Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 735) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.00000 | 1.00000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −20.0000 | −0.632456 | ||||||||
\(11\) | 10.0000 | 0.274101 | 0.137051 | − | 0.990564i | \(-0.456238\pi\) | ||||
0.137051 | + | 0.990564i | \(0.456238\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 24.0000 | 0.512031 | 0.256015 | − | 0.966673i | \(-0.417590\pi\) | ||||
0.256015 | + | 0.966673i | \(0.417590\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | 54.0000 | 0.770407 | 0.385204 | − | 0.922832i | \(-0.374131\pi\) | ||||
0.385204 | + | 0.922832i | \(0.374131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.0000 | 0.144894 | 0.0724471 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724471 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(20\) | −40.0000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 40.0000 | 0.387638 | ||||||||
\(23\) | 134.000 | 1.21482 | 0.607412 | − | 0.794387i | \(-0.292208\pi\) | ||||
0.607412 | + | 0.794387i | \(0.292208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 96.0000 | 0.724121 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −118.000 | −0.755588 | −0.377794 | − | 0.925890i | \(-0.623317\pi\) | ||||
−0.377794 | + | 0.925890i | \(0.623317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −144.000 | −0.834296 | −0.417148 | − | 0.908839i | \(-0.636970\pi\) | ||||
−0.417148 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(32\) | −256.000 | −1.41421 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 216.000 | 1.08952 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −378.000 | −1.67954 | −0.839768 | − | 0.542946i | \(-0.817309\pi\) | ||||
−0.839768 | + | 0.542946i | \(0.817309\pi\) | |||||||
\(38\) | 48.0000 | 0.204911 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 330.000 | 1.25701 | 0.628504 | − | 0.777806i | \(-0.283668\pi\) | ||||
0.628504 | + | 0.777806i | \(0.283668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 204.000 | 0.723482 | 0.361741 | − | 0.932279i | \(-0.382183\pi\) | ||||
0.361741 | + | 0.932279i | \(0.382183\pi\) | |||||||
\(44\) | 80.0000 | 0.274101 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 536.000 | 1.71802 | ||||||||
\(47\) | 312.000 | 0.968295 | 0.484148 | − | 0.874986i | \(-0.339130\pi\) | ||||
0.484148 | + | 0.874986i | \(0.339130\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 100.000 | 0.282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 192.000 | 0.512031 | ||||||||
\(53\) | −142.000 | −0.368023 | −0.184011 | − | 0.982924i | \(-0.558908\pi\) | ||||
−0.184011 | + | 0.982924i | \(0.558908\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.0000 | −0.122582 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −472.000 | −1.06856 | ||||||||
\(59\) | 108.000 | 0.238312 | 0.119156 | − | 0.992876i | \(-0.461981\pi\) | ||||
0.119156 | + | 0.992876i | \(0.461981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 168.000 | 0.352626 | 0.176313 | − | 0.984334i | \(-0.443583\pi\) | ||||
0.176313 | + | 0.984334i | \(0.443583\pi\) | |||||||
\(62\) | −576.000 | −1.17987 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | −120.000 | −0.228987 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 448.000 | 0.816894 | 0.408447 | − | 0.912782i | \(-0.366070\pi\) | ||||
0.408447 | + | 0.912782i | \(0.366070\pi\) | |||||||
\(68\) | 432.000 | 0.770407 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −146.000 | −0.244042 | −0.122021 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122021 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 360.000 | 0.577189 | 0.288595 | − | 0.957451i | \(-0.406812\pi\) | ||||
0.288595 | + | 0.957451i | \(0.406812\pi\) | |||||||
\(74\) | −1512.00 | −2.37522 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 96.0000 | 0.144894 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 236.000 | 0.336102 | 0.168051 | − | 0.985778i | \(-0.446253\pi\) | ||||
0.168051 | + | 0.985778i | \(0.446253\pi\) | |||||||
\(80\) | 320.000 | 0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1320.00 | 1.77768 | ||||||||
\(83\) | 324.000 | 0.428477 | 0.214239 | − | 0.976781i | \(-0.431273\pi\) | ||||
0.214239 | + | 0.976781i | \(0.431273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −270.000 | −0.344537 | ||||||||
\(86\) | 816.000 | 1.02316 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1194.00 | 1.42206 | 0.711032 | − | 0.703159i | \(-0.248228\pi\) | ||||
0.711032 | + | 0.703159i | \(0.248228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1072.00 | 1.21482 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1248.00 | 1.36938 | ||||||||
\(95\) | −60.0000 | −0.0647986 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1728.00 | 1.80878 | 0.904391 | − | 0.426705i | \(-0.140326\pi\) | ||||
0.904391 | + | 0.426705i | \(0.140326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 200.000 | 0.200000 | ||||||||
\(101\) | 1374.00 | 1.35364 | 0.676822 | − | 0.736146i | \(-0.263357\pi\) | ||||
0.676822 | + | 0.736146i | \(0.263357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 948.000 | 0.906886 | 0.453443 | − | 0.891285i | \(-0.350196\pi\) | ||||
0.453443 | + | 0.891285i | \(0.350196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −568.000 | −0.520463 | ||||||||
\(107\) | 550.000 | 0.496921 | 0.248460 | − | 0.968642i | \(-0.420075\pi\) | ||||
0.248460 | + | 0.968642i | \(0.420075\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 402.000 | 0.353253 | 0.176627 | − | 0.984278i | \(-0.443481\pi\) | ||||
0.176627 | + | 0.984278i | \(0.443481\pi\) | |||||||
\(110\) | −200.000 | −0.173357 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1490.00 | 1.24042 | 0.620210 | − | 0.784436i | \(-0.287047\pi\) | ||||
0.620210 | + | 0.784436i | \(0.287047\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −670.000 | −0.543285 | ||||||||
\(116\) | −944.000 | −0.755588 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 432.000 | 0.337024 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1231.00 | −0.924869 | ||||||||
\(122\) | 672.000 | 0.498689 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1152.00 | −0.834296 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 124.000 | 0.0866395 | 0.0433198 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433198 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −480.000 | −0.323837 | ||||||||
\(131\) | 228.000 | 0.152065 | 0.0760323 | − | 0.997105i | \(-0.475775\pi\) | ||||
0.0760323 | + | 0.997105i | \(0.475775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1792.00 | 1.15526 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2726.00 | 1.69998 | 0.849992 | − | 0.526795i | \(-0.176606\pi\) | ||||
0.849992 | + | 0.526795i | \(0.176606\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1848.00 | −1.12766 | −0.563832 | − | 0.825889i | \(-0.690673\pi\) | ||||
−0.563832 | + | 0.825889i | \(0.690673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −584.000 | −0.345128 | ||||||||
\(143\) | 240.000 | 0.140348 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 590.000 | 0.337909 | ||||||||
\(146\) | 1440.00 | 0.816269 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3024.00 | −1.67954 | ||||||||
\(149\) | 1030.00 | 0.566315 | 0.283157 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283157 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2040.00 | −1.09942 | −0.549711 | − | 0.835355i | \(-0.685262\pi\) | ||||
−0.549711 | + | 0.835355i | \(0.685262\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 720.000 | 0.373108 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2844.00 | 1.44571 | 0.722853 | − | 0.691002i | \(-0.242830\pi\) | ||||
0.722853 | + | 0.691002i | \(0.242830\pi\) | |||||||
\(158\) | 944.000 | 0.475320 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1280.00 | 0.632456 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −416.000 | −0.199900 | −0.0999498 | − | 0.994992i | \(-0.531868\pi\) | ||||
−0.0999498 | + | 0.994992i | \(0.531868\pi\) | |||||||
\(164\) | 2640.00 | 1.25701 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1296.00 | 0.605958 | ||||||||
\(167\) | −4056.00 | −1.87942 | −0.939709 | − | 0.341976i | \(-0.888904\pi\) | ||||
−0.939709 | + | 0.341976i | \(0.888904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1621.00 | −0.737824 | ||||||||
\(170\) | −1080.00 | −0.487248 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1632.00 | 0.723482 | ||||||||
\(173\) | 3534.00 | 1.55309 | 0.776546 | − | 0.630060i | \(-0.216970\pi\) | ||||
0.776546 | + | 0.630060i | \(0.216970\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −640.000 | −0.274101 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4776.00 | 2.01110 | ||||||||
\(179\) | 4198.00 | 1.75292 | 0.876462 | − | 0.481472i | \(-0.159898\pi\) | ||||
0.876462 | + | 0.481472i | \(0.159898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1812.00 | −0.744115 | −0.372058 | − | 0.928210i | \(-0.621348\pi\) | ||||
−0.372058 | + | 0.928210i | \(0.621348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1890.00 | 0.751111 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 540.000 | 0.211170 | ||||||||
\(188\) | 2496.00 | 0.968295 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −240.000 | −0.0916391 | ||||||||
\(191\) | 3158.00 | 1.19636 | 0.598180 | − | 0.801362i | \(-0.295891\pi\) | ||||
0.598180 | + | 0.801362i | \(0.295891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4530.00 | −1.68952 | −0.844758 | − | 0.535149i | \(-0.820256\pi\) | ||||
−0.844758 | + | 0.535149i | \(0.820256\pi\) | |||||||
\(194\) | 6912.00 | 2.55800 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −782.000 | −0.282818 | −0.141409 | − | 0.989951i | \(-0.545163\pi\) | ||||
−0.141409 | + | 0.989951i | \(0.545163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2796.00 | 0.995996 | 0.497998 | − | 0.867178i | \(-0.334069\pi\) | ||||
0.497998 | + | 0.867178i | \(0.334069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5496.00 | 1.91434 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1650.00 | −0.562151 | ||||||||
\(206\) | 3792.00 | 1.28253 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1536.00 | −0.512031 | ||||||||
\(209\) | 120.000 | 0.0397157 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1644.00 | −0.536387 | −0.268193 | − | 0.963365i | \(-0.586427\pi\) | ||||
−0.268193 | + | 0.963365i | \(0.586427\pi\) | |||||||
\(212\) | −1136.00 | −0.368023 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2200.00 | 0.702752 | ||||||||
\(215\) | −1020.00 | −0.323551 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1608.00 | 0.499576 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −400.000 | −0.122582 | ||||||||
\(221\) | 1296.00 | 0.394472 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3840.00 | −1.15312 | −0.576559 | − | 0.817055i | \(-0.695605\pi\) | ||||
−0.576559 | + | 0.817055i | \(0.695605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5960.00 | 1.75422 | ||||||||
\(227\) | 5532.00 | 1.61750 | 0.808748 | − | 0.588155i | \(-0.200145\pi\) | ||||
0.808748 | + | 0.588155i | \(0.200145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6900.00 | −1.99111 | −0.995556 | − | 0.0941671i | \(-0.969981\pi\) | ||||
−0.995556 | + | 0.0941671i | \(0.969981\pi\) | |||||||
\(230\) | −2680.00 | −0.768322 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5402.00 | −1.51887 | −0.759435 | − | 0.650583i | \(-0.774525\pi\) | ||||
−0.759435 | + | 0.650583i | \(0.774525\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1560.00 | −0.433035 | ||||||||
\(236\) | 864.000 | 0.238312 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2702.00 | −0.731288 | −0.365644 | − | 0.930755i | \(-0.619151\pi\) | ||||
−0.365644 | + | 0.930755i | \(0.619151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5196.00 | 1.38881 | 0.694406 | − | 0.719583i | \(-0.255667\pi\) | ||||
0.694406 | + | 0.719583i | \(0.255667\pi\) | |||||||
\(242\) | −4924.00 | −1.30796 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1344.00 | 0.352626 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 288.000 | 0.0741903 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −500.000 | −0.126491 | ||||||||
\(251\) | −1836.00 | −0.461702 | −0.230851 | − | 0.972989i | \(-0.574151\pi\) | ||||
−0.230851 | + | 0.972989i | \(0.574151\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1340.00 | 0.332984 | ||||||||
\(254\) | 496.000 | 0.122527 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | −6630.00 | −1.60921 | −0.804607 | − | 0.593808i | \(-0.797624\pi\) | ||||
−0.804607 | + | 0.593808i | \(0.797624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −960.000 | −0.228987 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 912.000 | 0.215052 | ||||||||
\(263\) | −3250.00 | −0.761991 | −0.380995 | − | 0.924577i | \(-0.624419\pi\) | ||||
−0.380995 | + | 0.924577i | \(0.624419\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 710.000 | 0.164585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3584.00 | 0.816894 | ||||||||
\(269\) | 1290.00 | 0.292389 | 0.146195 | − | 0.989256i | \(-0.453297\pi\) | ||||
0.146195 | + | 0.989256i | \(0.453297\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −960.000 | −0.215188 | −0.107594 | − | 0.994195i | \(-0.534315\pi\) | ||||
−0.107594 | + | 0.994195i | \(0.534315\pi\) | |||||||
\(272\) | −3456.00 | −0.770407 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10904.0 | 2.40414 | ||||||||
\(275\) | 250.000 | 0.0548202 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 434.000 | 0.0941391 | 0.0470696 | − | 0.998892i | \(-0.485012\pi\) | ||||
0.0470696 | + | 0.998892i | \(0.485012\pi\) | |||||||
\(278\) | −7392.00 | −1.59476 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3278.00 | −0.695904 | −0.347952 | − | 0.937512i | \(-0.613123\pi\) | ||||
−0.347952 | + | 0.937512i | \(0.613123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5040.00 | 1.05865 | 0.529323 | − | 0.848420i | \(-0.322446\pi\) | ||||
0.529323 | + | 0.848420i | \(0.322446\pi\) | |||||||
\(284\) | −1168.00 | −0.244042 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 960.000 | 0.198482 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 2360.00 | 0.477876 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2880.00 | 0.577189 | ||||||||
\(293\) | 1398.00 | 0.278744 | 0.139372 | − | 0.990240i | \(-0.455492\pi\) | ||||
0.139372 | + | 0.990240i | \(0.455492\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −540.000 | −0.106576 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4120.00 | 0.800890 | ||||||||
\(299\) | 3216.00 | 0.622027 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8160.00 | −1.55482 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −768.000 | −0.144894 | ||||||||
\(305\) | −840.000 | −0.157699 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5016.00 | 0.932502 | 0.466251 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466251 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2880.00 | 0.527655 | ||||||||
\(311\) | −5352.00 | −0.975833 | −0.487917 | − | 0.872890i | \(-0.662243\pi\) | ||||
−0.487917 | + | 0.872890i | \(0.662243\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 972.000 | 0.175529 | 0.0877647 | − | 0.996141i | \(-0.472028\pi\) | ||||
0.0877647 | + | 0.996141i | \(0.472028\pi\) | |||||||
\(314\) | 11376.0 | 2.04454 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1888.00 | 0.336102 | ||||||||
\(317\) | 2018.00 | 0.357546 | 0.178773 | − | 0.983890i | \(-0.442787\pi\) | ||||
0.178773 | + | 0.983890i | \(0.442787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1180.00 | −0.207108 | ||||||||
\(320\) | 2560.00 | 0.447214 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 648.000 | 0.111628 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 600.000 | 0.102406 | ||||||||
\(326\) | −1664.00 | −0.282701 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4308.00 | 0.715375 | 0.357687 | − | 0.933841i | \(-0.383565\pi\) | ||||
0.357687 | + | 0.933841i | \(0.383565\pi\) | |||||||
\(332\) | 2592.00 | 0.428477 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16224.0 | −2.65790 | ||||||||
\(335\) | −2240.00 | −0.365326 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7494.00 | 1.21135 | 0.605674 | − | 0.795713i | \(-0.292904\pi\) | ||||
0.605674 | + | 0.795713i | \(0.292904\pi\) | |||||||
\(338\) | −6484.00 | −1.04344 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2160.00 | −0.344537 | ||||||||
\(341\) | −1440.00 | −0.228681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14136.0 | 2.19640 | ||||||||
\(347\) | 9106.00 | 1.40875 | 0.704374 | − | 0.709829i | \(-0.251228\pi\) | ||||
0.704374 | + | 0.709829i | \(0.251228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5280.00 | −0.809834 | −0.404917 | − | 0.914354i | \(-0.632700\pi\) | ||||
−0.404917 | + | 0.914354i | \(0.632700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2560.00 | −0.387638 | ||||||||
\(353\) | 558.000 | 0.0841341 | 0.0420671 | − | 0.999115i | \(-0.486606\pi\) | ||||
0.0420671 | + | 0.999115i | \(0.486606\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 730.000 | 0.109139 | ||||||||
\(356\) | 9552.00 | 1.42206 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16792.0 | 2.47901 | ||||||||
\(359\) | −2794.00 | −0.410757 | −0.205378 | − | 0.978683i | \(-0.565843\pi\) | ||||
−0.205378 | + | 0.978683i | \(0.565843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6715.00 | −0.979006 | ||||||||
\(362\) | −7248.00 | −1.05234 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1800.00 | −0.258127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8952.00 | −1.27327 | −0.636636 | − | 0.771165i | \(-0.719674\pi\) | ||||
−0.636636 | + | 0.771165i | \(0.719674\pi\) | |||||||
\(368\) | −8576.00 | −1.21482 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7560.00 | 1.06223 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6194.00 | −0.859821 | −0.429910 | − | 0.902872i | \(-0.641455\pi\) | ||||
−0.429910 | + | 0.902872i | \(0.641455\pi\) | |||||||
\(374\) | 2160.00 | 0.298639 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2832.00 | −0.386884 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3588.00 | 0.486288 | 0.243144 | − | 0.969990i | \(-0.421821\pi\) | ||||
0.243144 | + | 0.969990i | \(0.421821\pi\) | |||||||
\(380\) | −480.000 | −0.0647986 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12632.0 | 1.69191 | ||||||||
\(383\) | −11928.0 | −1.59136 | −0.795682 | − | 0.605715i | \(-0.792887\pi\) | ||||
−0.795682 | + | 0.605715i | \(0.792887\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18120.0 | −2.38934 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13824.0 | 1.80878 | ||||||||
\(389\) | 2986.00 | 0.389193 | 0.194597 | − | 0.980883i | \(-0.437660\pi\) | ||||
0.194597 | + | 0.980883i | \(0.437660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7236.00 | 0.935909 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3128.00 | −0.399965 | ||||||||
\(395\) | −1180.00 | −0.150309 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9636.00 | 1.21818 | 0.609089 | − | 0.793102i | \(-0.291535\pi\) | ||||
0.609089 | + | 0.793102i | \(0.291535\pi\) | |||||||
\(398\) | 11184.0 | 1.40855 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1600.00 | −0.200000 | ||||||||
\(401\) | 8690.00 | 1.08219 | 0.541095 | − | 0.840962i | \(-0.318010\pi\) | ||||
0.541095 | + | 0.840962i | \(0.318010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3456.00 | −0.427185 | ||||||||
\(404\) | 10992.0 | 1.35364 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3780.00 | −0.460363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1044.00 | 0.126216 | 0.0631082 | − | 0.998007i | \(-0.479899\pi\) | ||||
0.0631082 | + | 0.998007i | \(0.479899\pi\) | |||||||
\(410\) | −6600.00 | −0.795002 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7584.00 | 0.906886 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1620.00 | −0.191621 | ||||||||
\(416\) | −6144.00 | −0.724121 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 480.000 | 0.0561664 | ||||||||
\(419\) | 468.000 | 0.0545663 | 0.0272832 | − | 0.999628i | \(-0.491314\pi\) | ||||
0.0272832 | + | 0.999628i | \(0.491314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15518.0 | −1.79644 | −0.898220 | − | 0.439547i | \(-0.855139\pi\) | ||||
−0.898220 | + | 0.439547i | \(0.855139\pi\) | |||||||
\(422\) | −6576.00 | −0.758566 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1350.00 | 0.154081 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4400.00 | 0.496921 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4080.00 | −0.457570 | ||||||||
\(431\) | 3830.00 | 0.428039 | 0.214019 | − | 0.976829i | \(-0.431344\pi\) | ||||
0.214019 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 852.000 | 0.0945601 | 0.0472800 | − | 0.998882i | \(-0.484945\pi\) | ||||
0.0472800 | + | 0.998882i | \(0.484945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3216.00 | 0.353253 | ||||||||
\(437\) | 1608.00 | 0.176021 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2916.00 | −0.317023 | −0.158511 | − | 0.987357i | \(-0.550669\pi\) | ||||
−0.158511 | + | 0.987357i | \(0.550669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5184.00 | 0.557868 | ||||||||
\(443\) | −12542.0 | −1.34512 | −0.672560 | − | 0.740042i | \(-0.734805\pi\) | ||||
−0.672560 | + | 0.740042i | \(0.734805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5970.00 | −0.635967 | ||||||||
\(446\) | −15360.0 | −1.63076 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14054.0 | 1.47717 | 0.738585 | − | 0.674160i | \(-0.235494\pi\) | ||||
0.738585 | + | 0.674160i | \(0.235494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3300.00 | 0.344548 | ||||||||
\(452\) | 11920.0 | 1.24042 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22128.0 | 2.28749 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4674.00 | 0.478426 | 0.239213 | − | 0.970967i | \(-0.423111\pi\) | ||||
0.239213 | + | 0.970967i | \(0.423111\pi\) | |||||||
\(458\) | −27600.0 | −2.81586 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5360.00 | −0.543285 | ||||||||
\(461\) | −12594.0 | −1.27237 | −0.636183 | − | 0.771538i | \(-0.719488\pi\) | ||||
−0.636183 | + | 0.771538i | \(0.719488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6388.00 | −0.641200 | −0.320600 | − | 0.947215i | \(-0.603885\pi\) | ||||
−0.320600 | + | 0.947215i | \(0.603885\pi\) | |||||||
\(464\) | 7552.00 | 0.755588 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21608.0 | −2.14801 | ||||||||
\(467\) | −15132.0 | −1.49941 | −0.749706 | − | 0.661771i | \(-0.769805\pi\) | ||||
−0.749706 | + | 0.661771i | \(0.769805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6240.00 | −0.612404 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2040.00 | 0.198307 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 300.000 | 0.0289788 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10808.0 | −1.03420 | ||||||||
\(479\) | 16056.0 | 1.53156 | 0.765780 | − | 0.643102i | \(-0.222353\pi\) | ||||
0.765780 | + | 0.643102i | \(0.222353\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9072.00 | −0.859974 | ||||||||
\(482\) | 20784.0 | 1.96408 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9848.00 | −0.924869 | ||||||||
\(485\) | −8640.00 | −0.808912 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5184.00 | 0.482360 | 0.241180 | − | 0.970480i | \(-0.422466\pi\) | ||||
0.241180 | + | 0.970480i | \(0.422466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12374.0 | 1.13733 | 0.568667 | − | 0.822568i | \(-0.307459\pi\) | ||||
0.568667 | + | 0.822568i | \(0.307459\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6372.00 | −0.582110 | ||||||||
\(494\) | 1152.00 | 0.104921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9216.00 | 0.834296 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21492.0 | 1.92808 | 0.964042 | − | 0.265749i | \(-0.0856194\pi\) | ||||
0.964042 | + | 0.265749i | \(0.0856194\pi\) | |||||||
\(500\) | −1000.00 | −0.0894427 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7344.00 | −0.652946 | ||||||||
\(503\) | 11688.0 | 1.03607 | 0.518034 | − | 0.855360i | \(-0.326664\pi\) | ||||
0.518034 | + | 0.855360i | \(0.326664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6870.00 | −0.605368 | ||||||||
\(506\) | 5360.00 | 0.470911 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 992.000 | 0.0866395 | ||||||||
\(509\) | −3774.00 | −0.328644 | −0.164322 | − | 0.986407i | \(-0.552544\pi\) | ||||
−0.164322 | + | 0.986407i | \(0.552544\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16384.0 | 1.41421 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26520.0 | −2.27577 | ||||||||
\(515\) | −4740.00 | −0.405572 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3120.00 | 0.265411 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18282.0 | −1.53733 | −0.768665 | − | 0.639652i | \(-0.779079\pi\) | ||||
−0.768665 | + | 0.639652i | \(0.779079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9372.00 | 0.783574 | 0.391787 | − | 0.920056i | \(-0.371857\pi\) | ||||
0.391787 | + | 0.920056i | \(0.371857\pi\) | |||||||
\(524\) | 1824.00 | 0.152065 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13000.0 | −1.07762 | ||||||||
\(527\) | −7776.00 | −0.642747 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5789.00 | 0.475795 | ||||||||
\(530\) | 2840.00 | 0.232758 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7920.00 | 0.643627 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2750.00 | −0.222230 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5160.00 | 0.413501 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14330.0 | 1.13881 | 0.569404 | − | 0.822058i | \(-0.307174\pi\) | ||||
0.569404 | + | 0.822058i | \(0.307174\pi\) | |||||||
\(542\) | −3840.00 | −0.304321 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13824.0 | −1.08952 | ||||||||
\(545\) | −2010.00 | −0.157980 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6712.00 | −0.524652 | −0.262326 | − | 0.964979i | \(-0.584490\pi\) | ||||
−0.262326 | + | 0.964979i | \(0.584490\pi\) | |||||||
\(548\) | 21808.0 | 1.69998 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1000.00 | 0.0775275 | ||||||||
\(551\) | −1416.00 | −0.109480 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1736.00 | 0.133133 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14784.0 | −1.12766 | ||||||||
\(557\) | 19066.0 | 1.45036 | 0.725182 | − | 0.688558i | \(-0.241756\pi\) | ||||
0.725182 | + | 0.688558i | \(0.241756\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4896.00 | 0.370445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13112.0 | −0.984157 | ||||||||
\(563\) | 15492.0 | 1.15970 | 0.579849 | − | 0.814724i | \(-0.303112\pi\) | ||||
0.579849 | + | 0.814724i | \(0.303112\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7450.00 | −0.554732 | ||||||||
\(566\) | 20160.0 | 1.49715 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8870.00 | −0.653514 | −0.326757 | − | 0.945108i | \(-0.605956\pi\) | ||||
−0.326757 | + | 0.945108i | \(0.605956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19136.0 | −1.40248 | −0.701241 | − | 0.712925i | \(-0.747370\pi\) | ||||
−0.701241 | + | 0.712925i | \(0.747370\pi\) | |||||||
\(572\) | 1920.00 | 0.140348 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3350.00 | 0.242965 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17532.0 | 1.26493 | 0.632467 | − | 0.774587i | \(-0.282042\pi\) | ||||
0.632467 | + | 0.774587i | \(0.282042\pi\) | |||||||
\(578\) | −7988.00 | −0.574839 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4720.00 | 0.337909 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1420.00 | −0.100875 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5592.00 | 0.394204 | ||||||||
\(587\) | −5700.00 | −0.400791 | −0.200395 | − | 0.979715i | \(-0.564223\pi\) | ||||
−0.200395 | + | 0.979715i | \(0.564223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1728.00 | −0.120885 | ||||||||
\(590\) | −2160.00 | −0.150722 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24192.0 | 1.67954 | ||||||||
\(593\) | −27042.0 | −1.87265 | −0.936325 | − | 0.351134i | \(-0.885796\pi\) | ||||
−0.936325 | + | 0.351134i | \(0.885796\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8240.00 | 0.566315 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12864.0 | 0.879679 | ||||||||
\(599\) | −12514.0 | −0.853603 | −0.426801 | − | 0.904345i | \(-0.640360\pi\) | ||||
−0.426801 | + | 0.904345i | \(0.640360\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4608.00 | −0.312752 | −0.156376 | − | 0.987698i | \(-0.549981\pi\) | ||||
−0.156376 | + | 0.987698i | \(0.549981\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16320.0 | −1.09942 | ||||||||
\(605\) | 6155.00 | 0.413614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15456.0 | −1.03351 | −0.516754 | − | 0.856134i | \(-0.672860\pi\) | ||||
−0.516754 | + | 0.856134i | \(0.672860\pi\) | |||||||
\(608\) | −3072.00 | −0.204911 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3360.00 | −0.223020 | ||||||||
\(611\) | 7488.00 | 0.495797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2050.00 | 0.135071 | 0.0675357 | − | 0.997717i | \(-0.478486\pi\) | ||||
0.0675357 | + | 0.997717i | \(0.478486\pi\) | |||||||
\(614\) | 20064.0 | 1.31876 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7318.00 | 0.477490 | 0.238745 | − | 0.971082i | \(-0.423264\pi\) | ||||
0.238745 | + | 0.971082i | \(0.423264\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5472.00 | −0.355312 | −0.177656 | − | 0.984093i | \(-0.556851\pi\) | ||||
−0.177656 | + | 0.984093i | \(0.556851\pi\) | |||||||
\(620\) | 5760.00 | 0.373108 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21408.0 | −1.38004 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 3888.00 | 0.248236 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22752.0 | 1.44571 | ||||||||
\(629\) | −20412.0 | −1.29393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22124.0 | −1.39579 | −0.697894 | − | 0.716201i | \(-0.745879\pi\) | ||||
−0.697894 | + | 0.716201i | \(0.745879\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8072.00 | 0.505647 | ||||||||
\(635\) | −620.000 | −0.0387464 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4720.00 | −0.292894 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1282.00 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9192.00 | −0.563759 | −0.281880 | − | 0.959450i | \(-0.590958\pi\) | ||||
−0.281880 | + | 0.959450i | \(0.590958\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2592.00 | 0.157865 | ||||||||
\(647\) | −17352.0 | −1.05437 | −0.527185 | − | 0.849750i | \(-0.676753\pi\) | ||||
−0.527185 | + | 0.849750i | \(0.676753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1080.00 | 0.0653216 | ||||||||
\(650\) | 2400.00 | 0.144824 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3328.00 | −0.199900 | ||||||||
\(653\) | −658.000 | −0.0394327 | −0.0197163 | − | 0.999806i | \(-0.506276\pi\) | ||||
−0.0197163 | + | 0.999806i | \(0.506276\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1140.00 | −0.0680053 | ||||||||
\(656\) | −21120.0 | −1.25701 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17666.0 | 1.04426 | 0.522132 | − | 0.852865i | \(-0.325137\pi\) | ||||
0.522132 | + | 0.852865i | \(0.325137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22392.0 | 1.31762 | 0.658811 | − | 0.752309i | \(-0.271060\pi\) | ||||
0.658811 | + | 0.752309i | \(0.271060\pi\) | |||||||
\(662\) | 17232.0 | 1.01169 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15812.0 | −0.917906 | ||||||||
\(668\) | −32448.0 | −1.87942 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8960.00 | −0.516649 | ||||||||
\(671\) | 1680.00 | 0.0966553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5010.00 | 0.286956 | 0.143478 | − | 0.989654i | \(-0.454171\pi\) | ||||
0.143478 | + | 0.989654i | \(0.454171\pi\) | |||||||
\(674\) | 29976.0 | 1.71310 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12968.0 | −0.737824 | ||||||||
\(677\) | 23286.0 | 1.32194 | 0.660970 | − | 0.750412i | \(-0.270145\pi\) | ||||
0.660970 | + | 0.750412i | \(0.270145\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5760.00 | −0.323404 | ||||||||
\(683\) | −23398.0 | −1.31083 | −0.655417 | − | 0.755267i | \(-0.727507\pi\) | ||||
−0.655417 | + | 0.755267i | \(0.727507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13630.0 | −0.760256 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13056.0 | −0.723482 | ||||||||
\(689\) | −3408.00 | −0.188439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15696.0 | 0.864116 | 0.432058 | − | 0.901846i | \(-0.357788\pi\) | ||||
0.432058 | + | 0.901846i | \(0.357788\pi\) | |||||||
\(692\) | 28272.0 | 1.55309 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36424.0 | 1.99227 | ||||||||
\(695\) | 9240.00 | 0.504307 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17820.0 | 0.968408 | ||||||||
\(698\) | −21120.0 | −1.14528 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21502.0 | −1.15852 | −0.579258 | − | 0.815144i | \(-0.696658\pi\) | ||||
−0.579258 | + | 0.815144i | \(0.696658\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4536.00 | −0.243355 | ||||||||
\(704\) | −5120.00 | −0.274101 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2232.00 | 0.118984 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8886.00 | −0.470692 | −0.235346 | − | 0.971912i | \(-0.575622\pi\) | ||||
−0.235346 | + | 0.971912i | \(0.575622\pi\) | |||||||
\(710\) | 2920.00 | 0.154346 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19296.0 | −1.01352 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1200.00 | −0.0627657 | ||||||||
\(716\) | 33584.0 | 1.75292 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11176.0 | −0.580898 | ||||||||
\(719\) | −21768.0 | −1.12908 | −0.564541 | − | 0.825405i | \(-0.690947\pi\) | ||||
−0.564541 | + | 0.825405i | \(0.690947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −26860.0 | −1.38452 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14496.0 | −0.744115 | ||||||||
\(725\) | −2950.00 | −0.151118 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22932.0 | −1.16988 | −0.584939 | − | 0.811078i | \(-0.698881\pi\) | ||||
−0.584939 | + | 0.811078i | \(0.698881\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7200.00 | −0.365047 | ||||||||
\(731\) | 11016.0 | 0.557375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6624.00 | 0.333783 | 0.166892 | − | 0.985975i | \(-0.446627\pi\) | ||||
0.166892 | + | 0.985975i | \(0.446627\pi\) | |||||||
\(734\) | −35808.0 | −1.80068 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34304.0 | −1.71802 | ||||||||
\(737\) | 4480.00 | 0.223912 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29144.0 | 1.45072 | 0.725358 | − | 0.688372i | \(-0.241674\pi\) | ||||
0.725358 | + | 0.688372i | \(0.241674\pi\) | |||||||
\(740\) | 15120.0 | 0.751111 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8954.00 | 0.442114 | 0.221057 | − | 0.975261i | \(-0.429049\pi\) | ||||
0.221057 | + | 0.975261i | \(0.429049\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5150.00 | −0.253264 | ||||||||
\(746\) | −24776.0 | −1.21597 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4320.00 | 0.211170 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24096.0 | 1.17081 | 0.585403 | − | 0.810742i | \(-0.300936\pi\) | ||||
0.585403 | + | 0.810742i | \(0.300936\pi\) | |||||||
\(752\) | −19968.0 | −0.968295 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11328.0 | −0.547137 | ||||||||
\(755\) | 10200.0 | 0.491677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23442.0 | 1.12551 | 0.562757 | − | 0.826622i | \(-0.309741\pi\) | ||||
0.562757 | + | 0.826622i | \(0.309741\pi\) | |||||||
\(758\) | 14352.0 | 0.687715 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7746.00 | 0.368978 | 0.184489 | − | 0.982835i | \(-0.440937\pi\) | ||||
0.184489 | + | 0.982835i | \(0.440937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25264.0 | 1.19636 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47712.0 | −2.25053 | ||||||||
\(767\) | 2592.00 | 0.122023 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19320.0 | 0.905978 | 0.452989 | − | 0.891516i | \(-0.350358\pi\) | ||||
0.452989 | + | 0.891516i | \(0.350358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −36240.0 | −1.68952 | ||||||||
\(773\) | 13638.0 | 0.634573 | 0.317286 | − | 0.948330i | \(-0.397228\pi\) | ||||
0.317286 | + | 0.948330i | \(0.397228\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3600.00 | −0.166859 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11944.0 | 0.550403 | ||||||||
\(779\) | 3960.00 | 0.182133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1460.00 | −0.0668923 | ||||||||
\(782\) | 28944.0 | 1.32357 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14220.0 | −0.646540 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39636.0 | 1.79526 | 0.897631 | − | 0.440748i | \(-0.145287\pi\) | ||||
0.897631 | + | 0.440748i | \(0.145287\pi\) | |||||||
\(788\) | −6256.00 | −0.282818 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4720.00 | −0.212570 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4032.00 | 0.180556 | ||||||||
\(794\) | 38544.0 | 1.72276 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22368.0 | 0.995996 | ||||||||
\(797\) | −20490.0 | −0.910656 | −0.455328 | − | 0.890324i | \(-0.650478\pi\) | ||||
−0.455328 | + | 0.890324i | \(0.650478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16848.0 | 0.745982 | ||||||||
\(800\) | −6400.00 | −0.282843 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34760.0 | 1.53045 | ||||||||
\(803\) | 3600.00 | 0.158208 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13824.0 | −0.604131 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8638.00 | 0.375397 | 0.187698 | − | 0.982227i | \(-0.439897\pi\) | ||||
0.187698 | + | 0.982227i | \(0.439897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44472.0 | −1.92555 | −0.962776 | − | 0.270300i | \(-0.912877\pi\) | ||||
−0.962776 | + | 0.270300i | \(0.912877\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15120.0 | −0.651051 | ||||||||
\(815\) | 2080.00 | 0.0893978 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2448.00 | 0.104828 | ||||||||
\(818\) | 4176.00 | 0.178497 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13200.0 | −0.562151 | ||||||||
\(821\) | −290.000 | −0.0123277 | −0.00616387 | − | 0.999981i | \(-0.501962\pi\) | ||||
−0.00616387 | + | 0.999981i | \(0.501962\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30692.0 | 1.29995 | 0.649973 | − | 0.759957i | \(-0.274780\pi\) | ||||
0.649973 | + | 0.759957i | \(0.274780\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3446.00 | 0.144896 | 0.0724481 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724481 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7332.00 | 0.307178 | 0.153589 | − | 0.988135i | \(-0.450917\pi\) | ||||
0.153589 | + | 0.988135i | \(0.450917\pi\) | |||||||
\(830\) | −6480.00 | −0.270993 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12288.0 | −0.512031 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20280.0 | 0.840501 | ||||||||
\(836\) | 960.000 | 0.0397157 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1872.00 | 0.0771685 | ||||||||
\(839\) | −48024.0 | −1.97613 | −0.988065 | − | 0.154039i | \(-0.950772\pi\) | ||||
−0.988065 | + | 0.154039i | \(0.950772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10465.0 | −0.429087 | ||||||||
\(842\) | −62072.0 | −2.54055 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13152.0 | −0.536387 | ||||||||
\(845\) | 8105.00 | 0.329965 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9088.00 | 0.368023 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5400.00 | 0.217904 | ||||||||
\(851\) | −50652.0 | −2.04034 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46380.0 | −1.86169 | −0.930845 | − | 0.365415i | \(-0.880927\pi\) | ||||
−0.930845 | + | 0.365415i | \(0.880927\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6210.00 | 0.247526 | 0.123763 | − | 0.992312i | \(-0.460504\pi\) | ||||
0.123763 | + | 0.992312i | \(0.460504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6492.00 | 0.257863 | 0.128931 | − | 0.991654i | \(-0.458845\pi\) | ||||
0.128931 | + | 0.991654i | \(0.458845\pi\) | |||||||
\(860\) | −8160.00 | −0.323551 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15320.0 | 0.605338 | ||||||||
\(863\) | −16354.0 | −0.645071 | −0.322536 | − | 0.946557i | \(-0.604535\pi\) | ||||
−0.322536 | + | 0.946557i | \(0.604535\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17670.0 | −0.694564 | ||||||||
\(866\) | 3408.00 | 0.133728 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2360.00 | 0.0921260 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10752.0 | 0.418275 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6432.00 | 0.248931 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35926.0 | −1.38328 | −0.691639 | − | 0.722243i | \(-0.743111\pi\) | ||||
−0.691639 | + | 0.722243i | \(0.743111\pi\) | |||||||
\(878\) | −11664.0 | −0.448338 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3200.00 | 0.122582 | ||||||||
\(881\) | −7098.00 | −0.271439 | −0.135719 | − | 0.990747i | \(-0.543335\pi\) | ||||
−0.135719 | + | 0.990747i | \(0.543335\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11340.0 | −0.432187 | −0.216094 | − | 0.976373i | \(-0.569332\pi\) | ||||
−0.216094 | + | 0.976373i | \(0.569332\pi\) | |||||||
\(884\) | 10368.0 | 0.394472 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50168.0 | −1.90229 | ||||||||
\(887\) | 22560.0 | 0.853992 | 0.426996 | − | 0.904254i | \(-0.359572\pi\) | ||||
0.426996 | + | 0.904254i | \(0.359572\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −23880.0 | −0.899393 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30720.0 | −1.15312 | ||||||||
\(893\) | 3744.00 | 0.140300 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20990.0 | −0.783931 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 56216.0 | 2.08903 | ||||||||
\(899\) | 16992.0 | 0.630384 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7668.00 | −0.283527 | ||||||||
\(902\) | 13200.0 | 0.487264 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9060.00 | 0.332779 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20676.0 | 0.756930 | 0.378465 | − | 0.925616i | \(-0.376452\pi\) | ||||
0.378465 | + | 0.925616i | \(0.376452\pi\) | |||||||
\(908\) | 44256.0 | 1.61750 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12962.0 | −0.471405 | −0.235703 | − | 0.971825i | \(-0.575739\pi\) | ||||
−0.235703 | + | 0.971825i | \(0.575739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3240.00 | 0.117446 | ||||||||
\(914\) | 18696.0 | 0.676596 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −55200.0 | −1.99111 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17496.0 | 0.628008 | 0.314004 | − | 0.949422i | \(-0.398329\pi\) | ||||
0.314004 | + | 0.949422i | \(0.398329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −50376.0 | −1.79940 | ||||||||
\(923\) | −3504.00 | −0.124957 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9450.00 | −0.335907 | ||||||||
\(926\) | −25552.0 | −0.906794 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30208.0 | 1.06856 | ||||||||
\(929\) | 19698.0 | 0.695662 | 0.347831 | − | 0.937557i | \(-0.386918\pi\) | ||||
0.347831 | + | 0.937557i | \(0.386918\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −43216.0 | −1.51887 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −60528.0 | −2.12049 | ||||||||
\(935\) | −2700.00 | −0.0944379 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26676.0 | −0.930061 | −0.465030 | − | 0.885295i | \(-0.653957\pi\) | ||||
−0.465030 | + | 0.885295i | \(0.653957\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12480.0 | −0.433035 | ||||||||
\(941\) | 20034.0 | 0.694038 | 0.347019 | − | 0.937858i | \(-0.387194\pi\) | ||||
0.347019 | + | 0.937858i | \(0.387194\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44220.0 | 1.52704 | ||||||||
\(944\) | −6912.00 | −0.238312 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8160.00 | 0.280449 | ||||||||
\(947\) | −42962.0 | −1.47421 | −0.737105 | − | 0.675778i | \(-0.763808\pi\) | ||||
−0.737105 | + | 0.675778i | \(0.763808\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8640.00 | 0.295539 | ||||||||
\(950\) | 1200.00 | 0.0409823 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24202.0 | 0.822644 | 0.411322 | − | 0.911490i | \(-0.365067\pi\) | ||||
0.411322 | + | 0.911490i | \(0.365067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15790.0 | −0.535029 | ||||||||
\(956\) | −21616.0 | −0.731288 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 64224.0 | 2.16595 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9055.00 | −0.303951 | ||||||||
\(962\) | −36288.0 | −1.21619 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 41568.0 | 1.38881 | ||||||||
\(965\) | 22650.0 | 0.755574 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27236.0 | 0.905740 | 0.452870 | − | 0.891577i | \(-0.350400\pi\) | ||||
0.452870 | + | 0.891577i | \(0.350400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34560.0 | −1.14397 | ||||||||
\(971\) | 35820.0 | 1.18385 | 0.591925 | − | 0.805993i | \(-0.298368\pi\) | ||||
0.591925 | + | 0.805993i | \(0.298368\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20736.0 | 0.682160 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10752.0 | −0.352626 | ||||||||
\(977\) | 10798.0 | 0.353591 | 0.176796 | − | 0.984248i | \(-0.443427\pi\) | ||||
0.176796 | + | 0.984248i | \(0.443427\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11940.0 | 0.389790 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 49496.0 | 1.60843 | ||||||||
\(983\) | 42576.0 | 1.38145 | 0.690724 | − | 0.723118i | \(-0.257292\pi\) | ||||
0.690724 | + | 0.723118i | \(0.257292\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3910.00 | 0.126480 | ||||||||
\(986\) | −25488.0 | −0.823228 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2304.00 | 0.0741903 | ||||||||
\(989\) | 27336.0 | 0.878902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45504.0 | −1.45861 | −0.729305 | − | 0.684189i | \(-0.760156\pi\) | ||||
−0.729305 | + | 0.684189i | \(0.760156\pi\) | |||||||
\(992\) | 36864.0 | 1.17987 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13980.0 | −0.445423 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4548.00 | −0.144470 | −0.0722350 | − | 0.997388i | \(-0.523013\pi\) | ||||
−0.0722350 | + | 0.997388i | \(0.523013\pi\) | |||||||
\(998\) | 85968.0 | 2.72672 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2205.4.a.r.1.1 | 1 | ||
3.2 | odd | 2 | 735.4.a.b.1.1 | yes | 1 | ||
7.6 | odd | 2 | 2205.4.a.s.1.1 | 1 | |||
21.20 | even | 2 | 735.4.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.4.a.a.1.1 | ✓ | 1 | 21.20 | even | 2 | ||
735.4.a.b.1.1 | yes | 1 | 3.2 | odd | 2 | ||
2205.4.a.r.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2205.4.a.s.1.1 | 1 | 7.6 | odd | 2 |