Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,6,Mod(1,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, 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("150.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(24.0575729719\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 150.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | −79.0000 | −0.609371 | −0.304686 | − | 0.952453i | \(-0.598551\pi\) | ||||
−0.304686 | + | 0.952453i | \(0.598551\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 150.000 | 0.373774 | 0.186887 | − | 0.982381i | \(-0.440160\pi\) | ||||
0.186887 | + | 0.982381i | \(0.440160\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 137.000 | 0.224834 | 0.112417 | − | 0.993661i | \(-0.464141\pi\) | ||||
0.112417 | + | 0.993661i | \(0.464141\pi\) | |||||||
\(14\) | −316.000 | −0.430891 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −2034.00 | −1.70698 | −0.853490 | − | 0.521109i | \(-0.825519\pi\) | ||||
−0.853490 | + | 0.521109i | \(0.825519\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | −1969.00 | −1.25130 | −0.625650 | − | 0.780104i | \(-0.715166\pi\) | ||||
−0.625650 | + | 0.780104i | \(0.715166\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 711.000 | 0.351821 | ||||||||
\(22\) | 600.000 | 0.264298 | ||||||||
\(23\) | −1350.00 | −0.532126 | −0.266063 | − | 0.963956i | \(-0.585723\pi\) | ||||
−0.266063 | + | 0.963956i | \(0.585723\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 548.000 | 0.158982 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −1264.00 | −0.304686 | ||||||||
\(29\) | −2946.00 | −0.650486 | −0.325243 | − | 0.945631i | \(-0.605446\pi\) | ||||
−0.325243 | + | 0.945631i | \(0.605446\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 713.000 | 0.133256 | 0.0666278 | − | 0.997778i | \(-0.478776\pi\) | ||||
0.0666278 | + | 0.997778i | \(0.478776\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −1350.00 | −0.215799 | ||||||||
\(34\) | −8136.00 | −1.20702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −3238.00 | −0.388841 | −0.194421 | − | 0.980918i | \(-0.562283\pi\) | ||||
−0.194421 | + | 0.980918i | \(0.562283\pi\) | |||||||
\(38\) | −7876.00 | −0.884803 | ||||||||
\(39\) | −1233.00 | −0.129808 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6564.00 | 0.609830 | 0.304915 | − | 0.952380i | \(-0.401372\pi\) | ||||
0.304915 | + | 0.952380i | \(0.401372\pi\) | |||||||
\(42\) | 2844.00 | 0.248775 | ||||||||
\(43\) | −19579.0 | −1.61480 | −0.807401 | − | 0.590003i | \(-0.799127\pi\) | ||||
−0.807401 | + | 0.590003i | \(0.799127\pi\) | |||||||
\(44\) | 2400.00 | 0.186887 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5400.00 | −0.376270 | ||||||||
\(47\) | −21150.0 | −1.39658 | −0.698290 | − | 0.715815i | \(-0.746055\pi\) | ||||
−0.698290 | + | 0.715815i | \(0.746055\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −10566.0 | −0.628667 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18306.0 | 0.985526 | ||||||||
\(52\) | 2192.00 | 0.112417 | ||||||||
\(53\) | −25896.0 | −1.26632 | −0.633159 | − | 0.774021i | \(-0.718242\pi\) | ||||
−0.633159 | + | 0.774021i | \(0.718242\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5056.00 | −0.215445 | ||||||||
\(57\) | 17721.0 | 0.722439 | ||||||||
\(58\) | −11784.0 | −0.459963 | ||||||||
\(59\) | 25350.0 | 0.948086 | 0.474043 | − | 0.880502i | \(-0.342794\pi\) | ||||
0.474043 | + | 0.880502i | \(0.342794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 50615.0 | 1.74163 | 0.870813 | − | 0.491615i | \(-0.163593\pi\) | ||||
0.870813 | + | 0.491615i | \(0.163593\pi\) | |||||||
\(62\) | 2852.00 | 0.0942259 | ||||||||
\(63\) | −6399.00 | −0.203124 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5400.00 | −0.152593 | ||||||||
\(67\) | −22519.0 | −0.612861 | −0.306431 | − | 0.951893i | \(-0.599135\pi\) | ||||
−0.306431 | + | 0.951893i | \(0.599135\pi\) | |||||||
\(68\) | −32544.0 | −0.853490 | ||||||||
\(69\) | 12150.0 | 0.307223 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33900.0 | 0.798094 | 0.399047 | − | 0.916931i | \(-0.369341\pi\) | ||||
0.399047 | + | 0.916931i | \(0.369341\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | 82442.0 | 1.81068 | 0.905339 | − | 0.424689i | \(-0.139617\pi\) | ||||
0.905339 | + | 0.424689i | \(0.139617\pi\) | |||||||
\(74\) | −12952.0 | −0.274952 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −31504.0 | −0.625650 | ||||||||
\(77\) | −11850.0 | −0.227767 | ||||||||
\(78\) | −4932.00 | −0.0917881 | ||||||||
\(79\) | −81472.0 | −1.46873 | −0.734363 | − | 0.678757i | \(-0.762519\pi\) | ||||
−0.734363 | + | 0.678757i | \(0.762519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 26256.0 | 0.431215 | ||||||||
\(83\) | 25782.0 | 0.410791 | 0.205396 | − | 0.978679i | \(-0.434152\pi\) | ||||
0.205396 | + | 0.978679i | \(0.434152\pi\) | |||||||
\(84\) | 11376.0 | 0.175910 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −78316.0 | −1.14184 | ||||||||
\(87\) | 26514.0 | 0.375558 | ||||||||
\(88\) | 9600.00 | 0.132149 | ||||||||
\(89\) | 103728. | 1.38810 | 0.694050 | − | 0.719926i | \(-0.255824\pi\) | ||||
0.694050 | + | 0.719926i | \(0.255824\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10823.0 | −0.137007 | ||||||||
\(92\) | −21600.0 | −0.266063 | ||||||||
\(93\) | −6417.00 | −0.0769351 | ||||||||
\(94\) | −84600.0 | −0.987531 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −57343.0 | −0.618801 | −0.309401 | − | 0.950932i | \(-0.600128\pi\) | ||||
−0.309401 | + | 0.950932i | \(0.600128\pi\) | |||||||
\(98\) | −42264.0 | −0.444534 | ||||||||
\(99\) | 12150.0 | 0.124591 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −91032.0 | −0.887954 | −0.443977 | − | 0.896038i | \(-0.646433\pi\) | ||||
−0.443977 | + | 0.896038i | \(0.646433\pi\) | |||||||
\(102\) | 73224.0 | 0.696872 | ||||||||
\(103\) | 191636. | 1.77985 | 0.889926 | − | 0.456104i | \(-0.150756\pi\) | ||||
0.889926 | + | 0.456104i | \(0.150756\pi\) | |||||||
\(104\) | 8768.00 | 0.0794909 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −103584. | −0.895423 | ||||||||
\(107\) | 9288.00 | 0.0784265 | 0.0392132 | − | 0.999231i | \(-0.487515\pi\) | ||||
0.0392132 | + | 0.999231i | \(0.487515\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | −20635.0 | −0.166356 | −0.0831780 | − | 0.996535i | \(-0.526507\pi\) | ||||
−0.0831780 | + | 0.996535i | \(0.526507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 29142.0 | 0.224498 | ||||||||
\(112\) | −20224.0 | −0.152343 | ||||||||
\(113\) | 176892. | 1.30320 | 0.651602 | − | 0.758561i | \(-0.274097\pi\) | ||||
0.651602 | + | 0.758561i | \(0.274097\pi\) | |||||||
\(114\) | 70884.0 | 0.510841 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −47136.0 | −0.325243 | ||||||||
\(117\) | 11097.0 | 0.0749447 | ||||||||
\(118\) | 101400. | 0.670398 | ||||||||
\(119\) | 160686. | 1.04019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −138551. | −0.860293 | ||||||||
\(122\) | 202460. | 1.23151 | ||||||||
\(123\) | −59076.0 | −0.352086 | ||||||||
\(124\) | 11408.0 | 0.0666278 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −25596.0 | −0.143630 | ||||||||
\(127\) | −256480. | −1.41106 | −0.705528 | − | 0.708682i | \(-0.749290\pi\) | ||||
−0.705528 | + | 0.708682i | \(0.749290\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 176211. | 0.932307 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 177600. | 0.904200 | 0.452100 | − | 0.891967i | \(-0.350675\pi\) | ||||
0.452100 | + | 0.891967i | \(0.350675\pi\) | |||||||
\(132\) | −21600.0 | −0.107899 | ||||||||
\(133\) | 155551. | 0.762507 | ||||||||
\(134\) | −90076.0 | −0.433358 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −130176. | −0.603509 | ||||||||
\(137\) | 260886. | 1.18754 | 0.593772 | − | 0.804634i | \(-0.297638\pi\) | ||||
0.593772 | + | 0.804634i | \(0.297638\pi\) | |||||||
\(138\) | 48600.0 | 0.217239 | ||||||||
\(139\) | −217684. | −0.955629 | −0.477815 | − | 0.878461i | \(-0.658571\pi\) | ||||
−0.477815 | + | 0.878461i | \(0.658571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 190350. | 0.806316 | ||||||||
\(142\) | 135600. | 0.564337 | ||||||||
\(143\) | 20550.0 | 0.0840372 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 329768. | 1.28034 | ||||||||
\(147\) | 95094.0 | 0.362961 | ||||||||
\(148\) | −51808.0 | −0.194421 | ||||||||
\(149\) | 421794. | 1.55645 | 0.778224 | − | 0.627987i | \(-0.216121\pi\) | ||||
0.778224 | + | 0.627987i | \(0.216121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −101917. | −0.363751 | −0.181876 | − | 0.983322i | \(-0.558217\pi\) | ||||
−0.181876 | + | 0.983322i | \(0.558217\pi\) | |||||||
\(152\) | −126016. | −0.442402 | ||||||||
\(153\) | −164754. | −0.568994 | ||||||||
\(154\) | −47400.0 | −0.161056 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −19728.0 | −0.0649040 | ||||||||
\(157\) | −101773. | −0.329521 | −0.164761 | − | 0.986334i | \(-0.552685\pi\) | ||||
−0.164761 | + | 0.986334i | \(0.552685\pi\) | |||||||
\(158\) | −325888. | −1.03855 | ||||||||
\(159\) | 233064. | 0.731109 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 106650. | 0.324262 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −202249. | −0.596235 | −0.298117 | − | 0.954529i | \(-0.596359\pi\) | ||||
−0.298117 | + | 0.954529i | \(0.596359\pi\) | |||||||
\(164\) | 105024. | 0.304915 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 103128. | 0.290473 | ||||||||
\(167\) | 231600. | 0.642610 | 0.321305 | − | 0.946976i | \(-0.395879\pi\) | ||||
0.321305 | + | 0.946976i | \(0.395879\pi\) | |||||||
\(168\) | 45504.0 | 0.124387 | ||||||||
\(169\) | −352524. | −0.949450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −159489. | −0.417100 | ||||||||
\(172\) | −313264. | −0.807401 | ||||||||
\(173\) | −174222. | −0.442576 | −0.221288 | − | 0.975209i | \(-0.571026\pi\) | ||||
−0.221288 | + | 0.975209i | \(0.571026\pi\) | |||||||
\(174\) | 106056. | 0.265560 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 38400.0 | 0.0934436 | ||||||||
\(177\) | −228150. | −0.547378 | ||||||||
\(178\) | 414912. | 0.981535 | ||||||||
\(179\) | −642066. | −1.49778 | −0.748888 | − | 0.662696i | \(-0.769412\pi\) | ||||
−0.748888 | + | 0.662696i | \(0.769412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −56071.0 | −0.127216 | −0.0636080 | − | 0.997975i | \(-0.520261\pi\) | ||||
−0.0636080 | + | 0.997975i | \(0.520261\pi\) | |||||||
\(182\) | −43292.0 | −0.0968789 | ||||||||
\(183\) | −455535. | −1.00553 | ||||||||
\(184\) | −86400.0 | −0.188135 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −25668.0 | −0.0544013 | ||||||||
\(187\) | −305100. | −0.638026 | ||||||||
\(188\) | −338400. | −0.698290 | ||||||||
\(189\) | 57591.0 | 0.117274 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −209694. | −0.415913 | −0.207957 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207957 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −715597. | −1.38285 | −0.691425 | − | 0.722448i | \(-0.743017\pi\) | ||||
−0.691425 | + | 0.722448i | \(0.743017\pi\) | |||||||
\(194\) | −229372. | −0.437558 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −169056. | −0.314333 | ||||||||
\(197\) | 508854. | 0.934174 | 0.467087 | − | 0.884211i | \(-0.345304\pi\) | ||||
0.467087 | + | 0.884211i | \(0.345304\pi\) | |||||||
\(198\) | 48600.0 | 0.0880995 | ||||||||
\(199\) | −986017. | −1.76503 | −0.882514 | − | 0.470286i | \(-0.844151\pi\) | ||||
−0.882514 | + | 0.470286i | \(0.844151\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 202671. | 0.353836 | ||||||||
\(202\) | −364128. | −0.627879 | ||||||||
\(203\) | 232734. | 0.396387 | ||||||||
\(204\) | 292896. | 0.492763 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 766544. | 1.25855 | ||||||||
\(207\) | −109350. | −0.177375 | ||||||||
\(208\) | 35072.0 | 0.0562085 | ||||||||
\(209\) | −295350. | −0.467704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 119495. | 0.184775 | 0.0923876 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923876 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(212\) | −414336. | −0.633159 | ||||||||
\(213\) | −305100. | −0.460780 | ||||||||
\(214\) | 37152.0 | 0.0554559 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | −56327.0 | −0.0812021 | ||||||||
\(218\) | −82540.0 | −0.117631 | ||||||||
\(219\) | −741978. | −1.04540 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −278658. | −0.383788 | ||||||||
\(222\) | 116568. | 0.158744 | ||||||||
\(223\) | 48545.0 | 0.0653706 | 0.0326853 | − | 0.999466i | \(-0.489594\pi\) | ||||
0.0326853 | + | 0.999466i | \(0.489594\pi\) | |||||||
\(224\) | −80896.0 | −0.107723 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 707568. | 0.921504 | ||||||||
\(227\) | −287652. | −0.370512 | −0.185256 | − | 0.982690i | \(-0.559311\pi\) | ||||
−0.185256 | + | 0.982690i | \(0.559311\pi\) | |||||||
\(228\) | 283536. | 0.361219 | ||||||||
\(229\) | 72065.0 | 0.0908104 | 0.0454052 | − | 0.998969i | \(-0.485542\pi\) | ||||
0.0454052 | + | 0.998969i | \(0.485542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 106650. | 0.131502 | ||||||||
\(232\) | −188544. | −0.229981 | ||||||||
\(233\) | −569148. | −0.686808 | −0.343404 | − | 0.939188i | \(-0.611580\pi\) | ||||
−0.343404 | + | 0.939188i | \(0.611580\pi\) | |||||||
\(234\) | 44388.0 | 0.0529939 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 405600. | 0.474043 | ||||||||
\(237\) | 733248. | 0.847969 | ||||||||
\(238\) | 642744. | 0.735522 | ||||||||
\(239\) | 696504. | 0.788731 | 0.394365 | − | 0.918954i | \(-0.370964\pi\) | ||||
0.394365 | + | 0.918954i | \(0.370964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 576137. | 0.638974 | 0.319487 | − | 0.947591i | \(-0.396489\pi\) | ||||
0.319487 | + | 0.947591i | \(0.396489\pi\) | |||||||
\(242\) | −554204. | −0.608319 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 809840. | 0.870813 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −236304. | −0.248962 | ||||||||
\(247\) | −269753. | −0.281335 | ||||||||
\(248\) | 45632.0 | 0.0471130 | ||||||||
\(249\) | −232038. | −0.237171 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.22492e6 | −1.22723 | −0.613613 | − | 0.789607i | \(-0.710285\pi\) | ||||
−0.613613 | + | 0.789607i | \(0.710285\pi\) | |||||||
\(252\) | −102384. | −0.101562 | ||||||||
\(253\) | −202500. | −0.198895 | ||||||||
\(254\) | −1.02592e6 | −0.997767 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 972132. | 0.918105 | 0.459053 | − | 0.888409i | \(-0.348189\pi\) | ||||
0.459053 | + | 0.888409i | \(0.348189\pi\) | |||||||
\(258\) | 704844. | 0.659240 | ||||||||
\(259\) | 255802. | 0.236949 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −238626. | −0.216829 | ||||||||
\(262\) | 710400. | 0.639366 | ||||||||
\(263\) | 1.76190e6 | 1.57070 | 0.785348 | − | 0.619055i | \(-0.212484\pi\) | ||||
0.785348 | + | 0.619055i | \(0.212484\pi\) | |||||||
\(264\) | −86400.0 | −0.0762964 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 622204. | 0.539174 | ||||||||
\(267\) | −933552. | −0.801420 | ||||||||
\(268\) | −360304. | −0.306431 | ||||||||
\(269\) | 1.74383e6 | 1.46935 | 0.734674 | − | 0.678421i | \(-0.237335\pi\) | ||||
0.734674 | + | 0.678421i | \(0.237335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.70426e6 | −1.40965 | −0.704826 | − | 0.709381i | \(-0.748975\pi\) | ||||
−0.704826 | + | 0.709381i | \(0.748975\pi\) | |||||||
\(272\) | −520704. | −0.426745 | ||||||||
\(273\) | 97407.0 | 0.0791013 | ||||||||
\(274\) | 1.04354e6 | 0.839720 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 194400. | 0.153611 | ||||||||
\(277\) | 1.46972e6 | 1.15089 | 0.575446 | − | 0.817840i | \(-0.304829\pi\) | ||||
0.575446 | + | 0.817840i | \(0.304829\pi\) | |||||||
\(278\) | −870736. | −0.675732 | ||||||||
\(279\) | 57753.0 | 0.0444185 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.22530e6 | −0.925715 | −0.462858 | − | 0.886433i | \(-0.653176\pi\) | ||||
−0.462858 | + | 0.886433i | \(0.653176\pi\) | |||||||
\(282\) | 761400. | 0.570151 | ||||||||
\(283\) | −637333. | −0.473043 | −0.236521 | − | 0.971626i | \(-0.576007\pi\) | ||||
−0.236521 | + | 0.971626i | \(0.576007\pi\) | |||||||
\(284\) | 542400. | 0.399047 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 82200.0 | 0.0594233 | ||||||||
\(287\) | −518556. | −0.371613 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 2.71730e6 | 1.91378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 516087. | 0.357265 | ||||||||
\(292\) | 1.31907e6 | 0.905339 | ||||||||
\(293\) | 35094.0 | 0.0238816 | 0.0119408 | − | 0.999929i | \(-0.496199\pi\) | ||||
0.0119408 | + | 0.999929i | \(0.496199\pi\) | |||||||
\(294\) | 380376. | 0.256652 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −207232. | −0.137476 | ||||||||
\(297\) | −109350. | −0.0719329 | ||||||||
\(298\) | 1.68718e6 | 1.10058 | ||||||||
\(299\) | −184950. | −0.119640 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.54674e6 | 0.984014 | ||||||||
\(302\) | −407668. | −0.257211 | ||||||||
\(303\) | 819288. | 0.512661 | ||||||||
\(304\) | −504064. | −0.312825 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −659016. | −0.402339 | ||||||||
\(307\) | 2.88040e6 | 1.74424 | 0.872120 | − | 0.489293i | \(-0.162745\pi\) | ||||
0.872120 | + | 0.489293i | \(0.162745\pi\) | |||||||
\(308\) | −189600. | −0.113884 | ||||||||
\(309\) | −1.72472e6 | −1.02760 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.38305e6 | −1.39712 | −0.698558 | − | 0.715554i | \(-0.746174\pi\) | ||||
−0.698558 | + | 0.715554i | \(0.746174\pi\) | |||||||
\(312\) | −78912.0 | −0.0458941 | ||||||||
\(313\) | −1.93081e6 | −1.11399 | −0.556993 | − | 0.830517i | \(-0.688045\pi\) | ||||
−0.556993 | + | 0.830517i | \(0.688045\pi\) | |||||||
\(314\) | −407092. | −0.233007 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.30355e6 | −0.734363 | ||||||||
\(317\) | −2.18995e6 | −1.22401 | −0.612007 | − | 0.790852i | \(-0.709638\pi\) | ||||
−0.612007 | + | 0.790852i | \(0.709638\pi\) | |||||||
\(318\) | 932256. | 0.516972 | ||||||||
\(319\) | −441900. | −0.243135 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −83592.0 | −0.0452796 | ||||||||
\(322\) | 426600. | 0.229288 | ||||||||
\(323\) | 4.00495e6 | 2.13595 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −808996. | −0.421602 | ||||||||
\(327\) | 185715. | 0.0960456 | ||||||||
\(328\) | 420096. | 0.215608 | ||||||||
\(329\) | 1.67085e6 | 0.851036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41429e6 | 0.709527 | 0.354764 | − | 0.934956i | \(-0.384561\pi\) | ||||
0.354764 | + | 0.934956i | \(0.384561\pi\) | |||||||
\(332\) | 412512. | 0.205396 | ||||||||
\(333\) | −262278. | −0.129614 | ||||||||
\(334\) | 926400. | 0.454394 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 182016. | 0.0879552 | ||||||||
\(337\) | 1.38208e6 | 0.662916 | 0.331458 | − | 0.943470i | \(-0.392459\pi\) | ||||
0.331458 | + | 0.943470i | \(0.392459\pi\) | |||||||
\(338\) | −1.41010e6 | −0.671362 | ||||||||
\(339\) | −1.59203e6 | −0.752405 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 106950. | 0.0498075 | ||||||||
\(342\) | −637956. | −0.294934 | ||||||||
\(343\) | 2.16247e6 | 0.992463 | ||||||||
\(344\) | −1.25306e6 | −0.570919 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −696888. | −0.312948 | ||||||||
\(347\) | −283758. | −0.126510 | −0.0632549 | − | 0.997997i | \(-0.520148\pi\) | ||||
−0.0632549 | + | 0.997997i | \(0.520148\pi\) | |||||||
\(348\) | 424224. | 0.187779 | ||||||||
\(349\) | 2.13809e6 | 0.939642 | 0.469821 | − | 0.882762i | \(-0.344318\pi\) | ||||
0.469821 | + | 0.882762i | \(0.344318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −99873.0 | −0.0432693 | ||||||||
\(352\) | 153600. | 0.0660746 | ||||||||
\(353\) | 3.16015e6 | 1.34980 | 0.674901 | − | 0.737908i | \(-0.264186\pi\) | ||||
0.674901 | + | 0.737908i | \(0.264186\pi\) | |||||||
\(354\) | −912600. | −0.387055 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.65965e6 | 0.694050 | ||||||||
\(357\) | −1.44617e6 | −0.600551 | ||||||||
\(358\) | −2.56826e6 | −1.05909 | ||||||||
\(359\) | −3.59564e6 | −1.47245 | −0.736225 | − | 0.676737i | \(-0.763393\pi\) | ||||
−0.736225 | + | 0.676737i | \(0.763393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.40086e6 | 0.565754 | ||||||||
\(362\) | −224284. | −0.0899553 | ||||||||
\(363\) | 1.24696e6 | 0.496690 | ||||||||
\(364\) | −173168. | −0.0685037 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.82214e6 | −0.711015 | ||||||||
\(367\) | −4.62043e6 | −1.79068 | −0.895339 | − | 0.445385i | \(-0.853067\pi\) | ||||
−0.895339 | + | 0.445385i | \(0.853067\pi\) | |||||||
\(368\) | −345600. | −0.133031 | ||||||||
\(369\) | 531684. | 0.203277 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.04578e6 | 0.771658 | ||||||||
\(372\) | −102672. | −0.0384676 | ||||||||
\(373\) | −3.51983e6 | −1.30993 | −0.654967 | − | 0.755657i | \(-0.727318\pi\) | ||||
−0.654967 | + | 0.755657i | \(0.727318\pi\) | |||||||
\(374\) | −1.22040e6 | −0.451152 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.35360e6 | −0.493765 | ||||||||
\(377\) | −403602. | −0.146251 | ||||||||
\(378\) | 230364. | 0.0829249 | ||||||||
\(379\) | 595061. | 0.212796 | 0.106398 | − | 0.994324i | \(-0.466068\pi\) | ||||
0.106398 | + | 0.994324i | \(0.466068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.30832e6 | 0.814673 | ||||||||
\(382\) | −838776. | −0.294095 | ||||||||
\(383\) | −1.30050e6 | −0.453016 | −0.226508 | − | 0.974009i | \(-0.572731\pi\) | ||||
−0.226508 | + | 0.974009i | \(0.572731\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.86239e6 | −0.977823 | ||||||||
\(387\) | −1.58590e6 | −0.538267 | ||||||||
\(388\) | −917488. | −0.309401 | ||||||||
\(389\) | 620724. | 0.207981 | 0.103991 | − | 0.994578i | \(-0.466839\pi\) | ||||
0.103991 | + | 0.994578i | \(0.466839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.74590e6 | 0.908328 | ||||||||
\(392\) | −676224. | −0.222267 | ||||||||
\(393\) | −1.59840e6 | −0.522040 | ||||||||
\(394\) | 2.03542e6 | 0.660561 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 194400. | 0.0622957 | ||||||||
\(397\) | 1.18622e6 | 0.377737 | 0.188869 | − | 0.982002i | \(-0.439518\pi\) | ||||
0.188869 | + | 0.982002i | \(0.439518\pi\) | |||||||
\(398\) | −3.94407e6 | −1.24806 | ||||||||
\(399\) | −1.39996e6 | −0.440233 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.13334e6 | 0.973077 | 0.486538 | − | 0.873659i | \(-0.338259\pi\) | ||||
0.486538 | + | 0.873659i | \(0.338259\pi\) | |||||||
\(402\) | 810684. | 0.250200 | ||||||||
\(403\) | 97681.0 | 0.0299604 | ||||||||
\(404\) | −1.45651e6 | −0.443977 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 930936. | 0.280288 | ||||||||
\(407\) | −485700. | −0.145339 | ||||||||
\(408\) | 1.17158e6 | 0.348436 | ||||||||
\(409\) | 567581. | 0.167772 | 0.0838860 | − | 0.996475i | \(-0.473267\pi\) | ||||
0.0838860 | + | 0.996475i | \(0.473267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.34797e6 | −0.685628 | ||||||||
\(412\) | 3.06618e6 | 0.889926 | ||||||||
\(413\) | −2.00265e6 | −0.577737 | ||||||||
\(414\) | −437400. | −0.125423 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 140288. | 0.0397454 | ||||||||
\(417\) | 1.95916e6 | 0.551733 | ||||||||
\(418\) | −1.18140e6 | −0.330717 | ||||||||
\(419\) | −6.09000e6 | −1.69466 | −0.847329 | − | 0.531068i | \(-0.821791\pi\) | ||||
−0.847329 | + | 0.531068i | \(0.821791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.07139e6 | 0.844558 | 0.422279 | − | 0.906466i | \(-0.361230\pi\) | ||||
0.422279 | + | 0.906466i | \(0.361230\pi\) | |||||||
\(422\) | 477980. | 0.130656 | ||||||||
\(423\) | −1.71315e6 | −0.465527 | ||||||||
\(424\) | −1.65734e6 | −0.447711 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.22040e6 | −0.325820 | ||||||||
\(427\) | −3.99858e6 | −1.06130 | ||||||||
\(428\) | 148608. | 0.0392132 | ||||||||
\(429\) | −184950. | −0.0485189 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −669150. | −0.173512 | −0.0867562 | − | 0.996230i | \(-0.527650\pi\) | ||||
−0.0867562 | + | 0.996230i | \(0.527650\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −3.25439e6 | −0.834161 | −0.417080 | − | 0.908870i | \(-0.636947\pi\) | ||||
−0.417080 | + | 0.908870i | \(0.636947\pi\) | |||||||
\(434\) | −225308. | −0.0574186 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −330160. | −0.0831780 | ||||||||
\(437\) | 2.65815e6 | 0.665849 | ||||||||
\(438\) | −2.96791e6 | −0.739206 | ||||||||
\(439\) | 1.58759e6 | 0.393168 | 0.196584 | − | 0.980487i | \(-0.437015\pi\) | ||||
0.196584 | + | 0.980487i | \(0.437015\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −855846. | −0.209556 | ||||||||
\(442\) | −1.11463e6 | −0.271379 | ||||||||
\(443\) | −213888. | −0.0517818 | −0.0258909 | − | 0.999665i | \(-0.508242\pi\) | ||||
−0.0258909 | + | 0.999665i | \(0.508242\pi\) | |||||||
\(444\) | 466272. | 0.112249 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 194180. | 0.0462240 | ||||||||
\(447\) | −3.79615e6 | −0.898616 | ||||||||
\(448\) | −323584. | −0.0761714 | ||||||||
\(449\) | 3.70724e6 | 0.867831 | 0.433916 | − | 0.900953i | \(-0.357132\pi\) | ||||
0.433916 | + | 0.900953i | \(0.357132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 984600. | 0.227939 | ||||||||
\(452\) | 2.83027e6 | 0.651602 | ||||||||
\(453\) | 917253. | 0.210012 | ||||||||
\(454\) | −1.15061e6 | −0.261992 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.13414e6 | 0.255421 | ||||||||
\(457\) | 3.83193e6 | 0.858275 | 0.429138 | − | 0.903239i | \(-0.358818\pi\) | ||||
0.429138 | + | 0.903239i | \(0.358818\pi\) | |||||||
\(458\) | 288260. | 0.0642127 | ||||||||
\(459\) | 1.48279e6 | 0.328509 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.58672e6 | 1.22435 | 0.612174 | − | 0.790723i | \(-0.290295\pi\) | ||||
0.612174 | + | 0.790723i | \(0.290295\pi\) | |||||||
\(462\) | 426600. | 0.0929856 | ||||||||
\(463\) | −4.40142e6 | −0.954203 | −0.477101 | − | 0.878848i | \(-0.658313\pi\) | ||||
−0.477101 | + | 0.878848i | \(0.658313\pi\) | |||||||
\(464\) | −754176. | −0.162621 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.27659e6 | −0.485647 | ||||||||
\(467\) | 3.35225e6 | 0.711287 | 0.355643 | − | 0.934622i | \(-0.384262\pi\) | ||||
0.355643 | + | 0.934622i | \(0.384262\pi\) | |||||||
\(468\) | 177552. | 0.0374724 | ||||||||
\(469\) | 1.77900e6 | 0.373460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 915957. | 0.190249 | ||||||||
\(472\) | 1.62240e6 | 0.335199 | ||||||||
\(473\) | −2.93685e6 | −0.603572 | ||||||||
\(474\) | 2.93299e6 | 0.599605 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.57098e6 | 0.520093 | ||||||||
\(477\) | −2.09758e6 | −0.422106 | ||||||||
\(478\) | 2.78602e6 | 0.557717 | ||||||||
\(479\) | 909966. | 0.181212 | 0.0906059 | − | 0.995887i | \(-0.471120\pi\) | ||||
0.0906059 | + | 0.995887i | \(0.471120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −443606. | −0.0874248 | ||||||||
\(482\) | 2.30455e6 | 0.451823 | ||||||||
\(483\) | −959850. | −0.187213 | ||||||||
\(484\) | −2.21682e6 | −0.430146 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −4.03579e6 | −0.771093 | −0.385546 | − | 0.922689i | \(-0.625987\pi\) | ||||
−0.385546 | + | 0.922689i | \(0.625987\pi\) | |||||||
\(488\) | 3.23936e6 | 0.615757 | ||||||||
\(489\) | 1.82024e6 | 0.344236 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 379944. | 0.0711239 | 0.0355620 | − | 0.999367i | \(-0.488678\pi\) | ||||
0.0355620 | + | 0.999367i | \(0.488678\pi\) | |||||||
\(492\) | −945216. | −0.176043 | ||||||||
\(493\) | 5.99216e6 | 1.11037 | ||||||||
\(494\) | −1.07901e6 | −0.198934 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 182528. | 0.0333139 | ||||||||
\(497\) | −2.67810e6 | −0.486335 | ||||||||
\(498\) | −928152. | −0.167705 | ||||||||
\(499\) | −7.42433e6 | −1.33477 | −0.667384 | − | 0.744714i | \(-0.732586\pi\) | ||||
−0.667384 | + | 0.744714i | \(0.732586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.08440e6 | −0.371011 | ||||||||
\(502\) | −4.89970e6 | −0.867780 | ||||||||
\(503\) | 2.29988e6 | 0.405309 | 0.202654 | − | 0.979250i | \(-0.435043\pi\) | ||||
0.202654 | + | 0.979250i | \(0.435043\pi\) | |||||||
\(504\) | −409536. | −0.0718151 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −810000. | −0.140640 | ||||||||
\(507\) | 3.17272e6 | 0.548165 | ||||||||
\(508\) | −4.10368e6 | −0.705528 | ||||||||
\(509\) | 6.73721e6 | 1.15262 | 0.576310 | − | 0.817231i | \(-0.304492\pi\) | ||||
0.576310 | + | 0.817231i | \(0.304492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.51292e6 | −1.10338 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 1.43540e6 | 0.240813 | ||||||||
\(514\) | 3.88853e6 | 0.649198 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.81938e6 | 0.466153 | ||||||||
\(517\) | −3.17250e6 | −0.522006 | ||||||||
\(518\) | 1.02321e6 | 0.167548 | ||||||||
\(519\) | 1.56800e6 | 0.255521 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.26806e6 | −1.49587 | −0.747936 | − | 0.663770i | \(-0.768955\pi\) | ||||
−0.747936 | + | 0.663770i | \(0.768955\pi\) | |||||||
\(522\) | −954504. | −0.153321 | ||||||||
\(523\) | 1.10620e7 | 1.76839 | 0.884197 | − | 0.467113i | \(-0.154706\pi\) | ||||
0.884197 | + | 0.467113i | \(0.154706\pi\) | |||||||
\(524\) | 2.84160e6 | 0.452100 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.04760e6 | 1.11065 | ||||||||
\(527\) | −1.45024e6 | −0.227465 | ||||||||
\(528\) | −345600. | −0.0539497 | ||||||||
\(529\) | −4.61384e6 | −0.716842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.05335e6 | 0.316029 | ||||||||
\(532\) | 2.48882e6 | 0.381253 | ||||||||
\(533\) | 899268. | 0.137111 | ||||||||
\(534\) | −3.73421e6 | −0.566690 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.44122e6 | −0.216679 | ||||||||
\(537\) | 5.77859e6 | 0.864742 | ||||||||
\(538\) | 6.97534e6 | 1.03899 | ||||||||
\(539\) | −1.58490e6 | −0.234979 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.30754e7 | −1.92072 | −0.960358 | − | 0.278771i | \(-0.910073\pi\) | ||||
−0.960358 | + | 0.278771i | \(0.910073\pi\) | |||||||
\(542\) | −6.81702e6 | −0.996774 | ||||||||
\(543\) | 504639. | 0.0734482 | ||||||||
\(544\) | −2.08282e6 | −0.301754 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 389628. | 0.0559331 | ||||||||
\(547\) | −1.84605e6 | −0.263800 | −0.131900 | − | 0.991263i | \(-0.542108\pi\) | ||||
−0.131900 | + | 0.991263i | \(0.542108\pi\) | |||||||
\(548\) | 4.17418e6 | 0.593772 | ||||||||
\(549\) | 4.09982e6 | 0.580542 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.80067e6 | 0.813953 | ||||||||
\(552\) | 777600. | 0.108620 | ||||||||
\(553\) | 6.43629e6 | 0.894999 | ||||||||
\(554\) | 5.87887e6 | 0.813803 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.48294e6 | −0.477815 | ||||||||
\(557\) | 6.48782e6 | 0.886055 | 0.443027 | − | 0.896508i | \(-0.353904\pi\) | ||||
0.443027 | + | 0.896508i | \(0.353904\pi\) | |||||||
\(558\) | 231012. | 0.0314086 | ||||||||
\(559\) | −2.68232e6 | −0.363063 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.74590e6 | 0.368364 | ||||||||
\(562\) | −4.90121e6 | −0.654579 | ||||||||
\(563\) | 3.01538e6 | 0.400932 | 0.200466 | − | 0.979701i | \(-0.435754\pi\) | ||||
0.200466 | + | 0.979701i | \(0.435754\pi\) | |||||||
\(564\) | 3.04560e6 | 0.403158 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.54933e6 | −0.334492 | ||||||||
\(567\) | −518319. | −0.0677079 | ||||||||
\(568\) | 2.16960e6 | 0.282169 | ||||||||
\(569\) | −3.49810e6 | −0.452952 | −0.226476 | − | 0.974017i | \(-0.572720\pi\) | ||||
−0.226476 | + | 0.974017i | \(0.572720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.23749e7 | −1.58837 | −0.794185 | − | 0.607676i | \(-0.792102\pi\) | ||||
−0.794185 | + | 0.607676i | \(0.792102\pi\) | |||||||
\(572\) | 328800. | 0.0420186 | ||||||||
\(573\) | 1.88725e6 | 0.240128 | ||||||||
\(574\) | −2.07422e6 | −0.262770 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 6.80687e6 | 0.851153 | 0.425577 | − | 0.904922i | \(-0.360071\pi\) | ||||
0.425577 | + | 0.904922i | \(0.360071\pi\) | |||||||
\(578\) | 1.08692e7 | 1.35325 | ||||||||
\(579\) | 6.44037e6 | 0.798389 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.03678e6 | −0.250325 | ||||||||
\(582\) | 2.06435e6 | 0.252624 | ||||||||
\(583\) | −3.88440e6 | −0.473317 | ||||||||
\(584\) | 5.27629e6 | 0.640172 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 140376. | 0.0168869 | ||||||||
\(587\) | 7.77113e6 | 0.930870 | 0.465435 | − | 0.885082i | \(-0.345898\pi\) | ||||
0.465435 | + | 0.885082i | \(0.345898\pi\) | |||||||
\(588\) | 1.52150e6 | 0.181480 | ||||||||
\(589\) | −1.40390e6 | −0.166743 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.57969e6 | −0.539345 | ||||||||
\(592\) | −828928. | −0.0972104 | ||||||||
\(593\) | −1.51222e7 | −1.76595 | −0.882976 | − | 0.469418i | \(-0.844464\pi\) | ||||
−0.882976 | + | 0.469418i | \(0.844464\pi\) | |||||||
\(594\) | −437400. | −0.0508643 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.74870e6 | 0.778224 | ||||||||
\(597\) | 8.87415e6 | 1.01904 | ||||||||
\(598\) | −739800. | −0.0845982 | ||||||||
\(599\) | −1.67012e6 | −0.190187 | −0.0950937 | − | 0.995468i | \(-0.530315\pi\) | ||||
−0.0950937 | + | 0.995468i | \(0.530315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.12220e6 | 0.465525 | 0.232763 | − | 0.972534i | \(-0.425223\pi\) | ||||
0.232763 | + | 0.972534i | \(0.425223\pi\) | |||||||
\(602\) | 6.18696e6 | 0.695803 | ||||||||
\(603\) | −1.82404e6 | −0.204287 | ||||||||
\(604\) | −1.63067e6 | −0.181876 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.27715e6 | 0.362506 | ||||||||
\(607\) | 6.81870e6 | 0.751155 | 0.375578 | − | 0.926791i | \(-0.377444\pi\) | ||||
0.375578 | + | 0.926791i | \(0.377444\pi\) | |||||||
\(608\) | −2.01626e6 | −0.221201 | ||||||||
\(609\) | −2.09461e6 | −0.228854 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.89755e6 | −0.313999 | ||||||||
\(612\) | −2.63606e6 | −0.284497 | ||||||||
\(613\) | 1.59466e7 | 1.71402 | 0.857010 | − | 0.515300i | \(-0.172319\pi\) | ||||
0.857010 | + | 0.515300i | \(0.172319\pi\) | |||||||
\(614\) | 1.15216e7 | 1.23336 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −758400. | −0.0805279 | ||||||||
\(617\) | −8.21952e6 | −0.869228 | −0.434614 | − | 0.900617i | \(-0.643115\pi\) | ||||
−0.434614 | + | 0.900617i | \(0.643115\pi\) | |||||||
\(618\) | −6.89890e6 | −0.726622 | ||||||||
\(619\) | −1.23323e7 | −1.29366 | −0.646828 | − | 0.762636i | \(-0.723905\pi\) | ||||
−0.646828 | + | 0.762636i | \(0.723905\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 984150. | 0.102408 | ||||||||
\(622\) | −9.53220e6 | −0.987910 | ||||||||
\(623\) | −8.19451e6 | −0.845869 | ||||||||
\(624\) | −315648. | −0.0324520 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.72325e6 | −0.787706 | ||||||||
\(627\) | 2.65815e6 | 0.270029 | ||||||||
\(628\) | −1.62837e6 | −0.164761 | ||||||||
\(629\) | 6.58609e6 | 0.663745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.01912e6 | −0.301861 | −0.150931 | − | 0.988544i | \(-0.548227\pi\) | ||||
−0.150931 | + | 0.988544i | \(0.548227\pi\) | |||||||
\(632\) | −5.21421e6 | −0.519273 | ||||||||
\(633\) | −1.07546e6 | −0.106680 | ||||||||
\(634\) | −8.75981e6 | −0.865509 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.72902e6 | 0.365555 | ||||||||
\(637\) | −1.44754e6 | −0.141346 | ||||||||
\(638\) | −1.76760e6 | −0.171922 | ||||||||
\(639\) | 2.74590e6 | 0.266031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.18052e7 | −1.13482 | −0.567411 | − | 0.823435i | \(-0.692055\pi\) | ||||
−0.567411 | + | 0.823435i | \(0.692055\pi\) | |||||||
\(642\) | −334368. | −0.0320175 | ||||||||
\(643\) | −2.85360e6 | −0.272186 | −0.136093 | − | 0.990696i | \(-0.543455\pi\) | ||||
−0.136093 | + | 0.990696i | \(0.543455\pi\) | |||||||
\(644\) | 1.70640e6 | 0.162131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.60198e7 | 1.51034 | ||||||||
\(647\) | −3.40192e6 | −0.319494 | −0.159747 | − | 0.987158i | \(-0.551068\pi\) | ||||
−0.159747 | + | 0.987158i | \(0.551068\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 3.80250e6 | 0.354370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 506943. | 0.0468821 | ||||||||
\(652\) | −3.23598e6 | −0.298117 | ||||||||
\(653\) | −9.39166e6 | −0.861905 | −0.430953 | − | 0.902375i | \(-0.641822\pi\) | ||||
−0.430953 | + | 0.902375i | \(0.641822\pi\) | |||||||
\(654\) | 742860. | 0.0679145 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.68038e6 | 0.152458 | ||||||||
\(657\) | 6.67780e6 | 0.603560 | ||||||||
\(658\) | 6.68340e6 | 0.601773 | ||||||||
\(659\) | 9.36659e6 | 0.840171 | 0.420086 | − | 0.907484i | \(-0.362000\pi\) | ||||
0.420086 | + | 0.907484i | \(0.362000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57748e7 | 1.40430 | 0.702150 | − | 0.712029i | \(-0.252223\pi\) | ||||
0.702150 | + | 0.712029i | \(0.252223\pi\) | |||||||
\(662\) | 5.65717e6 | 0.501712 | ||||||||
\(663\) | 2.50792e6 | 0.221580 | ||||||||
\(664\) | 1.65005e6 | 0.145237 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.04911e6 | −0.0916508 | ||||||||
\(667\) | 3.97710e6 | 0.346140 | ||||||||
\(668\) | 3.70560e6 | 0.321305 | ||||||||
\(669\) | −436905. | −0.0377417 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.59225e6 | 0.650975 | ||||||||
\(672\) | 728064. | 0.0621937 | ||||||||
\(673\) | −6.64515e6 | −0.565545 | −0.282773 | − | 0.959187i | \(-0.591254\pi\) | ||||
−0.282773 | + | 0.959187i | \(0.591254\pi\) | |||||||
\(674\) | 5.52832e6 | 0.468753 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.64038e6 | −0.474725 | ||||||||
\(677\) | −1.57780e7 | −1.32306 | −0.661532 | − | 0.749917i | \(-0.730094\pi\) | ||||
−0.661532 | + | 0.749917i | \(0.730094\pi\) | |||||||
\(678\) | −6.36811e6 | −0.532030 | ||||||||
\(679\) | 4.53010e6 | 0.377080 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.58887e6 | 0.213915 | ||||||||
\(682\) | 427800. | 0.0352192 | ||||||||
\(683\) | −1.96654e7 | −1.61306 | −0.806532 | − | 0.591190i | \(-0.798658\pi\) | ||||
−0.806532 | + | 0.591190i | \(0.798658\pi\) | |||||||
\(684\) | −2.55182e6 | −0.208550 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.64987e6 | 0.701777 | ||||||||
\(687\) | −648585. | −0.0524294 | ||||||||
\(688\) | −5.01222e6 | −0.403701 | ||||||||
\(689\) | −3.54775e6 | −0.284712 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 990464. | 0.0789121 | 0.0394560 | − | 0.999221i | \(-0.487437\pi\) | ||||
0.0394560 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(692\) | −2.78755e6 | −0.221288 | ||||||||
\(693\) | −959850. | −0.0759225 | ||||||||
\(694\) | −1.13503e6 | −0.0894560 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.69690e6 | 0.132780 | ||||||||
\(697\) | −1.33512e7 | −1.04097 | ||||||||
\(698\) | 8.55236e6 | 0.664427 | ||||||||
\(699\) | 5.12233e6 | 0.396529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.52919e6 | 0.501839 | 0.250920 | − | 0.968008i | \(-0.419267\pi\) | ||||
0.250920 | + | 0.968008i | \(0.419267\pi\) | |||||||
\(702\) | −399492. | −0.0305960 | ||||||||
\(703\) | 6.37562e6 | 0.486558 | ||||||||
\(704\) | 614400. | 0.0467218 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.26406e7 | 0.954455 | ||||||||
\(707\) | 7.19153e6 | 0.541094 | ||||||||
\(708\) | −3.65040e6 | −0.273689 | ||||||||
\(709\) | −2.02106e7 | −1.50996 | −0.754979 | − | 0.655749i | \(-0.772353\pi\) | ||||
−0.754979 | + | 0.655749i | \(0.772353\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.59923e6 | −0.489575 | ||||||||
\(712\) | 6.63859e6 | 0.490768 | ||||||||
\(713\) | −962550. | −0.0709087 | ||||||||
\(714\) | −5.78470e6 | −0.424654 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.02731e7 | −0.748888 | ||||||||
\(717\) | −6.26854e6 | −0.455374 | ||||||||
\(718\) | −1.43826e7 | −1.04118 | ||||||||
\(719\) | −2.27720e7 | −1.64277 | −0.821387 | − | 0.570371i | \(-0.806800\pi\) | ||||
−0.821387 | + | 0.570371i | \(0.806800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51392e7 | −1.08459 | ||||||||
\(722\) | 5.60345e6 | 0.400048 | ||||||||
\(723\) | −5.18523e6 | −0.368912 | ||||||||
\(724\) | −897136. | −0.0636080 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.98784e6 | 0.351213 | ||||||||
\(727\) | −7.09186e6 | −0.497650 | −0.248825 | − | 0.968548i | \(-0.580044\pi\) | ||||
−0.248825 | + | 0.968548i | \(0.580044\pi\) | |||||||
\(728\) | −692672. | −0.0484394 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.98237e7 | 2.75644 | ||||||||
\(732\) | −7.28856e6 | −0.502764 | ||||||||
\(733\) | −1.38982e7 | −0.955432 | −0.477716 | − | 0.878514i | \(-0.658535\pi\) | ||||
−0.477716 | + | 0.878514i | \(0.658535\pi\) | |||||||
\(734\) | −1.84817e7 | −1.26620 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.38240e6 | −0.0940674 | ||||||||
\(737\) | −3.37785e6 | −0.229072 | ||||||||
\(738\) | 2.12674e6 | 0.143738 | ||||||||
\(739\) | 1.54857e7 | 1.04309 | 0.521543 | − | 0.853225i | \(-0.325357\pi\) | ||||
0.521543 | + | 0.853225i | \(0.325357\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.42778e6 | 0.162429 | ||||||||
\(742\) | 8.18314e6 | 0.545645 | ||||||||
\(743\) | 159276. | 0.0105847 | 0.00529235 | − | 0.999986i | \(-0.498315\pi\) | ||||
0.00529235 | + | 0.999986i | \(0.498315\pi\) | |||||||
\(744\) | −410688. | −0.0272007 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.40793e7 | −0.926263 | ||||||||
\(747\) | 2.08834e6 | 0.136930 | ||||||||
\(748\) | −4.88160e6 | −0.319013 | ||||||||
\(749\) | −733752. | −0.0477908 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15554e7 | 0.747625 | 0.373812 | − | 0.927504i | \(-0.378050\pi\) | ||||
0.373812 | + | 0.927504i | \(0.378050\pi\) | |||||||
\(752\) | −5.41440e6 | −0.349145 | ||||||||
\(753\) | 1.10243e7 | 0.708540 | ||||||||
\(754\) | −1.61441e6 | −0.103415 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 921456. | 0.0586368 | ||||||||
\(757\) | −6.34402e6 | −0.402369 | −0.201185 | − | 0.979553i | \(-0.564479\pi\) | ||||
−0.201185 | + | 0.979553i | \(0.564479\pi\) | |||||||
\(758\) | 2.38024e6 | 0.150469 | ||||||||
\(759\) | 1.82250e6 | 0.114832 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.17748e7 | −0.737040 | −0.368520 | − | 0.929620i | \(-0.620135\pi\) | ||||
−0.368520 | + | 0.929620i | \(0.620135\pi\) | |||||||
\(762\) | 9.23328e6 | 0.576061 | ||||||||
\(763\) | 1.63016e6 | 0.101373 | ||||||||
\(764\) | −3.35510e6 | −0.207957 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.20200e6 | −0.320331 | ||||||||
\(767\) | 3.47295e6 | 0.213162 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −2.47869e7 | −1.51149 | −0.755745 | − | 0.654865i | \(-0.772725\pi\) | ||||
−0.755745 | + | 0.654865i | \(0.772725\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.74919e6 | −0.530068 | ||||||||
\(772\) | −1.14496e7 | −0.691425 | ||||||||
\(773\) | −1.38017e7 | −0.830774 | −0.415387 | − | 0.909645i | \(-0.636354\pi\) | ||||
−0.415387 | + | 0.909645i | \(0.636354\pi\) | |||||||
\(774\) | −6.34360e6 | −0.380613 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.66995e6 | −0.218779 | ||||||||
\(777\) | −2.30222e6 | −0.136802 | ||||||||
\(778\) | 2.48290e6 | 0.147065 | ||||||||
\(779\) | −1.29245e7 | −0.763081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.08500e6 | 0.298307 | ||||||||
\(782\) | 1.09836e7 | 0.642285 | ||||||||
\(783\) | 2.14763e6 | 0.125186 | ||||||||
\(784\) | −2.70490e6 | −0.157167 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.39360e6 | −0.369138 | ||||||||
\(787\) | −1.53795e7 | −0.885129 | −0.442565 | − | 0.896737i | \(-0.645931\pi\) | ||||
−0.442565 | + | 0.896737i | \(0.645931\pi\) | |||||||
\(788\) | 8.14166e6 | 0.467087 | ||||||||
\(789\) | −1.58571e7 | −0.906841 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.39745e7 | −0.794135 | ||||||||
\(792\) | 777600. | 0.0440497 | ||||||||
\(793\) | 6.93426e6 | 0.391577 | ||||||||
\(794\) | 4.74489e6 | 0.267101 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.57763e7 | −0.882514 | ||||||||
\(797\) | −2.33978e7 | −1.30475 | −0.652377 | − | 0.757894i | \(-0.726228\pi\) | ||||
−0.652377 | + | 0.757894i | \(0.726228\pi\) | |||||||
\(798\) | −5.59984e6 | −0.311292 | ||||||||
\(799\) | 4.30191e7 | 2.38393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.40197e6 | 0.462700 | ||||||||
\(802\) | 1.25334e7 | 0.688069 | ||||||||
\(803\) | 1.23663e7 | 0.676785 | ||||||||
\(804\) | 3.24274e6 | 0.176918 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 390724. | 0.0211852 | ||||||||
\(807\) | −1.56945e7 | −0.848328 | ||||||||
\(808\) | −5.82605e6 | −0.313939 | ||||||||
\(809\) | −2.80188e7 | −1.50515 | −0.752573 | − | 0.658509i | \(-0.771187\pi\) | ||||
−0.752573 | + | 0.658509i | \(0.771187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.65641e6 | −0.0884332 | −0.0442166 | − | 0.999022i | \(-0.514079\pi\) | ||||
−0.0442166 | + | 0.999022i | \(0.514079\pi\) | |||||||
\(812\) | 3.72374e6 | 0.198194 | ||||||||
\(813\) | 1.53383e7 | 0.813862 | ||||||||
\(814\) | −1.94280e6 | −0.102770 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.68634e6 | 0.246381 | ||||||||
\(817\) | 3.85511e7 | 2.02060 | ||||||||
\(818\) | 2.27032e6 | 0.118633 | ||||||||
\(819\) | −876663. | −0.0456691 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.97382e7 | 1.53978 | 0.769888 | − | 0.638179i | \(-0.220312\pi\) | ||||
0.769888 | + | 0.638179i | \(0.220312\pi\) | |||||||
\(822\) | −9.39190e6 | −0.484812 | ||||||||
\(823\) | −1.60108e7 | −0.823972 | −0.411986 | − | 0.911190i | \(-0.635165\pi\) | ||||
−0.411986 | + | 0.911190i | \(0.635165\pi\) | |||||||
\(824\) | 1.22647e7 | 0.629273 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.01060e6 | −0.408522 | ||||||||
\(827\) | 2.54748e7 | 1.29523 | 0.647614 | − | 0.761969i | \(-0.275767\pi\) | ||||
0.647614 | + | 0.761969i | \(0.275767\pi\) | |||||||
\(828\) | −1.74960e6 | −0.0886876 | ||||||||
\(829\) | 1.89971e7 | 0.960064 | 0.480032 | − | 0.877251i | \(-0.340625\pi\) | ||||
0.480032 | + | 0.877251i | \(0.340625\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.32275e7 | −0.664467 | ||||||||
\(832\) | 561152. | 0.0281043 | ||||||||
\(833\) | 2.14912e7 | 1.07312 | ||||||||
\(834\) | 7.83662e6 | 0.390134 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.72560e6 | −0.233852 | ||||||||
\(837\) | −519777. | −0.0256450 | ||||||||
\(838\) | −2.43600e7 | −1.19830 | ||||||||
\(839\) | 3.98539e7 | 1.95463 | 0.977317 | − | 0.211782i | \(-0.0679267\pi\) | ||||
0.977317 | + | 0.211782i | \(0.0679267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.18322e7 | −0.576868 | ||||||||
\(842\) | 1.22856e7 | 0.597193 | ||||||||
\(843\) | 1.10277e7 | 0.534462 | ||||||||
\(844\) | 1.91192e6 | 0.0923876 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.85260e6 | −0.329177 | ||||||||
\(847\) | 1.09455e7 | 0.524238 | ||||||||
\(848\) | −6.62938e6 | −0.316580 | ||||||||
\(849\) | 5.73600e6 | 0.273111 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.37130e6 | 0.206912 | ||||||||
\(852\) | −4.88160e6 | −0.230390 | ||||||||
\(853\) | 2.19179e7 | 1.03140 | 0.515700 | − | 0.856769i | \(-0.327532\pi\) | ||||
0.515700 | + | 0.856769i | \(0.327532\pi\) | |||||||
\(854\) | −1.59943e7 | −0.750450 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 594432. | 0.0277280 | ||||||||
\(857\) | −2.72213e7 | −1.26607 | −0.633033 | − | 0.774125i | \(-0.718190\pi\) | ||||
−0.633033 | + | 0.774125i | \(0.718190\pi\) | |||||||
\(858\) | −739800. | −0.0343081 | ||||||||
\(859\) | 3.76214e7 | 1.73961 | 0.869805 | − | 0.493396i | \(-0.164245\pi\) | ||||
0.869805 | + | 0.493396i | \(0.164245\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.66700e6 | 0.214551 | ||||||||
\(862\) | −2.67660e6 | −0.122692 | ||||||||
\(863\) | 2.51995e7 | 1.15177 | 0.575885 | − | 0.817531i | \(-0.304658\pi\) | ||||
0.575885 | + | 0.817531i | \(0.304658\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.30176e7 | −0.589841 | ||||||||
\(867\) | −2.44557e7 | −1.10492 | ||||||||
\(868\) | −901232. | −0.0406011 | ||||||||
\(869\) | −1.22208e7 | −0.548972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.08510e6 | −0.137792 | ||||||||
\(872\) | −1.32064e6 | −0.0588157 | ||||||||
\(873\) | −4.64478e6 | −0.206267 | ||||||||
\(874\) | 1.06326e7 | 0.470826 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.18716e7 | −0.522698 | ||||||||
\(877\) | 2.77307e6 | 0.121748 | 0.0608739 | − | 0.998145i | \(-0.480611\pi\) | ||||
0.0608739 | + | 0.998145i | \(0.480611\pi\) | |||||||
\(878\) | 6.35037e6 | 0.278012 | ||||||||
\(879\) | −315846. | −0.0137881 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.37827e7 | −0.598268 | −0.299134 | − | 0.954211i | \(-0.596698\pi\) | ||||
−0.299134 | + | 0.954211i | \(0.596698\pi\) | |||||||
\(882\) | −3.42338e6 | −0.148178 | ||||||||
\(883\) | −4.96322e6 | −0.214221 | −0.107110 | − | 0.994247i | \(-0.534160\pi\) | ||||
−0.107110 | + | 0.994247i | \(0.534160\pi\) | |||||||
\(884\) | −4.45853e6 | −0.191894 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −855552. | −0.0366153 | ||||||||
\(887\) | 4.12640e7 | 1.76101 | 0.880505 | − | 0.474037i | \(-0.157204\pi\) | ||||
0.880505 | + | 0.474037i | \(0.157204\pi\) | |||||||
\(888\) | 1.86509e6 | 0.0793719 | ||||||||
\(889\) | 2.02619e7 | 0.859857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 984150. | 0.0415305 | ||||||||
\(892\) | 776720. | 0.0326853 | ||||||||
\(893\) | 4.16444e7 | 1.74754 | ||||||||
\(894\) | −1.51846e7 | −0.635417 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.29434e6 | −0.0538613 | ||||||||
\(897\) | 1.66455e6 | 0.0690742 | ||||||||
\(898\) | 1.48290e7 | 0.613649 | ||||||||
\(899\) | −2.10050e6 | −0.0866808 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.26725e7 | 2.16158 | ||||||||
\(902\) | 3.93840e6 | 0.161177 | ||||||||
\(903\) | −1.39207e7 | −0.568121 | ||||||||
\(904\) | 1.13211e7 | 0.460752 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.66901e6 | 0.148501 | ||||||||
\(907\) | 1.66308e7 | 0.671268 | 0.335634 | − | 0.941992i | \(-0.391049\pi\) | ||||
0.335634 | + | 0.941992i | \(0.391049\pi\) | |||||||
\(908\) | −4.60243e6 | −0.185256 | ||||||||
\(909\) | −7.37359e6 | −0.295985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.64995e7 | 1.45711 | 0.728554 | − | 0.684989i | \(-0.240193\pi\) | ||||
0.728554 | + | 0.684989i | \(0.240193\pi\) | |||||||
\(912\) | 4.53658e6 | 0.180610 | ||||||||
\(913\) | 3.86730e6 | 0.153543 | ||||||||
\(914\) | 1.53277e7 | 0.606892 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.15304e6 | 0.0454052 | ||||||||
\(917\) | −1.40304e7 | −0.550994 | ||||||||
\(918\) | 5.93114e6 | 0.232291 | ||||||||
\(919\) | 6.83190e6 | 0.266841 | 0.133421 | − | 0.991060i | \(-0.457404\pi\) | ||||
0.133421 | + | 0.991060i | \(0.457404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.59236e7 | −1.00704 | ||||||||
\(922\) | 2.23469e7 | 0.865744 | ||||||||
\(923\) | 4.64430e6 | 0.179439 | ||||||||
\(924\) | 1.70640e6 | 0.0657508 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.76057e7 | −0.674723 | ||||||||
\(927\) | 1.55225e7 | 0.593284 | ||||||||
\(928\) | −3.01670e6 | −0.114991 | ||||||||
\(929\) | 5.05115e6 | 0.192022 | 0.0960111 | − | 0.995380i | \(-0.469392\pi\) | ||||
0.0960111 | + | 0.995380i | \(0.469392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.08045e7 | 0.786651 | ||||||||
\(932\) | −9.10637e6 | −0.343404 | ||||||||
\(933\) | 2.14474e7 | 0.806625 | ||||||||
\(934\) | 1.34090e7 | 0.502956 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 710208. | 0.0264970 | ||||||||
\(937\) | 8.30023e6 | 0.308845 | 0.154423 | − | 0.988005i | \(-0.450648\pi\) | ||||
0.154423 | + | 0.988005i | \(0.450648\pi\) | |||||||
\(938\) | 7.11600e6 | 0.264076 | ||||||||
\(939\) | 1.73773e7 | 0.643160 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.87332e7 | −1.79412 | −0.897059 | − | 0.441910i | \(-0.854301\pi\) | ||||
−0.897059 | + | 0.441910i | \(0.854301\pi\) | |||||||
\(942\) | 3.66383e6 | 0.134526 | ||||||||
\(943\) | −8.86140e6 | −0.324506 | ||||||||
\(944\) | 6.48960e6 | 0.237022 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.17474e7 | −0.426790 | ||||||||
\(947\) | −7.34777e6 | −0.266245 | −0.133122 | − | 0.991100i | \(-0.542500\pi\) | ||||
−0.133122 | + | 0.991100i | \(0.542500\pi\) | |||||||
\(948\) | 1.17320e7 | 0.423985 | ||||||||
\(949\) | 1.12946e7 | 0.407102 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.97096e7 | 0.706685 | ||||||||
\(952\) | 1.02839e7 | 0.367761 | ||||||||
\(953\) | −3.51437e7 | −1.25347 | −0.626737 | − | 0.779231i | \(-0.715610\pi\) | ||||
−0.626737 | + | 0.779231i | \(0.715610\pi\) | |||||||
\(954\) | −8.39030e6 | −0.298474 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.11441e7 | 0.394365 | ||||||||
\(957\) | 3.97710e6 | 0.140374 | ||||||||
\(958\) | 3.63986e6 | 0.128136 | ||||||||
\(959\) | −2.06100e7 | −0.723655 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.81208e7 | −0.982243 | ||||||||
\(962\) | −1.77442e6 | −0.0618187 | ||||||||
\(963\) | 752328. | 0.0261422 | ||||||||
\(964\) | 9.21819e6 | 0.319487 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.83940e6 | −0.132379 | ||||||||
\(967\) | 2.31186e6 | 0.0795050 | 0.0397525 | − | 0.999210i | \(-0.487343\pi\) | ||||
0.0397525 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(968\) | −8.86726e6 | −0.304159 | ||||||||
\(969\) | −3.60445e7 | −1.23319 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.73588e7 | −1.27158 | −0.635791 | − | 0.771861i | \(-0.719326\pi\) | ||||
−0.635791 | + | 0.771861i | \(0.719326\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 1.71970e7 | 0.582333 | ||||||||
\(974\) | −1.61432e7 | −0.545245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.29574e7 | 0.435406 | ||||||||
\(977\) | −1.02666e7 | −0.344104 | −0.172052 | − | 0.985088i | \(-0.555040\pi\) | ||||
−0.172052 | + | 0.985088i | \(0.555040\pi\) | |||||||
\(978\) | 7.28096e6 | 0.243412 | ||||||||
\(979\) | 1.55592e7 | 0.518837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.67144e6 | −0.0554520 | ||||||||
\(982\) | 1.51978e6 | 0.0502922 | ||||||||
\(983\) | 2.98404e7 | 0.984966 | 0.492483 | − | 0.870322i | \(-0.336089\pi\) | ||||
0.492483 | + | 0.870322i | \(0.336089\pi\) | |||||||
\(984\) | −3.78086e6 | −0.124481 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.39687e7 | 0.785148 | ||||||||
\(987\) | −1.50376e7 | −0.491346 | ||||||||
\(988\) | −4.31605e6 | −0.140668 | ||||||||
\(989\) | 2.64316e7 | 0.859278 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.34222e7 | −0.757605 | −0.378803 | − | 0.925477i | \(-0.623664\pi\) | ||||
−0.378803 | + | 0.925477i | \(0.623664\pi\) | |||||||
\(992\) | 730112. | 0.0235565 | ||||||||
\(993\) | −1.27286e7 | −0.409646 | ||||||||
\(994\) | −1.07124e7 | −0.343891 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.71261e6 | −0.118585 | ||||||||
\(997\) | −2.60709e7 | −0.830651 | −0.415326 | − | 0.909673i | \(-0.636332\pi\) | ||||
−0.415326 | + | 0.909673i | \(0.636332\pi\) | |||||||
\(998\) | −2.96973e7 | −0.943824 | ||||||||
\(999\) | 2.36050e6 | 0.0748326 |
(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 | 150.6.a.i.1.1 | yes | 1 | |
3.2 | odd | 2 | 450.6.a.e.1.1 | 1 | |||
5.2 | odd | 4 | 150.6.c.c.49.2 | 2 | |||
5.3 | odd | 4 | 150.6.c.c.49.1 | 2 | |||
5.4 | even | 2 | 150.6.a.g.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 450.6.c.g.199.1 | 2 | |||
15.8 | even | 4 | 450.6.c.g.199.2 | 2 | |||
15.14 | odd | 2 | 450.6.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.6.a.g.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
150.6.a.i.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
150.6.c.c.49.1 | 2 | 5.3 | odd | 4 | |||
150.6.c.c.49.2 | 2 | 5.2 | odd | 4 | |||
450.6.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.a.t.1.1 | 1 | 15.14 | odd | 2 | |||
450.6.c.g.199.1 | 2 | 15.2 | even | 4 | |||
450.6.c.g.199.2 | 2 | 15.8 | even | 4 |