Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(1,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("648.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.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: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.29952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.39417\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.80342 | −0.519074 | −0.259537 | − | 0.965733i | \(-0.583570\pi\) | ||||
−0.259537 | + | 0.965733i | \(0.583570\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.1228 | −1.41050 | −0.705249 | − | 0.708960i | \(-0.749165\pi\) | ||||
−0.705249 | + | 0.708960i | \(0.749165\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −37.2460 | −1.02092 | −0.510458 | − | 0.859903i | \(-0.670524\pi\) | ||||
−0.510458 | + | 0.859903i | \(0.670524\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.3373 | −0.647235 | −0.323618 | − | 0.946188i | \(-0.604899\pi\) | ||||
−0.323618 | + | 0.946188i | \(0.604899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −48.4744 | −0.691575 | −0.345787 | − | 0.938313i | \(-0.612388\pi\) | ||||
−0.345787 | + | 0.938313i | \(0.612388\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 88.1865 | 1.06481 | 0.532404 | − | 0.846490i | \(-0.321289\pi\) | ||||
0.532404 | + | 0.846490i | \(0.321289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 84.5259 | 0.766299 | 0.383149 | − | 0.923686i | \(-0.374839\pi\) | ||||
0.383149 | + | 0.923686i | \(0.374839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −91.3203 | −0.730562 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 176.724 | 1.13161 | 0.565806 | − | 0.824538i | \(-0.308565\pi\) | ||||
0.565806 | + | 0.824538i | \(0.308565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 155.384 | 0.900251 | 0.450126 | − | 0.892965i | \(-0.351379\pi\) | ||||
0.450126 | + | 0.892965i | \(0.351379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 151.601 | 0.732152 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −258.310 | −1.14773 | −0.573864 | − | 0.818951i | \(-0.694556\pi\) | ||||
−0.573864 | + | 0.818951i | \(0.694556\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 220.287 | 0.839098 | 0.419549 | − | 0.907733i | \(-0.362188\pi\) | ||||
0.419549 | + | 0.907733i | \(0.362188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −47.7615 | −0.169385 | −0.0846925 | − | 0.996407i | \(-0.526991\pi\) | ||||
−0.0846925 | + | 0.996407i | \(0.526991\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 129.499 | 0.401902 | 0.200951 | − | 0.979601i | \(-0.435597\pi\) | ||||
0.200951 | + | 0.979601i | \(0.435597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 339.399 | 0.989502 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 577.029 | 1.49549 | 0.747746 | − | 0.663985i | \(-0.231136\pi\) | ||||
0.747746 | + | 0.663985i | \(0.231136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 216.154 | 0.529931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −243.516 | −0.537339 | −0.268670 | − | 0.963232i | \(-0.586584\pi\) | ||||
−0.268670 | + | 0.963232i | \(0.586584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −687.632 | −1.44332 | −0.721658 | − | 0.692250i | \(-0.756619\pi\) | ||||
−0.721658 | + | 0.692250i | \(0.756619\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 176.060 | 0.335963 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 378.389 | 0.689964 | 0.344982 | − | 0.938609i | \(-0.387885\pi\) | ||||
0.344982 | + | 0.938609i | \(0.387885\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 332.826 | 0.556327 | 0.278163 | − | 0.960534i | \(-0.410274\pi\) | ||||
0.278163 | + | 0.960534i | \(0.410274\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1072.19 | 1.71904 | 0.859520 | − | 0.511103i | \(-0.170763\pi\) | ||||
0.859520 | + | 0.511103i | \(0.170763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 972.968 | 1.44000 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1260.21 | −1.79474 | −0.897370 | − | 0.441279i | \(-0.854525\pi\) | ||||
−0.897370 | + | 0.441279i | \(0.854525\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1226.09 | 1.62146 | 0.810731 | − | 0.585419i | \(-0.199070\pi\) | ||||
0.810731 | + | 0.585419i | \(0.199070\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 281.317 | 0.358978 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1095.81 | −1.30512 | −0.652559 | − | 0.757738i | \(-0.726305\pi\) | ||||
−0.652559 | + | 0.757738i | \(0.726305\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 792.495 | 0.912923 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −511.783 | −0.552714 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1128.60 | −1.18136 | −0.590681 | − | 0.806905i | \(-0.701141\pi\) | ||||
−0.590681 | + | 0.806905i | \(0.701141\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1235.65 | −1.21734 | −0.608670 | − | 0.793423i | \(-0.708297\pi\) | ||||
−0.608670 | + | 0.793423i | \(0.708297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1215.92 | 1.16319 | 0.581595 | − | 0.813479i | \(-0.302429\pi\) | ||||
0.581595 | + | 0.813479i | \(0.302429\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1779.08 | 1.60739 | 0.803694 | − | 0.595043i | \(-0.202865\pi\) | ||||
0.803694 | + | 0.595043i | \(0.202865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −974.934 | −0.856714 | −0.428357 | − | 0.903610i | \(-0.640907\pi\) | ||||
−0.428357 | + | 0.903610i | \(0.640907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1971.47 | 1.64124 | 0.820621 | − | 0.571473i | \(-0.193628\pi\) | ||||
0.820621 | + | 0.571473i | \(0.193628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −490.540 | −0.397766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1266.29 | 0.975464 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56.2621 | 0.0422705 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1255.40 | 0.898290 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −604.990 | −0.422710 | −0.211355 | − | 0.977409i | \(-0.567788\pi\) | ||||
−0.211355 | + | 0.977409i | \(0.567788\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1409.70 | 0.940197 | 0.470098 | − | 0.882614i | \(-0.344218\pi\) | ||||
0.470098 | + | 0.882614i | \(0.344218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2303.68 | −1.50191 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2263.55 | 1.41159 | 0.705795 | − | 0.708416i | \(-0.250590\pi\) | ||||
0.705795 | + | 0.708416i | \(0.250590\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1540.50 | 0.940027 | 0.470013 | − | 0.882659i | \(-0.344249\pi\) | ||||
0.470013 | + | 0.882659i | \(0.344249\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1129.94 | 0.660773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1025.60 | −0.587390 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 613.034 | 0.337058 | 0.168529 | − | 0.985697i | \(-0.446098\pi\) | ||||
0.168529 | + | 0.985697i | \(0.446098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2372.98 | 1.27888 | 0.639438 | − | 0.768843i | \(-0.279167\pi\) | ||||
0.639438 | + | 0.768843i | \(0.279167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −901.759 | −0.467297 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1768.06 | −0.898769 | −0.449385 | − | 0.893338i | \(-0.648357\pi\) | ||||
−0.449385 | + | 0.893338i | \(0.648357\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2208.05 | −1.08086 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2657.82 | 1.27715 | 0.638577 | − | 0.769558i | \(-0.279523\pi\) | ||||
0.638577 | + | 0.769558i | \(0.279523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3352.52 | −1.55345 | −0.776724 | − | 0.629842i | \(-0.783120\pi\) | ||||
−0.776724 | + | 0.629842i | \(0.783120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1276.65 | −0.581087 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.43589 | 0.00107050 | 0.000535251 | − | 1.00000i | \(-0.499830\pi\) | ||||
0.000535251 | 1.00000i | \(0.499830\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2385.54 | 1.03046 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1084.01 | 0.452642 | 0.226321 | − | 0.974053i | \(-0.427330\pi\) | ||||
0.226321 | + | 0.974053i | \(0.427330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 869.840 | 0.357208 | 0.178604 | − | 0.983921i | \(-0.442842\pi\) | ||||
0.178604 | + | 0.983921i | \(0.442842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1499.08 | 0.595756 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1805.48 | 0.706040 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −425.148 | −0.161061 | −0.0805304 | − | 0.996752i | \(-0.525661\pi\) | ||||
−0.0805304 | + | 0.996752i | \(0.525661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.70934 | −0.000637520 0 | −0.000318760 | − | 1.00000i | \(-0.500101\pi\) | ||||
−0.000318760 | 1.00000i | \(0.500101\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3079.44 | −1.11371 | −0.556855 | − | 0.830610i | \(-0.687992\pi\) | ||||
−0.556855 | + | 0.830610i | \(0.687992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3133.50 | 1.11622 | 0.558110 | − | 0.829767i | \(-0.311527\pi\) | ||||
0.558110 | + | 0.829767i | \(0.311527\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4616.51 | −1.59614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1278.42 | −0.435554 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3284.59 | −1.08708 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2787.75 | −0.909556 | −0.454778 | − | 0.890605i | \(-0.650281\pi\) | ||||
−0.454778 | + | 0.890605i | \(0.650281\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 277.180 | 0.0879233 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4059.06 | −1.26980 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1470.58 | 0.447611 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1146.60 | −0.344315 | −0.172157 | − | 0.985069i | \(-0.555074\pi\) | ||||
−0.172157 | + | 0.985069i | \(0.555074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −928.141 | −0.271378 | −0.135689 | − | 0.990751i | \(-0.543325\pi\) | ||||
−0.135689 | + | 0.990751i | \(0.543325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3517.76 | −1.01511 | −0.507554 | − | 0.861620i | \(-0.669450\pi\) | ||||
−0.507554 | + | 0.861620i | \(0.669450\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 976.524 | 0.274567 | 0.137284 | − | 0.990532i | \(-0.456163\pi\) | ||||
0.137284 | + | 0.990532i | \(0.456163\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −751.538 | −0.208617 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4540.97 | −1.22900 | −0.614500 | − | 0.788917i | \(-0.710642\pi\) | ||||
−0.614500 | + | 0.788917i | \(0.710642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7220.39 | 1.92990 | 0.964951 | − | 0.262432i | \(-0.0845244\pi\) | ||||
0.964951 | + | 0.262432i | \(0.0845244\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1969.68 | −0.513625 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2675.34 | −0.689182 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1285.44 | 0.323251 | 0.161626 | − | 0.986852i | \(-0.448326\pi\) | ||||
0.161626 | + | 0.986852i | \(0.448326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3148.25 | −0.782327 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2604.49 | 0.632155 | 0.316078 | − | 0.948733i | \(-0.397634\pi\) | ||||
0.316078 | + | 0.948733i | \(0.397634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6747.78 | 1.61887 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5353.68 | 1.25522 | 0.627609 | − | 0.778529i | \(-0.284034\pi\) | ||||
0.627609 | + | 0.778529i | \(0.284034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3348.75 | −0.776271 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7141.58 | −1.61870 | −0.809349 | − | 0.587328i | \(-0.800180\pi\) | ||||
−0.809349 | + | 0.587328i | \(0.800180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6334.52 | −1.41991 | −0.709953 | − | 0.704249i | \(-0.751284\pi\) | ||||
−0.709953 | + | 0.704249i | \(0.751284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3401.31 | 0.745843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7090.18 | 1.53793 | 0.768967 | − | 0.639289i | \(-0.220771\pi\) | ||||
0.768967 | + | 0.639289i | \(0.220771\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6741.01 | −1.43109 | −0.715543 | − | 0.698569i | \(-0.753821\pi\) | ||||
−0.715543 | + | 0.698569i | \(0.753821\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3559.66 | 0.747703 | 0.373852 | − | 0.927489i | \(-0.378037\pi\) | ||||
0.373852 | + | 0.927489i | \(0.378037\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5754.50 | −1.18354 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2563.23 | −0.521725 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2155.41 | 0.429763 | 0.214881 | − | 0.976640i | \(-0.431064\pi\) | ||||
0.214881 | + | 0.976640i | \(0.431064\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1413.22 | 0.278919 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2564.29 | −0.495975 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1247.66 | 0.238917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3990.62 | 0.749187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1552.85 | 0.288684 | 0.144342 | − | 0.989528i | \(-0.453893\pi\) | ||||
0.144342 | + | 0.989528i | \(0.453893\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8414.88 | −1.53429 | −0.767145 | − | 0.641474i | \(-0.778323\pi\) | ||||
−0.767145 | + | 0.641474i | \(0.778323\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5704.25 | −1.03011 | −0.515053 | − | 0.857158i | \(-0.672228\pi\) | ||||
−0.515053 | + | 0.857158i | \(0.672228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.363375 | 6.43823e−5 0 | 3.21911e−5 | − | 1.00000i | \(-0.499990\pi\) | ||||
3.21911e−5 | 1.00000i | \(0.499990\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6582.24 | −1.15528 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4274.79 | −0.736395 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2770.41 | 0.472846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3382.87 | −0.566881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8934.34 | 1.48361 | 0.741806 | − | 0.670615i | \(-0.233970\pi\) | ||||
0.741806 | + | 0.670615i | \(0.233970\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2195.95 | −0.358143 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9524.10 | −1.53950 | −0.769749 | − | 0.638347i | \(-0.779618\pi\) | ||||
−0.769749 | + | 0.638347i | \(0.779618\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5787.43 | −0.919081 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 94.0633 | 0.0148074 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8808.10 | −1.36266 | −0.681331 | − | 0.731976i | \(-0.738599\pi\) | ||||
−0.681331 | + | 0.731976i | \(0.738599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2311.23 | 0.354491 | 0.177246 | − | 0.984167i | \(-0.443281\pi\) | ||||
0.177246 | + | 0.984167i | \(0.443281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 165.608 | 0.0249701 | 0.0124850 | − | 0.999922i | \(-0.496026\pi\) | ||||
0.0124850 | + | 0.999922i | \(0.496026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1931.53 | −0.288775 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7007.10 | 1.03014 | 0.515071 | − | 0.857148i | \(-0.327766\pi\) | ||||
0.515071 | + | 0.857148i | \(0.327766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 917.854 | 0.133817 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6222.35 | −0.892309 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2915.52 | 0.414683 | 0.207342 | − | 0.978269i | \(-0.433519\pi\) | ||||
0.207342 | + | 0.978269i | \(0.433519\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15073.6 | −2.10939 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4087.11 | 0.567353 | 0.283676 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283676 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5361.32 | −0.732419 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5785.10 | 0.784065 | 0.392032 | − | 0.919951i | \(-0.371772\pi\) | ||||
0.392032 | + | 0.919951i | \(0.371772\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12970.9 | 1.73050 | 0.865252 | − | 0.501337i | \(-0.167158\pi\) | ||||
0.865252 | + | 0.501337i | \(0.167158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5646.54 | −0.747466 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4556.16 | 0.593847 | 0.296923 | − | 0.954901i | \(-0.404039\pi\) | ||||
0.296923 | + | 0.954901i | \(0.404039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4097.34 | −0.529953 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7313.52 | 0.931603 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3193.40 | 0.403709 | 0.201854 | − | 0.979416i | \(-0.435303\pi\) | ||||
0.201854 | + | 0.979416i | \(0.435303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15032.0 | −1.87197 | −0.935986 | − | 0.352038i | \(-0.885489\pi\) | ||||
−0.935986 | + | 0.352038i | \(0.885489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4713.93 | −0.582674 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9621.01 | 1.17173 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −633.869 | −0.0766328 | −0.0383164 | − | 0.999266i | \(-0.512199\pi\) | ||||
−0.0383164 | + | 0.999266i | \(0.512199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6361.30 | 0.757916 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7115.54 | −0.841658 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13989.9 | 1.63115 | 0.815574 | − | 0.578653i | \(-0.196422\pi\) | ||||
0.815574 | + | 0.578653i | \(0.196422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8853.43 | 1.02492 | 0.512458 | − | 0.858712i | \(-0.328735\pi\) | ||||
0.512458 | + | 0.858712i | \(0.328735\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4426.70 | 0.505238 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17962.8 | 2.03579 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16509.1 | −1.84504 | −0.922522 | − | 0.385945i | \(-0.873875\pi\) | ||||
−0.922522 | + | 0.385945i | \(0.873875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2218.19 | 0.246188 | 0.123094 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123094 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7454.04 | 0.815961 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1445.82 | −0.157187 | −0.0785936 | − | 0.996907i | \(-0.525043\pi\) | ||||
−0.0785936 | + | 0.996907i | \(0.525043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −985.625 | −0.105708 | −0.0528538 | − | 0.998602i | \(-0.516832\pi\) | ||||
−0.0528538 | + | 0.998602i | \(0.516832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6359.44 | 0.677453 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6682.65 | 0.702391 | 0.351196 | − | 0.936302i | \(-0.385775\pi\) | ||||
0.351196 | + | 0.936302i | \(0.385775\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8204.79 | −0.856649 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4599.18 | −0.473875 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4765.44 | 0.487785 | 0.243893 | − | 0.969802i | \(-0.421576\pi\) | ||||
0.243893 | + | 0.969802i | \(0.421576\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9834.66 | 0.993592 | 0.496796 | − | 0.867867i | \(-0.334510\pi\) | ||||
0.496796 | + | 0.867867i | \(0.334510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5580.51 | −0.560147 | −0.280074 | − | 0.959978i | \(-0.590359\pi\) | ||||
−0.280074 | + | 0.959978i | \(0.590359\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4459.02 | 0.441839 | 0.220920 | − | 0.975292i | \(-0.429094\pi\) | ||||
0.220920 | + | 0.975292i | \(0.429094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9884.58 | −0.973193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1778.92 | 0.172928 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8053.21 | −0.777909 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10269.3 | 0.979571 | 0.489785 | − | 0.871843i | \(-0.337075\pi\) | ||||
0.489785 | + | 0.871843i | \(0.337075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7836.44 | 0.742850 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6549.75 | 0.613214 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −904.158 | −0.0841300 | −0.0420650 | − | 0.999115i | \(-0.513394\pi\) | ||||
−0.0420650 | + | 0.999115i | \(0.513394\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20527.1 | 1.88671 | 0.943354 | − | 0.331789i | \(-0.107652\pi\) | ||||
0.943354 | + | 0.331789i | \(0.107652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8566.57 | −0.782594 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8694.34 | −0.784697 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4174.28 | −0.374482 | −0.187241 | − | 0.982314i | \(-0.559955\pi\) | ||||
−0.187241 | + | 0.982314i | \(0.559955\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4835.95 | 0.428676 | 0.214338 | − | 0.976760i | \(-0.431241\pi\) | ||||
0.214338 | + | 0.976760i | \(0.431241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7170.97 | 0.631889 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5204.54 | 0.453216 | 0.226608 | − | 0.973986i | \(-0.427236\pi\) | ||||
0.226608 | + | 0.973986i | \(0.427236\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28008.5 | −2.42470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7056.52 | −0.603781 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4823.32 | −0.410308 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12174.0 | 1.02371 | 0.511856 | − | 0.859071i | \(-0.328958\pi\) | ||||
0.511856 | + | 0.859071i | \(0.328958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11583.5 | 0.968470 | 0.484235 | − | 0.874938i | \(-0.339098\pi\) | ||||
0.484235 | + | 0.874938i | \(0.339098\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7532.14 | −0.622591 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5022.37 | −0.412786 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6682.91 | −0.543094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10324.8 | −0.834353 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12641.3 | −1.01020 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18249.3 | 1.45027 | 0.725137 | − | 0.688605i | \(-0.241777\pi\) | ||||
0.725137 | + | 0.688605i | \(0.241777\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5657.96 | 0.444698 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9610.00 | −0.751177 | −0.375588 | − | 0.926787i | \(-0.622559\pi\) | ||||
−0.375588 | + | 0.926787i | \(0.622559\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15584.6 | 1.20495 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32920.1 | 2.53148 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20247.0 | 1.54020 | 0.770101 | − | 0.637923i | \(-0.220206\pi\) | ||||
0.770101 | + | 0.637923i | \(0.220206\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1448.95 | 0.109632 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18344.2 | 1.37321 | 0.686603 | − | 0.727033i | \(-0.259101\pi\) | ||||
0.686603 | + | 0.727033i | \(0.259101\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11441.3 | −0.851926 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23668.6 | 1.74383 | 0.871914 | − | 0.489658i | \(-0.162878\pi\) | ||||
0.871914 | + | 0.489658i | \(0.162878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8851.13 | 0.648701 | 0.324351 | − | 0.945937i | \(-0.394854\pi\) | ||||
0.324351 | + | 0.945937i | \(0.394854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7718.93 | −0.559829 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16832.2 | 1.21444 | 0.607221 | − | 0.794533i | \(-0.292284\pi\) | ||||
0.607221 | + | 0.794533i | \(0.292284\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32029.0 | −2.28707 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21492.0 | −1.52677 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23298.5 | −1.63822 | −0.819109 | − | 0.573638i | \(-0.805532\pi\) | ||||
−0.819109 | + | 0.573638i | \(0.805532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13702.8 | 0.958595 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8720.33 | −0.603881 | −0.301940 | − | 0.953327i | \(-0.597634\pi\) | ||||
−0.301940 | + | 0.953327i | \(0.597634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7348.79 | −0.506338 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 366.400 | 0.0249928 | 0.0124964 | − | 0.999922i | \(-0.496022\pi\) | ||||
0.0124964 | + | 0.999922i | \(0.496022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5886.95 | 0.399557 | 0.199779 | − | 0.979841i | \(-0.435978\pi\) | ||||
0.199779 | + | 0.979841i | \(0.435978\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −326.513 | −0.0219415 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18187.1 | −1.21613 | −0.608067 | − | 0.793886i | \(-0.708055\pi\) | ||||
−0.608067 | + | 0.793886i | \(0.708055\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3928.65 | −0.260125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1998.47 | 0.131676 | 0.0658379 | − | 0.997830i | \(-0.479028\pi\) | ||||
0.0658379 | + | 0.997830i | \(0.479028\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15800.3 | 1.03095 | 0.515474 | − | 0.856905i | \(-0.327616\pi\) | ||||
0.515474 | + | 0.856905i | \(0.327616\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9766.86 | 0.634189 | 0.317095 | − | 0.948394i | \(-0.397293\pi\) | ||||
0.317095 | + | 0.948394i | \(0.397293\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28625.6 | 1.84087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4129.43 | 0.264283 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12521.4 | 0.793739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9966.80 | −0.628799 | −0.314399 | − | 0.949291i | \(-0.601803\pi\) | ||||
−0.314399 | + | 0.949291i | \(0.601803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3511.01 | 0.219418 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10296.5 | −0.640440 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12710.5 | 0.783206 | 0.391603 | − | 0.920134i | \(-0.371921\pi\) | ||||
0.391603 | + | 0.920134i | \(0.371921\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12811.4 | 0.785742 | 0.392871 | − | 0.919594i | \(-0.371482\pi\) | ||||
0.392871 | + | 0.919594i | \(0.371482\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3729.11 | 0.226594 | 0.113297 | − | 0.993561i | \(-0.463859\pi\) | ||||
0.113297 | + | 0.993561i | \(0.463859\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9069.97 | 0.548579 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3306.70 | −0.198164 | −0.0990820 | − | 0.995079i | \(-0.531591\pi\) | ||||
−0.0990820 | + | 0.995079i | \(0.531591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8181.07 | −0.488032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17957.0 | −1.06146 | −0.530732 | − | 0.847539i | \(-0.678083\pi\) | ||||
−0.530732 | + | 0.847539i | \(0.678083\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9695.14 | 0.570495 | 0.285247 | − | 0.958454i | \(-0.407924\pi\) | ||||
0.285247 | + | 0.958454i | \(0.407924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13369.2 | 0.779602 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14937.7 | 0.867153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25611.5 | 1.47350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21587.2 | 1.23644 | 0.618222 | − | 0.786003i | \(-0.287853\pi\) | ||||
0.618222 | + | 0.786003i | \(0.287853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20672.4 | 1.17356 | 0.586782 | − | 0.809745i | \(-0.300394\pi\) | ||||
0.586782 | + | 0.809745i | \(0.300394\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29482.2 | 1.66631 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24403.9 | 1.36719 | 0.683594 | − | 0.729862i | \(-0.260416\pi\) | ||||
0.683594 | + | 0.729862i | \(0.260416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13136.3 | −0.732719 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17505.5 | −0.967935 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5858.07 | −0.322506 | −0.161253 | − | 0.986913i | \(-0.551553\pi\) | ||||
−0.161253 | + | 0.986913i | \(0.551553\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8940.19 | −0.487943 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10678.3 | −0.580299 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10530.8 | 0.567393 | 0.283697 | − | 0.958914i | \(-0.408439\pi\) | ||||
0.283697 | + | 0.958914i | \(0.408439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22779.5 | −1.22211 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32278.5 | 1.71705 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3776.78 | −0.200057 | −0.100028 | − | 0.994985i | \(-0.531893\pi\) | ||||
−0.100028 | + | 0.994985i | \(0.531893\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13134.0 | 0.689861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6557.53 | −0.342990 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7109.15 | 0.368743 | 0.184372 | − | 0.982857i | \(-0.440975\pi\) | ||||
0.184372 | + | 0.982857i | \(0.440975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31763.3 | −1.64068 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16138.4 | −0.826713 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3660.36 | 0.186733 | 0.0933667 | − | 0.995632i | \(-0.470237\pi\) | ||||
0.0933667 | + | 0.995632i | \(0.470237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2315.21 | 0.117142 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36559.4 | −1.84223 | −0.921113 | − | 0.389296i | \(-0.872718\pi\) | ||||
−0.921113 | + | 0.389296i | \(0.872718\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14093.5 | −0.704396 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15735.7 | 0.783285 | 0.391642 | − | 0.920118i | \(-0.371907\pi\) | ||||
0.391642 | + | 0.920118i | \(0.371907\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23694.3 | −1.16993 | −0.584966 | − | 0.811058i | \(-0.698892\pi\) | ||||
−0.584966 | + | 0.811058i | \(0.698892\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3557.69 | −0.174958 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46474.6 | −2.26722 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17287.0 | −0.839962 | −0.419981 | − | 0.907533i | \(-0.637963\pi\) | ||||
−0.419981 | + | 0.907533i | \(0.637963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13771.4 | −0.663831 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18565.8 | 0.891394 | 0.445697 | − | 0.895184i | \(-0.352956\pi\) | ||||
0.445697 | + | 0.895184i | \(0.352956\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5937.47 | −0.282829 | −0.141415 | − | 0.989950i | \(-0.545165\pi\) | ||||
−0.141415 | + | 0.989950i | \(0.545165\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25468.0 | 1.20839 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7387.61 | 0.347785 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2489.54 | 0.116743 | 0.0583713 | − | 0.998295i | \(-0.481409\pi\) | ||||
0.0583713 | + | 0.998295i | \(0.481409\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16109.8 | −0.749584 | −0.374792 | − | 0.927109i | \(-0.622286\pi\) | ||||
−0.374792 | + | 0.927109i | \(0.622286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14189.7 | −0.657690 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19426.3 | 0.893479 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12396.4 | −0.567963 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10260.8 | 0.466528 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15810.0 | 0.716095 | 0.358047 | − | 0.933703i | \(-0.383443\pi\) | ||||
0.358047 | + | 0.933703i | \(0.383443\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −51500.2 | −2.31497 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20860.9 | 0.934164 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4185.16 | −0.186005 | −0.0930024 | − | 0.995666i | \(-0.529646\pi\) | ||||
−0.0930024 | + | 0.995666i | \(0.529646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6277.39 | −0.277945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39934.6 | −1.75500 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12814.3 | 0.561047 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35154.2 | −1.52776 | −0.763878 | − | 0.645360i | \(-0.776707\pi\) | ||||
−0.763878 | + | 0.645360i | \(0.776707\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3028.93 | −0.131147 | −0.0655734 | − | 0.997848i | \(-0.520888\pi\) | ||||
−0.0655734 | + | 0.997848i | \(0.520888\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15424.4 | −0.662938 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4211.91 | −0.180363 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4797.98 | −0.203959 | −0.101980 | − | 0.994786i | \(-0.532518\pi\) | ||||
−0.101980 | + | 0.994786i | \(0.532518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40058.7 | −1.69667 | −0.848335 | − | 0.529460i | \(-0.822394\pi\) | ||||
−0.848335 | + | 0.529460i | \(0.822394\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22168.6 | 0.932139 | 0.466069 | − | 0.884748i | \(-0.345670\pi\) | ||||
0.466069 | + | 0.884748i | \(0.345670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13091.9 | 0.548494 | 0.274247 | − | 0.961659i | \(-0.411571\pi\) | ||||
0.274247 | + | 0.961659i | \(0.411571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16452.2 | −0.684314 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19456.1 | 0.806354 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34790.3 | 1.43158 | 0.715790 | − | 0.698316i | \(-0.246067\pi\) | ||||
0.715790 | + | 0.698316i | \(0.246067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6842.23 | 0.280546 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7408.93 | 0.301627 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1469.72 | −0.0596225 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21833.9 | −0.879502 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47980.7 | 1.92594 | 0.962971 | − | 0.269604i | \(-0.0868928\pi\) | ||||
0.962971 | + | 0.269604i | \(0.0868928\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32015.4 | −1.27611 | −0.638055 | − | 0.769991i | \(-0.720261\pi\) | ||||
−0.638055 | + | 0.769991i | \(0.720261\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32513.5 | −1.29144 | −0.645719 | − | 0.763575i | \(-0.723442\pi\) | ||||
−0.645719 | + | 0.763575i | \(0.723442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25867.1 | −1.02031 | −0.510154 | − | 0.860083i | \(-0.670411\pi\) | ||||
−0.510154 | + | 0.860083i | \(0.670411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1365 | −0.000555670 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46937.7 | 1.83228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11479.3 | −0.446569 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32794.5 | −1.26704 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −574.703 | −0.0221281 | −0.0110641 | − | 0.999939i | \(-0.503522\pi\) | ||||
−0.0110641 | + | 0.999939i | \(0.503522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28334.1 | 1.08354 | 0.541771 | − | 0.840526i | \(-0.317754\pi\) | ||||
0.541771 | + | 0.840526i | \(0.317754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13424.9 | 0.511646 | 0.255823 | − | 0.966724i | \(-0.417654\pi\) | ||||
0.255823 | + | 0.966724i | \(0.417654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43763.1 | −1.65662 | −0.828310 | − | 0.560271i | \(-0.810697\pi\) | ||||
−0.828310 | + | 0.560271i | \(0.810697\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15804.0 | 0.596232 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11420.1 | 0.427948 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6290.99 | −0.234955 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27460.0 | 1.01874 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27971.2 | −1.03424 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5048.05 | −0.185417 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42797.1 | 1.56677 | 0.783383 | − | 0.621540i | \(-0.213493\pi\) | ||||
0.783383 | + | 0.621540i | \(0.213493\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2007.15 | 0.0729964 | 0.0364982 | − | 0.999334i | \(-0.488380\pi\) | ||||
0.0364982 | + | 0.999334i | \(0.488380\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45667.1 | −1.65538 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36825.2 | −1.32614 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43558.3 | −1.56350 | −0.781750 | − | 0.623592i | \(-0.785673\pi\) | ||||
−0.781750 | + | 0.623592i | \(0.785673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10097.0 | −0.360074 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23589.0 | 0.838487 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31508.1 | −1.11275 | −0.556376 | − | 0.830931i | \(-0.687808\pi\) | ||||
−0.556376 | + | 0.830931i | \(0.687808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29930.4 | 1.05363 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10477.9 | −0.366487 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20675.3 | −0.720846 | −0.360423 | − | 0.932789i | \(-0.617368\pi\) | ||||
−0.360423 | + | 0.932789i | \(0.617368\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1425.54 | −0.0493849 | −0.0246925 | − | 0.999695i | \(-0.507861\pi\) | ||||
−0.0246925 | + | 0.999695i | \(0.507861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18619.9 | 0.643000 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35661.7 | 1.22371 | 0.611853 | − | 0.790971i | \(-0.290424\pi\) | ||||
0.611853 | + | 0.790971i | \(0.290424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32527.2 | −1.11262 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10384.9 | 0.352991 | 0.176496 | − | 0.984301i | \(-0.443524\pi\) | ||||
0.176496 | + | 0.984301i | \(0.443524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2467.31 | 0.0836024 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −59130.1 | −1.99104 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5646.82 | −0.189548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.92005 | 0.000330920 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8443.39 | −0.280787 | −0.140394 | − | 0.990096i | \(-0.544837\pi\) | ||||
−0.140394 | + | 0.990096i | \(0.544837\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6938.43 | −0.229315 | −0.114657 | − | 0.993405i | \(-0.536577\pi\) | ||||
−0.114657 | + | 0.993405i | \(0.536577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40242.2 | −1.32590 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38777.5 | 1.26981 | 0.634903 | − | 0.772591i | \(-0.281040\pi\) | ||||
0.634903 | + | 0.772591i | \(0.281040\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40814.5 | 1.33242 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7592.55 | −0.246353 | −0.123176 | − | 0.992385i | \(-0.539308\pi\) | ||||
−0.123176 | + | 0.992385i | \(0.539308\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17871.3 | 0.578098 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4037.08 | −0.129799 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.96741 | 0.000191282 0 | 9.56412e−5 | − | 1.00000i | \(-0.499970\pi\) | ||||
9.56412e−5 | 1.00000i | \(0.499970\pi\) | ||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18185.0 | −0.579401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34771.7 | 1.10454 | 0.552272 | − | 0.833664i | \(-0.313761\pi\) | ||||
0.552272 | + | 0.833664i | \(0.313761\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 648.4.a.j.1.2 | yes | 4 | |
3.2 | odd | 2 | 648.4.a.g.1.3 | ✓ | 4 | ||
4.3 | odd | 2 | 1296.4.a.bb.1.2 | 4 | |||
9.2 | odd | 6 | 648.4.i.v.433.2 | 8 | |||
9.4 | even | 3 | 648.4.i.u.217.3 | 8 | |||
9.5 | odd | 6 | 648.4.i.v.217.2 | 8 | |||
9.7 | even | 3 | 648.4.i.u.433.3 | 8 | |||
12.11 | even | 2 | 1296.4.a.x.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.g.1.3 | ✓ | 4 | 3.2 | odd | 2 | ||
648.4.a.j.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
648.4.i.u.217.3 | 8 | 9.4 | even | 3 | |||
648.4.i.u.433.3 | 8 | 9.7 | even | 3 | |||
648.4.i.v.217.2 | 8 | 9.5 | odd | 6 | |||
648.4.i.v.433.2 | 8 | 9.2 | odd | 6 | |||
1296.4.a.x.1.3 | 4 | 12.11 | even | 2 | |||
1296.4.a.bb.1.2 | 4 | 4.3 | odd | 2 |