Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(1,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, 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("768.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1436.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 11x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.76644\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.612661 | 0.0547981 | 0.0273990 | − | 0.999625i | \(-0.491278\pi\) | ||||
0.0273990 | + | 0.999625i | \(0.491278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.7441 | 1.22807 | 0.614034 | − | 0.789279i | \(-0.289546\pi\) | ||||
0.614034 | + | 0.789279i | \(0.289546\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.2630 | 1.65182 | 0.825908 | − | 0.563805i | \(-0.190663\pi\) | ||||
0.825908 | + | 0.563805i | \(0.190663\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.9062 | 1.12873 | 0.564367 | − | 0.825524i | \(-0.309120\pi\) | ||||
0.564367 | + | 0.825524i | \(0.309120\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.83798 | −0.0316377 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 47.1643 | 0.672883 | 0.336442 | − | 0.941704i | \(-0.390777\pi\) | ||||
0.336442 | + | 0.941704i | \(0.390777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.1643 | 0.352144 | 0.176072 | − | 0.984377i | \(-0.443661\pi\) | ||||
0.176072 | + | 0.984377i | \(0.443661\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −68.2324 | −0.709026 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −109.488 | −0.992604 | −0.496302 | − | 0.868150i | \(-0.665309\pi\) | ||||
−0.496302 | + | 0.868150i | \(0.665309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.625 | −0.996997 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4250 | −0.0667542 | −0.0333771 | − | 0.999443i | \(-0.510626\pi\) | ||||
−0.0333771 | + | 0.999443i | \(0.510626\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −220.881 | −1.27972 | −0.639860 | − | 0.768492i | \(-0.721008\pi\) | ||||
−0.639860 | + | 0.768492i | \(0.721008\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −180.789 | −0.953676 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.9345 | 0.0672958 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 408.348 | 1.81438 | 0.907188 | − | 0.420725i | \(-0.138224\pi\) | ||||
0.907188 | + | 0.420725i | \(0.138224\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −158.718 | −0.651674 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 360.742 | 1.37411 | 0.687054 | − | 0.726606i | \(-0.258903\pi\) | ||||
0.687054 | + | 0.726606i | \(0.258903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −236.414 | −0.838436 | −0.419218 | − | 0.907886i | \(-0.637696\pi\) | ||||
−0.419218 | + | 0.907886i | \(0.637696\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.51395 | 0.0182660 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 129.113 | 0.400703 | 0.200352 | − | 0.979724i | \(-0.435792\pi\) | ||||
0.200352 | + | 0.979724i | \(0.435792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 174.296 | 0.508152 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −141.493 | −0.388489 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 117.819 | 0.305353 | 0.152677 | − | 0.988276i | \(-0.451211\pi\) | ||||
0.152677 | + | 0.988276i | \(0.451211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 36.9208 | 0.0905163 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −87.4928 | −0.203311 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −262.854 | −0.580012 | −0.290006 | − | 0.957025i | \(-0.593657\pi\) | ||||
−0.290006 | + | 0.957025i | \(0.593657\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 273.465 | 0.573993 | 0.286996 | − | 0.957932i | \(-0.407343\pi\) | ||||
0.286996 | + | 0.957932i | \(0.407343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 204.697 | 0.409356 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 32.4135 | 0.0618524 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 89.4077 | 0.163028 | 0.0815141 | − | 0.996672i | \(-0.474024\pi\) | ||||
0.0815141 | + | 0.996672i | \(0.474024\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 328.465 | 0.573080 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 350.521 | 0.585904 | 0.292952 | − | 0.956127i | \(-0.405362\pi\) | ||||
0.292952 | + | 0.956127i | \(0.405362\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −532.610 | −0.853936 | −0.426968 | − | 0.904267i | \(-0.640418\pi\) | ||||
−0.426968 | + | 0.904267i | \(0.640418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 373.874 | 0.575617 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1370.63 | 2.02854 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −166.561 | −0.237210 | −0.118605 | − | 0.992942i | \(-0.537842\pi\) | ||||
−0.118605 | + | 0.992942i | \(0.537842\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −361.934 | −0.478644 | −0.239322 | − | 0.970940i | \(-0.576925\pi\) | ||||
−0.239322 | + | 0.970940i | \(0.576925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.8957 | 0.0368727 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 31.2750 | 0.0385405 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −40.3285 | −0.0480316 | −0.0240158 | − | 0.999712i | \(-0.507645\pi\) | ||||
−0.0240158 | + | 0.999712i | \(0.507645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1203.31 | 1.38616 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 662.642 | 0.738846 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.8678 | 0.0192968 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −614.921 | −0.643667 | −0.321834 | − | 0.946796i | \(-0.604299\pi\) | ||||
−0.321834 | + | 0.946796i | \(0.604299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 542.367 | 0.550605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1664.99 | 1.64033 | 0.820163 | − | 0.572130i | \(-0.193883\pi\) | ||||
0.820163 | + | 0.572130i | \(0.193883\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −396.858 | −0.379647 | −0.189823 | − | 0.981818i | \(-0.560792\pi\) | ||||
−0.189823 | + | 0.981818i | \(0.560792\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −41.8034 | −0.0388532 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 350.630 | 0.316791 | 0.158396 | − | 0.987376i | \(-0.449368\pi\) | ||||
0.158396 | + | 0.987376i | \(0.449368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 597.009 | 0.524615 | 0.262308 | − | 0.964984i | \(-0.415516\pi\) | ||||
0.262308 | + | 0.964984i | \(0.415516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1225.04 | −1.04753 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 496.422 | 0.413270 | 0.206635 | − | 0.978418i | \(-0.433749\pi\) | ||||
0.206635 | + | 0.978418i | \(0.433749\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −67.0792 | −0.0543928 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 476.155 | 0.376244 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1072.71 | 0.826346 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2300.63 | 1.72849 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1082.23 | −0.793342 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −152.935 | −0.109432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1799.85 | 1.25756 | 0.628782 | − | 0.777581i | \(-0.283554\pi\) | ||||
0.628782 | + | 0.777581i | \(0.283554\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 709.241 | 0.484071 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1121.45 | 0.747949 | 0.373974 | − | 0.927439i | \(-0.377995\pi\) | ||||
0.373974 | + | 0.927439i | \(0.377995\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 663.316 | 0.432457 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.5419 | −0.0105459 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2449.55 | −1.52759 | −0.763793 | − | 0.645461i | \(-0.776665\pi\) | ||||
−0.763793 | + | 0.645461i | \(0.776665\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2457.56 | −1.49962 | −0.749811 | − | 0.661652i | \(-0.769856\pi\) | ||||
−0.749811 | + | 0.661652i | \(0.769856\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −387.339 | −0.231346 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3188.28 | 1.86446 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.38698 | −0.00365800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −522.888 | −0.293382 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2084.96 | 1.14635 | 0.573177 | − | 0.819432i | \(-0.305711\pi\) | ||||
0.573177 | + | 0.819432i | \(0.305711\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1057.80 | −0.570084 | −0.285042 | − | 0.958515i | \(-0.592008\pi\) | ||||
−0.285042 | + | 0.958515i | \(0.592008\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 424.478 | 0.224294 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −135.325 | −0.0701262 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3193.01 | 1.62312 | 0.811559 | − | 0.584270i | \(-0.198619\pi\) | ||||
0.811559 | + | 0.584270i | \(0.198619\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −353.458 | −0.176296 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2490.22 | −1.21899 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −846.854 | −0.406937 | −0.203469 | − | 0.979081i | \(-0.565221\pi\) | ||||
−0.203469 | + | 0.979081i | \(0.565221\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −110.762 | −0.0522596 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2630.15 | 1.21873 | 0.609363 | − | 0.792892i | \(-0.291425\pi\) | ||||
0.609363 | + | 0.792892i | \(0.291425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 602.062 | 0.274038 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 262.478 | 0.117381 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 429.843 | 0.188904 | 0.0944519 | − | 0.995529i | \(-0.469890\pi\) | ||||
0.0944519 | + | 0.995529i | \(0.469890\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2834.48 | −1.22438 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 788.563 | 0.334870 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1516.30 | −0.633149 | −0.316574 | − | 0.948568i | \(-0.602533\pi\) | ||||
−0.316574 | + | 0.948568i | \(0.602533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3380.20 | 1.38811 | 0.694056 | − | 0.719921i | \(-0.255822\pi\) | ||||
0.694056 | + | 0.719921i | \(0.255822\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −820.394 | −0.331395 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 250.179 | 0.0994244 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2842.26 | 1.11148 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −614.092 | −0.236342 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2799.71 | −1.06063 | −0.530314 | − | 0.847801i | \(-0.677926\pi\) | ||||
−0.530314 | + | 0.847801i | \(0.677926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 624.106 | 0.232768 | 0.116384 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116384 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −97.2406 | −0.0357105 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4779.25 | −1.72846 | −0.864232 | − | 0.503094i | \(-0.832195\pi\) | ||||
−0.864232 | + | 0.503094i | \(0.832195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2615.92 | −0.931846 | −0.465923 | − | 0.884825i | \(-0.654278\pi\) | ||||
−0.465923 | + | 0.884825i | \(0.654278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −268.223 | −0.0941244 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −237.107 | −0.0819787 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 221.013 | 0.0752985 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −985.395 | −0.330868 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1757.52 | 0.581677 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1745.78 | −0.569595 | −0.284798 | − | 0.958588i | \(-0.591926\pi\) | ||||
−0.284798 | + | 0.958588i | \(0.591926\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1051.56 | −0.338272 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −144.841 | −0.0459447 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5023.74 | −1.57158 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1597.83 | 0.493020 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2495.28 | 0.759505 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3385.60 | −1.01667 | −0.508333 | − | 0.861161i | \(-0.669738\pi\) | ||||
−0.508333 | + | 0.861161i | \(0.669738\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1121.62 | −0.332332 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3847.72 | 1.12503 | 0.562515 | − | 0.826787i | \(-0.309834\pi\) | ||||
0.562515 | + | 0.826787i | \(0.309834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1335.15 | −0.385279 | −0.192640 | − | 0.981270i | \(-0.561705\pi\) | ||||
−0.192640 | + | 0.981270i | \(0.561705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4111.89 | −1.17118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5146.38 | 1.44700 | 0.723499 | − | 0.690325i | \(-0.242532\pi\) | ||||
0.723499 | + | 0.690325i | \(0.242532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 79.1025 | 0.0219578 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 499.683 | 0.136953 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7085.07 | 1.91755 | 0.958777 | − | 0.284160i | \(-0.0917146\pi\) | ||||
0.958777 | + | 0.284160i | \(0.0917146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2538.40 | 0.678476 | 0.339238 | − | 0.940701i | \(-0.389831\pi\) | ||||
0.339238 | + | 0.940701i | \(0.389831\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 106.784 | 0.0278458 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1542.97 | 0.397477 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1085.80 | 0.276345 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1696.99 | 0.426746 | 0.213373 | − | 0.976971i | \(-0.431555\pi\) | ||||
0.213373 | + | 0.976971i | \(0.431555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6598.09 | −1.63960 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −86.6871 | −0.0212885 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −382.902 | −0.0929369 | −0.0464685 | − | 0.998920i | \(-0.514797\pi\) | ||||
−0.0464685 | + | 0.998920i | \(0.514797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9287.52 | 2.22818 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −93.8249 | −0.0222514 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5002.02 | 1.17277 | 0.586383 | − | 0.810034i | \(-0.300551\pi\) | ||||
0.586383 | + | 0.810034i | \(0.300551\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 72.1833 | 0.0167328 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 120.986 | 0.0277311 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6117.47 | −1.38658 | −0.693288 | − | 0.720661i | \(-0.743839\pi\) | ||||
−0.693288 | + | 0.720661i | \(0.743839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3956.12 | −0.886780 | −0.443390 | − | 0.896329i | \(-0.646224\pi\) | ||||
−0.443390 | + | 0.896329i | \(0.646224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3609.92 | −0.800301 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7510.25 | −1.64686 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4842.17 | −1.05032 | −0.525158 | − | 0.851004i | \(-0.675994\pi\) | ||||
−0.525158 | + | 0.851004i | \(0.675994\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1987.92 | −0.426573 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1878.68 | −0.398835 | −0.199417 | − | 0.979915i | \(-0.563905\pi\) | ||||
−0.199417 | + | 0.979915i | \(0.563905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5724.87 | −1.20250 | −0.601251 | − | 0.799060i | \(-0.705331\pi\) | ||||
−0.601251 | + | 0.799060i | \(0.705331\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −53.6034 | −0.0111410 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8204.77 | 1.68750 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2688.53 | −0.547228 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1844.76 | 0.371622 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5088.75 | 1.01464 | 0.507318 | − | 0.861759i | \(-0.330637\pi\) | ||||
0.507318 | + | 0.861759i | \(0.330637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −161.041 | −0.0317836 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1627.10 | −0.317892 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5792.61 | −1.12038 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5377.02 | −1.02966 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4994.98 | −0.947043 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 167.541 | 0.0314537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7219.21 | −1.34209 | −0.671046 | − | 0.741416i | \(-0.734155\pi\) | ||||
−0.671046 | + | 0.741416i | \(0.734155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1190.58 | 0.219189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1537.06 | 0.280252 | 0.140126 | − | 0.990134i | \(-0.455249\pi\) | ||||
0.140126 | + | 0.990134i | \(0.455249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2200.93 | 0.397456 | 0.198728 | − | 0.980055i | \(-0.436319\pi\) | ||||
0.198728 | + | 0.980055i | \(0.436319\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 125.410 | 0.0224319 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2840.41 | −0.503260 | −0.251630 | − | 0.967824i | \(-0.580967\pi\) | ||||
−0.251630 | + | 0.967824i | \(0.580967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −628.240 | −0.110266 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1051.89 | −0.182899 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1375.51 | 0.236952 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6593.41 | −1.12534 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1791.03 | −0.302887 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2936.56 | 0.492091 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2118.52 | 0.351795 | 0.175898 | − | 0.984408i | \(-0.443717\pi\) | ||||
0.175898 | + | 0.984408i | \(0.443717\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3675.13 | 0.604792 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 54.7766 | 0.00893364 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −659.599 | −0.106619 | −0.0533096 | − | 0.998578i | \(-0.516977\pi\) | ||||
−0.0533096 | + | 0.998578i | \(0.516977\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1489.27 | −0.238601 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13310.9 | −2.11386 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3837.03 | −0.604023 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 201.238 | 0.0314037 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8377.42 | 1.29603 | 0.648017 | − | 0.761626i | \(-0.275599\pi\) | ||||
0.648017 | + | 0.761626i | \(0.275599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3254.18 | −0.499119 | −0.249559 | − | 0.968360i | \(-0.580286\pi\) | ||||
−0.249559 | + | 0.968360i | \(0.580286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1428.47 | −0.217225 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11117.5 | 1.67627 | 0.838137 | − | 0.545459i | \(-0.183645\pi\) | ||||
0.838137 | + | 0.545459i | \(0.183645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 214.750 | 0.0321064 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3218.13 | −0.477091 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4756.56 | 0.699281 | 0.349640 | − | 0.936884i | \(-0.386304\pi\) | ||||
0.349640 | + | 0.936884i | \(0.386304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6008.45 | −0.875994 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6901.88 | −0.997946 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −326.310 | −0.0467940 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1837.40 | 0.261339 | 0.130670 | − | 0.991426i | \(-0.458287\pi\) | ||||
0.130670 | + | 0.991426i | \(0.458287\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3246.68 | 0.458036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2679.70 | 0.374995 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5598.07 | −0.777097 | −0.388549 | − | 0.921428i | \(-0.627023\pi\) | ||||
−0.388549 | + | 0.921428i | \(0.627023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 458.806 | 0.0631804 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −551.546 | −0.0753476 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3460.18 | 0.468965 | 0.234482 | − | 0.972120i | \(-0.424661\pi\) | ||||
0.234482 | + | 0.972120i | \(0.424661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5399.55 | −0.726055 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5059.63 | 0.675027 | 0.337513 | − | 0.941321i | \(-0.390414\pi\) | ||||
0.337513 | + | 0.941321i | \(0.390414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 839.732 | 0.111160 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2127.72 | −0.279479 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2192.22 | −0.285732 | −0.142866 | − | 0.989742i | \(-0.545632\pi\) | ||||
−0.142866 | + | 0.989742i | \(0.545632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5163.93 | −0.667906 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3364.34 | −0.431828 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −102.045 | −0.0129986 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5519.94 | 0.697828 | 0.348914 | − | 0.937155i | \(-0.386551\pi\) | ||||
0.348914 | + | 0.937155i | \(0.386551\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1989.95 | −0.249679 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7352.64 | −0.915645 | −0.457822 | − | 0.889044i | \(-0.651370\pi\) | ||||
−0.457822 | + | 0.889044i | \(0.651370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11685.9 | −1.44446 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 49.6256 | 0.00608868 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24608.2 | 2.99702 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11311.2 | 1.36749 | 0.683745 | − | 0.729721i | \(-0.260350\pi\) | ||||
0.683745 | + | 0.729721i | \(0.260350\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7348.66 | 0.881952 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5978.40 | −0.712295 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −221.743 | −0.0262288 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7372.68 | 0.865808 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13042.2 | 1.52065 | 0.760325 | − | 0.649543i | \(-0.225040\pi\) | ||||
0.760325 | + | 0.649543i | \(0.225040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4544.38 | 0.526080 | 0.263040 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263040 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1162.02 | 0.133568 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5877.83 | −0.670863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6219.72 | 0.704903 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9564.85 | −1.07645 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7713.83 | 0.862093 | 0.431047 | − | 0.902330i | \(-0.358144\pi\) | ||||
0.431047 | + | 0.902330i | \(0.358144\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15068.3 | −1.67237 | −0.836183 | − | 0.548451i | \(-0.815218\pi\) | ||||
−0.836183 | + | 0.548451i | \(0.815218\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.1609 | 0.00211195 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3193.14 | −0.349540 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11004.7 | −1.19642 | −0.598208 | − | 0.801341i | \(-0.704120\pi\) | ||||
−0.598208 | + | 0.801341i | \(0.704120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1568.67 | 0.169384 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2513.04 | −0.269522 | −0.134761 | − | 0.990878i | \(-0.543027\pi\) | ||||
−0.134761 | + | 0.990878i | \(0.543027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.7077 | −0.00263204 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6254.89 | −0.661848 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15752.7 | −1.65571 | −0.827855 | − | 0.560942i | \(-0.810439\pi\) | ||||
−0.827855 | + | 0.560942i | \(0.810439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21739.4 | 2.26977 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3173.40 | 0.329138 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 737.218 | 0.0759590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5257.06 | 0.538107 | 0.269053 | − | 0.963125i | \(-0.413289\pi\) | ||||
0.269053 | + | 0.963125i | \(0.413289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1273.43 | −0.129496 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8066.31 | −0.814936 | −0.407468 | − | 0.913220i | \(-0.633588\pi\) | ||||
−0.407468 | + | 0.913220i | \(0.633588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5683.43 | 0.570478 | 0.285239 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285239 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 405.975 | 0.0404874 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11139.3 | −1.10378 | −0.551891 | − | 0.833916i | \(-0.686094\pi\) | ||||
−0.551891 | + | 0.833916i | \(0.686094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2033.50 | 0.200210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9579.02 | −0.937108 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14247.0 | −1.38494 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3634.59 | −0.351087 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1060.37 | 0.101784 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3477.35 | 0.331699 | 0.165850 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165850 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21604.1 | 2.04795 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7470.65 | 0.703782 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −376.738 | −0.0352717 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 478.797 | 0.0445510 | 0.0222755 | − | 0.999752i | \(-0.492909\pi\) | ||||
0.0222755 | + | 0.999752i | \(0.492909\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2540.56 | 0.234945 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16601.8 | −1.52592 | −0.762961 | − | 0.646444i | \(-0.776255\pi\) | ||||
−0.762961 | + | 0.646444i | \(0.776255\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −491.687 | −0.0449178 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 332.287 | 0.0301721 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7972.29 | 0.719530 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9482.20 | −0.850664 | −0.425332 | − | 0.905037i | \(-0.639843\pi\) | ||||
−0.425332 | + | 0.905037i | \(0.639843\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7890.45 | −0.703631 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16561.2 | −1.46805 | −0.734023 | − | 0.679124i | \(-0.762360\pi\) | ||||
−0.734023 | + | 0.679124i | \(0.762360\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1020.08 | 0.0898867 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1806.19 | −0.158216 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4197.35 | 0.365509 | 0.182755 | − | 0.983159i | \(-0.441499\pi\) | ||||
0.182755 | + | 0.983159i | \(0.441499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12113.8 | −1.04869 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −787.435 | −0.0677702 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −243.140 | −0.0208039 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7780.73 | 0.661888 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1289.53 | −0.109064 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15755.5 | 1.32488 | 0.662440 | − | 0.749115i | \(-0.269521\pi\) | ||||
0.662440 | + | 0.749115i | \(0.269521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11555.1 | −0.966098 | −0.483049 | − | 0.875593i | \(-0.660471\pi\) | ||||
−0.483049 | + | 0.875593i | \(0.660471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8503.44 | 0.706897 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10417.7 | −0.861102 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −179.314 | −0.0147378 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2365.69 | −0.193337 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19085.5 | 1.55100 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 214.817 | 0.0173595 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4548.90 | 0.365549 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10503.6 | 0.839373 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7475.65 | 0.594091 | 0.297045 | − | 0.954863i | \(-0.403999\pi\) | ||||
0.297045 | + | 0.954863i | \(0.403999\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10140.6 | −0.801427 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 365.764 | 0.0287479 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6028.08 | −0.471192 | −0.235596 | − | 0.971851i | \(-0.575704\pi\) | ||||
−0.235596 | + | 0.971851i | \(0.575704\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2461.18 | 0.191331 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −304.037 | −0.0235071 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3788.29 | −0.291310 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −750.536 | −0.0574027 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19381.5 | 1.47436 | 0.737181 | − | 0.675696i | \(-0.236157\pi\) | ||||
0.737181 | + | 0.675696i | \(0.236157\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12507.7 | −0.946370 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8526.77 | −0.641712 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20565.0 | −1.53946 | −0.769728 | − | 0.638372i | \(-0.779608\pi\) | ||||
−0.769728 | + | 0.638372i | \(0.779608\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 304.139 | 0.0226464 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1842.28 | 0.136452 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15252.9 | −1.12379 | −0.561895 | − | 0.827209i | \(-0.689927\pi\) | ||||
−0.561895 | + | 0.827209i | \(0.689927\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16492.8 | 1.20876 | 0.604379 | − | 0.796697i | \(-0.293421\pi\) | ||||
0.604379 | + | 0.796697i | \(0.293421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8399.13 | 0.612354 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13644.9 | 0.989623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10298.2 | −0.743016 | −0.371508 | − | 0.928430i | \(-0.621159\pi\) | ||||
−0.371508 | + | 0.928430i | \(0.621159\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1872.32 | −0.134388 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8231.89 | −0.587808 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7100.14 | 0.504387 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 291.722 | 0.0206175 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13104.8 | 0.921453 | 0.460727 | − | 0.887542i | \(-0.347589\pi\) | ||||
0.460727 | + | 0.887542i | \(0.347589\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6441.82 | −0.450646 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14337.7 | 0.997929 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4163.34 | 0.288310 | 0.144155 | − | 0.989555i | \(-0.453954\pi\) | ||||
0.144155 | + | 0.989555i | \(0.453954\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 657.208 | 0.0452822 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7847.75 | 0.538001 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5718.60 | 0.390076 | 0.195038 | − | 0.980796i | \(-0.437517\pi\) | ||||
0.195038 | + | 0.980796i | \(0.437517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17473.0 | −1.18592 | −0.592959 | − | 0.805233i | \(-0.702040\pi\) | ||||
−0.592959 | + | 0.805233i | \(0.702040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 804.670 | 0.0543428 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1409.50 | 0.0947181 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5647.60 | −0.377643 | −0.188821 | − | 0.982011i | \(-0.560467\pi\) | ||||
−0.188821 | + | 0.982011i | \(0.560467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 711.322 | 0.0473304 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6830.87 | 0.452287 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16023.6 | −1.05577 | −0.527884 | − | 0.849317i | \(-0.677014\pi\) | ||||
−0.527884 | + | 0.849317i | \(0.677014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −663.038 | −0.0434736 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21022.1 | 1.37167 | 0.685834 | − | 0.727758i | \(-0.259438\pi\) | ||||
0.685834 | + | 0.727758i | \(0.259438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17824.2 | −1.15737 | −0.578686 | − | 0.815550i | \(-0.696434\pi\) | ||||
−0.578686 | + | 0.815550i | \(0.696434\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2956.18 | 0.191027 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −917.238 | −0.0589861 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15484.4 | 0.991001 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5272.57 | −0.335831 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19259.4 | 1.22086 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22339.0 | 1.40935 | 0.704677 | − | 0.709528i | \(-0.251092\pi\) | ||||
0.704677 | + | 0.709528i | \(0.251092\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5237.35 | 0.328856 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1102.70 | 0.0689121 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9221.34 | 0.573568 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3154.69 | 0.195301 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5268.43 | −0.324634 | −0.162317 | − | 0.986739i | \(-0.551897\pi\) | ||||
−0.162317 | + | 0.986739i | \(0.551897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21965.8 | 1.34719 | 0.673597 | − | 0.739099i | \(-0.264748\pi\) | ||||
0.673597 | + | 0.739099i | \(0.264748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 434.524 | 0.0265262 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3165.40 | −0.192341 | −0.0961706 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961706 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15840.4 | −0.958073 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15071.2 | 0.907354 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12094.7 | 0.724814 | 0.362407 | − | 0.932020i | \(-0.381955\pi\) | ||||
0.362407 | + | 0.932020i | \(0.381955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 687.067 | 0.0409861 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4793.49 | −0.284645 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7523.17 | 0.444706 | 0.222353 | − | 0.974966i | \(-0.428626\pi\) | ||||
0.222353 | + | 0.974966i | \(0.428626\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24141.1 | 1.42054 | 0.710271 | − | 0.703928i | \(-0.248572\pi\) | ||||
0.710271 | + | 0.703928i | \(0.248572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7485.84 | −0.438501 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 406.388 | 0.0236978 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1141.41 | 0.0662604 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10156.8 | 0.586972 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16479.8 | 0.948130 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 944.143 | 0.0540773 | 0.0270387 | − | 0.999634i | \(-0.491392\pi\) | ||||
0.0270387 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3364.87 | 0.191872 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4450.51 | 0.252654 | 0.126327 | − | 0.991989i | \(-0.459681\pi\) | ||||
0.126327 | + | 0.991989i | \(0.459681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13985.8 | −0.790468 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11543.1 | −0.649536 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1726.40 | −0.0967189 | −0.0483594 | − | 0.998830i | \(-0.515399\pi\) | ||||
−0.0483594 | + | 0.998830i | \(0.515399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1500.75 | −0.0837088 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4005.44 | 0.222441 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6233.37 | 0.344662 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 683.143 | 0.0376092 | 0.0188046 | − | 0.999823i | \(-0.494014\pi\) | ||||
0.0188046 | + | 0.999823i | \(0.494014\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12335.7 | 0.676181 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1505.65 | −0.0821764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17014.1 | 0.924614 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15439.1 | −0.835425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19533.2 | 1.05244 | 0.526220 | − | 0.850349i | \(-0.323609\pi\) | ||||
0.526220 | + | 0.850349i | \(0.323609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11909.2 | 0.638922 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −237.307 | −0.0126773 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37868.8 | 2.01443 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26081.9 | 1.38156 | 0.690779 | − | 0.723066i | \(-0.257268\pi\) | ||||
0.690779 | + | 0.723066i | \(0.257268\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1499.05 | −0.0790699 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24183.8 | 1.27025 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1953.34 | 0.102169 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21255.2 | −1.10710 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30077.3 | −1.56007 | −0.780036 | − | 0.625734i | \(-0.784800\pi\) | ||||
−0.780036 | + | 0.625734i | \(0.784800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9026.21 | −0.466232 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7615.20 | −0.391718 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1299.21 | 0.0665537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23049.9 | −1.17589 | −0.587946 | − | 0.808900i | \(-0.700063\pi\) | ||||
−0.587946 | + | 0.808900i | \(0.700063\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11150.3 | −0.564169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4444.57 | 0.223962 | 0.111981 | − | 0.993710i | \(-0.464280\pi\) | ||||
0.111981 | + | 0.993710i | \(0.464280\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −320.353 | −0.0160768 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5387.98 | 0.269293 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28465.1 | −1.41692 | −0.708462 | − | 0.705749i | \(-0.750610\pi\) | ||||
−0.708462 | + | 0.705749i | \(0.750610\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4628.91 | −0.229483 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4389.76 | −0.216749 | −0.108374 | − | 0.994110i | \(-0.534565\pi\) | ||||
−0.108374 | + | 0.994110i | \(0.534565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1277.38 | 0.0628180 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3257.41 | −0.159548 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7974.77 | 0.389041 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14121.9 | 0.686171 | 0.343085 | − | 0.939304i | \(-0.388528\pi\) | ||||
0.343085 | + | 0.939304i | \(0.388528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5090.98 | −0.246382 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −648.074 | −0.0312395 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17006.3 | 0.816516 | 0.408258 | − | 0.912866i | \(-0.366136\pi\) | ||||
0.408258 | + | 0.912866i | \(0.366136\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19794.3 | 0.946622 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4603.38 | 0.219280 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13578.5 | 0.644264 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 260.061 | 0.0122909 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13906.6 | −0.654679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12459.1 | −0.584248 | −0.292124 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292124 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1148.71 | 0.0536571 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27068.1 | 1.25947 | 0.629737 | − | 0.776808i | \(-0.283163\pi\) | ||||
0.629737 | + | 0.776808i | \(0.283163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27527.2 | 1.27588 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −27862.6 | −1.28644 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10520.8 | 0.483884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21123.4 | 0.967804 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 281.475 | 0.0128468 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1956.23 | 0.0889438 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6986.86 | −0.316461 | −0.158230 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158230 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15006.1 | −0.677097 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11290.7 | 0.507523 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14468.0 | 0.647885 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −216.550 | −0.00966067 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27271.5 | −1.21205 | −0.606027 | − | 0.795444i | \(-0.707238\pi\) | ||||
−0.606027 | + | 0.795444i | \(0.707238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6089.52 | 0.269627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −362.957 | −0.0160105 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32096.7 | −1.41054 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1525.66 | −0.0667981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18352.4 | 0.800540 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23785.9 | −1.03371 | −0.516853 | − | 0.856074i | \(-0.672897\pi\) | ||||
−0.516853 | + | 0.856074i | \(0.672897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21703.5 | −0.939718 | −0.469859 | − | 0.882741i | \(-0.655695\pi\) | ||||
−0.469859 | + | 0.882741i | \(0.655695\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11868.4 | 0.511982 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −518.835 | −0.0222994 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6894.83 | −0.295250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10829.7 | 0.462054 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33240.4 | −1.41303 | −0.706515 | − | 0.707698i | \(-0.749734\pi\) | ||||
−0.706515 | + | 0.707698i | \(0.749734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17227.5 | 0.729665 | 0.364832 | − | 0.931073i | \(-0.381126\pi\) | ||||
0.364832 | + | 0.931073i | \(0.381126\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22530.8 | 0.950812 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21678.4 | −0.911528 | −0.455764 | − | 0.890101i | \(-0.650634\pi\) | ||||
−0.455764 | + | 0.890101i | \(0.650634\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34269.8 | 1.43575 | 0.717877 | − | 0.696170i | \(-0.245114\pi\) | ||||
0.717877 | + | 0.696170i | \(0.245114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14526.5 | 0.606401 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8220.55 | 0.341927 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1611.39 | 0.0667838 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5963.77 | 0.246282 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33444.1 | −1.37618 | −0.688092 | − | 0.725623i | \(-0.741552\pi\) | ||||
−0.688092 | + | 0.725623i | \(0.741552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24280.3 | −0.995544 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5636.04 | 0.230267 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 368.860 | 0.0150168 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52325.8 | 2.12271 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17174.6 | 0.694265 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44709.3 | −1.80096 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37037.3 | −1.48667 | −0.743337 | − | 0.668917i | \(-0.766758\pi\) | ||||
−0.743337 | + | 0.668917i | \(0.766758\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 160.810 | 0.00643227 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35794.2 | −1.42673 | −0.713365 | − | 0.700793i | \(-0.752830\pi\) | ||||
−0.713365 | + | 0.700793i | \(0.752830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20582.1 | 0.817522 | 0.408761 | − | 0.912641i | \(-0.365961\pi\) | ||||
0.408761 | + | 0.912641i | \(0.365961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24614.3 | −0.974278 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25677.7 | −1.01284 | −0.506420 | − | 0.862287i | \(-0.669031\pi\) | ||||
−0.506420 | + | 0.862287i | \(0.669031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 263.348 | 0.0103516 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8065.60 | 0.315942 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10037.5 | −0.391827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4730.22 | 0.184015 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5534.29 | −0.214556 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3478.38 | −0.134389 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32783.0 | 1.26226 | 0.631131 | − | 0.775676i | \(-0.282591\pi\) | ||||
0.631131 | + | 0.775676i | \(0.282591\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15266.3 | −0.585800 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26615.7 | 1.01783 | 0.508914 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508914 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19203.4 | 0.731875 | 0.365937 | − | 0.930639i | \(-0.380748\pi\) | ||||
0.365937 | + | 0.930639i | \(0.380748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 483.122 | 0.0183503 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23198.0 | −0.878144 | −0.439072 | − | 0.898452i | \(-0.644693\pi\) | ||||
−0.439072 | + | 0.898452i | \(0.644693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40936.0 | 1.54438 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4881.30 | 0.183535 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3765.48 | 0.141105 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −928.979 | −0.0346953 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17377.8 | 0.646854 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2302.68 | 0.0854266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5556.86 | 0.205467 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16131.1 | 0.594472 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2070.92 | 0.0760659 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16151.3 | 0.591285 | 0.295643 | − | 0.955299i | \(-0.404466\pi\) | ||||
0.295643 | + | 0.955299i | \(0.404466\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14984.9 | 0.546776 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3487.34 | −0.126829 | −0.0634143 | − | 0.997987i | \(-0.520199\pi\) | ||||
−0.0634143 | + | 0.997987i | \(0.520199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21811.2 | −0.790632 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −502.624 | −0.0181598 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25506.3 | 0.918532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17055.5 | −0.612198 | −0.306099 | − | 0.952000i | \(-0.599024\pi\) | ||||
−0.306099 | + | 0.952000i | \(0.599024\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21657.6 | 0.774857 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18544.7 | 0.661329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50890.2 | −1.80893 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3571.73 | −0.126549 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55339.3 | −1.95438 | −0.977192 | − | 0.212359i | \(-0.931885\pi\) | ||||
−0.977192 | + | 0.212359i | \(0.931885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5083.22 | 0.178943 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4611.17 | −0.161804 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1741.34 | 0.0609069 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20457.6 | 0.713255 | 0.356627 | − | 0.934247i | \(-0.383927\pi\) | ||||
0.356627 | + | 0.934247i | \(0.383927\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6602.78 | −0.229471 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55891.0 | −1.93623 | −0.968116 | − | 0.250502i | \(-0.919404\pi\) | ||||
−0.968116 | + | 0.250502i | \(0.919404\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39497.0 | −1.36395 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −376.230 | −0.0129511 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54727.0 | 1.87792 | 0.938960 | − | 0.344027i | \(-0.111791\pi\) | ||||
0.938960 | + | 0.344027i | \(0.111791\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28178.4 | −0.963865 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8521.23 | 0.290557 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29958.8 | −1.01832 | −0.509160 | − | 0.860672i | \(-0.670044\pi\) | ||||
−0.509160 | + | 0.860672i | \(0.670044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1715.27 | −0.0581204 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1884.72 | 0.0636619 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −55713.0 | −1.87598 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18997.2 | 0.637682 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3155.67 | 0.105597 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 382.365 | 0.0127552 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13498.5 | −0.448896 | −0.224448 | − | 0.974486i | \(-0.572058\pi\) | ||||
−0.224448 | + | 0.974486i | \(0.572058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4126.53 | −0.136804 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9652.36 | 0.319010 | 0.159505 | − | 0.987197i | \(-0.449010\pi\) | ||||
0.159505 | + | 0.987197i | \(0.449010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −55895.1 | −1.84164 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19780.2 | 0.649717 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12169.8 | 0.398511 | 0.199256 | − | 0.979948i | \(-0.436148\pi\) | ||||
0.199256 | + | 0.979948i | \(0.436148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2430.32 | −0.0793394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5373.08 | 0.174872 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47545.2 | −1.54268 | −0.771341 | − | 0.636423i | \(-0.780413\pi\) | ||||
−0.771341 | + | 0.636423i | \(0.780413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2928.06 | −0.0947165 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8809.69 | −0.284109 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25884.5 | 0.832234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −892.350 | −0.0286039 | −0.0143019 | − | 0.999898i | \(-0.504553\pi\) | ||||
−0.0143019 | + | 0.999898i | \(0.504553\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6355.55 | −0.203109 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1602.67 | −0.0510634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4458.57 | 0.141629 | 0.0708146 | − | 0.997489i | \(-0.477440\pi\) | ||||
0.0708146 | + | 0.997489i | \(0.477440\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11025.4 | −0.349177 |
(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 | 768.4.a.r.1.2 | 3 | ||
3.2 | odd | 2 | 2304.4.a.bt.1.2 | 3 | |||
4.3 | odd | 2 | 768.4.a.t.1.2 | 3 | |||
8.3 | odd | 2 | 768.4.a.q.1.2 | 3 | |||
8.5 | even | 2 | 768.4.a.s.1.2 | 3 | |||
12.11 | even | 2 | 2304.4.a.bu.1.2 | 3 | |||
16.3 | odd | 4 | 96.4.d.a.49.5 | 6 | |||
16.5 | even | 4 | 24.4.d.a.13.5 | ✓ | 6 | ||
16.11 | odd | 4 | 96.4.d.a.49.2 | 6 | |||
16.13 | even | 4 | 24.4.d.a.13.6 | yes | 6 | ||
24.5 | odd | 2 | 2304.4.a.bv.1.2 | 3 | |||
24.11 | even | 2 | 2304.4.a.bw.1.2 | 3 | |||
48.5 | odd | 4 | 72.4.d.d.37.2 | 6 | |||
48.11 | even | 4 | 288.4.d.d.145.3 | 6 | |||
48.29 | odd | 4 | 72.4.d.d.37.1 | 6 | |||
48.35 | even | 4 | 288.4.d.d.145.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.4.d.a.13.5 | ✓ | 6 | 16.5 | even | 4 | ||
24.4.d.a.13.6 | yes | 6 | 16.13 | even | 4 | ||
72.4.d.d.37.1 | 6 | 48.29 | odd | 4 | |||
72.4.d.d.37.2 | 6 | 48.5 | odd | 4 | |||
96.4.d.a.49.2 | 6 | 16.11 | odd | 4 | |||
96.4.d.a.49.5 | 6 | 16.3 | odd | 4 | |||
288.4.d.d.145.3 | 6 | 48.11 | even | 4 | |||
288.4.d.d.145.4 | 6 | 48.35 | even | 4 | |||
768.4.a.q.1.2 | 3 | 8.3 | odd | 2 | |||
768.4.a.r.1.2 | 3 | 1.1 | even | 1 | trivial | ||
768.4.a.s.1.2 | 3 | 8.5 | even | 2 | |||
768.4.a.t.1.2 | 3 | 4.3 | odd | 2 | |||
2304.4.a.bt.1.2 | 3 | 3.2 | odd | 2 | |||
2304.4.a.bu.1.2 | 3 | 12.11 | even | 2 | |||
2304.4.a.bv.1.2 | 3 | 24.5 | odd | 2 | |||
2304.4.a.bw.1.2 | 3 | 24.11 | even | 2 |