Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 80x^{3} + 121x^{2} + 1212x + 1044 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.04116\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | 2.04116 | 0.392821 | 0.196410 | − | 0.980522i | \(-0.437072\pi\) | ||||
0.196410 | + | 0.980522i | \(0.437072\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −21.6113 | −1.16690 | −0.583450 | − | 0.812149i | \(-0.698298\pi\) | ||||
−0.583450 | + | 0.812149i | \(0.698298\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −22.8337 | −0.845692 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 30.3495 | 0.831884 | 0.415942 | − | 0.909391i | \(-0.363452\pi\) | ||||
0.415942 | + | 0.909391i | \(0.363452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 69.6786 | 1.48657 | 0.743284 | − | 0.668976i | \(-0.233267\pi\) | ||||
0.743284 | + | 0.668976i | \(0.233267\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.2058 | −0.175675 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −43.4506 | −0.619901 | −0.309950 | − | 0.950753i | \(-0.600312\pi\) | ||||
−0.309950 | + | 0.950753i | \(0.600312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.3892 | −0.173742 | −0.0868710 | − | 0.996220i | \(-0.527687\pi\) | ||||
−0.0868710 | + | 0.996220i | \(0.527687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −44.1120 | −0.458382 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −101.718 | −0.725026 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −158.105 | −1.01239 | −0.506195 | − | 0.862419i | \(-0.668948\pi\) | ||||
−0.506195 | + | 0.862419i | \(0.668948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.4782 | 0.269282 | 0.134641 | − | 0.990894i | \(-0.457012\pi\) | ||||
0.134641 | + | 0.990894i | \(0.457012\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 61.9480 | 0.326781 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 108.056 | 0.521853 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 39.6849 | 0.176328 | 0.0881642 | − | 0.996106i | \(-0.471900\pi\) | ||||
0.0881642 | + | 0.996106i | \(0.471900\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 142.225 | 0.583954 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −201.771 | −0.768571 | −0.384285 | − | 0.923214i | \(-0.625552\pi\) | ||||
−0.384285 | + | 0.923214i | \(0.625552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17.8927 | −0.0634562 | −0.0317281 | − | 0.999497i | \(-0.510101\pi\) | ||||
−0.0317281 | + | 0.999497i | \(0.510101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 114.168 | 0.378205 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.702668 | 0.00218074 | 0.00109037 | − | 0.999999i | \(-0.499653\pi\) | ||||
0.00109037 | + | 0.999999i | \(0.499653\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 124.048 | 0.361655 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −88.6894 | −0.243510 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −661.161 | −1.71354 | −0.856769 | − | 0.515701i | \(-0.827532\pi\) | ||||
−0.856769 | + | 0.515701i | \(0.827532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −151.748 | −0.372030 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −29.3705 | −0.0682495 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 732.679 | 1.61672 | 0.808361 | − | 0.588686i | \(-0.200355\pi\) | ||||
0.808361 | + | 0.588686i | \(0.200355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −875.997 | −1.83869 | −0.919344 | − | 0.393454i | \(-0.871280\pi\) | ||||
−0.919344 | + | 0.393454i | \(0.871280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 493.465 | 0.986838 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −348.393 | −0.664813 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −746.803 | −1.36174 | −0.680870 | − | 0.732404i | \(-0.738398\pi\) | ||||
−0.680870 | + | 0.732404i | \(0.738398\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 46.9466 | 0.0819087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 275.246 | 0.460079 | 0.230040 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230040 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −499.633 | −0.801063 | −0.400532 | − | 0.916283i | \(-0.631175\pi\) | ||||
−0.400532 | + | 0.916283i | \(0.631175\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 51.0289 | 0.0785641 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −655.892 | −0.970725 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 797.970 | 1.13644 | 0.568219 | − | 0.822877i | \(-0.307633\pi\) | ||||
0.568219 | + | 0.822877i | \(0.307633\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 408.887 | 0.560887 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1150.10 | 1.52097 | 0.760483 | − | 0.649358i | \(-0.224962\pi\) | ||||
0.760483 | + | 0.649358i | \(0.224962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 217.253 | 0.277228 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −322.716 | −0.397687 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1166.89 | 1.38978 | 0.694890 | − | 0.719116i | \(-0.255453\pi\) | ||||
0.694890 | + | 0.719116i | \(0.255453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1505.85 | −1.73468 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 94.8693 | 0.105779 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 71.9458 | 0.0776998 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 403.209 | 0.422058 | 0.211029 | − | 0.977480i | \(-0.432318\pi\) | ||||
0.211029 | + | 0.977480i | \(0.432318\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −692.991 | −0.703517 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 484.319 | 0.477144 | 0.238572 | − | 0.971125i | \(-0.423321\pi\) | ||||
0.238572 | + | 0.971125i | \(0.423321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2064.69 | 1.97514 | 0.987572 | − | 0.157167i | \(-0.0502361\pi\) | ||||
0.987572 | + | 0.157167i | \(0.0502361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 220.560 | 0.204995 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1436.43 | 1.29780 | 0.648902 | − | 0.760872i | \(-0.275228\pi\) | ||||
0.648902 | + | 0.760872i | \(0.275228\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1870.62 | 1.64379 | 0.821895 | − | 0.569639i | \(-0.192917\pi\) | ||||
0.821895 | + | 0.569639i | \(0.192917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 81.0030 | 0.0692654 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1606.67 | 1.33755 | 0.668775 | − | 0.743465i | \(-0.266819\pi\) | ||||
0.668775 | + | 0.743465i | \(0.266819\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1591.02 | −1.25718 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 939.023 | 0.723362 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −409.908 | −0.307970 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −411.847 | −0.301910 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2031.66 | 1.41953 | 0.709766 | − | 0.704438i | \(-0.248801\pi\) | ||||
0.709766 | + | 0.704438i | \(0.248801\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −36.5219 | −0.0249269 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 434.691 | 0.289917 | 0.144958 | − | 0.989438i | \(-0.453695\pi\) | ||||
0.144958 | + | 0.989438i | \(0.453695\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 310.968 | 0.202740 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 508.591 | 0.324241 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 939.729 | 0.586033 | 0.293016 | − | 0.956107i | \(-0.405341\pi\) | ||||
0.293016 | + | 0.956107i | \(0.405341\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 124.609 | 0.0760376 | 0.0380188 | − | 0.999277i | \(-0.487895\pi\) | ||||
0.0380188 | + | 0.999277i | \(0.487895\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.43426 | 0.000856639 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2114.71 | 1.23665 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 790.523 | 0.452754 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 253.201 | 0.142066 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1375.14 | 0.756079 | 0.378039 | − | 0.925789i | \(-0.376598\pi\) | ||||
0.378039 | + | 0.925789i | \(0.376598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1196.51 | 0.644838 | 0.322419 | − | 0.946597i | \(-0.395504\pi\) | ||||
0.322419 | + | 0.946597i | \(0.395504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 992.137 | 0.524245 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −232.391 | −0.120426 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −212.340 | −0.107940 | −0.0539699 | − | 0.998543i | \(-0.517188\pi\) | ||||
−0.0539699 | + | 0.998543i | \(0.517188\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1349.53 | −0.673113 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −497.060 | −0.243315 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1390.16 | −0.668013 | −0.334006 | − | 0.942571i | \(-0.608401\pi\) | ||||
−0.334006 | + | 0.942571i | \(0.608401\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −309.740 | −0.146141 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −362.349 | −0.167901 | −0.0839503 | − | 0.996470i | \(-0.526754\pi\) | ||||
−0.0839503 | + | 0.996470i | \(0.526754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2658.11 | 1.20988 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 328.557 | 0.146932 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 986.596 | 0.433581 | 0.216790 | − | 0.976218i | \(-0.430441\pi\) | ||||
0.216790 | + | 0.976218i | \(0.430441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −540.282 | −0.233380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1495.51 | 0.635082 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3977.44 | −1.66083 | −0.830413 | − | 0.557149i | \(-0.811895\pi\) | ||||
−0.830413 | + | 0.557149i | \(0.811895\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2512.70 | 1.03186 | 0.515932 | − | 0.856630i | \(-0.327446\pi\) | ||||
0.515932 | + | 0.856630i | \(0.327446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1788.05 | −0.722275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −198.424 | −0.0788565 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1318.70 | −0.515685 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2198.26 | 0.846032 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1977.49 | −0.749142 | −0.374571 | − | 0.927198i | \(-0.622210\pi\) | ||||
−0.374571 | + | 0.927198i | \(0.622210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1241.30 | −0.462957 | −0.231478 | − | 0.972840i | \(-0.574356\pi\) | ||||
−0.231478 | + | 0.972840i | \(0.574356\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −711.125 | −0.261152 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1969.91 | 0.712436 | 0.356218 | − | 0.934403i | \(-0.384066\pi\) | ||||
0.356218 | + | 0.934403i | \(0.384066\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4053.09 | 1.44380 | 0.721899 | − | 0.691998i | \(-0.243269\pi\) | ||||
0.721899 | + | 0.691998i | \(0.243269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1524.34 | −0.534919 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3416.85 | 1.18136 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1008.86 | 0.343715 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −525.175 | −0.176339 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −436.704 | −0.144533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −374.110 | −0.122061 | −0.0610303 | − | 0.998136i | \(-0.519439\pi\) | ||||
−0.0610303 | + | 0.998136i | \(0.519439\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 561.819 | 0.180729 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 89.4637 | 0.0283785 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1004.45 | −0.314225 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1019.83 | −0.314674 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3027.58 | −0.921524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3226.90 | −0.969010 | −0.484505 | − | 0.874788i | \(-0.661000\pi\) | ||||
−0.484505 | + | 0.874788i | \(0.661000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −570.842 | −0.169138 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3020.61 | −0.883194 | −0.441597 | − | 0.897213i | \(-0.645588\pi\) | ||||
−0.441597 | + | 0.897213i | \(0.645588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 934.761 | 0.269741 | 0.134871 | − | 0.990863i | \(-0.456938\pi\) | ||||
0.134871 | + | 0.990863i | \(0.456938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1338.78 | −0.381321 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3916.88 | −1.10130 | −0.550651 | − | 0.834736i | \(-0.685620\pi\) | ||||
−0.550651 | + | 0.834736i | \(0.685620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.51334 | −0.000975256 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1628.78 | 0.446416 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3200.06 | −0.866086 | −0.433043 | − | 0.901373i | \(-0.642560\pi\) | ||||
−0.433043 | + | 0.901373i | \(0.642560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3774.24 | −1.00880 | −0.504399 | − | 0.863471i | \(-0.668286\pi\) | ||||
−0.504399 | + | 0.863471i | \(0.668286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3581.00 | 0.945354 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −620.238 | −0.161737 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1002.62 | −0.258279 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2347.54 | 0.597467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3342.01 | −0.840420 | −0.420210 | − | 0.907427i | \(-0.638044\pi\) | ||||
−0.420210 | + | 0.907427i | \(0.638044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 698.039 | 0.173460 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 443.447 | 0.108901 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2899.20 | −0.703685 | −0.351842 | − | 0.936059i | \(-0.614445\pi\) | ||||
−0.351842 | + | 0.936059i | \(0.614445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −857.641 | −0.205758 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3610.11 | 0.856170 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6001.83 | 1.40718 | 0.703591 | − | 0.710605i | \(-0.251579\pi\) | ||||
0.703591 | + | 0.710605i | \(0.251579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3305.81 | 0.766317 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2381.81 | 0.545934 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8308.29 | 1.88314 | 0.941571 | − | 0.336813i | \(-0.109349\pi\) | ||||
0.941571 | + | 0.336813i | \(0.109349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2395.28 | 0.536911 | 0.268456 | − | 0.963292i | \(-0.413487\pi\) | ||||
0.268456 | + | 0.963292i | \(0.413487\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3073.66 | −0.681416 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 758.738 | 0.166377 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7466.49 | 1.61956 | 0.809780 | − | 0.586733i | \(-0.199586\pi\) | ||||
0.809780 | + | 0.586733i | \(0.199586\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1061.27 | −0.227729 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5570.87 | −1.18267 | −0.591335 | − | 0.806426i | \(-0.701399\pi\) | ||||
−0.591335 | + | 0.806426i | \(0.701399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5273.48 | 1.10769 | 0.553845 | − | 0.832620i | \(-0.313160\pi\) | ||||
0.553845 | + | 0.832620i | \(0.313160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 146.853 | 0.0305221 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4360.54 | 0.896845 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3025.05 | −0.615723 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 823.012 | 0.165793 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −511.514 | −0.101990 | −0.0509948 | − | 0.998699i | \(-0.516239\pi\) | ||||
−0.0509948 | + | 0.998699i | \(0.516239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3663.39 | −0.723020 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3087.10 | −0.603137 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1602.61 | 0.309971 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 386.685 | 0.0740471 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 988.570 | 0.187432 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4379.99 | 0.822286 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4157.46 | −0.772894 | −0.386447 | − | 0.922312i | \(-0.626298\pi\) | ||||
−0.386447 | + | 0.922312i | \(0.626298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4214.35 | 0.775877 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3408.45 | 0.621465 | 0.310733 | − | 0.950497i | \(-0.399426\pi\) | ||||
0.310733 | + | 0.950497i | \(0.399426\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4516.35 | 0.815589 | 0.407794 | − | 0.913074i | \(-0.366298\pi\) | ||||
0.407794 | + | 0.913074i | \(0.366298\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2467.33 | −0.441327 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2693.62 | 0.477251 | 0.238626 | − | 0.971112i | \(-0.423303\pi\) | ||||
0.238626 | + | 0.971112i | \(0.423303\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4798.40 | −0.842190 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2931.98 | 0.509804 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 625.217 | 0.107703 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1741.97 | 0.297314 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3818.23 | 0.645715 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.1856 | −0.00254470 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11024.4 | 1.83068 | 0.915338 | − | 0.402687i | \(-0.131924\pi\) | ||||
0.915338 | + | 0.402687i | \(0.131924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −906.152 | −0.149120 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3734.02 | 0.608989 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5218.80 | 0.843579 | 0.421790 | − | 0.906694i | \(-0.361402\pi\) | ||||
0.421790 | + | 0.906694i | \(0.361402\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3279.47 | 0.525417 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1410.59 | 0.224011 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4731.84 | 0.744885 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −234.733 | −0.0366307 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −93.8512 | −0.0145193 | −0.00725965 | − | 0.999974i | \(-0.502311\pi\) | ||||
−0.00725965 | + | 0.999974i | \(0.502311\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4540.27 | 0.696376 | 0.348188 | − | 0.937425i | \(-0.386797\pi\) | ||||
0.348188 | + | 0.937425i | \(0.386797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7087.59 | −1.07780 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4287.12 | 0.646403 | 0.323202 | − | 0.946330i | \(-0.395241\pi\) | ||||
0.323202 | + | 0.946330i | \(0.395241\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1376.23 | −0.205754 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1916.69 | 0.284151 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 176.418 | 0.0259359 | 0.0129680 | − | 0.999916i | \(-0.495872\pi\) | ||||
0.0129680 | + | 0.999916i | \(0.495872\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6651.95 | −0.969814 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −836.686 | −0.120977 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2498.17 | 0.358246 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7745.87 | 1.10172 | 0.550860 | − | 0.834598i | \(-0.314300\pi\) | ||||
0.550860 | + | 0.834598i | \(0.314300\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4607.18 | 0.649974 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14288.5 | 1.99953 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8268.02 | −1.14773 | −0.573863 | − | 0.818951i | \(-0.694556\pi\) | ||||
−0.573863 | + | 0.818951i | \(0.694556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −255.144 | −0.0351349 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11016.5 | −1.50499 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7229.18 | −0.979783 | −0.489892 | − | 0.871783i | \(-0.662964\pi\) | ||||
−0.489892 | + | 0.871783i | \(0.662964\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4146.93 | 0.557621 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 519.390 | 0.0692940 | 0.0346470 | − | 0.999400i | \(-0.488969\pi\) | ||||
0.0346470 | + | 0.999400i | \(0.488969\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3279.46 | 0.434121 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 408.557 | 0.0536644 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10746.4 | −1.40068 | −0.700341 | − | 0.713809i | \(-0.746969\pi\) | ||||
−0.700341 | + | 0.713809i | \(0.746969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −999.363 | −0.129258 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 887.271 | 0.113885 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3989.85 | −0.508231 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11738.8 | −1.48401 | −0.742004 | − | 0.670395i | \(-0.766125\pi\) | ||||
−0.742004 | + | 0.670395i | \(0.766125\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 634.734 | 0.0796403 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −94.4786 | −0.0117657 | −0.00588284 | − | 0.999983i | \(-0.501873\pi\) | ||||
−0.00588284 | + | 0.999983i | \(0.501873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3238.54 | 0.400306 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2044.43 | −0.250836 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1204.42 | 0.146685 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13712.5 | −1.65780 | −0.828901 | − | 0.559396i | \(-0.811033\pi\) | ||||
−0.828901 | + | 0.559396i | \(0.811033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1918.13 | 0.230206 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15834.1 | −1.88655 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5750.51 | −0.680197 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 254.347 | 0.0298691 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4392.60 | −0.512154 | −0.256077 | − | 0.966656i | \(-0.582430\pi\) | ||||
−0.256077 | + | 0.966656i | \(0.582430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 112.287 | 0.0129989 | 0.00649943 | − | 0.999979i | \(-0.497931\pi\) | ||||
0.00649943 | + | 0.999979i | \(0.497931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.0445 | −0.00184423 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1086.26 | −0.123980 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18931.4 | 2.14556 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4316.46 | 0.485782 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7035.30 | 0.786261 | 0.393131 | − | 0.919483i | \(-0.371392\pi\) | ||||
0.393131 | + | 0.919483i | \(0.371392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12046.0 | 1.33693 | 0.668467 | − | 0.743742i | \(-0.266951\pi\) | ||||
0.668467 | + | 0.743742i | \(0.266951\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1613.58 | 0.177851 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −330.951 | −0.0362277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2089.02 | 0.227115 | 0.113557 | − | 0.993531i | \(-0.463775\pi\) | ||||
0.113557 | + | 0.993531i | \(0.463775\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2832.47 | −0.305849 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7436.42 | 0.797551 | 0.398776 | − | 0.917049i | \(-0.369435\pi\) | ||||
0.398776 | + | 0.917049i | \(0.369435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5834.46 | −0.621528 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2806.87 | 0.297003 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1796.33 | 0.188806 | 0.0944032 | − | 0.995534i | \(-0.469906\pi\) | ||||
0.0944032 | + | 0.995534i | \(0.469906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6123.66 | −0.639361 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2442.26 | 0.253306 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7529.23 | 0.775770 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3232.73 | −0.330899 | −0.165450 | − | 0.986218i | \(-0.552907\pi\) | ||||
−0.165450 | + | 0.986218i | \(0.552907\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4419.72 | 0.449444 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10750.2 | −1.08609 | −0.543044 | − | 0.839704i | \(-0.682728\pi\) | ||||
−0.543044 | + | 0.839704i | \(0.682728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6598.81 | −0.662360 | −0.331180 | − | 0.943568i | \(-0.607447\pi\) | ||||
−0.331180 | + | 0.943568i | \(0.607447\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −474.346 | −0.0473060 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8153.38 | −0.807909 | −0.403954 | − | 0.914779i | \(-0.632365\pi\) | ||||
−0.403954 | + | 0.914779i | \(0.632365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16139.4 | 1.58901 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −433.418 | −0.0424010 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −543.036 | −0.0527882 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −359.729 | −0.0347484 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15096.8 | 1.44913 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15056.7 | −1.43624 | −0.718120 | − | 0.695919i | \(-0.754997\pi\) | ||||
−0.718120 | + | 0.695919i | \(0.754997\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2765.19 | 0.262124 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1014.58 | −0.0955793 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2016.04 | −0.188750 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2098.90 | −0.195298 | −0.0976491 | − | 0.995221i | \(-0.531132\pi\) | ||||
−0.0976491 | + | 0.995221i | \(0.531132\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2837.54 | −0.262409 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2245.71 | 0.206410 | 0.103205 | − | 0.994660i | \(-0.467090\pi\) | ||||
0.103205 | + | 0.994660i | \(0.467090\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6869.74 | 0.627581 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3464.95 | 0.314622 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5948.41 | −0.536866 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3216.32 | −0.288542 | −0.144271 | − | 0.989538i | \(-0.546084\pi\) | ||||
−0.144271 | + | 0.989538i | \(0.546084\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −739.611 | −0.0659548 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15459.5 | 1.37039 | 0.685193 | − | 0.728361i | \(-0.259718\pi\) | ||||
0.685193 | + | 0.728361i | \(0.259718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2421.59 | −0.213385 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5425.62 | 0.475267 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12581.8 | 1.09564 | 0.547818 | − | 0.836597i | \(-0.315459\pi\) | ||||
0.547818 | + | 0.836597i | \(0.315459\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10797.7 | 0.934761 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1463.64 | 0.125967 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10323.4 | −0.883311 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.3256 | 0.00181412 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2013.80 | 0.170320 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2681.76 | 0.225509 | 0.112754 | − | 0.993623i | \(-0.464033\pi\) | ||||
0.112754 | + | 0.993623i | \(0.464033\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9009.09 | 0.753232 | 0.376616 | − | 0.926370i | \(-0.377088\pi\) | ||||
0.376616 | + | 0.926370i | \(0.377088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1102.80 | −0.0916764 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2019.50 | −0.166928 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16729.8 | −1.36725 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14059.2 | −1.14253 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7182.16 | −0.580396 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8118.57 | −0.652406 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3764.78 | 0.300855 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22789.6 | 1.81109 | 0.905546 | − | 0.424249i | \(-0.139462\pi\) | ||||
0.905546 | + | 0.424249i | \(0.139462\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5128.80 | 0.405337 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9353.11 | −0.735125 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20709.0 | −1.61874 | −0.809371 | − | 0.587297i | \(-0.800192\pi\) | ||||
−0.809371 | + | 0.587297i | \(0.800192\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20002.3 | 1.55496 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2274.99 | 0.175895 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17245.2 | −1.32611 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −405.015 | −0.0309764 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 586.443 | 0.0446111 | 0.0223055 | − | 0.999751i | \(-0.492899\pi\) | ||||
0.0223055 | + | 0.999751i | \(0.492899\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1246.74 | −0.0943320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2691.68 | −0.202572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4988.10 | 0.373399 | 0.186699 | − | 0.982417i | \(-0.440221\pi\) | ||||
0.186699 | + | 0.982417i | \(0.440221\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8033.37 | −0.598170 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8836.57 | −0.654499 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5548.19 | 0.408773 | 0.204387 | − | 0.978890i | \(-0.434480\pi\) | ||||
0.204387 | + | 0.978890i | \(0.434480\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2684.93 | 0.196779 | 0.0983893 | − | 0.995148i | \(-0.468631\pi\) | ||||
0.0983893 | + | 0.995148i | \(0.468631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4036.36 | −0.294278 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1462.86 | 0.105546 | 0.0527728 | − | 0.998607i | \(-0.483194\pi\) | ||||
0.0527728 | + | 0.998607i | \(0.483194\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2533.68 | −0.181859 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24855.2 | −1.77481 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20065.9 | −1.42546 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7955.10 | 0.562227 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11020.7 | 0.774912 | 0.387456 | − | 0.921888i | \(-0.373354\pi\) | ||||
0.387456 | + | 0.921888i | \(0.373354\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −668.782 | −0.0467856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4020.88 | 0.279860 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7341.16 | 0.508373 | 0.254186 | − | 0.967155i | \(-0.418192\pi\) | ||||
0.254186 | + | 0.967155i | \(0.418192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4695.11 | −0.323497 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8272.98 | 0.567154 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12642.5 | 0.862366 | 0.431183 | − | 0.902264i | \(-0.358096\pi\) | ||||
0.431183 | + | 0.902264i | \(0.358096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7426.60 | 0.504056 | 0.252028 | − | 0.967720i | \(-0.418903\pi\) | ||||
0.252028 | + | 0.967720i | \(0.418903\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17052.3 | 1.15161 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2049.54 | 0.137728 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7506.30 | 0.501929 | 0.250965 | − | 0.967996i | \(-0.419252\pi\) | ||||
0.250965 | + | 0.967996i | \(0.419252\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6974.31 | 0.464061 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.9610 | 0.00324182 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23467.7 | 1.54625 | 0.773124 | − | 0.634254i | \(-0.218693\pi\) | ||||
0.773124 | + | 0.634254i | \(0.218693\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2059.23 | 0.135018 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1436.56 | 0.0937337 | 0.0468669 | − | 0.998901i | \(-0.485076\pi\) | ||||
0.0468669 | + | 0.998901i | \(0.485076\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12664.4 | −0.822332 | −0.411166 | − | 0.911561i | \(-0.634878\pi\) | ||||
−0.411166 | + | 0.911561i | \(0.634878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2339.52 | −0.151178 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25218.1 | −1.62173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −891.380 | −0.0567756 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1724.33 | −0.109306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5383.68 | −0.339653 | −0.169826 | − | 0.985474i | \(-0.554321\pi\) | ||||
−0.169826 | + | 0.985474i | \(0.554321\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −763.616 | −0.0479479 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10158.3 | −0.634834 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8643.47 | 0.537625 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6284.87 | −0.389085 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31245.1 | 1.92529 | 0.962643 | − | 0.270775i | \(-0.0872799\pi\) | ||||
0.962643 | + | 0.270775i | \(0.0872799\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22381.8 | −1.37271 | −0.686354 | − | 0.727268i | \(-0.740790\pi\) | ||||
−0.686354 | + | 0.727268i | \(0.740790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 182.609 | 0.0111477 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13062.8 | −0.793741 | −0.396870 | − | 0.917875i | \(-0.629904\pi\) | ||||
−0.396870 | + | 0.917875i | \(0.629904\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22236.4 | 1.34493 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2050.25 | −0.123434 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17486.1 | −1.04791 | −0.523955 | − | 0.851746i | \(-0.675544\pi\) | ||||
−0.523955 | + | 0.851746i | \(0.675544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2173.45 | −0.129655 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11408.5 | 0.677453 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29707.1 | 1.75603 | 0.878016 | − | 0.478631i | \(-0.158867\pi\) | ||||
0.878016 | + | 0.478631i | \(0.158867\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9905.74 | −0.582888 | −0.291444 | − | 0.956588i | \(-0.594136\pi\) | ||||
−0.291444 | + | 0.956588i | \(0.594136\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6179.76 | −0.361994 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1554.84 | −0.0906679 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3636.41 | −0.211098 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6586.61 | −0.380647 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26586.1 | −1.52957 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7803.48 | −0.446957 | −0.223478 | − | 0.974709i | \(-0.571741\pi\) | ||||
−0.223478 | + | 0.974709i | \(0.571741\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2542.96 | −0.145005 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29359.1 | 1.66671 | 0.833354 | − | 0.552740i | \(-0.186418\pi\) | ||||
0.833354 | + | 0.552740i | \(0.186418\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8713.86 | −0.492500 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6165.54 | −0.346937 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26055.8 | 1.45973 | 0.729866 | − | 0.683591i | \(-0.239583\pi\) | ||||
0.729866 | + | 0.683591i | \(0.239583\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4698.65 | −0.262082 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1907.99 | 0.105960 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −46068.8 | −2.54729 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15166.4 | −0.834959 | −0.417480 | − | 0.908686i | \(-0.637086\pi\) | ||||
−0.417480 | + | 0.908686i | \(0.637086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14976.4 | 0.820934 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −623.047 | −0.0340051 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8767.08 | 0.476437 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7994.95 | −0.432614 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26527.8 | −1.42930 | −0.714650 | − | 0.699482i | \(-0.753414\pi\) | ||||
−0.714650 | + | 0.699482i | \(0.753414\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −571.032 | −0.0306357 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.17128 | −0.000383101 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10466.7 | −0.556779 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21268.1 | 1.12657 | 0.563287 | − | 0.826261i | \(-0.309536\pi\) | ||||
0.563287 | + | 0.826261i | \(0.309536\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18220.6 | −0.961077 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1069.00 | 0.0561491 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10573.6 | −0.553047 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6531.82 | −0.340216 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27640.4 | 1.43368 | 0.716838 | − | 0.697240i | \(-0.245589\pi\) | ||||
0.716838 | + | 0.697240i | \(0.245589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44620.6 | −2.30480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7703.81 | −0.396276 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3952.62 | −0.202478 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10860.2 | 0.554036 | 0.277018 | − | 0.960865i | \(-0.410654\pi\) | ||||
0.277018 | + | 0.960865i | \(0.410654\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3730.57 | −0.189533 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 777.450 | 0.0393366 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2575.74 | −0.129791 | −0.0648956 | − | 0.997892i | \(-0.520671\pi\) | ||||
−0.0648956 | + | 0.997892i | \(0.520671\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1266.00 | −0.0635336 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22665.1 | −1.13281 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25649.2 | 1.27675 | 0.638377 | − | 0.769724i | \(-0.279606\pi\) | ||||
0.638377 | + | 0.769724i | \(0.279606\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2046.50 | −0.101457 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3767.84 | −0.186041 | −0.0930207 | − | 0.995664i | \(-0.529652\pi\) | ||||
−0.0930207 | + | 0.995664i | \(0.529652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6875.69 | −0.338129 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26261.1 | −1.28627 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31043.1 | −1.51441 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16030.6 | −0.778913 | −0.389456 | − | 0.921045i | \(-0.627337\pi\) | ||||
−0.389456 | + | 0.921045i | \(0.627337\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6821.55 | −0.330134 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5982.55 | −0.288380 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3408.80 | −0.163666 | −0.0818329 | − | 0.996646i | \(-0.526077\pi\) | ||||
−0.0818329 | + | 0.996646i | \(0.526077\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1424.81 | 0.0681385 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28208.1 | 1.34368 | 0.671841 | − | 0.740696i | \(-0.265504\pi\) | ||||
0.671841 | + | 0.740696i | \(0.265504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40426.6 | −1.91814 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4960.68 | −0.234450 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 51052.1 | 2.40337 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26349.3 | 1.23560 | 0.617802 | − | 0.786334i | \(-0.288023\pi\) | ||||
0.617802 | + | 0.786334i | \(0.288023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5917.71 | −0.276422 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29491.9 | 1.37225 | 0.686126 | − | 0.727482i | \(-0.259310\pi\) | ||||
0.686126 | + | 0.727482i | \(0.259310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1161.96 | 0.0538563 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1750.58 | −0.0808258 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2903.32 | 0.133533 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8353.56 | 0.382732 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16082.1 | 0.734009 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1061.70 | 0.0482722 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18485.5 | −0.837276 | −0.418638 | − | 0.908153i | \(-0.637492\pi\) | ||||
−0.418638 | + | 0.908153i | \(0.637492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12250.7 | 0.552770 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34722.3 | −1.56079 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61038.3 | −2.73333 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6747.67 | 0.301025 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36684.3 | 1.63039 | 0.815197 | − | 0.579184i | \(-0.196629\pi\) | ||||
0.815197 | + | 0.579184i | \(0.196629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.5313 | −0.00135184 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26644.5 | −1.17533 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15163.6 | −0.666391 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2485.30 | 0.108814 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16958.5 | 0.739737 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 216.567 | 0.00941173 | 0.00470586 | − | 0.999989i | \(-0.498502\pi\) | ||||
0.00470586 | + | 0.999989i | \(0.498502\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25897.5 | −1.12131 | −0.560657 | − | 0.828048i | \(-0.689451\pi\) | ||||
−0.560657 | + | 0.828048i | \(0.689451\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4889.14 | 0.210910 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6950.82 | 0.298744 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 257.462 | 0.0110250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34384.0 | 1.46700 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12735.6 | 0.541384 | 0.270692 | − | 0.962666i | \(-0.412748\pi\) | ||||
0.270692 | + | 0.962666i | \(0.412748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25798.2 | −1.09267 | −0.546336 | − | 0.837566i | \(-0.683978\pi\) | ||||
−0.546336 | + | 0.837566i | \(0.683978\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1548.70 | 0.0653562 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21295.2 | −0.895413 | −0.447706 | − | 0.894181i | \(-0.647759\pi\) | ||||
−0.447706 | + | 0.894181i | \(0.647759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43456.4 | −1.82063 | −0.910315 | − | 0.413915i | \(-0.864161\pi\) | ||||
−0.910315 | + | 0.413915i | \(0.864161\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15240.3 | 0.636197 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5389.94 | −0.224190 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1811.75 | 0.0750875 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4727.68 | −0.195236 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14245.5 | −0.586184 | −0.293092 | − | 0.956084i | \(-0.594684\pi\) | ||||
−0.293092 | + | 0.956084i | \(0.594684\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 608.090 | 0.0249330 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11371.0 | −0.464577 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13290.6 | −0.541076 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8858.64 | 0.359370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10764.0 | 0.435123 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 912.752 | 0.0367670 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1967.69 | 0.0789830 | 0.0394915 | − | 0.999220i | \(-0.487426\pi\) | ||||
0.0394915 | + | 0.999220i | \(0.487426\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1642.79 | −0.0657101 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32176.3 | −1.28252 | −0.641262 | − | 0.767322i | \(-0.721589\pi\) | ||||
−0.641262 | + | 0.767322i | \(0.721589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1273.26 | 0.0505741 | 0.0252871 | − | 0.999680i | \(-0.491950\pi\) | ||||
0.0252871 | + | 0.999680i | \(0.491950\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8900.54 | 0.352299 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −69.6881 | −0.00274880 | −0.00137440 | − | 0.999999i | \(-0.500437\pi\) | ||||
−0.00137440 | + | 0.999999i | \(0.500437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4932.98 | −0.193903 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6174.59 | −0.241869 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24218.0 | 0.945384 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52036.3 | −2.02432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9206.75 | −0.356931 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2701.41 | 0.104371 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20284.8 | −0.781038 | −0.390519 | − | 0.920595i | \(-0.627704\pi\) | ||||
−0.390519 | + | 0.920595i | \(0.627704\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1044.08 | −0.0400636 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29637.5 | −1.13339 | −0.566693 | − | 0.823929i | \(-0.691778\pi\) | ||||
−0.566693 | + | 0.823929i | \(0.691778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16749.3 | 0.638344 | 0.319172 | − | 0.947697i | \(-0.396595\pi\) | ||||
0.319172 | + | 0.947697i | \(0.396595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7477.56 | −0.284017 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22904.8 | 0.867042 | 0.433521 | − | 0.901143i | \(-0.357271\pi\) | ||||
0.433521 | + | 0.901143i | \(0.357271\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43906.7 | −1.65645 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12409.5 | 0.466593 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.1108 | −0.000378886 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19887.2 | 0.742744 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3271.17 | 0.121763 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7348.42 | −0.272618 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28727.8 | 1.06222 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 789.285 | 0.0290872 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12563.5 | −0.461463 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20869.7 | 0.764020 | 0.382010 | − | 0.924158i | \(-0.375232\pi\) | ||||
0.382010 | + | 0.924158i | \(0.375232\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11058.8 | −0.403517 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42361.0 | 1.54060 | 0.770298 | − | 0.637684i | \(-0.220108\pi\) | ||||
0.770298 | + | 0.637684i | \(0.220108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34905.0 | 1.26527 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8940.24 | 0.323011 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9394.22 | −0.338304 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14136.3 | −0.507413 | −0.253707 | − | 0.967281i | \(-0.581650\pi\) | ||||
−0.253707 | + | 0.967281i | \(0.581650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8486.01 | −0.303609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19178.7 | 0.683939 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 992.122 | 0.0352657 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −47144.5 | −1.67036 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7897.49 | −0.278911 | −0.139455 | − | 0.990228i | \(-0.544535\pi\) | ||||
−0.139455 | + | 0.990228i | \(0.544535\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1784.94 | −0.0628347 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6957.19 | 0.244124 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6593.52 | 0.230621 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21499.1 | 0.749567 | 0.374783 | − | 0.927112i | \(-0.377717\pi\) | ||||
0.374783 | + | 0.927112i | \(0.377717\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9218.58 | 0.320380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30258.7 | 1.04825 | 0.524125 | − | 0.851641i | \(-0.324392\pi\) | ||||
0.524125 | + | 0.851641i | \(0.324392\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4640.74 | −0.160258 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10991.3 | −0.378357 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12769.1 | 0.438163 | 0.219082 | − | 0.975707i | \(-0.429694\pi\) | ||||
0.219082 | + | 0.975707i | \(0.429694\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34813.8 | −1.19083 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5498.09 | 0.187474 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28174.8 | 0.957683 | 0.478841 | − | 0.877901i | \(-0.341057\pi\) | ||||
0.478841 | + | 0.877901i | \(0.341057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9887.45 | 0.335027 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9794.28 | −0.330830 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20308.8 | −0.683841 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27630.8 | −0.927487 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32799.0 | −1.09754 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6206.50 | 0.207041 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2696.72 | 0.0896800 | 0.0448400 | − | 0.998994i | \(-0.485722\pi\) | ||||
0.0448400 | + | 0.998994i | \(0.485722\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1276.17 | 0.0423079 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29192.7 | 0.964817 | 0.482408 | − | 0.875946i | \(-0.339762\pi\) | ||||
0.482408 | + | 0.875946i | \(0.339762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2692.97 | −0.0887283 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3555.62 | 0.116791 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1150.88 | −0.0376867 | −0.0188433 | − | 0.999822i | \(-0.505998\pi\) | ||||
−0.0188433 | + | 0.999822i | \(0.505998\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35414.6 | 1.15613 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42713.2 | −1.39014 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9924.92 | 0.322030 | 0.161015 | − | 0.986952i | \(-0.448523\pi\) | ||||
0.161015 | + | 0.986952i | \(0.448523\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9849.53 | −0.318611 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.9961 | −0.000999612 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −411.533 | −0.0132315 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32446.8 | −1.04007 | −0.520034 | − | 0.854146i | \(-0.674081\pi\) | ||||
−0.520034 | + | 0.854146i | \(0.674081\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22502.4 | 0.719127 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20265.4 | −0.645686 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49280.6 | 1.56543 | 0.782715 | − | 0.622381i | \(-0.213834\pi\) | ||||
0.782715 | + | 0.622381i | \(0.213834\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4036.68 | −0.127843 |
(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 | 1840.4.a.o.1.3 | 5 | ||
4.3 | odd | 2 | 460.4.a.b.1.3 | ✓ | 5 | ||
20.3 | even | 4 | 2300.4.c.d.1749.5 | 10 | |||
20.7 | even | 4 | 2300.4.c.d.1749.6 | 10 | |||
20.19 | odd | 2 | 2300.4.a.c.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.4.a.b.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
1840.4.a.o.1.3 | 5 | 1.1 | even | 1 | trivial | ||
2300.4.a.c.1.3 | 5 | 20.19 | odd | 2 | |||
2300.4.c.d.1749.5 | 10 | 20.3 | even | 4 | |||
2300.4.c.d.1749.6 | 10 | 20.7 | even | 4 |