Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [968,4,Mod(1,968)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(968, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("968.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 968 = 2^{3} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 968.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: | \(57.1138488856\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4 x^{9} - 193 x^{8} + 670 x^{7} + 10959 x^{6} - 33408 x^{5} - 177207 x^{4} + 365822 x^{3} + \cdots - 781744 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{2} \) |
Twist minimal: | no (minimal twist has level 88) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.614830\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 968.1 |
$q$-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 | ||||||||
\(3\) | 1.00320 | 0.193067 | 0.0965334 | − | 0.995330i | \(-0.469225\pi\) | ||||
0.0965334 | + | 0.995330i | \(0.469225\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.07450 | 0.543320 | 0.271660 | − | 0.962393i | \(-0.412427\pi\) | ||||
0.271660 | + | 0.962393i | \(0.412427\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.7097 | −1.44219 | −0.721093 | − | 0.692838i | \(-0.756360\pi\) | ||||
−0.721093 | + | 0.692838i | \(0.756360\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.9936 | −0.962725 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 82.1765 | 1.75320 | 0.876602 | − | 0.481216i | \(-0.159805\pi\) | ||||
0.876602 | + | 0.481216i | \(0.159805\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.09397 | 0.104897 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −103.876 | −1.48198 | −0.740992 | − | 0.671513i | \(-0.765645\pi\) | ||||
−0.740992 | + | 0.671513i | \(0.765645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.7485 | −0.347125 | −0.173562 | − | 0.984823i | \(-0.555528\pi\) | ||||
−0.173562 | + | 0.984823i | \(0.555528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26.7953 | −0.278438 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 104.319 | 0.945739 | 0.472870 | − | 0.881132i | \(-0.343218\pi\) | ||||
0.472870 | + | 0.881132i | \(0.343218\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −88.1005 | −0.704804 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −53.1634 | −0.378937 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 13.3542 | 0.0855109 | 0.0427555 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427555 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 333.592 | 1.93274 | 0.966370 | − | 0.257154i | \(-0.0827847\pi\) | ||||
0.966370 | + | 0.257154i | \(0.0827847\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −162.248 | −0.783569 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 71.0862 | 0.315851 | 0.157926 | − | 0.987451i | \(-0.449519\pi\) | ||||
0.157926 | + | 0.987451i | \(0.449519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 82.4398 | 0.338485 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −319.439 | −1.21678 | −0.608390 | − | 0.793639i | \(-0.708184\pi\) | ||||
−0.608390 | + | 0.793639i | \(0.708184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 103.144 | 0.365797 | 0.182898 | − | 0.983132i | \(-0.441452\pi\) | ||||
0.182898 | + | 0.983132i | \(0.441452\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −157.898 | −0.523068 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 402.885 | 1.25036 | 0.625179 | − | 0.780481i | \(-0.285026\pi\) | ||||
0.625179 | + | 0.780481i | \(0.285026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 370.407 | 1.07990 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −104.209 | −0.286122 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.0627 | 0.0364465 | 0.0182233 | − | 0.999834i | \(-0.494199\pi\) | ||||
0.0182233 | + | 0.999834i | \(0.494199\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −28.8407 | −0.0670182 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 246.416 | 0.543739 | 0.271869 | − | 0.962334i | \(-0.412358\pi\) | ||||
0.271869 | + | 0.962334i | \(0.412358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 832.874 | 1.74817 | 0.874087 | − | 0.485770i | \(-0.161461\pi\) | ||||
0.874087 | + | 0.485770i | \(0.161461\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 694.280 | 1.38843 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 499.181 | 0.952550 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 63.6175 | 0.116002 | 0.0580009 | − | 0.998317i | \(-0.481527\pi\) | ||||
0.0580009 | + | 0.998317i | \(0.481527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 104.653 | 0.182591 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 309.079 | 0.516633 | 0.258317 | − | 0.966060i | \(-0.416832\pi\) | ||||
0.258317 | + | 0.966060i | \(0.416832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −408.308 | −0.654642 | −0.327321 | − | 0.944913i | \(-0.606146\pi\) | ||||
−0.327321 | + | 0.944913i | \(0.606146\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −88.3828 | −0.136074 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 855.680 | 1.21863 | 0.609314 | − | 0.792929i | \(-0.291445\pi\) | ||||
0.609314 | + | 0.792929i | \(0.291445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 648.493 | 0.889565 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 524.312 | 0.693382 | 0.346691 | − | 0.937979i | \(-0.387305\pi\) | ||||
0.346691 | + | 0.937979i | \(0.387305\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −630.998 | −0.805192 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.3970 | 0.0165093 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −392.146 | −0.467049 | −0.233524 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233524 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2194.91 | −2.52845 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 334.661 | 0.373148 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −174.633 | −0.188600 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1438.66 | 1.50591 | 0.752957 | − | 0.658069i | \(-0.228627\pi\) | ||||
0.752957 | + | 0.658069i | \(0.228627\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −730.622 | −0.719798 | −0.359899 | − | 0.932991i | \(-0.617189\pi\) | ||||
−0.359899 | + | 0.932991i | \(0.617189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 272.665 | 0.260839 | 0.130420 | − | 0.991459i | \(-0.458368\pi\) | ||||
0.130420 | + | 0.991459i | \(0.458368\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −162.768 | −0.151281 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1845.38 | −1.66729 | −0.833645 | − | 0.552301i | \(-0.813750\pi\) | ||||
−0.833645 | + | 0.552301i | \(0.813750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1492.17 | −1.31123 | −0.655615 | − | 0.755096i | \(-0.727590\pi\) | ||||
−0.655615 | + | 0.755096i | \(0.727590\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 71.3140 | 0.0609804 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 877.631 | 0.730624 | 0.365312 | − | 0.930885i | \(-0.380962\pi\) | ||||
0.365312 | + | 0.930885i | \(0.380962\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 633.685 | 0.513839 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2136.06 | −1.68785 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2774.51 | 2.13730 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −320.462 | −0.234920 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1294.48 | −0.926254 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 197.150 | 0.137750 | 0.0688751 | − | 0.997625i | \(-0.478059\pi\) | ||||
0.0688751 | + | 0.997625i | \(0.478059\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 103.474 | 0.0706232 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1597.71 | 1.06559 | 0.532796 | − | 0.846244i | \(-0.321141\pi\) | ||||
0.532796 | + | 0.846244i | \(0.321141\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 767.864 | 0.500619 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −322.941 | −0.205884 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1401.86 | 0.874225 | 0.437112 | − | 0.899407i | \(-0.356001\pi\) | ||||
0.437112 | + | 0.899407i | \(0.356001\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −79.6678 | −0.0486139 | −0.0243070 | − | 0.999705i | \(-0.507738\pi\) | ||||
−0.0243070 | + | 0.999705i | \(0.507738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 404.176 | 0.241403 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 81.1202 | 0.0464598 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 371.594 | 0.208493 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2509.33 | 1.37968 | 0.689841 | − | 0.723961i | \(-0.257680\pi\) | ||||
0.689841 | + | 0.723961i | \(0.257680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −726.307 | −0.391430 | −0.195715 | − | 0.980661i | \(-0.562703\pi\) | ||||
−0.195715 | + | 0.980661i | \(0.562703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2700.12 | 1.42674 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2026.41 | 1.05010 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −596.004 | −0.302970 | −0.151485 | − | 0.988460i | \(-0.548406\pi\) | ||||
−0.151485 | + | 0.988460i | \(0.548406\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.1078 | 0.00703662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2786.33 | −1.36393 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1800.34 | 0.865113 | 0.432557 | − | 0.901607i | \(-0.357612\pi\) | ||||
0.432557 | + | 0.901607i | \(0.357612\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1038.60 | 0.481251 | 0.240626 | − | 0.970618i | \(-0.422647\pi\) | ||||
0.240626 | + | 0.970618i | \(0.422647\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4555.97 | 2.07372 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 747.278 | 0.334186 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 877.749 | 0.385746 | 0.192873 | − | 0.981224i | \(-0.438219\pi\) | ||||
0.192873 | + | 0.981224i | \(0.438219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2353.13 | 1.01646 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 247.205 | 0.104978 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 927.009 | 0.387083 | 0.193542 | − | 0.981092i | \(-0.438003\pi\) | ||||
0.193542 | + | 0.981092i | \(0.438003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1583.57 | 0.650310 | 0.325155 | − | 0.945661i | \(-0.394584\pi\) | ||||
0.325155 | + | 0.945661i | \(0.394584\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 835.543 | 0.337514 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 431.813 | 0.171608 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1419.98 | 0.546498 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2504.87 | 0.948933 | 0.474466 | − | 0.880274i | \(-0.342641\pi\) | ||||
0.474466 | + | 0.880274i | \(0.342641\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3233.84 | 1.20610 | 0.603049 | − | 0.797704i | \(-0.293952\pi\) | ||||
0.603049 | + | 0.797704i | \(0.293952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 500.781 | 0.183906 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2262.30 | −0.818185 | −0.409092 | − | 0.912493i | \(-0.634155\pi\) | ||||
−0.409092 | + | 0.912493i | \(0.634155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 488.243 | 0.173923 | 0.0869614 | − | 0.996212i | \(-0.472284\pi\) | ||||
0.0869614 | + | 0.996212i | \(0.472284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 63.8214 | 0.0223961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −356.687 | −0.123323 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1940.43 | −0.661100 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2711.62 | −0.910487 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3698.90 | −1.20684 | −0.603418 | − | 0.797425i | \(-0.706195\pi\) | ||||
−0.603418 | + | 0.797425i | \(0.706195\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 310.070 | 0.0997447 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 626.547 | 0.198745 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8910.15 | −2.78737 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −409.617 | −0.126390 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8536.20 | −2.59822 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4494.02 | −1.34951 | −0.674757 | − | 0.738040i | \(-0.735751\pi\) | ||||
−0.674757 | + | 0.738040i | \(0.735751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2290.05 | 0.678532 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2887.89 | 0.844389 | 0.422194 | − | 0.906505i | \(-0.361260\pi\) | ||||
0.422194 | + | 0.906505i | \(0.361260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2826.69 | 0.815690 | 0.407845 | − | 0.913051i | \(-0.366280\pi\) | ||||
0.407845 | + | 0.913051i | \(0.366280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3248.03 | 0.913242 | 0.456621 | − | 0.889661i | \(-0.349060\pi\) | ||||
0.456621 | + | 0.889661i | \(0.349060\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2447.33 | 0.679344 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 858.422 | 0.235276 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3726.85 | 1.00866 | 0.504330 | − | 0.863511i | \(-0.331739\pi\) | ||||
0.504330 | + | 0.863511i | \(0.331739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2906.13 | −0.776766 | −0.388383 | − | 0.921498i | \(-0.626966\pi\) | ||||
−0.388383 | + | 0.921498i | \(0.626966\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2085.98 | 0.550683 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2250.04 | 0.586733 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2362.45 | −0.608580 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 525.992 | 0.133869 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5471.07 | 1.37582 | 0.687911 | − | 0.725795i | \(-0.258528\pi\) | ||||
0.687911 | + | 0.725795i | \(0.258528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −633.020 | −0.155456 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5352.44 | −1.29913 | −0.649565 | − | 0.760306i | \(-0.725049\pi\) | ||||
−0.649565 | + | 0.760306i | \(0.725049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1898.69 | −0.455517 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −347.124 | −0.0823235 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5152.87 | 1.20814 | 0.604068 | − | 0.796933i | \(-0.293545\pi\) | ||||
0.604068 | + | 0.796933i | \(0.293545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 85.4241 | 0.0198021 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −393.402 | −0.0901716 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2450.74 | 0.555480 | 0.277740 | − | 0.960656i | \(-0.410415\pi\) | ||||
0.277740 | + | 0.960656i | \(0.410415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −179.064 | −0.0401378 | −0.0200689 | − | 0.999799i | \(-0.506389\pi\) | ||||
−0.0200689 | + | 0.999799i | \(0.506389\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2201.94 | −0.488159 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5106.41 | −1.10763 | −0.553817 | − | 0.832638i | \(-0.686829\pi\) | ||||
−0.553817 | + | 0.832638i | \(0.686829\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8671.26 | −1.86070 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5251.29 | −1.11482 | −0.557412 | − | 0.830236i | \(-0.688206\pi\) | ||||
−0.557412 | + | 0.830236i | \(0.688206\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6186.40 | 1.29945 | 0.649723 | − | 0.760171i | \(-0.274885\pi\) | ||||
0.649723 | + | 0.760171i | \(0.274885\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −175.193 | −0.0364123 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8532.11 | 1.75482 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5877.32 | 1.19628 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1443.27 | 0.290742 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3508.95 | −0.699641 | −0.349821 | − | 0.936817i | \(-0.613757\pi\) | ||||
−0.349821 | + | 0.936817i | \(0.613757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1496.85 | 0.295424 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8572.56 | 1.65807 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2754.94 | −0.527548 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −732.963 | −0.138969 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5059.29 | 0.949817 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1744.41 | −0.324295 | −0.162148 | − | 0.986767i | \(-0.551842\pi\) | ||||
−0.162148 | + | 0.986767i | \(0.551842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 273.539 | 0.0503594 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2926.97 | −0.533676 | −0.266838 | − | 0.963741i | \(-0.585979\pi\) | ||||
−0.266838 | + | 0.963741i | \(0.585979\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6794.84 | −1.22705 | −0.613525 | − | 0.789675i | \(-0.710249\pi\) | ||||
−0.613525 | + | 0.789675i | \(0.710249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4217.40 | 0.754361 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10367.2 | −1.83684 | −0.918420 | − | 0.395608i | \(-0.870534\pi\) | ||||
−0.918420 | + | 0.395608i | \(0.870534\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1851.30 | −0.321898 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2986.30 | 0.514434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7239.78 | −1.23566 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1496.95 | −0.253155 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10760.9 | −1.80325 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3982.48 | −0.661320 | −0.330660 | − | 0.943750i | \(-0.607271\pi\) | ||||
−0.330660 | + | 0.943750i | \(0.607271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1847.78 | −0.304078 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 386.445 | 0.0630260 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7461.83 | −1.20615 | −0.603074 | − | 0.797685i | \(-0.706058\pi\) | ||||
−0.603074 | + | 0.797685i | \(0.706058\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 880.443 | 0.141059 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −732.027 | −0.115235 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 635.716 | 0.0992052 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1992.95 | 0.308320 | 0.154160 | − | 0.988046i | \(-0.450733\pi\) | ||||
0.154160 | + | 0.988046i | \(0.450733\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1412.29 | −0.216613 | −0.108307 | − | 0.994118i | \(-0.534543\pi\) | ||||
−0.108307 | + | 0.994118i | \(0.534543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4368.78 | −0.664354 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1224.00 | 0.184553 | 0.0922763 | − | 0.995733i | \(-0.470586\pi\) | ||||
0.0922763 | + | 0.995733i | \(0.470586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1877.50 | 0.280697 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2783.40 | 0.412642 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5513.65 | 0.810583 | 0.405291 | − | 0.914188i | \(-0.367170\pi\) | ||||
0.405291 | + | 0.914188i | \(0.367170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6032.52 | −0.879504 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2480.27 | −0.355680 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2764.74 | 0.393238 | 0.196619 | − | 0.980480i | \(-0.437004\pi\) | ||||
0.196619 | + | 0.980480i | \(0.437004\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8303.36 | 1.17142 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −375.611 | −0.0525627 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3977.72 | 0.552168 | 0.276084 | − | 0.961134i | \(-0.410963\pi\) | ||||
0.276084 | + | 0.961134i | \(0.410963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1298.63 | −0.178829 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1097.40 | 0.149918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14533.5 | −1.96976 | −0.984878 | − | 0.173249i | \(-0.944574\pi\) | ||||
−0.984878 | + | 0.173249i | \(0.944574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 197.782 | 0.0265950 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5198.09 | −0.693499 | −0.346749 | − | 0.937958i | \(-0.612715\pi\) | ||||
−0.346749 | + | 0.937958i | \(0.612715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2681.07 | −0.352162 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6181.85 | 0.805738 | 0.402869 | − | 0.915258i | \(-0.368013\pi\) | ||||
0.402869 | + | 0.915258i | \(0.368013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10836.3 | −1.40157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1602.83 | 0.205730 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5197.83 | 0.662104 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −636.976 | −0.0805263 | −0.0402631 | − | 0.999189i | \(-0.512820\pi\) | ||||
−0.0402631 | + | 0.999189i | \(0.512820\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 770.325 | 0.0966528 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4495.73 | 0.559866 | 0.279933 | − | 0.960020i | \(-0.409688\pi\) | ||||
0.279933 | + | 0.960020i | \(0.409688\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27413.4 | 3.38849 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3939.27 | 0.483318 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3569.38 | 0.431527 | 0.215763 | − | 0.976446i | \(-0.430776\pi\) | ||||
0.215763 | + | 0.976446i | \(0.430776\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1406.35 | 0.168784 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6581.68 | −0.784173 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3184.93 | 0.376728 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −79.9231 | −0.00938574 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12382.2 | −1.44370 | −0.721850 | − | 0.692050i | \(-0.756708\pi\) | ||||
−0.721850 | + | 0.692050i | \(0.756708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12996.9 | 1.50459 | 0.752294 | − | 0.658827i | \(-0.228947\pi\) | ||||
0.752294 | + | 0.658827i | \(0.228947\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10472.4 | −1.20375 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9151.56 | 1.04451 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22245.8 | −2.52119 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3054.63 | −0.341383 | −0.170692 | − | 0.985324i | \(-0.554600\pi\) | ||||
−0.170692 | + | 0.985324i | \(0.554600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11674.8 | −1.29574 | −0.647870 | − | 0.761751i | \(-0.724340\pi\) | ||||
−0.647870 | + | 0.761751i | \(0.724340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 81.3802 | 0.00896984 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2999.02 | −0.328289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9542.32 | 1.03743 | 0.518713 | − | 0.854948i | \(-0.326411\pi\) | ||||
0.518713 | + | 0.854948i | \(0.326411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9628.20 | −1.03965 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9040.66 | −0.969604 | −0.484802 | − | 0.874624i | \(-0.661108\pi\) | ||||
−0.484802 | + | 0.874624i | \(0.661108\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2382.09 | −0.253757 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2517.37 | 0.266371 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9642.72 | −1.01351 | −0.506757 | − | 0.862089i | \(-0.669156\pi\) | ||||
−0.506757 | + | 0.862089i | \(0.669156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −728.634 | −0.0755722 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13333.0 | −1.37376 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3403.31 | 0.348359 | 0.174180 | − | 0.984714i | \(-0.444273\pi\) | ||||
0.174180 | + | 0.984714i | \(0.444273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5522.43 | 0.561579 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2127.43 | 0.214933 | 0.107467 | − | 0.994209i | \(-0.465726\pi\) | ||||
0.107467 | + | 0.994209i | \(0.465726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14223.3 | 1.42768 | 0.713839 | − | 0.700310i | \(-0.246955\pi\) | ||||
0.713839 | + | 0.700310i | \(0.246955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2032.90 | 0.202739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2991.19 | −0.296393 | −0.148197 | − | 0.988958i | \(-0.547347\pi\) | ||||
−0.148197 | + | 0.988958i | \(0.547347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1699.20 | −0.167296 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −597.914 | −0.0584935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2532.76 | 0.244655 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −365.541 | −0.0350880 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17489.0 | −1.66826 | −0.834128 | − | 0.551570i | \(-0.814029\pi\) | ||||
−0.834128 | + | 0.551570i | \(0.814029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5841.61 | 0.553752 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2795.25 | −0.263330 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8739.14 | 0.818193 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10994.1 | 1.02298 | 0.511489 | − | 0.859290i | \(-0.329094\pi\) | ||||
0.511489 | + | 0.859290i | \(0.329094\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1806.11 | 0.167025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21268.6 | −1.95487 | −0.977433 | − | 0.211244i | \(-0.932249\pi\) | ||||
−0.977433 | + | 0.211244i | \(0.932249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1387.19 | −0.126726 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8255.41 | −0.745082 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3306.52 | 0.296633 | 0.148317 | − | 0.988940i | \(-0.452615\pi\) | ||||
0.148317 | + | 0.988940i | \(0.452615\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1041.92 | 0.0929136 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5078.26 | 0.450156 | 0.225078 | − | 0.974341i | \(-0.427736\pi\) | ||||
0.225078 | + | 0.974341i | \(0.427736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4438.16 | −0.391080 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4570.57 | 0.400367 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2057.27 | 0.179149 | 0.0895744 | − | 0.995980i | \(-0.471449\pi\) | ||||
0.0895744 | + | 0.995980i | \(0.471449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10905.8 | 0.944117 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1528.37 | 0.131538 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1656.30 | 0.141719 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 880.562 | 0.0744747 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13584.7 | −1.14234 | −0.571168 | − | 0.820833i | \(-0.693509\pi\) | ||||
−0.571168 | + | 0.820833i | \(0.693509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4068.26 | 0.340139 | 0.170069 | − | 0.985432i | \(-0.445601\pi\) | ||||
0.170069 | + | 0.985432i | \(0.445601\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2360.68 | 0.196244 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34652.4 | −2.86429 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1284.56 | −0.105577 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6405.23 | −0.523471 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26250.3 | −2.13326 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11209.8 | −0.905872 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 929.980 | 0.0747329 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19884.1 | 1.58020 | 0.790098 | − | 0.612981i | \(-0.210030\pi\) | ||||
0.790098 | + | 0.612981i | \(0.210030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1588.65 | 0.125553 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9064.19 | −0.712417 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3811.32 | 0.297916 | 0.148958 | − | 0.988844i | \(-0.452408\pi\) | ||||
0.148958 | + | 0.988844i | \(0.452408\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21649.4 | −1.68301 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −383.914 | −0.0296830 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22854.9 | −1.75749 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 433.197 | 0.0331319 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15397.2 | 1.17128 | 0.585638 | − | 0.810573i | \(-0.300844\pi\) | ||||
0.585638 | + | 0.810573i | \(0.300844\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8475.99 | 0.641317 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18752.4 | −1.40376 | −0.701881 | − | 0.712294i | \(-0.747656\pi\) | ||||
−0.701881 | + | 0.712294i | \(0.747656\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5331.17 | 0.396963 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17321.0 | −1.28292 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3445.50 | 0.253854 | 0.126927 | − | 0.991912i | \(-0.459489\pi\) | ||||
0.126927 | + | 0.991912i | \(0.459489\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20827.4 | 1.52645 | 0.763223 | − | 0.646135i | \(-0.223616\pi\) | ||||
0.763223 | + | 0.646135i | \(0.223616\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2512.90 | 0.183207 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9190.55 | −0.666561 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3937.49 | 0.284090 | 0.142045 | − | 0.989860i | \(-0.454632\pi\) | ||||
0.142045 | + | 0.989860i | \(0.454632\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3244.20 | 0.232857 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14004.2 | −0.999986 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12975.5 | −0.917044 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9657.58 | −0.679064 | −0.339532 | − | 0.940594i | \(-0.610269\pi\) | ||||
−0.339532 | + | 0.940594i | \(0.610269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9590.30 | −0.670902 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2269.55 | −0.157964 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4048.54 | 0.280360 | 0.140180 | − | 0.990126i | \(-0.455232\pi\) | ||||
0.140180 | + | 0.990126i | \(0.455232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16853.7 | 1.16124 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 489.808 | 0.0335787 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 880.647 | 0.0600706 | 0.0300353 | − | 0.999549i | \(-0.490438\pi\) | ||||
0.0300353 | + | 0.999549i | \(0.490438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2500.43 | 0.169708 | 0.0848541 | − | 0.996393i | \(-0.472958\pi\) | ||||
0.0848541 | + | 0.996393i | \(0.472958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1653.65 | −0.111678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20857.7 | 1.39471 | 0.697353 | − | 0.716728i | \(-0.254361\pi\) | ||||
0.697353 | + | 0.716728i | \(0.254361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −357.830 | −0.0238095 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33107.7 | 2.19213 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2145.90 | −0.141390 | −0.0706949 | − | 0.997498i | \(-0.522522\pi\) | ||||
−0.0706949 | + | 0.997498i | \(0.522522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1946.65 | −0.127637 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23302.7 | −1.52047 | −0.760235 | − | 0.649649i | \(-0.774916\pi\) | ||||
−0.760235 | + | 0.649649i | \(0.774916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29666.2 | 1.92631 | 0.963155 | − | 0.268945i | \(-0.0866751\pi\) | ||||
0.963155 | + | 0.268945i | \(0.0866751\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5545.95 | −0.358376 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10474.1 | 0.673572 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3149.25 | 0.201552 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7384.18 | −0.468087 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12224.9 | −0.771261 | −0.385630 | − | 0.922653i | \(-0.626016\pi\) | ||||
−0.385630 | + | 0.922653i | \(0.626016\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3710.75 | −0.233000 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1197.59 | 0.0748424 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30438.7 | 1.89329 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8034.08 | −0.497376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8068.91 | 0.497196 | 0.248598 | − | 0.968607i | \(-0.420030\pi\) | ||||
0.248598 | + | 0.968607i | \(0.420030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22154.7 | 1.35878 | 0.679389 | − | 0.733778i | \(-0.262245\pi\) | ||||
0.679389 | + | 0.733778i | \(0.262245\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 628.554 | 0.0383710 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18371.7 | 1.11633 | 0.558164 | − | 0.829730i | \(-0.311506\pi\) | ||||
0.558164 | + | 0.829730i | \(0.311506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8938.70 | −0.538149 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13966.3 | 0.836973 | 0.418486 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418486 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9705.29 | 0.578957 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10613.4 | 0.630241 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11074.6 | 0.654634 | 0.327317 | − | 0.944915i | \(-0.393855\pi\) | ||||
0.327317 | + | 0.944915i | \(0.393855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9471.84 | −0.557355 | −0.278678 | − | 0.960385i | \(-0.589896\pi\) | ||||
−0.278678 | + | 0.960385i | \(0.589896\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8563.55 | −0.501630 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4664.39 | 0.271996 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1393.10 | 0.0808710 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4508.42 | −0.260546 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21421.9 | 1.22698 | 0.613488 | − | 0.789704i | \(-0.289766\pi\) | ||||
0.613488 | + | 0.789704i | \(0.289766\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4683.72 | 0.267076 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22221.8 | 1.26152 | 0.630762 | − | 0.775976i | \(-0.282742\pi\) | ||||
0.630762 | + | 0.775976i | \(0.282742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38426.1 | −2.17181 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2897.15 | 0.163023 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30048.5 | −1.68342 | −0.841709 | − | 0.539931i | \(-0.818450\pi\) | ||||
−0.841709 | + | 0.539931i | \(0.818450\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8515.59 | 0.474984 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2835.75 | 0.157483 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1155.63 | 0.0638982 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27578.9 | −1.51831 | −0.759155 | − | 0.650910i | \(-0.774387\pi\) | ||||
−0.759155 | + | 0.650910i | \(0.774387\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −483.942 | −0.0264129 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33182.2 | 1.80325 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3258.43 | 0.176317 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15938.5 | −0.858756 | −0.429378 | − | 0.903125i | \(-0.641267\pi\) | ||||
−0.429378 | + | 0.903125i | \(0.641267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2043.62 | −0.109640 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2455.17 | 0.131159 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19514.7 | 1.03808 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20279.0 | 1.07418 | 0.537089 | − | 0.843526i | \(-0.319524\pi\) | ||||
0.537089 | + | 0.843526i | \(0.319524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22242.2 | −1.17320 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34800.0 | 1.82787 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3738.79 | 0.194739 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1841.51 | 0.0955170 | 0.0477585 | − | 0.998859i | \(-0.484792\pi\) | ||||
0.0477585 | + | 0.998859i | \(0.484792\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7282.79 | −0.376179 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2915.45 | −0.149968 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1176.51 | −0.0602684 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5678.11 | −0.289669 | −0.144834 | − | 0.989456i | \(-0.546265\pi\) | ||||
−0.144834 | + | 0.989456i | \(0.546265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15416.6 | −0.783247 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10714.2 | −0.542106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −200.997 | −0.0101282 | −0.00506412 | − | 0.999987i | \(-0.501612\pi\) | ||||
−0.00506412 | + | 0.999987i | \(0.501612\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2257.25 | 0.113279 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2831.33 | −0.140937 | −0.0704684 | − | 0.997514i | \(-0.522449\pi\) | ||||
−0.0704684 | + | 0.997514i | \(0.522449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2370.02 | −0.117497 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2213.01 | 0.109270 | 0.0546349 | − | 0.998506i | \(-0.482601\pi\) | ||||
0.0546349 | + | 0.998506i | \(0.482601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15242.9 | 0.749609 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13628.7 | −0.667536 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49289.6 | 2.40454 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3565.52 | −0.173246 | −0.0866229 | − | 0.996241i | \(-0.527608\pi\) | ||||
−0.0866229 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5488.61 | 0.265625 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4411.95 | −0.212672 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29497.0 | 1.41623 | 0.708116 | − | 0.706096i | \(-0.249545\pi\) | ||||
0.708116 | + | 0.706096i | \(0.249545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4012.34 | −0.191127 | −0.0955633 | − | 0.995423i | \(-0.530465\pi\) | ||||
−0.0955633 | + | 0.995423i | \(0.530465\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39855.4 | 1.89104 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16401.9 | 0.775178 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20249.6 | 0.953285 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21327.7 | 1.00013 | 0.500064 | − | 0.865989i | \(-0.333310\pi\) | ||||
0.500064 | + | 0.865989i | \(0.333310\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5369.60 | −0.250819 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35031.9 | −1.63002 | −0.815012 | − | 0.579444i | \(-0.803270\pi\) | ||||
−0.815012 | + | 0.579444i | \(0.803270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29389.6 | −1.36220 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1904.77 | −0.0879451 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9183.40 | 0.422374 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −709.956 | −0.0324033 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3620.43 | −0.164610 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6605.92 | −0.299207 | −0.149603 | − | 0.988746i | \(-0.547800\pi\) | ||||
−0.149603 | + | 0.988746i | \(0.547800\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5169.39 | 0.233251 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23441.2 | −1.05370 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68442.6 | 3.06490 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 85.6979 | 0.00382313 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8918.42 | 0.396370 | 0.198185 | − | 0.980165i | \(-0.436495\pi\) | ||||
0.198185 | + | 0.980165i | \(0.436495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41850.3 | −1.85301 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10193.3 | 0.449640 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16925.5 | −0.741052 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2458.59 | 0.107245 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14598.4 | 0.634429 | 0.317214 | − | 0.948354i | \(-0.397253\pi\) | ||||
0.317214 | + | 0.948354i | \(0.397253\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38930.1 | −1.68560 | −0.842799 | − | 0.538229i | \(-0.819094\pi\) | ||||
−0.842799 | + | 0.538229i | \(0.819094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −179.637 | −0.00774927 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10936.2 | 0.470033 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2965.23 | −0.126977 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 57053.5 | 2.43420 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16851.6 | −0.716352 | −0.358176 | − | 0.933654i | \(-0.616601\pi\) | ||||
−0.358176 | + | 0.933654i | \(0.616601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32099.8 | 1.35957 | 0.679787 | − | 0.733409i | \(-0.262072\pi\) | ||||
0.679787 | + | 0.733409i | \(0.262072\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31223.7 | 1.31288 | 0.656441 | − | 0.754378i | \(-0.272061\pi\) | ||||
0.656441 | + | 0.754378i | \(0.272061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4263.24 | −0.178611 | −0.0893055 | − | 0.996004i | \(-0.528465\pi\) | ||||
−0.0893055 | + | 0.996004i | \(0.528465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5122.78 | −0.213847 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38476.5 | −1.60040 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6308.95 | 0.261473 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17734.9 | −0.732387 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27031.7 | −1.11232 | −0.556162 | − | 0.831074i | \(-0.687727\pi\) | ||||
−0.556162 | + | 0.831074i | \(0.687727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24210.7 | −0.992688 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5268.12 | −0.215235 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27675.2 | 1.12670 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6206.22 | 0.250880 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7415.64 | 0.298713 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23561.8 | −0.945767 | −0.472884 | − | 0.881125i | \(-0.656787\pi\) | ||||
−0.472884 | + | 0.881125i | \(0.656787\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4539.34 | 0.181570 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25690.2 | 1.02399 | 0.511996 | − | 0.858988i | \(-0.328906\pi\) | ||||
0.511996 | + | 0.858988i | \(0.328906\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38906.7 | −1.54538 | −0.772689 | − | 0.634785i | \(-0.781089\pi\) | ||||
−0.772689 | + | 0.634785i | \(0.781089\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8559.45 | 0.338798 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29165.7 | 1.15042 | 0.575209 | − | 0.818007i | \(-0.304921\pi\) | ||||
0.575209 | + | 0.818007i | \(0.304921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5331.89 | 0.209583 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5896.15 | 0.230962 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5227.86 | 0.203375 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37395.9 | −1.44978 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34575.1 | 1.33583 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22564.5 | 0.868812 | 0.434406 | − | 0.900717i | \(-0.356958\pi\) | ||||
0.434406 | + | 0.900717i | \(0.356958\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3520.19 | −0.135077 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1485.31 | 0.0568008 | 0.0284004 | − | 0.999597i | \(-0.490959\pi\) | ||||
0.0284004 | + | 0.999597i | \(0.490959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33378.6 | 1.27212 | 0.636058 | − | 0.771641i | \(-0.280564\pi\) | ||||
0.636058 | + | 0.771641i | \(0.280564\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1501.65 | 0.0570366 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51592.0 | −1.95297 | −0.976487 | − | 0.215575i | \(-0.930838\pi\) | ||||
−0.976487 | + | 0.215575i | \(0.930838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5265.83 | −0.198662 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11582.4 | −0.434030 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5631.12 | 0.210310 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8600.03 | 0.320119 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4454.87 | 0.165270 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1460.79 | −0.0540132 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2763.76 | −0.101852 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9619.42 | 0.353326 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14723.5 | 0.539013 | 0.269506 | − | 0.962999i | \(-0.413139\pi\) | ||||
0.269506 | + | 0.962999i | \(0.413139\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18991.5 | 0.692967 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1602.51 | 0.0582806 | 0.0291403 | − | 0.999575i | \(-0.490723\pi\) | ||||
0.0291403 | + | 0.999575i | \(0.490723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5075.50 | 0.183378 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42674.3 | −1.53678 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2334.19 | 0.0837844 | 0.0418922 | − | 0.999122i | \(-0.486661\pi\) | ||||
0.0418922 | + | 0.999122i | \(0.486661\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1750.00 | −0.0626106 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25399.0 | 0.905763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6262.73 | −0.222613 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7087.54 | −0.251117 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9082.59 | 0.320765 | 0.160382 | − | 0.987055i | \(-0.448727\pi\) | ||||
0.160382 | + | 0.987055i | \(0.448727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10648.7 | −0.374861 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2936.35 | −0.103035 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16688.9 | −0.581861 | −0.290931 | − | 0.956744i | \(-0.593965\pi\) | ||||
−0.290931 | + | 0.956744i | \(0.593965\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6816.61 | −0.236903 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22357.1 | 0.774518 | 0.387259 | − | 0.921971i | \(-0.373422\pi\) | ||||
0.387259 | + | 0.921971i | \(0.373422\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33323.5 | −1.15076 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8625.65 | 0.296923 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39734.1 | −1.36345 | −0.681724 | − | 0.731610i | \(-0.738769\pi\) | ||||
−0.681724 | + | 0.731610i | \(0.738769\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33553.3 | −1.14772 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10400.4 | −0.354633 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16514.8 | 0.561349 | 0.280674 | − | 0.959803i | \(-0.409442\pi\) | ||||
0.280674 | + | 0.959803i | \(0.409442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15215.8 | 0.515574 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37443.2 | −1.26080 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81492.9 | 2.73549 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 47968.1 | 1.60514 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19644.0 | 0.655297 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8015.15 | −0.266546 | −0.133273 | − | 0.991079i | \(-0.542549\pi\) | ||||
−0.133273 | + | 0.991079i | \(0.542549\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2995.87 | 0.0993200 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2803.91 | −0.0926691 | −0.0463345 | − | 0.998926i | \(-0.514754\pi\) | ||||
−0.0463345 | + | 0.998926i | \(0.514754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2127.90 | 0.0701104 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7262.98 | −0.238566 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13053.3 | −0.427443 | −0.213722 | − | 0.976895i | \(-0.568559\pi\) | ||||
−0.213722 | + | 0.976895i | \(0.568559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38786.9 | 1.26235 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18628.5 | −0.604431 | −0.302216 | − | 0.953240i | \(-0.597726\pi\) | ||||
−0.302216 | + | 0.953240i | \(0.597726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13742.4 | −0.444536 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10795.4 | −0.348148 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10759.8 | 0.345949 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35006.9 | 1.12213 | 0.561065 | − | 0.827772i | \(-0.310392\pi\) | ||||
0.561065 | + | 0.827772i | \(0.310392\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3995.24 | −0.127679 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2965.83 | 0.0944957 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39681.8 | 1.26052 | 0.630258 | − | 0.776385i | \(-0.282949\pi\) | ||||
0.630258 | + | 0.776385i | \(0.282949\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3779.18 | −0.119688 |
(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 | 968.4.a.r.1.6 | 10 | ||
4.3 | odd | 2 | 1936.4.a.by.1.5 | 10 | |||
11.2 | odd | 10 | 88.4.i.b.81.3 | yes | 20 | ||
11.6 | odd | 10 | 88.4.i.b.25.3 | ✓ | 20 | ||
11.10 | odd | 2 | 968.4.a.s.1.6 | 10 | |||
44.35 | even | 10 | 176.4.m.f.81.3 | 20 | |||
44.39 | even | 10 | 176.4.m.f.113.3 | 20 | |||
44.43 | even | 2 | 1936.4.a.bx.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
88.4.i.b.25.3 | ✓ | 20 | 11.6 | odd | 10 | ||
88.4.i.b.81.3 | yes | 20 | 11.2 | odd | 10 | ||
176.4.m.f.81.3 | 20 | 44.35 | even | 10 | |||
176.4.m.f.113.3 | 20 | 44.39 | even | 10 | |||
968.4.a.r.1.6 | 10 | 1.1 | even | 1 | trivial | ||
968.4.a.s.1.6 | 10 | 11.10 | odd | 2 | |||
1936.4.a.bx.1.5 | 10 | 44.43 | even | 2 | |||
1936.4.a.by.1.5 | 10 | 4.3 | odd | 2 |