Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,4,Mod(1,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, 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("1440.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.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: | \(84.9627504083\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.16773.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 17x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.14660\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.5864 | 1.21955 | 0.609776 | − | 0.792574i | \(-0.291260\pi\) | ||||
0.609776 | + | 0.792574i | \(0.291260\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.39560 | 0.175304 | 0.0876521 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876521 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 78.5364 | 1.67555 | 0.837773 | − | 0.546019i | \(-0.183858\pi\) | ||||
0.837773 | + | 0.546019i | \(0.183858\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 56.1548 | 0.801150 | 0.400575 | − | 0.916264i | \(-0.368810\pi\) | ||||
0.400575 | + | 0.916264i | \(0.368810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 82.9180 | 1.00119 | 0.500597 | − | 0.865680i | \(-0.333114\pi\) | ||||
0.500597 | + | 0.865680i | \(0.333114\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.2548 | −0.0929681 | −0.0464841 | − | 0.998919i | \(-0.514802\pi\) | ||||
−0.0464841 | + | 0.998919i | \(0.514802\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −135.836 | −0.869797 | −0.434899 | − | 0.900479i | \(-0.643216\pi\) | ||||
−0.434899 | + | 0.900479i | \(0.643216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.2188 | 0.256191 | 0.128096 | − | 0.991762i | \(-0.459114\pi\) | ||||
0.128096 | + | 0.991762i | \(0.459114\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −112.932 | −0.545400 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 128.628 | 0.571524 | 0.285762 | − | 0.958301i | \(-0.407753\pi\) | ||||
0.285762 | + | 0.958301i | \(0.407753\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 174.218 | 0.663615 | 0.331808 | − | 0.943347i | \(-0.392341\pi\) | ||||
0.331808 | + | 0.943347i | \(0.392341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −270.455 | −0.959164 | −0.479582 | − | 0.877497i | \(-0.659212\pi\) | ||||
−0.479582 | + | 0.877497i | \(0.659212\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −596.964 | −1.85268 | −0.926342 | − | 0.376684i | \(-0.877064\pi\) | ||||
−0.926342 | + | 0.376684i | \(0.877064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 167.146 | 0.487305 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.289677 | 0.000750759 0 | 0.000375379 | − | 1.00000i | \(-0.499881\pi\) | ||||
0.000375379 | 1.00000i | \(0.499881\pi\) | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −31.9780 | −0.0783984 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 655.760 | 1.44699 | 0.723497 | − | 0.690327i | \(-0.242533\pi\) | ||||
0.723497 | + | 0.690327i | \(0.242533\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.7433 | 0.102310 | 0.0511552 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511552 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −392.682 | −0.749327 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 358.755 | 0.654163 | 0.327082 | − | 0.944996i | \(-0.393935\pi\) | ||||
0.327082 | + | 0.944996i | \(0.393935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −97.3007 | −0.162640 | −0.0813202 | − | 0.996688i | \(-0.525914\pi\) | ||||
−0.0813202 | + | 0.996688i | \(0.525914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −617.219 | −0.989589 | −0.494794 | − | 0.869010i | \(-0.664757\pi\) | ||||
−0.494794 | + | 0.869010i | \(0.664757\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 144.454 | 0.213792 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 448.728 | 0.639062 | 0.319531 | − | 0.947576i | \(-0.396475\pi\) | ||||
0.319531 | + | 0.947576i | \(0.396475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 723.684 | 0.957044 | 0.478522 | − | 0.878076i | \(-0.341173\pi\) | ||||
0.478522 | + | 0.878076i | \(0.341173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −280.774 | −0.358285 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −112.835 | −0.134388 | −0.0671939 | − | 0.997740i | \(-0.521405\pi\) | ||||
−0.0671939 | + | 0.997740i | \(0.521405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1773.86 | 2.04341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −414.590 | −0.447748 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −396.743 | −0.415290 | −0.207645 | − | 0.978204i | \(-0.566580\pi\) | ||||
−0.207645 | + | 0.978204i | \(0.566580\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1816.33 | 1.78942 | 0.894712 | − | 0.446643i | \(-0.147381\pi\) | ||||
0.894712 | + | 0.446643i | \(0.147381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1467.15 | 1.40352 | 0.701759 | − | 0.712414i | \(-0.252398\pi\) | ||||
0.701759 | + | 0.712414i | \(0.252398\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1216.78 | −1.09935 | −0.549674 | − | 0.835379i | \(-0.685248\pi\) | ||||
−0.549674 | + | 0.835379i | \(0.685248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1210.40 | −1.06363 | −0.531813 | − | 0.846862i | \(-0.678489\pi\) | ||||
−0.531813 | + | 0.846862i | \(0.678489\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2382.43 | −1.98336 | −0.991682 | − | 0.128712i | \(-0.958916\pi\) | ||||
−0.991682 | + | 0.128712i | \(0.958916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 51.2738 | 0.0415766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1268.34 | 0.977043 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1290.10 | −0.969268 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1855.59 | 1.29651 | 0.648255 | − | 0.761423i | \(-0.275499\pi\) | ||||
0.648255 | + | 0.761423i | \(0.275499\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 289.842 | 0.193310 | 0.0966550 | − | 0.995318i | \(-0.469186\pi\) | ||||
0.0966550 | + | 0.995318i | \(0.469186\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1872.82 | 1.22101 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1193.52 | 0.744303 | 0.372152 | − | 0.928172i | \(-0.378620\pi\) | ||||
0.372152 | + | 0.928172i | \(0.378620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 709.062 | 0.432675 | 0.216338 | − | 0.976319i | \(-0.430589\pi\) | ||||
0.216338 | + | 0.976319i | \(0.430589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 502.288 | 0.293730 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 679.180 | 0.388985 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1658.38 | 0.911809 | 0.455905 | − | 0.890029i | \(-0.349316\pi\) | ||||
0.455905 | + | 0.890029i | \(0.349316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1180.56 | −0.636242 | −0.318121 | − | 0.948050i | \(-0.603052\pi\) | ||||
−0.318121 | + | 0.948050i | \(0.603052\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −221.094 | −0.114572 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 683.954 | 0.347678 | 0.173839 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173839 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −231.618 | −0.113379 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2452.67 | 1.17858 | 0.589288 | − | 0.807923i | \(-0.299408\pi\) | ||||
0.589288 | + | 0.807923i | \(0.299408\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2855.65 | 1.32321 | 0.661606 | − | 0.749851i | \(-0.269875\pi\) | ||||
0.661606 | + | 0.749851i | \(0.269875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3970.97 | 1.80745 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3596.35 | −1.58049 | −0.790247 | − | 0.612789i | \(-0.790048\pi\) | ||||
−0.790247 | + | 0.612789i | \(0.790048\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 564.660 | 0.243910 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1281.58 | −0.535139 | −0.267570 | − | 0.963539i | \(-0.586221\pi\) | ||||
−0.267570 | + | 0.963539i | \(0.586221\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2385.39 | 0.979583 | 0.489791 | − | 0.871840i | \(-0.337073\pi\) | ||||
0.489791 | + | 0.871840i | \(0.337073\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −643.142 | −0.255593 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 359.144 | 0.140445 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −929.171 | −0.352002 | −0.176001 | − | 0.984390i | \(-0.556316\pi\) | ||||
−0.176001 | + | 0.984390i | \(0.556316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2126.98 | −0.793282 | −0.396641 | − | 0.917974i | \(-0.629824\pi\) | ||||
−0.396641 | + | 0.917974i | \(0.629824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1655.73 | 0.598811 | 0.299406 | − | 0.954126i | \(-0.403212\pi\) | ||||
0.299406 | + | 0.954126i | \(0.403212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5009.24 | 1.78440 | 0.892201 | − | 0.451639i | \(-0.149160\pi\) | ||||
0.892201 | + | 0.451639i | \(0.149160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3068.05 | −1.06076 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −871.088 | −0.296778 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 530.311 | 0.175514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4958.57 | 1.61783 | 0.808915 | − | 0.587925i | \(-0.200055\pi\) | ||||
0.808915 | + | 0.587925i | \(0.200055\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1352.28 | 0.428951 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 998.743 | 0.312438 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4410.20 | 1.34236 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4155.51 | 1.24786 | 0.623931 | − | 0.781479i | \(-0.285535\pi\) | ||||
0.623931 | + | 0.781479i | \(0.285535\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5168.08 | 1.51109 | 0.755545 | − | 0.655096i | \(-0.227372\pi\) | ||||
0.755545 | + | 0.655096i | \(0.227372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4391.41 | −1.26722 | −0.633608 | − | 0.773654i | \(-0.718427\pi\) | ||||
−0.633608 | + | 0.773654i | \(0.718427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2756.05 | −0.774913 | −0.387456 | − | 0.921888i | \(-0.626646\pi\) | ||||
−0.387456 | + | 0.921888i | \(0.626646\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2984.82 | 0.828545 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4742.41 | −1.28352 | −0.641759 | − | 0.766906i | \(-0.721795\pi\) | ||||
−0.641759 | + | 0.766906i | \(0.721795\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1389.76 | 0.371461 | 0.185730 | − | 0.982601i | \(-0.440535\pi\) | ||||
0.185730 | + | 0.982601i | \(0.440535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −835.729 | −0.217930 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6512.09 | 1.67755 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5966.89 | −1.50051 | −0.750253 | − | 0.661151i | \(-0.770068\pi\) | ||||
−0.750253 | + | 0.661151i | \(0.770068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −65.5854 | −0.0162977 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4707.74 | −1.14265 | −0.571324 | − | 0.820725i | \(-0.693570\pi\) | ||||
−0.571324 | + | 0.820725i | \(0.693570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2905.25 | 0.697002 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1137.88 | −0.266787 | −0.133393 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133393 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.44839 | −0.000335749 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2700.80 | 0.612158 | 0.306079 | − | 0.952006i | \(-0.400983\pi\) | ||||
0.306079 | + | 0.952006i | \(0.400983\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 521.725 | 0.116947 | 0.0584734 | − | 0.998289i | \(-0.481377\pi\) | ||||
0.0584734 | + | 0.998289i | \(0.481377\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 159.890 | 0.0350608 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2017.18 | −0.437548 | −0.218774 | − | 0.975776i | \(-0.570206\pi\) | ||||
−0.218774 | + | 0.975776i | \(0.570206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3532.33 | −0.749898 | −0.374949 | − | 0.927045i | \(-0.622340\pi\) | ||||
−0.374949 | + | 0.927045i | \(0.622340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1839.14 | 0.386309 | 0.193155 | − | 0.981168i | \(-0.438128\pi\) | ||||
0.193155 | + | 0.981168i | \(0.438128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3934.95 | 0.809313 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1759.64 | −0.358159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8569.30 | 1.70861 | 0.854307 | − | 0.519769i | \(-0.173982\pi\) | ||||
0.854307 | + | 0.519769i | \(0.173982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3278.80 | −0.647116 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −805.373 | −0.155772 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6108.61 | −1.16975 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −243.716 | −0.0457546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4574.84 | −0.850488 | −0.425244 | − | 0.905079i | \(-0.639812\pi\) | ||||
−0.425244 | + | 0.905079i | \(0.639812\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2963.60 | −0.540355 | −0.270177 | − | 0.962811i | \(-0.587082\pi\) | ||||
−0.270177 | + | 0.962811i | \(0.587082\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2131.23 | 0.384869 | 0.192435 | − | 0.981310i | \(-0.438362\pi\) | ||||
0.192435 | + | 0.981310i | \(0.438362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8492.05 | 1.50461 | 0.752305 | − | 0.658815i | \(-0.228942\pi\) | ||||
0.752305 | + | 0.658815i | \(0.228942\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −868.753 | −0.152479 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4656.25 | 0.802107 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1963.41 | 0.335109 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13483.3 | −2.25944 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6073.88 | 1.00861 | 0.504306 | − | 0.863525i | \(-0.331748\pi\) | ||||
0.504306 | + | 0.863525i | \(0.331748\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1793.78 | −0.292551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6616.84 | −1.06956 | −0.534781 | − | 0.844991i | \(-0.679606\pi\) | ||||
−0.534781 | + | 0.844991i | \(0.679606\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 282.806 | 0.0449114 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3971.92 | −0.625257 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6346.58 | 0.981850 | 0.490925 | − | 0.871202i | \(-0.336659\pi\) | ||||
0.490925 | + | 0.871202i | \(0.336659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4000.58 | 0.613599 | 0.306799 | − | 0.951774i | \(-0.400742\pi\) | ||||
0.306799 | + | 0.951774i | \(0.400742\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 952.711 | 0.143648 | 0.0718239 | − | 0.997417i | \(-0.477118\pi\) | ||||
0.0718239 | + | 0.997417i | \(0.477118\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 486.504 | 0.0727350 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3226.49 | 0.474339 | 0.237169 | − | 0.971468i | \(-0.423780\pi\) | ||||
0.237169 | + | 0.971468i | \(0.423780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4016 | 0.00239125 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3086.09 | 0.442557 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9864.26 | 1.40303 | 0.701513 | − | 0.712657i | \(-0.252508\pi\) | ||||
0.701513 | + | 0.712657i | \(0.252508\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.54276 | 0.000915589 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4388.19 | −0.609147 | −0.304573 | − | 0.952489i | \(-0.598514\pi\) | ||||
−0.304573 | + | 0.952489i | \(0.598514\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10668.1 | −1.45738 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4973.16 | −0.674022 | −0.337011 | − | 0.941501i | \(-0.609416\pi\) | ||||
−0.337011 | + | 0.941501i | \(0.609416\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4210.82 | −0.561783 | −0.280892 | − | 0.959739i | \(-0.590630\pi\) | ||||
−0.280892 | + | 0.959739i | \(0.590630\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −722.268 | −0.0956109 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1520.60 | 0.198194 | 0.0990972 | − | 0.995078i | \(-0.468405\pi\) | ||||
0.0990972 | + | 0.995078i | \(0.468405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −575.855 | −0.0744814 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2243.64 | −0.285797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8353.74 | 1.05608 | 0.528038 | − | 0.849221i | \(-0.322928\pi\) | ||||
0.528038 | + | 0.849221i | \(0.322928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3496.50 | −0.435429 | −0.217714 | − | 0.976012i | \(-0.569860\pi\) | ||||
−0.217714 | + | 0.976012i | \(0.569860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3472.78 | 0.429260 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 822.655 | 0.100190 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1233.74 | −0.149155 | −0.0745777 | − | 0.997215i | \(-0.523761\pi\) | ||||
−0.0745777 | + | 0.997215i | \(0.523761\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14811.3 | 1.76468 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3618.42 | −0.428003 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13879.9 | 1.61832 | 0.809159 | − | 0.587590i | \(-0.199923\pi\) | ||||
0.809159 | + | 0.587590i | \(0.199923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9607.40 | 1.11220 | 0.556100 | − | 0.831116i | \(-0.312297\pi\) | ||||
0.556100 | + | 0.831116i | \(0.312297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1403.87 | 0.160230 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1100.94 | 0.124773 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13349.8 | −1.49196 | −0.745981 | − | 0.665968i | \(-0.768019\pi\) | ||||
−0.745981 | + | 0.665968i | \(0.768019\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7546.88 | 0.837598 | 0.418799 | − | 0.908079i | \(-0.362451\pi\) | ||||
0.418799 | + | 0.908079i | \(0.362451\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −850.305 | −0.0930792 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9884.96 | 1.07468 | 0.537339 | − | 0.843367i | \(-0.319430\pi\) | ||||
0.537339 | + | 0.843367i | \(0.319430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4358.12 | 0.467405 | 0.233703 | − | 0.972308i | \(-0.424916\pi\) | ||||
0.233703 | + | 0.972308i | \(0.424916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 564.176 | 0.0601000 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4821.91 | 0.506816 | 0.253408 | − | 0.967360i | \(-0.418449\pi\) | ||||
0.253408 | + | 0.967360i | \(0.418449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1114.23 | 0.116335 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8869.28 | −0.913842 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7952.00 | 0.813958 | 0.406979 | − | 0.913438i | \(-0.366582\pi\) | ||||
0.406979 | + | 0.913438i | \(0.366582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14851.4 | −1.50043 | −0.750215 | − | 0.661194i | \(-0.770050\pi\) | ||||
−0.750215 | + | 0.661194i | \(0.770050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6129.34 | −0.615237 | −0.307618 | − | 0.951510i | \(-0.599532\pi\) | ||||
−0.307618 | + | 0.951510i | \(0.599532\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8441.69 | −0.836477 | −0.418238 | − | 0.908337i | \(-0.637352\pi\) | ||||
−0.418238 | + | 0.908337i | \(0.637352\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8102.99 | 0.797785 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1729.72 | −0.168145 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2072.95 | 0.200239 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18616.3 | 1.77579 | 0.887894 | − | 0.460049i | \(-0.152168\pi\) | ||||
0.887894 | + | 0.460049i | \(0.152168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10102.0 | 0.957614 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1983.72 | 0.185724 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16711.5 | −1.55497 | −0.777484 | − | 0.628903i | \(-0.783504\pi\) | ||||
−0.777484 | + | 0.628903i | \(0.783504\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2982.33 | −0.274115 | −0.137058 | − | 0.990563i | \(-0.543765\pi\) | ||||
−0.137058 | + | 0.990563i | \(0.543765\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7627.85 | −0.696838 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2197.67 | −0.198348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10128.7 | −0.908662 | −0.454331 | − | 0.890833i | \(-0.650122\pi\) | ||||
−0.454331 | + | 0.890833i | \(0.650122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20086.0 | 1.78050 | 0.890249 | − | 0.455475i | \(-0.150530\pi\) | ||||
0.890249 | + | 0.455475i | \(0.150530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9081.67 | −0.800255 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14570.7 | 1.26883 | 0.634416 | − | 0.772992i | \(-0.281241\pi\) | ||||
0.634416 | + | 0.772992i | \(0.281241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13940.7 | −1.20685 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7335.74 | −0.627672 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3817.94 | −0.324783 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16023.8 | −1.34743 | −0.673717 | − | 0.738989i | \(-0.735303\pi\) | ||||
−0.673717 | + | 0.738989i | \(0.735303\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18506.3 | −1.54727 | −0.773636 | − | 0.633631i | \(-0.781564\pi\) | ||||
−0.773636 | + | 0.633631i | \(0.781564\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2483.10 | 0.205247 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12061.8 | −0.991357 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13682.4 | 1.11192 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6083.88 | 0.491643 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1069.00 | 0.0854266 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20604.1 | −1.63741 | −0.818704 | − | 0.574216i | \(-0.805307\pi\) | ||||
−0.818704 | + | 0.574216i | \(0.805307\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6051.99 | 0.475668 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18362.0 | −1.43529 | −0.717646 | − | 0.696408i | \(-0.754780\pi\) | ||||
−0.717646 | + | 0.696408i | \(0.754780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11263.3 | −0.870837 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10135.2 | 0.779369 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6329.02 | −0.481452 | −0.240726 | − | 0.970593i | \(-0.577386\pi\) | ||||
−0.240726 | + | 0.970593i | \(0.577386\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21240.6 | −1.60712 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9929.10 | −0.743271 | −0.371635 | − | 0.928379i | \(-0.621203\pi\) | ||||
−0.371635 | + | 0.928379i | \(0.621203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11912.1 | 0.886987 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12881.6 | −0.949074 | −0.474537 | − | 0.880236i | \(-0.657385\pi\) | ||||
−0.474537 | + | 0.880236i | \(0.657385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16052.6 | −1.17650 | −0.588251 | − | 0.808679i | \(-0.700183\pi\) | ||||
−0.588251 | + | 0.808679i | \(0.700183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −256.369 | −0.0185936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21368.2 | −1.54172 | −0.770858 | − | 0.637007i | \(-0.780172\pi\) | ||||
−0.770858 | + | 0.637007i | \(0.780172\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16345.4 | 1.16716 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.85266 | 0.000131611 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13913.6 | 0.978321 | 0.489160 | − | 0.872194i | \(-0.337303\pi\) | ||||
0.489160 | + | 0.872194i | \(0.337303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3666.53 | 0.256497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5244.77 | −0.363199 | −0.181600 | − | 0.983373i | \(-0.558127\pi\) | ||||
−0.181600 | + | 0.983373i | \(0.558127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6341.68 | −0.436947 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3140.90 | 0.214246 | 0.107123 | − | 0.994246i | \(-0.465836\pi\) | ||||
0.107123 | + | 0.994246i | \(0.465836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22736.7 | −1.54317 | −0.771587 | − | 0.636124i | \(-0.780537\pi\) | ||||
−0.771587 | + | 0.636124i | \(0.780537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6450.48 | 0.433470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.5200 | 0.00184020 | 0.000920102 | − | 1.00000i | \(-0.499707\pi\) | ||||
0.000920102 | 1.00000i | \(0.499707\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46883.4 | −3.10425 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10729.4 | −0.706944 | −0.353472 | − | 0.935445i | \(-0.614999\pi\) | ||||
−0.353472 | + | 0.935445i | \(0.614999\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9914.94 | −0.646937 | −0.323469 | − | 0.946239i | \(-0.604849\pi\) | ||||
−0.323469 | + | 0.946239i | \(0.604849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6432.47 | 0.417678 | 0.208839 | − | 0.977950i | \(-0.433031\pi\) | ||||
0.208839 | + | 0.977950i | \(0.433031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2548.54 | −0.163893 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7223.10 | 0.457876 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19656.6 | −1.24012 | −0.620061 | − | 0.784554i | \(-0.712892\pi\) | ||||
−0.620061 | + | 0.784554i | \(0.712892\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9277.94 | −0.579817 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13127.0 | 0.816502 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16342.0 | −1.00698 | −0.503488 | − | 0.864002i | \(-0.667950\pi\) | ||||
−0.503488 | + | 0.864002i | \(0.667950\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3375.38 | 0.207017 | 0.103508 | − | 0.994629i | \(-0.466993\pi\) | ||||
0.103508 | + | 0.994629i | \(0.466993\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13862.2 | 0.842319 | 0.421160 | − | 0.906986i | \(-0.361623\pi\) | ||||
0.421160 | + | 0.906986i | \(0.361623\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4193.98 | 0.253664 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14818.2 | −0.888025 | −0.444013 | − | 0.896021i | \(-0.646445\pi\) | ||||
−0.444013 | + | 0.896021i | \(0.646445\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1449.21 | −0.0864509 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4730.05 | −0.279600 | −0.139800 | − | 0.990180i | \(-0.544646\pi\) | ||||
−0.139800 | + | 0.990180i | \(0.544646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10646.7 | 0.626486 | 0.313243 | − | 0.949673i | \(-0.398585\pi\) | ||||
0.313243 | + | 0.949673i | \(0.398585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9364.10 | −0.546052 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1392.97 | 0.0808635 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 311.742 | 0.0179354 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4179.96 | −0.239414 | −0.119707 | − | 0.992809i | \(-0.538196\pi\) | ||||
−0.119707 | + | 0.992809i | \(0.538196\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31610.0 | 1.79449 | 0.897245 | − | 0.441534i | \(-0.145565\pi\) | ||||
0.897245 | + | 0.441534i | \(0.145565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8961.00 | −0.506468 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12901.6 | 0.722790 | 0.361395 | − | 0.932413i | \(-0.382301\pi\) | ||||
0.361395 | + | 0.932413i | \(0.382301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5967.61 | −0.332862 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.7502 | 0.00125793 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5650.46 | −0.311076 | −0.155538 | − | 0.987830i | \(-0.549711\pi\) | ||||
−0.155538 | + | 0.987830i | \(0.549711\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3545.31 | −0.193498 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9783.16 | 0.531655 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17485.6 | 0.942112 | 0.471056 | − | 0.882103i | \(-0.343873\pi\) | ||||
0.471056 | + | 0.882103i | \(0.343873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10665.6 | 0.572207 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41024.4 | 2.18230 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21485.3 | −1.13808 | −0.569039 | − | 0.822310i | \(-0.692685\pi\) | ||||
−0.569039 | + | 0.822310i | \(0.692685\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −453.453 | −0.0238176 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2511.44 | −0.131360 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3342.83 | 0.173389 | 0.0866944 | − | 0.996235i | \(-0.472370\pi\) | ||||
0.0866944 | + | 0.996235i | \(0.472370\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33137.6 | 1.71166 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3395.90 | −0.173959 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29934.3 | −1.52710 | −0.763549 | − | 0.645750i | \(-0.776545\pi\) | ||||
−0.763549 | + | 0.645750i | \(0.776545\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15187.4 | −0.768434 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8732.45 | 0.440028 | 0.220014 | − | 0.975497i | \(-0.429390\pi\) | ||||
0.220014 | + | 0.975497i | \(0.429390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2294.45 | 0.114677 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25004.3 | −1.24465 | −0.622327 | − | 0.782758i | \(-0.713812\pi\) | ||||
−0.622327 | + | 0.782758i | \(0.713812\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29841.4 | −1.47345 | −0.736727 | − | 0.676190i | \(-0.763630\pi\) | ||||
−0.736727 | + | 0.676190i | \(0.763630\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8291.89 | −0.407773 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27482.6 | −1.34071 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16131.9 | 0.783836 | 0.391918 | − | 0.920000i | \(-0.371812\pi\) | ||||
0.391918 | + | 0.920000i | \(0.371812\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5902.80 | 0.284536 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9728.98 | 0.467115 | 0.233557 | − | 0.972343i | \(-0.424963\pi\) | ||||
0.233557 | + | 0.972343i | \(0.424963\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12912.5 | 0.615082 | 0.307541 | − | 0.951535i | \(-0.400494\pi\) | ||||
0.307541 | + | 0.951535i | \(0.400494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27338.6 | −1.29715 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 51501.0 | 2.42450 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32798.5 | 1.53803 | 0.769014 | − | 0.639232i | \(-0.220747\pi\) | ||||
0.769014 | + | 0.639232i | \(0.220747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3174.82 | 0.147724 | 0.0738618 | − | 0.997268i | \(-0.476468\pi\) | ||||
0.0738618 | + | 0.997268i | \(0.476468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1105.47 | 0.0512382 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14445.8 | 0.664408 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −622.297 | −0.0285115 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3419.77 | −0.155487 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18315.6 | 0.829582 | 0.414791 | − | 0.909917i | \(-0.363855\pi\) | ||||
0.414791 | + | 0.909917i | \(0.363855\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −53810.5 | −2.41881 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3828.12 | 0.171426 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32597.9 | −1.44878 | −0.724389 | − | 0.689391i | \(-0.757878\pi\) | ||||
−0.724389 | + | 0.689391i | \(0.757878\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33522.4 | −1.48428 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3947.48 | −0.173479 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1158.09 | 0.0507048 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11753.1 | 0.510774 | 0.255387 | − | 0.966839i | \(-0.417797\pi\) | ||||
0.255387 | + | 0.966839i | \(0.417797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35501.2 | −1.53713 | −0.768567 | − | 0.639769i | \(-0.779030\pi\) | ||||
−0.768567 | + | 0.639769i | \(0.779030\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12263.4 | −0.527076 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22425.6 | −0.960310 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25528.6 | 1.08520 | 0.542602 | − | 0.839990i | \(-0.317439\pi\) | ||||
0.542602 | + | 0.839990i | \(0.317439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30522.5 | −1.29277 | −0.646384 | − | 0.763013i | \(-0.723719\pi\) | ||||
−0.646384 | + | 0.763013i | \(0.723719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43126.4 | 1.81336 | 0.906682 | − | 0.421814i | \(-0.138606\pi\) | ||||
0.906682 | + | 0.421814i | \(0.138606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19469.8 | −0.815699 | −0.407849 | − | 0.913049i | \(-0.633721\pi\) | ||||
−0.407849 | + | 0.913049i | \(0.633721\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9386.04 | 0.390404 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14278.2 | −0.591759 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21999.5 | −0.905252 | −0.452626 | − | 0.891700i | \(-0.649513\pi\) | ||||
−0.452626 | + | 0.891700i | \(0.649513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5937.56 | −0.243452 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19854.9 | −0.808317 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29138.6 | −1.18207 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1319.05 | −0.0531335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4233.65 | −0.169938 | −0.0849691 | − | 0.996384i | \(-0.527079\pi\) | ||||
−0.0849691 | + | 0.996384i | \(0.527079\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26604.8 | 1.06045 | 0.530223 | − | 0.847858i | \(-0.322108\pi\) | ||||
0.530223 | + | 0.847858i | \(0.322108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32033.5 | 1.27237 | 0.636187 | − | 0.771535i | \(-0.280511\pi\) | ||||
0.636187 | + | 0.771535i | \(0.280511\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34015.1 | 1.34170 | 0.670851 | − | 0.741592i | \(-0.265929\pi\) | ||||
0.670851 | + | 0.741592i | \(0.265929\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17981.7 | 0.706818 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2869.89 | 0.112030 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28175.4 | 1.09608 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2823.30 | −0.109080 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34479.6 | 1.32759 | 0.663793 | − | 0.747916i | \(-0.268946\pi\) | ||||
0.663793 | + | 0.747916i | \(0.268946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33877.5 | 1.29553 | 0.647765 | − | 0.761841i | \(-0.275704\pi\) | ||||
0.647765 | + | 0.761841i | \(0.275704\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3423.93 | −0.130492 | −0.0652460 | − | 0.997869i | \(-0.520783\pi\) | ||||
−0.0652460 | + | 0.997869i | \(0.520783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38158.8 | 1.44447 | 0.722237 | − | 0.691646i | \(-0.243114\pi\) | ||||
0.722237 | + | 0.691646i | \(0.243114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41911.0 | 1.58116 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −49499.1 | −1.85490 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6407.91 | 0.239322 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6006.51 | −0.222834 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.2668 | 0.000601470 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11926.9 | −0.438083 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5349.09 | 0.195826 | 0.0979128 | − | 0.995195i | \(-0.468783\pi\) | ||||
0.0979128 | + | 0.995195i | \(0.468783\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53491.9 | −1.94541 | −0.972703 | − | 0.232054i | \(-0.925455\pi\) | ||||
−0.972703 | + | 0.232054i | \(0.925455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4628.39 | 0.167774 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6546.49 | 0.235752 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30116.2 | 1.08100 | 0.540502 | − | 0.841343i | \(-0.318234\pi\) | ||||
0.540502 | + | 0.841343i | \(0.318234\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7641.65 | −0.272511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3215.71 | 0.114305 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3791.12 | 0.133889 | 0.0669444 | − | 0.997757i | \(-0.478675\pi\) | ||||
0.0669444 | + | 0.997757i | \(0.478675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13859.4 | 0.487888 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1795.72 | −0.0628088 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38027.5 | −1.32583 | −0.662916 | − | 0.748693i | \(-0.730682\pi\) | ||||
−0.662916 | + | 0.748693i | \(0.730682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25378.5 | −0.879187 | −0.439594 | − | 0.898197i | \(-0.644878\pi\) | ||||
−0.439594 | + | 0.898197i | \(0.644878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1786.56 | −0.0616951 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18643.7 | 0.639744 | 0.319872 | − | 0.947461i | \(-0.396360\pi\) | ||||
0.319872 | + | 0.947461i | \(0.396360\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48474.1 | −1.65810 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38558.2 | −1.31062 | −0.655311 | − | 0.755360i | \(-0.727462\pi\) | ||||
−0.655311 | + | 0.755360i | \(0.727462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4645.85 | 0.157420 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26957.4 | 0.907716 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27835.7 | −0.934366 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10634.9 | 0.354767 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33635.3 | 1.11855 | 0.559275 | − | 0.828982i | \(-0.311080\pi\) | ||||
0.559275 | + | 0.828982i | \(0.311080\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37902.0 | −1.25266 | −0.626329 | − | 0.779559i | \(-0.715443\pi\) | ||||
−0.626329 | + | 0.779559i | \(0.715443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16015.2 | 0.527670 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50034.8 | 1.63844 | 0.819219 | − | 0.573481i | \(-0.194407\pi\) | ||||
0.819219 | + | 0.573481i | \(0.194407\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −721.649 | −0.0235587 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3864.79 | 0.125400 | 0.0626998 | − | 0.998032i | \(-0.480029\pi\) | ||||
0.0626998 | + | 0.998032i | \(0.480029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8278.64 | −0.267796 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2773.46 | 0.0891717 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33515.9 | 1.07434 | 0.537168 | − | 0.843476i | \(-0.319494\pi\) | ||||
0.537168 | + | 0.843476i | \(0.319494\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25046.2 | −0.798009 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21937.2 | −0.696848 | −0.348424 | − | 0.937337i | \(-0.613283\pi\) | ||||
−0.348424 | + | 0.937337i | \(0.613283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1440.4.a.bi.1.3 | yes | 3 | |
3.2 | odd | 2 | 1440.4.a.bk.1.3 | yes | 3 | ||
4.3 | odd | 2 | 1440.4.a.bh.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 1440.4.a.bj.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.4.a.bh.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
1440.4.a.bi.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
1440.4.a.bj.1.1 | yes | 3 | 12.11 | even | 2 | ||
1440.4.a.bk.1.3 | yes | 3 | 3.2 | odd | 2 |