Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,6,Mod(1,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.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: | \(40.4167225929\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 252.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 96.0000 | 1.71730 | 0.858650 | − | 0.512562i | \(-0.171304\pi\) | ||||
0.858650 | + | 0.512562i | \(0.171304\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 720.000 | 1.79412 | 0.897059 | − | 0.441912i | \(-0.145700\pi\) | ||||
0.897059 | + | 0.441912i | \(0.145700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 572.000 | 0.938723 | 0.469362 | − | 0.883006i | \(-0.344484\pi\) | ||||
0.469362 | + | 0.883006i | \(0.344484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1254.00 | −1.05239 | −0.526193 | − | 0.850365i | \(-0.676381\pi\) | ||||
−0.526193 | + | 0.850365i | \(0.676381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −94.0000 | −0.0597371 | −0.0298685 | − | 0.999554i | \(-0.509509\pi\) | ||||
−0.0298685 | + | 0.999554i | \(0.509509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −96.0000 | −0.0378400 | −0.0189200 | − | 0.999821i | \(-0.506023\pi\) | ||||
−0.0189200 | + | 0.999821i | \(0.506023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6091.00 | 1.94912 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4374.00 | 0.965792 | 0.482896 | − | 0.875678i | \(-0.339585\pi\) | ||||
0.482896 | + | 0.875678i | \(0.339585\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6244.00 | −1.16697 | −0.583484 | − | 0.812125i | \(-0.698311\pi\) | ||||
−0.583484 | + | 0.812125i | \(0.698311\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4704.00 | 0.649078 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10798.0 | −1.29670 | −0.648349 | − | 0.761343i | \(-0.724540\pi\) | ||||
−0.648349 | + | 0.761343i | \(0.724540\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12006.0 | −1.11542 | −0.557710 | − | 0.830036i | \(-0.688320\pi\) | ||||
−0.557710 | + | 0.830036i | \(0.688320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9160.00 | −0.755482 | −0.377741 | − | 0.925911i | \(-0.623299\pi\) | ||||
−0.377741 | + | 0.925911i | \(0.623299\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 25836.0 | 1.70601 | 0.853003 | − | 0.521906i | \(-0.174779\pi\) | ||||
0.853003 | + | 0.521906i | \(0.174779\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1014.00 | −0.0495848 | −0.0247924 | − | 0.999693i | \(-0.507892\pi\) | ||||
−0.0247924 | + | 0.999693i | \(0.507892\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 69120.0 | 3.08104 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1242.00 | −0.0464506 | −0.0232253 | − | 0.999730i | \(-0.507394\pi\) | ||||
−0.0232253 | + | 0.999730i | \(0.507394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7592.00 | 0.261235 | 0.130618 | − | 0.991433i | \(-0.458304\pi\) | ||||
0.130618 | + | 0.991433i | \(0.458304\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 54912.0 | 1.61207 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 41132.0 | 1.11942 | 0.559710 | − | 0.828689i | \(-0.310913\pi\) | ||||
0.559710 | + | 0.828689i | \(0.310913\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37632.0 | 0.885955 | 0.442977 | − | 0.896533i | \(-0.353922\pi\) | ||||
0.442977 | + | 0.896533i | \(0.353922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13438.0 | −0.295140 | −0.147570 | − | 0.989052i | \(-0.547145\pi\) | ||||
−0.147570 | + | 0.989052i | \(0.547145\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 35280.0 | 0.678113 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6248.00 | 0.112635 | 0.0563175 | − | 0.998413i | \(-0.482064\pi\) | ||||
0.0563175 | + | 0.998413i | \(0.482064\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 25254.0 | 0.402379 | 0.201189 | − | 0.979552i | \(-0.435519\pi\) | ||||
0.201189 | + | 0.979552i | \(0.435519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −120384. | −1.80726 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 45126.0 | 0.603882 | 0.301941 | − | 0.953327i | \(-0.402365\pi\) | ||||
0.301941 | + | 0.953327i | \(0.402365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28028.0 | 0.354804 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9024.00 | −0.102586 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 107222. | 1.15706 | 0.578528 | − | 0.815662i | \(-0.303627\pi\) | ||||
0.578528 | + | 0.815662i | \(0.303627\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −47136.0 | −0.459779 | −0.229890 | − | 0.973217i | \(-0.573837\pi\) | ||||
−0.229890 | + | 0.973217i | \(0.573837\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 122204. | 1.13499 | 0.567495 | − | 0.823377i | \(-0.307912\pi\) | ||||
0.567495 | + | 0.823377i | \(0.307912\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 129636. | 1.09463 | 0.547314 | − | 0.836928i | \(-0.315651\pi\) | ||||
0.547314 | + | 0.836928i | \(0.315651\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −220558. | −1.77810 | −0.889051 | − | 0.457809i | \(-0.848635\pi\) | ||||
−0.889051 | + | 0.457809i | \(0.848635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −170694. | −1.25754 | −0.628770 | − | 0.777591i | \(-0.716441\pi\) | ||||
−0.628770 | + | 0.777591i | \(0.716441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9216.00 | −0.0649827 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −61446.0 | −0.397765 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 357349. | 2.21886 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 284736. | 1.62992 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −249808. | −1.37435 | −0.687175 | − | 0.726492i | \(-0.741149\pi\) | ||||
−0.687175 | + | 0.726492i | \(0.741149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12210.0 | −0.0621638 | −0.0310819 | − | 0.999517i | \(-0.509895\pi\) | ||||
−0.0310819 | + | 0.999517i | \(0.509895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4606.00 | −0.0225785 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13902.0 | 0.0632814 | 0.0316407 | − | 0.999499i | \(-0.489927\pi\) | ||||
0.0316407 | + | 0.999499i | \(0.489927\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −431794. | −1.89557 | −0.947785 | − | 0.318911i | \(-0.896683\pi\) | ||||
−0.947785 | + | 0.318911i | \(0.896683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 411840. | 1.68418 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 419904. | 1.65856 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −326814. | −1.20597 | −0.602983 | − | 0.797754i | \(-0.706021\pi\) | ||||
−0.602983 | + | 0.797754i | \(0.706021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 173480. | 0.619166 | 0.309583 | − | 0.950872i | \(-0.399811\pi\) | ||||
0.309583 | + | 0.950872i | \(0.399811\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −599424. | −2.00403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −54532.0 | −0.176564 | −0.0882820 | − | 0.996096i | \(-0.528138\pi\) | ||||
−0.0882820 | + | 0.996096i | \(0.528138\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4704.00 | −0.0143022 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104960. | 0.309425 | 0.154712 | − | 0.987960i | \(-0.450555\pi\) | ||||
0.154712 | + | 0.987960i | \(0.450555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −160788. | −0.446131 | −0.223066 | − | 0.974803i | \(-0.571606\pi\) | ||||
−0.223066 | + | 0.974803i | \(0.571606\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −44109.0 | −0.118798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −360564. | −0.915940 | −0.457970 | − | 0.888968i | \(-0.651423\pi\) | ||||
−0.457970 | + | 0.888968i | \(0.651423\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 298459. | 0.736698 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 312732. | 0.729524 | 0.364762 | − | 0.931101i | \(-0.381150\pi\) | ||||
0.364762 | + | 0.931101i | \(0.381150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −123820. | −0.280928 | −0.140464 | − | 0.990086i | \(-0.544859\pi\) | ||||
−0.140464 | + | 0.990086i | \(0.544859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.03661e6 | −2.22682 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −902880. | −1.88810 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −323448. | −0.641536 | −0.320768 | − | 0.947158i | \(-0.603941\pi\) | ||||
−0.320768 | + | 0.947158i | \(0.603941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −619954. | −1.19803 | −0.599013 | − | 0.800739i | \(-0.704440\pi\) | ||||
−0.599013 | + | 0.800739i | \(0.704440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 499362. | 0.916748 | 0.458374 | − | 0.888759i | \(-0.348432\pi\) | ||||
0.458374 | + | 0.888759i | \(0.348432\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −785932. | −1.40686 | −0.703432 | − | 0.710762i | \(-0.748350\pi\) | ||||
−0.703432 | + | 0.710762i | \(0.748350\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 214326. | 0.365035 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.15258e6 | −1.91551 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −67680.0 | −0.107175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.06276e6 | 1.64335 | 0.821676 | − | 0.569955i | \(-0.193039\pi\) | ||||
0.821676 | + | 0.569955i | \(0.193039\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −879360. | −1.29739 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −305956. | −0.441072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −717288. | −0.987900 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 707720. | 0.953014 | 0.476507 | − | 0.879171i | \(-0.341903\pi\) | ||||
0.476507 | + | 0.879171i | \(0.341903\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.04437e6 | 1.34520 | 0.672602 | − | 0.740005i | \(-0.265177\pi\) | ||||
0.672602 | + | 0.740005i | \(0.265177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −539716. | −0.680106 | −0.340053 | − | 0.940406i | \(-0.610445\pi\) | ||||
−0.340053 | + | 0.940406i | \(0.610445\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −177114. | −0.213729 | −0.106864 | − | 0.994274i | \(-0.534081\pi\) | ||||
−0.106864 | + | 0.994274i | \(0.534081\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.48026e6 | 2.92972 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 655464. | 0.742257 | 0.371128 | − | 0.928582i | \(-0.378971\pi\) | ||||
0.371128 | + | 0.928582i | \(0.378971\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.38709e6 | 1.53838 | 0.769189 | − | 0.639021i | \(-0.220660\pi\) | ||||
0.769189 | + | 0.639021i | \(0.220660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 230496. | 0.245329 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −53768.0 | −0.0560766 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.88811e6 | −1.89166 | −0.945830 | − | 0.324663i | \(-0.894749\pi\) | ||||
−0.945830 | + | 0.324663i | \(0.894749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −69120.0 | −0.0678895 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −346194. | −0.326954 | −0.163477 | − | 0.986547i | \(-0.552271\pi\) | ||||
−0.163477 | + | 0.986547i | \(0.552271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −529102. | −0.490106 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 929088. | 0.828262 | 0.414131 | − | 0.910217i | \(-0.364086\pi\) | ||||
0.414131 | + | 0.910217i | \(0.364086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −97344.0 | −0.0851519 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −382068. | −0.321929 | −0.160964 | − | 0.986960i | \(-0.551460\pi\) | ||||
−0.160964 | + | 0.986960i | \(0.551460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.58056e6 | −1.30734 | −0.653669 | − | 0.756781i | \(-0.726771\pi\) | ||||
−0.653669 | + | 0.756781i | \(0.726771\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.38552e6 | 3.49695 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.36911e6 | −1.07211 | −0.536056 | − | 0.844182i | \(-0.680086\pi\) | ||||
−0.536056 | + | 0.844182i | \(0.680086\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 394854. | 0.298312 | 0.149156 | − | 0.988814i | \(-0.452344\pi\) | ||||
0.149156 | + | 0.988814i | \(0.452344\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 673034. | 0.499541 | 0.249770 | − | 0.968305i | \(-0.419645\pi\) | ||||
0.249770 | + | 0.968305i | \(0.419645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −588294. | −0.421589 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 152659. | 0.107517 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.83468e6 | −1.24851 | −0.624254 | − | 0.781222i | \(-0.714597\pi\) | ||||
−0.624254 | + | 0.781222i | \(0.714597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −119232. | −0.0797697 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −54912.0 | −0.0355213 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −448840. | −0.285545 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 728832. | 0.448619 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.51056e6 | −0.914727 | −0.457363 | − | 0.889280i | \(-0.651206\pi\) | ||||
−0.457363 | + | 0.889280i | \(0.651206\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.87529e6 | 1.09943 | 0.549714 | − | 0.835353i | \(-0.314737\pi\) | ||||
0.549714 | + | 0.835353i | \(0.314737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.51076e6 | −0.871636 | −0.435818 | − | 0.900035i | \(-0.643541\pi\) | ||||
−0.435818 | + | 0.900035i | \(0.643541\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.02709e6 | −1.13299 | −0.566495 | − | 0.824065i | \(-0.691701\pi\) | ||||
−0.566495 | + | 0.824065i | \(0.691701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.14928e6 | 1.73274 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 117876. | 0.0628665 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.48405e6 | 1.82968 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.26596e6 | 0.644810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.54009e6 | 0.772637 | 0.386319 | − | 0.922365i | \(-0.373747\pi\) | ||||
0.386319 | + | 0.922365i | \(0.373747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.94867e6 | 1.92238 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.01166e6 | 0.485245 | 0.242622 | − | 0.970121i | \(-0.421992\pi\) | ||||
0.242622 | + | 0.970121i | \(0.421992\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.49568e6 | −2.09368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.15748e6 | 0.961885 | 0.480942 | − | 0.876752i | \(-0.340295\pi\) | ||||
0.480942 | + | 0.876752i | \(0.340295\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.15798e6 | −0.508906 | −0.254453 | − | 0.967085i | \(-0.581895\pi\) | ||||
−0.254453 | + | 0.967085i | \(0.581895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.17566e6 | 1.35643 | 0.678215 | − | 0.734863i | \(-0.262754\pi\) | ||||
0.678215 | + | 0.734863i | \(0.262754\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.61267e6 | 1.52145 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 74616.0 | 0.0305560 | 0.0152780 | − | 0.999883i | \(-0.495137\pi\) | ||||
0.0152780 | + | 0.999883i | \(0.495137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.46726e6 | −0.996431 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.29005e6 | −0.506843 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.79807e6 | −0.696854 | −0.348427 | − | 0.937336i | \(-0.613284\pi\) | ||||
−0.348427 | + | 0.937336i | \(0.613284\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −49686.0 | −0.0187413 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.20461e6 | 0.820463 | 0.410231 | − | 0.911981i | \(-0.365448\pi\) | ||||
0.410231 | + | 0.911981i | \(0.365448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.50193e6 | 0.906612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −177568. | −0.0634990 | −0.0317495 | − | 0.999496i | \(-0.510108\pi\) | ||||
−0.0317495 | + | 0.999496i | \(0.510108\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.87468e6 | 1.00137 | 0.500683 | − | 0.865630i | \(-0.333082\pi\) | ||||
0.500683 | + | 0.865630i | \(0.333082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.38688e6 | 1.16452 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.79965e6 | 1.60818 | 0.804091 | − | 0.594506i | \(-0.202652\pi\) | ||||
0.804091 | + | 0.594506i | \(0.202652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 120384. | 0.0398223 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 599808. | 0.193428 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.81643e6 | −0.896855 | −0.448428 | − | 0.893819i | \(-0.648016\pi\) | ||||
−0.448428 | + | 0.893819i | \(0.648016\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.83797e6 | 0.881347 | 0.440673 | − | 0.897667i | \(-0.354740\pi\) | ||||
0.440673 | + | 0.897667i | \(0.354740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.57157e6 | −1.09546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.77456e6 | −2.32643 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 154286. | 0.0456056 | 0.0228028 | − | 0.999740i | \(-0.492741\pi\) | ||||
0.0228028 | + | 0.999740i | \(0.492741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −60858.0 | −0.0175567 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.42438e6 | 0.691005 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.72865e6 | −1.03757 | −0.518783 | − | 0.854906i | \(-0.673615\pi\) | ||||
−0.518783 | + | 0.854906i | \(0.673615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.32623e6 | −0.639658 | −0.319829 | − | 0.947475i | \(-0.603626\pi\) | ||||
−0.319829 | + | 0.947475i | \(0.603626\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.63811e6 | −2.05123 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 372008. | 0.0987376 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.61482e6 | 0.678031 | 0.339015 | − | 0.940781i | \(-0.389906\pi\) | ||||
0.339015 | + | 0.940781i | \(0.389906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.19226e6 | −0.305598 | −0.152799 | − | 0.988257i | \(-0.548829\pi\) | ||||
−0.152799 | + | 0.988257i | \(0.548829\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9024.00 | 0.00226045 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.05793e6 | 0.261996 | 0.130998 | − | 0.991383i | \(-0.458182\pi\) | ||||
0.130998 | + | 0.991383i | \(0.458182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.12756e6 | −0.999272 | −0.499636 | − | 0.866235i | \(-0.666533\pi\) | ||||
−0.499636 | + | 0.866235i | \(0.666533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.33210e6 | 1.03705 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.75823e6 | −0.879766 | −0.439883 | − | 0.898055i | \(-0.644980\pi\) | ||||
−0.439883 | + | 0.898055i | \(0.644980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.64432e6 | −2.00120 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.69069e6 | 0.609305 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −451114. | −0.101041 | −0.0505203 | − | 0.998723i | \(-0.516088\pi\) | ||||
−0.0505203 | + | 0.998723i | \(0.516088\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.95186e6 | 0.427756 | 0.213878 | − | 0.976860i | \(-0.431390\pi\) | ||||
0.213878 | + | 0.976860i | \(0.431390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.20218e6 | −1.56139 | −0.780695 | − | 0.624913i | \(-0.785135\pi\) | ||||
−0.780695 | + | 0.624913i | \(0.785135\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.17801e6 | −1.52304 | −0.761521 | − | 0.648140i | \(-0.775547\pi\) | ||||
−0.761521 | + | 0.648140i | \(0.775547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.01547e6 | 0.423101 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.59520e6 | −1.35542 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −572554. | −0.116435 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.17632e6 | −1.22996 | −0.614980 | − | 0.788543i | \(-0.710836\pi\) | ||||
−0.614980 | + | 0.788543i | \(0.710836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.17646e6 | −1.21724 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.02933e7 | 1.98701 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.59330e6 | 1.45080 | 0.725401 | − | 0.688327i | \(-0.241655\pi\) | ||||
0.725401 | + | 0.688327i | \(0.241655\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51878e6 | 0.284309 | 0.142155 | − | 0.989844i | \(-0.454597\pi\) | ||||
0.142155 | + | 0.989844i | \(0.454597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.48500e6 | −1.01639 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.84397e6 | 0.334859 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.47576e6 | 0.265316 | 0.132658 | − | 0.991162i | \(-0.457649\pi\) | ||||
0.132658 | + | 0.991162i | \(0.457649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.31309e6 | 0.231406 | 0.115703 | − | 0.993284i | \(-0.463088\pi\) | ||||
0.115703 | + | 0.993284i | \(0.463088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.52506e6 | −0.789579 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.40932e6 | −0.754357 | −0.377178 | − | 0.926141i | \(-0.623106\pi\) | ||||
−0.377178 | + | 0.926141i | \(0.623106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −658462. | −0.111552 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.17316e7 | 1.94912 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.86019e7 | 3.06078 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.97629e6 | −0.480376 | −0.240188 | − | 0.970726i | \(-0.577209\pi\) | ||||
−0.240188 | + | 0.970726i | \(0.577209\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.34627e6 | 1.01453 | 0.507265 | − | 0.861790i | \(-0.330657\pi\) | ||||
0.507265 | + | 0.861790i | \(0.330657\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.82998e6 | 1.22810 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.42713e6 | −0.998568 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.86743e6 | −1.04707 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.24451e7 | 1.87980 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.72872e6 | 0.256302 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.36667e6 | −0.200756 | −0.100378 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100378 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.11736e7 | −3.05353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.55818e6 | −1.36586 | −0.682931 | − | 0.730483i | \(-0.739295\pi\) | ||||
−0.682931 | + | 0.730483i | \(0.739295\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −411156. | −0.0576936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 306152. | 0.0425720 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.94287e6 | −0.948202 | −0.474101 | − | 0.880470i | \(-0.657227\pi\) | ||||
−0.474101 | + | 0.880470i | \(0.657227\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.23952e6 | −0.709189 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.24662e6 | −0.697604 | −0.348802 | − | 0.937196i | \(-0.613411\pi\) | ||||
−0.348802 | + | 0.937196i | \(0.613411\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.63866e7 | −2.15958 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.46551e6 | −0.448731 | −0.224366 | − | 0.974505i | \(-0.572031\pi\) | ||||
−0.224366 | + | 0.974505i | \(0.572031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.90069e6 | 0.629023 | 0.314512 | − | 0.949254i | \(-0.398159\pi\) | ||||
0.314512 | + | 0.949254i | \(0.398159\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −584736. | −0.0737548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.28346e6 | 0.285531 | 0.142766 | − | 0.989757i | \(-0.454401\pi\) | ||||
0.142766 | + | 0.989757i | \(0.454401\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.23745e6 | 0.152085 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −730080. | −0.0889609 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.03157e7 | −1.23568 | −0.617838 | − | 0.786305i | \(-0.711991\pi\) | ||||
−0.617838 | + | 0.786305i | \(0.711991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 586936. | 0.0697112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.52838e6 | −0.412039 | −0.206020 | − | 0.978548i | \(-0.566051\pi\) | ||||
−0.206020 | + | 0.978548i | \(0.566051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.89882e6 | −0.683081 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.92260e6 | −0.332815 | −0.166407 | − | 0.986057i | \(-0.553217\pi\) | ||||
−0.166407 | + | 0.986057i | \(0.553217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.17567e7 | −1.32770 | −0.663849 | − | 0.747866i | \(-0.731078\pi\) | ||||
−0.663849 | + | 0.747866i | \(0.731078\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.43055e7 | 3.81044 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.71491e6 | −0.519400 | −0.259700 | − | 0.965689i | \(-0.583624\pi\) | ||||
−0.259700 | + | 0.965689i | \(0.583624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.47782e7 | 1.60147 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 213842. | 0.0229849 | 0.0114924 | − | 0.999934i | \(-0.496342\pi\) | ||||
0.0114924 | + | 0.999934i | \(0.496342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 336666. | 0.0356030 | 0.0178015 | − | 0.999842i | \(-0.494333\pi\) | ||||
0.0178015 | + | 0.999842i | \(0.494333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.42655e7 | 1.49645 | 0.748223 | − | 0.663447i | \(-0.230907\pi\) | ||||
0.748223 | + | 0.663447i | \(0.230907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.21117e6 | 0.228246 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.30028e6 | 0.849949 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.35407e7 | 1.36463 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.59637e6 | −0.659525 | −0.329763 | − | 0.944064i | \(-0.606969\pi\) | ||||
−0.329763 | + | 0.944064i | \(0.606969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.39816e7 | −2.36017 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.37337e6 | 0.134103 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.02490e7 | 0.985225 | 0.492613 | − | 0.870249i | \(-0.336042\pi\) | ||||
0.492613 | + | 0.870249i | \(0.336042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.16543e6 | −0.397312 | −0.198656 | − | 0.980069i | \(-0.563658\pi\) | ||||
−0.198656 | + | 0.980069i | \(0.563658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.35051e6 | 0.314666 | 0.157333 | − | 0.987546i | \(-0.449710\pi\) | ||||
0.157333 | + | 0.987546i | \(0.449710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −894240. | −0.0833379 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.05408e6 | 0.830924 | 0.415462 | − | 0.909611i | \(-0.363620\pi\) | ||||
0.415462 | + | 0.909611i | \(0.363620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.17216e6 | −0.106754 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.45382e6 | −0.578899 | −0.289450 | − | 0.957193i | \(-0.593472\pi\) | ||||
−0.289450 | + | 0.957193i | \(0.593472\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.43167e7 | 1.27450 | 0.637250 | − | 0.770657i | \(-0.280072\pi\) | ||||
0.637250 | + | 0.770657i | \(0.280072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −442176. | −0.0387740 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −419904. | −0.0365456 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.46624e6 | 0.468686 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.27250e7 | 1.93404 | 0.967020 | − | 0.254701i | \(-0.0819771\pi\) | ||||
0.967020 | + | 0.254701i | \(0.0819771\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.53249e6 | 0.715491 | 0.357746 | − | 0.933819i | \(-0.383546\pi\) | ||||
0.357746 | + | 0.933819i | \(0.383546\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.25388e6 | 0.437326 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.24921e7 | 1.84492 | 0.922461 | − | 0.386090i | \(-0.126175\pi\) | ||||
0.922461 | + | 0.386090i | \(0.126175\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.33459e6 | 0.108673 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −580008. | −0.0465464 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.26894e7 | −1.01099 | −0.505495 | − | 0.862830i | \(-0.668690\pi\) | ||||
−0.505495 | + | 0.862830i | \(0.668690\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.14522e7 | −3.25526 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50555e7 | 1.17385 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.13939e6 | 0.395018 | 0.197509 | − | 0.980301i | \(-0.436715\pi\) | ||||
0.197509 | + | 0.980301i | \(0.436715\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.01501e6 | 0.0774610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.30966e6 | −0.173780 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.16065e7 | −0.867132 | −0.433566 | − | 0.901122i | \(-0.642745\pi\) | ||||
−0.433566 | + | 0.901122i | \(0.642745\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 599424. | 0.0441581 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.95366e7 | 2.89224 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.50998e7 | −1.08930 | −0.544650 | − | 0.838663i | \(-0.683338\pi\) | ||||
−0.544650 | + | 0.838663i | \(0.683338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.98800e6 | 0.428986 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.66420e7 | 1.88245 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.32536e7 | −1.63175 | −0.815874 | − | 0.578229i | \(-0.803744\pi\) | ||||
−0.815874 | + | 0.578229i | \(0.803744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.14866e7 | 0.795059 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.37814e7 | 1.63485 | 0.817423 | − | 0.576038i | \(-0.195402\pi\) | ||||
0.817423 | + | 0.576038i | \(0.195402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.96150e7 | 2.00837 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.51392e6 | −0.169333 | −0.0846663 | − | 0.996409i | \(-0.526982\pi\) | ||||
−0.0846663 | + | 0.996409i | \(0.526982\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.22646e7 | 1.47959 | 0.739797 | − | 0.672830i | \(-0.234922\pi\) | ||||
0.739797 | + | 0.672830i | \(0.234922\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.13741e7 | −2.07101 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.35216e6 | 0.413730 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.30108e7 | 1.48878 | 0.744392 | − | 0.667743i | \(-0.232740\pi\) | ||||
0.744392 | + | 0.667743i | \(0.232740\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.66541e7 | 1.06329 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.59335e7 | 1.01058 | 0.505290 | − | 0.862950i | \(-0.331386\pi\) | ||||
0.505290 | + | 0.862950i | \(0.331386\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.68629e7 | −1.05553 | −0.527764 | − | 0.849391i | \(-0.676969\pi\) | ||||
−0.527764 | + | 0.849391i | \(0.676969\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.08073e7 | −0.672059 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −710424. | −0.0436043 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.75402e7 | −1.67939 | −0.839694 | − | 0.543060i | \(-0.817265\pi\) | ||||
−0.839694 | + | 0.543060i | \(0.817265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.26820e7 | −1.36532 | −0.682658 | − | 0.730738i | \(-0.739176\pi\) | ||||
−0.682658 | + | 0.730738i | \(0.739176\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.80322e7 | −2.27456 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.12856e6 | 0.0666320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.70950e7 | 1.58951 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.23507e6 | −0.303213 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.34266e7 | −1.34826 | −0.674129 | − | 0.738614i | \(-0.735481\pi\) | ||||
−0.674129 | + | 0.738614i | \(0.735481\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.36401e6 | −0.475306 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.34262e6 | 0.245228 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.82051e7 | 1.01519 | 0.507594 | − | 0.861596i | \(-0.330535\pi\) | ||||
0.507594 | + | 0.861596i | \(0.330535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.23983e7 | −1.79538 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.67536e6 | −0.529515 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −451584. | −0.0245612 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.47411e7 | −0.791878 | −0.395939 | − | 0.918277i | \(-0.629581\pi\) | ||||
−0.395939 | + | 0.918277i | \(0.629581\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.69629e7 | 0.905625 | 0.452812 | − | 0.891606i | \(-0.350421\pi\) | ||||
0.452812 | + | 0.891606i | \(0.350421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00762e7 | 0.531375 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 861040. | 0.0451303 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.03929e6 | −0.416255 | −0.208128 | − | 0.978102i | \(-0.566737\pi\) | ||||
−0.208128 | + | 0.978102i | \(0.566737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 386648. | 0.0198983 | 0.00994915 | − | 0.999951i | \(-0.496833\pi\) | ||||
0.00994915 | + | 0.999951i | \(0.496833\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.55021e7 | −1.80505 | −0.902526 | − | 0.430635i | \(-0.858290\pi\) | ||||
−0.902526 | + | 0.430635i | \(0.858290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.48814e7 | 1.25745 | 0.628723 | − | 0.777630i | \(-0.283578\pi\) | ||||
0.628723 | + | 0.777630i | \(0.283578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.01085e6 | −0.150341 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.54356e7 | −0.766141 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.41458e7 | −1.67468 | −0.837340 | − | 0.546682i | \(-0.815891\pi\) | ||||
−0.837340 | + | 0.546682i | \(0.815891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.37927e6 | −0.0672450 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.23446e6 | −0.204012 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.75101e7 | 0.838649 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.03661e6 | 0.0490671 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.50701e7 | 1.17973 | 0.589865 | − | 0.807502i | \(-0.299181\pi\) | ||||
0.589865 | + | 0.807502i | \(0.299181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.81938e7 | 0.846199 | 0.423099 | − | 0.906083i | \(-0.360942\pi\) | ||||
0.423099 | + | 0.906083i | \(0.360942\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.91797e6 | 0.319886 | 0.159943 | − | 0.987126i | \(-0.448869\pi\) | ||||
0.159943 | + | 0.987126i | \(0.448869\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.78069e7 | 1.27094 | 0.635471 | − | 0.772125i | \(-0.280806\pi\) | ||||
0.635471 | + | 0.772125i | \(0.280806\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.46141e7 | −1.57294 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.49856e6 | 0.202080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.35275e7 | 1.05083 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.39521e7 | 0.616053 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.79587e6 | 0.166653 | 0.0833263 | − | 0.996522i | \(-0.473446\pi\) | ||||
0.0833263 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.48904e7 | −1.08042 | −0.540210 | − | 0.841530i | \(-0.681655\pi\) | ||||
−0.540210 | + | 0.841530i | \(0.681655\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.13568e6 | −0.135341 | −0.0676705 | − | 0.997708i | \(-0.521557\pi\) | ||||
−0.0676705 | + | 0.997708i | \(0.521557\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.02437e7 | 0.863933 | 0.431966 | − | 0.901890i | \(-0.357820\pi\) | ||||
0.431966 | + | 0.901890i | \(0.357820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.22406e7 | −0.519455 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.42858e6 | −0.101912 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.00223e7 | 1.25281 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.73113e7 | −1.12705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.27156e6 | 0.0521823 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.18867e7 | −0.482437 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.86324e6 | −0.277020 | −0.138510 | − | 0.990361i | \(-0.544231\pi\) | ||||
−0.138510 | + | 0.990361i | \(0.544231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.40661e6 | 0.375523 | 0.187762 | − | 0.982215i | \(-0.439877\pi\) | ||||
0.187762 | + | 0.982215i | \(0.439877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.81829e7 | 0.721914 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −598290. | −0.0234957 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.10280e7 | −0.821313 | −0.410656 | − | 0.911790i | \(-0.634700\pi\) | ||||
−0.410656 | + | 0.911790i | \(0.634700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.15255e7 | 0.831666 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.57706e7 | −2.52742 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.30928e7 | 1.63819 | 0.819096 | − | 0.573656i | \(-0.194475\pi\) | ||||
0.819096 | + | 0.573656i | \(0.194475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −225694. | −0.00853387 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.66765e7 | −3.24244 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.85862e6 | −0.143576 | −0.0717882 | − | 0.997420i | \(-0.522871\pi\) | ||||
−0.0717882 | + | 0.997420i | \(0.522871\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.59601e7 | −0.587572 | −0.293786 | − | 0.955871i | \(-0.594915\pi\) | ||||
−0.293786 | + | 0.955871i | \(0.594915\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.15258e6 | 0.0422076 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.66831e6 | 0.169155 | 0.0845775 | − | 0.996417i | \(-0.473046\pi\) | ||||
0.0845775 | + | 0.996417i | \(0.473046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.68654e6 | −0.277054 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.43457e7 | 1.22501 | 0.612505 | − | 0.790466i | \(-0.290162\pi\) | ||||
0.612505 | + | 0.790466i | \(0.290162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.10510e7 | −1.10171 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 681198. | 0.0239181 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.03584e7 | 0.361813 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.95156e7 | −2.05737 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.28181e7 | −0.784718 | −0.392359 | − | 0.919812i | \(-0.628341\pi\) | ||||
−0.392359 | + | 0.919812i | \(0.628341\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.94042e7 | −1.68157 | −0.840786 | − | 0.541367i | \(-0.817907\pi\) | ||||
−0.840786 | + | 0.541367i | \(0.817907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.11579e7 | −0.716458 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.17542e6 | −0.240498 | −0.120249 | − | 0.992744i | \(-0.538369\pi\) | ||||
−0.120249 | + | 0.992744i | \(0.538369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.24907e7 | 1.08343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.22279e6 | 0.139385 | 0.0696924 | − | 0.997569i | \(-0.477798\pi\) | ||||
0.0696924 | + | 0.997569i | \(0.477798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.79388e7 | 1.57433 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 879360. | 0.0285875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.65645e7 | 0.535789 | 0.267895 | − | 0.963448i | \(-0.413672\pi\) | ||||
0.267895 | + | 0.963448i | \(0.413672\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.54495e7 | −2.41601 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.40973e7 | −1.40499 | −0.702496 | − | 0.711687i | \(-0.747931\pi\) | ||||
−0.702496 | + | 0.711687i | \(0.747931\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 252.6.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 28.6.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 1008.6.a.bb.1.1 | 1 | |||
12.11 | even | 2 | 112.6.a.e.1.1 | 1 | |||
15.2 | even | 4 | 700.6.e.d.449.2 | 2 | |||
15.8 | even | 4 | 700.6.e.d.449.1 | 2 | |||
15.14 | odd | 2 | 700.6.a.d.1.1 | 1 | |||
21.2 | odd | 6 | 196.6.e.f.165.1 | 2 | |||
21.5 | even | 6 | 196.6.e.e.165.1 | 2 | |||
21.11 | odd | 6 | 196.6.e.f.177.1 | 2 | |||
21.17 | even | 6 | 196.6.e.e.177.1 | 2 | |||
21.20 | even | 2 | 196.6.a.d.1.1 | 1 | |||
24.5 | odd | 2 | 448.6.a.i.1.1 | 1 | |||
24.11 | even | 2 | 448.6.a.h.1.1 | 1 | |||
84.83 | odd | 2 | 784.6.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.6.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
112.6.a.e.1.1 | 1 | 12.11 | even | 2 | |||
196.6.a.d.1.1 | 1 | 21.20 | even | 2 | |||
196.6.e.e.165.1 | 2 | 21.5 | even | 6 | |||
196.6.e.e.177.1 | 2 | 21.17 | even | 6 | |||
196.6.e.f.165.1 | 2 | 21.2 | odd | 6 | |||
196.6.e.f.177.1 | 2 | 21.11 | odd | 6 | |||
252.6.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
448.6.a.h.1.1 | 1 | 24.11 | even | 2 | |||
448.6.a.i.1.1 | 1 | 24.5 | odd | 2 | |||
700.6.a.d.1.1 | 1 | 15.14 | odd | 2 | |||
700.6.e.d.449.1 | 2 | 15.8 | even | 4 | |||
700.6.e.d.449.2 | 2 | 15.2 | even | 4 | |||
784.6.a.f.1.1 | 1 | 84.83 | odd | 2 | |||
1008.6.a.bb.1.1 | 1 | 4.3 | odd | 2 |