0.830802 | −0.415401 | − | 0.909638i | \(-0.636359\pi\) | ||||
−0.415401 | + | 0.909638i | \(0.636359\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.82204e6 | −0.184570 |
(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 | 448.6.a.d.1.1 | 1 | ||
4.3 | odd | 2 | 448.6.a.n.1.1 | 1 | |||
8.3 | odd | 2 | 224.6.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 224.6.a.b.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
224.6.a.b.1.1 | yes | 1 | 8.5 | even | 2 | ||
448.6.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
448.6.a.n.1.1 | 1 | 4.3 | odd | 2 |