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: | \(3\) |
Coefficient field: | 3.3.367637.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 107x + 282 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.76097\) of defining polynomial | ||
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 | ||||||||
\(3\) | 7.52194 | 0.482533 | 0.241266 | − | 0.970459i | \(-0.422437\pi\) | ||||
0.241266 | + | 0.970459i | \(0.422437\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −72.6328 | −1.29930 | −0.649648 | − | 0.760235i | \(-0.725084\pi\) | ||||
−0.649648 | + | 0.760235i | \(0.725084\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −186.420 | −0.767162 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.4503 | 0.0758770 | 0.0379385 | − | 0.999280i | \(-0.487921\pi\) | ||||
0.0379385 | + | 0.999280i | \(0.487921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1145.83 | 1.88045 | 0.940225 | − | 0.340555i | \(-0.110615\pi\) | ||||
0.940225 | + | 0.340555i | \(0.110615\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −546.340 | −0.626953 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −514.240 | −0.431563 | −0.215781 | − | 0.976442i | \(-0.569230\pi\) | ||||
−0.215781 | + | 0.976442i | \(0.569230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2319.63 | −1.47413 | −0.737063 | − | 0.675824i | \(-0.763788\pi\) | ||||
−0.737063 | + | 0.675824i | \(0.763788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 368.575 | 0.182380 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 409.434 | 0.161385 | 0.0806927 | − | 0.996739i | \(-0.474287\pi\) | ||||
0.0806927 | + | 0.996739i | \(0.474287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2150.53 | 0.688169 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3230.07 | −0.852714 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1693.66 | 0.373965 | 0.186982 | − | 0.982363i | \(-0.440129\pi\) | ||||
0.186982 | + | 0.982363i | \(0.440129\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7030.24 | −1.31391 | −0.656955 | − | 0.753930i | \(-0.728156\pi\) | ||||
−0.656955 | + | 0.753930i | \(0.728156\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 229.045 | 0.0366131 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3559.01 | −0.491088 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3935.80 | −0.472638 | −0.236319 | − | 0.971676i | \(-0.575941\pi\) | ||||
−0.236319 | + | 0.971676i | \(0.575941\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8618.86 | 0.907378 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9236.29 | −0.858100 | −0.429050 | − | 0.903281i | \(-0.641152\pi\) | ||||
−0.429050 | + | 0.903281i | \(0.641152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21356.2 | 1.76138 | 0.880691 | − | 0.473691i | \(-0.157079\pi\) | ||||
0.880691 | + | 0.473691i | \(0.157079\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13540.2 | 0.996770 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9948.52 | 0.656922 | 0.328461 | − | 0.944518i | \(-0.393470\pi\) | ||||
0.328461 | + | 0.944518i | \(0.393470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3868.09 | −0.208243 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 34576.4 | 1.69079 | 0.845396 | − | 0.534140i | \(-0.179364\pi\) | ||||
0.845396 | + | 0.534140i | \(0.179364\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2211.69 | −0.0985866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17448.1 | −0.711314 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 46307.9 | 1.73191 | 0.865954 | − | 0.500123i | \(-0.166712\pi\) | ||||
0.865954 | + | 0.500123i | \(0.166712\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33817.6 | 1.16364 | 0.581819 | − | 0.813318i | \(-0.302341\pi\) | ||||
0.581819 | + | 0.813318i | \(0.302341\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9134.60 | −0.289960 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −83224.8 | −2.44326 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −49266.7 | −1.34081 | −0.670404 | − | 0.741996i | \(-0.733879\pi\) | ||||
−0.670404 | + | 0.741996i | \(0.733879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3079.74 | 0.0778737 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 49543.4 | 1.16638 | 0.583190 | − | 0.812336i | \(-0.301804\pi\) | ||||
0.583190 | + | 0.812336i | \(0.301804\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33822.3 | 0.742841 | 0.371420 | − | 0.928465i | \(-0.378871\pi\) | ||||
0.371420 | + | 0.928465i | \(0.378871\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 16176.1 | 0.332064 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1492.07 | 0.0286788 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −622.967 | −0.0112305 | −0.00561523 | − | 0.999984i | \(-0.501787\pi\) | ||||
−0.00561523 | + | 0.999984i | \(0.501787\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 21003.7 | 0.355700 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 97253.4 | 1.54956 | 0.774782 | − | 0.632228i | \(-0.217860\pi\) | ||||
0.774782 | + | 0.632228i | \(0.217860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 37350.7 | 0.560728 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12739.6 | 0.180450 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16975.2 | −0.227164 | −0.113582 | − | 0.993529i | \(-0.536232\pi\) | ||||
−0.113582 | + | 0.993529i | \(0.536232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 56145.6 | 0.710743 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −52881.0 | −0.634005 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 168481. | 1.91532 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −65462.3 | −0.706419 | −0.353209 | − | 0.935544i | \(-0.614910\pi\) | ||||
−0.353209 | + | 0.935544i | \(0.614910\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5676.56 | −0.0582100 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 121485. | 1.18500 | 0.592500 | − | 0.805570i | \(-0.298141\pi\) | ||||
0.592500 | + | 0.805570i | \(0.298141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 83208.1 | 0.772810 | 0.386405 | − | 0.922329i | \(-0.373717\pi\) | ||||
0.386405 | + | 0.922329i | \(0.373717\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −26770.6 | −0.236966 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 33139.0 | 0.279821 | 0.139910 | − | 0.990164i | \(-0.455319\pi\) | ||||
0.139910 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12724.1 | −0.102580 | −0.0512899 | − | 0.998684i | \(-0.516333\pi\) | ||||
−0.0512899 | + | 0.998684i | \(0.516333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −29604.9 | −0.228063 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20385.5 | −0.150184 | −0.0750922 | − | 0.997177i | \(-0.523925\pi\) | ||||
−0.0750922 | + | 0.997177i | \(0.523925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −29738.3 | −0.209687 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −213606. | −1.44261 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25197.8 | −0.163115 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −160124. | −0.994243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −69474.8 | −0.414061 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 70778.7 | 0.405161 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −235783. | −1.29719 | −0.648594 | − | 0.761135i | \(-0.724643\pi\) | ||||
−0.648594 | + | 0.761135i | \(0.724643\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 160640. | 0.849925 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15276.4 | 0.0777755 | 0.0388878 | − | 0.999244i | \(-0.487619\pi\) | ||||
0.0388878 | + | 0.999244i | \(0.487619\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −113662. | −0.557167 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 234609. | 1.10793 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 148016. | 0.673763 | 0.336881 | − | 0.941547i | \(-0.390628\pi\) | ||||
0.336881 | + | 0.941547i | \(0.390628\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 143481. | 0.629879 | 0.314939 | − | 0.949112i | \(-0.398016\pi\) | ||||
0.314939 | + | 0.949112i | \(0.398016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 74832.1 | 0.316986 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34890.9 | 0.142683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −123015. | −0.485891 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18060.2 | 0.0689332 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 35178.8 | 0.129812 | 0.0649061 | − | 0.997891i | \(-0.479325\pi\) | ||||
0.0649061 | + | 0.997891i | \(0.479325\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37656.6 | −0.134400 | −0.0671998 | − | 0.997740i | \(-0.521407\pi\) | ||||
−0.0671998 | + | 0.997740i | \(0.521407\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 95864.9 | 0.331079 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 510626. | 1.70716 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −440876. | −1.42747 | −0.713736 | − | 0.700415i | \(-0.752998\pi\) | ||||
−0.713736 | + | 0.700415i | \(0.752998\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 260082. | 0.815863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20062.3 | 0.0609979 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 273443. | 0.806118 | 0.403059 | − | 0.915174i | \(-0.367947\pi\) | ||||
0.403059 | + | 0.915174i | \(0.367947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16636.2 | −0.0475713 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 657930. | 1.82553 | 0.912764 | − | 0.408487i | \(-0.133944\pi\) | ||||
0.912764 | + | 0.408487i | \(0.133944\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 941632. | 2.53609 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 432426. | 1.13089 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −605134. | −1.53722 | −0.768610 | − | 0.639717i | \(-0.779051\pi\) | ||||
−0.768610 | + | 0.639717i | \(0.779051\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 105376. | 0.260103 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 348325. | 0.835703 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 370201. | 0.863585 | 0.431793 | − | 0.901973i | \(-0.357881\pi\) | ||||
0.431793 | + | 0.901973i | \(0.357881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −330624. | −0.750132 | −0.375066 | − | 0.926998i | \(-0.622380\pi\) | ||||
−0.375066 | + | 0.926998i | \(0.622380\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 254374. | 0.561494 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 285868. | 0.614097 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15658.8 | −0.0327457 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −158274. | −0.322295 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20402.0 | −0.0404660 | −0.0202330 | − | 0.999795i | \(-0.506441\pi\) | ||||
−0.0202330 | + | 0.999795i | \(0.506441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 97967.0 | 0.189316 | 0.0946578 | − | 0.995510i | \(-0.469824\pi\) | ||||
0.0946578 | + | 0.995510i | \(0.469824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −626012. | −1.17895 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 950513. | 1.74499 | 0.872494 | − | 0.488625i | \(-0.162501\pi\) | ||||
0.872494 | + | 0.488625i | \(0.162501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 780360. | 1.39689 | 0.698445 | − | 0.715664i | \(-0.253876\pi\) | ||||
0.698445 | + | 0.715664i | \(0.253876\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −370581. | −0.646984 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 82989.2 | 0.141345 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 670858. | 1.11493 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −76326.8 | −0.123809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −70633.4 | −0.111852 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −262454. | −0.405833 | −0.202917 | − | 0.979196i | \(-0.565042\pi\) | ||||
−0.202917 | + | 0.979196i | \(0.565042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 372663. | 0.562817 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.55116e6 | −2.28856 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −344482. | −0.496612 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 254409. | 0.358445 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −589232. | −0.811532 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 404645. | 0.544894 | 0.272447 | − | 0.962171i | \(-0.412167\pi\) | ||||
0.272447 | + | 0.962171i | \(0.412167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −400902. | −0.527937 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −418192. | −0.538656 | −0.269328 | − | 0.963048i | \(-0.586802\pi\) | ||||
−0.269328 | + | 0.963048i | \(0.586802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −434849. | −0.547961 | −0.273981 | − | 0.961735i | \(-0.588340\pi\) | ||||
−0.273981 | + | 0.961735i | \(0.588340\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11223.2 | 0.0138385 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −188015. | −0.226884 | −0.113442 | − | 0.993545i | \(-0.536188\pi\) | ||||
−0.113442 | + | 0.993545i | \(0.536188\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −722589. | −0.853536 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4685.92 | −0.00541906 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.49827e6 | 1.69666 | 0.848331 | − | 0.529466i | \(-0.177608\pi\) | ||||
0.848331 | + | 0.529466i | \(0.177608\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 34638.8 | 0.0384167 | 0.0192084 | − | 0.999816i | \(-0.493885\pi\) | ||||
0.0192084 | + | 0.999816i | \(0.493885\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 942897. | 1.02435 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −174391. | −0.185614 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.65790e6 | −2.77202 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 731534. | 0.747715 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −880721. | −0.882376 | −0.441188 | − | 0.897415i | \(-0.645443\pi\) | ||||
−0.441188 | + | 0.897415i | \(0.645443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12467.4 | 0.0122454 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 280950. | 0.270569 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 245881. | 0.232216 | 0.116108 | − | 0.993237i | \(-0.462958\pi\) | ||||
0.116108 | + | 0.993237i | \(0.462958\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −192854. | −0.178640 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −315732. | −0.286892 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.44452e6 | −1.28776 | −0.643878 | − | 0.765128i | \(-0.722675\pi\) | ||||
−0.643878 | + | 0.765128i | \(0.722675\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.51138e6 | −2.19684 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −127686. | −0.109614 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 428084. | 0.360702 | 0.180351 | − | 0.983602i | \(-0.442277\pi\) | ||||
0.180351 | + | 0.983602i | \(0.442277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 37799.8 | 0.0312655 | 0.0156328 | − | 0.999878i | \(-0.495024\pi\) | ||||
0.0156328 | + | 0.999878i | \(0.495024\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 422324. | 0.342957 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 65484.2 | 0.0522162 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.06008e6 | 1.61319 | 0.806593 | − | 0.591107i | \(-0.201309\pi\) | ||||
0.806593 | + | 0.591107i | \(0.201309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.31058e6 | 1.00798 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.21937e6 | 0.921235 | 0.460617 | − | 0.887599i | \(-0.347628\pi\) | ||||
0.460617 | + | 0.887599i | \(0.347628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.27677e6 | −0.947645 | −0.473823 | − | 0.880620i | \(-0.657126\pi\) | ||||
−0.473823 | + | 0.880620i | \(0.657126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.26731e6 | 0.924207 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −452578. | −0.324331 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.15541e6 | −0.813754 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −492404. | −0.340870 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.11406e6 | −1.43863 | −0.719313 | − | 0.694686i | \(-0.755543\pi\) | ||||
−0.719313 | + | 0.694686i | \(0.755543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.36347e6 | −2.25026 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −98356.8 | −0.0647013 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 469141. | 0.303477 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.04646e6 | 0.665740 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 913801. | 0.571801 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.45627e6 | −1.51191 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.75588e6 | −1.06329 | −0.531643 | − | 0.846969i | \(-0.678425\pi\) | ||||
−0.531643 | + | 0.846969i | \(0.678425\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 625886. | 0.372906 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −792917. | −0.464865 | −0.232432 | − | 0.972613i | \(-0.574668\pi\) | ||||
−0.232432 | + | 0.972613i | \(0.574668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.19228e6 | −1.26484 | −0.632420 | − | 0.774626i | \(-0.717938\pi\) | ||||
−0.632420 | + | 0.774626i | \(0.717938\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 663472. | 0.376744 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.08545e6 | −0.606685 | −0.303342 | − | 0.952882i | \(-0.598103\pi\) | ||||
−0.303342 | + | 0.952882i | \(0.598103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 51572.4 | 0.0283753 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 249270. | 0.135023 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.19285e6 | 0.636178 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.46414e6 | 1.29407 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −95710.2 | −0.0494981 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 487477. | 0.248293 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.77389e6 | 0.889933 | 0.444967 | − | 0.895547i | \(-0.353216\pi\) | ||||
0.444967 | + | 0.895547i | \(0.353216\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 733713. | 0.362590 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.57838e6 | 1.74211 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.08310e6 | −1.47881 | −0.739407 | − | 0.673259i | \(-0.764894\pi\) | ||||
−0.739407 | + | 0.673259i | \(0.764894\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −153338. | −0.0724689 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −214073. | −0.0996956 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −223690. | −0.101181 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.14121e6 | −1.40047 | −0.700234 | − | 0.713914i | \(-0.746921\pi\) | ||||
−0.700234 | + | 0.713914i | \(0.746921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.21743e6 | 0.974511 | 0.487256 | − | 0.873259i | \(-0.337998\pi\) | ||||
0.487256 | + | 0.873259i | \(0.337998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.70111e6 | −1.60348 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 923780. | 0.394577 | 0.197288 | − | 0.980345i | \(-0.436786\pi\) | ||||
0.197288 | + | 0.980345i | \(0.436786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.59848e6 | −1.51547 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −189536. | −0.0787085 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −311845. | −0.127703 | −0.0638517 | − | 0.997959i | \(-0.520338\pi\) | ||||
−0.0638517 | + | 0.997959i | \(0.520338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.90458e6 | 1.17305 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.20444e6 | −0.479755 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.45661e6 | −0.965170 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.27344e6 | 0.493531 | 0.246765 | − | 0.969075i | \(-0.420632\pi\) | ||||
0.246765 | + | 0.969075i | \(0.420632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.72183e6 | 0.658302 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.69424e6 | 0.639059 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −406594. | −0.151317 | −0.0756587 | − | 0.997134i | \(-0.524106\pi\) | ||||
−0.0756587 | + | 0.997134i | \(0.524106\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 532393. | 0.195503 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.94064e6 | 0.703222 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.05172e6 | 1.44891 | 0.724455 | − | 0.689322i | \(-0.242092\pi\) | ||||
0.724455 | + | 0.689322i | \(0.242092\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.77354e6 | −0.625935 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.95208e6 | −1.02833 | −0.514163 | − | 0.857692i | \(-0.671897\pi\) | ||||
−0.514163 | + | 0.857692i | \(0.671897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −108373. | −0.0372622 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.98124e6 | −1.35127 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.34441e6 | −0.785523 | −0.392761 | − | 0.919640i | \(-0.628480\pi\) | ||||
−0.392761 | + | 0.919640i | \(0.628480\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −210547. | −0.0696479 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 114908. | 0.0375292 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 45247.8 | 0.0145917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −799866. | −0.254707 | −0.127354 | − | 0.991857i | \(-0.540648\pi\) | ||||
−0.127354 | + | 0.991857i | \(0.540648\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −854957. | −0.268851 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.66435e6 | 1.44854 | 0.724269 | − | 0.689517i | \(-0.242177\pi\) | ||||
0.724269 | + | 0.689517i | \(0.242177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.05545e6 | −2.47074 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.52556e6 | −0.462159 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −119846. | −0.0358623 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.45860e6 | −1.02233 | −0.511165 | − | 0.859482i | \(-0.670786\pi\) | ||||
−0.511165 | + | 0.859482i | \(0.670786\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.11337e6 | 0.325113 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.26909e6 | 0.654600 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.06379e6 | −2.01334 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.07925e6 | 0.303937 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.36121e6 | −0.657052 | −0.328526 | − | 0.944495i | \(-0.606552\pi\) | ||||
−0.328526 | + | 0.944495i | \(0.606552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.57530e6 | −0.983123 | −0.491561 | − | 0.870843i | \(-0.663574\pi\) | ||||
−0.491561 | + | 0.870843i | \(0.663574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.85461e6 | −0.503966 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.10589e6 | −0.296988 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.65706e6 | 0.439814 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 262447. | 0.0688491 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.65850e6 | 1.46726 | 0.733631 | − | 0.679548i | \(-0.237824\pi\) | ||||
0.733631 | + | 0.679548i | \(0.237824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.09905e6 | 1.56330 | 0.781650 | − | 0.623717i | \(-0.214378\pi\) | ||||
0.781650 | + | 0.623717i | \(0.214378\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −925312. | −0.234458 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −949734. | −0.237902 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.81345e6 | −0.696753 | −0.348376 | − | 0.937355i | \(-0.613267\pi\) | ||||
−0.348376 | + | 0.937355i | \(0.613267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −447595. | −0.109595 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.64719e6 | 1.85137 | 0.925683 | − | 0.378300i | \(-0.123491\pi\) | ||||
0.925683 | + | 0.378300i | \(0.123491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.23296e6 | 0.295153 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 264613. | 0.0626386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.32460e6 | −0.310076 | −0.155038 | − | 0.987909i | \(-0.549550\pi\) | ||||
−0.155038 | + | 0.987909i | \(0.549550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −281248. | −0.0651100 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −283250. | −0.0648522 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.07802e6 | −0.923465 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.79243e6 | 1.29739 | 0.648694 | − | 0.761049i | \(-0.275315\pi\) | ||||
0.648694 | + | 0.761049i | \(0.275315\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.66104e6 | 0.367999 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.41695e6 | 0.967988 | 0.483994 | − | 0.875071i | \(-0.339186\pi\) | ||||
0.483994 | + | 0.875071i | \(0.339186\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.22867e6 | 0.483163 | 0.241582 | − | 0.970380i | \(-0.422334\pi\) | ||||
0.241582 | + | 0.970380i | \(0.422334\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.84090e6 | 0.823760 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.80111e6 | 0.382164 | 0.191082 | − | 0.981574i | \(-0.438800\pi\) | ||||
0.191082 | + | 0.981574i | \(0.438800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.41407e6 | −0.506778 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.31624e6 | −0.688802 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 650304. | 0.133648 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.98843e6 | −1.01445 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.44575e6 | −1.29711 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.08283e6 | 1.21134 | 0.605672 | − | 0.795715i | \(-0.292905\pi\) | ||||
0.605672 | + | 0.795715i | \(0.292905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.50976e6 | −0.888772 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 150907. | 0.0294335 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.75471e6 | 0.917847 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.08489e6 | 1.54473 | 0.772364 | − | 0.635180i | \(-0.219074\pi\) | ||||
0.772364 | + | 0.635180i | \(0.219074\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.05682e6 | 0.388978 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.16092e6 | 0.404516 | 0.202258 | − | 0.979332i | \(-0.435172\pi\) | ||||
0.202258 | + | 0.979332i | \(0.435172\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −870947. | −0.161389 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 412305. | 0.0756319 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.42763e6 | 0.440850 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.38369e6 | 0.788113 | 0.394056 | − | 0.919086i | \(-0.371071\pi\) | ||||
0.394056 | + | 0.919086i | \(0.371071\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.94891e6 | 0.880877 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.50358e6 | 1.14613 | 0.573063 | − | 0.819511i | \(-0.305755\pi\) | ||||
0.573063 | + | 0.819511i | \(0.305755\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.82378e6 | −1.53967 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.08290e6 | 1.22375 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.90877e6 | −1.52413 | −0.762067 | − | 0.647498i | \(-0.775815\pi\) | ||||
−0.762067 | + | 0.647498i | \(0.775815\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.65729e6 | 0.280767 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.49257e6 | 1.25701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.04364e6 | −1.00411 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 302935. | 0.0498452 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.55178e6 | −0.741759 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.87271e6 | −0.463658 | −0.231829 | − | 0.972756i | \(-0.574471\pi\) | ||||
−0.231829 | + | 0.972756i | \(0.574471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.21693e6 | 0.993852 | 0.496926 | − | 0.867793i | \(-0.334462\pi\) | ||||
0.496926 | + | 0.867793i | \(0.334462\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 792631. | 0.125508 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.61523e6 | 0.567035 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.26871e6 | −0.973955 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.63274e6 | −1.32865 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.05832e7 | −1.61361 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.40698e6 | −0.363570 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.78463e6 | 0.416708 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 73111.2 | 0.0108396 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.30994e6 | 0.926898 | 0.463449 | − | 0.886124i | \(-0.346612\pi\) | ||||
0.463449 | + | 0.886124i | \(0.346612\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.48693e6 | −0.361963 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 924190. | 0.133282 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.07052e7 | 1.52976 | 0.764882 | − | 0.644170i | \(-0.222797\pi\) | ||||
0.764882 | + | 0.644170i | \(0.222797\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.30429e6 | −0.892700 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.92866e6 | −0.551271 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30525.4 | −0.00424471 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.15028e6 | 0.296322 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.92588e6 | −1.08245 | −0.541227 | − | 0.840877i | \(-0.682040\pi\) | ||||
−0.541227 | + | 0.840877i | \(0.682040\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.44706e7 | 3.31219 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −117784. | −0.0158009 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.39442e6 | −1.11614 | −0.558072 | − | 0.829793i | \(-0.688459\pi\) | ||||
−0.558072 | + | 0.829793i | \(0.688459\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.48065e6 | 0.195134 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.02918e6 | 0.134442 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.87124e6 | −0.501267 | −0.250634 | − | 0.968082i | \(-0.580639\pi\) | ||||
−0.250634 | + | 0.968082i | \(0.580639\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.27091e7 | 1.63126 | 0.815631 | − | 0.578572i | \(-0.196390\pi\) | ||||
0.815631 | + | 0.578572i | \(0.196390\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −153463. | −0.0195261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 880498. | 0.111060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.77969e6 | −0.597669 | −0.298834 | − | 0.954305i | \(-0.596598\pi\) | ||||
−0.298834 | + | 0.954305i | \(0.596598\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 736902. | 0.0913510 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.76542e6 | 0.585680 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.05286e6 | 0.128292 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.55148e7 | 1.87438 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.61275e6 | 0.312970 | 0.156485 | − | 0.987680i | \(-0.449984\pi\) | ||||
0.156485 | + | 0.987680i | \(0.449984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.63075e7 | 1.93687 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.14970e6 | 0.842014 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.43447e7 | −1.67516 | −0.837579 | − | 0.546316i | \(-0.816030\pi\) | ||||
−0.837579 | + | 0.546316i | \(0.816030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.83019e6 | 0.211935 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.86982e6 | 0.674045 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.08290e6 | −0.806574 | −0.403287 | − | 0.915074i | \(-0.632132\pi\) | ||||
−0.403287 | + | 0.915074i | \(0.632132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.48490e7 | −1.67691 | −0.838457 | − | 0.544967i | \(-0.816542\pi\) | ||||
−0.838457 | + | 0.544967i | \(0.816542\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.18432e6 | 1.02862 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.16302e7 | 1.29182 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.20896e7 | 1.33181 | 0.665903 | − | 0.746038i | \(-0.268046\pi\) | ||||
0.665903 | + | 0.746038i | \(0.268046\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 624240. | 0.0682038 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.13993e7 | 1.23531 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.66773e7 | 1.79257 | 0.896284 | − | 0.443480i | \(-0.146256\pi\) | ||||
0.896284 | + | 0.443480i | \(0.146256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.04615e6 | 0.537988 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.01868e7 | −1.07727 | −0.538634 | − | 0.842540i | \(-0.681059\pi\) | ||||
−0.538634 | + | 0.842540i | \(0.681059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.88545e6 | −0.617381 | −0.308690 | − | 0.951163i | \(-0.599891\pi\) | ||||
−0.308690 | + | 0.951163i | \(0.599891\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.32250e6 | −0.137615 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −831784. | −0.0858599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.18613e7 | −1.21459 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −531300. | −0.0539723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.02395e6 | 0.203973 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.09945e7 | −1.09926 | −0.549632 | − | 0.835407i | \(-0.685232\pi\) | ||||
−0.549632 | + | 0.835407i | \(0.685232\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.97417e6 | −0.195828 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.71256e7 | 1.68543 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.75114e6 | 0.268636 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.23591e6 | −0.894803 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −453144. | −0.0435604 | −0.0217802 | − | 0.999763i | \(-0.506933\pi\) | ||||
−0.0217802 | + | 0.999763i | \(0.506933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.72050e7 | −1.64107 | −0.820537 | − | 0.571593i | \(-0.806326\pi\) | ||||
−0.820537 | + | 0.571593i | \(0.806326\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.16678e7 | −1.10430 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.68036e6 | 0.439560 | 0.219780 | − | 0.975549i | \(-0.429466\pi\) | ||||
0.219780 | + | 0.975549i | \(0.429466\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.41009e6 | 0.131412 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.59117e6 | −0.239631 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.29058e6 | −0.852629 | −0.426314 | − | 0.904575i | \(-0.640188\pi\) | ||||
−0.426314 | + | 0.904575i | \(0.640188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.10957e6 | −0.101053 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.30516e6 | −0.569879 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.60390e7 | −1.43868 | −0.719339 | − | 0.694659i | \(-0.755555\pi\) | ||||
−0.719339 | + | 0.694659i | \(0.755555\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.02455e6 | 0.536316 | 0.268158 | − | 0.963375i | \(-0.413585\pi\) | ||||
0.268158 | + | 0.963375i | \(0.413585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.43217e6 | −0.391591 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.25558e6 | 0.723925 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 693441. | 0.0603524 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.04372e6 | 0.262929 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.02976e6 | 0.0882934 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.58601e6 | −0.134980 | −0.0674898 | − | 0.997720i | \(-0.521499\pi\) | ||||
−0.0674898 | + | 0.997720i | \(0.521499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.94636e6 | −0.586811 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.60343e6 | −0.469875 | −0.234938 | − | 0.972010i | \(-0.575489\pi\) | ||||
−0.234938 | + | 0.972010i | \(0.575489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.20765e6 | −0.267001 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.14562e6 | −0.259919 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.55974e6 | 0.209963 | 0.104982 | − | 0.994474i | \(-0.466522\pi\) | ||||
0.104982 | + | 0.994474i | \(0.466522\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.07508e7 | −0.875417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.27091e6 | −0.264409 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.96187e7 | 3.17945 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.02347e7 | 0.815415 | 0.407708 | − | 0.913113i | \(-0.366328\pi\) | ||||
0.407708 | + | 0.913113i | \(0.366328\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −278151. | −0.0220013 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.04214e7 | −0.818399 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.74967e6 | 0.370324 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.41424e6 | −0.109479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.25770e7 | 0.966677 | 0.483339 | − | 0.875434i | \(-0.339424\pi\) | ||||
0.483339 | + | 0.875434i | \(0.339424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.12960e6 | 0.696728 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.43527e6 | −0.411859 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.95275e6 | 0.447888 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.54796e7 | 1.90361 | 0.951804 | − | 0.306706i | \(-0.0992269\pi\) | ||||
0.951804 | + | 0.306706i | \(0.0992269\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 116134. | 0.00861558 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.87842e6 | −0.212046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.53422e6 | −0.185387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.12699e7 | 0.818695 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.61567e6 | −0.693677 | −0.346839 | − | 0.937925i | \(-0.612745\pi\) | ||||
−0.346839 | + | 0.937925i | \(0.612745\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.07720e6 | 0.292095 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 260551. | 0.0185373 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.64226e6 | 0.257351 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.37720e7 | −0.966409 | −0.483204 | − | 0.875508i | \(-0.660527\pi\) | ||||
−0.483204 | + | 0.875508i | \(0.660527\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.98851e6 | 0.138582 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.09822e7 | −0.760147 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.99018e7 | −1.36814 | −0.684072 | − | 0.729414i | \(-0.739793\pi\) | ||||
−0.684072 | + | 0.729414i | \(0.739793\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.31176e6 | −0.0895646 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.50019e6 | −0.101736 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.83447e7 | 1.23566 | 0.617832 | − | 0.786310i | \(-0.288011\pi\) | ||||
0.617832 | + | 0.786310i | \(0.288011\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.99926e7 | −1.33759 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.37153e7 | 1.57600 | 0.788000 | − | 0.615675i | \(-0.211116\pi\) | ||||
0.788000 | + | 0.615675i | \(0.211116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.55514e6 | −0.168664 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.81300e7 | −1.18877 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.62381e6 | 0.105762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.63612e7 | 1.05856 | 0.529279 | − | 0.848448i | \(-0.322462\pi\) | ||||
0.529279 | + | 0.848448i | \(0.322462\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.62473e6 | −0.425775 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.73510e6 | 0.174625 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.73349e6 | −0.363646 | −0.181823 | − | 0.983331i | \(-0.558200\pi\) | ||||
−0.181823 | + | 0.983331i | \(0.558200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 93778.9 | 0.00590882 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.71654e6 | −0.483015 | −0.241508 | − | 0.970399i | \(-0.577642\pi\) | ||||
−0.241508 | + | 0.970399i | \(0.577642\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −623483. | −0.0387715 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.96294e6 | −0.430169 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.30610e7 | 3.25677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.68723e7 | −1.63866 | −0.819330 | − | 0.573322i | \(-0.805654\pi\) | ||||
−0.819330 | + | 0.573322i | \(0.805654\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.84950e6 | 0.112052 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.92190e6 | −0.175880 | −0.0879401 | − | 0.996126i | \(-0.528028\pi\) | ||||
−0.0879401 | + | 0.996126i | \(0.528028\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.51187e7 | −0.904192 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.45064e6 | −0.0861998 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.14248e7 | 1.26495 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.50861e6 | 0.0885014 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.47064e6 | −0.318885 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.20221e7 | 1.85471 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.40079e7 | 1.38171 | 0.690855 | − | 0.722994i | \(-0.257234\pi\) | ||||
0.690855 | + | 0.722994i | \(0.257234\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.08656e7 | −0.621384 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −998888. | −0.0567644 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.87492e7 | 2.18816 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.88905e7 | −1.06005 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.26503e6 | 0.0705433 | 0.0352717 | − | 0.999378i | \(-0.488770\pi\) | ||||
0.0352717 | + | 0.999378i | \(0.488770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.11593e6 | −0.283503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.16452e6 | 0.174272 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.02990e6 | 0.0563645 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.45718e6 | −0.0792543 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.22002e6 | 0.174050 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.50966e7 | 1.88536 | 0.942679 | − | 0.333702i | \(-0.108298\pi\) | ||||
0.942679 | + | 0.333702i | \(0.108298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.24676e7 | −0.665629 | −0.332814 | − | 0.942992i | \(-0.607998\pi\) | ||||
−0.332814 | + | 0.942992i | \(0.607998\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 284328. | 0.0150866 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.98610e7 | −1.04738 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.95386e7 | −2.59650 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.04667e7 | −0.545255 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.42888e6 | −0.281094 | −0.140547 | − | 0.990074i | \(-0.544886\pi\) | ||||
−0.140547 | + | 0.990074i | \(0.544886\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.65454e7 | −0.851487 | −0.425744 | − | 0.904844i | \(-0.639987\pi\) | ||||
−0.425744 | + | 0.904844i | \(0.639987\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 492568. | 0.0251960 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.05506e7 | 0.536429 | 0.268214 | − | 0.963359i | \(-0.413566\pi\) | ||||
0.268214 | + | 0.963359i | \(0.413566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.49412e6 | 0.429271 | 0.214636 | − | 0.976694i | \(-0.431144\pi\) | ||||
0.214636 | + | 0.976694i | \(0.431144\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.54958e7 | 0.778415 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.23469e6 | −0.0616518 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.77873e7 | −2.37190 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.27082e7 | 1.12039 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.01104e6 | −0.294812 | −0.147406 | − | 0.989076i | \(-0.547092\pi\) | ||||
−0.147406 | + | 0.989076i | \(0.547092\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.76427e7 | −0.860150 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.17204e6 | 0.444526 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.83934e7 | −3.29513 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.84607e6 | −0.375788 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.60377e6 | −0.457270 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.61145e6 | −0.0762768 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.12183e6 | 0.0527903 | 0.0263951 | − | 0.999652i | \(-0.491597\pi\) | ||||
0.0263951 | + | 0.999652i | \(0.491597\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.14083e7 | −1.46936 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.05078e6 | 0.281423 | 0.140711 | − | 0.990051i | \(-0.455061\pi\) | ||||
0.140711 | + | 0.990051i | \(0.455061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.36344e7 | −1.55525 | −0.777625 | − | 0.628728i | \(-0.783576\pi\) | ||||
−0.777625 | + | 0.628728i | \(0.783576\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.40427e6 | −0.156500 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.90095e7 | −0.868846 | −0.434423 | − | 0.900709i | \(-0.643048\pi\) | ||||
−0.434423 | + | 0.900709i | \(0.643048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.39526e7 | 1.99730 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.69095e6 | −0.392663 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18969.5 | −0.000852133 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.64513e7 | −2.52132 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.22035e7 | 0.541938 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.46816e6 | 0.153136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.94632e7 | 1.29354 | 0.646772 | − | 0.762684i | \(-0.276119\pi\) | ||||
0.646772 | + | 0.762684i | \(0.276119\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.59018e7 | −0.694184 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.76458e7 | 1.63409 | 0.817047 | − | 0.576571i | \(-0.195610\pi\) | ||||
0.817047 | + | 0.576571i | \(0.195610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.89106e6 | 0.124783 | 0.0623915 | − | 0.998052i | \(-0.480127\pi\) | ||||
0.0623915 | + | 0.998052i | \(0.480127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.52998e7 | −1.08582 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.21452e7 | 0.945085 | 0.472542 | − | 0.881308i | \(-0.343336\pi\) | ||||
0.472542 | + | 0.881308i | \(0.343336\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.15534e7 | −0.490291 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 639570. | 0.0269894 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.30769e7 | −0.968385 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.68888e7 | −1.12205 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.52885e6 | 0.146438 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.19068e7 | −0.491356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.77806e7 | −0.729683 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.87138e6 | 0.321241 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.40141e7 | 0.974643 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.93856e7 | −1.58972 | −0.794858 | − | 0.606795i | \(-0.792455\pi\) | ||||
−0.794858 | + | 0.606795i | \(0.792455\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.26472e7 | −0.909087 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.88553e6 | −0.0752726 | −0.0376363 | − | 0.999292i | \(-0.511983\pi\) | ||||
−0.0376363 | + | 0.999292i | \(0.511983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.96140e6 | 0.117576 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.84759e7 | −0.729546 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 748544. | 0.0293964 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.46417e7 | 0.571877 | 0.285939 | − | 0.958248i | \(-0.407695\pi\) | ||||
0.285939 | + | 0.958248i | \(0.407695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.32077e7 | −0.513070 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.67683e7 | 2.19332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.46405e6 | −0.325255 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.55117e7 | −0.592870 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.94772e7 | −1.50075 | −0.750373 | − | 0.661014i | \(-0.770126\pi\) | ||||
−0.750373 | + | 0.661014i | \(0.770126\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.56943e6 | −0.210589 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.96427e6 | −0.224312 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.13734e6 | 0.0425463 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.93619e7 | −0.720441 | −0.360221 | − | 0.932867i | \(-0.617299\pi\) | ||||
−0.360221 | + | 0.932867i | \(0.617299\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.64902e7 | −0.610327 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.57379e7 | 1.31569 | 0.657847 | − | 0.753151i | \(-0.271467\pi\) | ||||
0.657847 | + | 0.753151i | \(0.271467\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.78165e6 | −0.138485 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.14959e7 | 0.418757 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.81761e6 | −0.355739 | −0.177869 | − | 0.984054i | \(-0.556920\pi\) | ||||
−0.177869 | + | 0.984054i | \(0.556920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.87546e7 | 1.39687 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.16472e6 | −0.292745 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.44558e7 | −0.515596 | −0.257798 | − | 0.966199i | \(-0.582997\pi\) | ||||
−0.257798 | + | 0.966199i | \(0.582997\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.48186e6 | 0.0525772 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 387925. | 0.0136920 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.25278e6 | 0.254658 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.07951e7 | 0.726361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.17779e6 | −0.214668 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.11562e6 | −0.245977 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.66324e7 | −0.571989 | −0.285995 | − | 0.958231i | \(-0.592324\pi\) | ||||
−0.285995 | + | 0.958231i | \(0.592324\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.97252e6 | 0.306977 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.74729e7 | 0.935098 | 0.467549 | − | 0.883967i | \(-0.345137\pi\) | ||||
0.467549 | + | 0.883967i | \(0.345137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.03056e6 | 0.238072 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.85351e7 | 0.624429 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.45569e7 | −1.49341 | −0.746705 | − | 0.665156i | \(-0.768365\pi\) | ||||
−0.746705 | + | 0.665156i | \(0.768365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −516900. | −0.0172365 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.37204e6 | 0.0786954 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.82935e7 | 1.92414 | 0.962070 | − | 0.272803i | \(-0.0879507\pi\) | ||||
0.962070 | + | 0.272803i | \(0.0879507\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.90384e7 | −2.26725 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.66678e6 | 0.119810 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.74397e6 | 0.284261 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.41083e7 | −0.456343 | −0.228172 | − | 0.973621i | \(-0.573275\pi\) | ||||
−0.228172 | + | 0.973621i | \(0.573275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.33431e7 | 0.429422 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.66797e7 | −1.81497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.20913e6 | 0.134108 | 0.0670540 | − | 0.997749i | \(-0.478640\pi\) | ||||
0.0670540 | + | 0.997749i | \(0.478640\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.27129e7 | 0.403025 |
(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.bb.1.2 | 3 | ||
4.3 | odd | 2 | 448.6.a.ba.1.2 | 3 | |||
8.3 | odd | 2 | 224.6.a.f.1.2 | yes | 3 | ||
8.5 | even | 2 | 224.6.a.e.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.e.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
224.6.a.f.1.2 | yes | 3 | 8.3 | odd | 2 | ||
448.6.a.ba.1.2 | 3 | 4.3 | odd | 2 | |||
448.6.a.bb.1.2 | 3 | 1.1 | even | 1 | trivial |