Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, 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("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000 | 0.431959 | 0.215980 | − | 0.976398i | \(-0.430705\pi\) | ||||
0.215980 | + | 0.976398i | \(0.430705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.0000 | −0.548202 | −0.274101 | − | 0.961701i | \(-0.588380\pi\) | ||||
−0.274101 | + | 0.961701i | \(0.588380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.0000 | −0.469362 | −0.234681 | − | 0.972072i | \(-0.575405\pi\) | ||||
−0.234681 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.0000 | 0.199735 | 0.0998676 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998676 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −76.0000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.0000 | 0.249392 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 56.0000 | 0.507687 | 0.253844 | − | 0.967245i | \(-0.418305\pi\) | ||||
0.253844 | + | 0.967245i | \(0.418305\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −154.000 | −0.986106 | −0.493053 | − | 0.869999i | \(-0.664119\pi\) | ||||
−0.493053 | + | 0.869999i | \(0.664119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −160.000 | −0.926995 | −0.463498 | − | 0.886098i | \(-0.653406\pi\) | ||||
−0.463498 | + | 0.886098i | \(0.653406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −60.0000 | −0.316505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 162.000 | 0.719801 | 0.359900 | − | 0.932991i | \(-0.382811\pi\) | ||||
0.359900 | + | 0.932991i | \(0.382811\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −66.0000 | −0.270986 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −390.000 | −1.48556 | −0.742778 | − | 0.669538i | \(-0.766492\pi\) | ||||
−0.742778 | + | 0.669538i | \(0.766492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 388.000 | 1.37603 | 0.688017 | − | 0.725695i | \(-0.258482\pi\) | ||||
0.688017 | + | 0.725695i | \(0.258482\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −544.000 | −1.68831 | −0.844155 | − | 0.536099i | \(-0.819897\pi\) | ||||
−0.844155 | + | 0.536099i | \(0.819897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.0000 | 0.115317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 210.000 | 0.544259 | 0.272129 | − | 0.962261i | \(-0.412272\pi\) | ||||
0.272129 | + | 0.962261i | \(0.412272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −228.000 | −0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 380.000 | 0.838505 | 0.419252 | − | 0.907870i | \(-0.362292\pi\) | ||||
0.419252 | + | 0.907870i | \(0.362292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −794.000 | −1.66658 | −0.833289 | − | 0.552837i | \(-0.813545\pi\) | ||||
−0.833289 | + | 0.552837i | \(0.813545\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 72.0000 | 0.143986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −148.000 | −0.269867 | −0.134933 | − | 0.990855i | \(-0.543082\pi\) | ||||
−0.134933 | + | 0.990855i | \(0.543082\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 168.000 | 0.293113 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 840.000 | 1.40408 | 0.702040 | − | 0.712138i | \(-0.252273\pi\) | ||||
0.702040 | + | 0.712138i | \(0.252273\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −858.000 | −1.37563 | −0.687817 | − | 0.725884i | \(-0.741431\pi\) | ||||
−0.687817 | + | 0.725884i | \(0.741431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −160.000 | −0.236801 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −144.000 | −0.205079 | −0.102540 | − | 0.994729i | \(-0.532697\pi\) | ||||
−0.102540 | + | 0.994729i | \(0.532697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 316.000 | 0.417898 | 0.208949 | − | 0.977927i | \(-0.432996\pi\) | ||||
0.208949 | + | 0.977927i | \(0.432996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −462.000 | −0.569329 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1098.00 | 1.30773 | 0.653864 | − | 0.756612i | \(-0.273147\pi\) | ||||
0.653864 | + | 0.756612i | \(0.273147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −176.000 | −0.202745 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −480.000 | −0.535201 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −994.000 | −1.04047 | −0.520234 | − | 0.854024i | \(-0.674155\pi\) | ||||
−0.520234 | + | 0.854024i | \(0.674155\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −180.000 | −0.182734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −834.000 | −0.821645 | −0.410822 | − | 0.911715i | \(-0.634758\pi\) | ||||
−0.410822 | + | 0.911715i | \(0.634758\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1672.00 | 1.59949 | 0.799743 | − | 0.600343i | \(-0.204969\pi\) | ||||
0.799743 | + | 0.600343i | \(0.204969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −732.000 | −0.661356 | −0.330678 | − | 0.943744i | \(-0.607277\pi\) | ||||
−0.330678 | + | 0.943744i | \(0.607277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −970.000 | −0.852378 | −0.426189 | − | 0.904634i | \(-0.640144\pi\) | ||||
−0.426189 | + | 0.904634i | \(0.640144\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 486.000 | 0.415577 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1938.00 | −1.61338 | −0.806689 | − | 0.590976i | \(-0.798743\pi\) | ||||
−0.806689 | + | 0.590976i | \(0.798743\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −198.000 | −0.156454 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112.000 | 0.0862775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1170.00 | −0.857686 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −528.000 | −0.368917 | −0.184458 | − | 0.982840i | \(-0.559053\pi\) | ||||
−0.184458 | + | 0.982840i | \(0.559053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1164.00 | 0.794453 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −636.000 | −0.424180 | −0.212090 | − | 0.977250i | \(-0.568027\pi\) | ||||
−0.212090 | + | 0.977250i | \(0.568027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −608.000 | −0.396393 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1754.00 | −1.09383 | −0.546914 | − | 0.837189i | \(-0.684197\pi\) | ||||
−0.546914 | + | 0.837189i | \(0.684197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2508.00 | 1.53040 | 0.765201 | − | 0.643792i | \(-0.222640\pi\) | ||||
0.765201 | + | 0.643792i | \(0.222640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1632.00 | −0.974746 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 440.000 | 0.257305 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −837.000 | −0.469623 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1486.00 | 0.817033 | 0.408516 | − | 0.912751i | \(-0.366046\pi\) | ||||
0.408516 | + | 0.912751i | \(0.366046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2120.00 | −1.14254 | −0.571269 | − | 0.820763i | \(-0.693549\pi\) | ||||
−0.571269 | + | 0.820763i | \(0.693549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 126.000 | 0.0665784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1850.00 | 0.940421 | 0.470210 | − | 0.882554i | \(-0.344178\pi\) | ||||
0.470210 | + | 0.882554i | \(0.344178\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 630.000 | 0.314228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 448.000 | 0.219300 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1172.00 | −0.563179 | −0.281589 | − | 0.959535i | \(-0.590862\pi\) | ||||
−0.281589 | + | 0.959535i | \(0.590862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1656.00 | −0.767336 | −0.383668 | − | 0.923471i | \(-0.625339\pi\) | ||||
−0.383668 | + | 0.923471i | \(0.625339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1713.00 | −0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −684.000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2666.00 | 1.17163 | 0.585816 | − | 0.810444i | \(-0.300774\pi\) | ||||
0.585816 | + | 0.810444i | \(0.300774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1140.00 | 0.484111 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1132.00 | −0.472680 | −0.236340 | − | 0.971670i | \(-0.575948\pi\) | ||||
−0.236340 | + | 0.971670i | \(0.575948\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2866.00 | −1.17695 | −0.588475 | − | 0.808515i | \(-0.700272\pi\) | ||||
−0.588475 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2382.00 | −0.962199 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −280.000 | −0.109495 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 216.000 | 0.0831306 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1888.00 | −0.715240 | −0.357620 | − | 0.933867i | \(-0.616412\pi\) | ||||
−0.357620 | + | 0.933867i | \(0.616412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1282.00 | −0.478137 | −0.239068 | − | 0.971003i | \(-0.576842\pi\) | ||||
−0.239068 | + | 0.971003i | \(0.576842\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −350.000 | −0.126581 | −0.0632905 | − | 0.997995i | \(-0.520159\pi\) | ||||
−0.0632905 | + | 0.997995i | \(0.520159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3400.00 | 1.21115 | 0.605577 | − | 0.795787i | \(-0.292942\pi\) | ||||
0.605577 | + | 0.795787i | \(0.292942\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −444.000 | −0.155808 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1232.00 | −0.425958 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 504.000 | 0.169229 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1520.00 | 0.503065 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4652.00 | −1.51781 | −0.758903 | − | 0.651204i | \(-0.774264\pi\) | ||||
−0.758903 | + | 0.651204i | \(0.774264\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2520.00 | 0.810646 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1280.00 | −0.400424 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2574.00 | −0.794223 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −308.000 | −0.0937481 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4016.00 | 1.20597 | 0.602985 | − | 0.797753i | \(-0.293978\pi\) | ||||
0.602985 | + | 0.797753i | \(0.293978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2316.00 | 0.677173 | 0.338587 | − | 0.940935i | \(-0.390051\pi\) | ||||
0.338587 | + | 0.940935i | \(0.390051\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 94.0000 | 0.0271253 | 0.0135627 | − | 0.999908i | \(-0.495683\pi\) | ||||
0.0135627 | + | 0.999908i | \(0.495683\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −480.000 | −0.136717 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4230.00 | 1.18934 | 0.594671 | − | 0.803969i | \(-0.297282\pi\) | ||||
0.594671 | + | 0.803969i | \(0.297282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −432.000 | −0.118403 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2064.00 | −0.558615 | −0.279308 | − | 0.960202i | \(-0.590105\pi\) | ||||
−0.279308 | + | 0.960202i | \(0.590105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4562.00 | 1.21935 | 0.609677 | − | 0.792650i | \(-0.291299\pi\) | ||||
0.609677 | + | 0.792650i | \(0.291299\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1672.00 | 0.430716 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 948.000 | 0.241273 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2532.00 | −0.636727 | −0.318363 | − | 0.947969i | \(-0.603133\pi\) | ||||
−0.318363 | + | 0.947969i | \(0.603133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1120.00 | −0.278315 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3522.00 | −0.854850 | −0.427425 | − | 0.904051i | \(-0.640579\pi\) | ||||
−0.427425 | + | 0.904051i | \(0.640579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1296.00 | 0.310925 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1386.00 | −0.328702 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2232.00 | −0.523312 | −0.261656 | − | 0.965161i | \(-0.584269\pi\) | ||||
−0.261656 | + | 0.965161i | \(0.584269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3294.00 | 0.755017 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2806.00 | 0.636003 | 0.318002 | − | 0.948090i | \(-0.396988\pi\) | ||||
0.318002 | + | 0.948090i | \(0.396988\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4848.00 | −1.08670 | −0.543349 | − | 0.839507i | \(-0.682844\pi\) | ||||
−0.543349 | + | 0.839507i | \(0.682844\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −528.000 | −0.117055 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7790.00 | −1.68973 | −0.844866 | − | 0.534978i | \(-0.820320\pi\) | ||||
−0.844866 | + | 0.534978i | \(0.820320\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1440.00 | −0.308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −118.000 | −0.0250509 | −0.0125254 | − | 0.999922i | \(-0.503987\pi\) | ||||
−0.0125254 | + | 0.999922i | \(0.503987\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6508.00 | −1.36700 | −0.683499 | − | 0.729951i | \(-0.739543\pi\) | ||||
−0.683499 | + | 0.729951i | \(0.739543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3120.00 | −0.641700 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2982.00 | −0.600715 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8770.00 | 1.74863 | 0.874315 | − | 0.485358i | \(-0.161311\pi\) | ||||
0.874315 | + | 0.485358i | \(0.161311\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −540.000 | −0.105502 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1232.00 | −0.238289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3104.00 | 0.594391 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2502.00 | −0.474377 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4292.00 | −0.797907 | −0.398953 | − | 0.916971i | \(-0.630626\pi\) | ||||
−0.398953 | + | 0.916971i | \(0.630626\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5016.00 | 0.923464 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9464.00 | 1.72558 | 0.862788 | − | 0.505566i | \(-0.168716\pi\) | ||||
0.862788 | + | 0.505566i | \(0.168716\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9578.00 | −1.72965 | −0.864825 | − | 0.502073i | \(-0.832571\pi\) | ||||
−0.864825 | + | 0.502073i | \(0.832571\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 186.000 | 0.0329552 | 0.0164776 | − | 0.999864i | \(-0.494755\pi\) | ||||
0.0164776 | + | 0.999864i | \(0.494755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3080.00 | 0.540586 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2196.00 | −0.381834 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1064.00 | −0.183290 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2910.00 | −0.492120 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4352.00 | −0.729281 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 492.000 | 0.0817002 | 0.0408501 | − | 0.999165i | \(-0.486993\pi\) | ||||
0.0408501 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1458.00 | 0.239934 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2290.00 | −0.370161 | −0.185080 | − | 0.982723i | \(-0.559255\pi\) | ||||
−0.185080 | + | 0.982723i | \(0.559255\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5814.00 | −0.931484 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3200.00 | 0.508181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4976.00 | −0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6092.00 | −0.942466 | −0.471233 | − | 0.882009i | \(-0.656191\pi\) | ||||
−0.471233 | + | 0.882009i | \(0.656191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5766.00 | 0.884375 | 0.442188 | − | 0.896923i | \(-0.354203\pi\) | ||||
0.442188 | + | 0.896923i | \(0.354203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −594.000 | −0.0903287 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9374.00 | 1.41339 | 0.706696 | − | 0.707517i | \(-0.250185\pi\) | ||||
0.706696 | + | 0.707517i | \(0.250185\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 336.000 | 0.0498123 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3528.00 | 0.518665 | 0.259332 | − | 0.965788i | \(-0.416497\pi\) | ||||
0.259332 | + | 0.965788i | \(0.416497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1083.00 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2793.00 | −0.403842 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7616.00 | 1.08325 | 0.541624 | − | 0.840621i | \(-0.317810\pi\) | ||||
0.541624 | + | 0.840621i | \(0.317810\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3510.00 | −0.495185 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1680.00 | 0.235098 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3406.00 | −0.472804 | −0.236402 | − | 0.971655i | \(-0.575968\pi\) | ||||
−0.236402 | + | 0.971655i | \(0.575968\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3388.00 | 0.462841 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12284.0 | 1.66487 | 0.832436 | − | 0.554121i | \(-0.186945\pi\) | ||||
0.832436 | + | 0.554121i | \(0.186945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1584.00 | −0.212994 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5424.00 | 0.723638 | 0.361819 | − | 0.932248i | \(-0.382156\pi\) | ||||
0.361819 | + | 0.932248i | \(0.382156\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3492.00 | 0.458678 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3486.00 | 0.454363 | 0.227182 | − | 0.973852i | \(-0.427049\pi\) | ||||
0.227182 | + | 0.973852i | \(0.427049\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 784.000 | 0.101403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1908.00 | −0.244900 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3626.00 | 0.458397 | 0.229199 | − | 0.973380i | \(-0.426389\pi\) | ||||
0.229199 | + | 0.973380i | \(0.426389\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1824.00 | −0.228858 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5874.00 | 0.731505 | 0.365753 | − | 0.930712i | \(-0.380812\pi\) | ||||
0.365753 | + | 0.930712i | \(0.380812\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3520.00 | 0.435096 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3240.00 | −0.394597 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12662.0 | −1.53080 | −0.765398 | − | 0.643557i | \(-0.777458\pi\) | ||||
−0.765398 | + | 0.643557i | \(0.777458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5262.00 | −0.631521 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3040.00 | 0.362200 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7524.00 | 0.883578 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6396.00 | −0.745740 | −0.372870 | − | 0.927884i | \(-0.621626\pi\) | ||||
−0.372870 | + | 0.927884i | \(0.621626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8286.00 | 0.959228 | 0.479614 | − | 0.877480i | \(-0.340777\pi\) | ||||
0.479614 | + | 0.877480i | \(0.340777\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4896.00 | −0.562770 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6352.00 | −0.719894 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1320.00 | 0.148555 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4112.00 | 0.459555 | 0.229777 | − | 0.973243i | \(-0.426200\pi\) | ||||
0.229777 | + | 0.973243i | \(0.426200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5330.00 | −0.591555 | −0.295778 | − | 0.955257i | \(-0.595579\pi\) | ||||
−0.295778 | + | 0.955257i | \(0.595579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4256.00 | −0.465886 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11272.0 | −1.22547 | −0.612737 | − | 0.790287i | \(-0.709932\pi\) | ||||
−0.612737 | + | 0.790287i | \(0.709932\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2511.00 | −0.271137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14196.0 | 1.52251 | 0.761255 | − | 0.648452i | \(-0.224583\pi\) | ||||
0.761255 | + | 0.648452i | \(0.224583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4458.00 | 0.471714 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5886.00 | −0.618658 | −0.309329 | − | 0.950955i | \(-0.600104\pi\) | ||||
−0.309329 | + | 0.950955i | \(0.600104\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7800.00 | 0.814385 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6360.00 | −0.659644 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7526.00 | 0.770353 | 0.385177 | − | 0.922843i | \(-0.374141\pi\) | ||||
0.385177 | + | 0.922843i | \(0.374141\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 378.000 | 0.0384391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8502.00 | 0.858954 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12672.0 | 1.27196 | 0.635980 | − | 0.771705i | \(-0.280596\pi\) | ||||
0.635980 | + | 0.771705i | \(0.280596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16540.0 | 1.63893 | 0.819465 | − | 0.573130i | \(-0.194271\pi\) | ||||
0.819465 | + | 0.573130i | \(0.194271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1184.00 | −0.116572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5550.00 | 0.542952 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7760.00 | −0.754345 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1890.00 | 0.181420 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8864.00 | −0.845525 | −0.422763 | − | 0.906241i | \(-0.638940\pi\) | ||||
−0.422763 | + | 0.906241i | \(0.638940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3564.00 | −0.337847 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1344.00 | 0.126613 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3688.00 | 0.343161 | 0.171580 | − | 0.985170i | \(-0.445113\pi\) | ||||
0.171580 | + | 0.985170i | \(0.445113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3516.00 | −0.325151 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16140.0 | 1.48348 | 0.741739 | − | 0.670688i | \(-0.234001\pi\) | ||||
0.741739 | + | 0.670688i | \(0.234001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2156.00 | −0.196960 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6720.00 | 0.606505 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1580.00 | −0.141745 | −0.0708723 | − | 0.997485i | \(-0.522578\pi\) | ||||
−0.0708723 | + | 0.997485i | \(0.522578\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4968.00 | −0.443022 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15000.0 | 1.32966 | 0.664828 | − | 0.746996i | \(-0.268505\pi\) | ||||
0.664828 | + | 0.746996i | \(0.268505\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5139.00 | −0.450160 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20486.0 | 1.78394 | 0.891971 | − | 0.452094i | \(-0.149323\pi\) | ||||
0.891971 | + | 0.452094i | \(0.149323\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6864.00 | −0.594218 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2052.00 | −0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10880.0 | 0.925535 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7998.00 | 0.676442 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7706.00 | 0.647996 | 0.323998 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323998 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3932.00 | −0.328746 | −0.164373 | − | 0.986398i | \(-0.552560\pi\) | ||||
−0.164373 | + | 0.986398i | \(0.552560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2240.00 | −0.185154 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9031.00 | −0.742254 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3420.00 | 0.279502 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8580.00 | 0.697263 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3396.00 | −0.272902 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5580.00 | 0.445914 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23930.0 | −1.90172 | −0.950860 | − | 0.309620i | \(-0.899798\pi\) | ||||
−0.950860 | + | 0.309620i | \(0.899798\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8598.00 | −0.679513 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11468.0 | 0.896410 | 0.448205 | − | 0.893931i | \(-0.352063\pi\) | ||||
0.448205 | + | 0.893931i | \(0.352063\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7146.00 | −0.555526 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11704.0 | 0.904913 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1152.00 | −0.0885859 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11498.0 | 0.874660 | 0.437330 | − | 0.899301i | \(-0.355924\pi\) | ||||
0.437330 | + | 0.899301i | \(0.355924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8536.00 | −0.645857 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −840.000 | −0.0632172 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16988.0 | 1.27169 | 0.635843 | − | 0.771819i | \(-0.280653\pi\) | ||||
0.635843 | + | 0.771819i | \(0.280653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 648.000 | 0.0479955 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17366.0 | −1.27947 | −0.639737 | − | 0.768594i | \(-0.720957\pi\) | ||||
−0.639737 | + | 0.768594i | \(0.720957\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24860.0 | 1.82199 | 0.910997 | − | 0.412413i | \(-0.135314\pi\) | ||||
0.910997 | + | 0.412413i | \(0.135314\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5664.00 | −0.412944 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26302.0 | 1.89769 | 0.948845 | − | 0.315744i | \(-0.102254\pi\) | ||||
0.948845 | + | 0.315744i | \(0.102254\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3846.00 | −0.276052 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2528.00 | 0.180515 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4200.00 | −0.298364 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7812.00 | 0.549294 | 0.274647 | − | 0.961545i | \(-0.411439\pi\) | ||||
0.274647 | + | 0.961545i | \(0.411439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12160.0 | 0.850669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1050.00 | −0.0730816 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7986.00 | −0.553028 | −0.276514 | − | 0.961010i | \(-0.589179\pi\) | ||||
−0.276514 | + | 0.961010i | \(0.589179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10200.0 | 0.699260 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21048.0 | 1.43572 | 0.717861 | − | 0.696186i | \(-0.245121\pi\) | ||||
0.717861 | + | 0.696186i | \(0.245121\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1738.00 | 0.117961 | 0.0589804 | − | 0.998259i | \(-0.481215\pi\) | ||||
0.0589804 | + | 0.998259i | \(0.481215\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1332.00 | −0.0899556 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18576.0 | 1.24214 | 0.621068 | − | 0.783757i | \(-0.286699\pi\) | ||||
0.621068 | + | 0.783757i | \(0.286699\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3696.00 | −0.245927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11968.0 | 0.792428 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13602.0 | 0.896215 | 0.448107 | − | 0.893980i | \(-0.352098\pi\) | ||||
0.448107 | + | 0.893980i | \(0.352098\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19578.0 | −1.27744 | −0.638720 | − | 0.769439i | \(-0.720536\pi\) | ||||
−0.638720 | + | 0.769439i | \(0.720536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12308.0 | −0.799193 | −0.399596 | − | 0.916691i | \(-0.630850\pi\) | ||||
−0.399596 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1512.00 | 0.0977045 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8784.00 | 0.564885 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4560.00 | 0.290445 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2268.00 | 0.143770 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8600.00 | 0.542568 | 0.271284 | − | 0.962499i | \(-0.412552\pi\) | ||||
0.271284 | + | 0.962499i | \(0.412552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13956.0 | −0.876305 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6138.00 | 0.381784 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7560.00 | 0.468027 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6978.00 | 0.429976 | 0.214988 | − | 0.976617i | \(-0.431029\pi\) | ||||
0.214988 | + | 0.976617i | \(0.431029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7668.00 | −0.470290 | −0.235145 | − | 0.971960i | \(-0.575556\pi\) | ||||
−0.235145 | + | 0.971960i | \(0.575556\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15384.0 | −0.934787 | −0.467394 | − | 0.884049i | \(-0.654807\pi\) | ||||
−0.467394 | + | 0.884049i | \(0.654807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7600.00 | −0.459670 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3840.00 | −0.231185 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2186.00 | 0.131003 | 0.0655014 | − | 0.997852i | \(-0.479135\pi\) | ||||
0.0655014 | + | 0.997852i | \(0.479135\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7722.00 | −0.458545 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1524.00 | 0.0900859 | 0.0450430 | − | 0.998985i | \(-0.485658\pi\) | ||||
0.0450430 | + | 0.998985i | \(0.485658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4242.00 | −0.249614 | −0.124807 | − | 0.992181i | \(-0.539831\pi\) | ||||
−0.124807 | + | 0.992181i | \(0.539831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −924.000 | −0.0541255 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8624.00 | −0.500634 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12048.0 | 0.696267 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15880.0 | 0.913622 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24354.0 | −1.39491 | −0.697457 | − | 0.716626i | \(-0.745685\pi\) | ||||
−0.697457 | + | 0.716626i | \(0.745685\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 322.000 | 0.0182799 | 0.00913993 | − | 0.999958i | \(-0.497091\pi\) | ||||
0.00913993 | + | 0.999958i | \(0.497091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7952.00 | −0.449440 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6948.00 | 0.390966 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7932.00 | −0.444377 | −0.222189 | − | 0.975004i | \(-0.571320\pi\) | ||||
−0.222189 | + | 0.975004i | \(0.571320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 282.000 | 0.0156608 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4620.00 | −0.255454 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20684.0 | −1.13872 | −0.569361 | − | 0.822088i | \(-0.692809\pi\) | ||||
−0.569361 | + | 0.822088i | \(0.692809\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1440.00 | −0.0789337 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5460.00 | −0.296718 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12690.0 | 0.686666 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25222.0 | 1.35895 | 0.679473 | − | 0.733700i | \(-0.262208\pi\) | ||||
0.679473 | + | 0.733700i | \(0.262208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12312.0 | −0.660535 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6672.00 | −0.354917 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23678.0 | 1.25423 | 0.627113 | − | 0.778928i | \(-0.284236\pi\) | ||||
0.627113 | + | 0.778928i | \(0.284236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1296.00 | −0.0683598 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8960.00 | −0.470624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6192.00 | −0.322517 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8432.00 | −0.437358 | −0.218679 | − | 0.975797i | \(-0.570175\pi\) | ||||
−0.218679 | + | 0.975797i | \(0.570175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13376.0 | 0.690913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13686.0 | 0.703994 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8312.00 | 0.424037 | 0.212019 | − | 0.977266i | \(-0.431996\pi\) | ||||
0.212019 | + | 0.977266i | \(0.431996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5432.00 | 0.274842 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26298.0 | 1.32516 | 0.662578 | − | 0.748993i | \(-0.269462\pi\) | ||||
0.662578 | + | 0.748993i | \(0.269462\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2960.00 | 0.147942 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16956.0 | −0.844028 | −0.422014 | − | 0.906589i | \(-0.638677\pi\) | ||||
−0.422014 | + | 0.906589i | \(0.638677\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5016.00 | 0.248674 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17880.0 | −0.882845 | −0.441422 | − | 0.897299i | \(-0.645526\pi\) | ||||
−0.441422 | + | 0.897299i | \(0.645526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2844.00 | 0.139299 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5856.00 | −0.285679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22032.0 | −1.07052 | −0.535259 | − | 0.844688i | \(-0.679786\pi\) | ||||
−0.535259 | + | 0.844688i | \(0.679786\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7596.00 | −0.367614 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11534.0 | −0.553779 | −0.276889 | − | 0.960902i | \(-0.589304\pi\) | ||||
−0.276889 | + | 0.960902i | \(0.589304\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3360.00 | −0.160685 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38250.0 | 1.82203 | 0.911013 | − | 0.412378i | \(-0.135302\pi\) | ||||
0.911013 | + | 0.412378i | \(0.135302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7760.00 | −0.368192 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8360.00 | −0.393562 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19330.0 | 0.906447 | 0.453223 | − | 0.891397i | \(-0.350274\pi\) | ||||
0.453223 | + | 0.891397i | \(0.350274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10566.0 | −0.493548 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40674.0 | 1.89255 | 0.946276 | − | 0.323361i | \(-0.104813\pi\) | ||||
0.946276 | + | 0.323361i | \(0.104813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3888.00 | 0.179513 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29640.0 | 1.36324 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16800.0 | −0.769720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4158.00 | −0.189776 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7004.00 | 0.317237 | 0.158619 | − | 0.987340i | \(-0.449296\pi\) | ||||
0.158619 | + | 0.987340i | \(0.449296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6696.00 | −0.302134 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15504.0 | −0.696914 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17468.0 | 0.782228 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12198.0 | −0.542127 | −0.271064 | − | 0.962561i | \(-0.587375\pi\) | ||||
−0.271064 | + | 0.962561i | \(0.587375\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7616.00 | −0.337215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9882.00 | 0.435909 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17160.0 | 0.754126 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8418.00 | 0.367197 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25734.0 | −1.11837 | −0.559184 | − | 0.829044i | \(-0.688885\pi\) | ||||
−0.559184 | + | 0.829044i | \(0.688885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15668.0 | −0.678394 | −0.339197 | − | 0.940715i | \(-0.610155\pi\) | ||||
−0.339197 | + | 0.940715i | \(0.610155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14544.0 | −0.627405 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29488.0 | −1.26274 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1584.00 | −0.0675817 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34450.0 | −1.46445 | −0.732225 | − | 0.681063i | \(-0.761518\pi\) | ||||
−0.732225 | + | 0.681063i | \(0.761518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38792.0 | −1.64302 | −0.821509 | − | 0.570195i | \(-0.806868\pi\) | ||||
−0.821509 | + | 0.570195i | \(0.806868\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20460.0 | −0.860295 | −0.430147 | − | 0.902759i | \(-0.641538\pi\) | ||||
−0.430147 | + | 0.902759i | \(0.641538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5542.00 | 0.232185 | 0.116093 | − | 0.993238i | \(-0.462963\pi\) | ||||
0.116093 | + | 0.993238i | \(0.462963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23370.0 | −0.975567 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3906.00 | −0.162467 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4320.00 | −0.178400 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25240.0 | −1.03860 | −0.519298 | − | 0.854593i | \(-0.673806\pi\) | ||||
−0.519298 | + | 0.854593i | \(0.673806\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −673.000 | −0.0275944 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −354.000 | −0.0144631 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7448.00 | −0.302144 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19524.0 | −0.789237 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9072.00 | 0.365434 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37330.0 | 1.49842 | 0.749212 | − | 0.662331i | \(-0.230433\pi\) | ||||
0.749212 | + | 0.662331i | \(0.230433\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3894.00 | 0.155212 | 0.0776059 | − | 0.996984i | \(-0.475272\pi\) | ||||
0.0776059 | + | 0.996984i | \(0.475272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20324.0 | −0.807271 | −0.403636 | − | 0.914920i | \(-0.632254\pi\) | ||||
−0.403636 | + | 0.914920i | \(0.632254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9360.00 | −0.370485 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6288.00 | 0.248026 | 0.124013 | − | 0.992281i | \(-0.460424\pi\) | ||||
0.124013 | + | 0.992281i | \(0.460424\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14151.0 | −0.554317 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2880.00 | 0.112425 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3256.00 | 0.126665 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8946.00 | −0.346823 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24650.0 | 0.949112 | 0.474556 | − | 0.880225i | \(-0.342609\pi\) | ||||
0.474556 | + | 0.880225i | \(0.342609\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26310.0 | 1.00957 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9426.00 | 0.360465 | 0.180233 | − | 0.983624i | \(-0.442315\pi\) | ||||
0.180233 | + | 0.983624i | \(0.442315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9316.00 | −0.355049 | −0.177525 | − | 0.984116i | \(-0.556809\pi\) | ||||
−0.177525 | + | 0.984116i | \(0.556809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6968.00 | 0.263768 | 0.131884 | − | 0.991265i | \(-0.457897\pi\) | ||||
0.131884 | + | 0.991265i | \(0.457897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4224.00 | −0.159357 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1620.00 | −0.0609114 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41344.0 | 1.54930 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3696.00 | −0.137576 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24640.0 | 0.914116 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2940.00 | 0.108708 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9312.00 | 0.343172 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35964.0 | −1.31661 | −0.658305 | − | 0.752751i | \(-0.728726\pi\) | ||||
−0.658305 | + | 0.752751i | \(0.728726\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7506.00 | −0.273882 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47888.0 | −1.74160 | −0.870801 | − | 0.491635i | \(-0.836399\pi\) | ||||
−0.870801 | + | 0.491635i | \(0.836399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6320.00 | −0.229093 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5088.00 | −0.183229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12760.0 | 0.458013 | 0.229006 | − | 0.973425i | \(-0.426452\pi\) | ||||
0.229006 | + | 0.973425i | \(0.426452\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12876.0 | −0.460672 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18480.0 | −0.659021 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15048.0 | 0.533162 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25054.0 | −0.884817 | −0.442409 | − | 0.896814i | \(-0.645876\pi\) | ||||
−0.442409 | + | 0.896814i | \(0.645876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21204.0 | 0.746437 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28392.0 | 0.996262 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28282.0 | −0.986054 | −0.493027 | − | 0.870014i | \(-0.664110\pi\) | ||||
−0.493027 | + | 0.870014i | \(0.664110\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28734.0 | −0.998614 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30634.0 | −1.06125 | −0.530627 | − | 0.847605i | \(-0.678043\pi\) | ||||
−0.530627 | + | 0.847605i | \(0.678043\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21840.0 | −0.754198 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48572.0 | 1.66671 | 0.833357 | − | 0.552735i | \(-0.186416\pi\) | ||||
0.833357 | + | 0.552735i | \(0.186416\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18876.0 | 0.645670 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 558.000 | 0.0190267 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12906.0 | −0.438685 | −0.219342 | − | 0.975648i | \(-0.570391\pi\) | ||||
−0.219342 | + | 0.975648i | \(0.570391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9240.00 | 0.312107 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14032.0 | −0.472489 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4191.00 | −0.140680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6588.00 | −0.220452 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5880.00 | −0.195541 | −0.0977705 | − | 0.995209i | \(-0.531171\pi\) | ||||
−0.0977705 | + | 0.995209i | \(0.531171\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3192.00 | −0.105822 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55444.0 | −1.83242 | −0.916211 | − | 0.400695i | \(-0.868769\pi\) | ||||
−0.916211 | + | 0.400695i | \(0.868769\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20064.0 | 0.661071 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32050.0 | −1.04951 | −0.524755 | − | 0.851254i | \(-0.675843\pi\) | ||||
−0.524755 | + | 0.851254i | \(0.675843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21960.0 | −0.716900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8730.00 | −0.284126 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29880.0 | 0.969506 | 0.484753 | − | 0.874651i | \(-0.338910\pi\) | ||||
0.484753 | + | 0.874651i | \(0.338910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13056.0 | −0.421051 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21728.0 | 0.698595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5216.00 | −0.167196 | −0.0835982 | − | 0.996500i | \(-0.526641\pi\) | ||||
−0.0835982 | + | 0.996500i | \(0.526641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1476.00 | 0.0471696 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6750.00 | −0.214418 | −0.107209 | − | 0.994237i | \(-0.534191\pi\) | ||||
−0.107209 | + | 0.994237i | \(0.534191\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4374.00 | 0.138526 |
(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 | 1200.4.a.bf.1.1 | 1 | ||
4.3 | odd | 2 | 600.4.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 1200.4.f.g.49.1 | 2 | |||
5.3 | odd | 4 | 1200.4.f.g.49.2 | 2 | |||
5.4 | even | 2 | 240.4.a.d.1.1 | 1 | |||
12.11 | even | 2 | 1800.4.a.k.1.1 | 1 | |||
15.14 | odd | 2 | 720.4.a.f.1.1 | 1 | |||
20.3 | even | 4 | 600.4.f.g.49.1 | 2 | |||
20.7 | even | 4 | 600.4.f.g.49.2 | 2 | |||
20.19 | odd | 2 | 120.4.a.f.1.1 | ✓ | 1 | ||
40.19 | odd | 2 | 960.4.a.g.1.1 | 1 | |||
40.29 | even | 2 | 960.4.a.v.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.f.h.649.2 | 2 | |||
60.47 | odd | 4 | 1800.4.f.h.649.1 | 2 | |||
60.59 | even | 2 | 360.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.a.f.1.1 | ✓ | 1 | 20.19 | odd | 2 | ||
240.4.a.d.1.1 | 1 | 5.4 | even | 2 | |||
360.4.a.e.1.1 | 1 | 60.59 | even | 2 | |||
600.4.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
600.4.f.g.49.1 | 2 | 20.3 | even | 4 | |||
600.4.f.g.49.2 | 2 | 20.7 | even | 4 | |||
720.4.a.f.1.1 | 1 | 15.14 | odd | 2 | |||
960.4.a.g.1.1 | 1 | 40.19 | odd | 2 | |||
960.4.a.v.1.1 | 1 | 40.29 | even | 2 | |||
1200.4.a.bf.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1200.4.f.g.49.1 | 2 | 5.2 | odd | 4 | |||
1200.4.f.g.49.2 | 2 | 5.3 | odd | 4 | |||
1800.4.a.k.1.1 | 1 | 12.11 | even | 2 | |||
1800.4.f.h.649.1 | 2 | 60.47 | odd | 4 | |||
1800.4.f.h.649.2 | 2 | 60.23 | odd | 4 |