Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(108.563514411\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 81x^{4} + 161x^{3} + 1520x^{2} - 3915x + 588 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-6.42830\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 6.42830 | 1.23713 | 0.618564 | − | 0.785735i | \(-0.287715\pi\) | ||||
0.618564 | + | 0.785735i | \(0.287715\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.32258 | −0.449377 | −0.224689 | − | 0.974431i | \(-0.572136\pi\) | ||||
−0.224689 | + | 0.974431i | \(0.572136\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 14.3231 | 0.530485 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.59730 | −0.0437822 | −0.0218911 | − | 0.999760i | \(-0.506969\pi\) | ||||
−0.0218911 | + | 0.999760i | \(0.506969\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.1241 | 0.215993 | 0.107997 | − | 0.994151i | \(-0.465556\pi\) | ||||
0.107997 | + | 0.994151i | \(0.465556\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −32.1415 | −0.553260 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −43.6876 | −0.623282 | −0.311641 | − | 0.950200i | \(-0.600879\pi\) | ||||
−0.311641 | + | 0.950200i | \(0.600879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48.9819 | 0.591432 | 0.295716 | − | 0.955276i | \(-0.404442\pi\) | ||||
0.295716 | + | 0.955276i | \(0.404442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −53.5001 | −0.555937 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −81.4910 | −0.580850 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 200.736 | 1.28537 | 0.642685 | − | 0.766130i | \(-0.277820\pi\) | ||||
0.642685 | + | 0.766130i | \(0.277820\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −34.6948 | −0.201012 | −0.100506 | − | 0.994936i | \(-0.532046\pi\) | ||||
−0.100506 | + | 0.994936i | \(0.532046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.2679 | −0.0541642 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 41.6129 | 0.200968 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 92.5057 | 0.411023 | 0.205511 | − | 0.978655i | \(-0.434114\pi\) | ||||
0.205511 | + | 0.978655i | \(0.434114\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 65.0806 | 0.267211 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 253.390 | 0.965190 | 0.482595 | − | 0.875844i | \(-0.339694\pi\) | ||||
0.482595 | + | 0.875844i | \(0.339694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −446.151 | −1.58227 | −0.791133 | − | 0.611645i | \(-0.790508\pi\) | ||||
−0.791133 | + | 0.611645i | \(0.790508\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −71.6154 | −0.237240 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −315.028 | −0.977693 | −0.488847 | − | 0.872370i | \(-0.662582\pi\) | ||||
−0.488847 | + | 0.872370i | \(0.662582\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −273.735 | −0.798060 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −280.837 | −0.771079 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −515.242 | −1.33536 | −0.667678 | − | 0.744450i | \(-0.732712\pi\) | ||||
−0.667678 | + | 0.744450i | \(0.732712\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.98651 | 0.0195800 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 314.870 | 0.731677 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −98.7342 | −0.217866 | −0.108933 | − | 0.994049i | \(-0.534743\pi\) | ||||
−0.108933 | + | 0.994049i | \(0.534743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −309.934 | −0.650541 | −0.325271 | − | 0.945621i | \(-0.605455\pi\) | ||||
−0.325271 | + | 0.945621i | \(0.605455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −119.205 | −0.238388 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −50.6204 | −0.0965951 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 395.169 | 0.720560 | 0.360280 | − | 0.932844i | \(-0.382681\pi\) | ||||
0.360280 | + | 0.932844i | \(0.382681\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 147.851 | 0.257959 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 700.646 | 1.17115 | 0.585573 | − | 0.810620i | \(-0.300869\pi\) | ||||
0.585573 | + | 0.810620i | \(0.300869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −531.139 | −0.851578 | −0.425789 | − | 0.904823i | \(-0.640003\pi\) | ||||
−0.425789 | + | 0.904823i | \(0.640003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 160.708 | 0.247426 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.2937 | 0.0196747 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −107.360 | −0.152898 | −0.0764492 | − | 0.997073i | \(-0.524358\pi\) | ||||
−0.0764492 | + | 0.997073i | \(0.524358\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −910.573 | −1.24907 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −531.243 | −0.702549 | −0.351274 | − | 0.936273i | \(-0.614252\pi\) | ||||
−0.351274 | + | 0.936273i | \(0.614252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 218.438 | 0.278740 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1290.39 | 1.59017 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 228.493 | 0.272137 | 0.136068 | − | 0.990699i | \(-0.456553\pi\) | ||||
0.136068 | + | 0.990699i | \(0.456553\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −84.2584 | −0.0970625 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −223.028 | −0.248677 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −244.909 | −0.264496 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −618.384 | −0.647292 | −0.323646 | − | 0.946178i | \(-0.604909\pi\) | ||||
−0.323646 | + | 0.946178i | \(0.604909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.8783 | −0.0232258 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1075.77 | −1.05983 | −0.529915 | − | 0.848051i | \(-0.677776\pi\) | ||||
−0.529915 | + | 0.848051i | \(0.677776\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −459.840 | −0.439897 | −0.219948 | − | 0.975512i | \(-0.570589\pi\) | ||||
−0.219948 | + | 0.975512i | \(0.570589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 267.500 | 0.248623 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1518.68 | −1.37212 | −0.686058 | − | 0.727547i | \(-0.740660\pi\) | ||||
−0.686058 | + | 0.727547i | \(0.740660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1186.57 | −1.04268 | −0.521342 | − | 0.853348i | \(-0.674568\pi\) | ||||
−0.521342 | + | 0.853348i | \(0.674568\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 594.655 | 0.508488 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1678.95 | −1.39772 | −0.698862 | − | 0.715257i | \(-0.746310\pi\) | ||||
−0.698862 | + | 0.715257i | \(0.746310\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 145.008 | 0.114581 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 363.594 | 0.280089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1328.45 | −0.998083 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1628.87 | 1.19406 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 692.369 | 0.483763 | 0.241881 | − | 0.970306i | \(-0.422236\pi\) | ||||
0.241881 | + | 0.970306i | \(0.422236\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2868.00 | −1.95746 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 269.315 | 0.179620 | 0.0898099 | − | 0.995959i | \(-0.471374\pi\) | ||||
0.0898099 | + | 0.995959i | \(0.471374\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −407.656 | −0.265776 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 407.455 | 0.259764 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −995.345 | −0.620716 | −0.310358 | − | 0.950620i | \(-0.600449\pi\) | ||||
−0.310358 | + | 0.950620i | \(0.600449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3496 | 0.00936647 | 0.00468323 | − | 0.999989i | \(-0.498509\pi\) | ||||
0.00468323 | + | 0.999989i | \(0.498509\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2025.10 | −1.20953 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.1712 | −0.00945667 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1003.68 | −0.574835 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1759.65 | −0.987302 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1861.91 | 1.02372 | 0.511859 | − | 0.859070i | \(-0.328957\pi\) | ||||
0.511859 | + | 0.859070i | \(0.328957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3009.27 | 1.62180 | 0.810898 | − | 0.585187i | \(-0.198979\pi\) | ||||
0.810898 | + | 0.585187i | \(0.198979\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −625.741 | −0.330642 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 173.474 | 0.0898952 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2413.34 | 1.22679 | 0.613394 | − | 0.789777i | \(-0.289804\pi\) | ||||
0.613394 | + | 0.789777i | \(0.289804\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3312.13 | −1.65201 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −191.419 | −0.0937016 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −386.040 | −0.185503 | −0.0927515 | − | 0.995689i | \(-0.529566\pi\) | ||||
−0.0927515 | + | 0.995689i | \(0.529566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 51.3397 | 0.0242230 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1032.55 | −0.478448 | −0.239224 | − | 0.970964i | \(-0.576893\pi\) | ||||
−0.239224 | + | 0.970964i | \(0.576893\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2094.50 | −0.953347 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 701.571 | 0.313746 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2988.81 | −1.31350 | −0.656748 | − | 0.754111i | \(-0.728068\pi\) | ||||
−0.656748 | + | 0.754111i | \(0.728068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −208.065 | −0.0898754 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −634.693 | −0.269528 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1517.25 | −0.633545 | −0.316773 | − | 0.948502i | \(-0.602599\pi\) | ||||
−0.316773 | + | 0.948502i | \(0.602599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3680.36 | −1.51138 | −0.755689 | − | 0.654931i | \(-0.772698\pi\) | ||||
−0.755689 | + | 0.654931i | \(0.772698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1992.35 | −0.804803 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −462.529 | −0.183815 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 69.7823 | 0.0272887 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 678.216 | 0.261021 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 568.256 | 0.215275 | 0.107638 | − | 0.994190i | \(-0.465671\pi\) | ||||
0.107638 | + | 0.994190i | \(0.465671\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1256.14 | 0.468492 | 0.234246 | − | 0.972177i | \(-0.424738\pi\) | ||||
0.234246 | + | 0.972177i | \(0.424738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −325.403 | −0.119500 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3655.52 | −1.32206 | −0.661028 | − | 0.750361i | \(-0.729879\pi\) | ||||
−0.661028 | + | 0.750361i | \(0.729879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3030.78 | 1.07963 | 0.539815 | − | 0.841784i | \(-0.318494\pi\) | ||||
0.539815 | + | 0.841784i | \(0.318494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2540.26 | 0.891425 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1670.64 | −0.577616 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1266.95 | −0.431646 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 329.431 | 0.110614 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −78.2388 | −0.0258942 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2306.60 | 0.752574 | 0.376287 | − | 0.926503i | \(-0.377201\pi\) | ||||
0.376287 | + | 0.926503i | \(0.377201\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4503.97 | 1.44886 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2230.76 | 0.707611 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 288.750 | 0.0903301 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3414.33 | −1.05351 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −442.296 | −0.134625 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −984.280 | −0.295571 | −0.147785 | − | 0.989019i | \(-0.547214\pi\) | ||||
−0.147785 | + | 0.989019i | \(0.547214\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 358.077 | 0.106097 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1638.64 | 0.479120 | 0.239560 | − | 0.970882i | \(-0.422997\pi\) | ||||
0.239560 | + | 0.970882i | \(0.422997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2472.33 | 0.713432 | 0.356716 | − | 0.934213i | \(-0.383896\pi\) | ||||
0.356716 | + | 0.934213i | \(0.383896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 85.4558 | 0.0243402 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −304.031 | −0.0854837 | −0.0427419 | − | 0.999086i | \(-0.513609\pi\) | ||||
−0.0427419 | + | 0.999086i | \(0.513609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1575.14 | 0.437238 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −690.144 | −0.189155 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −220.665 | −0.0597224 | −0.0298612 | − | 0.999554i | \(-0.509507\pi\) | ||||
−0.0298612 | + | 0.999554i | \(0.509507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3743.94 | −1.00070 | −0.500349 | − | 0.865824i | \(-0.666795\pi\) | ||||
−0.500349 | + | 0.865824i | \(0.666795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3653.18 | −0.964409 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1368.67 | 0.356903 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 495.896 | 0.127745 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3414.99 | −0.869142 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1936.75 | −0.487038 | −0.243519 | − | 0.969896i | \(-0.578302\pi\) | ||||
−0.243519 | + | 0.969896i | \(0.578302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.7379 | −0.00912923 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1404.19 | 0.344837 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3292.09 | 0.799047 | 0.399523 | − | 0.916723i | \(-0.369176\pi\) | ||||
0.399523 | + | 0.916723i | \(0.369176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −769.887 | −0.184704 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2875.16 | 0.681869 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2260.19 | 0.529920 | 0.264960 | − | 0.964259i | \(-0.414641\pi\) | ||||
0.264960 | + | 0.964259i | \(0.414641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2576.21 | 0.597190 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1468.82 | 0.336668 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2151.40 | 0.487633 | 0.243817 | − | 0.969821i | \(-0.421600\pi\) | ||||
0.243817 | + | 0.969821i | \(0.421600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5832.47 | 1.30737 | 0.653685 | − | 0.756767i | \(-0.273222\pi\) | ||||
0.653685 | + | 0.756767i | \(0.273222\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −541.639 | −0.120079 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −39.9325 | −0.00875645 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4848.03 | 1.05159 | 0.525795 | − | 0.850612i | \(-0.323768\pi\) | ||||
0.525795 | + | 0.850612i | \(0.323768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −496.936 | −0.106634 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3055.68 | −0.648706 | −0.324353 | − | 0.945936i | \(-0.605147\pi\) | ||||
−0.324353 | + | 0.945936i | \(0.605147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6960.33 | −1.46201 | −0.731005 | − | 0.682372i | \(-0.760948\pi\) | ||||
−0.731005 | + | 0.682372i | \(0.760948\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1574.35 | −0.327216 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2108.86 | −0.433735 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3004.39 | −0.611519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3975.16 | −0.800783 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3248.07 | 0.647626 | 0.323813 | − | 0.946121i | \(-0.395035\pi\) | ||||
0.323813 | + | 0.946121i | \(0.395035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 493.671 | 0.0974326 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 130.166 | 0.0254309 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 232.854 | 0.0450377 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3713.13 | 0.711034 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6915.36 | −1.31115 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1549.67 | 0.290931 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1354.90 | 0.251883 | 0.125941 | − | 0.992038i | \(-0.459805\pi\) | ||||
0.125941 | + | 0.992038i | \(0.459805\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2955.99 | −0.544208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 907.288 | 0.165426 | 0.0827132 | − | 0.996573i | \(-0.473641\pi\) | ||||
0.0827132 | + | 0.996573i | \(0.473641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5522.93 | 0.997363 | 0.498681 | − | 0.866785i | \(-0.333818\pi\) | ||||
0.498681 | + | 0.866785i | \(0.333818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 596.025 | 0.106610 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5610.21 | 0.994009 | 0.497004 | − | 0.867748i | \(-0.334433\pi\) | ||||
0.497004 | + | 0.867748i | \(0.334433\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −320.636 | −0.0562764 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9762.54 | −1.69748 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2139.90 | −0.368629 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 253.102 | 0.0431987 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7627.62 | −1.28993 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2621.85 | 0.439353 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6674.82 | 1.10840 | 0.554202 | − | 0.832383i | \(-0.313024\pi\) | ||||
0.554202 | + | 0.832383i | \(0.313024\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1324.97 | 0.218041 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1975.84 | −0.322244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7375.54 | 1.19220 | 0.596100 | − | 0.802910i | \(-0.296716\pi\) | ||||
0.596100 | + | 0.802910i | \(0.296716\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10792.8 | −1.72916 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.4180 | 0.00880074 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5132.83 | 0.808007 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −739.255 | −0.115363 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2053.90 | 0.317750 | 0.158875 | − | 0.987299i | \(-0.449213\pi\) | ||||
0.158875 | + | 0.987299i | \(0.449213\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −478.454 | −0.0733841 | −0.0366920 | − | 0.999327i | \(-0.511682\pi\) | ||||
−0.0366920 | + | 0.999327i | \(0.511682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −825.021 | −0.125460 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 109.570 | 0.0165207 | 0.00826034 | − | 0.999966i | \(-0.497371\pi\) | ||||
0.00826034 | + | 0.999966i | \(0.497371\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3503.23 | −0.523753 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2337.29 | 0.346506 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5835.58 | 0.857912 | 0.428956 | − | 0.903325i | \(-0.358882\pi\) | ||||
0.428956 | + | 0.903325i | \(0.358882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4459.78 | −0.650208 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8539.67 | −1.23476 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2655.70 | 0.380837 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7693.84 | 1.09432 | 0.547160 | − | 0.837028i | \(-0.315709\pi\) | ||||
0.547160 | + | 0.837028i | \(0.315709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3629.32 | 0.512019 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4288.14 | 0.600079 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8726.57 | −1.21138 | −0.605690 | − | 0.795701i | \(-0.707103\pi\) | ||||
−0.605690 | + | 0.795701i | \(0.707103\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −803.538 | −0.110652 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2032.27 | 0.277631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9893.96 | −1.34095 | −0.670473 | − | 0.741934i | \(-0.733909\pi\) | ||||
−0.670473 | + | 0.741934i | \(0.733909\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4450.76 | 0.598476 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3010.04 | −0.401582 | −0.200791 | − | 0.979634i | \(-0.564351\pi\) | ||||
−0.200791 | + | 0.979634i | \(0.564351\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −66.4684 | −0.00879881 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6390.26 | −0.839368 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8778.85 | −1.14423 | −0.572115 | − | 0.820173i | \(-0.693877\pi\) | ||||
−0.572115 | + | 0.820173i | \(0.693877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1004.81 | −0.129963 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1731.24 | 0.222213 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 536.801 | 0.0683782 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10697.1 | −1.35232 | −0.676161 | − | 0.736753i | \(-0.736358\pi\) | ||||
−0.676161 | + | 0.736753i | \(0.736358\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2620.53 | −0.328799 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −369.210 | −0.0459787 | −0.0229893 | − | 0.999736i | \(-0.507318\pi\) | ||||
−0.0229893 | + | 0.999736i | \(0.507318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −351.252 | −0.0434172 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4552.86 | 0.558601 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −147.760 | −0.0179955 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6327.37 | −0.764959 | −0.382480 | − | 0.923964i | \(-0.624930\pi\) | ||||
−0.382480 | + | 0.923964i | \(0.624930\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6398.38 | −0.767905 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 821.723 | 0.0979040 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2656.22 | 0.314189 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 98.6721 | 0.0115875 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4130.29 | 0.481571 | 0.240785 | − | 0.970578i | \(-0.422595\pi\) | ||||
0.240785 | + | 0.970578i | \(0.422595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5578.43 | −0.645786 | −0.322893 | − | 0.946435i | \(-0.604655\pi\) | ||||
−0.322893 | + | 0.946435i | \(0.604655\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4512.18 | −0.518651 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1092.19 | −0.124656 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2579.45 | 0.292338 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −103.953 | −0.0116991 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1572.83 | −0.175779 | −0.0878894 | − | 0.996130i | \(-0.528012\pi\) | ||||
−0.0878894 | + | 0.996130i | \(0.528012\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −723.228 | −0.0802681 | −0.0401341 | − | 0.999194i | \(-0.512779\pi\) | ||||
−0.0401341 | + | 0.999194i | \(0.512779\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6451.96 | −0.711144 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1126.58 | 0.123322 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10176.6 | −1.10638 | −0.553192 | − | 0.833054i | \(-0.686590\pi\) | ||||
−0.553192 | + | 0.833054i | \(0.686590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3920.72 | −0.423359 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10665.1 | −1.14382 | −0.571910 | − | 0.820316i | \(-0.693797\pi\) | ||||
−0.571910 | + | 0.820316i | \(0.693797\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1142.46 | −0.121703 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11968.9 | 1.26647 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6922.86 | −0.727640 | −0.363820 | − | 0.931469i | \(-0.618528\pi\) | ||||
−0.363820 | + | 0.931469i | \(0.618528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −404.740 | −0.0422582 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19344.5 | 2.00637 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 421.292 | 0.0434076 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 606.753 | 0.0621065 | 0.0310533 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310533 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3560.15 | 0.362034 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14239.6 | 1.43862 | 0.719308 | − | 0.694691i | \(-0.244459\pi\) | ||||
0.719308 | + | 0.694691i | \(0.244459\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2927.25 | 0.293825 | 0.146913 | − | 0.989149i | \(-0.453066\pi\) | ||||
0.146913 | + | 0.989149i | \(0.453066\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1115.14 | 0.111212 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2195.75 | −0.217575 | −0.108787 | − | 0.994065i | \(-0.534697\pi\) | ||||
−0.108787 | + | 0.994065i | \(0.534697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3288.82 | −0.323803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15513.7 | 1.51769 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 712.638 | 0.0692751 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1224.55 | 0.118286 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7379.85 | −0.708386 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8272.52 | −0.789104 | −0.394552 | − | 0.918874i | \(-0.629100\pi\) | ||||
−0.394552 | + | 0.918874i | \(0.629100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 936.535 | 0.0887782 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1230.50 | −0.115921 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3091.92 | 0.289478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7983.87 | −0.742883 | −0.371441 | − | 0.928456i | \(-0.621136\pi\) | ||||
−0.371441 | + | 0.928456i | \(0.621136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2481.58 | −0.229491 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 519.669 | 0.0477645 | 0.0238822 | − | 0.999715i | \(-0.492397\pi\) | ||||
0.0238822 | + | 0.999715i | \(0.492397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8769.67 | −0.801148 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 114.391 | 0.0103869 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5831.19 | −0.526287 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −862.162 | −0.0773460 | −0.0386730 | − | 0.999252i | \(-0.512313\pi\) | ||||
−0.0386730 | + | 0.999252i | \(0.512313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6637.52 | −0.591901 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14142.2 | 1.25362 | 0.626809 | − | 0.779173i | \(-0.284361\pi\) | ||||
0.626809 | + | 0.779173i | \(0.284361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5378.84 | 0.473970 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13464.1 | −1.17941 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7163.46 | −0.623801 | −0.311900 | − | 0.950115i | \(-0.600966\pi\) | ||||
−0.311900 | + | 0.950115i | \(0.600966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4420.45 | 0.382680 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3991.58 | −0.343533 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2299.20 | 0.196728 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 503.195 | 0.0428056 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19212.9 | −1.62496 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5219.95 | 0.438944 | 0.219472 | − | 0.975619i | \(-0.429566\pi\) | ||||
0.219472 | + | 0.975619i | \(0.429566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13888.9 | −1.16123 | −0.580613 | − | 0.814180i | \(-0.697187\pi\) | ||||
−0.580613 | + | 0.814180i | \(0.697187\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1337.50 | −0.111187 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1515.73 | 0.125287 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1414.18 | −0.115575 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2565.33 | 0.208475 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7593.40 | 0.613629 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9753.34 | −0.783776 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 437.237 | 0.0349409 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10331.1 | −0.821012 | −0.410506 | − | 0.911858i | \(-0.634648\pi\) | ||||
−0.410506 | + | 0.911858i | \(0.634648\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23658.5 | −1.86977 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5932.84 | 0.466303 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19121.6 | 1.49466 | 0.747332 | − | 0.664451i | \(-0.231335\pi\) | ||||
0.747332 | + | 0.664451i | \(0.231335\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4439.22 | −0.345102 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9832.42 | 0.760209 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 893.514 | 0.0687090 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2973.27 | −0.227403 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10080.2 | −0.766808 | −0.383404 | − | 0.923581i | \(-0.625248\pi\) | ||||
−0.383404 | + | 0.923581i | \(0.625248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4516.87 | −0.341759 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 448.582 | 0.0337596 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11517.1 | −0.862144 | −0.431072 | − | 0.902318i | \(-0.641864\pi\) | ||||
−0.431072 | + | 0.902318i | \(0.641864\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8394.77 | 0.625081 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7578.32 | 0.561304 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5771.86 | −0.425253 | −0.212627 | − | 0.977134i | \(-0.568202\pi\) | ||||
−0.212627 | + | 0.977134i | \(0.568202\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12608.7 | 0.924092 | 0.462046 | − | 0.886856i | \(-0.347116\pi\) | ||||
0.462046 | + | 0.886856i | \(0.347116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3652.92 | 0.266323 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9818.70 | 0.708419 | 0.354209 | − | 0.935166i | \(-0.384750\pi\) | ||||
0.354209 | + | 0.935166i | \(0.384750\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8074.86 | 0.579585 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4421.32 | 0.315709 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 822.997 | 0.0584649 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −725.040 | −0.0512422 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7452.02 | −0.523983 | −0.261991 | − | 0.965070i | \(-0.584379\pi\) | ||||
−0.261991 | + | 0.965070i | \(0.584379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1699.41 | −0.118885 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23498.8 | −1.63555 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5386.06 | 0.372983 | 0.186492 | − | 0.982457i | \(-0.440288\pi\) | ||||
0.186492 | + | 0.982457i | \(0.440288\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1817.97 | −0.125260 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19482.8 | 1.33564 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5750.26 | −0.392236 | −0.196118 | − | 0.980580i | \(-0.562834\pi\) | ||||
−0.196118 | + | 0.980580i | \(0.562834\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −894.738 | −0.0607273 | −0.0303637 | − | 0.999539i | \(-0.509667\pi\) | ||||
−0.0303637 | + | 0.999539i | \(0.509667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5660.03 | 0.382246 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6642.24 | 0.446356 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6015.58 | 0.402248 | 0.201124 | − | 0.979566i | \(-0.435541\pi\) | ||||
0.201124 | + | 0.979566i | \(0.435541\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10739.4 | −0.714585 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3189.37 | −0.211175 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4533.12 | 0.298680 | 0.149340 | − | 0.988786i | \(-0.452285\pi\) | ||||
0.149340 | + | 0.988786i | \(0.452285\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8144.33 | −0.534002 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11378.8 | −0.742455 | −0.371227 | − | 0.928542i | \(-0.621063\pi\) | ||||
−0.371227 | + | 0.928542i | \(0.621063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17167.2 | 1.11471 | 0.557357 | − | 0.830273i | \(-0.311816\pi\) | ||||
0.557357 | + | 0.830273i | \(0.311816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1874.29 | −0.121116 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1901.65 | −0.122292 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −502.943 | −0.0320344 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4041.35 | −0.256183 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24289.5 | −1.53241 | −0.766206 | − | 0.642595i | \(-0.777858\pi\) | ||||
−0.766206 | + | 0.642595i | \(0.777858\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14827.5 | 0.931030 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3461.85 | −0.216345 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2771.31 | −0.172376 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10035.4 | 0.621275 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22941.6 | −1.41363 | −0.706816 | − | 0.707397i | \(-0.749869\pi\) | ||||
−0.706816 | + | 0.707397i | \(0.749869\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8623.66 | 0.528902 | 0.264451 | − | 0.964399i | \(-0.414809\pi\) | ||||
0.264451 | + | 0.964399i | \(0.414809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14340.0 | 0.875405 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30451.5 | 1.85034 | 0.925172 | − | 0.379547i | \(-0.123920\pi\) | ||||
0.925172 | + | 0.379547i | \(0.123920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 157.708 | 0.00953866 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1856.17 | 0.111750 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20330.4 | 1.21836 | 0.609182 | − | 0.793031i | \(-0.291498\pi\) | ||||
0.609182 | + | 0.793031i | \(0.291498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1346.58 | −0.0803284 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7607.56 | −0.451749 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29029.8 | −1.71599 | −0.857996 | − | 0.513656i | \(-0.828291\pi\) | ||||
−0.857996 | + | 0.513656i | \(0.828291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31721.6 | 1.86661 | 0.933304 | − | 0.359088i | \(-0.116912\pi\) | ||||
0.933304 | + | 0.359088i | \(0.116912\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2843.21 | −0.166548 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2038.28 | 0.118859 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4616.93 | 0.268018 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6327.25 | −0.365658 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 495.059 | 0.0284822 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −266.739 | −0.0152779 | −0.00763895 | − | 0.999971i | \(-0.502432\pi\) | ||||
−0.00763895 | + | 0.999971i | \(0.502432\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2037.28 | −0.116170 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5439.22 | −0.308783 | −0.154391 | − | 0.988010i | \(-0.549342\pi\) | ||||
−0.154391 | + | 0.988010i | \(0.549342\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5146.55 | 0.290878 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10533.7 | 0.592733 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2914.19 | 0.163263 | 0.0816314 | − | 0.996663i | \(-0.473987\pi\) | ||||
0.0816314 | + | 0.996663i | \(0.473987\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4976.73 | 0.277593 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15892.9 | 0.882606 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5216.35 | −0.288428 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29045.8 | 1.59907 | 0.799533 | − | 0.600622i | \(-0.205080\pi\) | ||||
0.799533 | + | 0.600622i | \(0.205080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 190.406 | 0.0104371 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −76.7482 | −0.00418881 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11070.0 | −0.601586 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1954.40 | −0.105754 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19177.9 | 1.03329 | 0.516646 | − | 0.856199i | \(-0.327180\pi\) | ||||
0.516646 | + | 0.856199i | \(0.327180\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4531.10 | 0.243092 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10125.5 | 0.540919 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8953.16 | 0.476264 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20890.1 | 1.10655 | 0.553276 | − | 0.832998i | \(-0.313377\pi\) | ||||
0.553276 | + | 0.832998i | \(0.313377\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1537.73 | −0.0811102 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −797.979 | −0.0419138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 80.8560 | 0.00422915 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1418.50 | −0.0738842 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6739.88 | −0.349590 | −0.174795 | − | 0.984605i | \(-0.555926\pi\) | ||||
−0.174795 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3827.06 | 0.197680 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24067.2 | −1.23799 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5018.40 | 0.257074 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9983.95 | −0.509332 | −0.254666 | − | 0.967029i | \(-0.581966\pi\) | ||||
−0.254666 | + | 0.967029i | \(0.581966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1101.72 | 0.0559731 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19491.3 | 0.986198 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13884.2 | 0.699622 | 0.349811 | − | 0.936820i | \(-0.386246\pi\) | ||||
0.349811 | + | 0.936820i | \(0.386246\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8798.25 | 0.441535 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −631.203 | −0.0315477 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27623.4 | 1.37502 | 0.687512 | − | 0.726173i | \(-0.258703\pi\) | ||||
0.687512 | + | 0.726173i | \(0.258703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3187.77 | 0.158037 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.0253 | 0.00172941 | 0.000864706 | − | 1.00000i | \(-0.499725\pi\) | ||||
0.000864706 | 1.00000i | \(0.499725\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9309.57 | −0.457820 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7609.04 | −0.372691 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12639.3 | 0.616598 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25497.7 | 1.23891 | 0.619456 | − | 0.785031i | \(-0.287353\pi\) | ||||
0.619456 | + | 0.785031i | \(0.287353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12450.0 | −0.602528 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15046.4 | −0.725289 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16363.0 | −0.785630 | −0.392815 | − | 0.919617i | \(-0.628499\pi\) | ||||
−0.392815 | + | 0.919617i | \(0.628499\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −236.163 | −0.0112940 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19026.0 | −0.906299 | −0.453150 | − | 0.891435i | \(-0.649700\pi\) | ||||
−0.453150 | + | 0.891435i | \(0.649700\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9875.31 | 0.468559 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3128.71 | 0.147867 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −999.592 | −0.0470576 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16422.8 | −0.770121 | −0.385060 | − | 0.922891i | \(-0.625819\pi\) | ||||
−0.385060 | + | 0.922891i | \(0.625819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21162.6 | 0.988523 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30887.7 | −1.43720 | −0.718599 | − | 0.695425i | \(-0.755216\pi\) | ||||
−0.718599 | + | 0.695425i | \(0.755216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −867.369 | −0.0402023 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4949.06 | −0.228503 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12411.5 | 0.570844 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1119.14 | −0.0512754 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16358.2 | −0.746608 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12066.7 | −0.548636 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18026.5 | 0.816486 | 0.408243 | − | 0.912873i | \(-0.366142\pi\) | ||||
0.408243 | + | 0.912873i | \(0.366142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14529.2 | 0.655579 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13973.2 | 0.628105 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3137.80 | −0.140513 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16560.7 | 0.738800 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5024.03 | −0.223288 | −0.111644 | − | 0.993748i | \(-0.535612\pi\) | ||||
−0.111644 | + | 0.993748i | \(0.535612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13762.8 | 0.609379 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3272.72 | 0.144364 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 848.390 | 0.0372840 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 957.097 | 0.0419046 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13829.9 | 0.603265 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13539.5 | 0.588408 | 0.294204 | − | 0.955743i | \(-0.404946\pi\) | ||||
0.294204 | + | 0.955743i | \(0.404946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8701.18 | 0.376745 | 0.188372 | − | 0.982098i | \(-0.439679\pi\) | ||||
0.188372 | + | 0.982098i | \(0.439679\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37492.9 | 1.61738 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1930.20 | 0.0829595 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21853.3 | −0.935802 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1206.84 | −0.0514901 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24130.0 | 1.02575 | 0.512876 | − | 0.858463i | \(-0.328580\pi\) | ||||
0.512876 | + | 0.858463i | \(0.328580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −740.011 | −0.0313428 | −0.0156714 | − | 0.999877i | \(-0.504989\pi\) | ||||
−0.0156714 | + | 0.999877i | \(0.504989\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −256.699 | −0.0108328 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26735.3 | 1.12416 | 0.562078 | − | 0.827084i | \(-0.310002\pi\) | ||||
0.562078 | + | 0.827084i | \(0.310002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16817.0 | −0.704558 | −0.352279 | − | 0.935895i | \(-0.614593\pi\) | ||||
−0.352279 | + | 0.935895i | \(0.614593\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31164.6 | 1.30095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11958.8 | 0.497417 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5162.73 | 0.213968 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2827.31 | 0.116758 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4657.60 | −0.191655 | −0.0958273 | − | 0.995398i | \(-0.530550\pi\) | ||||
−0.0958273 | + | 0.995398i | \(0.530550\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15905.9 | 0.652177 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19642.8 | −0.802532 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10472.5 | 0.426350 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11056.1 | 0.448516 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44743.1 | −1.80869 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2127.63 | 0.0857042 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28392.0 | 1.13965 | 0.569826 | − | 0.821765i | \(-0.307011\pi\) | ||||
0.569826 | + | 0.821765i | \(0.307011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3507.86 | −0.140311 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9369.46 | −0.373459 | −0.186730 | − | 0.982411i | \(-0.559789\pi\) | ||||
−0.186730 | + | 0.982411i | \(0.559789\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1622.41 | 0.0644423 | 0.0322211 | − | 0.999481i | \(-0.489742\pi\) | ||||
0.0322211 | + | 0.999481i | \(0.489742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13556.4 | −0.536585 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29507.8 | 1.16391 | 0.581956 | − | 0.813220i | \(-0.302288\pi\) | ||||
0.581956 | + | 0.813220i | \(0.302288\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14944.0 | 0.587413 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19313.2 | −0.756528 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 171.487 | 0.00669423 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4000.72 | 0.155636 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8857.16 | −0.343379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1040.32 | 0.0401935 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50395.7 | −1.94041 | −0.970207 | − | 0.242279i | \(-0.922105\pi\) | ||||
−0.970207 | + | 0.242279i | \(0.922105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20879.6 | 0.801196 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2847.84 | 0.108906 | 0.0544529 | − | 0.998516i | \(-0.482659\pi\) | ||||
0.0544529 | + | 0.998516i | \(0.482659\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47218.4 | 1.79958 | 0.899788 | − | 0.436328i | \(-0.143721\pi\) | ||||
0.899788 | + | 0.436328i | \(0.143721\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3173.47 | 0.120537 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22706.5 | 0.859536 | 0.429768 | − | 0.902939i | \(-0.358595\pi\) | ||||
0.429768 | + | 0.902939i | \(0.358595\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5762.30 | −0.217392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1454.46 | 0.0546871 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15430.7 | −0.578239 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7586.25 | 0.283330 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1496.85 | 0.0557174 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6964.49 | −0.258374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22509.7 | 0.832304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23869.1 | 0.879640 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18401.8 | 0.675908 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32574.6 | 1.19253 | 0.596264 | − | 0.802788i | \(-0.296651\pi\) | ||||
0.596264 | + | 0.802788i | \(0.296651\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15408.3 | −0.562224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21063.3 | −0.766037 | −0.383018 | − | 0.923741i | \(-0.625115\pi\) | ||||
−0.383018 | + | 0.923741i | \(0.625115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 848.556 | 0.0307591 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9961.76 | 0.359919 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2241.40 | −0.0807170 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40325.8 | 1.44747 | 0.723736 | − | 0.690077i | \(-0.242423\pi\) | ||||
0.723736 | + | 0.690077i | \(0.242423\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8709.69 | 0.311611 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7093.39 | 0.252960 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2312.64 | 0.0822046 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6586.33 | −0.233359 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30365.3 | 1.07239 | 0.536196 | − | 0.844093i | \(-0.319861\pi\) | ||||
0.536196 | + | 0.844093i | \(0.319861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13408.0 | −0.471998 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5832.32 | 0.204653 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −348.911 | −0.0122039 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5133.76 | −0.178989 | −0.0894945 | − | 0.995987i | \(-0.528525\pi\) | ||||
−0.0894945 | + | 0.995987i | \(0.528525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35503.1 | 1.23387 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14510.2 | −0.502677 | −0.251339 | − | 0.967899i | \(-0.580871\pi\) | ||||
−0.251339 | + | 0.967899i | \(0.580871\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5827.96 | 0.201256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3391.08 | −0.116732 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28776.6 | −0.987448 | −0.493724 | − | 0.869619i | \(-0.664365\pi\) | ||||
−0.493724 | + | 0.869619i | \(0.664365\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5377.29 | −0.183935 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36064.1 | 1.22972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −658.129 | −0.0223703 | −0.0111851 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111851 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2841.28 | −0.0962740 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2061.15 | −0.0696211 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8283.84 | 0.278936 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28587.3 | −0.959594 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21752.2 | −0.727886 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6280.71 | −0.209516 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26064.0 | −0.866765 | −0.433382 | − | 0.901210i | \(-0.642680\pi\) | ||||
−0.433382 | + | 0.901210i | \(0.642680\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13755.9 | −0.456041 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25739.5 | 0.850691 | 0.425345 | − | 0.905031i | \(-0.360153\pi\) | ||||
0.425345 | + | 0.905031i | \(0.360153\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −127.749 | −0.00420908 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1627.02 | 0.0534422 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7083.18 | −0.231946 | −0.115973 | − | 0.993252i | \(-0.536999\pi\) | ||||
−0.115973 | + | 0.993252i | \(0.536999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −364.972 | −0.0119148 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16995.3 | −0.553128 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42357.2 | −1.37435 | −0.687175 | − | 0.726492i | \(-0.741149\pi\) | ||||
−0.687175 | + | 0.726492i | \(0.741149\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18277.6 | 0.591241 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16854.0 | 0.543536 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10261.5 | −0.329925 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23366.7 | 0.749007 | 0.374504 | − | 0.927225i | \(-0.377813\pi\) | ||||
0.374504 | + | 0.927225i | \(0.377813\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42907.8 | 1.37124 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15153.9 | −0.482825 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48861.4 | 1.55211 | 0.776056 | − | 0.630664i | \(-0.217218\pi\) | ||||
0.776056 | + | 0.630664i | \(0.217218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7538.39 | −0.238743 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1840.4.a.s.1.6 | 6 | ||
4.3 | odd | 2 | 920.4.a.b.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.4.a.b.1.1 | ✓ | 6 | 4.3 | odd | 2 | ||
1840.4.a.s.1.6 | 6 | 1.1 | even | 1 | trivial |