Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{177}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.15207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-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 | ||||||||
\(5\) | −20.3041 | −1.81606 | −0.908029 | − | 0.418908i | \(-0.862413\pi\) | ||||
−0.908029 | + | 0.418908i | \(0.862413\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.9124 | −0.847313 | −0.423656 | − | 0.905823i | \(-0.639254\pi\) | ||||
−0.423656 | + | 0.905823i | \(0.639254\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.6083 | −1.07971 | −0.539854 | − | 0.841759i | \(-0.681521\pi\) | ||||
−0.539854 | + | 0.841759i | \(0.681521\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 60.9124 | 1.04850 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 102.737 | 1.46573 | 0.732866 | − | 0.680373i | \(-0.238182\pi\) | ||||
0.732866 | + | 0.680373i | \(0.238182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 61.2165 | 0.739160 | 0.369580 | − | 0.929199i | \(-0.379502\pi\) | ||||
0.369580 | + | 0.929199i | \(0.379502\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 148.129 | 1.34291 | 0.671457 | − | 0.741044i | \(-0.265669\pi\) | ||||
0.671457 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 287.258 | 2.29806 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 159.217 | 1.01951 | 0.509755 | − | 0.860320i | \(-0.329736\pi\) | ||||
0.509755 | + | 0.860320i | \(0.329736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 121.217 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 92.7372 | 0.489196 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −357.908 | −1.59026 | −0.795130 | − | 0.606439i | \(-0.792598\pi\) | ||||
−0.795130 | + | 0.606439i | \(0.792598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 151.825 | 0.623370 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −466.737 | −1.77786 | −0.888928 | − | 0.458047i | \(-0.848549\pi\) | ||||
−0.888928 | + | 0.458047i | \(0.848549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −185.567 | −0.658109 | −0.329055 | − | 0.944311i | \(-0.606730\pi\) | ||||
−0.329055 | + | 0.944311i | \(0.606730\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −182.737 | −0.605352 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 131.392 | 0.407776 | 0.203888 | − | 0.978994i | \(-0.434642\pi\) | ||||
0.203888 | + | 0.978994i | \(0.434642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −308.212 | −0.846240 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 200.175 | 0.518796 | 0.259398 | − | 0.965771i | \(-0.416476\pi\) | ||||
0.259398 | + | 0.965771i | \(0.416476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 627.650 | 1.53877 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −183.650 | −0.426754 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 591.908 | 1.30610 | 0.653049 | − | 0.757316i | \(-0.273490\pi\) | ||||
0.653049 | + | 0.757316i | \(0.273490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −70.5158 | −0.148010 | −0.0740051 | − | 0.997258i | \(-0.523578\pi\) | ||||
−0.0740051 | + | 0.997258i | \(0.523578\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1027.56 | 1.96081 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −643.041 | −1.17254 | −0.586269 | − | 0.810117i | \(-0.699404\pi\) | ||||
−0.586269 | + | 0.810117i | \(0.699404\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −444.387 | −0.775332 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −522.397 | −0.873198 | −0.436599 | − | 0.899656i | \(-0.643817\pi\) | ||||
−0.436599 | + | 0.899656i | \(0.643817\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 576.175 | 0.923784 | 0.461892 | − | 0.886936i | \(-0.347171\pi\) | ||||
0.461892 | + | 0.886936i | \(0.347171\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −861.774 | −1.32679 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 280.774 | 0.399867 | 0.199934 | − | 0.979809i | \(-0.435927\pi\) | ||||
0.199934 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 557.732 | 0.737579 | 0.368790 | − | 0.929513i | \(-0.379772\pi\) | ||||
0.368790 | + | 0.929513i | \(0.379772\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2085.99 | −2.66185 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −477.650 | −0.588614 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1228.89 | 1.46362 | 0.731811 | − | 0.681508i | \(-0.238675\pi\) | ||||
0.731811 | + | 0.681508i | \(0.238675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −363.650 | −0.405470 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1242.95 | −1.34236 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −65.0413 | −0.0680819 | −0.0340410 | − | 0.999420i | \(-0.510838\pi\) | ||||
−0.0340410 | + | 0.999420i | \(0.510838\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −278.212 | −0.282438 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −303.511 | −0.299014 | −0.149507 | − | 0.988761i | \(-0.547769\pi\) | ||||
−0.149507 | + | 0.988761i | \(0.547769\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −174.268 | −0.166710 | −0.0833549 | − | 0.996520i | \(-0.526564\pi\) | ||||
−0.0833549 | + | 0.996520i | \(0.526564\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1945.42 | 1.75767 | 0.878835 | − | 0.477126i | \(-0.158321\pi\) | ||||
0.878835 | + | 0.477126i | \(0.158321\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1102.87 | −0.969132 | −0.484566 | − | 0.874755i | \(-0.661023\pi\) | ||||
−0.484566 | + | 0.874755i | \(0.661023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1073.72 | 0.918137 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 80.0827 | 0.0666685 | 0.0333343 | − | 0.999444i | \(-0.489387\pi\) | ||||
0.0333343 | + | 0.999444i | \(0.489387\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3007.63 | −2.43881 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −455.474 | −0.359903 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −375.423 | −0.282061 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1400.21 | 1.02645 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3294.51 | −2.35736 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1981.12 | −1.38422 | −0.692112 | − | 0.721791i | \(-0.743319\pi\) | ||||
−0.692112 | + | 0.721791i | \(0.743319\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 556.701 | 0.379959 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2854.25 | −1.90364 | −0.951820 | − | 0.306658i | \(-0.900789\pi\) | ||||
−0.951820 | + | 0.306658i | \(0.900789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 548.212 | 0.349500 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −535.474 | −0.333932 | −0.166966 | − | 0.985963i | \(-0.553397\pi\) | ||||
−0.166966 | + | 0.985963i | \(0.553397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2326.43 | −1.41961 | −0.709804 | − | 0.704399i | \(-0.751216\pi\) | ||||
−0.709804 | + | 0.704399i | \(0.751216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −394.175 | −0.235429 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1564.42 | 0.914851 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3232.75 | −1.85149 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2061.04 | 1.13320 | 0.566601 | − | 0.823992i | \(-0.308258\pi\) | ||||
0.566601 | + | 0.823992i | \(0.308258\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1113.03 | −0.599849 | −0.299925 | − | 0.953963i | \(-0.596962\pi\) | ||||
−0.299925 | + | 0.953963i | \(0.596962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 924.635 | 0.488577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2461.20 | −1.27541 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1537.30 | 0.781464 | 0.390732 | − | 0.920505i | \(-0.372222\pi\) | ||||
0.390732 | + | 0.920505i | \(0.372222\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −600.526 | −0.299527 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2043.52 | −0.981967 | −0.490984 | − | 0.871169i | \(-0.663363\pi\) | ||||
−0.490984 | + | 0.871169i | \(0.663363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1882.95 | −0.888408 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2513.44 | −1.16464 | −0.582322 | − | 0.812958i | \(-0.697856\pi\) | ||||
−0.582322 | + | 0.812958i | \(0.697856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 364.197 | 0.165770 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 550.949 | 0.246387 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1591.00 | −0.699197 | −0.349599 | − | 0.936900i | \(-0.613682\pi\) | ||||
−0.349599 | + | 0.936900i | \(0.613682\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1775.72 | −0.754076 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2552.27 | 1.06573 | 0.532866 | − | 0.846200i | \(-0.321115\pi\) | ||||
0.532866 | + | 0.846200i | \(0.321115\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3361.33 | 1.38036 | 0.690182 | − | 0.723636i | \(-0.257530\pi\) | ||||
0.690182 | + | 0.723636i | \(0.257530\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 211.547 | 0.0854537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7267.00 | 2.88800 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3175.85 | −1.24193 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3868.64 | −1.46558 | −0.732789 | − | 0.680456i | \(-0.761782\pi\) | ||||
−0.732789 | + | 0.680456i | \(0.761782\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2693.17 | 1.00445 | 0.502224 | − | 0.864738i | \(-0.332515\pi\) | ||||
0.502224 | + | 0.864738i | \(0.332515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3082.67 | −1.13208 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1064.86 | −0.385116 | −0.192558 | − | 0.981286i | \(-0.561678\pi\) | ||||
−0.192558 | + | 0.981286i | \(0.561678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1625.92 | −0.579187 | −0.289594 | − | 0.957150i | \(-0.593520\pi\) | ||||
−0.289594 | + | 0.957150i | \(0.593520\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1929.12 | 0.676965 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9476.70 | 3.22869 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1333.16 | 0.447638 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1892.35 | −0.626300 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1138.04 | 0.371309 | 0.185654 | − | 0.982615i | \(-0.440560\pi\) | ||||
0.185654 | + | 0.982615i | \(0.440560\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1567.19 | 0.504141 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3767.78 | 1.19516 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1728.53 | −0.533347 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5199.35 | −1.58256 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3535.78 | −1.06176 | −0.530881 | − | 0.847446i | \(-0.678139\pi\) | ||||
−0.530881 | + | 0.847446i | \(0.678139\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2585.32 | 0.766021 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3055.21 | 0.893309 | 0.446655 | − | 0.894706i | \(-0.352615\pi\) | ||||
0.446655 | + | 0.894706i | \(0.352615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 321.703 | 0.0928329 | 0.0464164 | − | 0.998922i | \(-0.485220\pi\) | ||||
0.0464164 | + | 0.998922i | \(0.485220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −906.939 | −0.255002 | −0.127501 | − | 0.991838i | \(-0.540696\pi\) | ||||
−0.127501 | + | 0.991838i | \(0.540696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2667.80 | −0.740544 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −842.321 | −0.230863 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4290.84 | −1.16130 | −0.580651 | − | 0.814152i | \(-0.697202\pi\) | ||||
−0.580651 | + | 0.814152i | \(0.697202\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6985.64 | 1.86716 | 0.933579 | − | 0.358373i | \(-0.116668\pi\) | ||||
0.933579 | + | 0.358373i | \(0.116668\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3098.06 | −0.798077 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1673.20 | −0.425842 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5666.63 | 1.42500 | 0.712499 | − | 0.701673i | \(-0.247563\pi\) | ||||
0.712499 | + | 0.701673i | \(0.247563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4579.02 | −1.13787 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6257.97 | 1.53682 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −840.596 | −0.204027 | −0.102013 | − | 0.994783i | \(-0.532528\pi\) | ||||
−0.102013 | + | 0.994783i | \(0.532528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1432.95 | 0.339836 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3386.69 | 0.794039 | 0.397019 | − | 0.917810i | \(-0.370045\pi\) | ||||
0.397019 | + | 0.917810i | \(0.370045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4064.38 | −0.942163 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3686.68 | −0.845023 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7929.42 | −1.79727 | −0.898635 | − | 0.438698i | \(-0.855440\pi\) | ||||
−0.898635 | + | 0.438698i | \(0.855440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5080.25 | −1.13876 | −0.569379 | − | 0.822075i | \(-0.692816\pi\) | ||||
−0.569379 | + | 0.822075i | \(0.692816\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8879.83 | −1.94718 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −195.329 | −0.0423688 | −0.0211844 | − | 0.999776i | \(-0.506744\pi\) | ||||
−0.0211844 | + | 0.999776i | \(0.506744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1090.95 | 0.234098 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4029.83 | 0.855514 | 0.427757 | − | 0.903894i | \(-0.359304\pi\) | ||||
0.427757 | + | 0.903894i | \(0.359304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6927.28 | −1.45507 | −0.727534 | − | 0.686072i | \(-0.759333\pi\) | ||||
−0.727534 | + | 0.686072i | \(0.759333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3728.85 | 0.775010 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5641.93 | 1.14837 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 195.124 | 0.0393071 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 911.009 | 0.181644 | 0.0908221 | − | 0.995867i | \(-0.471051\pi\) | ||||
0.0908221 | + | 0.995867i | \(0.471051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12018.2 | −2.37195 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 834.635 | 0.163065 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7496.55 | −1.44996 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 910.533 | 0.172636 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1431.76 | 0.268795 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3310.72 | −0.615482 | −0.307741 | − | 0.951470i | \(-0.599573\pi\) | ||||
−0.307741 | + | 0.951470i | \(0.599573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 522.803 | 0.0962499 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4979.13 | −0.907847 | −0.453924 | − | 0.891041i | \(-0.649976\pi\) | ||||
−0.453924 | + | 0.891041i | \(0.649976\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5116.19 | 0.923911 | 0.461955 | − | 0.886903i | \(-0.347148\pi\) | ||||
0.461955 | + | 0.886903i | \(0.347148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 978.317 | 0.173337 | 0.0866684 | − | 0.996237i | \(-0.472378\pi\) | ||||
0.0866684 | + | 0.996237i | \(0.472378\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4921.77 | −0.863843 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5836.26 | −1.01479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6289.22 | 1.08341 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14537.6 | −2.48124 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3308.60 | 0.559529 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9092.36 | 1.50985 | 0.754926 | − | 0.655810i | \(-0.227673\pi\) | ||||
0.754926 | + | 0.655810i | \(0.227673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3221.17 | −0.530087 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13056.4 | 2.12939 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −621.406 | −0.100445 | −0.0502227 | − | 0.998738i | \(-0.515993\pi\) | ||||
−0.0502227 | + | 0.998738i | \(0.515993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −240.248 | −0.0384911 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3747.09 | −0.595063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9022.89 | 1.40805 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4276.85 | 0.661652 | 0.330826 | − | 0.943692i | \(-0.392673\pi\) | ||||
0.330826 | + | 0.943692i | \(0.392673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7497.41 | 1.14993 | 0.574967 | − | 0.818177i | \(-0.305015\pi\) | ||||
0.574967 | + | 0.818177i | \(0.305015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1366.42 | 0.207790 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2295.77 | 0.346151 | 0.173076 | − | 0.984909i | \(-0.444629\pi\) | ||||
0.173076 | + | 0.984909i | \(0.444629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10606.8 | 1.58578 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 681.808 | 0.100235 | 0.0501176 | − | 0.998743i | \(-0.484040\pi\) | ||||
0.0501176 | + | 0.998743i | \(0.484040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3111.54 | −0.453643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1126.27 | 0.162848 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11698.7 | −1.67764 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8497.77 | −1.20867 | −0.604333 | − | 0.796732i | \(-0.706560\pi\) | ||||
−0.604333 | + | 0.796732i | \(0.706560\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4200.63 | −0.592619 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12306.1 | 1.70828 | 0.854138 | − | 0.520046i | \(-0.174085\pi\) | ||||
0.854138 | + | 0.520046i | \(0.174085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9883.52 | 1.36102 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8057.67 | −1.10077 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7064.19 | 0.957423 | 0.478711 | − | 0.877972i | \(-0.341104\pi\) | ||||
0.478711 | + | 0.877972i | \(0.341104\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5943.37 | 0.799182 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3082.91 | −0.411304 | −0.205652 | − | 0.978625i | \(-0.565931\pi\) | ||||
−0.205652 | + | 0.978625i | \(0.565931\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1670.10 | −0.219370 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9990.11 | 1.30210 | 0.651052 | − | 0.759033i | \(-0.274328\pi\) | ||||
0.651052 | + | 0.759033i | \(0.274328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15218.4 | 1.96835 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8562.74 | 1.09907 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5700.87 | −0.726182 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8327.91 | −1.05281 | −0.526405 | − | 0.850234i | \(-0.676460\pi\) | ||||
−0.526405 | + | 0.850234i | \(0.676460\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9715.82 | −1.20994 | −0.604969 | − | 0.796249i | \(-0.706815\pi\) | ||||
−0.604969 | + | 0.796249i | \(0.706815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6134.56 | −0.758273 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1644.63 | −0.201784 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11063.8 | 1.34745 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13341.8 | −1.61299 | −0.806493 | − | 0.591244i | \(-0.798637\pi\) | ||||
−0.806493 | + | 0.591244i | \(0.798637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1606.42 | 0.192796 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11324.3 | −1.33949 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6979.30 | 0.819611 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4281.34 | −0.499181 | −0.249591 | − | 0.968351i | \(-0.580296\pi\) | ||||
−0.249591 | + | 0.968351i | \(0.580296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3296.60 | −0.381631 | −0.190815 | − | 0.981626i | \(-0.561113\pi\) | ||||
−0.190815 | + | 0.981626i | \(0.561113\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1182.53 | 0.135925 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29512.1 | 3.36834 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4693.27 | −0.528189 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4122.73 | 0.460754 | 0.230377 | − | 0.973101i | \(-0.426004\pi\) | ||||
0.230377 | + | 0.973101i | \(0.426004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1070.60 | −0.118822 | −0.0594110 | − | 0.998234i | \(-0.518922\pi\) | ||||
−0.0594110 | + | 0.998234i | \(0.518922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9698.26 | 1.06896 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9067.94 | 0.992628 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.22847 | −0.000677150 0 | −0.000338575 | − | 1.00000i | \(-0.500108\pi\) | ||||
−0.000338575 | 1.00000i | \(0.500108\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6835.85 | −0.733140 | −0.366570 | − | 0.930390i | \(-0.619468\pi\) | ||||
−0.366570 | + | 0.930390i | \(0.619468\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24951.6 | −2.65802 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6183.12 | −0.654254 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5590.94 | 0.587646 | 0.293823 | − | 0.955860i | \(-0.405072\pi\) | ||||
0.293823 | + | 0.955860i | \(0.405072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14428.0 | 1.50640 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3339.09 | 0.346323 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7615.65 | −0.779530 | −0.389765 | − | 0.920914i | \(-0.627444\pi\) | ||||
−0.389765 | + | 0.920914i | \(0.627444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2773.90 | −0.282080 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12191.7 | −1.23172 | −0.615860 | − | 0.787855i | \(-0.711192\pi\) | ||||
−0.615860 | + | 0.787855i | \(0.711192\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4210.28 | 0.422610 | 0.211305 | − | 0.977420i | \(-0.432229\pi\) | ||||
0.211305 | + | 0.977420i | \(0.432229\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7383.59 | 0.736357 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16128.2 | −1.59812 | −0.799062 | − | 0.601248i | \(-0.794670\pi\) | ||||
−0.799062 | + | 0.601248i | \(0.794670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4611.90 | −0.451178 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5736.32 | 0.557624 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17584.9 | 1.69864 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1801.58 | 0.172932 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3736.70 | 0.356438 | 0.178219 | − | 0.983991i | \(-0.442966\pi\) | ||||
0.178219 | + | 0.983991i | \(0.442966\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18113.1 | 1.71702 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1320.61 | 0.123641 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15812.5 | 1.47132 | 0.735661 | − | 0.677350i | \(-0.236872\pi\) | ||||
0.735661 | + | 0.677350i | \(0.236872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6130.55 | 0.566939 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2564.56 | 0.235717 | 0.117858 | − | 0.993030i | \(-0.462397\pi\) | ||||
0.117858 | + | 0.993030i | \(0.462397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16357.5 | 1.49433 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5648.85 | 0.512923 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8511.36 | −0.763569 | −0.381784 | − | 0.924251i | \(-0.624690\pi\) | ||||
−0.381784 | + | 0.924251i | \(0.624690\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7540.31 | 0.672407 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6486.89 | −0.575022 | −0.287511 | − | 0.957777i | \(-0.592828\pi\) | ||||
−0.287511 | + | 0.957777i | \(0.592828\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6162.53 | 0.543027 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1092.59 | −0.0957074 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13980.3 | 1.21742 | 0.608710 | − | 0.793393i | \(-0.291687\pi\) | ||||
0.608710 | + | 0.793393i | \(0.291687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1652.85 | −0.142251 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3538.35 | 0.302754 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4061.63 | −0.345513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4772.99 | 0.403682 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10684.8 | 0.898485 | 0.449242 | − | 0.893410i | \(-0.351694\pi\) | ||||
0.449242 | + | 0.893410i | \(0.351694\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2500.29 | −0.209044 | −0.104522 | − | 0.994523i | \(-0.533331\pi\) | ||||
−0.104522 | + | 0.994523i | \(0.533331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12453.4 | 1.02938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9775.18 | 0.803418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5327.17 | 0.435366 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23620.8 | 1.91957 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39500.0 | −3.19203 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7656.82 | −0.615300 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8780.94 | −0.697823 | −0.348911 | − | 0.937156i | \(-0.613449\pi\) | ||||
−0.348911 | + | 0.937156i | \(0.613449\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10084.0 | −0.796954 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22392.7 | 1.76000 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10965.6 | −0.857140 | −0.428570 | − | 0.903509i | \(-0.640982\pi\) | ||||
−0.428570 | + | 0.903509i | \(0.640982\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −634.642 | −0.0493367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9746.69 | 0.753580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21801.0 | −1.66739 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3156.31 | 0.240103 | 0.120051 | − | 0.992768i | \(-0.461694\pi\) | ||||
0.120051 | + | 0.992768i | \(0.461694\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9391.22 | 0.710566 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9527.56 | 0.717030 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16805.3 | 1.25801 | 0.629003 | − | 0.777403i | \(-0.283464\pi\) | ||||
0.629003 | + | 0.777403i | \(0.283464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1626.01 | −0.121074 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16899.6 | −1.24511 | −0.622557 | − | 0.782575i | \(-0.713906\pi\) | ||||
−0.622557 | + | 0.782575i | \(0.713906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7998.44 | −0.586207 | −0.293104 | − | 0.956081i | \(-0.594688\pi\) | ||||
−0.293104 | + | 0.956081i | \(0.594688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11605.9 | 0.846152 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 42551.2 | 3.08610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23385.2 | −1.68724 | −0.843619 | − | 0.536942i | \(-0.819579\pi\) | ||||
−0.843619 | + | 0.536942i | \(0.819579\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8079.50 | −0.579918 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6187.90 | −0.439582 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9248.01 | 0.653604 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7583.02 | 0.533194 | 0.266597 | − | 0.963808i | \(-0.414101\pi\) | ||||
0.266597 | + | 0.963808i | \(0.414101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7420.46 | 0.519108 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3194.57 | 0.222347 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10593.1 | −0.733567 | −0.366783 | − | 0.930306i | \(-0.619541\pi\) | ||||
−0.366783 | + | 0.930306i | \(0.619541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4877.75 | 0.334394 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22125.1 | −1.50919 | −0.754597 | − | 0.656188i | \(-0.772168\pi\) | ||||
−0.754597 | + | 0.656188i | \(0.772168\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19841.6 | 1.34669 | 0.673343 | − | 0.739331i | \(-0.264858\pi\) | ||||
0.673343 | + | 0.739331i | \(0.264858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5787.37 | −0.390846 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7622.64 | 0.512239 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15507.5 | −1.03695 | −0.518475 | − | 0.855093i | \(-0.673500\pi\) | ||||
−0.518475 | + | 0.855093i | \(0.673500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6649.51 | −0.440279 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14042.8 | −0.925255 | −0.462628 | − | 0.886553i | \(-0.653093\pi\) | ||||
−0.462628 | + | 0.886553i | \(0.653093\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −28430.1 | −1.86408 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13175.9 | 0.859708 | 0.429854 | − | 0.902898i | \(-0.358565\pi\) | ||||
0.429854 | + | 0.902898i | \(0.358565\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10828.3 | −0.703109 | −0.351555 | − | 0.936167i | \(-0.614347\pi\) | ||||
−0.351555 | + | 0.936167i | \(0.614347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3999.48 | −0.258444 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30984.9 | 1.98303 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5677.05 | 0.361594 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36770.4 | −2.33089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23922.2 | −1.50923 | −0.754617 | − | 0.656166i | \(-0.772177\pi\) | ||||
−0.754617 | + | 0.656166i | \(0.772177\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3414.13 | −0.214375 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40225.0 | 2.51383 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4701.57 | −0.291066 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21962.6 | −1.35331 | −0.676654 | − | 0.736301i | \(-0.736571\pi\) | ||||
−0.676654 | + | 0.736301i | \(0.736571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17927.1 | −1.09950 | −0.549749 | − | 0.835330i | \(-0.685276\pi\) | ||||
−0.549749 | + | 0.835330i | \(0.685276\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11303.3 | −0.690028 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −850.926 | −0.0517054 | −0.0258527 | − | 0.999666i | \(-0.508230\pi\) | ||||
−0.0258527 | + | 0.999666i | \(0.508230\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18297.3 | −1.10667 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18674.9 | 1.11915 | 0.559575 | − | 0.828780i | \(-0.310964\pi\) | ||||
0.559575 | + | 0.828780i | \(0.310964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57953.0 | 3.45712 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5185.58 | 0.307928 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −777.121 | −0.0459368 | −0.0229684 | − | 0.999736i | \(-0.507312\pi\) | ||||
−0.0229684 | + | 0.999736i | \(0.507312\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21963.4 | −1.29240 | −0.646201 | − | 0.763167i | \(-0.723643\pi\) | ||||
−0.646201 | + | 0.763167i | \(0.723643\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15598.1 | 0.913693 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23584.6 | 1.36911 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10607.3 | 0.613009 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2179.81 | 0.125411 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29380.0 | 1.68279 | 0.841393 | − | 0.540423i | \(-0.181736\pi\) | ||||
0.841393 | + | 0.540423i | \(0.181736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7755.96 | −0.442262 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7898.58 | −0.448400 | −0.224200 | − | 0.974543i | \(-0.571977\pi\) | ||||
−0.224200 | + | 0.974543i | \(0.571977\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9165.62 | −0.515752 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3097.04 | 0.173507 | 0.0867533 | − | 0.996230i | \(-0.472351\pi\) | ||||
0.0867533 | + | 0.996230i | \(0.472351\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10872.3 | 0.606439 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −965.109 | −0.0535971 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10130.5 | −0.560148 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26926.3 | −1.48238 | −0.741189 | − | 0.671296i | \(-0.765738\pi\) | ||||
−0.741189 | + | 0.671296i | \(0.765738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 47236.2 | 2.57809 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −47951.3 | −2.60586 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2720.82 | 0.147226 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16209.3 | −0.873347 | −0.436674 | − | 0.899620i | \(-0.643844\pi\) | ||||
−0.436674 | + | 0.899620i | \(0.643844\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21909.9 | −1.17546 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8003.39 | 0.427553 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8277.60 | −0.438465 | −0.219233 | − | 0.975673i | \(-0.570355\pi\) | ||||
−0.219233 | + | 0.975673i | \(0.570355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2526.96 | 0.133289 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17955.7 | 0.943121 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31764.3 | −1.66142 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12872.5 | 0.670478 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2334.31 | 0.121078 | 0.0605389 | − | 0.998166i | \(-0.480718\pi\) | ||||
0.0605389 | + | 0.998166i | \(0.480718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20956.9 | −1.07800 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 45736.2 | 2.34290 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18885.8 | 0.963462 | 0.481731 | − | 0.876319i | \(-0.340008\pi\) | ||||
0.481731 | + | 0.876319i | \(0.340008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19064.6 | −0.964611 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3071.96 | −0.154796 | −0.0773980 | − | 0.997000i | \(-0.524661\pi\) | ||||
−0.0773980 | + | 0.997000i | \(0.524661\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19878.0 | 0.993506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27388.4 | −1.36333 | −0.681663 | − | 0.731666i | \(-0.738743\pi\) | ||||
−0.681663 | + | 0.731666i | \(0.738743\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9294.19 | 0.460770 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30541.6 | −1.50803 | −0.754013 | − | 0.656859i | \(-0.771885\pi\) | ||||
−0.754013 | + | 0.656859i | \(0.771885\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −41847.7 | −2.05796 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5019.59 | 0.245860 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36868.0 | −1.79139 | −0.895695 | − | 0.444670i | \(-0.853321\pi\) | ||||
−0.895695 | + | 0.444670i | \(0.853321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16999.9 | −0.822723 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22599.1 | 1.08936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1804.07 | 0.0866184 | 0.0433092 | − | 0.999062i | \(-0.486210\pi\) | ||||
0.0433092 | + | 0.999062i | \(0.486210\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13737.1 | 0.656948 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17838.8 | 0.849746 | 0.424873 | − | 0.905253i | \(-0.360319\pi\) | ||||
0.424873 | + | 0.905253i | \(0.360319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18773.9 | −0.887284 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29955.4 | −1.41021 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6804.58 | −0.319089 | −0.159544 | − | 0.987191i | \(-0.551003\pi\) | ||||
−0.159544 | + | 0.987191i | \(0.551003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2521.79 | 0.117795 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23600.9 | 1.09814 | 0.549072 | − | 0.835775i | \(-0.314981\pi\) | ||||
0.549072 | + | 0.835775i | \(0.314981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34820.4 | 1.61392 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28572.0 | −1.31412 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16148.5 | 0.739872 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4298.85 | −0.196205 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31213.5 | −1.41918 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9183.98 | −0.415977 | −0.207988 | − | 0.978131i | \(-0.566692\pi\) | ||||
−0.207988 | + | 0.978131i | \(0.566692\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10160.1 | −0.458438 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3568.68 | 0.159808 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12193.2 | 0.543958 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11076.9 | −0.492302 | −0.246151 | − | 0.969231i | \(-0.579166\pi\) | ||||
−0.246151 | + | 0.969231i | \(0.579166\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13498.8 | 0.597690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11060.0 | 0.487874 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17811.0 | −0.782734 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23788.3 | 1.03765 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32258.3 | 1.40190 | 0.700952 | − | 0.713209i | \(-0.252759\pi\) | ||||
0.700952 | + | 0.713209i | \(0.252759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17693.9 | −0.766114 | −0.383057 | − | 0.923725i | \(-0.625129\pi\) | ||||
−0.383057 | + | 0.923725i | \(0.625129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15240.8 | 0.657462 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 41491.9 | 1.78331 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11359.8 | −0.486448 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18430.7 | −0.783480 | −0.391740 | − | 0.920076i | \(-0.628127\pi\) | ||||
−0.391740 | + | 0.920076i | \(0.628127\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32285.9 | −1.36746 | −0.683729 | − | 0.729736i | \(-0.739643\pi\) | ||||
−0.683729 | + | 0.729736i | \(0.739643\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26639.5 | 1.12420 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36266.1 | 1.52491 | 0.762453 | − | 0.647044i | \(-0.223995\pi\) | ||||
0.762453 | + | 0.647044i | \(0.223995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31156.2 | 1.30531 | 0.652654 | − | 0.757656i | \(-0.273655\pi\) | ||||
0.652654 | + | 0.757656i | \(0.273655\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 585.986 | 0.0244616 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51033.1 | 2.11506 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3272.85 | −0.135157 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 85.5051 | 0.00351843 | 0.00175922 | − | 0.999998i | \(-0.499440\pi\) | ||||
0.00175922 | + | 0.999998i | \(0.499440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 960.906 | 0.0393992 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12089.5 | −0.493931 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7394.70 | −0.301048 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20781.8 | 0.840083 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53016.5 | −2.13558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1148.37 | −0.0460956 | −0.0230478 | − | 0.999734i | \(-0.507337\pi\) | ||||
−0.0230478 | + | 0.999734i | \(0.507337\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11186.5 | −0.447452 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11674.6 | 0.465340 | 0.232670 | − | 0.972556i | \(-0.425254\pi\) | ||||
0.232670 | + | 0.972556i | \(0.425254\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47503.1 | 1.88683 | 0.943413 | − | 0.331619i | \(-0.107595\pi\) | ||||
0.943413 | + | 0.331619i | \(0.107595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10361.9 | −0.408717 | −0.204359 | − | 0.978896i | \(-0.565511\pi\) | ||||
−0.204359 | + | 0.978896i | \(0.565511\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32303.8 | 1.26978 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16925.8 | −0.663011 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8679.39 | −0.338813 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32543.2 | 1.26600 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −585.372 | −0.0226940 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26153.1 | −1.00699 | −0.503493 | − | 0.863999i | \(-0.667952\pi\) | ||||
−0.503493 | + | 0.863999i | \(0.667952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2733.03 | −0.104872 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35711.7 | −1.36567 | −0.682837 | − | 0.730571i | \(-0.739254\pi\) | ||||
−0.682837 | + | 0.730571i | \(0.739254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5654.75 | 0.215513 | 0.107756 | − | 0.994177i | \(-0.465633\pi\) | ||||
0.107756 | + | 0.994177i | \(0.465633\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36054.5 | 1.36945 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8344.44 | −0.315873 | −0.157936 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157936 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2503.90 | −0.0941459 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8043.35 | 0.301411 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51821.7 | −1.93543 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22489.6 | 0.837132 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19299.7 | 0.715996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20565.4 | 0.760415 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −68249.0 | −2.50682 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52612.1 | 1.92608 | 0.963040 | − | 0.269358i | \(-0.0868116\pi\) | ||||
0.963040 | + | 0.269358i | \(0.0868116\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2731.60 | −0.0996715 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24706.6 | −0.898536 | −0.449268 | − | 0.893397i | \(-0.648315\pi\) | ||||
−0.449268 | + | 0.893397i | \(0.648315\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17240.8 | −0.624960 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4295.29 | −0.155189 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42479.2 | 1.52477 | 0.762383 | − | 0.647127i | \(-0.224030\pi\) | ||||
0.762383 | + | 0.647127i | \(0.224030\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9932.17 | 0.355349 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26437.6 | 0.942799 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −102812. | −3.65452 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1568.41 | −0.0555699 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9423.54 | −0.332805 | −0.166403 | − | 0.986058i | \(-0.553215\pi\) | ||||
−0.166403 | + | 0.986058i | \(0.553215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14937.4 | 0.524146 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 64483.0 | 2.25542 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33158.7 | 1.15608 | 0.578041 | − | 0.816008i | \(-0.303817\pi\) | ||||
0.578041 | + | 0.816008i | \(0.303817\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15348.6 | −0.533420 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15005.1 | −0.519822 | −0.259911 | − | 0.965633i | \(-0.583693\pi\) | ||||
−0.259911 | + | 0.965633i | \(0.583693\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −69137.3 | −2.38751 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7631.38 | 0.261865 | 0.130933 | − | 0.991391i | \(-0.458203\pi\) | ||||
0.130933 | + | 0.991391i | \(0.458203\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29159.2 | −0.997417 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2934.95 | −0.100076 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42615.3 | −1.44853 | −0.724263 | − | 0.689524i | \(-0.757820\pi\) | ||||
−0.724263 | + | 0.689524i | \(0.757820\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 78549.5 | 2.66157 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14765.3 | 0.498740 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15097.6 | −0.506782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17508.8 | 0.585890 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54682.4 | −1.82413 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34795.1 | 1.15712 | 0.578559 | − | 0.815640i | \(-0.303615\pi\) | ||||
0.578559 | + | 0.815640i | \(0.303615\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18867.6 | −0.625507 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7714.99 | −0.254980 | −0.127490 | − | 0.991840i | \(-0.540692\pi\) | ||||
−0.127490 | + | 0.991840i | \(0.540692\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43612.9 | 1.43254 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22817.7 | 0.747188 | 0.373594 | − | 0.927592i | \(-0.378125\pi\) | ||||
0.373594 | + | 0.927592i | \(0.378125\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37988.0 | −1.24015 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9925.80 | −0.323044 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10924.8 | 0.354473 | 0.177237 | − | 0.984168i | \(-0.443284\pi\) | ||||
0.177237 | + | 0.984168i | \(0.443284\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21621.0 | 0.699393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27487.8 | −0.883784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49279.5 | −1.57963 | −0.789816 | − | 0.613343i | \(-0.789824\pi\) | ||||
−0.789816 | + | 0.613343i | \(0.789824\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27277.1 | −0.871714 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33012.8 | 1.05184 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49601.6 | 1.57563 | 0.787813 | − | 0.615914i | \(-0.211213\pi\) | ||||
0.787813 | + | 0.615914i | \(0.211213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9663.50 | 0.306046 |
(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 | 1176.4.a.p.1.1 | 2 | ||
4.3 | odd | 2 | 2352.4.a.bv.1.1 | 2 | |||
7.6 | odd | 2 | 168.4.a.h.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 504.4.a.j.1.1 | 2 | |||
28.27 | even | 2 | 336.4.a.n.1.2 | 2 | |||
56.13 | odd | 2 | 1344.4.a.bd.1.1 | 2 | |||
56.27 | even | 2 | 1344.4.a.bl.1.1 | 2 | |||
84.83 | odd | 2 | 1008.4.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.h.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
336.4.a.n.1.2 | 2 | 28.27 | even | 2 | |||
504.4.a.j.1.1 | 2 | 21.20 | even | 2 | |||
1008.4.a.y.1.1 | 2 | 84.83 | odd | 2 | |||
1176.4.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.bd.1.1 | 2 | 56.13 | odd | 2 | |||
1344.4.a.bl.1.1 | 2 | 56.27 | even | 2 | |||
2352.4.a.bv.1.1 | 2 | 4.3 | odd | 2 |