Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,6,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, 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("588.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(94.3056860500\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 699x^{2} - 686x + 59664 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-22.4831\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-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 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 92.8255 | 1.66051 | 0.830257 | − | 0.557381i | \(-0.188194\pi\) | ||||
0.830257 | + | 0.557381i | \(0.188194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 140.762 | 0.350756 | 0.175378 | − | 0.984501i | \(-0.443885\pi\) | ||||
0.175378 | + | 0.984501i | \(0.443885\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1111.24 | 1.82369 | 0.911844 | − | 0.410537i | \(-0.134659\pi\) | ||||
0.911844 | + | 0.410537i | \(0.134659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 835.430 | 0.958698 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −54.8869 | −0.0460624 | −0.0230312 | − | 0.999735i | \(-0.507332\pi\) | ||||
−0.0230312 | + | 0.999735i | \(0.507332\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1711.86 | 1.08789 | 0.543943 | − | 0.839122i | \(-0.316931\pi\) | ||||
0.543943 | + | 0.839122i | \(0.316931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3287.91 | −1.29599 | −0.647993 | − | 0.761646i | \(-0.724391\pi\) | ||||
−0.647993 | + | 0.761646i | \(0.724391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5491.58 | 1.75731 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3790.72 | −0.837003 | −0.418501 | − | 0.908216i | \(-0.637445\pi\) | ||||
−0.418501 | + | 0.908216i | \(0.637445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4847.32 | 0.905936 | 0.452968 | − | 0.891527i | \(-0.350365\pi\) | ||||
0.452968 | + | 0.891527i | \(0.350365\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1266.86 | 0.202509 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11366.7 | −1.36499 | −0.682496 | − | 0.730889i | \(-0.739106\pi\) | ||||
−0.682496 | + | 0.730889i | \(0.739106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10001.2 | 1.05291 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10385.6 | 0.964881 | 0.482440 | − | 0.875929i | \(-0.339751\pi\) | ||||
0.482440 | + | 0.875929i | \(0.339751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7137.16 | 0.588646 | 0.294323 | − | 0.955706i | \(-0.404906\pi\) | ||||
0.294323 | + | 0.955706i | \(0.404906\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7518.87 | 0.553505 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16415.1 | 1.08392 | 0.541961 | − | 0.840404i | \(-0.317682\pi\) | ||||
0.541961 | + | 0.840404i | \(0.317682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −493.983 | −0.0265942 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −20974.3 | −1.02565 | −0.512824 | − | 0.858494i | \(-0.671401\pi\) | ||||
−0.512824 | + | 0.858494i | \(0.671401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13066.3 | 0.582435 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15406.7 | 0.628092 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 36211.9 | 1.35432 | 0.677161 | − | 0.735835i | \(-0.263210\pi\) | ||||
0.677161 | + | 0.735835i | \(0.263210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4948.70 | −0.170281 | −0.0851405 | − | 0.996369i | \(-0.527134\pi\) | ||||
−0.0851405 | + | 0.996369i | \(0.527134\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 103152. | 3.02826 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −22965.6 | −0.625015 | −0.312507 | − | 0.949915i | \(-0.601169\pi\) | ||||
−0.312507 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −29591.2 | −0.748238 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −26341.8 | −0.620154 | −0.310077 | − | 0.950711i | \(-0.600355\pi\) | ||||
−0.310077 | + | 0.950711i | \(0.600355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55387.4 | −1.21648 | −0.608238 | − | 0.793755i | \(-0.708123\pi\) | ||||
−0.608238 | + | 0.793755i | \(0.708123\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 49424.2 | 1.01458 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −49956.6 | −0.900586 | −0.450293 | − | 0.892881i | \(-0.648680\pi\) | ||||
−0.450293 | + | 0.892881i | \(0.648680\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −44858.9 | −0.714749 | −0.357374 | − | 0.933961i | \(-0.616328\pi\) | ||||
−0.357374 | + | 0.933961i | \(0.616328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5094.91 | −0.0764873 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −34116.5 | −0.483244 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −127945. | −1.71217 | −0.856087 | − | 0.516831i | \(-0.827111\pi\) | ||||
−0.856087 | + | 0.516831i | \(0.827111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 43625.9 | 0.523042 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 158904. | 1.80645 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 65685.9 | 0.708831 | 0.354415 | − | 0.935088i | \(-0.384680\pi\) | ||||
0.354415 | + | 0.935088i | \(0.384680\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11401.8 | 0.116919 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −175783. | −1.71464 | −0.857320 | − | 0.514784i | \(-0.827872\pi\) | ||||
−0.857320 | + | 0.514784i | \(0.827872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 154109. | 1.43132 | 0.715659 | − | 0.698450i | \(-0.246127\pi\) | ||||
0.715659 | + | 0.698450i | \(0.246127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 183362. | 1.54828 | 0.774141 | − | 0.633013i | \(-0.218182\pi\) | ||||
0.774141 | + | 0.633013i | \(0.218182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −134645. | −1.08548 | −0.542741 | − | 0.839900i | \(-0.682613\pi\) | ||||
−0.542741 | + | 0.839900i | \(0.682613\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −102300. | −0.788079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 176955. | 1.30367 | 0.651833 | − | 0.758362i | \(-0.274000\pi\) | ||||
0.651833 | + | 0.758362i | \(0.274000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −305202. | −2.15200 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 90010.7 | 0.607896 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −141237. | −0.876970 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 93470.8 | 0.557074 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 219679. | 1.25752 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 144432. | 0.794608 | 0.397304 | − | 0.917687i | \(-0.369946\pi\) | ||||
0.397304 | + | 0.917687i | \(0.369946\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 64234.4 | 0.339855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 237508. | 1.20920 | 0.604602 | − | 0.796527i | \(-0.293332\pi\) | ||||
0.604602 | + | 0.796527i | \(0.293332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 67669.8 | 0.319566 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −96203.3 | −0.437914 | −0.218957 | − | 0.975735i | \(-0.570265\pi\) | ||||
−0.218957 | + | 0.975735i | \(0.570265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 391373. | 1.71812 | 0.859060 | − | 0.511874i | \(-0.171049\pi\) | ||||
0.859060 | + | 0.511874i | \(0.171049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 147736. | 0.625802 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 156421. | 0.639669 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −351876. | −1.38985 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −80678.8 | −0.297710 | −0.148855 | − | 0.988859i | \(-0.547559\pi\) | ||||
−0.148855 | + | 0.988859i | \(0.547559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 95682.6 | 0.341500 | 0.170750 | − | 0.985314i | \(-0.445381\pi\) | ||||
0.170750 | + | 0.985314i | \(0.445381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4445.84 | −0.0153541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 449955. | 1.50432 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 195625. | 0.633397 | 0.316699 | − | 0.948526i | \(-0.397426\pi\) | ||||
0.316699 | + | 0.948526i | \(0.397426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −188769. | −0.592158 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 37645.7 | 0.110980 | 0.0554902 | − | 0.998459i | \(-0.482328\pi\) | ||||
0.0554902 | + | 0.998459i | \(0.482328\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 117597. | 0.336269 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −646778. | −1.79458 | −0.897292 | − | 0.441437i | \(-0.854469\pi\) | ||||
−0.897292 | + | 0.441437i | \(0.854469\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 863568. | 2.32584 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 138661. | 0.362629 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 386908. | 0.982863 | 0.491431 | − | 0.870916i | \(-0.336474\pi\) | ||||
0.491431 | + | 0.870916i | \(0.336474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 325907. | 0.781918 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 27410.5 | 0.0639418 | 0.0319709 | − | 0.999489i | \(-0.489822\pi\) | ||||
0.0319709 | + | 0.999489i | \(0.489822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 196155. | 0.445044 | 0.222522 | − | 0.974928i | \(-0.428571\pi\) | ||||
0.222522 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −44538.3 | −0.0983118 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.05512e6 | −2.26659 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7726.02 | −0.0161567 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 266982. | 0.529540 | 0.264770 | − | 0.964312i | \(-0.414704\pi\) | ||||
0.264770 | + | 0.964312i | \(0.414704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −101364. | −0.195880 | −0.0979398 | − | 0.995192i | \(-0.531225\pi\) | ||||
−0.0979398 | + | 0.995192i | \(0.531225\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 928366. | 1.74837 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 362366. | 0.665245 | 0.332623 | − | 0.943060i | \(-0.392066\pi\) | ||||
0.332623 | + | 0.943060i | \(0.392066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −225413. | −0.403502 | −0.201751 | − | 0.979437i | \(-0.564663\pi\) | ||||
−0.201751 | + | 0.979437i | \(0.564663\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −206690. | −0.360852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 964053. | 1.60220 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −266321. | −0.431995 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 240965. | 0.381583 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −327801. | −0.506878 | −0.253439 | − | 0.967351i | \(-0.581562\pi\) | ||||
−0.253439 | + | 0.967351i | \(0.581562\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −237076. | −0.358046 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 662511. | 0.977455 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −498486. | −0.702333 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −60992.7 | −0.0840035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −109690. | −0.147708 | −0.0738538 | − | 0.997269i | \(-0.523530\pi\) | ||||
−0.0738538 | + | 0.997269i | \(0.523530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 444818. | 0.585769 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.21747e6 | −1.56817 | −0.784083 | − | 0.620656i | \(-0.786866\pi\) | ||||
−0.784083 | + | 0.620656i | \(0.786866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.33603e6 | 1.68355 | 0.841776 | − | 0.539827i | \(-0.181510\pi\) | ||||
0.841776 | + | 0.539827i | \(0.181510\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 46788.4 | 0.0564610 | 0.0282305 | − | 0.999601i | \(-0.491013\pi\) | ||||
0.0282305 | + | 0.999601i | \(0.491013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.52374e6 | 1.79987 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −449609. | −0.519954 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 86350.2 | 0.0977841 | 0.0488921 | − | 0.998804i | \(-0.484431\pi\) | ||||
0.0488921 | + | 0.998804i | \(0.484431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −825299. | −0.915311 | −0.457655 | − | 0.889130i | \(-0.651311\pi\) | ||||
−0.457655 | + | 0.889130i | \(0.651311\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.90229e6 | 1.98397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −403730. | −0.412660 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 130188. | 0.130432 | 0.0652162 | − | 0.997871i | \(-0.479226\pi\) | ||||
0.0652162 | + | 0.997871i | \(0.479226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −462814. | −0.454574 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −45854.2 | −0.0441600 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −102790. | −0.0970775 | −0.0485388 | − | 0.998821i | \(-0.515456\pi\) | ||||
−0.0485388 | + | 0.998821i | \(0.515456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −307048. | −0.279001 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −35500.7 | −0.0316481 | −0.0158241 | − | 0.999875i | \(-0.505037\pi\) | ||||
−0.0158241 | + | 0.999875i | \(0.505037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.94695e6 | −1.70310 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.15150e6 | −0.988524 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.04634e6 | −0.881643 | −0.440821 | − | 0.897595i | \(-0.645313\pi\) | ||||
−0.440821 | + | 0.897595i | \(0.645313\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −177278. | −0.146633 | −0.0733167 | − | 0.997309i | \(-0.523358\pi\) | ||||
−0.0733167 | + | 0.997309i | \(0.523358\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 773008. | 0.616385 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 145586. | 0.114004 | 0.0570020 | − | 0.998374i | \(-0.481846\pi\) | ||||
0.0570020 | + | 0.998374i | \(0.481846\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 392633. | 0.301979 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.03073e6 | −0.778714 | −0.389357 | − | 0.921087i | \(-0.627303\pi\) | ||||
−0.389357 | + | 0.921087i | \(0.627303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.11726e6 | 0.829257 | 0.414628 | − | 0.909991i | \(-0.363912\pi\) | ||||
0.414628 | + | 0.909991i | \(0.363912\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.43014e6 | 1.04296 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41684e6 | −0.997878 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 591173. | 0.409244 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.02032e6 | 1.37484 | 0.687418 | − | 0.726262i | \(-0.258744\pi\) | ||||
0.687418 | + | 0.726262i | \(0.258744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.36139e6 | 2.24887 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 102616. | 0.0675030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.65367e6 | −2.36347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.58204e6 | −0.989948 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −459366. | −0.282754 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 535150. | 0.324063 | 0.162031 | − | 0.986786i | \(-0.448195\pi\) | ||||
0.162031 | + | 0.986786i | \(0.448195\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.38698e6 | 0.826372 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.30019e6 | 1.34854 | 0.674268 | − | 0.738487i | \(-0.264459\pi\) | ||||
0.674268 | + | 0.738487i | \(0.264459\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.75727e6 | 1.59081 | 0.795404 | − | 0.606079i | \(-0.207258\pi\) | ||||
0.795404 | + | 0.606079i | \(0.207258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.54809e6 | 1.42418 | 0.712092 | − | 0.702086i | \(-0.247748\pi\) | ||||
0.712092 | + | 0.702086i | \(0.247748\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −533591. | −0.293584 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.65026e6 | 0.893901 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −93958.7 | −0.0501107 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.10248e6 | 3.20478 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.21180e6 | −0.626703 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −489335. | −0.245491 | −0.122746 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122746 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −920703. | −0.454998 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.13179e6 | −1.03785 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.47140e6 | −0.705757 | −0.352878 | − | 0.935669i | \(-0.614797\pi\) | ||||
−0.352878 | + | 0.935669i | \(0.614797\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.59259e6 | 0.752672 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 682320. | 0.317762 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.74682e6 | −1.24246 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.41925e6 | −1.07859 | −0.539296 | − | 0.842116i | \(-0.681310\pi\) | ||||
−0.539296 | + | 0.842116i | \(0.681310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.58571e6 | 1.13636 | 0.568180 | − | 0.822905i | \(-0.307648\pi\) | ||||
0.568180 | + | 0.822905i | \(0.307648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 810096. | 0.350969 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.00440e6 | −0.429010 | −0.214505 | − | 0.976723i | \(-0.568814\pi\) | ||||
−0.214505 | + | 0.976723i | \(0.568814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.44519e6 | −1.02977 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.26765e6 | −0.928625 | −0.464313 | − | 0.885671i | \(-0.653699\pi\) | ||||
−0.464313 | + | 0.885671i | \(0.653699\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 454359. | 0.183498 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.27113e6 | −0.506319 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.14136e6 | −2.01998 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.78623e6 | −1.85493 | −0.927467 | − | 0.373905i | \(-0.878019\pi\) | ||||
−0.927467 | + | 0.373905i | \(0.878019\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 841237. | 0.321627 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.62701e6 | −1.72198 | −0.860991 | − | 0.508619i | \(-0.830156\pi\) | ||||
−0.860991 | + | 0.508619i | \(0.830156\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.97711e6 | 0.726028 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.21241e6 | −1.52643 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −497760. | −0.178001 | −0.0890004 | − | 0.996032i | \(-0.528367\pi\) | ||||
−0.0890004 | + | 0.996032i | \(0.528367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.29988e6 | 0.458767 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.38749e6 | −0.483318 | −0.241659 | − | 0.970361i | \(-0.577692\pi\) | ||||
−0.241659 | + | 0.970361i | \(0.577692\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 578110. | 0.196215 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −586055. | −0.196365 | −0.0981826 | − | 0.995168i | \(-0.531303\pi\) | ||||
−0.0981826 | + | 0.995168i | \(0.531303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 180463. | 0.0596962 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.13757e6 | 0.698135 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.63725e6 | −1.49544 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.05336e6 | −0.972302 | −0.486151 | − | 0.873875i | \(-0.661600\pi\) | ||||
−0.486151 | + | 0.873875i | \(0.661600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.52316e6 | 1.71525 | 0.857624 | − | 0.514278i | \(-0.171940\pi\) | ||||
0.857624 | + | 0.514278i | \(0.171940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.38655e6 | 1.65214 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 609028. | 0.184502 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.60000e6 | −0.478779 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.34927e6 | 0.990016 | 0.495008 | − | 0.868888i | \(-0.335165\pi\) | ||||
0.495008 | + | 0.868888i | \(0.335165\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −865829. | −0.252830 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.16405e6 | −1.18685 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.52236e6 | 0.991957 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.97012e6 | −0.826493 | −0.413247 | − | 0.910619i | \(-0.635605\pi\) | ||||
−0.413247 | + | 0.910619i | \(0.635605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.41478e6 | −1.48894 | −0.744468 | − | 0.667658i | \(-0.767297\pi\) | ||||
−0.744468 | + | 0.667658i | \(0.767297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.32962e6 | 0.361307 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −301416. | −0.0809458 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.40779e6 | 0.369313 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.05950e6 | −1.31194 | −0.655970 | − | 0.754787i | \(-0.727740\pi\) | ||||
−0.655970 | + | 0.754787i | \(0.727740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.84174e6 | −0.984711 | −0.492355 | − | 0.870394i | \(-0.663864\pi\) | ||||
−0.492355 | + | 0.870394i | \(0.663864\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.16688e6 | −0.802433 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.62843e6 | −1.40989 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.52572e6 | 0.377844 | 0.188922 | − | 0.981992i | \(-0.439501\pi\) | ||||
0.188922 | + | 0.981992i | \(0.439501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.47014e6 | −0.355916 | −0.177958 | − | 0.984038i | \(-0.556949\pi\) | ||||
−0.177958 | + | 0.984038i | \(0.556949\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.18766e7 | −2.84309 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −726110. | −0.171883 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.05071e6 | −1.41641 | −0.708207 | − | 0.706004i | \(-0.750496\pi\) | ||||
−0.708207 | + | 0.706004i | \(0.750496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.46191e6 | 0.338437 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 861144. | 0.197165 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.75420e6 | −1.28883 | −0.644413 | − | 0.764678i | \(-0.722898\pi\) | ||||
−0.644413 | + | 0.764678i | \(0.722898\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −40012.6 | −0.00886472 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.83684e6 | −0.621703 | −0.310851 | − | 0.950458i | \(-0.600614\pi\) | ||||
−0.310851 | + | 0.950458i | \(0.600614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.19089e6 | 1.12535 | 0.562677 | − | 0.826677i | \(-0.309771\pi\) | ||||
0.562677 | + | 0.826677i | \(0.309771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.04960e6 | 0.868519 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.08904e6 | −0.231074 | −0.115537 | − | 0.993303i | \(-0.536859\pi\) | ||||
−0.115537 | + | 0.993303i | \(0.536859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.76063e6 | 0.365692 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00464e6 | 0.206471 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.40081e6 | 1.91175 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.69892e6 | −0.341883 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.69411e6 | 1.13393 | 0.566966 | − | 0.823741i | \(-0.308117\pi\) | ||||
0.566966 | + | 0.823741i | \(0.308117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.26312e7 | −2.48932 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.09733e6 | 1.17702 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.11425e6 | −0.786083 | −0.393042 | − | 0.919521i | \(-0.628577\pi\) | ||||
−0.393042 | + | 0.919521i | \(0.628577\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 338811. | 0.0640745 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −609530. | −0.114101 | −0.0570507 | − | 0.998371i | \(-0.518170\pi\) | ||||
−0.0570507 | + | 0.998371i | \(0.518170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 208061. | 0.0385544 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.05837e6 | 0.194145 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 995793. | 0.179027 | 0.0895133 | − | 0.995986i | \(-0.471469\pi\) | ||||
0.0895133 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.82100e6 | −1.03610 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.02730e7 | −1.81042 | −0.905209 | − | 0.424966i | \(-0.860286\pi\) | ||||
−0.905209 | + | 0.424966i | \(0.860286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.63171e7 | −2.84718 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.77211e6 | 1.34282 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.78427e6 | 0.476339 | 0.238170 | − | 0.971224i | \(-0.423453\pi\) | ||||
0.238170 | + | 0.971224i | \(0.423453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.24794e6 | 0.209364 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.43053e7 | 2.37672 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.31062e6 | 0.380192 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.48218e6 | 0.567456 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.04536e6 | −0.168721 | −0.0843607 | − | 0.996435i | \(-0.526885\pi\) | ||||
−0.0843607 | + | 0.996435i | \(0.526885\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.63156e6 | 0.580550 | 0.290275 | − | 0.956943i | \(-0.406253\pi\) | ||||
0.290275 | + | 0.956943i | \(0.406253\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −266055. | −0.0417296 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.37400e6 | 0.679579 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.93317e6 | 0.451440 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.15410e7 | 1.75964 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.70207e7 | 2.57094 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 246695. | 0.0369168 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.44884e6 | −1.38799 | −0.693994 | − | 0.719981i | \(-0.744150\pi\) | ||||
−0.693994 | + | 0.719981i | \(0.744150\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.76540e6 | 0.256946 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.24985e7 | −1.80246 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.69014e6 | 0.384421 | 0.192210 | − | 0.981354i | \(-0.438434\pi\) | ||||
0.192210 | + | 0.981354i | \(0.438434\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −400845. | −0.0567604 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.48918e6 | −0.910564 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.49609e6 | −1.30862 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.88981e6 | −1.21410 | −0.607050 | − | 0.794664i | \(-0.707647\pi\) | ||||
−0.607050 | + | 0.794664i | \(0.707647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.93112e6 | 1.07351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −69534.1 | −0.00932805 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.25993e6 | −0.167523 | −0.0837615 | − | 0.996486i | \(-0.526693\pi\) | ||||
−0.0837615 | + | 0.996486i | \(0.526693\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.64259e7 | 2.16476 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.82038e6 | −0.753651 | −0.376826 | − | 0.926284i | \(-0.622984\pi\) | ||||
−0.376826 | + | 0.926284i | \(0.622984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.65961e6 | 0.598080 | 0.299040 | − | 0.954241i | \(-0.403334\pi\) | ||||
0.299040 | + | 0.954241i | \(0.403334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.40284e6 | 0.305730 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.80558e7 | −2.27744 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.52478e6 | 0.190664 | 0.0953319 | − | 0.995446i | \(-0.469609\pi\) | ||||
0.0953319 | + | 0.995446i | \(0.469609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −912273. | −0.113091 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.95240e6 | −0.359752 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.35529e6 | 1.00942 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50087e7 | 1.79783 | 0.898914 | − | 0.438124i | \(-0.144357\pi\) | ||||
0.898914 | + | 0.438124i | \(0.144357\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.29792e6 | 0.985556 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.26129e6 | 0.384079 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.07946e6 | 0.826729 | 0.413364 | − | 0.910566i | \(-0.364354\pi\) | ||||
0.413364 | + | 0.910566i | \(0.364354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.02871e6 | −0.232962 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.17521e6 | −0.247705 | −0.123853 | − | 0.992301i | \(-0.539525\pi\) | ||||
−0.123853 | + | 0.992301i | \(0.539525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.69785e6 | −0.304671 | −0.152336 | − | 0.988329i | \(-0.548679\pi\) | ||||
−0.152336 | + | 0.988329i | \(0.548679\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.86021e6 | −0.208338 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.31104e7 | −1.45622 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.98834e6 | −0.549521 | −0.274760 | − | 0.961513i | \(-0.588598\pi\) | ||||
−0.274760 | + | 0.961513i | \(0.588598\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.82411e7 | 1.97673 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.11364e6 | 0.119700 | 0.0598500 | − | 0.998207i | \(-0.480938\pi\) | ||||
0.0598500 | + | 0.998207i | \(0.480938\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.67647e6 | 0.925029 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.14757e6 | −0.544364 | −0.272182 | − | 0.962246i | \(-0.587745\pi\) | ||||
−0.272182 | + | 0.962246i | \(0.587745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −243176. | −0.0255091 | −0.0127545 | − | 0.999919i | \(-0.504060\pi\) | ||||
−0.0127545 | + | 0.999919i | \(0.504060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.39689e6 | −0.249413 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.23066e6 | 0.330819 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.16869e6 | 0.220307 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 623884. | 0.0628749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.94255e6 | 0.994087 | 0.497044 | − | 0.867726i | \(-0.334419\pi\) | ||||
0.497044 | + | 0.867726i | \(0.334419\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.95021e6 | −0.292646 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.34069e7 | 1.31946 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.13369e6 | −0.206718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.15553e7 | −1.11080 | −0.555402 | − | 0.831582i | \(-0.687436\pi\) | ||||
−0.555402 | + | 0.831582i | \(0.687436\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.35139e6 | −0.128900 | −0.0644500 | − | 0.997921i | \(-0.520529\pi\) | ||||
−0.0644500 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.96260e6 | 0.564334 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.75536e7 | −1.64856 | −0.824279 | − | 0.566183i | \(-0.808419\pi\) | ||||
−0.824279 | + | 0.566183i | \(0.808419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.09728e6 | 0.475036 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.99873e6 | −0.734071 | −0.367035 | − | 0.930207i | \(-0.619627\pi\) | ||||
−0.367035 | + | 0.930207i | \(0.619627\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.20468e7 | 2.00790 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.48638e6 | −0.405492 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 229419. | 0.0205786 | 0.0102893 | − | 0.999947i | \(-0.496725\pi\) | ||||
0.0102893 | + | 0.999947i | \(0.496725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.28557e6 | 0.292488 | 0.146244 | − | 0.989249i | \(-0.453282\pi\) | ||||
0.146244 | + | 0.989249i | \(0.453282\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −548935. | −0.0484994 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.24635e7 | 1.08474 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −987206. | −0.0852791 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −696590. | −0.0597271 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.22188e6 | 0.699734 | 0.349867 | − | 0.936799i | \(-0.386227\pi\) | ||||
0.349867 | + | 0.936799i | \(0.386227\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.00336e6 | 0.338194 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.15405e7 | −1.80628 | −0.903138 | − | 0.429351i | \(-0.858742\pi\) | ||||
−0.903138 | + | 0.429351i | \(0.858742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.09572e7 | −0.905381 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.61741e7 | −1.32669 | −0.663344 | − | 0.748314i | \(-0.730863\pi\) | ||||
−0.663344 | + | 0.748314i | \(0.730863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.93012e6 | −0.727162 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.20242e7 | 0.971999 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.33076e7 | −1.87046 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.06464e7 | −0.848215 | −0.424108 | − | 0.905612i | \(-0.639412\pi\) | ||||
−0.424108 | + | 0.905612i | \(0.639412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.63294e7 | 2.85296 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −570036. | −0.0444447 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 421096. | 0.0325978 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.55461e6 | −0.350071 | −0.175035 | − | 0.984562i | \(-0.556004\pi\) | ||||
−0.175035 | + | 0.984562i | \(0.556004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.94582e7 | −1.48496 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.37136e7 | 1.03915 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.31035e7 | 0.978974 | 0.489487 | − | 0.872011i | \(-0.337184\pi\) | ||||
0.489487 | + | 0.872011i | \(0.337184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.04649e6 | −0.300195 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.59375e7 | −1.17408 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.45199e7 | 1.06218 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 777151. | 0.0564557 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.79188e7 | −1.29267 | −0.646335 | − | 0.763054i | \(-0.723699\pi\) | ||||
−0.646335 | + | 0.763054i | \(0.723699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.42769e6 | −0.528455 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.08171e7 | −1.47087 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.41466e7 | −0.992693 | −0.496347 | − | 0.868125i | \(-0.665325\pi\) | ||||
−0.496347 | + | 0.868125i | \(0.665325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −391737. | −0.0271145 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.24448e7 | 0.855517 | 0.427758 | − | 0.903893i | \(-0.359303\pi\) | ||||
0.427758 | + | 0.903893i | \(0.359303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.23269e6 | −0.219228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.76664e6 | −0.118998 | −0.0594988 | − | 0.998228i | \(-0.518950\pi\) | ||||
−0.0594988 | + | 0.998228i | \(0.518950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.71206e7 | 1.14544 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.73250e6 | 0.380953 | 0.190477 | − | 0.981692i | \(-0.438997\pi\) | ||||
0.190477 | + | 0.981692i | \(0.438997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.48906e6 | −0.494352 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.63357e6 | −0.238250 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.63132e7 | 1.70245 | 0.851224 | − | 0.524803i | \(-0.175861\pi\) | ||||
0.851224 | + | 0.524803i | \(0.175861\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.17169e6 | 0.0753052 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.88179e6 | 0.567066 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.63104e7 | 1.03449 | 0.517245 | − | 0.855838i | \(-0.326958\pi\) | ||||
0.517245 | + | 0.855838i | \(0.326958\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.16532e6 | −0.262449 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.68416e7 | −1.05420 | −0.527098 | − | 0.849804i | \(-0.676720\pi\) | ||||
−0.527098 | + | 0.849804i | \(0.676720\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −412688. | −0.0254958 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.02402e7 | 2.46986 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.19890e7 | −0.731084 | −0.365542 | − | 0.930795i | \(-0.619116\pi\) | ||||
−0.365542 | + | 0.930795i | \(0.619116\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −925112. | −0.0560477 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.69774e7 | −1.02193 | −0.510965 | − | 0.859601i | \(-0.670712\pi\) | ||||
−0.510965 | + | 0.859601i | \(0.670712\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.66195e7 | 1.59201 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.77787e7 | 1.04968 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.70793e6 | −0.217523 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.76344e6 | −0.161081 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.81590e7 | 1.05177 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.19500e7 | 1.83880 | 0.919400 | − | 0.393323i | \(-0.128675\pi\) | ||||
0.919400 | + | 0.393323i | \(0.128675\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −319507. | −0.0182720 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.49921e6 | −0.310540 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.75226e7 | −0.983287 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.63006e7 | 0.908988 | 0.454494 | − | 0.890750i | \(-0.349820\pi\) | ||||
0.454494 | + | 0.890750i | \(0.349820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −900972. | −0.0499280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.03635e7 | −0.570725 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.79646e6 | −0.426686 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.41707e6 | −0.509017 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.51398e7 | −1.35049 | −0.675244 | − | 0.737594i | \(-0.735962\pi\) | ||||
−0.675244 | + | 0.737594i | \(0.735962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.27245e7 | 1.21323 | 0.606613 | − | 0.794997i | \(-0.292528\pi\) | ||||
0.606613 | + | 0.794997i | \(0.292528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.59551e6 | −0.0846588 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.49448e6 | 0.184284 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.22178e7 | 0.640380 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.10488e7 | 0.572080 | 0.286040 | − | 0.958218i | \(-0.407661\pi\) | ||||
0.286040 | + | 0.958218i | \(0.407661\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.30479e6 | −0.375931 | −0.187966 | − | 0.982176i | \(-0.560189\pi\) | ||||
−0.187966 | + | 0.982176i | \(0.560189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.95707e6 | 0.355870 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.01208e7 | 1.53145 | 0.765724 | − | 0.643170i | \(-0.222381\pi\) | ||||
0.765724 | + | 0.643170i | \(0.222381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.35804e7 | −0.686318 | −0.343159 | − | 0.939277i | \(-0.611497\pi\) | ||||
−0.343159 | + | 0.939277i | \(0.611497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.31027e6 | 0.0658203 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00375e7 | −2.97993 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.53370e6 | 0.174347 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.78208e7 | 1.85492 | 0.927460 | − | 0.373922i | \(-0.121987\pi\) | ||||
0.927460 | + | 0.373922i | \(0.121987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.14158e6 | −0.299426 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.27654e6 | −0.449591 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.01611e7 | 3.86209 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.00554e7 | 0.478772 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.73727e7 | 1.76901 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.36325e7 | 1.58265 | 0.791327 | − | 0.611393i | \(-0.209391\pi\) | ||||
0.791327 | + | 0.611393i | \(0.209391\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.28712e7 | 0.602150 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.71796e7 | 0.799028 | 0.399514 | − | 0.916727i | \(-0.369179\pi\) | ||||
0.399514 | + | 0.916727i | \(0.369179\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.49154e7 | −1.15209 | −0.576043 | − | 0.817420i | \(-0.695404\pi\) | ||||
−0.576043 | + | 0.817420i | \(0.695404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.70839e7 | −1.69495 | −0.847477 | − | 0.530832i | \(-0.821880\pi\) | ||||
−0.847477 | + | 0.530832i | \(0.821880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.59150e7 | 1.63206 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.27516e7 | −0.576125 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.03201e6 | −0.315886 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.55203e7 | −1.13983 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.32055e6 | 0.236277 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.35684e7 | 1.03474 | 0.517370 | − | 0.855762i | \(-0.326911\pi\) | ||||
0.517370 | + | 0.855762i | \(0.326911\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.81829e7 | 0.793762 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.52124e7 | −1.52847 | −0.764234 | − | 0.644939i | \(-0.776883\pi\) | ||||
−0.764234 | + | 0.644939i | \(0.776883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.08063e7 | 1.76127 | 0.880634 | − | 0.473796i | \(-0.157117\pi\) | ||||
0.880634 | + | 0.473796i | \(0.157117\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.02525e7 | 1.29839 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.02857e6 | −0.257280 | −0.128640 | − | 0.991691i | \(-0.541061\pi\) | ||||
−0.128640 | + | 0.991691i | \(0.541061\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 923542. | 0.0389729 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.81003e7 | 1.17918 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.54440e6 | 0.106176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.28830e7 | −1.36455 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.83748e7 | −0.758271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.15122e6 | 0.0472438 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.82082e7 | 0.739002 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.42799e7 | 0.576377 | 0.288188 | − | 0.957574i | \(-0.406947\pi\) | ||||
0.288188 | + | 0.957574i | \(0.406947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.42384e7 | −0.571546 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.11130e7 | 0.842855 | 0.421428 | − | 0.906862i | \(-0.361529\pi\) | ||||
0.421428 | + | 0.906862i | \(0.361529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.31445e6 | −0.250702 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.13429e6 | −0.163248 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.65736e7 | 0.647334 | 0.323667 | − | 0.946171i | \(-0.395084\pi\) | ||||
0.323667 | + | 0.946171i | \(0.395084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.81635e6 | 0.187098 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.92721e7 | −1.13097 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.24212e7 | −2.39871 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.24829e7 | 0.477106 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.63934e7 | −0.623203 | −0.311601 | − | 0.950213i | \(-0.600865\pi\) | ||||
−0.311601 | + | 0.950213i | \(0.600865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.07017e7 | 0.778577 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −717172. | −0.0268284 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.68057e7 | 0.997420 | 0.498710 | − | 0.866769i | \(-0.333807\pi\) | ||||
0.498710 | + | 0.866769i | \(0.333807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.48154e7 | 0.918454 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.62875e6 | 0.207223 | 0.103611 | − | 0.994618i | \(-0.466960\pi\) | ||||
0.103611 | + | 0.994618i | \(0.466960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.41470e7 | −1.25047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.76782e7 | −1.00291 | −0.501456 | − | 0.865183i | \(-0.667202\pi\) | ||||
−0.501456 | + | 0.865183i | \(0.667202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.15488e7 | −2.21847 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.29328e7 | 0.822253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.40114e7 | −0.856416 | −0.428208 | − | 0.903680i | \(-0.640855\pi\) | ||||
−0.428208 | + | 0.903680i | \(0.640855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.47828e7 | 0.879309 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.80232e6 | −0.169501 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.13264e6 | −0.179280 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.48523e7 | 0.516094 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.40914e6 | −0.325261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.43801e7 | −0.494535 | −0.247267 | − | 0.968947i | \(-0.579533\pi\) | ||||
−0.247267 | + | 0.968947i | \(0.579533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −845628. | −0.0289314 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.87782e7 | 1.66027 | 0.830133 | − | 0.557566i | \(-0.188265\pi\) | ||||
0.830133 | + | 0.557566i | \(0.188265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.49223e7 | 1.85028 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.70305e7 | −1.57632 | −0.788158 | − | 0.615472i | \(-0.788965\pi\) | ||||
−0.788158 | + | 0.615472i | \(0.788965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.80098e7 | −0.600555 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.09062e7 | −0.361827 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.44416e6 | −0.245715 | −0.122858 | − | 0.992424i | \(-0.539206\pi\) | ||||
−0.122858 | + | 0.992424i | \(0.539206\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.36368e7 | 1.10465 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.34663e7 | −0.762877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.62294e7 | −1.49532 | −0.747659 | − | 0.664082i | \(-0.768822\pi\) | ||||
−0.747659 | + | 0.664082i | \(0.768822\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.40401e6 | −0.141734 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.09241e7 | −0.670021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.18781e6 | 0.197151 | 0.0985755 | − | 0.995130i | \(-0.468571\pi\) | ||||
0.0985755 | + | 0.995130i | \(0.468571\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.28633e6 | −0.262693 |
(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 | 588.6.a.p.1.4 | 4 | ||
7.2 | even | 3 | 588.6.i.o.361.1 | 8 | |||
7.3 | odd | 6 | 84.6.i.c.37.4 | yes | 8 | ||
7.4 | even | 3 | 588.6.i.o.373.1 | 8 | |||
7.5 | odd | 6 | 84.6.i.c.25.4 | ✓ | 8 | ||
7.6 | odd | 2 | 588.6.a.n.1.1 | 4 | |||
21.5 | even | 6 | 252.6.k.f.109.1 | 8 | |||
21.17 | even | 6 | 252.6.k.f.37.1 | 8 | |||
28.3 | even | 6 | 336.6.q.i.289.4 | 8 | |||
28.19 | even | 6 | 336.6.q.i.193.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.i.c.25.4 | ✓ | 8 | 7.5 | odd | 6 | ||
84.6.i.c.37.4 | yes | 8 | 7.3 | odd | 6 | ||
252.6.k.f.37.1 | 8 | 21.17 | even | 6 | |||
252.6.k.f.109.1 | 8 | 21.5 | even | 6 | |||
336.6.q.i.193.4 | 8 | 28.19 | even | 6 | |||
336.6.q.i.289.4 | 8 | 28.3 | even | 6 | |||
588.6.a.n.1.1 | 4 | 7.6 | odd | 2 | |||
588.6.a.p.1.4 | 4 | 1.1 | even | 1 | trivial | ||
588.6.i.o.361.1 | 8 | 7.2 | even | 3 | |||
588.6.i.o.373.1 | 8 | 7.4 | even | 3 |