Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(34.6931230834\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.82475 | −0.878753 | −0.439376 | − | 0.898303i | \(-0.644801\pi\) | ||||
−0.439376 | + | 0.898303i | \(0.644801\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.1752 | −0.388545 | −0.194273 | − | 0.980948i | \(-0.562235\pi\) | ||||
−0.194273 | + | 0.980948i | \(0.562235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.1238 | 0.557341 | 0.278670 | − | 0.960387i | \(-0.410106\pi\) | ||||
0.278670 | + | 0.960387i | \(0.410106\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −29.4743 | −0.507348 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 78.5980 | 1.12134 | 0.560671 | − | 0.828039i | \(-0.310543\pi\) | ||||
0.560671 | + | 0.828039i | \(0.310543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −73.1752 | −0.883555 | −0.441778 | − | 0.897125i | \(-0.645652\pi\) | ||||
−0.441778 | + | 0.897125i | \(0.645652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −96.0000 | −0.870321 | −0.435161 | − | 0.900353i | \(-0.643308\pi\) | ||||
−0.435161 | + | 0.900353i | \(0.643308\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −28.4743 | −0.227794 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 173.021 | 1.10790 | 0.553951 | − | 0.832549i | \(-0.313120\pi\) | ||||
0.553951 | + | 0.832549i | \(0.313120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −67.2475 | −0.389613 | −0.194807 | − | 0.980842i | \(-0.562408\pi\) | ||||
−0.194807 | + | 0.980842i | \(0.562408\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42.5257 | −0.224327 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −301.670 | −1.34039 | −0.670193 | − | 0.742187i | \(-0.733789\pi\) | ||||
−0.670193 | + | 0.742187i | \(0.733789\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 78.3713 | 0.321781 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −472.042 | −1.79806 | −0.899031 | − | 0.437886i | \(-0.855727\pi\) | ||||
−0.899031 | + | 0.437886i | \(0.855727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −463.670 | −1.64440 | −0.822198 | − | 0.569201i | \(-0.807253\pi\) | ||||
−0.822198 | + | 0.569201i | \(0.807253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −88.4228 | −0.292918 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 91.1960 | 0.283028 | 0.141514 | − | 0.989936i | \(-0.454803\pi\) | ||||
0.141514 | + | 0.989936i | \(0.454803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 235.794 | 0.647407 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −163.268 | −0.423144 | −0.211572 | − | 0.977362i | \(-0.567858\pi\) | ||||
−0.211572 | + | 0.977362i | \(0.567858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 139.268 | 0.341435 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −219.526 | −0.510121 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 600.526 | 1.32512 | 0.662558 | − | 0.749011i | \(-0.269471\pi\) | ||||
0.662558 | + | 0.749011i | \(0.269471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −571.691 | −1.19996 | −0.599980 | − | 0.800015i | \(-0.704825\pi\) | ||||
−0.599980 | + | 0.800015i | \(0.704825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −256.659 | −0.489764 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −539.423 | −0.983597 | −0.491798 | − | 0.870709i | \(-0.663660\pi\) | ||||
−0.491798 | + | 0.870709i | \(0.663660\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −288.000 | −0.502480 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1064.39 | −1.77916 | −0.889578 | − | 0.456783i | \(-0.849002\pi\) | ||||
−0.889578 | + | 0.456783i | \(0.849002\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 442.680 | 0.709751 | 0.354875 | − | 0.934914i | \(-0.384523\pi\) | ||||
0.354875 | + | 0.934914i | \(0.384523\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −85.4228 | −0.131517 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −45.7010 | −0.0650856 | −0.0325428 | − | 0.999470i | \(-0.510361\pi\) | ||||
−0.0325428 | + | 0.999470i | \(0.510361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 686.464 | 0.907822 | 0.453911 | − | 0.891047i | \(-0.350028\pi\) | ||||
0.453911 | + | 0.891047i | \(0.350028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −772.206 | −0.985382 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 519.062 | 0.639647 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −660.145 | −0.786238 | −0.393119 | − | 0.919488i | \(-0.628604\pi\) | ||||
−0.393119 | + | 0.919488i | \(0.628604\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −201.743 | −0.224943 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 718.929 | 0.776427 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −658.320 | −0.689095 | −0.344548 | − | 0.938769i | \(-0.611968\pi\) | ||||
−0.344548 | + | 0.938769i | \(0.611968\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −127.577 | −0.129515 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1803.90 | 1.77717 | 0.888586 | − | 0.458709i | \(-0.151688\pi\) | ||||
0.888586 | + | 0.458709i | \(0.151688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1074.91 | 1.02829 | 0.514145 | − | 0.857703i | \(-0.328109\pi\) | ||||
0.514145 | + | 0.857703i | \(0.328109\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1659.35 | −1.49921 | −0.749605 | − | 0.661885i | \(-0.769757\pi\) | ||||
−0.749605 | + | 0.661885i | \(0.769757\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 598.928 | 0.526302 | 0.263151 | − | 0.964755i | \(-0.415238\pi\) | ||||
0.263151 | + | 0.964755i | \(0.415238\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −905.011 | −0.773872 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −781.650 | −0.650720 | −0.325360 | − | 0.945590i | \(-0.605486\pi\) | ||||
−0.325360 | + | 0.945590i | \(0.605486\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 943.176 | 0.764797 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 235.114 | 0.185780 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1130.06 | −0.849033 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1416.12 | −1.03811 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1507.85 | 1.07893 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 25.3722 | 0.0177277 | 0.00886385 | − | 0.999961i | \(-0.497179\pi\) | ||||
0.00886385 | + | 0.999961i | \(0.497179\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1391.01 | −0.949393 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 475.577 | 0.317186 | 0.158593 | − | 0.987344i | \(-0.449304\pi\) | ||||
0.158593 | + | 0.987344i | \(0.449304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −265.268 | −0.169116 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1058.54 | 0.660123 | 0.330062 | − | 0.943959i | \(-0.392930\pi\) | ||||
0.330062 | + | 0.943959i | \(0.392930\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2580.99 | −1.57494 | −0.787470 | − | 0.616352i | \(-0.788610\pi\) | ||||
−0.787470 | + | 0.616352i | \(0.788610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 273.588 | 0.163406 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −370.311 | −0.216552 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1699.89 | −0.973571 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −101.875 | −0.0560131 | −0.0280066 | − | 0.999608i | \(-0.508916\pi\) | ||||
−0.0280066 | + | 0.999608i | \(0.508916\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1778.42 | −0.958450 | −0.479225 | − | 0.877692i | \(-0.659082\pi\) | ||||
−0.479225 | + | 0.877692i | \(0.659082\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 707.382 | 0.373781 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 660.690 | 0.342374 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1399.26 | −0.711292 | −0.355646 | − | 0.934621i | \(-0.615739\pi\) | ||||
−0.355646 | + | 0.934621i | \(0.615739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −489.805 | −0.244302 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3615.43 | 1.73731 | 0.868656 | − | 0.495415i | \(-0.164984\pi\) | ||||
0.868656 | + | 0.495415i | \(0.164984\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 417.805 | 0.197128 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1076.72 | 0.498917 | 0.249459 | − | 0.968385i | \(-0.419747\pi\) | ||||
0.249459 | + | 0.968385i | \(0.419747\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1514.55 | −0.689372 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −658.577 | −0.294518 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1873.63 | −0.823407 | −0.411704 | − | 0.911318i | \(-0.635066\pi\) | ||||
−0.411704 | + | 0.911318i | \(0.635066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1801.58 | 0.765056 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2692.29 | −1.12420 | −0.562099 | − | 0.827070i | \(-0.690006\pi\) | ||||
−0.562099 | + | 0.827070i | \(0.690006\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −461.670 | −0.189589 | −0.0947947 | − | 0.995497i | \(-0.530219\pi\) | ||||
−0.0947947 | + | 0.995497i | \(0.530219\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1715.07 | −0.692797 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2963.84 | 1.17787 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1114.15 | −0.435692 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3764.83 | −1.42625 | −0.713124 | − | 0.701038i | \(-0.752720\pi\) | ||||
−0.713124 | + | 0.701038i | \(0.752720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2926.20 | 1.09136 | 0.545680 | − | 0.837994i | \(-0.316272\pi\) | ||||
0.545680 | + | 0.837994i | \(0.316272\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −769.978 | −0.282766 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5045.55 | 1.82477 | 0.912387 | − | 0.409330i | \(-0.134237\pi\) | ||||
0.912387 | + | 0.409330i | \(0.134237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4292.25 | −1.52899 | −0.764496 | − | 0.644628i | \(-0.777012\pi\) | ||||
−0.764496 | + | 0.644628i | \(0.777012\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1618.27 | −0.567880 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4637.69 | 1.58005 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −864.000 | −0.290107 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1037.28 | 0.343301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3625.76 | 1.18297 | 0.591487 | − | 0.806315i | \(-0.298541\pi\) | ||||
0.591487 | + | 0.806315i | \(0.298541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3193.18 | −1.02720 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4555.45 | 1.44502 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1328.04 | 0.409775 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2053.28 | 0.624969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3145.00 | 0.944417 | 0.472208 | − | 0.881487i | \(-0.343457\pi\) | ||||
0.472208 | + | 0.881487i | \(0.343457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −256.268 | −0.0759313 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1545.75 | 0.451959 | 0.225980 | − | 0.974132i | \(-0.427442\pi\) | ||||
0.225980 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4072.15 | 1.17509 | 0.587544 | − | 0.809192i | \(-0.300095\pi\) | ||||
0.587544 | + | 0.809192i | \(0.300095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3015.71 | −0.847922 | −0.423961 | − | 0.905680i | \(-0.639361\pi\) | ||||
−0.423961 | + | 0.905680i | \(0.639361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −895.978 | −0.248711 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −137.103 | −0.0375772 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4647.38 | 1.25780 | 0.628900 | − | 0.777486i | \(-0.283505\pi\) | ||||
0.628900 | + | 0.777486i | \(0.283505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1118.28 | −0.298898 | −0.149449 | − | 0.988769i | \(-0.547750\pi\) | ||||
−0.149449 | + | 0.988769i | \(0.547750\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1911.61 | −0.492441 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2059.39 | 0.524131 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −883.518 | −0.222180 | −0.111090 | − | 0.993810i | \(-0.535434\pi\) | ||||
−0.111090 | + | 0.993810i | \(0.535434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1360.82 | 0.338159 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2316.62 | −0.568911 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5868.89 | 1.42448 | 0.712240 | − | 0.701937i | \(-0.247681\pi\) | ||||
0.712240 | + | 0.701937i | \(0.247681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1557.19 | 0.369301 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4875.61 | 1.14313 | 0.571565 | − | 0.820557i | \(-0.306336\pi\) | ||||
0.571565 | + | 0.820557i | \(0.306336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1604.07 | 0.371839 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1980.43 | −0.453935 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5527.10 | 1.25276 | 0.626382 | − | 0.779516i | \(-0.284535\pi\) | ||||
0.626382 | + | 0.779516i | \(0.284535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3224.73 | 0.722836 | 0.361418 | − | 0.932404i | \(-0.382293\pi\) | ||||
0.361418 | + | 0.932404i | \(0.382293\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 403.630 | 0.0885083 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1958.04 | −0.424720 | −0.212360 | − | 0.977191i | \(-0.568115\pi\) | ||||
−0.212360 | + | 0.977191i | \(0.568115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −605.228 | −0.129871 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8531.16 | 1.81113 | 0.905563 | − | 0.424212i | \(-0.139449\pi\) | ||||
0.905563 | + | 0.424212i | \(0.139449\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7909.86 | −1.66146 | −0.830728 | − | 0.556678i | \(-0.812076\pi\) | ||||
−0.830728 | + | 0.556678i | \(0.812076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2156.79 | 0.448270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1264.65 | 0.257408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1974.96 | −0.397849 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8321.41 | 1.65919 | 0.829594 | − | 0.558367i | \(-0.188572\pi\) | ||||
0.829594 | + | 0.558367i | \(0.188572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5900.02 | −1.16445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −382.732 | −0.0747756 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2507.88 | −0.485065 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5411.69 | 1.02605 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5616.72 | 1.05447 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2541.79 | −0.472533 | −0.236267 | − | 0.971688i | \(-0.575924\pi\) | ||||
−0.236267 | + | 0.971688i | \(0.575924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3224.72 | 0.593683 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 607.709 | 0.110804 | 0.0554020 | − | 0.998464i | \(-0.482356\pi\) | ||||
0.0554020 | + | 0.998464i | \(0.482356\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11027.3 | −1.99137 | −0.995684 | − | 0.0928043i | \(-0.970417\pi\) | ||||
−0.995684 | + | 0.0928043i | \(0.970417\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7261.60 | 1.28660 | 0.643300 | − | 0.765614i | \(-0.277565\pi\) | ||||
0.643300 | + | 0.765614i | \(0.277565\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2452.61 | −0.430470 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4978.05 | −0.865570 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5751.43 | −0.990768 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −743.855 | −0.126959 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1796.78 | 0.303860 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6632.73 | 1.10141 | 0.550706 | − | 0.834699i | \(-0.314358\pi\) | ||||
0.550706 | + | 0.834699i | \(0.314358\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2715.03 | −0.446795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5299.69 | 0.864338 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8104.59 | 1.31005 | 0.655023 | − | 0.755609i | \(-0.272659\pi\) | ||||
0.655023 | + | 0.755609i | \(0.272659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2344.95 | −0.375694 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 953.250 | 0.151382 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2829.53 | 0.441556 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5937.28 | −0.918530 | −0.459265 | − | 0.888299i | \(-0.651887\pi\) | ||||
−0.459265 | + | 0.888299i | \(0.651887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −268.472 | −0.0411775 | −0.0205888 | − | 0.999788i | \(-0.506554\pi\) | ||||
−0.0205888 | + | 0.999788i | \(0.506554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 705.341 | 0.107260 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2662.81 | −0.401493 | −0.200747 | − | 0.979643i | \(-0.564337\pi\) | ||||
−0.200747 | + | 0.979643i | \(0.564337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10457.4 | 1.56344 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1563.27 | −0.229823 | −0.114911 | − | 0.993376i | \(-0.536658\pi\) | ||||
−0.114911 | + | 0.993376i | \(0.536658\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1504.38 | −0.219330 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3390.19 | −0.490189 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4349.22 | −0.623695 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1210.82 | −0.172218 | −0.0861091 | − | 0.996286i | \(-0.527443\pi\) | ||||
−0.0861091 | + | 0.996286i | \(0.527443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4248.37 | −0.599354 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4771.86 | −0.662406 | −0.331203 | − | 0.943559i | \(-0.607455\pi\) | ||||
−0.331203 | + | 0.943559i | \(0.607455\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4523.54 | 0.622919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4519.95 | 0.617479 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4118.66 | −0.558209 | −0.279104 | − | 0.960261i | \(-0.590038\pi\) | ||||
−0.279104 | + | 0.960261i | \(0.590038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 76.1166 | 0.0102351 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3535.98 | −0.471749 | −0.235875 | − | 0.971783i | \(-0.575796\pi\) | ||||
−0.235875 | + | 0.971783i | \(0.575796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4173.03 | −0.548132 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9606.46 | 1.25210 | 0.626050 | − | 0.779783i | \(-0.284671\pi\) | ||||
0.626050 | + | 0.779783i | \(0.284671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7545.41 | −0.975928 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1426.73 | 0.183127 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 449.001 | 0.0571941 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5367.07 | −0.678503 | −0.339252 | − | 0.940696i | \(-0.610174\pi\) | ||||
−0.339252 | + | 0.940696i | \(0.610174\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14065.8 | −1.75166 | −0.875828 | − | 0.482624i | \(-0.839684\pi\) | ||||
−0.875828 | + | 0.482624i | \(0.839684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1756.76 | −0.217147 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −795.805 | −0.0976392 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4276.25 | 0.520801 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3272.44 | −0.395628 | −0.197814 | − | 0.980240i | \(-0.563384\pi\) | ||||
−0.197814 | + | 0.980240i | \(0.563384\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3175.61 | 0.381122 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6744.34 | −0.797751 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7742.97 | −0.909293 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8077.07 | −0.941744 | −0.470872 | − | 0.882202i | \(-0.656061\pi\) | ||||
−0.470872 | + | 0.882202i | \(0.656061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8051.68 | 0.932101 | 0.466051 | − | 0.884758i | \(-0.345676\pi\) | ||||
0.466051 | + | 0.884758i | \(0.345676\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 820.764 | 0.0943426 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2238.02 | −0.255435 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1110.93 | −0.125026 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9900.22 | −1.10644 | −0.553221 | − | 0.833034i | \(-0.686602\pi\) | ||||
−0.553221 | + | 0.833034i | \(0.686602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 511.795 | 0.0568021 | 0.0284010 | − | 0.999597i | \(-0.490958\pi\) | ||||
0.0284010 | + | 0.999597i | \(0.490958\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5099.66 | −0.562092 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7024.82 | 0.768977 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1302.26 | 0.141580 | 0.0707898 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707898 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8200.32 | −0.879479 | −0.439739 | − | 0.898125i | \(-0.644929\pi\) | ||||
−0.439739 | + | 0.898125i | \(0.644929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6485.76 | 0.690909 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −305.626 | −0.0323392 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5788.12 | −0.608370 | −0.304185 | − | 0.952613i | \(-0.598384\pi\) | ||||
−0.304185 | + | 0.952613i | \(0.598384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6691.31 | 0.698628 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5335.27 | −0.553362 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7259.18 | 0.743041 | 0.371521 | − | 0.928425i | \(-0.378836\pi\) | ||||
0.371521 | + | 0.928425i | \(0.378836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2122.15 | 0.215802 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5966.92 | 0.602835 | 0.301418 | − | 0.953492i | \(-0.402540\pi\) | ||||
0.301418 | + | 0.953492i | \(0.402540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8884.02 | −0.891740 | −0.445870 | − | 0.895098i | \(-0.647106\pi\) | ||||
−0.445870 | + | 0.895098i | \(0.647106\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1982.07 | 0.197669 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4029.36 | 0.399265 | 0.199632 | − | 0.979871i | \(-0.436025\pi\) | ||||
0.199632 | + | 0.979871i | \(0.436025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4197.77 | −0.410665 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6572.64 | 0.638923 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2083.61 | 0.201269 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1469.41 | −0.141048 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17440.7 | 1.66364 | 0.831820 | − | 0.555045i | \(-0.187299\pi\) | ||||
0.831820 | + | 0.555045i | \(0.187299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7880.76 | −0.747052 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6467.83 | 0.605544 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4272.28 | −0.397526 | −0.198763 | − | 0.980048i | \(-0.563692\pi\) | ||||
−0.198763 | + | 0.980048i | \(0.563692\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10846.3 | 1.00304 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2013.29 | 0.185048 | 0.0925240 | − | 0.995710i | \(-0.470507\pi\) | ||||
0.0925240 | + | 0.995710i | \(0.470507\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13599.1 | 1.24234 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1253.41 | 0.113812 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4880.46 | −0.437834 | −0.218917 | − | 0.975743i | \(-0.570252\pi\) | ||||
−0.218917 | + | 0.975743i | \(0.570252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3230.16 | 0.288050 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12961.9 | −1.14899 | −0.574496 | − | 0.818508i | \(-0.694802\pi\) | ||||
−0.574496 | + | 0.818508i | \(0.694802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17722.8 | −1.56170 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4543.65 | −0.398009 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8155.38 | −0.710178 | −0.355089 | − | 0.934832i | \(-0.615550\pi\) | ||||
−0.355089 | + | 0.934832i | \(0.615550\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1975.73 | −0.170040 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10560.7 | −0.903612 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1292.73 | −0.109969 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5620.89 | −0.475394 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 332.018 | 0.0279193 | 0.0139597 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139597 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7254.83 | −0.606561 | −0.303281 | − | 0.952901i | \(-0.598082\pi\) | ||||
−0.303281 | + | 0.952901i | \(0.598082\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5285.52 | −0.436890 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2951.00 | −0.242541 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5404.73 | 0.441705 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12331.5 | −1.00213 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16302.7 | 1.31744 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8076.87 | −0.649055 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5410.19 | 0.429949 | 0.214974 | − | 0.976620i | \(-0.431033\pi\) | ||||
0.214974 | + | 0.976620i | \(0.431033\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1385.01 | −0.109459 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5884.32 | −0.462489 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18673.9 | −1.45967 | −0.729834 | − | 0.683625i | \(-0.760403\pi\) | ||||
−0.729834 | + | 0.683625i | \(0.760403\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5145.22 | −0.399987 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12660.8 | −0.978893 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8891.51 | 0.680042 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8209.48 | −0.624500 | −0.312250 | − | 0.950000i | \(-0.601083\pi\) | ||||
−0.312250 | + | 0.950000i | \(0.601083\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12112.8 | −0.916489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3342.44 | −0.251547 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17522.2 | −1.31167 | −0.655837 | − | 0.754902i | \(-0.727684\pi\) | ||||
−0.655837 | + | 0.754902i | \(0.727684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7679.51 | 0.571822 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9056.83 | −0.667279 | −0.333640 | − | 0.942701i | \(-0.608277\pi\) | ||||
−0.333640 | + | 0.942701i | \(0.608277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10716.5 | 0.785417 | 0.392709 | − | 0.919663i | \(-0.371538\pi\) | ||||
0.392709 | + | 0.919663i | \(0.371538\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11294.5 | −0.823444 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2733.53 | 0.198254 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3217.23 | −0.232123 | −0.116062 | − | 0.993242i | \(-0.537027\pi\) | ||||
−0.116062 | + | 0.993242i | \(0.537027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8778.59 | 0.630097 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2314.37 | 0.164411 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2309.93 | −0.163255 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3248.45 | −0.228412 | −0.114206 | − | 0.993457i | \(-0.536432\pi\) | ||||
−0.114206 | + | 0.993457i | \(0.536432\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4920.85 | 0.344245 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15136.6 | 1.05353 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21110.4 | 1.46189 | 0.730945 | − | 0.682437i | \(-0.239080\pi\) | ||||
0.730945 | + | 0.682437i | \(0.239080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12876.7 | −0.882764 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15738.0 | −1.07352 | −0.536758 | − | 0.843736i | \(-0.680351\pi\) | ||||
−0.536758 | + | 0.843736i | \(0.680351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4856.96 | 0.329650 | 0.164825 | − | 0.986323i | \(-0.447294\pi\) | ||||
0.164825 | + | 0.986323i | \(0.447294\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4854.80 | −0.327866 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11102.6 | 0.746089 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17258.6 | 1.15404 | 0.577022 | − | 0.816729i | \(-0.304215\pi\) | ||||
0.577022 | + | 0.816729i | \(0.304215\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2382.38 | 0.157743 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16117.1 | 1.06193 | 0.530964 | − | 0.847394i | \(-0.321830\pi\) | ||||
0.530964 | + | 0.847394i | \(0.321830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13913.1 | 0.912243 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17507.3 | −1.14233 | −0.571164 | − | 0.820836i | \(-0.693508\pi\) | ||||
−0.571164 | + | 0.820836i | \(0.693508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9718.49 | −0.631048 | −0.315524 | − | 0.948918i | \(-0.602180\pi\) | ||||
−0.315524 | + | 0.948918i | \(0.602180\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2592.00 | −0.167493 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11254.9 | −0.720316 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3111.83 | 0.198205 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23710.7 | −1.50303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5144.78 | 0.324580 | 0.162290 | − | 0.986743i | \(-0.448112\pi\) | ||||
0.162290 | + | 0.986743i | \(0.448112\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10877.3 | 0.682990 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −249.275 | −0.0155783 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9579.53 | −0.593052 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21686.1 | 1.33627 | 0.668135 | − | 0.744040i | \(-0.267093\pi\) | ||||
0.668135 | + | 0.744040i | \(0.267093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14171.1 | 0.869132 | 0.434566 | − | 0.900640i | \(-0.356902\pi\) | ||||
0.434566 | + | 0.900640i | \(0.356902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13666.3 | 0.834281 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20053.3 | −1.21851 | −0.609254 | − | 0.792975i | \(-0.708531\pi\) | ||||
−0.609254 | + | 0.792975i | \(0.708531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8512.60 | −0.514867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23641.2 | 1.41677 | 0.708385 | − | 0.705827i | \(-0.249424\pi\) | ||||
0.708385 | + | 0.705827i | \(0.249424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4672.43 | −0.278728 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3984.12 | 0.236584 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2367.34 | 0.139937 | 0.0699685 | − | 0.997549i | \(-0.477710\pi\) | ||||
0.0699685 | + | 0.997549i | \(0.477710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 389.981 | 0.0229478 | 0.0114739 | − | 0.999934i | \(-0.496348\pi\) | ||||
0.0114739 | + | 0.999934i | \(0.496348\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6159.83 | 0.360826 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16610.0 | −0.964230 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9435.01 | 0.545259 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8103.86 | 0.466239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28764.5 | 1.64753 | 0.823766 | − | 0.566930i | \(-0.191869\pi\) | ||||
0.823766 | + | 0.566930i | \(0.191869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −768.805 | −0.0438390 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1762.12 | 0.100035 | 0.0500176 | − | 0.998748i | \(-0.484072\pi\) | ||||
0.0500176 | + | 0.998748i | \(0.484072\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4637.24 | 0.260939 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2228.87 | −0.124869 | −0.0624344 | − | 0.998049i | \(-0.519886\pi\) | ||||
−0.0624344 | + | 0.998049i | \(0.519886\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10399.9 | −0.580085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12216.4 | 0.678437 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4265.18 | −0.235835 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17344.3 | −0.954859 | −0.477429 | − | 0.878670i | \(-0.658431\pi\) | ||||
−0.477429 | + | 0.878670i | \(0.658431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25357.6 | 1.38398 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37101.5 | −2.01624 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9047.14 | −0.489548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23697.7 | −1.27682 | −0.638409 | − | 0.769697i | \(-0.720407\pi\) | ||||
−0.638409 | + | 0.769697i | \(0.720407\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22074.8 | 1.18431 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2687.93 | −0.143594 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22791.0 | −1.20724 | −0.603620 | − | 0.797272i | \(-0.706275\pi\) | ||||
−0.603620 | + | 0.797272i | \(0.706275\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −411.309 | −0.0216952 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6455.76 | 0.339089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3638.21 | 0.190296 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13942.2 | 0.726191 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31844.8 | −1.65175 | −0.825876 | − | 0.563852i | \(-0.809319\pi\) | ||||
−0.825876 | + | 0.563852i | \(0.809319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3354.83 | −0.172569 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4926.64 | −0.252373 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22500.0 | 1.14784 | 0.573920 | − | 0.818912i | \(-0.305422\pi\) | ||||
0.573920 | + | 0.818912i | \(0.305422\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36443.6 | −1.84393 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3222.75 | 0.162394 | 0.0811972 | − | 0.996698i | \(-0.474126\pi\) | ||||
0.0811972 | + | 0.996698i | \(0.474126\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7646.45 | 0.382172 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18359.5 | 0.913893 | 0.456946 | − | 0.889494i | \(-0.348943\pi\) | ||||
0.456946 | + | 0.889494i | \(0.348943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5734.84 | −0.284311 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12890.4 | 0.636478 | 0.318239 | − | 0.948010i | \(-0.396909\pi\) | ||||
0.318239 | + | 0.948010i | \(0.396909\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1000.90 | 0.0492217 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6178.18 | 0.302607 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15390.2 | 0.747798 | 0.373899 | − | 0.927469i | \(-0.378021\pi\) | ||||
0.373899 | + | 0.927469i | \(0.378021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2650.55 | −0.128276 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17472.6 | 0.842241 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13974.6 | 0.670957 | 0.335479 | − | 0.942048i | \(-0.391102\pi\) | ||||
0.335479 | + | 0.942048i | \(0.391102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4082.47 | 0.195236 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3375.14 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6949.85 | −0.328461 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15688.0 | 0.738540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31253.9 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17606.7 | 0.822423 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23163.5 | −1.07779 | −0.538897 | − | 0.842372i | \(-0.681159\pi\) | ||||
−0.538897 | + | 0.842372i | \(0.681159\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1914.82 | 0.0887516 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34541.8 | 1.58869 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15088.0 | 0.691283 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4671.56 | 0.213216 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13747.4 | 0.625050 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9902.95 | 0.448541 | 0.224271 | − | 0.974527i | \(-0.428000\pi\) | ||||
0.224271 | + | 0.974527i | \(0.428000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14626.8 | 0.659986 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14934.7 | −0.668786 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4812.21 | 0.214681 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16844.5 | −0.748638 | −0.374319 | − | 0.927300i | \(-0.622123\pi\) | ||||
−0.374319 | + | 0.927300i | \(0.622123\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7167.83 | 0.317371 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5941.30 | −0.262079 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6275.10 | −0.275770 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16581.3 | 0.723284 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34430.7 | −1.49631 | −0.748157 | − | 0.663522i | \(-0.769061\pi\) | ||||
−0.748157 | + | 0.663522i | \(0.769061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 62.4498 | 0.00270396 | 0.00135198 | − | 0.999999i | \(-0.499570\pi\) | ||||
0.00135198 | + | 0.999999i | \(0.499570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9674.20 | 0.417329 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35520.7 | −1.52667 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33929.2 | 1.45292 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38951.7 | 1.65581 | 0.827906 | − | 0.560866i | \(-0.189532\pi\) | ||||
0.827906 | + | 0.560866i | \(0.189532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35482.3 | −1.50284 | −0.751420 | − | 0.659825i | \(-0.770631\pi\) | ||||
−0.751420 | + | 0.659825i | \(0.770631\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1210.89 | 0.0511003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7945.87 | 0.334105 | 0.167053 | − | 0.985948i | \(-0.446575\pi\) | ||||
0.167053 | + | 0.985948i | \(0.446575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40636.4 | −1.70249 | −0.851243 | − | 0.524772i | \(-0.824151\pi\) | ||||
−0.851243 | + | 0.524772i | \(0.824151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5874.13 | −0.245212 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10578.5 | −0.438425 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1815.68 | −0.0749811 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27723.5 | −1.14079 | −0.570394 | − | 0.821371i | \(-0.693209\pi\) | ||||
−0.570394 | + | 0.821371i | \(0.693209\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5547.19 | 0.227446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25593.5 | 1.04565 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14880.1 | 0.605787 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23729.6 | −0.959243 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28960.3 | 1.16657 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37599.1 | −1.50922 | −0.754612 | − | 0.656171i | \(-0.772175\pi\) | ||||
−0.754612 | + | 0.656171i | \(0.772175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6470.36 | 0.258809 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25610.0 | −1.02079 | −0.510397 | − | 0.859939i | \(-0.670502\pi\) | ||||
−0.510397 | + | 0.859939i | \(0.670502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3979.39 | 0.158062 | 0.0790309 | − | 0.996872i | \(-0.474817\pi\) | ||||
0.0790309 | + | 0.996872i | \(0.474817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24820.3 | −0.979020 | −0.489510 | − | 0.871998i | \(-0.662824\pi\) | ||||
−0.489510 | + | 0.871998i | \(0.662824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18407.9 | 0.723571 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3793.94 | 0.148615 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 647.823 | 0.0252887 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14091.7 | −0.548198 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5924.88 | −0.229698 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50019.4 | 1.92593 | 0.962963 | − | 0.269635i | \(-0.0869030\pi\) | ||||
0.962963 | + | 0.269635i | \(0.0869030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24964.2 | 0.957933 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10386.4 | 0.397193 | 0.198596 | − | 0.980081i | \(-0.436362\pi\) | ||||
0.198596 | + | 0.980081i | \(0.436362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36366.4 | 1.38599 | 0.692994 | − | 0.720944i | \(-0.256291\pi\) | ||||
0.692994 | + | 0.720944i | \(0.256291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17700.0 | −0.672295 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7607.31 | 0.287969 | 0.143984 | − | 0.989580i | \(-0.454008\pi\) | ||||
0.143984 | + | 0.989580i | \(0.454008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1148.20 | −0.0431717 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6673.29 | −0.250071 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26451.1 | 0.987891 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7523.64 | −0.280053 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11635.2 | −0.431653 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12832.6 | −0.474489 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4535.80 | 0.166602 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25803.1 | 0.944628 | 0.472314 | − | 0.881430i | \(-0.343419\pi\) | ||||
0.472314 | + | 0.881430i | \(0.343419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16235.1 | 0.592391 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8165.21 | 0.296954 | 0.148477 | − | 0.988916i | \(-0.452563\pi\) | ||||
0.148477 | + | 0.988916i | \(0.452563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9730.80 | −0.352730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16850.2 | 0.608797 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 593.607 | 0.0213072 | 0.0106536 | − | 0.999943i | \(-0.496609\pi\) | ||||
0.0106536 | + | 0.999943i | \(0.496609\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7625.37 | −0.272817 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27805.9 | −0.991596 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8589.84 | 0.305332 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9674.17 | 0.342763 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33147.4 | 1.17065 | 0.585323 | − | 0.810800i | \(-0.300968\pi\) | ||||
0.585323 | + | 0.810800i | \(0.300968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1823.13 | 0.0639727 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10946.2 | 0.382866 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24883.8 | 0.867575 | 0.433788 | − | 0.901015i | \(-0.357177\pi\) | ||||
0.433788 | + | 0.901015i | \(0.357177\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33081.8 | −1.14972 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26130.3 | 0.905232 | 0.452616 | − | 0.891706i | \(-0.350491\pi\) | ||||
0.452616 | + | 0.891706i | \(0.350491\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45316.0 | 1.56489 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7968.69 | 0.273440 | 0.136720 | − | 0.990610i | \(-0.456344\pi\) | ||||
0.136720 | + | 0.990610i | \(0.456344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11564.5 | 0.395573 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21784.8 | 0.742819 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6742.36 | −0.229178 | −0.114589 | − | 0.993413i | \(-0.536555\pi\) | ||||
−0.114589 | + | 0.993413i | \(0.536555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36988.5 | 1.25332 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7357.84 | −0.248532 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25268.8 | −0.848202 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14934.2 | −0.499737 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28749.2 | −0.959035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7202.50 | −0.239521 | −0.119760 | − | 0.992803i | \(-0.538213\pi\) | ||||
−0.119760 | + | 0.992803i | \(0.538213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17254.3 | −0.572020 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13705.7 | −0.452973 | −0.226487 | − | 0.974014i | \(-0.572724\pi\) | ||||
−0.226487 | + | 0.974014i | \(0.572724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2231.56 | −0.0732997 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56548.0 | −1.85172 | −0.925860 | − | 0.377868i | \(-0.876657\pi\) | ||||
−0.925860 | + | 0.377868i | \(0.876657\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9357.71 | 0.305489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5390.35 | 0.175434 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17363.7 | −0.563395 | −0.281698 | − | 0.959503i | \(-0.590897\pi\) | ||||
−0.281698 | + | 0.959503i | \(0.590897\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49571.2 | −1.60352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44512.3 | 1.43115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49039.4 | 1.57194 | 0.785968 | − | 0.618267i | \(-0.212165\pi\) | ||||
0.785968 | + | 0.618267i | \(0.212165\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19898.2 | 0.635901 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42170.3 | 1.34361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9116.60 | 0.289595 | 0.144797 | − | 0.989461i | \(-0.453747\pi\) | ||||
0.144797 | + | 0.989461i | \(0.453747\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8145.10 | −0.257957 |
(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 | 588.4.a.h.1.1 | 2 | ||
3.2 | odd | 2 | 1764.4.a.p.1.2 | 2 | |||
4.3 | odd | 2 | 2352.4.a.bp.1.1 | 2 | |||
7.2 | even | 3 | 588.4.i.i.361.2 | 4 | |||
7.3 | odd | 6 | 84.4.i.b.37.1 | yes | 4 | ||
7.4 | even | 3 | 588.4.i.i.373.2 | 4 | |||
7.5 | odd | 6 | 84.4.i.b.25.1 | ✓ | 4 | ||
7.6 | odd | 2 | 588.4.a.g.1.2 | 2 | |||
21.2 | odd | 6 | 1764.4.k.z.361.1 | 4 | |||
21.5 | even | 6 | 252.4.k.d.109.2 | 4 | |||
21.11 | odd | 6 | 1764.4.k.z.1549.1 | 4 | |||
21.17 | even | 6 | 252.4.k.d.37.2 | 4 | |||
21.20 | even | 2 | 1764.4.a.x.1.1 | 2 | |||
28.3 | even | 6 | 336.4.q.h.289.1 | 4 | |||
28.19 | even | 6 | 336.4.q.h.193.1 | 4 | |||
28.27 | even | 2 | 2352.4.a.cb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.b.25.1 | ✓ | 4 | 7.5 | odd | 6 | ||
84.4.i.b.37.1 | yes | 4 | 7.3 | odd | 6 | ||
252.4.k.d.37.2 | 4 | 21.17 | even | 6 | |||
252.4.k.d.109.2 | 4 | 21.5 | even | 6 | |||
336.4.q.h.193.1 | 4 | 28.19 | even | 6 | |||
336.4.q.h.289.1 | 4 | 28.3 | even | 6 | |||
588.4.a.g.1.2 | 2 | 7.6 | odd | 2 | |||
588.4.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
588.4.i.i.361.2 | 4 | 7.2 | even | 3 | |||
588.4.i.i.373.2 | 4 | 7.4 | even | 3 | |||
1764.4.a.p.1.2 | 2 | 3.2 | odd | 2 | |||
1764.4.a.x.1.1 | 2 | 21.20 | even | 2 | |||
1764.4.k.z.361.1 | 4 | 21.2 | odd | 6 | |||
1764.4.k.z.1549.1 | 4 | 21.11 | odd | 6 | |||
2352.4.a.bp.1.1 | 2 | 4.3 | odd | 2 | |||
2352.4.a.cb.1.2 | 2 | 28.27 | even | 2 |