Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.183945.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 12x^{2} + 3x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.24486\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33012 | −0.470268 | −0.235134 | − | 0.971963i | \(-0.575553\pi\) | ||||
−0.235134 | + | 0.971963i | \(0.575553\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.23078 | −0.778848 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.6979 | −0.577630 | −0.288815 | − | 0.957385i | \(-0.593261\pi\) | ||||
−0.288815 | + | 0.957385i | \(0.593261\pi\) | |||||||
\(8\) | 18.9286 | 0.836535 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.2588 | 0.308604 | 0.154302 | − | 0.988024i | \(-0.450687\pi\) | ||||
0.154302 | + | 0.988024i | \(0.450687\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.74029 | 0.0584630 | 0.0292315 | − | 0.999573i | \(-0.490694\pi\) | ||||
0.0292315 | + | 0.999573i | \(0.490694\pi\) | |||||||
\(14\) | 14.2294 | 0.271641 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 24.6689 | 0.385452 | ||||||||
\(17\) | −29.5692 | −0.421858 | −0.210929 | − | 0.977501i | \(-0.567649\pi\) | ||||
−0.210929 | + | 0.977501i | \(0.567649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31.1126 | −0.375669 | −0.187835 | − | 0.982201i | \(-0.560147\pi\) | ||||
−0.187835 | + | 0.982201i | \(0.560147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.9755 | −0.145127 | ||||||||
\(23\) | 116.944 | 1.06020 | 0.530098 | − | 0.847936i | \(-0.322155\pi\) | ||||
0.530098 | + | 0.847936i | \(0.322155\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.64491 | −0.0274933 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 66.6560 | 0.449886 | ||||||||
\(29\) | 108.384 | 0.694016 | 0.347008 | − | 0.937862i | \(-0.387198\pi\) | ||||
0.347008 | + | 0.937862i | \(0.387198\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 70.7730 | 0.410039 | 0.205019 | − | 0.978758i | \(-0.434274\pi\) | ||||
0.205019 | + | 0.978758i | \(0.434274\pi\) | |||||||
\(32\) | −184.242 | −1.01780 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 39.3305 | 0.198386 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 282.289 | 1.25427 | 0.627136 | − | 0.778910i | \(-0.284227\pi\) | ||||
0.627136 | + | 0.778910i | \(0.284227\pi\) | |||||||
\(38\) | 41.3834 | 0.176665 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −425.545 | −1.62095 | −0.810475 | − | 0.585773i | \(-0.800791\pi\) | ||||
−0.810475 | + | 0.585773i | \(0.800791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 312.868 | 1.10958 | 0.554789 | − | 0.831991i | \(-0.312799\pi\) | ||||
0.554789 | + | 0.831991i | \(0.312799\pi\) | |||||||
\(44\) | −70.1509 | −0.240355 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −155.549 | −0.498576 | ||||||||
\(47\) | −193.619 | −0.600900 | −0.300450 | − | 0.953798i | \(-0.597137\pi\) | ||||
−0.300450 | + | 0.953798i | \(0.597137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −228.556 | −0.666344 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17.0741 | −0.0455338 | ||||||||
\(53\) | 103.349 | 0.267850 | 0.133925 | − | 0.990991i | \(-0.457242\pi\) | ||||
0.133925 | + | 0.990991i | \(0.457242\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −202.496 | −0.483208 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −144.164 | −0.326374 | ||||||||
\(59\) | −494.531 | −1.09123 | −0.545614 | − | 0.838036i | \(-0.683704\pi\) | ||||
−0.545614 | + | 0.838036i | \(0.683704\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 424.769 | 0.891575 | 0.445787 | − | 0.895139i | \(-0.352924\pi\) | ||||
0.445787 | + | 0.895139i | \(0.352924\pi\) | |||||||
\(62\) | −94.1365 | −0.192828 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 47.7120 | 0.0931875 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −586.687 | −1.06978 | −0.534889 | − | 0.844922i | \(-0.679647\pi\) | ||||
−0.534889 | + | 0.844922i | \(0.679647\pi\) | |||||||
\(68\) | 184.239 | 0.328563 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1139.86 | −1.90531 | −0.952653 | − | 0.304060i | \(-0.901658\pi\) | ||||
−0.952653 | + | 0.304060i | \(0.901658\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 302.564 | 0.485102 | 0.242551 | − | 0.970139i | \(-0.422016\pi\) | ||||
0.242551 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(74\) | −375.478 | −0.589844 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 193.856 | 0.292589 | ||||||||
\(77\) | −120.445 | −0.178259 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −525.354 | −0.748189 | −0.374095 | − | 0.927391i | \(-0.622046\pi\) | ||||
−0.374095 | + | 0.927391i | \(0.622046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 566.026 | 0.762281 | ||||||||
\(83\) | 1009.07 | 1.33446 | 0.667228 | − | 0.744854i | \(-0.267481\pi\) | ||||
0.667228 | + | 0.744854i | \(0.267481\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −416.151 | −0.521799 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 213.113 | 0.258158 | ||||||||
\(89\) | −1424.57 | −1.69668 | −0.848340 | − | 0.529451i | \(-0.822398\pi\) | ||||
−0.848340 | + | 0.529451i | \(0.822398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.3152 | −0.0337700 | ||||||||
\(92\) | −728.652 | −0.825731 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 257.537 | 0.282584 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 25.6808 | 0.0268814 | 0.0134407 | − | 0.999910i | \(-0.495722\pi\) | ||||
0.0134407 | + | 0.999910i | \(0.495722\pi\) | |||||||
\(98\) | 304.007 | 0.313360 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1523.35 | −1.50078 | −0.750392 | − | 0.660993i | \(-0.770135\pi\) | ||||
−0.750392 | + | 0.660993i | \(0.770135\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1237.75 | −1.18407 | −0.592034 | − | 0.805913i | \(-0.701675\pi\) | ||||
−0.592034 | + | 0.805913i | \(0.701675\pi\) | |||||||
\(104\) | 51.8699 | 0.0489064 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −137.466 | −0.125961 | ||||||||
\(107\) | −465.820 | −0.420865 | −0.210432 | − | 0.977608i | \(-0.567487\pi\) | ||||
−0.210432 | + | 0.977608i | \(0.567487\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 748.032 | 0.657325 | 0.328663 | − | 0.944447i | \(-0.393402\pi\) | ||||
0.328663 | + | 0.944447i | \(0.393402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −263.905 | −0.222649 | ||||||||
\(113\) | 324.843 | 0.270431 | 0.135215 | − | 0.990816i | \(-0.456827\pi\) | ||||
0.135215 | + | 0.990816i | \(0.456827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −675.319 | −0.540533 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 657.786 | 0.513170 | ||||||||
\(119\) | 316.327 | 0.243678 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1204.24 | −0.904764 | ||||||||
\(122\) | −564.993 | −0.419279 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −440.971 | −0.319358 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −29.9720 | −0.0209416 | −0.0104708 | − | 0.999945i | \(-0.503333\pi\) | ||||
−0.0104708 | + | 0.999945i | \(0.503333\pi\) | |||||||
\(128\) | 1410.47 | 0.973978 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −906.495 | −0.604587 | −0.302293 | − | 0.953215i | \(-0.597752\pi\) | ||||
−0.302293 | + | 0.953215i | \(0.597752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 332.838 | 0.216998 | ||||||||
\(134\) | 780.363 | 0.503083 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −559.704 | −0.352899 | ||||||||
\(137\) | −2359.95 | −1.47171 | −0.735855 | − | 0.677139i | \(-0.763220\pi\) | ||||
−0.735855 | + | 0.677139i | \(0.763220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1709.46 | 1.04313 | 0.521563 | − | 0.853213i | \(-0.325349\pi\) | ||||
0.521563 | + | 0.853213i | \(0.325349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1516.15 | 0.896005 | ||||||||
\(143\) | 30.8522 | 0.0180419 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −402.446 | −0.228128 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1758.88 | −0.976886 | ||||||||
\(149\) | −119.170 | −0.0655221 | −0.0327611 | − | 0.999463i | \(-0.510430\pi\) | ||||
−0.0327611 | + | 0.999463i | \(0.510430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 768.157 | 0.413985 | 0.206992 | − | 0.978343i | \(-0.433632\pi\) | ||||
0.206992 | + | 0.978343i | \(0.433632\pi\) | |||||||
\(152\) | −588.919 | −0.314261 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 160.206 | 0.0838294 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1999.27 | −1.01630 | −0.508151 | − | 0.861268i | \(-0.669671\pi\) | ||||
−0.508151 | + | 0.861268i | \(0.669671\pi\) | |||||||
\(158\) | 698.783 | 0.351850 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1251.05 | −0.612401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1206.73 | −0.579867 | −0.289934 | − | 0.957047i | \(-0.593633\pi\) | ||||
−0.289934 | + | 0.957047i | \(0.593633\pi\) | |||||||
\(164\) | 2651.48 | 1.26247 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1342.18 | −0.627552 | ||||||||
\(167\) | 102.994 | 0.0477239 | 0.0238619 | − | 0.999715i | \(-0.492404\pi\) | ||||
0.0238619 | + | 0.999715i | \(0.492404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2189.49 | −0.996582 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1949.41 | −0.864193 | ||||||||
\(173\) | 308.318 | 0.135497 | 0.0677485 | − | 0.997702i | \(-0.478418\pi\) | ||||
0.0677485 | + | 0.997702i | \(0.478418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 277.741 | 0.118952 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1894.85 | 0.797895 | ||||||||
\(179\) | −3145.61 | −1.31349 | −0.656743 | − | 0.754115i | \(-0.728066\pi\) | ||||
−0.656743 | + | 0.754115i | \(0.728066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2321.35 | 0.953284 | 0.476642 | − | 0.879098i | \(-0.341854\pi\) | ||||
0.476642 | + | 0.879098i | \(0.341854\pi\) | |||||||
\(182\) | 38.9927 | 0.0158809 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2213.59 | 0.886891 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −332.912 | −0.130187 | ||||||||
\(188\) | 1206.40 | 0.468009 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2261.68 | 0.856804 | 0.428402 | − | 0.903588i | \(-0.359077\pi\) | ||||
0.428402 | + | 0.903588i | \(0.359077\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4792.77 | −1.78752 | −0.893760 | − | 0.448545i | \(-0.851942\pi\) | ||||
−0.893760 | + | 0.448545i | \(0.851942\pi\) | |||||||
\(194\) | −34.1585 | −0.0126414 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1424.08 | 0.518981 | ||||||||
\(197\) | 2262.41 | 0.818223 | 0.409111 | − | 0.912484i | \(-0.365839\pi\) | ||||
0.409111 | + | 0.912484i | \(0.365839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2188.42 | −0.779562 | −0.389781 | − | 0.920908i | \(-0.627449\pi\) | ||||
−0.389781 | + | 0.920908i | \(0.627449\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2026.24 | 0.705771 | ||||||||
\(203\) | −1159.48 | −0.400884 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1646.35 | 0.556830 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 67.6000 | 0.0225347 | ||||||||
\(209\) | −350.289 | −0.115933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4907.42 | −1.60114 | −0.800570 | − | 0.599240i | \(-0.795470\pi\) | ||||
−0.800570 | + | 0.599240i | \(0.795470\pi\) | |||||||
\(212\) | −643.943 | −0.208614 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 619.596 | 0.197919 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −757.119 | −0.236851 | ||||||||
\(218\) | −994.971 | −0.309119 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −81.0281 | −0.0246631 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5787.33 | 1.73789 | 0.868943 | − | 0.494912i | \(-0.164800\pi\) | ||||
0.868943 | + | 0.494912i | \(0.164800\pi\) | |||||||
\(224\) | 1970.99 | 0.587912 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −432.080 | −0.127175 | ||||||||
\(227\) | 4358.48 | 1.27437 | 0.637186 | − | 0.770710i | \(-0.280098\pi\) | ||||
0.637186 | + | 0.770710i | \(0.280098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3944.00 | 1.13811 | 0.569054 | − | 0.822300i | \(-0.307310\pi\) | ||||
0.569054 | + | 0.822300i | \(0.307310\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2051.57 | 0.580569 | ||||||||
\(233\) | −5530.41 | −1.55497 | −0.777487 | − | 0.628899i | \(-0.783506\pi\) | ||||
−0.777487 | + | 0.628899i | \(0.783506\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3081.32 | 0.849901 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −420.752 | −0.114594 | ||||||||
\(239\) | −3823.19 | −1.03473 | −0.517367 | − | 0.855763i | \(-0.673088\pi\) | ||||
−0.517367 | + | 0.855763i | \(0.673088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3976.26 | 1.06280 | 0.531398 | − | 0.847122i | \(-0.321667\pi\) | ||||
0.531398 | + | 0.847122i | \(0.321667\pi\) | |||||||
\(242\) | 1601.78 | 0.425481 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2646.64 | −0.694401 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −85.2574 | −0.0219628 | ||||||||
\(248\) | 1339.64 | 0.343012 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1758.83 | 0.442297 | 0.221148 | − | 0.975240i | \(-0.429019\pi\) | ||||
0.221148 | + | 0.975240i | \(0.429019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1316.64 | 0.327181 | ||||||||
\(254\) | 39.8663 | 0.00984817 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2257.79 | −0.551218 | ||||||||
\(257\) | 3396.20 | 0.824316 | 0.412158 | − | 0.911112i | \(-0.364775\pi\) | ||||
0.412158 | + | 0.911112i | \(0.364775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3019.89 | −0.724504 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1205.75 | 0.284318 | ||||||||
\(263\) | −4664.71 | −1.09368 | −0.546841 | − | 0.837236i | \(-0.684170\pi\) | ||||
−0.546841 | + | 0.837236i | \(0.684170\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −442.714 | −0.102047 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3655.52 | 0.833195 | ||||||||
\(269\) | 214.904 | 0.0487099 | 0.0243549 | − | 0.999703i | \(-0.492247\pi\) | ||||
0.0243549 | + | 0.999703i | \(0.492247\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3260.69 | 0.730896 | 0.365448 | − | 0.930832i | \(-0.380916\pi\) | ||||
0.365448 | + | 0.930832i | \(0.380916\pi\) | |||||||
\(272\) | −729.440 | −0.162606 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3139.02 | 0.692098 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1992.86 | 0.432273 | 0.216136 | − | 0.976363i | \(-0.430654\pi\) | ||||
0.216136 | + | 0.976363i | \(0.430654\pi\) | |||||||
\(278\) | −2273.78 | −0.490549 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3029.98 | 0.643251 | 0.321626 | − | 0.946867i | \(-0.395771\pi\) | ||||
0.321626 | + | 0.946867i | \(0.395771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4950.46 | −1.03984 | −0.519920 | − | 0.854215i | \(-0.674038\pi\) | ||||
−0.519920 | + | 0.854215i | \(0.674038\pi\) | |||||||
\(284\) | 7102.23 | 1.48394 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −41.0372 | −0.00848454 | ||||||||
\(287\) | 4552.42 | 0.936309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4038.66 | −0.822036 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1885.21 | −0.377821 | ||||||||
\(293\) | −8087.47 | −1.61254 | −0.806272 | − | 0.591546i | \(-0.798518\pi\) | ||||
−0.806272 | + | 0.591546i | \(0.798518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5343.35 | 1.04924 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 158.510 | 0.0308130 | ||||||||
\(299\) | 320.460 | 0.0619822 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3347.01 | −0.640926 | ||||||||
\(302\) | −1021.74 | −0.194684 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −767.514 | −0.144802 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 272.579 | 0.0506740 | 0.0253370 | − | 0.999679i | \(-0.491934\pi\) | ||||
0.0253370 | + | 0.999679i | \(0.491934\pi\) | |||||||
\(308\) | 750.464 | 0.138836 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9093.68 | 1.65806 | 0.829028 | − | 0.559208i | \(-0.188895\pi\) | ||||
0.829028 | + | 0.559208i | \(0.188895\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8213.36 | 1.48322 | 0.741608 | − | 0.670834i | \(-0.234064\pi\) | ||||
0.741608 | + | 0.670834i | \(0.234064\pi\) | |||||||
\(314\) | 2659.27 | 0.477935 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3273.37 | 0.582726 | ||||||||
\(317\) | 4859.27 | 0.860959 | 0.430480 | − | 0.902600i | \(-0.358344\pi\) | ||||
0.430480 | + | 0.902600i | \(0.358344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1220.27 | 0.214176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1664.04 | 0.287992 | ||||||||
\(323\) | 919.973 | 0.158479 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1605.09 | 0.272693 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8054.99 | −1.35598 | ||||||||
\(329\) | 2071.31 | 0.347098 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10784.9 | 1.79091 | 0.895454 | − | 0.445155i | \(-0.146851\pi\) | ||||
0.895454 | + | 0.445155i | \(0.146851\pi\) | |||||||
\(332\) | −6287.30 | −1.03934 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −136.994 | −0.0224430 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4752.67 | −0.768232 | −0.384116 | − | 0.923285i | \(-0.625494\pi\) | ||||
−0.384116 | + | 0.923285i | \(0.625494\pi\) | |||||||
\(338\) | 2912.28 | 0.468661 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 796.816 | 0.126540 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6114.42 | 0.962530 | ||||||||
\(344\) | 5922.16 | 0.928202 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −410.099 | −0.0637199 | ||||||||
\(347\) | 10303.2 | 1.59397 | 0.796984 | − | 0.604000i | \(-0.206427\pi\) | ||||
0.796984 | + | 0.604000i | \(0.206427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9058.09 | −1.38931 | −0.694654 | − | 0.719344i | \(-0.744442\pi\) | ||||
−0.694654 | + | 0.719344i | \(0.744442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2074.33 | −0.314097 | ||||||||
\(353\) | −1275.21 | −0.192273 | −0.0961366 | − | 0.995368i | \(-0.530649\pi\) | ||||
−0.0961366 | + | 0.995368i | \(0.530649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8876.21 | 1.32146 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4184.03 | 0.617690 | ||||||||
\(359\) | 2556.89 | 0.375899 | 0.187949 | − | 0.982179i | \(-0.439816\pi\) | ||||
0.187949 | + | 0.982179i | \(0.439816\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5891.01 | −0.858873 | ||||||||
\(362\) | −3087.67 | −0.448299 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 182.657 | 0.0263017 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 754.620 | 0.107332 | 0.0536660 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536660 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(368\) | 2884.88 | 0.408655 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1105.61 | −0.154718 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6177.49 | −0.857529 | −0.428765 | − | 0.903416i | \(-0.641051\pi\) | ||||
−0.428765 | + | 0.903416i | \(0.641051\pi\) | |||||||
\(374\) | 442.813 | 0.0612227 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3664.95 | −0.502674 | ||||||||
\(377\) | 297.004 | 0.0405743 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8146.93 | 1.10417 | 0.552084 | − | 0.833789i | \(-0.313833\pi\) | ||||
0.552084 | + | 0.833789i | \(0.313833\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3008.30 | −0.402927 | ||||||||
\(383\) | −4710.88 | −0.628498 | −0.314249 | − | 0.949341i | \(-0.601753\pi\) | ||||
−0.314249 | + | 0.949341i | \(0.601753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6374.96 | 0.840614 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −160.012 | −0.0209365 | ||||||||
\(389\) | −9508.93 | −1.23939 | −0.619694 | − | 0.784844i | \(-0.712743\pi\) | ||||
−0.619694 | + | 0.784844i | \(0.712743\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3457.94 | −0.447252 | ||||||||
\(392\) | −4326.25 | −0.557420 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3009.27 | −0.384784 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9615.34 | 1.21557 | 0.607783 | − | 0.794103i | \(-0.292059\pi\) | ||||
0.607783 | + | 0.794103i | \(0.292059\pi\) | |||||||
\(398\) | 2910.86 | 0.366603 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −481.837 | −0.0600045 | −0.0300022 | − | 0.999550i | \(-0.509551\pi\) | ||||
−0.0300022 | + | 0.999550i | \(0.509551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 193.938 | 0.0239721 | ||||||||
\(404\) | 9491.68 | 1.16888 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1542.25 | 0.188523 | ||||||||
\(407\) | 3178.22 | 0.387073 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12331.6 | 1.49085 | 0.745423 | − | 0.666592i | \(-0.232248\pi\) | ||||
0.745423 | + | 0.666592i | \(0.232248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7712.15 | 0.922209 | ||||||||
\(413\) | 5290.42 | 0.630326 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −504.875 | −0.0595037 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 465.926 | 0.0545196 | ||||||||
\(419\) | 553.776 | 0.0645674 | 0.0322837 | − | 0.999479i | \(-0.489722\pi\) | ||||
0.0322837 | + | 0.999479i | \(0.489722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −522.671 | −0.0605070 | −0.0302535 | − | 0.999542i | \(-0.509631\pi\) | ||||
−0.0302535 | + | 0.999542i | \(0.509631\pi\) | |||||||
\(422\) | 6527.45 | 0.752965 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1956.25 | 0.224066 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4544.11 | −0.515000 | ||||||||
\(428\) | 2902.42 | 0.327789 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1294.01 | −0.144618 | −0.0723089 | − | 0.997382i | \(-0.523037\pi\) | ||||
−0.0723089 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −179.997 | −0.0199771 | −0.00998856 | − | 0.999950i | \(-0.503180\pi\) | ||||
−0.00998856 | + | 0.999950i | \(0.503180\pi\) | |||||||
\(434\) | 1007.06 | 0.111383 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4660.82 | −0.511956 | ||||||||
\(437\) | −3638.43 | −0.398283 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6068.09 | −0.659714 | −0.329857 | − | 0.944031i | \(-0.607000\pi\) | ||||
−0.329857 | + | 0.944031i | \(0.607000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 107.777 | 0.0115983 | ||||||||
\(443\) | −15649.3 | −1.67838 | −0.839190 | − | 0.543838i | \(-0.816971\pi\) | ||||
−0.839190 | + | 0.543838i | \(0.816971\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7697.84 | −0.817272 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −510.416 | −0.0538279 | ||||||||
\(449\) | −7274.81 | −0.764631 | −0.382316 | − | 0.924032i | \(-0.624873\pi\) | ||||
−0.382316 | + | 0.924032i | \(0.624873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4791.11 | −0.500232 | ||||||||
\(452\) | −2024.03 | −0.210624 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5797.29 | −0.599296 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4356.56 | −0.445933 | −0.222967 | − | 0.974826i | \(-0.571574\pi\) | ||||
−0.222967 | + | 0.974826i | \(0.571574\pi\) | |||||||
\(458\) | −5245.98 | −0.535216 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9318.22 | −0.941416 | −0.470708 | − | 0.882289i | \(-0.656001\pi\) | ||||
−0.470708 | + | 0.882289i | \(0.656001\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18699.8 | −1.87701 | −0.938503 | − | 0.345270i | \(-0.887787\pi\) | ||||
−0.938503 | + | 0.345270i | \(0.887787\pi\) | |||||||
\(464\) | 2673.72 | 0.267510 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7356.10 | 0.731255 | ||||||||
\(467\) | −5345.39 | −0.529669 | −0.264834 | − | 0.964294i | \(-0.585317\pi\) | ||||
−0.264834 | + | 0.964294i | \(0.585317\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6276.29 | 0.617936 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9360.81 | −0.912852 | ||||||||
\(473\) | 3522.50 | 0.342420 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1970.96 | −0.189788 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5085.30 | 0.486603 | ||||||||
\(479\) | −16930.5 | −1.61498 | −0.807489 | − | 0.589883i | \(-0.799174\pi\) | ||||
−0.807489 | + | 0.589883i | \(0.799174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 773.553 | 0.0733285 | ||||||||
\(482\) | −5288.90 | −0.499799 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7503.36 | 0.704673 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3052.84 | 0.284060 | 0.142030 | − | 0.989862i | \(-0.454637\pi\) | ||||
0.142030 | + | 0.989862i | \(0.454637\pi\) | |||||||
\(488\) | 8040.29 | 0.745834 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7591.68 | −0.697775 | −0.348888 | − | 0.937165i | \(-0.613440\pi\) | ||||
−0.348888 | + | 0.937165i | \(0.613440\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3204.84 | −0.292776 | ||||||||
\(494\) | 113.403 | 0.0103284 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1745.89 | 0.158050 | ||||||||
\(497\) | 12194.1 | 1.10056 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3688.97 | −0.330944 | −0.165472 | − | 0.986215i | \(-0.552915\pi\) | ||||
−0.165472 | + | 0.986215i | \(0.552915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2339.46 | −0.207998 | ||||||||
\(503\) | −2212.28 | −0.196105 | −0.0980523 | − | 0.995181i | \(-0.531261\pi\) | ||||
−0.0980523 | + | 0.995181i | \(0.531261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1751.29 | −0.153863 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 186.749 | 0.0163103 | ||||||||
\(509\) | −13842.8 | −1.20544 | −0.602722 | − | 0.797952i | \(-0.705917\pi\) | ||||
−0.602722 | + | 0.797952i | \(0.705917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3236.79 | −0.280209 | ||||||||
\(512\) | −8280.64 | −0.714758 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4517.35 | −0.387649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2179.91 | −0.185440 | ||||||||
\(518\) | 4016.81 | 0.340711 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21683.4 | −1.82335 | −0.911677 | − | 0.410908i | \(-0.865212\pi\) | ||||
−0.911677 | + | 0.410908i | \(0.865212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2021.57 | 0.169020 | 0.0845098 | − | 0.996423i | \(-0.473068\pi\) | ||||
0.0845098 | + | 0.996423i | \(0.473068\pi\) | |||||||
\(524\) | 5648.17 | 0.470881 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6204.62 | 0.514324 | ||||||||
\(527\) | −2092.70 | −0.172978 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1508.89 | 0.124015 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2073.84 | −0.169008 | ||||||||
\(533\) | −1166.12 | −0.0947657 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −11105.2 | −0.894908 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −285.848 | −0.0229067 | ||||||||
\(539\) | −2573.26 | −0.205636 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9538.79 | −0.758049 | −0.379025 | − | 0.925387i | \(-0.623740\pi\) | ||||
−0.379025 | + | 0.925387i | \(0.623740\pi\) | |||||||
\(542\) | −4337.11 | −0.343717 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5447.88 | 0.429367 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7163.31 | −0.559929 | −0.279964 | − | 0.960010i | \(-0.590323\pi\) | ||||
−0.279964 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(548\) | 14704.3 | 1.14624 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3372.12 | −0.260720 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5620.16 | 0.432176 | ||||||||
\(554\) | −2650.75 | −0.203284 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10651.3 | −0.812436 | ||||||||
\(557\) | −14886.5 | −1.13243 | −0.566214 | − | 0.824258i | \(-0.691592\pi\) | ||||
−0.566214 | + | 0.824258i | \(0.691592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 857.348 | 0.0648693 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4030.24 | −0.302501 | ||||||||
\(563\) | 8134.04 | 0.608897 | 0.304448 | − | 0.952529i | \(-0.401528\pi\) | ||||
0.304448 | + | 0.952529i | \(0.401528\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6584.71 | 0.489003 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21576.0 | −1.59386 | ||||||||
\(569\) | −10031.8 | −0.739115 | −0.369557 | − | 0.929208i | \(-0.620491\pi\) | ||||
−0.369557 | + | 0.929208i | \(0.620491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2507.05 | −0.183742 | −0.0918712 | − | 0.995771i | \(-0.529285\pi\) | ||||
−0.0918712 | + | 0.995771i | \(0.529285\pi\) | |||||||
\(572\) | −192.234 | −0.0140519 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6055.26 | −0.440316 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5378.18 | 0.388036 | 0.194018 | − | 0.980998i | \(-0.437848\pi\) | ||||
0.194018 | + | 0.980998i | \(0.437848\pi\) | |||||||
\(578\) | 5371.90 | 0.386577 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10794.9 | −0.770821 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1163.58 | 0.0826594 | ||||||||
\(584\) | 5727.13 | 0.405805 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10757.3 | 0.758328 | ||||||||
\(587\) | −6153.77 | −0.432697 | −0.216349 | − | 0.976316i | \(-0.569415\pi\) | ||||
−0.216349 | + | 0.976316i | \(0.569415\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2201.93 | −0.154039 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6963.77 | 0.483461 | ||||||||
\(593\) | 14278.1 | 0.988753 | 0.494376 | − | 0.869248i | \(-0.335396\pi\) | ||||
0.494376 | + | 0.869248i | \(0.335396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 742.523 | 0.0510318 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −426.250 | −0.0291483 | ||||||||
\(599\) | −2071.22 | −0.141282 | −0.0706410 | − | 0.997502i | \(-0.522504\pi\) | ||||
−0.0706410 | + | 0.997502i | \(0.522504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12307.3 | 0.835319 | 0.417660 | − | 0.908604i | \(-0.362850\pi\) | ||||
0.417660 | + | 0.908604i | \(0.362850\pi\) | |||||||
\(602\) | 4451.93 | 0.301407 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4786.22 | −0.322431 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22963.7 | 1.53553 | 0.767765 | − | 0.640732i | \(-0.221369\pi\) | ||||
0.767765 | + | 0.640732i | \(0.221369\pi\) | |||||||
\(608\) | 5732.23 | 0.382356 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −530.573 | −0.0351304 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12746.7 | 0.839862 | 0.419931 | − | 0.907556i | \(-0.362054\pi\) | ||||
0.419931 | + | 0.907556i | \(0.362054\pi\) | |||||||
\(614\) | −362.563 | −0.0238304 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2279.85 | −0.149120 | ||||||||
\(617\) | −13959.6 | −0.910844 | −0.455422 | − | 0.890276i | \(-0.650512\pi\) | ||||
−0.455422 | + | 0.890276i | \(0.650512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15542.0 | 1.00918 | 0.504591 | − | 0.863358i | \(-0.331643\pi\) | ||||
0.504591 | + | 0.863358i | \(0.331643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12095.7 | −0.779730 | ||||||||
\(623\) | 15239.9 | 0.980053 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10924.7 | −0.697509 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12457.0 | 0.791545 | ||||||||
\(629\) | −8347.06 | −0.529124 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12297.5 | −0.775844 | −0.387922 | − | 0.921692i | \(-0.626807\pi\) | ||||
−0.387922 | + | 0.921692i | \(0.626807\pi\) | |||||||
\(632\) | −9944.24 | −0.625887 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6463.41 | −0.404882 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −626.309 | −0.0389565 | ||||||||
\(638\) | −1623.11 | −0.100720 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16523.4 | −1.01815 | −0.509075 | − | 0.860722i | \(-0.670013\pi\) | ||||
−0.509075 | + | 0.860722i | \(0.670013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25293.3 | 1.55128 | 0.775639 | − | 0.631177i | \(-0.217428\pi\) | ||||
0.775639 | + | 0.631177i | \(0.217428\pi\) | |||||||
\(644\) | 7795.02 | 0.476967 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1223.67 | −0.0745276 | ||||||||
\(647\) | −1442.91 | −0.0876763 | −0.0438381 | − | 0.999039i | \(-0.513959\pi\) | ||||
−0.0438381 | + | 0.999039i | \(0.513959\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5567.81 | −0.336757 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7518.87 | 0.451628 | ||||||||
\(653\) | 9042.22 | 0.541883 | 0.270941 | − | 0.962596i | \(-0.412665\pi\) | ||||
0.270941 | + | 0.962596i | \(0.412665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10497.7 | −0.624799 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2755.09 | −0.163229 | ||||||||
\(659\) | 10084.1 | 0.596085 | 0.298042 | − | 0.954553i | \(-0.403666\pi\) | ||||
0.298042 | + | 0.954553i | \(0.403666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4181.32 | 0.246043 | 0.123022 | − | 0.992404i | \(-0.460742\pi\) | ||||
0.123022 | + | 0.992404i | \(0.460742\pi\) | |||||||
\(662\) | −14345.2 | −0.842207 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19100.3 | 1.11632 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12674.9 | 0.735793 | ||||||||
\(668\) | −641.731 | −0.0371696 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4782.37 | 0.275143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21108.5 | −1.20902 | −0.604512 | − | 0.796596i | \(-0.706632\pi\) | ||||
−0.604512 | + | 0.796596i | \(0.706632\pi\) | |||||||
\(674\) | 6321.61 | 0.361275 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13642.2 | 0.776186 | ||||||||
\(677\) | −19793.4 | −1.12367 | −0.561834 | − | 0.827250i | \(-0.689904\pi\) | ||||
−0.561834 | + | 0.827250i | \(0.689904\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −274.730 | −0.0155275 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1059.86 | −0.0595075 | ||||||||
\(683\) | −7226.49 | −0.404852 | −0.202426 | − | 0.979298i | \(-0.564883\pi\) | ||||
−0.202426 | + | 0.979298i | \(0.564883\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8132.91 | −0.452647 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7718.11 | 0.427689 | ||||||||
\(689\) | 283.205 | 0.0156593 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1152.43 | −0.0634451 | −0.0317225 | − | 0.999497i | \(-0.510099\pi\) | ||||
−0.0317225 | + | 0.999497i | \(0.510099\pi\) | |||||||
\(692\) | −1921.06 | −0.105531 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13704.5 | −0.749593 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12583.0 | 0.683810 | ||||||||
\(698\) | 12048.3 | 0.653347 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13364.5 | −0.720073 | −0.360036 | − | 0.932938i | \(-0.617236\pi\) | ||||
−0.360036 | + | 0.932938i | \(0.617236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8782.74 | −0.471191 | ||||||||
\(704\) | 537.178 | 0.0287580 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1696.18 | 0.0904200 | ||||||||
\(707\) | 16296.6 | 0.866898 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15588.0 | −0.825696 | −0.412848 | − | 0.910800i | \(-0.635466\pi\) | ||||
−0.412848 | + | 0.910800i | \(0.635466\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −26965.2 | −1.41933 | ||||||||
\(713\) | 8276.47 | 0.434721 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19599.6 | 1.02301 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3400.97 | −0.176773 | ||||||||
\(719\) | −1086.42 | −0.0563513 | −0.0281757 | − | 0.999603i | \(-0.508970\pi\) | ||||
−0.0281757 | + | 0.999603i | \(0.508970\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13241.3 | 0.683953 | ||||||||
\(722\) | 7835.74 | 0.403900 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14463.8 | −0.742463 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27592.3 | −1.40762 | −0.703811 | − | 0.710387i | \(-0.748520\pi\) | ||||
−0.703811 | + | 0.710387i | \(0.748520\pi\) | |||||||
\(728\) | −554.897 | −0.0282498 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9251.24 | −0.468084 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28759.0 | 1.44916 | 0.724582 | − | 0.689189i | \(-0.242033\pi\) | ||||
0.724582 | + | 0.689189i | \(0.242033\pi\) | |||||||
\(734\) | −1003.73 | −0.0504748 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21546.0 | −1.07907 | ||||||||
\(737\) | −6605.36 | −0.330138 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 113.264 | 0.00563800 | 0.00281900 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281900 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1470.59 | 0.0727589 | ||||||||
\(743\) | −37767.7 | −1.86482 | −0.932411 | − | 0.361399i | \(-0.882299\pi\) | ||||
−0.932411 | + | 0.361399i | \(0.882299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8216.80 | 0.403269 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2074.30 | 0.101396 | ||||||||
\(749\) | 4983.27 | 0.243104 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26372.9 | 1.28144 | 0.640720 | − | 0.767774i | \(-0.278636\pi\) | ||||
0.640720 | + | 0.767774i | \(0.278636\pi\) | |||||||
\(752\) | −4776.38 | −0.231618 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −395.051 | −0.0190808 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13224.5 | −0.634943 | −0.317472 | − | 0.948268i | \(-0.602834\pi\) | ||||
−0.317472 | + | 0.948268i | \(0.602834\pi\) | |||||||
\(758\) | −10836.4 | −0.519255 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1709.91 | −0.0814511 | −0.0407256 | − | 0.999170i | \(-0.512967\pi\) | ||||
−0.0407256 | + | 0.999170i | \(0.512967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8002.33 | −0.379691 | ||||||||
\(764\) | −14092.0 | −0.667320 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6266.03 | 0.295563 | ||||||||
\(767\) | −1355.16 | −0.0637965 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4705.78 | −0.220669 | −0.110335 | − | 0.993894i | \(-0.535192\pi\) | ||||
−0.110335 | + | 0.993894i | \(0.535192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29862.7 | 1.39221 | ||||||||
\(773\) | 19109.6 | 0.889164 | 0.444582 | − | 0.895738i | \(-0.353352\pi\) | ||||
0.444582 | + | 0.895738i | \(0.353352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 486.103 | 0.0224872 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12648.0 | 0.582844 | ||||||||
\(779\) | 13239.8 | 0.608941 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12833.4 | −0.587985 | ||||||||
\(782\) | 4599.47 | 0.210328 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5638.23 | −0.256844 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17209.4 | 0.779480 | 0.389740 | − | 0.920925i | \(-0.372565\pi\) | ||||
0.389740 | + | 0.920925i | \(0.372565\pi\) | |||||||
\(788\) | −14096.6 | −0.637271 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3475.12 | −0.156209 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1163.99 | 0.0521242 | ||||||||
\(794\) | −12789.5 | −0.571642 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13635.6 | 0.607160 | ||||||||
\(797\) | 34775.4 | 1.54556 | 0.772779 | − | 0.634676i | \(-0.218866\pi\) | ||||
0.772779 | + | 0.634676i | \(0.218866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5725.17 | 0.253494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 640.901 | 0.0282182 | ||||||||
\(803\) | 3406.50 | 0.149704 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −257.961 | −0.0112733 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28835.0 | −1.25546 | ||||||||
\(809\) | −22233.7 | −0.966250 | −0.483125 | − | 0.875551i | \(-0.660498\pi\) | ||||
−0.483125 | + | 0.875551i | \(0.660498\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3576.54 | −0.154857 | −0.0774287 | − | 0.996998i | \(-0.524671\pi\) | ||||
−0.0774287 | + | 0.996998i | \(0.524671\pi\) | |||||||
\(812\) | 7224.47 | 0.312228 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4227.42 | −0.182028 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9734.12 | −0.416834 | ||||||||
\(818\) | −16402.4 | −0.701097 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29910.6 | 1.27148 | 0.635741 | − | 0.771902i | \(-0.280694\pi\) | ||||
0.635741 | + | 0.771902i | \(0.280694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34421.1 | 1.45789 | 0.728945 | − | 0.684572i | \(-0.240011\pi\) | ||||
0.728945 | + | 0.684572i | \(0.240011\pi\) | |||||||
\(824\) | −23428.9 | −0.990515 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7036.89 | −0.296422 | ||||||||
\(827\) | 30778.8 | 1.29417 | 0.647087 | − | 0.762416i | \(-0.275987\pi\) | ||||
0.647087 | + | 0.762416i | \(0.275987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21156.8 | 0.886375 | 0.443188 | − | 0.896429i | \(-0.353848\pi\) | ||||
0.443188 | + | 0.896429i | \(0.353848\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 130.745 | 0.00544802 | ||||||||
\(833\) | 6758.21 | 0.281102 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2182.57 | 0.0902941 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −736.588 | −0.0303640 | ||||||||
\(839\) | 20004.9 | 0.823178 | 0.411589 | − | 0.911370i | \(-0.364974\pi\) | ||||
0.411589 | + | 0.911370i | \(0.364974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12641.8 | −0.518342 | ||||||||
\(842\) | 695.215 | 0.0284545 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30577.0 | 1.24704 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12882.8 | 0.522618 | ||||||||
\(848\) | 2549.50 | 0.103243 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33012.0 | 1.32977 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32918.6 | −1.32135 | −0.660675 | − | 0.750672i | \(-0.729730\pi\) | ||||
−0.660675 | + | 0.750672i | \(0.729730\pi\) | |||||||
\(854\) | 6044.21 | 0.242188 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8817.33 | −0.352068 | ||||||||
\(857\) | −8865.73 | −0.353381 | −0.176691 | − | 0.984266i | \(-0.556539\pi\) | ||||
−0.176691 | + | 0.984266i | \(0.556539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32088.1 | −1.27454 | −0.637271 | − | 0.770640i | \(-0.719937\pi\) | ||||
−0.637271 | + | 0.770640i | \(0.719937\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1721.19 | 0.0680091 | ||||||||
\(863\) | −40687.9 | −1.60491 | −0.802453 | − | 0.596715i | \(-0.796472\pi\) | ||||
−0.802453 | + | 0.596715i | \(0.796472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 239.417 | 0.00939460 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4717.44 | 0.184471 | ||||||||
\(869\) | −5914.83 | −0.230894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1607.69 | −0.0625425 | ||||||||
\(872\) | 14159.2 | 0.549876 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4839.54 | 0.187300 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18440.9 | 0.710041 | 0.355021 | − | 0.934858i | \(-0.384474\pi\) | ||||
0.355021 | + | 0.934858i | \(0.384474\pi\) | |||||||
\(878\) | 8071.29 | 0.310242 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13603.8 | 0.520230 | 0.260115 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260115 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1727.71 | 0.0658461 | 0.0329231 | − | 0.999458i | \(-0.489518\pi\) | ||||
0.0329231 | + | 0.999458i | \(0.489518\pi\) | |||||||
\(884\) | 504.868 | 0.0192088 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20815.5 | 0.789289 | ||||||||
\(887\) | −7445.07 | −0.281827 | −0.140914 | − | 0.990022i | \(-0.545004\pi\) | ||||
−0.140914 | + | 0.990022i | \(0.545004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 320.636 | 0.0120965 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36059.6 | −1.35355 | ||||||||
\(893\) | 6024.00 | 0.225739 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −15089.0 | −0.562599 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9676.36 | 0.359582 | ||||||||
\(899\) | 7670.68 | 0.284574 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3055.94 | −0.112994 | ||||||||
\(902\) | 6372.74 | 0.235243 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6148.84 | 0.226225 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16050.6 | −0.587598 | −0.293799 | − | 0.955867i | \(-0.594920\pi\) | ||||
−0.293799 | + | 0.955867i | \(0.594920\pi\) | |||||||
\(908\) | −27156.7 | −0.992541 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52398.4 | 1.90564 | 0.952818 | − | 0.303541i | \(-0.0981689\pi\) | ||||
0.952818 | + | 0.303541i | \(0.0981689\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11360.9 | 0.411818 | ||||||||
\(914\) | 5794.75 | 0.209708 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24574.2 | −0.886413 | ||||||||
\(917\) | 9697.55 | 0.349227 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34880.1 | 1.25200 | 0.626001 | − | 0.779822i | \(-0.284691\pi\) | ||||
0.626001 | + | 0.779822i | \(0.284691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12394.3 | 0.442718 | ||||||||
\(923\) | −3123.55 | −0.111390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24873.0 | 0.882696 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19968.9 | −0.706370 | ||||||||
\(929\) | 42172.6 | 1.48938 | 0.744692 | − | 0.667408i | \(-0.232596\pi\) | ||||
0.744692 | + | 0.667408i | \(0.232596\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7110.96 | 0.250325 | ||||||||
\(932\) | 34458.8 | 1.21109 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7110.01 | 0.249086 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33853.9 | 1.18032 | 0.590159 | − | 0.807287i | \(-0.299065\pi\) | ||||
0.590159 | + | 0.807287i | \(0.299065\pi\) | |||||||
\(938\) | −8348.21 | −0.290596 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14665.4 | −0.508053 | −0.254027 | − | 0.967197i | \(-0.581755\pi\) | ||||
−0.254027 | + | 0.967197i | \(0.581755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49764.9 | −1.71853 | ||||||||
\(944\) | −12199.6 | −0.420616 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4685.35 | −0.161029 | ||||||||
\(947\) | 43534.3 | 1.49385 | 0.746925 | − | 0.664908i | \(-0.231529\pi\) | ||||
0.746925 | + | 0.664908i | \(0.231529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 829.113 | 0.0283605 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5987.63 | 0.203845 | ||||||||
\(953\) | 3831.21 | 0.130226 | 0.0651128 | − | 0.997878i | \(-0.479259\pi\) | ||||
0.0651128 | + | 0.997878i | \(0.479259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 23821.5 | 0.805901 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22519.6 | 0.759473 | ||||||||
\(959\) | 25246.4 | 0.850104 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24782.2 | −0.831868 | ||||||||
\(962\) | −1028.92 | −0.0344840 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24775.2 | −0.827756 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27975.3 | −0.930324 | −0.465162 | − | 0.885225i | \(-0.654004\pi\) | ||||
−0.465162 | + | 0.885225i | \(0.654004\pi\) | |||||||
\(968\) | −22794.6 | −0.756867 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39865.6 | 1.31756 | 0.658779 | − | 0.752337i | \(-0.271073\pi\) | ||||
0.658779 | + | 0.752337i | \(0.271073\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18287.5 | −0.602540 | ||||||||
\(974\) | −4060.64 | −0.133584 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10478.6 | 0.343659 | ||||||||
\(977\) | −38912.9 | −1.27424 | −0.637121 | − | 0.770764i | \(-0.719875\pi\) | ||||
−0.637121 | + | 0.770764i | \(0.719875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16038.9 | −0.523602 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10097.8 | 0.328141 | ||||||||
\(983\) | −27331.9 | −0.886829 | −0.443415 | − | 0.896317i | \(-0.646233\pi\) | ||||
−0.443415 | + | 0.896317i | \(0.646233\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4262.81 | 0.137683 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 531.221 | 0.0171056 | ||||||||
\(989\) | 36588.0 | 1.17637 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47040.3 | −1.50786 | −0.753928 | − | 0.656957i | \(-0.771843\pi\) | ||||
−0.753928 | + | 0.656957i | \(0.771843\pi\) | |||||||
\(992\) | −13039.3 | −0.417338 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16219.6 | −0.517559 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60011.9 | −1.90632 | −0.953158 | − | 0.302473i | \(-0.902188\pi\) | ||||
−0.953158 | + | 0.302473i | \(0.902188\pi\) | |||||||
\(998\) | 4906.76 | 0.155632 | ||||||||
\(999\) | 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 | 675.4.a.z.1.2 | yes | 4 | |
3.2 | odd | 2 | 675.4.a.v.1.3 | yes | 4 | ||
5.2 | odd | 4 | 675.4.b.p.649.4 | 8 | |||
5.3 | odd | 4 | 675.4.b.p.649.5 | 8 | |||
5.4 | even | 2 | 675.4.a.u.1.3 | ✓ | 4 | ||
15.2 | even | 4 | 675.4.b.q.649.5 | 8 | |||
15.8 | even | 4 | 675.4.b.q.649.4 | 8 | |||
15.14 | odd | 2 | 675.4.a.y.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.4.a.u.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
675.4.a.v.1.3 | yes | 4 | 3.2 | odd | 2 | ||
675.4.a.y.1.2 | yes | 4 | 15.14 | odd | 2 | ||
675.4.a.z.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
675.4.b.p.649.4 | 8 | 5.2 | odd | 4 | |||
675.4.b.p.649.5 | 8 | 5.3 | odd | 4 | |||
675.4.b.q.649.4 | 8 | 15.8 | even | 4 | |||
675.4.b.q.649.5 | 8 | 15.2 | even | 4 |