Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,4,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(72.6903531271\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 144x^{5} + 354x^{4} + 5172x^{3} - 6504x^{2} - 34432x + 18816 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 616) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.517294\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-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 | ||||||||
\(3\) | −0.517294 | −0.0995533 | −0.0497767 | − | 0.998760i | \(-0.515851\pi\) | ||||
−0.0497767 | + | 0.998760i | \(0.515851\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.39668 | −0.661580 | −0.330790 | − | 0.943704i | \(-0.607315\pi\) | ||||
−0.330790 | + | 0.943704i | \(0.607315\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.7324 | −0.990089 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −78.8766 | −1.68280 | −0.841401 | − | 0.540411i | \(-0.818269\pi\) | ||||
−0.841401 | + | 0.540411i | \(0.818269\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.82626 | 0.0658624 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 57.7886 | 0.824459 | 0.412229 | − | 0.911080i | \(-0.364750\pi\) | ||||
0.412229 | + | 0.911080i | \(0.364750\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −106.951 | −1.29138 | −0.645692 | − | 0.763598i | \(-0.723431\pi\) | ||||
−0.645692 | + | 0.763598i | \(0.723431\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.62106 | 0.0376276 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.8823 | 0.107723 | 0.0538614 | − | 0.998548i | \(-0.482847\pi\) | ||||
0.0538614 | + | 0.998548i | \(0.482847\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −70.2891 | −0.562313 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.7955 | 0.198120 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 139.466 | 0.893041 | 0.446521 | − | 0.894773i | \(-0.352663\pi\) | ||||
0.446521 | + | 0.894773i | \(0.352663\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −297.397 | −1.72303 | −0.861517 | − | 0.507728i | \(-0.830485\pi\) | ||||
−0.861517 | + | 0.507728i | \(0.830485\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.69024 | 0.0300165 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 51.7768 | 0.250054 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −136.832 | −0.607972 | −0.303986 | − | 0.952676i | \(-0.598318\pi\) | ||||
−0.303986 | + | 0.952676i | \(0.598318\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 40.8024 | 0.167529 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 126.644 | 0.482401 | 0.241200 | − | 0.970475i | \(-0.422459\pi\) | ||||
0.241200 | + | 0.970475i | \(0.422459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −265.571 | −0.941841 | −0.470920 | − | 0.882176i | \(-0.656078\pi\) | ||||
−0.470920 | + | 0.882176i | \(0.656078\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 197.731 | 0.655023 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 587.057 | 1.82194 | 0.910969 | − | 0.412474i | \(-0.135335\pi\) | ||||
0.910969 | + | 0.412474i | \(0.135335\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −29.8937 | −0.0820776 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 154.322 | 0.399959 | 0.199979 | − | 0.979800i | \(-0.435913\pi\) | ||||
0.199979 | + | 0.979800i | \(0.435913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 81.3635 | 0.199474 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 55.3253 | 0.128562 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −199.082 | −0.439292 | −0.219646 | − | 0.975580i | \(-0.570490\pi\) | ||||
−0.219646 | + | 0.975580i | \(0.570490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 385.652 | 0.809471 | 0.404736 | − | 0.914434i | \(-0.367364\pi\) | ||||
0.404736 | + | 0.914434i | \(0.367364\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 187.127 | 0.374219 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 583.425 | 1.11331 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −772.165 | −1.40799 | −0.703993 | − | 0.710207i | \(-0.748601\pi\) | ||||
−0.703993 | + | 0.710207i | \(0.748601\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.14663 | −0.0107242 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −163.931 | −0.274015 | −0.137008 | − | 0.990570i | \(-0.543748\pi\) | ||||
−0.137008 | + | 0.990570i | \(0.543748\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 426.710 | 0.684146 | 0.342073 | − | 0.939673i | \(-0.388871\pi\) | ||||
0.342073 | + | 0.939673i | \(0.388871\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 36.3601 | 0.0559801 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −886.257 | −1.26217 | −0.631087 | − | 0.775712i | \(-0.717391\pi\) | ||||
−0.631087 | + | 0.775712i | \(0.717391\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 707.397 | 0.970366 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 89.9744 | 0.118988 | 0.0594938 | − | 0.998229i | \(-0.481051\pi\) | ||||
0.0594938 | + | 0.998229i | \(0.481051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −427.444 | −0.545445 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −72.1450 | −0.0889052 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1391.62 | 1.65743 | 0.828717 | − | 0.559667i | \(-0.189071\pi\) | ||||
0.828717 | + | 0.559667i | \(0.189071\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 552.136 | 0.636040 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 153.842 | 0.171534 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 791.085 | 0.854354 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1418.66 | −1.48498 | −0.742489 | − | 0.669858i | \(-0.766355\pi\) | ||||
−0.742489 | + | 0.669858i | \(0.766355\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 294.056 | 0.298523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −614.172 | −0.605073 | −0.302537 | − | 0.953138i | \(-0.597833\pi\) | ||||
−0.302537 | + | 0.953138i | \(0.597833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 650.855 | 0.622627 | 0.311314 | − | 0.950307i | \(-0.399231\pi\) | ||||
0.311314 | + | 0.950307i | \(0.399231\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −26.7838 | −0.0248937 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −417.533 | −0.377237 | −0.188619 | − | 0.982050i | \(-0.560401\pi\) | ||||
−0.188619 | + | 0.982050i | \(0.560401\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1260.90 | 1.10801 | 0.554003 | − | 0.832515i | \(-0.313100\pi\) | ||||
0.554003 | + | 0.832515i | \(0.313100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 70.7821 | 0.0605256 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −484.972 | −0.403737 | −0.201869 | − | 0.979413i | \(-0.564701\pi\) | ||||
−0.201869 | + | 0.979413i | \(0.564701\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −87.8895 | −0.0712673 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2108.56 | 1.66612 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −404.520 | −0.311616 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −65.5121 | −0.0480246 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1444.49 | 1.03359 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −469.263 | −0.327877 | −0.163939 | − | 0.986471i | \(-0.552420\pi\) | ||||
−0.163939 | + | 0.986471i | \(0.552420\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 137.378 | 0.0937634 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1005.42 | −0.670563 | −0.335282 | − | 0.942118i | \(-0.608831\pi\) | ||||
−0.335282 | + | 0.942118i | \(0.608831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 748.659 | 0.488098 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −205.594 | −0.131072 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 486.764 | 0.303555 | 0.151778 | − | 0.988415i | \(-0.451500\pi\) | ||||
0.151778 | + | 0.988415i | \(0.451500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 540.533 | 0.329837 | 0.164919 | − | 0.986307i | \(-0.447264\pi\) | ||||
0.164919 | + | 0.986307i | \(0.447264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −303.681 | −0.181380 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 867.643 | 0.507384 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1031.59 | −0.590818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −25.3474 | −0.0142219 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2083.81 | 1.14572 | 0.572860 | − | 0.819654i | \(-0.305834\pi\) | ||||
0.572860 | + | 0.819654i | \(0.305834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1831.37 | 0.986983 | 0.493492 | − | 0.869750i | \(-0.335720\pi\) | ||||
0.493492 | + | 0.869750i | \(0.335720\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1544.83 | −0.816288 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2199.75 | 1.13992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −228.649 | −0.116231 | −0.0581153 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581153 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −79.8301 | −0.0398172 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −83.1760 | −0.0407154 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2382.99 | 1.14509 | 0.572546 | − | 0.819872i | \(-0.305956\pi\) | ||||
0.572546 | + | 0.819872i | \(0.305956\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −42.0889 | −0.0198583 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2700.28 | −1.25122 | −0.625610 | − | 0.780136i | \(-0.715150\pi\) | ||||
−0.625610 | + | 0.780136i | \(0.715150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4024.52 | 1.83183 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2859.07 | 1.27859 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2567.05 | 1.12815 | 0.564073 | − | 0.825725i | \(-0.309234\pi\) | ||||
0.564073 | + | 0.825725i | \(0.309234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 492.023 | 0.212534 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 102.984 | 0.0437330 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1810.02 | −0.755793 | −0.377897 | − | 0.925848i | \(-0.623353\pi\) | ||||
−0.377897 | + | 0.925848i | \(0.623353\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1046.75 | −0.429859 | −0.214929 | − | 0.976630i | \(-0.568952\pi\) | ||||
−0.214929 | + | 0.976630i | \(0.568952\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −199.496 | −0.0805855 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1012.10 | 0.402222 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −635.675 | −0.248584 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −194.568 | −0.0748823 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1387.86 | −0.525771 | −0.262886 | − | 0.964827i | \(-0.584674\pi\) | ||||
−0.262886 | + | 0.964827i | \(0.584674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −518.006 | −0.193196 | −0.0965981 | − | 0.995323i | \(-0.530796\pi\) | ||||
−0.0965981 | + | 0.995323i | \(0.530796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −301.803 | −0.110833 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1633.42 | −0.590742 | −0.295371 | − | 0.955383i | \(-0.595443\pi\) | ||||
−0.295371 | + | 0.955383i | \(0.595443\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2959.23 | 1.05414 | 0.527071 | − | 0.849821i | \(-0.323290\pi\) | ||||
0.527071 | + | 0.849821i | \(0.323290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 399.437 | 0.140170 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −976.263 | −0.337538 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −936.744 | −0.319147 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −317.642 | −0.106655 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1176.46 | 0.389367 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 622.680 | 0.203161 | 0.101581 | − | 0.994827i | \(-0.467610\pi\) | ||||
0.101581 | + | 0.994827i | \(0.467610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 84.8007 | 0.0272791 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1964.34 | 0.623103 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2081.78 | 0.651246 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −220.735 | −0.0681090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4558.17 | −1.38740 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3635.58 | 1.09173 | 0.545866 | − | 0.837872i | \(-0.316201\pi\) | ||||
0.545866 | + | 0.837872i | \(0.316201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1879.00 | 0.556740 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2986.85 | −0.873322 | −0.436661 | − | 0.899626i | \(-0.643839\pi\) | ||||
−0.436661 | + | 0.899626i | \(0.643839\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −268.330 | −0.0774312 | −0.0387156 | − | 0.999250i | \(-0.512327\pi\) | ||||
−0.0387156 | + | 0.999250i | \(0.512327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −39.8316 | −0.0113452 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3608.12 | 1.01449 | 0.507244 | − | 0.861803i | \(-0.330664\pi\) | ||||
0.507244 | + | 0.861803i | \(0.330664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4342.28 | −1.20536 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 458.455 | 0.125654 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 89.9305 | 0.0243394 | 0.0121697 | − | 0.999926i | \(-0.496126\pi\) | ||||
0.0121697 | + | 0.999926i | \(0.496126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5090.89 | −1.36072 | −0.680359 | − | 0.732879i | \(-0.738176\pi\) | ||||
−0.680359 | + | 0.732879i | \(0.738176\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1116.41 | −0.294723 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −362.438 | −0.0945114 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8435.96 | 2.17315 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −46.5432 | −0.0118456 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5539.36 | 1.39299 | 0.696496 | − | 0.717561i | \(-0.254741\pi\) | ||||
0.696496 | + | 0.717561i | \(0.254741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −130.705 | −0.0324797 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 221.114 | 0.0543009 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4669.77 | −1.13343 | −0.566716 | − | 0.823913i | \(-0.691786\pi\) | ||||
−0.566716 | + | 0.823913i | \(0.691786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 957.821 | 0.229792 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3728.26 | −0.884191 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3691.28 | 0.865453 | 0.432726 | − | 0.901525i | \(-0.357552\pi\) | ||||
0.432726 | + | 0.901525i | \(0.357552\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1141.47 | −0.264604 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −719.878 | −0.165003 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −850.050 | −0.192671 | −0.0963354 | − | 0.995349i | \(-0.530712\pi\) | ||||
−0.0963354 | + | 0.995349i | \(0.530712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7458.57 | 1.67187 | 0.835933 | − | 0.548831i | \(-0.184927\pi\) | ||||
0.835933 | + | 0.548831i | \(0.184927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −285.617 | −0.0633199 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 773.180 | 0.169544 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5368.97 | −1.16458 | −0.582292 | − | 0.812980i | \(-0.697844\pi\) | ||||
−0.582292 | + | 0.812980i | \(0.697844\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7950.14 | 1.70596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6478.43 | 1.37534 | 0.687670 | − | 0.726023i | \(-0.258633\pi\) | ||||
0.687670 | + | 0.726023i | \(0.258633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3841.89 | −0.806985 | −0.403493 | − | 0.914983i | \(-0.632204\pi\) | ||||
−0.403493 | + | 0.914983i | \(0.632204\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −409.224 | −0.0850537 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −886.507 | −0.182330 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1573.47 | −0.320267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 733.863 | 0.147834 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2179.76 | 0.434618 | 0.217309 | − | 0.976103i | \(-0.430272\pi\) | ||||
0.217309 | + | 0.976103i | \(0.430272\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1472.54 | 0.290627 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −305.750 | −0.0597354 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −937.234 | −0.181276 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1859.00 | 0.355982 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 317.708 | 0.0602370 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2852.55 | −0.535529 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7685.42 | 1.42876 | 0.714382 | − | 0.699756i | \(-0.246708\pi\) | ||||
0.714382 | + | 0.699756i | \(0.246708\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −336.683 | −0.0619846 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2699.99 | 0.492291 | 0.246146 | − | 0.969233i | \(-0.420836\pi\) | ||||
0.246146 | + | 0.969233i | \(0.420836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3484.31 | 0.629217 | 0.314609 | − | 0.949222i | \(-0.398127\pi\) | ||||
0.314609 | + | 0.949222i | \(0.398127\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1384.12 | −0.247575 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.35952 | −0.00130395 | −0.000651975 | − | 1.00000i | \(-0.500208\pi\) | ||||
−0.000651975 | 1.00000i | \(0.500208\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1534.13 | −0.269262 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 215.987 | 0.0375552 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6180.57 | −1.06469 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5544.16 | 0.946261 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −652.258 | −0.110306 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4109.40 | −0.688628 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8152.84 | −1.35384 | −0.676919 | − | 0.736058i | \(-0.736685\pi\) | ||||
−0.676919 | + | 0.736058i | \(0.736685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3657.84 | 0.601947 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5711.46 | 0.931494 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −669.429 | −0.108208 | −0.0541041 | − | 0.998535i | \(-0.517230\pi\) | ||||
−0.0541041 | + | 0.998535i | \(0.517230\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 250.873 | 0.0401934 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3271.37 | 0.519515 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 45.4647 | 0.00709489 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5364.50 | −0.829917 | −0.414959 | − | 0.909840i | \(-0.636204\pi\) | ||||
−0.414959 | + | 0.909840i | \(0.636204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1520.78 | −0.233254 | −0.116627 | − | 0.993176i | \(-0.537208\pi\) | ||||
−0.116627 | + | 0.993176i | \(0.537208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2192.41 | −0.333397 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9736.69 | −1.46808 | −0.734040 | − | 0.679107i | \(-0.762367\pi\) | ||||
−0.734040 | + | 0.679107i | \(0.762367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1212.55 | 0.181283 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 209.256 | 0.0310224 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5802.44 | −0.853040 | −0.426520 | − | 0.904478i | \(-0.640261\pi\) | ||||
−0.426520 | + | 0.904478i | \(0.640261\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4579.58 | 0.667675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −62.5926 | −0.00905030 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3156.24 | −0.452617 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2947.86 | −0.419283 | −0.209641 | − | 0.977778i | \(-0.567230\pi\) | ||||
−0.209641 | + | 0.977778i | \(0.567230\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3385.49 | −0.477620 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1080.26 | −0.151170 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11014.4 | 1.52896 | 0.764480 | − | 0.644647i | \(-0.222996\pi\) | ||||
0.764480 | + | 0.644647i | \(0.222996\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −747.227 | −0.102898 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11000.6 | −1.50281 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9879.25 | −1.33895 | −0.669476 | − | 0.742833i | \(-0.733481\pi\) | ||||
−0.669476 | + | 0.742833i | \(0.733481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 242.747 | 0.0326412 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4246.20 | −0.566503 | −0.283251 | − | 0.959046i | \(-0.591413\pi\) | ||||
−0.283251 | + | 0.959046i | \(0.591413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −569.545 | −0.0753940 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7099.34 | 0.932506 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13848.9 | −1.80505 | −0.902525 | − | 0.430637i | \(-0.858289\pi\) | ||||
−0.902525 | + | 0.430637i | \(0.858289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 686.661 | 0.0888131 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 520.097 | 0.0667568 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6555.36 | 0.835028 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7536.27 | 0.952731 | 0.476366 | − | 0.879247i | \(-0.341954\pi\) | ||||
0.476366 | + | 0.879247i | \(0.341954\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −387.277 | −0.0485917 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15424.3 | 1.92083 | 0.960413 | − | 0.278582i | \(-0.0898643\pi\) | ||||
0.960413 | + | 0.278582i | \(0.0898643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23457.7 | 2.89953 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5232.39 | −0.641974 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1505.15 | 0.183310 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 259.112 | 0.0313259 | 0.0156629 | − | 0.999877i | \(-0.495014\pi\) | ||||
0.0156629 | + | 0.999877i | \(0.495014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −251.800 | −0.0302199 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1393.57 | 0.166037 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −665.512 | −0.0787198 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −279.614 | −0.0328364 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10193.3 | −1.18848 | −0.594241 | − | 0.804287i | \(-0.702548\pi\) | ||||
−0.594241 | + | 0.804287i | \(0.702548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14180.9 | −1.64166 | −0.820828 | − | 0.571176i | \(-0.806488\pi\) | ||||
−0.820828 | + | 0.571176i | \(0.806488\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15693.5 | −1.80388 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4061.91 | −0.463604 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2699.57 | −0.305951 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −448.827 | −0.0505118 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15237.2 | 1.70290 | 0.851448 | − | 0.524439i | \(-0.175725\pi\) | ||||
0.851448 | + | 0.524439i | \(0.175725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17620.3 | 1.95561 | 0.977805 | − | 0.209518i | \(-0.0671893\pi\) | ||||
0.977805 | + | 0.209518i | \(0.0671893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 533.634 | 0.0588179 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1270.83 | −0.139112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7168.92 | 0.779394 | 0.389697 | − | 0.920943i | \(-0.372580\pi\) | ||||
0.389697 | + | 0.920943i | \(0.372580\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1309.89 | −0.141441 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10441.2 | −1.11981 | −0.559904 | − | 0.828558i | \(-0.689162\pi\) | ||||
−0.559904 | + | 0.828558i | \(0.689162\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10293.4 | −1.09652 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1077.94 | −0.114060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5927.94 | 0.623066 | 0.311533 | − | 0.950235i | \(-0.399158\pi\) | ||||
0.311533 | + | 0.950235i | \(0.399158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1393.08 | −0.145449 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −947.355 | −0.0982575 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4083.98 | −0.420791 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15408.6 | −1.57721 | −0.788604 | − | 0.614901i | \(-0.789196\pi\) | ||||
−0.788604 | + | 0.614901i | \(0.789196\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1606.26 | 0.163342 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3831.23 | −0.387068 | −0.193534 | − | 0.981094i | \(-0.561995\pi\) | ||||
−0.193534 | + | 0.981094i | \(0.561995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3890.07 | −0.390468 | −0.195234 | − | 0.980757i | \(-0.562547\pi\) | ||||
−0.195234 | + | 0.980757i | \(0.562547\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1137.92 | −0.113483 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2931.13 | −0.290443 | −0.145221 | − | 0.989399i | \(-0.546389\pi\) | ||||
−0.145221 | + | 0.989399i | \(0.546389\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5405.16 | 0.532168 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 118.279 | 0.0115711 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2921.28 | 0.283976 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7517.51 | 0.726162 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4125.41 | −0.395995 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3133.99 | −0.298947 | −0.149473 | − | 0.988766i | \(-0.547758\pi\) | ||||
−0.149473 | + | 0.988766i | \(0.547758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10792.8 | 1.02310 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 43.0264 | 0.00405335 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10493.4 | 0.982431 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12714.8 | −1.18309 | −0.591544 | − | 0.806272i | \(-0.701482\pi\) | ||||
−0.591544 | + | 0.806272i | \(0.701482\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1232.71 | −0.113998 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1714.36 | −0.157572 | −0.0787862 | − | 0.996892i | \(-0.525104\pi\) | ||||
−0.0787862 | + | 0.996892i | \(0.525104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8059.55 | 0.736276 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2175.04 | −0.197497 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1147.52 | 0.103568 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20481.3 | −1.83741 | −0.918706 | − | 0.394942i | \(-0.870765\pi\) | ||||
−0.918706 | + | 0.394942i | \(0.870765\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1396.84 | 0.124563 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2345.46 | −0.207911 | −0.103955 | − | 0.994582i | \(-0.533150\pi\) | ||||
−0.103955 | + | 0.994582i | \(0.533150\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4542.84 | 0.400304 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2081.86 | −0.182364 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18843.5 | 1.64091 | 0.820457 | − | 0.571708i | \(-0.193719\pi\) | ||||
0.820457 | + | 0.571708i | \(0.193719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2986.97 | −0.258583 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2972.76 | −0.255849 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4814.17 | −0.411917 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6457.63 | −0.549335 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1327.92 | −0.112311 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9379.26 | 0.788700 | 0.394350 | − | 0.918960i | \(-0.370970\pi\) | ||||
0.394350 | + | 0.918960i | \(0.370970\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5745.10 | −0.480336 | −0.240168 | − | 0.970731i | \(-0.577203\pi\) | ||||
−0.240168 | + | 0.970731i | \(0.577203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −254.521 | −0.0211585 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17186.2 | −1.42057 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12025.8 | −0.988396 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5321.93 | 0.434938 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9989.23 | −0.811786 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3088.36 | 0.249573 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 936.311 | 0.0752417 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13581.0 | −1.07929 | −0.539644 | − | 0.841893i | \(-0.681441\pi\) | ||||
−0.539644 | + | 0.841893i | \(0.681441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 541.478 | 0.0427938 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9326.50 | −0.733034 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21441.9 | −1.67603 | −0.838017 | − | 0.545645i | \(-0.816285\pi\) | ||||
−0.838017 | + | 0.545645i | \(0.816285\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10309.4 | −0.801449 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14916.1 | −1.15326 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6203.80 | 0.477057 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −523.553 | −0.0400425 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7104.61 | 0.540452 | 0.270226 | − | 0.962797i | \(-0.412902\pi\) | ||||
0.270226 | + | 0.962797i | \(0.412902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20947.3 | 1.58493 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 328.831 | 0.0247473 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2015.82 | 0.150900 | 0.0754501 | − | 0.997150i | \(-0.475961\pi\) | ||||
0.0754501 | + | 0.997150i | \(0.475961\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3587.18 | 0.267104 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4951.78 | −0.366764 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24979.6 | −1.84042 | −0.920212 | − | 0.391421i | \(-0.871984\pi\) | ||||
−0.920212 | + | 0.391421i | \(0.871984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17670.1 | −1.29505 | −0.647523 | − | 0.762046i | \(-0.724195\pi\) | ||||
−0.647523 | + | 0.762046i | \(0.724195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 717.934 | 0.0523423 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −835.194 | −0.0605739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7744.82 | −0.558789 | −0.279394 | − | 0.960176i | \(-0.590134\pi\) | ||||
−0.279394 | + | 0.960176i | \(0.590134\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 267.961 | 0.0192333 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −629.821 | −0.0449731 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1697.55 | −0.120592 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15596.4 | −1.10227 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6418.51 | −0.451312 | −0.225656 | − | 0.974207i | \(-0.572453\pi\) | ||||
−0.225656 | + | 0.974207i | \(0.572453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31807.0 | 2.22510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 844.957 | 0.0588103 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1577.72 | 0.109257 | 0.0546285 | − | 0.998507i | \(-0.482603\pi\) | ||||
0.0546285 | + | 0.998507i | \(0.482603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2992.11 | 0.206159 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1530.79 | −0.104943 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18754.0 | −1.27925 | −0.639623 | − | 0.768688i | \(-0.720910\pi\) | ||||
−0.639623 | + | 0.768688i | \(0.720910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18851.7 | −1.27949 | −0.639747 | − | 0.768586i | \(-0.720961\pi\) | ||||
−0.639747 | + | 0.768586i | \(0.720961\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20641.8 | 1.39403 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −894.999 | −0.0601436 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1628.13 | 0.108869 | 0.0544347 | − | 0.998517i | \(-0.482664\pi\) | ||||
0.0544347 | + | 0.998517i | \(0.482664\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 505.015 | 0.0336030 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46305.1 | −3.06596 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29472.2 | −1.94188 | −0.970939 | − | 0.239327i | \(-0.923073\pi\) | ||||
−0.970939 | + | 0.239327i | \(0.923073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 484.572 | 0.0317721 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26335.9 | 1.71839 | 0.859194 | − | 0.511650i | \(-0.170966\pi\) | ||||
0.859194 | + | 0.511650i | \(0.170966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6196.40 | 0.402349 | 0.201175 | − | 0.979555i | \(-0.435524\pi\) | ||||
0.201175 | + | 0.979555i | \(0.435524\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 330.273 | 0.0213421 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9741.36 | −0.626451 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1898.31 | −0.121492 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −608.578 | −0.0387628 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7907.31 | −0.501248 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2060.70 | 0.130008 | 0.0650042 | − | 0.997885i | \(-0.479294\pi\) | ||||
0.0650042 | + | 0.997885i | \(0.479294\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −322.109 | −0.0202254 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3470.99 | 0.216917 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3864.95 | −0.240400 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4382.28 | 0.271299 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30191.4 | 1.86036 | 0.930178 | − | 0.367108i | \(-0.119652\pi\) | ||||
0.930178 | + | 0.367108i | \(0.119652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4434.88 | 0.271998 | 0.135999 | − | 0.990709i | \(-0.456576\pi\) | ||||
0.135999 | + | 0.990709i | \(0.456576\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1016.14 | −0.0620319 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28348.5 | 1.72256 | 0.861279 | − | 0.508133i | \(-0.169664\pi\) | ||||
0.861279 | + | 0.508133i | \(0.169664\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2189.90 | 0.132452 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1076.89 | −0.0648337 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27303.9 | 1.63627 | 0.818134 | − | 0.575028i | \(-0.195009\pi\) | ||||
0.818134 | + | 0.575028i | \(0.195009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7436.76 | 0.443631 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11407.0 | −0.677366 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10101.6 | −0.597123 | −0.298562 | − | 0.954390i | \(-0.596507\pi\) | ||||
−0.298562 | + | 0.954390i | \(0.596507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6035.78 | 0.355166 | 0.177583 | − | 0.984106i | \(-0.443172\pi\) | ||||
0.177583 | + | 0.984106i | \(0.443172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2357.92 | 0.138120 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5537.60 | −0.322915 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1657.17 | 0.0962010 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1880.66 | −0.108686 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4242.18 | −0.244065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29125.1 | 1.66819 | 0.834094 | − | 0.551622i | \(-0.185991\pi\) | ||||
0.834094 | + | 0.551622i | \(0.185991\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1953.72 | −0.111405 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23472.4 | 1.33252 | 0.666260 | − | 0.745720i | \(-0.267894\pi\) | ||||
0.666260 | + | 0.745720i | \(0.267894\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9930.60 | 0.561269 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1545.08 | 0.0869421 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13568.7 | −0.760162 | −0.380081 | − | 0.924953i | \(-0.624104\pi\) | ||||
−0.380081 | + | 0.924953i | \(0.624104\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3600.44 | −0.200826 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 138.806 | 0.00770853 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12172.4 | −0.673052 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3113.95 | 0.171433 | 0.0857166 | − | 0.996320i | \(-0.472682\pi\) | ||||
0.0857166 | + | 0.996320i | \(0.472682\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2058.40 | −0.112831 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3998.15 | −0.218214 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7318.57 | 0.397720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1866.46 | −0.100996 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29130.5 | 1.56953 | 0.784766 | − | 0.619792i | \(-0.212783\pi\) | ||||
0.784766 | + | 0.619792i | \(0.212783\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14634.3 | 0.785126 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2246.24 | 0.119997 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4299.20 | 0.228696 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17391.2 | −0.921213 | −0.460606 | − | 0.887605i | \(-0.652368\pi\) | ||||
−0.460606 | + | 0.887605i | \(0.652368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23691.8 | 1.24966 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3533.75 | −0.185610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6417.68 | −0.335675 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.5205 | −0.00242307 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13940.8 | 0.723095 | 0.361548 | − | 0.932354i | \(-0.382249\pi\) | ||||
0.361548 | + | 0.932354i | \(0.382249\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4555.98 | −0.235331 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2633.49 | 0.135464 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9802.94 | −0.502168 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34506.6 | 1.76035 | 0.880177 | − | 0.474645i | \(-0.157424\pi\) | ||||
0.880177 | + | 0.474645i | \(0.157424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18522.2 | −0.941025 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15347.0 | −0.776509 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20926.4 | −1.05448 | −0.527240 | − | 0.849717i | \(-0.676773\pi\) | ||||
−0.527240 | + | 0.849717i | \(0.676773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 187.487 | 0.00940892 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8493.82 | 0.424524 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16313.8 | −0.812061 | −0.406030 | − | 0.913860i | \(-0.633087\pi\) | ||||
−0.406030 | + | 0.913860i | \(0.633087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4363.87 | −0.216344 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11806.0 | 0.582933 | 0.291466 | − | 0.956581i | \(-0.405857\pi\) | ||||
0.291466 | + | 0.956581i | \(0.405857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15413.3 | −0.757984 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2405.23 | −0.117808 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2922.73 | 0.142582 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21437.1 | −1.04161 | −0.520806 | − | 0.853675i | \(-0.674368\pi\) | ||||
−0.520806 | + | 0.853675i | \(0.674368\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2865.48 | −0.138677 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13546.0 | −0.652968 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16573.8 | 0.795753 | 0.397876 | − | 0.917439i | \(-0.369747\pi\) | ||||
0.397876 | + | 0.917439i | \(0.369747\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 67.6130 | 0.00323346 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19353.4 | −0.921892 | −0.460946 | − | 0.887428i | \(-0.652490\pi\) | ||||
−0.460946 | + | 0.887428i | \(0.652490\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8826.32 | −0.418787 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11426.6 | 0.540039 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15702.9 | 0.739242 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17968.4 | −0.842595 | −0.421298 | − | 0.906922i | \(-0.638425\pi\) | ||||
−0.421298 | + | 0.906922i | \(0.638425\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2415.64 | 0.112837 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23031.6 | −1.07166 | −0.535828 | − | 0.844327i | \(-0.680000\pi\) | ||||
−0.535828 | + | 0.844327i | \(0.680000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20903.8 | 0.968884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −495.475 | −0.0228765 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13544.7 | −0.622965 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1803.25 | 0.0826187 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3876.52 | 0.176929 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1691.25 | 0.0768957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10354.5 | −0.468992 | −0.234496 | − | 0.972117i | \(-0.575344\pi\) | ||||
−0.234496 | + | 0.972117i | \(0.575344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1909.48 | −0.0861587 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3394.80 | 0.152598 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30419.0 | −1.36218 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 590.478 | 0.0263422 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27274.5 | −1.21219 | −0.606093 | − | 0.795394i | \(-0.707264\pi\) | ||||
−0.606093 | + | 0.795394i | \(0.707264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33925.2 | 1.50211 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37201.4 | −1.64101 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4693.81 | −0.206278 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 615.226 | 0.0269365 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 439.726 | 0.0191810 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30138.1 | 1.30976 | 0.654881 | − | 0.755732i | \(-0.272719\pi\) | ||||
0.654881 | + | 0.755732i | \(0.272719\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1563.55 | 0.0676989 | 0.0338494 | − | 0.999427i | \(-0.489223\pi\) | ||||
0.0338494 | + | 0.999427i | \(0.489223\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3858.27 | −0.166440 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17626.2 | −0.757570 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28403.1 | 1.21628 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14759.9 | −0.629736 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3178.02 | 0.135096 | 0.0675478 | − | 0.997716i | \(-0.478482\pi\) | ||||
0.0675478 | + | 0.997716i | \(0.478482\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18229.6 | −0.772105 | −0.386053 | − | 0.922477i | \(-0.626162\pi\) | ||||
−0.386053 | + | 0.922477i | \(0.626162\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −399.961 | −0.0168786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3016.88 | −0.126853 | −0.0634263 | − | 0.997987i | \(-0.520203\pi\) | ||||
−0.0634263 | + | 0.997987i | \(0.520203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22135.9 | 0.927397 | 0.463699 | − | 0.885993i | \(-0.346522\pi\) | ||||
0.463699 | + | 0.885993i | \(0.346522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2777.33 | 0.115938 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2831.64 | 0.117780 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19973.1 | 0.827781 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8266.29 | −0.341368 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42000.8 | 1.72828 | 0.864140 | − | 0.503251i | \(-0.167863\pi\) | ||||
0.864140 | + | 0.503251i | \(0.167863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4938.21 | −0.202477 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3351.25 | −0.136920 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29768.1 | −1.21190 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −847.000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1987.39 | 0.0803381 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1625.87 | −0.0654925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6205.24 | −0.249078 | −0.124539 | − | 0.992215i | \(-0.539745\pi\) | ||||
−0.124539 | + | 0.992215i | \(0.539745\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21147.6 | −0.845886 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8749.81 | −0.348761 | −0.174380 | − | 0.984678i | \(-0.555792\pi\) | ||||
−0.174380 | + | 0.984678i | \(0.555792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37194.1 | −1.47735 | −0.738677 | − | 0.674059i | \(-0.764549\pi\) | ||||
−0.738677 | + | 0.674059i | \(0.764549\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 458.585 | 0.0181516 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17442.3 | 0.687997 | 0.343999 | − | 0.938970i | \(-0.388218\pi\) | ||||
0.343999 | + | 0.938970i | \(0.388218\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18987.7 | −0.746358 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 813.949 | 0.0318837 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9748.82 | 0.380560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60905.8 | 2.36936 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37924.1 | 1.47026 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10111.4 | −0.390662 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35990.5 | 1.38576 | 0.692882 | − | 0.721051i | \(-0.256341\pi\) | ||||
0.692882 | + | 0.721051i | \(0.256341\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1127.58 | −0.0432677 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5116.00 | −0.195644 | −0.0978220 | − | 0.995204i | \(-0.531188\pi\) | ||||
−0.0978220 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3155.66 | 0.120268 | 0.0601340 | − | 0.998190i | \(-0.480847\pi\) | ||||
0.0601340 | + | 0.998190i | \(0.480847\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −761.739 | −0.0289328 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30997.1 | 1.17337 | 0.586687 | − | 0.809814i | \(-0.300432\pi\) | ||||
0.586687 | + | 0.809814i | \(0.300432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3284.84 | 0.123926 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7781.36 | −0.292576 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −62786.6 | −2.35282 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13388.1 | 0.500017 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 484.826 | 0.0180467 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41476.8 | −1.53874 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8918.08 | 0.329749 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −961.647 | −0.0354392 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7742.49 | 0.284386 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26954.0 | 0.986760 | 0.493380 | − | 0.869814i | \(-0.335761\pi\) | ||||
0.493380 | + | 0.869814i | \(0.335761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16418.3 | 0.599076 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35664.9 | 1.29707 | 0.648536 | − | 0.761184i | \(-0.275382\pi\) | ||||
0.648536 | + | 0.761184i | \(0.275382\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −989.718 | −0.0358761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1475.61 | 0.0533137 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7037.93 | 0.253449 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17489.2 | 0.627764 | 0.313882 | − | 0.949462i | \(-0.398370\pi\) | ||||
0.313882 | + | 0.949462i | \(0.398370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3975.62 | −0.142238 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12930.4 | 0.461113 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9617.76 | 0.341870 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17398.9 | −0.616456 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50623.1 | 1.78783 | 0.893913 | − | 0.448240i | \(-0.147949\pi\) | ||||
0.893913 | + | 0.448240i | \(0.147949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5240.61 | −0.184484 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1396.69 | −0.0490092 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4701.89 | 0.164458 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33135.9 | −1.15529 | −0.577643 | − | 0.816290i | \(-0.696027\pi\) | ||||
−0.577643 | + | 0.816290i | \(0.696027\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1802.41 | −0.0626406 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18090.3 | 0.626701 | 0.313351 | − | 0.949638i | \(-0.398548\pi\) | ||||
0.313351 | + | 0.949638i | \(0.398548\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1504.82 | 0.0519656 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1439.16 | 0.0495406 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37534.9 | 1.28798 | 0.643991 | − | 0.765033i | \(-0.277277\pi\) | ||||
0.643991 | + | 0.765033i | \(0.277277\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33657.5 | −1.15128 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.80704 | 0.000129812 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5610.39 | 0.190701 | 0.0953507 | − | 0.995444i | \(-0.469603\pi\) | ||||
0.0953507 | + | 0.995444i | \(0.469603\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10265.6 | 0.347840 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 793.595 | 0.0268059 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3407.35 | −0.114733 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58654.0 | 1.96885 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11161.7 | 0.373499 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3831.52 | 0.127815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43421.0 | 1.44398 | 0.721989 | − | 0.691905i | \(-0.243228\pi\) | ||||
0.721989 | + | 0.691905i | \(0.243228\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3197.17 | 0.105994 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34695.7 | 1.14669 | 0.573346 | − | 0.819313i | \(-0.305645\pi\) | ||||
0.573346 | + | 0.819313i | \(0.305645\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3783.73 | −0.124667 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2867.96 | −0.0942034 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41221.1 | −1.34983 | −0.674914 | − | 0.737897i | \(-0.735819\pi\) | ||||
−0.674914 | + | 0.737897i | \(0.735819\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15307.8 | −0.499735 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33707.0 | −1.09702 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29994.9 | −0.973232 | −0.486616 | − | 0.873616i | \(-0.661769\pi\) | ||||
−0.486616 | + | 0.873616i | \(0.661769\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12081.9 | 0.390823 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2125.77 | 0.0685552 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3155.59 | −0.101458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32670.1 | −1.04722 | −0.523612 | − | 0.851957i | \(-0.675416\pi\) | ||||
−0.523612 | + | 0.851957i | \(0.675416\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4217.41 | 0.134779 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21888.5 | −0.697399 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10699.6 | −0.339879 | −0.169939 | − | 0.985454i | \(-0.554357\pi\) | ||||
−0.169939 | + | 0.985454i | \(0.554357\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3803.30 | −0.120451 |
(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 | 1232.4.a.bc.1.4 | 7 | ||
4.3 | odd | 2 | 616.4.a.k.1.4 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.4.a.k.1.4 | ✓ | 7 | 4.3 | odd | 2 | ||
1232.4.a.bc.1.4 | 7 | 1.1 | even | 1 | trivial |