Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [207,6,Mod(1,207)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(207, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("207.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.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: | \(33.1994507013\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 251 x^{8} + 296 x^{7} + 21169 x^{6} - 9042 x^{5} - 685949 x^{4} - 270764 x^{3} + 6230110 x^{2} + 11573432 x + 5446216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(11.3536\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 207.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.3536 | −1.83028 | −0.915139 | − | 0.403137i | \(-0.867920\pi\) | ||||
−0.915139 | + | 0.403137i | \(0.867920\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 75.1975 | 2.34992 | ||||||||
\(5\) | 71.3591 | 1.27651 | 0.638255 | − | 0.769825i | \(-0.279656\pi\) | ||||
0.638255 | + | 0.769825i | \(0.279656\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −210.967 | −1.62731 | −0.813653 | − | 0.581351i | \(-0.802524\pi\) | ||||
−0.813653 | + | 0.581351i | \(0.802524\pi\) | |||||||
\(8\) | −447.250 | −2.47073 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −738.825 | −2.33637 | ||||||||
\(11\) | 170.188 | 0.424080 | 0.212040 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212040 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 605.525 | 0.993743 | 0.496871 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496871 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(14\) | 2184.27 | 2.97842 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2224.34 | 2.17221 | ||||||||
\(17\) | 1337.03 | 1.12207 | 0.561033 | − | 0.827794i | \(-0.310404\pi\) | ||||
0.561033 | + | 0.827794i | \(0.310404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1794.65 | −1.14050 | −0.570251 | − | 0.821471i | \(-0.693154\pi\) | ||||
−0.570251 | + | 0.821471i | \(0.693154\pi\) | |||||||
\(20\) | 5366.03 | 2.99970 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1762.07 | −0.776185 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1967.12 | 0.629480 | ||||||||
\(26\) | −6269.38 | −1.81883 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −15864.2 | −3.82404 | ||||||||
\(29\) | 3006.00 | 0.663734 | 0.331867 | − | 0.943326i | \(-0.392321\pi\) | ||||
0.331867 | + | 0.943326i | \(0.392321\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9214.34 | −1.72211 | −0.861053 | − | 0.508515i | \(-0.830195\pi\) | ||||
−0.861053 | + | 0.508515i | \(0.830195\pi\) | |||||||
\(32\) | −8717.97 | −1.50501 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13843.1 | −2.05369 | ||||||||
\(35\) | −15054.4 | −2.07727 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6021.35 | 0.723085 | 0.361543 | − | 0.932356i | \(-0.382250\pi\) | ||||
0.361543 | + | 0.932356i | \(0.382250\pi\) | |||||||
\(38\) | 18581.1 | 2.08744 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −31915.4 | −3.15392 | ||||||||
\(41\) | 6606.07 | 0.613739 | 0.306869 | − | 0.951752i | \(-0.400719\pi\) | ||||
0.306869 | + | 0.951752i | \(0.400719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22934.8 | 1.89158 | 0.945790 | − | 0.324779i | \(-0.105290\pi\) | ||||
0.945790 | + | 0.324779i | \(0.105290\pi\) | |||||||
\(44\) | 12797.7 | 0.996555 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5477.07 | −0.381640 | ||||||||
\(47\) | −20179.5 | −1.33250 | −0.666249 | − | 0.745729i | \(-0.732101\pi\) | ||||
−0.666249 | + | 0.745729i | \(0.732101\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 27700.0 | 1.64812 | ||||||||
\(50\) | −20366.9 | −1.15212 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 45534.0 | 2.33522 | ||||||||
\(53\) | −3604.41 | −0.176256 | −0.0881281 | − | 0.996109i | \(-0.528088\pi\) | ||||
−0.0881281 | + | 0.996109i | \(0.528088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12144.5 | 0.541343 | ||||||||
\(56\) | 94355.0 | 4.02064 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −31123.0 | −1.21482 | ||||||||
\(59\) | −37190.1 | −1.39090 | −0.695452 | − | 0.718572i | \(-0.744796\pi\) | ||||
−0.695452 | + | 0.718572i | \(0.744796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31681.4 | −1.09013 | −0.545067 | − | 0.838392i | \(-0.683496\pi\) | ||||
−0.545067 | + | 0.838392i | \(0.683496\pi\) | |||||||
\(62\) | 95401.8 | 3.15194 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 19083.7 | 0.582388 | ||||||||
\(65\) | 43209.8 | 1.26852 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3782.79 | −0.102950 | −0.0514749 | − | 0.998674i | \(-0.516392\pi\) | ||||
−0.0514749 | + | 0.998674i | \(0.516392\pi\) | |||||||
\(68\) | 100541. | 2.63677 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 155868. | 3.80199 | ||||||||
\(71\) | 6321.88 | 0.148833 | 0.0744167 | − | 0.997227i | \(-0.476291\pi\) | ||||
0.0744167 | + | 0.997227i | \(0.476291\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12637.8 | 0.277564 | 0.138782 | − | 0.990323i | \(-0.455681\pi\) | ||||
0.138782 | + | 0.990323i | \(0.455681\pi\) | |||||||
\(74\) | −62342.8 | −1.32345 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −134953. | −2.68009 | ||||||||
\(77\) | −35904.1 | −0.690108 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 79327.3 | 1.43006 | 0.715032 | − | 0.699092i | \(-0.246412\pi\) | ||||
0.715032 | + | 0.699092i | \(0.246412\pi\) | |||||||
\(80\) | 158727. | 2.77285 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −68396.7 | −1.12331 | ||||||||
\(83\) | 114368. | 1.82226 | 0.911130 | − | 0.412118i | \(-0.135211\pi\) | ||||
0.911130 | + | 0.412118i | \(0.135211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 95409.1 | 1.43233 | ||||||||
\(86\) | −237459. | −3.46212 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −76116.8 | −1.04779 | ||||||||
\(89\) | 63683.3 | 0.852217 | 0.426109 | − | 0.904672i | \(-0.359884\pi\) | ||||
0.426109 | + | 0.904672i | \(0.359884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −127746. | −1.61712 | ||||||||
\(92\) | 39779.5 | 0.489992 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 208931. | 2.43884 | ||||||||
\(95\) | −128065. | −1.45586 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 151168. | 1.63129 | 0.815644 | − | 0.578553i | \(-0.196383\pi\) | ||||
0.815644 | + | 0.578553i | \(0.196383\pi\) | |||||||
\(98\) | −286795. | −3.01652 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 147923. | 1.47923 | ||||||||
\(101\) | 188855. | 1.84215 | 0.921074 | − | 0.389387i | \(-0.127313\pi\) | ||||
0.921074 | + | 0.389387i | \(0.127313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 143432. | 1.33215 | 0.666074 | − | 0.745886i | \(-0.267974\pi\) | ||||
0.666074 | + | 0.745886i | \(0.267974\pi\) | |||||||
\(104\) | −270821. | −2.45527 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 37318.7 | 0.322598 | ||||||||
\(107\) | 88610.8 | 0.748216 | 0.374108 | − | 0.927385i | \(-0.377949\pi\) | ||||
0.374108 | + | 0.927385i | \(0.377949\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −94789.3 | −0.764176 | −0.382088 | − | 0.924126i | \(-0.624795\pi\) | ||||
−0.382088 | + | 0.924126i | \(0.624795\pi\) | |||||||
\(110\) | −125739. | −0.990809 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −469262. | −3.53485 | ||||||||
\(113\) | 84969.6 | 0.625990 | 0.312995 | − | 0.949755i | \(-0.398668\pi\) | ||||
0.312995 | + | 0.949755i | \(0.398668\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 37749.0 | 0.266171 | ||||||||
\(116\) | 226044. | 1.55972 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 385052. | 2.54574 | ||||||||
\(119\) | −282069. | −1.82594 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −132087. | −0.820156 | ||||||||
\(122\) | 328018. | 1.99525 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −692895. | −4.04681 | ||||||||
\(125\) | −82625.0 | −0.472973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −826.453 | −0.00454683 | −0.00227342 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227342 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(128\) | 81389.9 | 0.439082 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −447378. | −2.32175 | ||||||||
\(131\) | 262321. | 1.33554 | 0.667768 | − | 0.744370i | \(-0.267250\pi\) | ||||
0.667768 | + | 0.744370i | \(0.267250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 378612. | 1.85594 | ||||||||
\(134\) | 39165.6 | 0.188427 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −597986. | −2.77232 | ||||||||
\(137\) | −12970.6 | −0.0590415 | −0.0295207 | − | 0.999564i | \(-0.509398\pi\) | ||||
−0.0295207 | + | 0.999564i | \(0.509398\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −89440.8 | −0.392644 | −0.196322 | − | 0.980539i | \(-0.562900\pi\) | ||||
−0.196322 | + | 0.980539i | \(0.562900\pi\) | |||||||
\(140\) | −1.13205e6 | −4.88143 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −65454.4 | −0.272407 | ||||||||
\(143\) | 103053. | 0.421427 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 214506. | 0.847264 | ||||||||
\(146\) | −130847. | −0.508020 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 452790. | 1.69919 | ||||||||
\(149\) | 317159. | 1.17034 | 0.585170 | − | 0.810911i | \(-0.301028\pi\) | ||||
0.585170 | + | 0.810911i | \(0.301028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −96753.6 | −0.345322 | −0.172661 | − | 0.984981i | \(-0.555237\pi\) | ||||
−0.172661 | + | 0.984981i | \(0.555237\pi\) | |||||||
\(152\) | 802658. | 2.81787 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 371737. | 1.26309 | ||||||||
\(155\) | −657527. | −2.19829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 133196. | 0.431261 | 0.215631 | − | 0.976475i | \(-0.430819\pi\) | ||||
0.215631 | + | 0.976475i | \(0.430819\pi\) | |||||||
\(158\) | −821325. | −2.61741 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −622107. | −1.92117 | ||||||||
\(161\) | −111601. | −0.339317 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 45781.6 | 0.134965 | 0.0674827 | − | 0.997720i | \(-0.478503\pi\) | ||||
0.0674827 | + | 0.997720i | \(0.478503\pi\) | |||||||
\(164\) | 496760. | 1.44224 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.18413e6 | −3.33525 | ||||||||
\(167\) | −38039.4 | −0.105546 | −0.0527731 | − | 0.998607i | \(-0.516806\pi\) | ||||
−0.0527731 | + | 0.998607i | \(0.516806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4631.97 | −0.0124752 | ||||||||
\(170\) | −987830. | −2.62156 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.72464e6 | 4.44506 | ||||||||
\(173\) | 685175. | 1.74055 | 0.870275 | − | 0.492566i | \(-0.163941\pi\) | ||||
0.870275 | + | 0.492566i | \(0.163941\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −414998. | −1.02436 | ||||||||
\(176\) | 378557. | 0.921190 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −659352. | −1.55980 | ||||||||
\(179\) | 326298. | 0.761170 | 0.380585 | − | 0.924746i | \(-0.375723\pi\) | ||||
0.380585 | + | 0.924746i | \(0.375723\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −359932. | −0.816627 | −0.408313 | − | 0.912842i | \(-0.633883\pi\) | ||||
−0.408313 | + | 0.912842i | \(0.633883\pi\) | |||||||
\(182\) | 1.32263e6 | 2.95979 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −236595. | −0.515183 | ||||||||
\(185\) | 429678. | 0.923026 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 227547. | 0.475846 | ||||||||
\(188\) | −1.51745e6 | −3.13126 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.32593e6 | 2.66463 | ||||||||
\(191\) | −310829. | −0.616508 | −0.308254 | − | 0.951304i | \(-0.599745\pi\) | ||||
−0.308254 | + | 0.951304i | \(0.599745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −136244. | −0.263284 | −0.131642 | − | 0.991297i | \(-0.542025\pi\) | ||||
−0.131642 | + | 0.991297i | \(0.542025\pi\) | |||||||
\(194\) | −1.56514e6 | −2.98571 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.08297e6 | 3.87296 | ||||||||
\(197\) | −823205. | −1.51127 | −0.755635 | − | 0.654992i | \(-0.772672\pi\) | ||||
−0.755635 | + | 0.654992i | \(0.772672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 654175. | 1.17101 | 0.585506 | − | 0.810668i | \(-0.300896\pi\) | ||||
0.585506 | + | 0.810668i | \(0.300896\pi\) | |||||||
\(200\) | −879797. | −1.55528 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.95533e6 | −3.37165 | ||||||||
\(203\) | −634167. | −1.08010 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 471403. | 0.783444 | ||||||||
\(206\) | −1.48504e6 | −2.43820 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.34689e6 | 2.15862 | ||||||||
\(209\) | −305428. | −0.483664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 812196. | 1.25590 | 0.627950 | − | 0.778254i | \(-0.283894\pi\) | ||||
0.627950 | + | 0.778254i | \(0.283894\pi\) | |||||||
\(212\) | −271043. | −0.414188 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −917442. | −1.36944 | ||||||||
\(215\) | 1.63661e6 | 2.41462 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.94392e6 | 2.80239 | ||||||||
\(218\) | 981413. | 1.39865 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 913235. | 1.27211 | ||||||||
\(221\) | 809604. | 1.11504 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −252062. | −0.339426 | −0.169713 | − | 0.985494i | \(-0.554284\pi\) | ||||
−0.169713 | + | 0.985494i | \(0.554284\pi\) | |||||||
\(224\) | 1.83920e6 | 2.44912 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −879744. | −1.14574 | ||||||||
\(227\) | 999309. | 1.28717 | 0.643584 | − | 0.765376i | \(-0.277447\pi\) | ||||
0.643584 | + | 0.765376i | \(0.277447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 963621. | 1.21428 | 0.607138 | − | 0.794596i | \(-0.292317\pi\) | ||||
0.607138 | + | 0.794596i | \(0.292317\pi\) | |||||||
\(230\) | −390839. | −0.487167 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.34444e6 | −1.63991 | ||||||||
\(233\) | −86902.2 | −0.104868 | −0.0524338 | − | 0.998624i | \(-0.516698\pi\) | ||||
−0.0524338 | + | 0.998624i | \(0.516698\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.43999e6 | −1.70095 | ||||||||
\(236\) | −2.79660e6 | −3.26852 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.92043e6 | 3.34199 | ||||||||
\(239\) | 1.42740e6 | 1.61641 | 0.808206 | − | 0.588900i | \(-0.200439\pi\) | ||||
0.808206 | + | 0.588900i | \(0.200439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −137084. | −0.152035 | −0.0760176 | − | 0.997106i | \(-0.524221\pi\) | ||||
−0.0760176 | + | 0.997106i | \(0.524221\pi\) | |||||||
\(242\) | 1.36758e6 | 1.50111 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.38236e6 | −2.56173 | ||||||||
\(245\) | 1.97665e6 | 2.10385 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.08671e6 | −1.13336 | ||||||||
\(248\) | 4.12112e6 | 4.25486 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 855468. | 0.865672 | ||||||||
\(251\) | −947694. | −0.949476 | −0.474738 | − | 0.880127i | \(-0.657457\pi\) | ||||
−0.474738 | + | 0.880127i | \(0.657457\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 90029.6 | 0.0884269 | ||||||||
\(254\) | 8556.78 | 0.00832197 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.45336e6 | −1.38603 | ||||||||
\(257\) | 1.25100e6 | 1.18148 | 0.590739 | − | 0.806862i | \(-0.298836\pi\) | ||||
0.590739 | + | 0.806862i | \(0.298836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.27030e6 | −1.17668 | ||||||||
\(260\) | 3.24926e6 | 2.98093 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.71598e6 | −2.44440 | ||||||||
\(263\) | −305663. | −0.272492 | −0.136246 | − | 0.990675i | \(-0.543504\pi\) | ||||
−0.136246 | + | 0.990675i | \(0.543504\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −257208. | −0.224993 | ||||||||
\(266\) | −3.92000e6 | −3.39689 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −284456. | −0.241924 | ||||||||
\(269\) | −712.235 | −0.000600127 0 | −0.000300063 | − | 1.00000i | \(-0.500096\pi\) | ||||
−0.000300063 | 1.00000i | \(0.500096\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −726592. | −0.600990 | −0.300495 | − | 0.953783i | \(-0.597152\pi\) | ||||
−0.300495 | + | 0.953783i | \(0.597152\pi\) | |||||||
\(272\) | 2.97401e6 | 2.43736 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 134292. | 0.108062 | ||||||||
\(275\) | 334782. | 0.266950 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −650868. | −0.509675 | −0.254837 | − | 0.966984i | \(-0.582022\pi\) | ||||
−0.254837 | + | 0.966984i | \(0.582022\pi\) | |||||||
\(278\) | 926036. | 0.718648 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.73309e6 | 5.13238 | ||||||||
\(281\) | −667888. | −0.504589 | −0.252294 | − | 0.967650i | \(-0.581185\pi\) | ||||
−0.252294 | + | 0.967650i | \(0.581185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.91825e6 | −1.42377 | −0.711883 | − | 0.702298i | \(-0.752157\pi\) | ||||
−0.711883 | + | 0.702298i | \(0.752157\pi\) | |||||||
\(284\) | 475390. | 0.349747 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.06698e6 | −0.771328 | ||||||||
\(287\) | −1.39366e6 | −0.998740 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 367787. | 0.259031 | ||||||||
\(290\) | −2.22091e6 | −1.55073 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 950328. | 0.652254 | ||||||||
\(293\) | −357387. | −0.243203 | −0.121602 | − | 0.992579i | \(-0.538803\pi\) | ||||
−0.121602 | + | 0.992579i | \(0.538803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.65385e6 | −1.77550 | ||||||||
\(296\) | −2.69305e6 | −1.78655 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.28375e6 | −2.14205 | ||||||||
\(299\) | 320323. | 0.207210 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.83849e6 | −3.07818 | ||||||||
\(302\) | 1.00175e6 | 0.632036 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.99191e6 | −2.47741 | ||||||||
\(305\) | −2.26076e6 | −1.39157 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 242810. | 0.147035 | 0.0735176 | − | 0.997294i | \(-0.476577\pi\) | ||||
0.0735176 | + | 0.997294i | \(0.476577\pi\) | |||||||
\(308\) | −2.69990e6 | −1.62170 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.80779e6 | 4.02348 | ||||||||
\(311\) | 510526. | 0.299307 | 0.149654 | − | 0.988738i | \(-0.452184\pi\) | ||||
0.149654 | + | 0.988738i | \(0.452184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 268272. | 0.154780 | 0.0773901 | − | 0.997001i | \(-0.475341\pi\) | ||||
0.0773901 | + | 0.997001i | \(0.475341\pi\) | |||||||
\(314\) | −1.37906e6 | −0.789328 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.96522e6 | 3.36054 | ||||||||
\(317\) | −1.17566e6 | −0.657102 | −0.328551 | − | 0.944486i | \(-0.606560\pi\) | ||||
−0.328551 | + | 0.944486i | \(0.606560\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 511586. | 0.281477 | ||||||||
\(320\) | 1.36180e6 | 0.743424 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.15548e6 | 0.621044 | ||||||||
\(323\) | −2.39950e6 | −1.27972 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.19114e6 | 0.625541 | ||||||||
\(326\) | −474006. | −0.247024 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.95457e6 | −1.51638 | ||||||||
\(329\) | 4.25721e6 | 2.16838 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.74833e6 | 1.88047 | 0.940237 | − | 0.340520i | \(-0.110603\pi\) | ||||
0.940237 | + | 0.340520i | \(0.110603\pi\) | |||||||
\(332\) | 8.60021e6 | 4.28217 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 393846. | 0.193179 | ||||||||
\(335\) | −269937. | −0.131417 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.05514e6 | −1.46540 | −0.732701 | − | 0.680551i | \(-0.761740\pi\) | ||||
−0.732701 | + | 0.680551i | \(0.761740\pi\) | |||||||
\(338\) | 47957.7 | 0.0228332 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.17453e6 | 3.36586 | ||||||||
\(341\) | −1.56817e6 | −0.730312 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.29806e6 | −1.05469 | ||||||||
\(344\) | −1.02576e7 | −4.67359 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.09405e6 | −3.18569 | ||||||||
\(347\) | 4.00997e6 | 1.78779 | 0.893896 | − | 0.448274i | \(-0.147961\pi\) | ||||
0.893896 | + | 0.448274i | \(0.147961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.17172e6 | 0.514944 | 0.257472 | − | 0.966286i | \(-0.417111\pi\) | ||||
0.257472 | + | 0.966286i | \(0.417111\pi\) | |||||||
\(350\) | 4.29673e6 | 1.87486 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.48370e6 | −0.638247 | ||||||||
\(353\) | −2.17711e6 | −0.929917 | −0.464958 | − | 0.885333i | \(-0.653931\pi\) | ||||
−0.464958 | + | 0.885333i | \(0.653931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 451124. | 0.189988 | ||||||||
\(356\) | 4.78882e6 | 2.00264 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.37837e6 | −1.39315 | ||||||||
\(359\) | −1.01162e6 | −0.414269 | −0.207135 | − | 0.978312i | \(-0.566414\pi\) | ||||
−0.207135 | + | 0.978312i | \(0.566414\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 744669. | 0.300743 | ||||||||
\(362\) | 3.72660e6 | 1.49465 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.60616e6 | −3.80011 | ||||||||
\(365\) | 901820. | 0.354313 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.83005e6 | −0.709249 | −0.354625 | − | 0.935009i | \(-0.615391\pi\) | ||||
−0.354625 | + | 0.935009i | \(0.615391\pi\) | |||||||
\(368\) | 1.17668e6 | 0.452937 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.44872e6 | −1.68939 | ||||||||
\(371\) | 760411. | 0.286823 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 206897. | 0.0769986 | 0.0384993 | − | 0.999259i | \(-0.487742\pi\) | ||||
0.0384993 | + | 0.999259i | \(0.487742\pi\) | |||||||
\(374\) | −2.35593e6 | −0.870931 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.02530e6 | 3.29225 | ||||||||
\(377\) | 1.82021e6 | 0.659581 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.49105e6 | 1.60602 | 0.803008 | − | 0.595968i | \(-0.203232\pi\) | ||||
0.803008 | + | 0.595968i | \(0.203232\pi\) | |||||||
\(380\) | −9.63014e6 | −3.42116 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.21821e6 | 1.12838 | ||||||||
\(383\) | 2.30581e6 | 0.803204 | 0.401602 | − | 0.915814i | \(-0.368453\pi\) | ||||
0.401602 | + | 0.915814i | \(0.368453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.56208e6 | −0.880930 | ||||||||
\(386\) | 1.41062e6 | 0.481883 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.13675e7 | 3.83340 | ||||||||
\(389\) | −1.17176e6 | −0.392612 | −0.196306 | − | 0.980543i | \(-0.562895\pi\) | ||||
−0.196306 | + | 0.980543i | \(0.562895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 707288. | 0.233967 | ||||||||
\(392\) | −1.23888e7 | −4.07207 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.52315e6 | 2.76605 | ||||||||
\(395\) | 5.66073e6 | 1.82549 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.03765e6 | 0.330428 | 0.165214 | − | 0.986258i | \(-0.447169\pi\) | ||||
0.165214 | + | 0.986258i | \(0.447169\pi\) | |||||||
\(398\) | −6.77308e6 | −2.14328 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.37556e6 | 1.36736 | ||||||||
\(401\) | −6.13691e6 | −1.90585 | −0.952925 | − | 0.303205i | \(-0.901943\pi\) | ||||
−0.952925 | + | 0.303205i | \(0.901943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.57952e6 | −1.71133 | ||||||||
\(404\) | 1.42014e7 | 4.32890 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.56592e6 | 1.97688 | ||||||||
\(407\) | 1.02476e6 | 0.306646 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.13261e6 | −0.630380 | −0.315190 | − | 0.949029i | \(-0.602068\pi\) | ||||
−0.315190 | + | 0.949029i | \(0.602068\pi\) | |||||||
\(410\) | −4.88073e6 | −1.43392 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.07857e7 | 3.13044 | ||||||||
\(413\) | 7.84588e6 | 2.26343 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.16122e6 | 2.32614 | ||||||||
\(416\) | −5.27895e6 | −1.49560 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.16229e6 | 0.885240 | ||||||||
\(419\) | 6.05469e6 | 1.68483 | 0.842417 | − | 0.538826i | \(-0.181132\pi\) | ||||
0.842417 | + | 0.538826i | \(0.181132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.62140e6 | −1.27077 | −0.635386 | − | 0.772194i | \(-0.719159\pi\) | ||||
−0.635386 | + | 0.772194i | \(0.719159\pi\) | |||||||
\(422\) | −8.40917e6 | −2.29865 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.61207e6 | 0.435482 | ||||||||
\(425\) | 2.63010e6 | 0.706318 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.68373e6 | 1.77398 | ||||||||
\(428\) | 6.66331e6 | 1.75825 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.69448e7 | −4.41943 | ||||||||
\(431\) | −1.49369e6 | −0.387319 | −0.193659 | − | 0.981069i | \(-0.562036\pi\) | ||||
−0.193659 | + | 0.981069i | \(0.562036\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.44271e6 | −1.90770 | −0.953852 | − | 0.300276i | \(-0.902921\pi\) | ||||
−0.953852 | + | 0.300276i | \(0.902921\pi\) | |||||||
\(434\) | −2.01266e7 | −5.12916 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.12792e6 | −1.79575 | ||||||||
\(437\) | −949370. | −0.237811 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.11446e6 | −0.523647 | −0.261823 | − | 0.965116i | \(-0.584324\pi\) | ||||
−0.261823 | + | 0.965116i | \(0.584324\pi\) | |||||||
\(440\) | −5.43163e6 | −1.33751 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.38234e6 | −2.04084 | ||||||||
\(443\) | −2.16454e6 | −0.524031 | −0.262015 | − | 0.965064i | \(-0.584387\pi\) | ||||
−0.262015 | + | 0.965064i | \(0.584387\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.54438e6 | 1.08786 | ||||||||
\(446\) | 2.60975e6 | 0.621244 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.02602e6 | −0.947723 | ||||||||
\(449\) | −5.65548e6 | −1.32390 | −0.661948 | − | 0.749550i | \(-0.730270\pi\) | ||||
−0.661948 | + | 0.749550i | \(0.730270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.12428e6 | 0.260274 | ||||||||
\(452\) | 6.38950e6 | 1.47103 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.03465e7 | −2.35588 | ||||||||
\(455\) | −9.11583e6 | −2.06427 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 213062. | 0.0477216 | 0.0238608 | − | 0.999715i | \(-0.492404\pi\) | ||||
0.0238608 | + | 0.999715i | \(0.492404\pi\) | |||||||
\(458\) | −9.97697e6 | −2.22246 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.83863e6 | 0.625481 | ||||||||
\(461\) | −2.84868e6 | −0.624296 | −0.312148 | − | 0.950033i | \(-0.601049\pi\) | ||||
−0.312148 | + | 0.950033i | \(0.601049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −981530. | −0.212790 | −0.106395 | − | 0.994324i | \(-0.533931\pi\) | ||||
−0.106395 | + | 0.994324i | \(0.533931\pi\) | |||||||
\(464\) | 6.68637e6 | 1.44177 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 899753. | 0.191937 | ||||||||
\(467\) | −1.12083e6 | −0.237820 | −0.118910 | − | 0.992905i | \(-0.537940\pi\) | ||||
−0.118910 | + | 0.992905i | \(0.537940\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 798043. | 0.167531 | ||||||||
\(470\) | 1.49092e7 | 3.11321 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.66333e7 | 3.43655 | ||||||||
\(473\) | 3.90324e6 | 0.802182 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.53030e6 | −0.717923 | ||||||||
\(476\) | −2.12108e7 | −4.29082 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.47788e7 | −2.95848 | ||||||||
\(479\) | −8.75292e6 | −1.74307 | −0.871534 | − | 0.490335i | \(-0.836874\pi\) | ||||
−0.871534 | + | 0.490335i | \(0.836874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.64608e6 | 0.718561 | ||||||||
\(482\) | 1.41932e6 | 0.278267 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.93260e6 | −1.92730 | ||||||||
\(485\) | 1.07872e7 | 2.08236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.58029e6 | 0.875126 | 0.437563 | − | 0.899188i | \(-0.355842\pi\) | ||||
0.437563 | + | 0.899188i | \(0.355842\pi\) | |||||||
\(488\) | 1.41695e7 | 2.69343 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.04655e7 | −3.85062 | ||||||||
\(491\) | −3.32030e6 | −0.621546 | −0.310773 | − | 0.950484i | \(-0.600588\pi\) | ||||
−0.310773 | + | 0.950484i | \(0.600588\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.01911e6 | 0.744753 | ||||||||
\(494\) | 1.12513e7 | 2.07437 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.04958e7 | −3.74077 | ||||||||
\(497\) | −1.33371e6 | −0.242197 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.33617e6 | 1.67848 | 0.839242 | − | 0.543758i | \(-0.182999\pi\) | ||||
0.839242 | + | 0.543758i | \(0.182999\pi\) | |||||||
\(500\) | −6.21319e6 | −1.11145 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.81207e6 | 1.73781 | ||||||||
\(503\) | −7.75961e6 | −1.36748 | −0.683738 | − | 0.729728i | \(-0.739647\pi\) | ||||
−0.683738 | + | 0.729728i | \(0.739647\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.34765e7 | 2.35152 | ||||||||
\(506\) | −932133. | −0.161846 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −62147.2 | −0.0106847 | ||||||||
\(509\) | 8.78414e6 | 1.50281 | 0.751406 | − | 0.659840i | \(-0.229376\pi\) | ||||
0.751406 | + | 0.659840i | \(0.229376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.66615e6 | −0.451681 | ||||||||
\(512\) | 1.24430e7 | 2.09774 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.29524e7 | −2.16244 | ||||||||
\(515\) | 1.02352e7 | 1.70050 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.43432e6 | −0.565086 | ||||||||
\(518\) | 1.31523e7 | 2.15365 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.93256e7 | −3.13418 | ||||||||
\(521\) | −6.42822e6 | −1.03752 | −0.518760 | − | 0.854920i | \(-0.673606\pi\) | ||||
−0.518760 | + | 0.854920i | \(0.673606\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.75955e6 | −0.760872 | −0.380436 | − | 0.924807i | \(-0.624226\pi\) | ||||
−0.380436 | + | 0.924807i | \(0.624226\pi\) | |||||||
\(524\) | 1.97259e7 | 3.13840 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.16472e6 | 0.498736 | ||||||||
\(527\) | −1.23198e7 | −1.93232 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 2.66303e6 | 0.411800 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.84706e7 | 4.36132 | ||||||||
\(533\) | 4.00014e6 | 0.609898 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.32319e6 | 0.955106 | ||||||||
\(536\) | 1.69185e6 | 0.254361 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7374.22 | 0.00109840 | ||||||||
\(539\) | 4.71422e6 | 0.698936 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.85812e6 | 1.15432 | 0.577159 | − | 0.816632i | \(-0.304161\pi\) | ||||
0.577159 | + | 0.816632i | \(0.304161\pi\) | |||||||
\(542\) | 7.52286e6 | 1.09998 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.16562e7 | −1.68872 | ||||||||
\(545\) | −6.76408e6 | −0.975479 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.00196e7 | 1.43180 | 0.715902 | − | 0.698201i | \(-0.246016\pi\) | ||||
0.715902 | + | 0.698201i | \(0.246016\pi\) | |||||||
\(548\) | −975353. | −0.138743 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.46620e6 | −0.488593 | ||||||||
\(551\) | −5.39472e6 | −0.756990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.67354e7 | −2.32715 | ||||||||
\(554\) | 6.73884e6 | 0.932847 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.72572e6 | −0.922682 | ||||||||
\(557\) | −5.74512e6 | −0.784623 | −0.392312 | − | 0.919832i | \(-0.628325\pi\) | ||||
−0.392312 | + | 0.919832i | \(0.628325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.38876e7 | 1.87974 | ||||||||
\(560\) | −3.34861e7 | −4.51227 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.91506e6 | 0.923539 | ||||||||
\(563\) | 1.23215e6 | 0.163829 | 0.0819146 | − | 0.996639i | \(-0.473897\pi\) | ||||
0.0819146 | + | 0.996639i | \(0.473897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.06336e6 | 0.799084 | ||||||||
\(566\) | 1.98608e7 | 2.60589 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.82746e6 | −0.367728 | ||||||||
\(569\) | 8.80266e6 | 1.13981 | 0.569906 | − | 0.821710i | \(-0.306980\pi\) | ||||
0.569906 | + | 0.821710i | \(0.306980\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.49333e6 | −0.961800 | −0.480900 | − | 0.876776i | \(-0.659690\pi\) | ||||
−0.480900 | + | 0.876776i | \(0.659690\pi\) | |||||||
\(572\) | 7.74935e6 | 0.990320 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.44294e7 | 1.82797 | ||||||||
\(575\) | 1.04061e6 | 0.131256 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.36469e7 | −1.70646 | −0.853228 | − | 0.521538i | \(-0.825358\pi\) | ||||
−0.853228 | + | 0.521538i | \(0.825358\pi\) | |||||||
\(578\) | −3.80793e6 | −0.474099 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.61303e7 | 1.99100 | ||||||||
\(581\) | −2.41279e7 | −2.96537 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −613429. | −0.0747468 | ||||||||
\(584\) | −5.65224e6 | −0.685786 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.70024e6 | 0.445130 | ||||||||
\(587\) | 2.92745e6 | 0.350666 | 0.175333 | − | 0.984509i | \(-0.443900\pi\) | ||||
0.175333 | + | 0.984509i | \(0.443900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.65365e7 | 1.96406 | ||||||||
\(590\) | 2.74770e7 | 3.24967 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.33935e7 | 1.57069 | ||||||||
\(593\) | 5.29722e6 | 0.618603 | 0.309301 | − | 0.950964i | \(-0.399905\pi\) | ||||
0.309301 | + | 0.950964i | \(0.399905\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.01282e7 | −2.33084 | ||||||||
\(596\) | 2.38496e7 | 2.75020 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.31650e6 | −0.379252 | ||||||||
\(599\) | −1.35436e7 | −1.54229 | −0.771147 | − | 0.636657i | \(-0.780317\pi\) | ||||
−0.771147 | + | 0.636657i | \(0.780317\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.10785e6 | −0.350973 | −0.175486 | − | 0.984482i | \(-0.556150\pi\) | ||||
−0.175486 | + | 0.984482i | \(0.556150\pi\) | |||||||
\(602\) | 5.00959e7 | 5.63392 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.27562e6 | −0.811480 | ||||||||
\(605\) | −9.42561e6 | −1.04694 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.80425e6 | −0.639402 | −0.319701 | − | 0.947518i | \(-0.603582\pi\) | ||||
−0.319701 | + | 0.947518i | \(0.603582\pi\) | |||||||
\(608\) | 1.56457e7 | 1.71647 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.34070e7 | 2.54696 | ||||||||
\(611\) | −1.22192e7 | −1.32416 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.53122e6 | −0.272069 | −0.136035 | − | 0.990704i | \(-0.543436\pi\) | ||||
−0.136035 | + | 0.990704i | \(0.543436\pi\) | |||||||
\(614\) | −2.51397e6 | −0.269115 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.60581e7 | 1.70507 | ||||||||
\(617\) | 1.03128e7 | 1.09059 | 0.545296 | − | 0.838244i | \(-0.316417\pi\) | ||||
0.545296 | + | 0.838244i | \(0.316417\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.15021e6 | −0.435355 | −0.217677 | − | 0.976021i | \(-0.569848\pi\) | ||||
−0.217677 | + | 0.976021i | \(0.569848\pi\) | |||||||
\(620\) | −4.94444e7 | −5.16580 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.28580e6 | −0.547816 | ||||||||
\(623\) | −1.34351e7 | −1.38682 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20433e7 | −1.23323 | ||||||||
\(626\) | −2.77759e6 | −0.283291 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.00160e7 | 1.01343 | ||||||||
\(629\) | 8.05071e6 | 0.811349 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.70512e7 | 1.70483 | 0.852416 | − | 0.522864i | \(-0.175136\pi\) | ||||
0.852416 | + | 0.522864i | \(0.175136\pi\) | |||||||
\(632\) | −3.54792e7 | −3.53330 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.21723e7 | 1.20268 | ||||||||
\(635\) | −58975.0 | −0.00580408 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.67730e7 | 1.63781 | ||||||||
\(638\) | −5.29677e6 | −0.515181 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.80791e6 | 0.560493 | ||||||||
\(641\) | 1.64702e7 | 1.58327 | 0.791633 | − | 0.610997i | \(-0.209231\pi\) | ||||
0.791633 | + | 0.610997i | \(0.209231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.28693e6 | 0.599668 | 0.299834 | − | 0.953991i | \(-0.403069\pi\) | ||||
0.299834 | + | 0.953991i | \(0.403069\pi\) | |||||||
\(644\) | −8.39215e6 | −0.797367 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.48435e7 | 2.34224 | ||||||||
\(647\) | −5.21472e6 | −0.489746 | −0.244873 | − | 0.969555i | \(-0.578746\pi\) | ||||
−0.244873 | + | 0.969555i | \(0.578746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.32932e6 | −0.589855 | ||||||||
\(650\) | −1.23327e7 | −1.14491 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.44266e6 | 0.317158 | ||||||||
\(653\) | 4.72335e6 | 0.433479 | 0.216739 | − | 0.976230i | \(-0.430458\pi\) | ||||
0.216739 | + | 0.976230i | \(0.430458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.87190e7 | 1.70483 | ||||||||
\(656\) | 1.46941e7 | 1.33317 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.40776e7 | −3.96874 | ||||||||
\(659\) | 5.27529e6 | 0.473187 | 0.236593 | − | 0.971609i | \(-0.423969\pi\) | ||||
0.236593 | + | 0.971609i | \(0.423969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.64941e6 | 0.235855 | 0.117928 | − | 0.993022i | \(-0.462375\pi\) | ||||
0.117928 | + | 0.993022i | \(0.462375\pi\) | |||||||
\(662\) | −3.88088e7 | −3.44179 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.11513e7 | −4.50232 | ||||||||
\(665\) | 2.70174e7 | 2.36913 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.59018e6 | 0.138398 | ||||||||
\(668\) | −2.86047e6 | −0.248025 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.79482e6 | 0.240529 | ||||||||
\(671\) | −5.39181e6 | −0.462305 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.58779e6 | −0.220237 | −0.110119 | − | 0.993918i | \(-0.535123\pi\) | ||||
−0.110119 | + | 0.993918i | \(0.535123\pi\) | |||||||
\(674\) | 3.16318e7 | 2.68209 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −348313. | −0.0293158 | ||||||||
\(677\) | 1.06620e7 | 0.894064 | 0.447032 | − | 0.894518i | \(-0.352481\pi\) | ||||
0.447032 | + | 0.894518i | \(0.352481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.18915e7 | −2.65461 | ||||||||
\(680\) | −4.26718e7 | −3.53890 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.62363e7 | 1.33667 | ||||||||
\(683\) | −1.21075e7 | −0.993119 | −0.496559 | − | 0.868003i | \(-0.665404\pi\) | ||||
−0.496559 | + | 0.868003i | \(0.665404\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −925568. | −0.0753671 | ||||||||
\(686\) | 2.37932e7 | 1.93038 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.10149e7 | 4.10890 | ||||||||
\(689\) | −2.18256e6 | −0.175153 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.66501e7 | 1.32654 | 0.663271 | − | 0.748379i | \(-0.269168\pi\) | ||||
0.663271 | + | 0.748379i | \(0.269168\pi\) | |||||||
\(692\) | 5.15235e7 | 4.09015 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.15177e7 | −3.27216 | ||||||||
\(695\) | −6.38242e6 | −0.501214 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.83250e6 | 0.688655 | ||||||||
\(698\) | −1.21315e7 | −0.942490 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.12068e7 | −2.40716 | ||||||||
\(701\) | −569003. | −0.0437340 | −0.0218670 | − | 0.999761i | \(-0.506961\pi\) | ||||
−0.0218670 | + | 0.999761i | \(0.506961\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.08062e7 | −0.824679 | ||||||||
\(704\) | 3.24782e6 | 0.246979 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.25410e7 | 1.70201 | ||||||||
\(707\) | −3.98421e7 | −2.99774 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.70513e6 | −0.127392 | −0.0636959 | − | 0.997969i | \(-0.520289\pi\) | ||||
−0.0636959 | + | 0.997969i | \(0.520289\pi\) | |||||||
\(710\) | −4.67077e6 | −0.347730 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.84824e7 | −2.10560 | ||||||||
\(713\) | −4.87439e6 | −0.359084 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.35380e6 | 0.537956 | ||||||||
\(716\) | 2.45368e7 | 1.78869 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.04740e7 | 0.758228 | ||||||||
\(719\) | −7.59885e6 | −0.548183 | −0.274092 | − | 0.961704i | \(-0.588377\pi\) | ||||
−0.274092 | + | 0.961704i | \(0.588377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.02593e7 | −2.16781 | ||||||||
\(722\) | −7.71002e6 | −0.550443 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.70660e7 | −1.91901 | ||||||||
\(725\) | 5.91318e6 | 0.417807 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.24703e6 | 0.508539 | 0.254269 | − | 0.967133i | \(-0.418165\pi\) | ||||
0.254269 | + | 0.967133i | \(0.418165\pi\) | |||||||
\(728\) | 5.71343e7 | 3.99548 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.33710e6 | −0.648493 | ||||||||
\(731\) | 3.06645e7 | 2.12248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.57843e6 | 0.314743 | 0.157372 | − | 0.987539i | \(-0.449698\pi\) | ||||
0.157372 | + | 0.987539i | \(0.449698\pi\) | |||||||
\(734\) | 1.89477e7 | 1.29812 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.61181e6 | −0.313817 | ||||||||
\(737\) | −643787. | −0.0436590 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.79403e7 | −1.20842 | −0.604211 | − | 0.796825i | \(-0.706511\pi\) | ||||
−0.604211 | + | 0.796825i | \(0.706511\pi\) | |||||||
\(740\) | 3.23107e7 | 2.16904 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.87301e6 | −0.524966 | ||||||||
\(743\) | 1.58719e7 | 1.05477 | 0.527383 | − | 0.849628i | \(-0.323173\pi\) | ||||
0.527383 | + | 0.849628i | \(0.323173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.26322e7 | 1.49395 | ||||||||
\(746\) | −2.14214e6 | −0.140929 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.71109e7 | 1.11820 | ||||||||
\(749\) | −1.86939e7 | −1.21758 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.95699e7 | −1.91316 | −0.956578 | − | 0.291478i | \(-0.905853\pi\) | ||||
−0.956578 | + | 0.291478i | \(0.905853\pi\) | |||||||
\(752\) | −4.48862e7 | −2.89446 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.88458e7 | −1.20722 | ||||||||
\(755\) | −6.90425e6 | −0.440808 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.81021e6 | 0.622212 | 0.311106 | − | 0.950375i | \(-0.399301\pi\) | ||||
0.311106 | + | 0.950375i | \(0.399301\pi\) | |||||||
\(758\) | −4.64986e7 | −2.93946 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.72769e7 | 3.59704 | ||||||||
\(761\) | 1.09443e7 | 0.685056 | 0.342528 | − | 0.939508i | \(-0.388717\pi\) | ||||
0.342528 | + | 0.939508i | \(0.388717\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.99974e7 | 1.24355 | ||||||||
\(764\) | −2.33736e7 | −1.44874 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.38735e7 | −1.47009 | ||||||||
\(767\) | −2.25196e7 | −1.38220 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.68373e6 | 0.285612 | 0.142806 | − | 0.989751i | \(-0.454388\pi\) | ||||
0.142806 | + | 0.989751i | \(0.454388\pi\) | |||||||
\(770\) | 2.65269e7 | 1.61235 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.02452e7 | −0.618697 | ||||||||
\(773\) | 1.32674e7 | 0.798612 | 0.399306 | − | 0.916818i | \(-0.369251\pi\) | ||||
0.399306 | + | 0.916818i | \(0.369251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.81258e7 | −1.08403 | ||||||||
\(776\) | −6.76100e7 | −4.03048 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21319e7 | 0.718589 | ||||||||
\(779\) | −1.18556e7 | −0.699970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07591e6 | 0.0631173 | ||||||||
\(782\) | −7.32299e6 | −0.428225 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.16142e7 | 3.58006 | ||||||||
\(785\) | 9.50472e6 | 0.550510 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.05678e7 | 0.608204 | 0.304102 | − | 0.952639i | \(-0.401644\pi\) | ||||
0.304102 | + | 0.952639i | \(0.401644\pi\) | |||||||
\(788\) | −6.19029e7 | −3.55137 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.86091e7 | −3.34116 | ||||||||
\(791\) | −1.79258e7 | −1.01868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.91839e7 | −1.08331 | ||||||||
\(794\) | −1.07435e7 | −0.604775 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.91923e7 | 2.75178 | ||||||||
\(797\) | 6.69757e6 | 0.373483 | 0.186742 | − | 0.982409i | \(-0.440207\pi\) | ||||
0.186742 | + | 0.982409i | \(0.440207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.69806e7 | −1.49515 | ||||||||
\(800\) | −1.71493e7 | −0.947376 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.35393e7 | 3.48824 | ||||||||
\(803\) | 2.15080e6 | 0.117709 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.96378e6 | −0.433141 | ||||||||
\(806\) | 5.77682e7 | 3.13221 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.44654e7 | −4.55145 | ||||||||
\(809\) | −2.87439e7 | −1.54409 | −0.772047 | − | 0.635566i | \(-0.780767\pi\) | ||||
−0.772047 | + | 0.635566i | \(0.780767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.11987e6 | 0.326731 | 0.163365 | − | 0.986566i | \(-0.447765\pi\) | ||||
0.163365 | + | 0.986566i | \(0.447765\pi\) | |||||||
\(812\) | −4.76877e7 | −2.53815 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.06100e7 | −0.561248 | ||||||||
\(815\) | 3.26694e6 | 0.172285 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.11600e7 | −2.15735 | ||||||||
\(818\) | 2.20802e7 | 1.15377 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.54483e7 | 1.84103 | ||||||||
\(821\) | −2.55802e7 | −1.32448 | −0.662241 | − | 0.749291i | \(-0.730395\pi\) | ||||
−0.662241 | + | 0.749291i | \(0.730395\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.38465e7 | −0.712589 | −0.356295 | − | 0.934374i | \(-0.615960\pi\) | ||||
−0.356295 | + | 0.934374i | \(0.615960\pi\) | |||||||
\(824\) | −6.41499e7 | −3.29138 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.12332e7 | −4.14270 | ||||||||
\(827\) | 6.70325e6 | 0.340817 | 0.170409 | − | 0.985373i | \(-0.445491\pi\) | ||||
0.170409 | + | 0.985373i | \(0.445491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.66094e7 | −0.839395 | −0.419698 | − | 0.907664i | \(-0.637864\pi\) | ||||
−0.419698 | + | 0.907664i | \(0.637864\pi\) | |||||||
\(830\) | −8.44982e7 | −4.25748 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.15557e7 | 0.578744 | ||||||||
\(833\) | 3.70357e7 | 1.84930 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.71446e6 | −0.134731 | ||||||||
\(836\) | −2.29674e7 | −1.13657 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.26880e7 | −3.08372 | ||||||||
\(839\) | −1.49591e7 | −0.733668 | −0.366834 | − | 0.930286i | \(-0.619558\pi\) | ||||
−0.366834 | + | 0.930286i | \(0.619558\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.14751e7 | −0.559457 | ||||||||
\(842\) | 4.78482e7 | 2.32587 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.10751e7 | 2.95126 | ||||||||
\(845\) | −330533. | −0.0159248 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.78660e7 | 1.33464 | ||||||||
\(848\) | −8.01744e6 | −0.382865 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.72311e7 | −1.29276 | ||||||||
\(851\) | 3.18529e6 | 0.150774 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.51212e7 | 1.65271 | 0.826356 | − | 0.563148i | \(-0.190410\pi\) | ||||
0.826356 | + | 0.563148i | \(0.190410\pi\) | |||||||
\(854\) | −6.92008e7 | −3.24688 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.96312e7 | −1.84864 | ||||||||
\(857\) | 2.92814e7 | 1.36188 | 0.680941 | − | 0.732338i | \(-0.261571\pi\) | ||||
0.680941 | + | 0.732338i | \(0.261571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.71049e7 | −1.25333 | −0.626664 | − | 0.779289i | \(-0.715580\pi\) | ||||
−0.626664 | + | 0.779289i | \(0.715580\pi\) | |||||||
\(860\) | 1.23069e8 | 5.67417 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.54651e7 | 0.708901 | ||||||||
\(863\) | 1.47872e7 | 0.675863 | 0.337931 | − | 0.941171i | \(-0.390273\pi\) | ||||
0.337931 | + | 0.941171i | \(0.390273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.88935e7 | 2.22183 | ||||||||
\(866\) | 7.70590e7 | 3.49163 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.46178e8 | 6.58540 | ||||||||
\(869\) | 1.35006e7 | 0.606462 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.29058e6 | −0.102306 | ||||||||
\(872\) | 4.23946e7 | 1.88807 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.82941e6 | 0.435260 | ||||||||
\(875\) | 1.74311e7 | 0.769671 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.07960e7 | −0.473982 | −0.236991 | − | 0.971512i | \(-0.576161\pi\) | ||||
−0.236991 | + | 0.971512i | \(0.576161\pi\) | |||||||
\(878\) | 2.18923e7 | 0.958420 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.70135e7 | 1.17591 | ||||||||
\(881\) | 6.00778e6 | 0.260780 | 0.130390 | − | 0.991463i | \(-0.458377\pi\) | ||||
0.130390 | + | 0.991463i | \(0.458377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.06315e7 | 0.458875 | 0.229437 | − | 0.973323i | \(-0.426311\pi\) | ||||
0.229437 | + | 0.973323i | \(0.426311\pi\) | |||||||
\(884\) | 6.08802e7 | 2.62027 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.24109e7 | 0.959123 | ||||||||
\(887\) | 3.31806e6 | 0.141604 | 0.0708020 | − | 0.997490i | \(-0.477444\pi\) | ||||
0.0708020 | + | 0.997490i | \(0.477444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 174354. | 0.00739908 | ||||||||
\(890\) | −4.70508e7 | −1.99110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.89544e7 | −0.797623 | ||||||||
\(893\) | 3.62152e7 | 1.51972 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.32843e7 | 0.971642 | ||||||||
\(896\) | −1.71706e7 | −0.714520 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.85547e7 | 2.42310 | ||||||||
\(899\) | −2.76983e7 | −1.14302 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.81920e6 | −0.197771 | ||||||||
\(902\) | −1.16403e7 | −0.476375 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.80027e7 | −1.54665 | ||||||||
\(905\) | −2.56844e7 | −1.04243 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.63923e7 | −1.87253 | −0.936263 | − | 0.351301i | \(-0.885739\pi\) | ||||
−0.936263 | + | 0.351301i | \(0.885739\pi\) | |||||||
\(908\) | 7.51455e7 | 3.02474 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.43818e7 | 3.77820 | ||||||||
\(911\) | 1.40524e7 | 0.560987 | 0.280494 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280494 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.94642e7 | 0.772785 | ||||||||
\(914\) | −2.20596e6 | −0.0873439 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.24619e7 | 2.85345 | ||||||||
\(917\) | −5.53411e7 | −2.17332 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.17102e6 | 0.241028 | 0.120514 | − | 0.992712i | \(-0.461546\pi\) | ||||
0.120514 | + | 0.992712i | \(0.461546\pi\) | |||||||
\(920\) | −1.68832e7 | −0.657637 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.94941e7 | 1.14264 | ||||||||
\(923\) | 3.82806e6 | 0.147902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.18447e7 | 0.455168 | ||||||||
\(926\) | 1.01624e7 | 0.389465 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.62062e7 | −0.998930 | ||||||||
\(929\) | 4.76811e6 | 0.181262 | 0.0906310 | − | 0.995885i | \(-0.471112\pi\) | ||||
0.0906310 | + | 0.995885i | \(0.471112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.97118e7 | −1.87969 | ||||||||
\(932\) | −6.53483e6 | −0.246430 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.16047e7 | 0.435277 | ||||||||
\(935\) | 1.62375e7 | 0.607422 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.20047e6 | −0.193506 | −0.0967528 | − | 0.995308i | \(-0.530846\pi\) | ||||
−0.0967528 | + | 0.995308i | \(0.530846\pi\) | |||||||
\(938\) | −8.26264e6 | −0.306628 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.08284e8 | −3.99709 | ||||||||
\(941\) | 2.95702e7 | 1.08863 | 0.544316 | − | 0.838881i | \(-0.316789\pi\) | ||||
0.544316 | + | 0.838881i | \(0.316789\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.49461e6 | 0.127973 | ||||||||
\(944\) | −8.27235e7 | −3.02133 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.04127e7 | −1.46822 | ||||||||
\(947\) | −3.00430e7 | −1.08860 | −0.544299 | − | 0.838891i | \(-0.683204\pi\) | ||||
−0.544299 | + | 0.838891i | \(0.683204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.65249e6 | 0.275827 | ||||||||
\(950\) | 3.65514e7 | 1.31400 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.26155e8 | 4.51142 | ||||||||
\(953\) | 2.08186e7 | 0.742540 | 0.371270 | − | 0.928525i | \(-0.378922\pi\) | ||||
0.371270 | + | 0.928525i | \(0.378922\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.21805e7 | −0.786979 | ||||||||
\(956\) | 1.07337e8 | 3.79844 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.06245e7 | 3.19030 | ||||||||
\(959\) | 2.73636e6 | 0.0960785 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.62749e7 | 1.96565 | ||||||||
\(962\) | −3.77501e7 | −1.31517 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.03084e7 | −0.357271 | ||||||||
\(965\) | −9.72226e6 | −0.336085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.35812e7 | −0.467058 | −0.233529 | − | 0.972350i | \(-0.575027\pi\) | ||||
−0.233529 | + | 0.972350i | \(0.575027\pi\) | |||||||
\(968\) | 5.90759e7 | 2.02639 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.11687e8 | −3.81130 | ||||||||
\(971\) | −809935. | −0.0275678 | −0.0137839 | − | 0.999905i | \(-0.504388\pi\) | ||||
−0.0137839 | + | 0.999905i | \(0.504388\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.88690e7 | 0.638951 | ||||||||
\(974\) | −4.74226e7 | −1.60172 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.04703e7 | −2.36800 | ||||||||
\(977\) | 5.74719e6 | 0.192628 | 0.0963140 | − | 0.995351i | \(-0.469295\pi\) | ||||
0.0963140 | + | 0.995351i | \(0.469295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.08381e7 | 0.361409 | ||||||||
\(980\) | 1.48639e8 | 4.94387 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.43771e7 | 1.13760 | ||||||||
\(983\) | −1.84120e7 | −0.607740 | −0.303870 | − | 0.952714i | \(-0.598279\pi\) | ||||
−0.303870 | + | 0.952714i | \(0.598279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.87432e7 | −1.92915 | ||||||||
\(986\) | −4.16123e7 | −1.36311 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.17176e7 | −2.66332 | ||||||||
\(989\) | 1.21325e7 | 0.394422 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.13190e6 | 0.0366120 | 0.0183060 | − | 0.999832i | \(-0.494173\pi\) | ||||
0.0183060 | + | 0.999832i | \(0.494173\pi\) | |||||||
\(992\) | 8.03304e7 | 2.59180 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.38087e7 | 0.443289 | ||||||||
\(995\) | 4.66813e7 | 1.49481 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.72081e7 | 1.18549 | 0.592747 | − | 0.805389i | \(-0.298043\pi\) | ||||
0.592747 | + | 0.805389i | \(0.298043\pi\) | |||||||
\(998\) | −9.66631e7 | −3.07209 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 207.6.a.i.1.1 | yes | 10 | |
3.2 | odd | 2 | 207.6.a.h.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
207.6.a.h.1.10 | ✓ | 10 | 3.2 | odd | 2 | ||
207.6.a.i.1.1 | yes | 10 | 1.1 | even | 1 | trivial |