Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6024,2,Mod(1,6024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6024 = 2^{3} \cdot 3 \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6024.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: | \(48.1018821776\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - x^{17} - 57 x^{16} + 51 x^{15} + 1328 x^{14} - 1116 x^{13} - 16275 x^{12} + 13699 x^{11} + 112394 x^{10} - 101250 x^{9} - 432956 x^{8} + 439806 x^{7} + 844117 x^{6} + \cdots + 44032 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.693705\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6024.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.693705 | 0.310234 | 0.155117 | − | 0.987896i | \(-0.450425\pi\) | ||||
0.155117 | + | 0.987896i | \(0.450425\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.39358 | −1.28265 | −0.641326 | − | 0.767268i | \(-0.721615\pi\) | ||||
−0.641326 | + | 0.767268i | \(0.721615\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.07073 | 1.52888 | 0.764441 | − | 0.644693i | \(-0.223015\pi\) | ||||
0.764441 | + | 0.644693i | \(0.223015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.83146 | 1.06266 | 0.531328 | − | 0.847166i | \(-0.321693\pi\) | ||||
0.531328 | + | 0.847166i | \(0.321693\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.693705 | 0.179114 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.10131 | 0.752179 | 0.376089 | − | 0.926583i | \(-0.377269\pi\) | ||||
0.376089 | + | 0.926583i | \(0.377269\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00606 | 1.37788 | 0.688942 | − | 0.724817i | \(-0.258076\pi\) | ||||
0.688942 | + | 0.724817i | \(0.258076\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.39358 | −0.740540 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.28131 | 0.267172 | 0.133586 | − | 0.991037i | \(-0.457351\pi\) | ||||
0.133586 | + | 0.991037i | \(0.457351\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.51877 | −0.903755 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.22100 | 0.783821 | 0.391910 | − | 0.920003i | \(-0.371814\pi\) | ||||
0.391910 | + | 0.920003i | \(0.371814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.03025 | −0.903459 | −0.451729 | − | 0.892155i | \(-0.649193\pi\) | ||||
−0.451729 | + | 0.892155i | \(0.649193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.07073 | 0.882701 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.35414 | −0.397923 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.18338 | −1.01654 | −0.508271 | − | 0.861197i | \(-0.669715\pi\) | ||||
−0.508271 | + | 0.861197i | \(0.669715\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.83146 | 0.613525 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.22552 | 0.659916 | 0.329958 | − | 0.943996i | \(-0.392965\pi\) | ||||
0.329958 | + | 0.943996i | \(0.392965\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.19268 | 0.791877 | 0.395938 | − | 0.918277i | \(-0.370419\pi\) | ||||
0.395938 | + | 0.918277i | \(0.370419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.693705 | 0.103411 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.33431 | −0.632224 | −0.316112 | − | 0.948722i | \(-0.602378\pi\) | ||||
−0.316112 | + | 0.948722i | \(0.602378\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.51638 | 0.645197 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.10131 | 0.434271 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.40817 | −0.880230 | −0.440115 | − | 0.897942i | \(-0.645062\pi\) | ||||
−0.440115 | + | 0.897942i | \(0.645062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.51759 | 0.474312 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00606 | 0.795522 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0793 | 1.31221 | 0.656105 | − | 0.754669i | \(-0.272203\pi\) | ||||
0.656105 | + | 0.754669i | \(0.272203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.50602 | −1.21712 | −0.608560 | − | 0.793508i | \(-0.708253\pi\) | ||||
−0.608560 | + | 0.793508i | \(0.708253\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.39358 | −0.427551 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.65790 | 0.329672 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.04614 | −0.860823 | −0.430412 | − | 0.902633i | \(-0.641632\pi\) | ||||
−0.430412 | + | 0.902633i | \(0.641632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.28131 | 0.154252 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.91100 | 0.345472 | 0.172736 | − | 0.984968i | \(-0.444739\pi\) | ||||
0.172736 | + | 0.984968i | \(0.444739\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.05497 | 0.240516 | 0.120258 | − | 0.992743i | \(-0.461628\pi\) | ||||
0.120258 | + | 0.992743i | \(0.461628\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.51877 | −0.521783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.2079 | −1.96102 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6914 | 1.20288 | 0.601441 | − | 0.798917i | \(-0.294594\pi\) | ||||
0.601441 | + | 0.798917i | \(0.294594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.04092 | 0.772842 | 0.386421 | − | 0.922323i | \(-0.373711\pi\) | ||||
0.386421 | + | 0.922323i | \(0.373711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.15140 | 0.233352 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.22100 | 0.452539 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.33632 | 0.141650 | 0.0708251 | − | 0.997489i | \(-0.477437\pi\) | ||||
0.0708251 | + | 0.997489i | \(0.477437\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0024 | −1.36302 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.03025 | −0.521612 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.16643 | 0.427467 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.67805 | −0.881122 | −0.440561 | − | 0.897723i | \(-0.645220\pi\) | ||||
−0.440561 | + | 0.897723i | \(0.645220\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.07073 | 0.509628 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.1912 | 1.51158 | 0.755791 | − | 0.654813i | \(-0.227253\pi\) | ||||
0.755791 | + | 0.654813i | \(0.227253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.67044 | −0.952856 | −0.476428 | − | 0.879213i | \(-0.658069\pi\) | ||||
−0.476428 | + | 0.879213i | \(0.658069\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.35414 | −0.229741 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.61924 | −0.736580 | −0.368290 | − | 0.929711i | \(-0.620057\pi\) | ||||
−0.368290 | + | 0.929711i | \(0.620057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.715961 | −0.0685766 | −0.0342883 | − | 0.999412i | \(-0.510916\pi\) | ||||
−0.0342883 | + | 0.999412i | \(0.510916\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.18338 | −0.586901 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.55725 | −0.240566 | −0.120283 | − | 0.992740i | \(-0.538380\pi\) | ||||
−0.120283 | + | 0.992740i | \(0.538380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.888851 | 0.0828858 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.83146 | 0.354219 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.5246 | −0.964784 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.7123 | 1.33748 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.22552 | 0.381003 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.60322 | −0.590610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.5687 | 1.38150 | 0.690750 | − | 0.723094i | \(-0.257280\pi\) | ||||
0.690750 | + | 0.723094i | \(0.257280\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.19268 | 0.457190 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.68807 | −0.759081 | −0.379540 | − | 0.925175i | \(-0.623918\pi\) | ||||
−0.379540 | + | 0.925175i | \(0.623918\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.3820 | −1.76735 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.693705 | 0.0597046 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6471 | 0.995082 | 0.497541 | − | 0.867440i | \(-0.334236\pi\) | ||||
0.497541 | + | 0.867440i | \(0.334236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.8127 | 1.76531 | 0.882654 | − | 0.470023i | \(-0.155754\pi\) | ||||
0.882654 | + | 0.470023i | \(0.155754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.33431 | −0.365015 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.4283 | 1.62468 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.92813 | 0.243168 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.51638 | 0.372505 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.23090 | −0.592378 | −0.296189 | − | 0.955129i | \(-0.595716\pi\) | ||||
−0.296189 | + | 0.955129i | \(0.595716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.71992 | 0.465480 | 0.232740 | − | 0.972539i | \(-0.425231\pi\) | ||||
0.232740 | + | 0.972539i | \(0.425231\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.10131 | 0.250726 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.48951 | −0.280284 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.9148 | −1.90861 | −0.954303 | − | 0.298840i | \(-0.903400\pi\) | ||||
−0.954303 | + | 0.298840i | \(0.903400\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.40817 | −0.508201 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.34823 | −0.342689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.25523 | 0.254969 | 0.127485 | − | 0.991841i | \(-0.459310\pi\) | ||||
0.127485 | + | 0.991841i | \(0.459310\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.51759 | 0.273844 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.6189 | 1.51815 | 0.759077 | − | 0.651000i | \(-0.225650\pi\) | ||||
0.759077 | + | 0.651000i | \(0.225650\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.68010 | 0.129239 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00606 | 0.459295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.4915 | 0.949709 | 0.474855 | − | 0.880064i | \(-0.342501\pi\) | ||||
0.474855 | + | 0.880064i | \(0.342501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.3348 | 1.15920 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0793 | 0.757605 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5394 | 1.31096 | 0.655479 | − | 0.755213i | \(-0.272467\pi\) | ||||
0.655479 | + | 0.755213i | \(0.272467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.88595 | 0.214511 | 0.107255 | − | 0.994232i | \(-0.465794\pi\) | ||||
0.107255 | + | 0.994232i | \(0.465794\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.50602 | −0.702705 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.28944 | −0.315366 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.7259 | 1.14999 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.39358 | −0.246847 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.22169 | −0.233113 | −0.116557 | − | 0.993184i | \(-0.537186\pi\) | ||||
−0.116557 | + | 0.993184i | \(0.537186\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2520 | 0.881918 | 0.440959 | − | 0.897527i | \(-0.354638\pi\) | ||||
0.440959 | + | 0.897527i | \(0.354638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.65790 | 0.190336 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.06249 | −0.503182 | −0.251591 | − | 0.967834i | \(-0.580954\pi\) | ||||
−0.251591 | + | 0.967834i | \(0.580954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8918 | 1.41009 | 0.705046 | − | 0.709162i | \(-0.250926\pi\) | ||||
0.705046 | + | 0.709162i | \(0.250926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.04614 | −0.496996 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.3243 | −1.00537 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.93127 | 0.204728 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.28131 | 0.0890573 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 30.4551 | 2.10662 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.40796 | 0.509985 | 0.254992 | − | 0.966943i | \(-0.417927\pi\) | ||||
0.254992 | + | 0.966943i | \(0.417927\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.91100 | 0.199458 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.60219 | 0.245667 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.0705 | 1.15882 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.05497 | 0.138862 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.8826 | 0.799308 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.474828 | 0.0317969 | 0.0158984 | − | 0.999874i | \(-0.494939\pi\) | ||||
0.0158984 | + | 0.999874i | \(0.494939\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.51877 | −0.301252 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.8443 | −1.11799 | −0.558996 | − | 0.829170i | \(-0.688813\pi\) | ||||
−0.558996 | + | 0.829170i | \(0.688813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.13575 | 0.141134 | 0.0705670 | − | 0.997507i | \(-0.477519\pi\) | ||||
0.0705670 | + | 0.997507i | \(0.477519\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.2079 | −1.13220 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.3369 | 1.46334 | 0.731670 | − | 0.681659i | \(-0.238741\pi\) | ||||
0.731670 | + | 0.681659i | \(0.238741\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00673 | −0.196138 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.6914 | 0.694484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3907 | 1.06023 | 0.530114 | − | 0.847926i | \(-0.322149\pi\) | ||||
0.530114 | + | 0.847926i | \(0.322149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1952 | −0.914396 | −0.457198 | − | 0.889365i | \(-0.651147\pi\) | ||||
−0.457198 | + | 0.889365i | \(0.651147\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.13303 | 0.200162 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.0120 | 1.46422 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.04092 | 0.446200 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.49718 | 0.408474 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.15140 | 0.134726 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2880 | −0.704127 | −0.352063 | − | 0.935976i | \(-0.614520\pi\) | ||||
−0.352063 | + | 0.935976i | \(0.614520\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.9838 | 1.30387 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.22100 | 0.261274 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.0221 | −0.926302 | −0.463151 | − | 0.886279i | \(-0.653281\pi\) | ||||
−0.463151 | + | 0.886279i | \(0.653281\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.44538 | −0.273077 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.33632 | 0.0817817 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.2636 | 0.808694 | 0.404347 | − | 0.914606i | \(-0.367499\pi\) | ||||
0.404347 | + | 0.914606i | \(0.367499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2457 | 0.804618 | 0.402309 | − | 0.915504i | \(-0.368208\pi\) | ||||
0.402309 | + | 0.915504i | \(0.368208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.0024 | −0.786939 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.9135 | −1.38173 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4428 | −0.927868 | −0.463934 | − | 0.885870i | \(-0.653563\pi\) | ||||
−0.463934 | + | 0.885870i | \(0.653563\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.03025 | −0.301153 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0074 | 0.835612 | 0.417806 | − | 0.908536i | \(-0.362799\pi\) | ||||
0.417806 | + | 0.908536i | \(0.362799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.8561 | −1.18033 | −0.590163 | − | 0.807284i | \(-0.700936\pi\) | ||||
−0.590163 | + | 0.807284i | \(0.700936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.16643 | 0.246798 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.3397 | −0.846443 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.38186 | −0.434227 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.67805 | −0.508716 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.3819 | 1.42441 | 0.712204 | − | 0.701973i | \(-0.247697\pi\) | ||||
0.712204 | + | 0.701973i | \(0.247697\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.99204 | 0.407093 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.07073 | 0.294234 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.90929 | 0.283912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.6218 | −1.01570 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.1912 | 0.872712 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.59437 | −0.377592 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.02581 | −0.515130 | −0.257565 | − | 0.966261i | \(-0.582920\pi\) | ||||
−0.257565 | + | 0.966261i | \(0.582920\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.67044 | −0.550132 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.83059 | 0.217213 | 0.108606 | − | 0.994085i | \(-0.465361\pi\) | ||||
0.108606 | + | 0.994085i | \(0.465361\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6014 | 0.599227 | 0.299613 | − | 0.954061i | \(-0.403142\pi\) | ||||
0.299613 | + | 0.954061i | \(0.403142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.35414 | −0.132641 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.40231 | 0.415755 | 0.207878 | − | 0.978155i | \(-0.433344\pi\) | ||||
0.207878 | + | 0.978155i | \(0.433344\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.4036 | 1.19837 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.61924 | −0.425264 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.6267 | 1.03642 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.3135 | −0.960381 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.715961 | −0.0395927 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.7088 | 0.810924 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.57955 | −0.196750 | −0.0983749 | − | 0.995149i | \(-0.531364\pi\) | ||||
−0.0983749 | + | 0.995149i | \(0.531364\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.18338 | −0.338847 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.88794 | −0.267057 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.48567 | 0.0809297 | 0.0404649 | − | 0.999181i | \(-0.487116\pi\) | ||||
0.0404649 | + | 0.999181i | \(0.487116\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.55725 | −0.138891 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.5070 | −1.38128 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.42836 | 0.455088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.888851 | 0.0478541 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.06849 | 0.0573595 | 0.0286797 | − | 0.999589i | \(-0.490870\pi\) | ||||
0.0286797 | + | 0.999589i | \(0.490870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5151 | 1.31226 | 0.656131 | − | 0.754647i | \(-0.272192\pi\) | ||||
0.656131 | + | 0.754647i | \(0.272192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.83146 | 0.204508 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.78487 | 0.307897 | 0.153949 | − | 0.988079i | \(-0.450801\pi\) | ||||
0.153949 | + | 0.988079i | \(0.450801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.01937 | 0.107177 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.5246 | −0.557018 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.3651 | −1.39150 | −0.695749 | − | 0.718285i | \(-0.744927\pi\) | ||||
−0.695749 | + | 0.718285i | \(0.744927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0727 | 0.898563 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.7123 | 0.772195 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.42554 | 0.0746161 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4810 | −1.01690 | −0.508450 | − | 0.861091i | \(-0.669781\pi\) | ||||
−0.508450 | + | 0.861091i | \(0.669781\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.22552 | 0.219972 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.7466 | 1.12903 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.24977 | 0.0647105 | 0.0323552 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323552 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.60322 | −0.340989 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.1726 | 0.832932 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.7550 | −0.963379 | −0.481690 | − | 0.876342i | \(-0.659977\pi\) | ||||
−0.481690 | + | 0.876342i | \(0.659977\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.5687 | 0.797610 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.7851 | −1.93073 | −0.965365 | − | 0.260904i | \(-0.915979\pi\) | ||||
−0.965365 | + | 0.260904i | \(0.915979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.9372 | −0.608377 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.19268 | 0.263959 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.0969 | −0.866848 | −0.433424 | − | 0.901190i | \(-0.642695\pi\) | ||||
−0.433424 | + | 0.901190i | \(0.642695\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.97375 | 0.200961 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.68807 | −0.438255 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.41670 | 0.373175 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.16723 | 0.359713 | 0.179856 | − | 0.983693i | \(-0.442437\pi\) | ||||
0.179856 | + | 0.983693i | \(0.442437\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.3820 | −1.02038 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.1232 | −1.90378 | −0.951891 | − | 0.306437i | \(-0.900863\pi\) | ||||
−0.951891 | + | 0.306437i | \(0.900863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.2732 | −0.960066 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.693705 | 0.0344705 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −31.3543 | −1.55417 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.8724 | 1.67488 | 0.837441 | − | 0.546528i | \(-0.184051\pi\) | ||||
0.837441 | + | 0.546528i | \(0.184051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.6471 | 0.574511 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −34.2048 | −1.68311 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.88432 | 0.239762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.8127 | 1.01920 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.2717 | −0.550660 | −0.275330 | − | 0.961350i | \(-0.588787\pi\) | ||||
−0.275330 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.3100 | −1.67217 | −0.836085 | − | 0.548601i | \(-0.815161\pi\) | ||||
−0.836085 | + | 0.548601i | \(0.815161\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.33431 | −0.210741 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.0141 | −0.679785 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.2594 | 1.56114 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.4283 | 0.938008 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.8027 | 1.24287 | 0.621436 | − | 0.783465i | \(-0.286550\pi\) | ||||
0.621436 | + | 0.783465i | \(0.286550\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.4503 | −0.646381 | −0.323190 | − | 0.946334i | \(-0.604755\pi\) | ||||
−0.323190 | + | 0.946334i | \(0.604755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.92813 | 0.140393 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.69562 | 0.368132 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.7102 | −1.41799 | −0.708995 | − | 0.705214i | \(-0.750851\pi\) | ||||
−0.708995 | + | 0.705214i | \(0.750851\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.51638 | 0.215066 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3143 | 0.537560 | 0.268780 | − | 0.963202i | \(-0.413380\pi\) | ||||
0.268780 | + | 0.963202i | \(0.413380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.927015 | 0.0439447 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.23090 | −0.342010 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.6462 | −1.82383 | −0.911913 | − | 0.410384i | \(-0.865395\pi\) | ||||
−0.911913 | + | 0.410384i | \(0.865395\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.4265 | 1.00893 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.71992 | 0.268745 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.01980 | −0.422855 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.6469 | 0.825486 | 0.412743 | − | 0.910847i | \(-0.364571\pi\) | ||||
0.412743 | + | 0.910847i | \(0.364571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.10131 | 0.144757 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.4542 | −1.69784 | −0.848921 | − | 0.528519i | \(-0.822747\pi\) | ||||
−0.848921 | + | 0.528519i | \(0.822747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2739 | 1.12811 | 0.564053 | − | 0.825739i | \(-0.309241\pi\) | ||||
0.564053 | + | 0.825739i | \(0.309241\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.48951 | −0.161822 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.187624 | −0.00868221 | −0.00434110 | − | 0.999991i | \(-0.501382\pi\) | ||||
−0.00434110 | + | 0.999991i | \(0.501382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.9116 | 1.10414 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.9148 | −1.10193 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.3307 | 1.21069 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.1400 | −1.24527 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.40817 | −0.293410 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.1735 | −1.51573 | −0.757867 | − | 0.652409i | \(-0.773759\pi\) | ||||
−0.757867 | + | 0.652409i | \(0.773759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.6914 | −1.08023 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.34823 | −0.197851 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.02000 | −0.273354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.5776 | 1.92938 | 0.964688 | − | 0.263396i | \(-0.0848427\pi\) | ||||
0.964688 | + | 0.263396i | \(0.0848427\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.25523 | 0.147207 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2273 | 0.596942 | 0.298471 | − | 0.954419i | \(-0.403523\pi\) | ||||
0.298471 | + | 0.954419i | \(0.403523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.0907 | 0.589574 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.51759 | 0.158104 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.87870 | −0.443120 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0630 | 0.763846 | 0.381923 | − | 0.924194i | \(-0.375262\pi\) | ||||
0.381923 | + | 0.924194i | \(0.375262\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.6189 | 0.876507 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.53644 | −0.113094 | −0.0565471 | − | 0.998400i | \(-0.518009\pi\) | ||||
−0.0565471 | + | 0.998400i | \(0.518009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5382 | 0.468944 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.68010 | 0.0746160 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.8897 | −1.81240 | −0.906201 | − | 0.422847i | \(-0.861031\pi\) | ||||
−0.906201 | + | 0.422847i | \(0.861031\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.97369 | −0.308498 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.00606 | 0.265174 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.70843 | −0.295609 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.9781 | −0.966597 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.4915 | 0.548315 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.2017 | −1.10411 | −0.552054 | − | 0.833808i | \(-0.686156\pi\) | ||||
−0.552054 | + | 0.833808i | \(0.686156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.15204 | −0.269010 | −0.134505 | − | 0.990913i | \(-0.542944\pi\) | ||||
−0.134505 | + | 0.990913i | \(0.542944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.3348 | 0.669266 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.6004 | −0.679563 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3582 | −0.928619 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0793 | 0.437404 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.1899 | 0.701264 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.28550 | −0.228512 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.5394 | 0.756882 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.9014 | 0.986431 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.50258 | −0.236574 | −0.118287 | − | 0.992979i | \(-0.537740\pi\) | ||||
−0.118287 | + | 0.992979i | \(0.537740\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.88595 | 0.123848 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.496665 | −0.0212748 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.2024 | 0.949306 | 0.474653 | − | 0.880173i | \(-0.342573\pi\) | ||||
0.474653 | + | 0.880173i | \(0.342573\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.50602 | −0.405707 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.3516 | 1.08001 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.2823 | −1.54288 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.28944 | −0.182077 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.5670 | −1.76125 | −0.880626 | − | 0.473813i | \(-0.842877\pi\) | ||||
−0.880626 | + | 0.473813i | \(0.842877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.8956 | 0.841493 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.7259 | 0.663949 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.6524 | 0.743959 | 0.371979 | − | 0.928241i | \(-0.378679\pi\) | ||||
0.371979 | + | 0.928241i | \(0.378679\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.77398 | −0.0746318 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.39358 | −0.142517 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.3115 | −1.39649 | −0.698246 | − | 0.715858i | \(-0.746036\pi\) | ||||
−0.698246 | + | 0.715858i | \(0.746036\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.4041 | 1.85825 | 0.929127 | − | 0.369760i | \(-0.120560\pi\) | ||||
0.929127 | + | 0.369760i | \(0.120560\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.22169 | −0.134588 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.78995 | −0.241458 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.7325 | 1.15452 | 0.577260 | − | 0.816560i | \(-0.304122\pi\) | ||||
0.577260 | + | 0.816560i | \(0.304122\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.2520 | 0.509176 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.8939 | −0.991287 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.4941 | −1.34577 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.65790 | 0.109891 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.1948 | −0.709706 | −0.354853 | − | 0.934922i | \(-0.615469\pi\) | ||||
−0.354853 | + | 0.934922i | \(0.615469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.2119 | −1.24486 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.06249 | −0.290512 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.2007 | −0.870610 | −0.435305 | − | 0.900283i | \(-0.643359\pi\) | ||||
−0.435305 | + | 0.900283i | \(0.643359\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.30093 | −0.299309 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.8918 | 0.814117 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.1790 | 1.11050 | 0.555252 | − | 0.831682i | \(-0.312622\pi\) | ||||
0.555252 | + | 0.831682i | \(0.312622\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6950 | −0.436259 | −0.218130 | − | 0.975920i | \(-0.569996\pi\) | ||||
−0.218130 | + | 0.975920i | \(0.569996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.04614 | −0.286941 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2060 | 0.414932 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.3530 | 1.15081 | 0.575407 | − | 0.817867i | \(-0.304844\pi\) | ||||
0.575407 | + | 0.817867i | \(0.304844\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.3243 | −0.580451 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6068 | −0.671837 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.75349 | −0.151602 | −0.0758010 | − | 0.997123i | \(-0.524151\pi\) | ||||
−0.0758010 | + | 0.997123i | \(0.524151\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.93127 | 0.118200 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.9051 | 1.64678 | 0.823389 | − | 0.567478i | \(-0.192081\pi\) | ||||
0.823389 | + | 0.567478i | \(0.192081\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.84390 | 0.0741127 | 0.0370563 | − | 0.999313i | \(-0.488202\pi\) | ||||
0.0370563 | + | 0.999313i | \(0.488202\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.28131 | 0.0514172 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.53492 | −0.181688 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.0132 | 0.720528 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 30.4551 | 1.21626 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.1766 | −0.764621 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.1801 | 1.00240 | 0.501202 | − | 0.865330i | \(-0.332891\pi\) | ||||
0.501202 | + | 0.865330i | \(0.332891\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.40796 | 0.294440 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.8001 | 0.428589 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.3043 | 0.685623 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.91100 | 0.115157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.7359 | 0.819017 | 0.409508 | − | 0.912306i | \(-0.365700\pi\) | ||||
0.409508 | + | 0.912306i | \(0.365700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.4230 | −1.19976 | −0.599882 | − | 0.800088i | \(-0.704786\pi\) | ||||
−0.599882 | + | 0.800088i | \(0.704786\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.60219 | 0.141836 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.3132 | −1.34899 | −0.674496 | − | 0.738279i | \(-0.735639\pi\) | ||||
−0.674496 | + | 0.738279i | \(0.735639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.1093 | 2.00622 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.0705 | 0.669047 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.6874 | −0.613894 | −0.306947 | − | 0.951727i | \(-0.599307\pi\) | ||||
−0.306947 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.02696 | −0.235493 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.05497 | 0.0801718 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.4806 | −1.22631 | −0.613155 | − | 0.789962i | \(-0.710100\pi\) | ||||
−0.613155 | + | 0.789962i | \(0.710100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.3891 | 1.06531 | 0.532657 | − | 0.846331i | \(-0.321194\pi\) | ||||
0.532657 | + | 0.846331i | \(0.321194\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.8826 | 0.461481 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.1391 | −0.548291 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.40842 | 0.209415 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.474828 | 0.0183579 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.2024 | −1.86083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.8967 | −0.921149 | −0.460575 | − | 0.887621i | \(-0.652357\pi\) | ||||
−0.460575 | + | 0.887621i | \(0.652357\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.51877 | −0.173928 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.16212 | 0.0446637 | 0.0223319 | − | 0.999751i | \(-0.492891\pi\) | ||||
0.0223319 | + | 0.999751i | \(0.492891\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.4496 | 1.13017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.8443 | −0.645473 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.6893 | −0.638598 | −0.319299 | − | 0.947654i | \(-0.603447\pi\) | ||||
−0.319299 | + | 0.947654i | \(0.603447\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.07967 | 0.308708 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.13575 | 0.0814838 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.5527 | −0.935382 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.93496 | 0.225777 | 0.112888 | − | 0.993608i | \(-0.463990\pi\) | ||||
0.112888 | + | 0.993608i | \(0.463990\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.2079 | −0.653675 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.4379 | 0.547659 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.1047 | 0.496375 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.3369 | 0.844860 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.5746 | −0.626013 | −0.313006 | − | 0.949751i | \(-0.601336\pi\) | ||||
−0.313006 | + | 0.949751i | \(0.601336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.1377 | −1.40068 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.00673 | −0.113240 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −51.5526 | −1.93883 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.34699 | −0.238366 | −0.119183 | − | 0.992872i | \(-0.538028\pi\) | ||||
−0.119183 | + | 0.992872i | \(0.538028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.6914 | 0.400960 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.44531 | −0.241379 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.4775 | 0.504030 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.3907 | 0.612123 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.0405 | 0.411742 | 0.205871 | − | 0.978579i | \(-0.433997\pi\) | ||||
0.205871 | + | 0.978579i | \(0.433997\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.8174 | 1.22218 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.1952 | −0.527927 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.0738 | −0.708382 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3769 | 0.533211 | 0.266605 | − | 0.963806i | \(-0.414098\pi\) | ||||
0.266605 | + | 0.963806i | \(0.414098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.1041 | 0.595633 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.7241 | 1.35644 | 0.678218 | − | 0.734861i | \(-0.262753\pi\) | ||||
0.678218 | + | 0.734861i | \(0.262753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.13303 | 0.115564 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.7291 | −1.31610 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.8580 | 1.98120 | 0.990600 | − | 0.136789i | \(-0.0436784\pi\) | ||||
0.990600 | + | 0.136789i | \(0.0436784\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.0120 | 0.845366 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5704 | 0.828029 | 0.414014 | − | 0.910270i | \(-0.364126\pi\) | ||||
0.414014 | + | 0.910270i | \(0.364126\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.01611 | −0.183776 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.04092 | 0.257614 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.8565 | 0.944776 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.93159 | 0.362409 | 0.181204 | − | 0.983445i | \(-0.442000\pi\) | ||||
0.181204 | + | 0.983445i | \(0.442000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.00000 | 0.0364420 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.96793 | 0.144408 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.4794 | −0.562609 | −0.281304 | − | 0.959619i | \(-0.590767\pi\) | ||||
−0.281304 | + | 0.959619i | \(0.590767\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.49718 | 0.235833 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.66788 | −0.205460 | −0.102730 | − | 0.994709i | \(-0.532758\pi\) | ||||
−0.102730 | + | 0.994709i | \(0.532758\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.42967 | 0.0879599 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.15140 | 0.0777839 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.6184 | 1.39443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.3596 | −1.38328 | −0.691641 | − | 0.722242i | \(-0.743112\pi\) | ||||
−0.691641 | + | 0.722242i | \(0.743112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2880 | −0.406528 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.9003 | 0.679796 | 0.339898 | − | 0.940462i | \(-0.389607\pi\) | ||||
0.339898 | + | 0.940462i | \(0.389607\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.7305 | 0.816505 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.9838 | 0.752789 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.3787 | 0.909288 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.7609 | 0.528186 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.22100 | 0.150846 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.5898 | −0.592115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.5875 | −1.05468 | −0.527340 | − | 0.849654i | \(-0.676811\pi\) | ||||
−0.527340 | + | 0.849654i | \(0.676811\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.0221 | −0.534800 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.67824 | 0.308563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.4219 | −1.29338 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.44538 | −0.157661 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.1718 | 0.891633 | 0.445816 | − | 0.895124i | \(-0.352913\pi\) | ||||
0.445816 | + | 0.895124i | \(0.352913\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.4421 | −0.475546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.33632 | 0.0472167 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.4202 | 0.367720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.01639 | −0.106314 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.2636 | 0.466900 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.8237 | 1.11886 | 0.559431 | − | 0.828877i | \(-0.311020\pi\) | ||||
0.559431 | + | 0.828877i | \(0.311020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.80329 | 0.203781 | 0.101891 | − | 0.994796i | \(-0.467511\pi\) | ||||
0.101891 | + | 0.994796i | \(0.467511\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.2457 | 0.464546 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.25817 | 0.0791001 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.1875 | 1.09111 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.0024 | −0.454340 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.45101 | −0.329842 | −0.164921 | − | 0.986307i | \(-0.552737\pi\) | ||||
−0.164921 | + | 0.986307i | \(0.552737\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.2383 | −1.61176 | −0.805882 | − | 0.592076i | \(-0.798309\pi\) | ||||
−0.805882 | + | 0.592076i | \(0.798309\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.9135 | −0.797745 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.87014 | −0.238898 | −0.119449 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119449 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.15593 | 0.109610 | 0.0548050 | − | 0.998497i | \(-0.482546\pi\) | ||||
0.0548050 | + | 0.998497i | \(0.482546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.4428 | −0.535705 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.0067 | 0.485304 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.6097 | 0.470983 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.03025 | −0.173871 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.2050 | 0.732077 | 0.366039 | − | 0.930600i | \(-0.380714\pi\) | ||||
0.366039 | + | 0.930600i | \(0.380714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1831 | −0.385625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.0074 | 0.482441 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.16549 | 0.0400942 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −49.9274 | −1.71552 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.8561 | −0.681461 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.92283 | −0.271591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.6002 | −1.08197 | −0.540985 | − | 0.841032i | \(-0.681948\pi\) | ||||
−0.540985 | + | 0.841032i | \(0.681948\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.16643 | 0.142489 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.2412 | −0.349832 | −0.174916 | − | 0.984583i | \(-0.555965\pi\) | ||||
−0.174916 | + | 0.984583i | \(0.555965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.3519 | −0.694399 | −0.347200 | − | 0.937791i | \(-0.612867\pi\) | ||||
−0.347200 | + | 0.937791i | \(0.612867\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.3397 | −0.488694 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.843947 | 0.0287283 | 0.0143641 | − | 0.999897i | \(-0.495428\pi\) | ||||
0.0143641 | + | 0.999897i | \(0.495428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.66539 | 0.294632 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.38186 | −0.250701 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.2134 | 1.83906 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.9970 | −0.914759 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.67805 | −0.293707 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.4085 | 0.757547 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0910 | −0.374517 | −0.187258 | − | 0.982311i | \(-0.559960\pi\) | ||||
−0.187258 | + | 0.982311i | \(0.559960\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.3819 | 0.822382 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.37418 | −0.315824 | −0.157912 | − | 0.987453i | \(-0.550476\pi\) | ||||
−0.157912 | + | 0.987453i | \(0.550476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.4958 | −0.420518 | −0.210259 | − | 0.977646i | \(-0.567431\pi\) | ||||
−0.210259 | + | 0.977646i | \(0.567431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.99204 | 0.235035 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.4508 | 0.988862 | 0.494431 | − | 0.869217i | \(-0.335376\pi\) | ||||
0.494431 | + | 0.869217i | \(0.335376\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.8337 | −1.77198 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.07073 | 0.169876 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.0321 | −0.871132 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.1672 | 0.406704 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.90929 | 0.163917 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.2327 | −0.708150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.8737 | −0.662090 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.6218 | −0.586416 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.00199 | 0.0665485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.6496 | −1.28334 | −0.641670 | − | 0.766981i | \(-0.721758\pi\) | ||||
−0.641670 | + | 0.766981i | \(0.721758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1912 | 0.503860 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.3850 | 1.43741 | 0.718705 | − | 0.695316i | \(-0.244735\pi\) | ||||
0.718705 | + | 0.695316i | \(0.244735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.7026 | 1.18158 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.59437 | −0.218003 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.4837 | 0.973637 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.8276 | 1.18184 | 0.590922 | − | 0.806729i | \(-0.298764\pi\) | ||||
0.590922 | + | 0.806729i | \(0.298764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.02581 | −0.297411 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.1534 | 0.367118 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.9413 | 0.918704 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.67044 | −0.317619 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.8382 | 0.913343 | 0.456671 | − | 0.889636i | \(-0.349042\pi\) | ||||
0.456671 | + | 0.889636i | \(0.349042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.1256 | 0.889007 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.83059 | 0.125408 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.9091 | 0.356767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4256 | −0.405928 | −0.202964 | − | 0.979186i | \(-0.565057\pi\) | ||||
−0.202964 | + | 0.979186i | \(0.565057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.6014 | 0.345964 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.0448 | −0.457848 | −0.228924 | − | 0.973444i | \(-0.573521\pi\) | ||||
−0.228924 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.41421 | 0.176311 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.35414 | −0.0765802 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.1617 | 1.33758 | 0.668788 | − | 0.743453i | \(-0.266813\pi\) | ||||
0.668788 | + | 0.743453i | \(0.266813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.87352 | 0.255585 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.40231 | 0.240036 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.2204 | −0.914149 | −0.457074 | − | 0.889428i | \(-0.651103\pi\) | ||||
−0.457074 | + | 0.889428i | \(0.651103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.23490 | −0.0723197 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.4036 | 0.691879 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.5255 | −1.27634 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.69662 | −0.183762 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.61924 | −0.245527 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.49927 | 0.273601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.6825 | 1.56552 | 0.782761 | − | 0.622322i | \(-0.213810\pi\) | ||||
0.782761 | + | 0.622322i | \(0.213810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.6267 | 0.598375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.4086 | 1.39305 | 0.696524 | − | 0.717534i | \(-0.254729\pi\) | ||||
0.696524 | + | 0.717534i | \(0.254729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −70.6295 | −2.26428 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.3135 | −0.554476 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.7387 | −1.11139 | −0.555695 | − | 0.831386i | \(-0.687548\pi\) | ||||
−0.555695 | + | 0.831386i | \(0.687548\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.77614 | 0.216566 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.715961 | −0.0228589 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.1559 | −0.451504 | −0.225752 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225752 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.89928 | −0.156104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.7088 | 0.468187 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.65344 | 0.211567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0177 | −0.699416 | −0.349708 | − | 0.936859i | \(-0.613719\pi\) | ||||
−0.349708 | + | 0.936859i | \(0.613719\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.57955 | −0.113594 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.7990 | 0.437459 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.9683 | 0.537393 | 0.268696 | − | 0.963225i | \(-0.413407\pi\) | ||||
0.268696 | + | 0.963225i | \(0.413407\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.18338 | −0.195634 |
(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 | 6024.2.a.q.1.10 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6024.2.a.q.1.10 | ✓ | 18 | 1.1 | even | 1 | trivial |