Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −1.16746 | −0.674034 | −0.337017 | − | 0.941499i | \(-0.609418\pi\) | ||||
−0.337017 | + | 0.941499i | \(0.609418\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.71362 | 1.21357 | 0.606784 | − | 0.794866i | \(-0.292459\pi\) | ||||
0.606784 | + | 0.794866i | \(0.292459\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.33257 | −0.503666 | −0.251833 | − | 0.967771i | \(-0.581033\pi\) | ||||
−0.251833 | + | 0.967771i | \(0.581033\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.63703 | −0.545678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.08555 | 1.53335 | 0.766676 | − | 0.642034i | \(-0.221909\pi\) | ||||
0.766676 | + | 0.642034i | \(0.221909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.388876 | −0.107855 | −0.0539274 | − | 0.998545i | \(-0.517174\pi\) | ||||
−0.0539274 | + | 0.998545i | \(0.517174\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.16805 | −0.817987 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.121828 | 0.0295476 | 0.0147738 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147738 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.29355 | −1.67326 | −0.836628 | − | 0.547772i | \(-0.815476\pi\) | ||||
−0.836628 | + | 0.547772i | \(0.815476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.55573 | 0.339488 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.31839 | 1.52599 | 0.762995 | − | 0.646404i | \(-0.223728\pi\) | ||||
0.762995 | + | 0.646404i | \(0.223728\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.36375 | 0.472749 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.41356 | 1.04184 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.97697 | −1.66698 | −0.833491 | − | 0.552533i | \(-0.813661\pi\) | ||||
−0.833491 | + | 0.552533i | \(0.813661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.78388 | −1.21842 | −0.609211 | − | 0.793008i | \(-0.708514\pi\) | ||||
−0.609211 | + | 0.793008i | \(0.708514\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.93718 | −1.03353 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.61610 | −0.611233 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.924411 | −0.151972 | −0.0759861 | − | 0.997109i | \(-0.524210\pi\) | ||||
−0.0759861 | + | 0.997109i | \(0.524210\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.453997 | 0.0726978 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.63874 | 0.412101 | 0.206051 | − | 0.978541i | \(-0.433939\pi\) | ||||
0.206051 | + | 0.978541i | \(0.433939\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12279 | 0.171225 | 0.0856123 | − | 0.996329i | \(-0.472715\pi\) | ||||
0.0856123 | + | 0.996329i | \(0.472715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.44229 | −0.662218 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.220348 | −0.0321410 | −0.0160705 | − | 0.999871i | \(-0.505116\pi\) | ||||
−0.0160705 | + | 0.999871i | \(0.505116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.22424 | −0.746321 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.142229 | −0.0199161 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.43226 | −1.02090 | −0.510450 | − | 0.859908i | \(-0.670521\pi\) | ||||
−0.510450 | + | 0.859908i | \(0.670521\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.8003 | 1.86083 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.51494 | 1.12783 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.34714 | 0.175382 | 0.0876911 | − | 0.996148i | \(-0.472051\pi\) | ||||
0.0876911 | + | 0.996148i | \(0.472051\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.43689 | −1.08023 | −0.540116 | − | 0.841590i | \(-0.681620\pi\) | ||||
−0.540116 | + | 0.841590i | \(0.681620\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.18147 | 0.274840 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.05526 | −0.130889 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.702187 | 0.0857858 | 0.0428929 | − | 0.999080i | \(-0.486343\pi\) | ||||
0.0428929 | + | 0.999080i | \(0.486343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.54394 | −1.02857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1923 | −1.20960 | −0.604801 | − | 0.796377i | \(-0.706747\pi\) | ||||
−0.604801 | + | 0.796377i | \(0.706747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.50346 | 0.878213 | 0.439107 | − | 0.898435i | \(-0.355295\pi\) | ||||
0.439107 | + | 0.898435i | \(0.355295\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.75958 | −0.318649 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.77688 | −0.772297 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.63081 | 0.633516 | 0.316758 | − | 0.948506i | \(-0.397406\pi\) | ||||
0.316758 | + | 0.948506i | \(0.397406\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.40901 | −0.156557 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.3504 | 1.46540 | 0.732698 | − | 0.680554i | \(-0.238261\pi\) | ||||
0.732698 | + | 0.680554i | \(0.238261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.330595 | 0.0358581 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.4803 | 1.12360 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3464 | −1.62672 | −0.813358 | − | 0.581763i | \(-0.802363\pi\) | ||||
−0.813358 | + | 0.581763i | \(0.802363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.518206 | 0.0543228 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.91992 | 0.821257 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.7919 | −2.03061 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.99311 | 0.202370 | 0.101185 | − | 0.994868i | \(-0.467737\pi\) | ||||
0.101185 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.32523 | −0.836717 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.89841 | 0.586914 | 0.293457 | − | 0.955972i | \(-0.405194\pi\) | ||||
0.293457 | + | 0.955972i | \(0.405194\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5548 | 1.04000 | 0.519999 | − | 0.854167i | \(-0.325932\pi\) | ||||
0.519999 | + | 0.854167i | \(0.325932\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.22166 | 0.411992 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.5575 | −1.11730 | −0.558652 | − | 0.829402i | \(-0.688681\pi\) | ||||
−0.558652 | + | 0.829402i | \(0.688681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.87019 | 0.658044 | 0.329022 | − | 0.944322i | \(-0.393281\pi\) | ||||
0.329022 | + | 0.944322i | \(0.393281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.07921 | 0.102434 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.1734 | −1.89776 | −0.948879 | − | 0.315640i | \(-0.897781\pi\) | ||||
−0.948879 | + | 0.315640i | \(0.897781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.8593 | 1.85189 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.636603 | 0.0588540 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.162345 | −0.0148821 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.8628 | 1.35117 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.08062 | −0.277770 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.15380 | −0.639855 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6903 | −1.03734 | −0.518672 | − | 0.854974i | \(-0.673573\pi\) | ||||
−0.518672 | + | 0.854974i | \(0.673573\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.31082 | −0.115411 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.88778 | −0.427048 | −0.213524 | − | 0.976938i | \(-0.568494\pi\) | ||||
−0.213524 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.71920 | 0.842762 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.6903 | 1.26434 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0170 | −1.11212 | −0.556058 | − | 0.831144i | \(-0.687687\pi\) | ||||
−0.556058 | + | 0.831144i | \(0.687687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8290 | 0.918508 | 0.459254 | − | 0.888305i | \(-0.348117\pi\) | ||||
0.459254 | + | 0.888305i | \(0.348117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.257247 | 0.0216641 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.97765 | −0.165379 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.3601 | −2.02300 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.09910 | 0.503045 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.00950 | −0.0827014 | −0.0413507 | − | 0.999145i | \(-0.513166\pi\) | ||||
−0.0413507 | + | 0.999145i | \(0.513166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.8268 | −1.93900 | −0.969499 | − | 0.245096i | \(-0.921181\pi\) | ||||
−0.969499 | + | 0.245096i | \(0.921181\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.199437 | −0.0161235 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.4089 | −1.47864 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.34943 | 0.746166 | 0.373083 | − | 0.927798i | \(-0.378301\pi\) | ||||
0.373083 | + | 0.927798i | \(0.378301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.67687 | 0.688121 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.75230 | −0.768589 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.19941 | 0.642227 | 0.321114 | − | 0.947041i | \(-0.395943\pi\) | ||||
0.321114 | + | 0.947041i | \(0.395943\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.1113 | −1.25426 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.554966 | −0.0429446 | −0.0214723 | − | 0.999769i | \(-0.506835\pi\) | ||||
−0.0214723 | + | 0.999769i | \(0.506835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8488 | −0.988367 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9398 | 0.913059 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.4573 | −1.55534 | −0.777669 | − | 0.628674i | \(-0.783598\pi\) | ||||
−0.777669 | + | 0.628674i | \(0.783598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.14987 | −0.238108 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.57273 | −0.118214 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.3716 | 1.29842 | 0.649208 | − | 0.760611i | \(-0.275100\pi\) | ||||
0.649208 | + | 0.760611i | \(0.275100\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.98576 | 0.147601 | 0.0738003 | − | 0.997273i | \(-0.476487\pi\) | ||||
0.0738003 | + | 0.997273i | \(0.476487\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.84973 | 0.728113 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.50850 | −0.184429 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.619562 | 0.0453069 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.21397 | −0.524739 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.1242 | 0.949632 | 0.474816 | − | 0.880085i | \(-0.342515\pi\) | ||||
0.474816 | + | 0.880085i | \(0.342515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.5078 | 1.33222 | 0.666109 | − | 0.745854i | \(-0.267959\pi\) | ||||
0.666109 | + | 0.745854i | \(0.267959\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.23198 | 0.0882237 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.0169 | 0.998664 | 0.499332 | − | 0.866411i | \(-0.333579\pi\) | ||||
0.499332 | + | 0.866411i | \(0.333579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.4832 | −1.02669 | −0.513343 | − | 0.858184i | \(-0.671593\pi\) | ||||
−0.513343 | + | 0.858184i | \(0.671593\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.819776 | −0.0578226 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.9625 | 0.839602 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.16054 | 0.500113 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.9805 | −0.832700 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −37.0917 | −2.56569 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.38189 | −0.0951330 | −0.0475665 | − | 0.998868i | \(-0.515147\pi\) | ||||
−0.0475665 | + | 0.998868i | \(0.515147\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.8991 | 0.815313 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.04684 | 0.207793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.04003 | 0.613677 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.75999 | −0.591946 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0473759 | −0.00318685 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.77343 | −0.185723 | −0.0928613 | − | 0.995679i | \(-0.529601\pi\) | ||||
−0.0928613 | + | 0.995679i | \(0.529601\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.86953 | −0.257969 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6621 | −0.840414 | −0.420207 | − | 0.907428i | \(-0.638043\pi\) | ||||
−0.420207 | + | 0.907428i | \(0.638043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.8252 | 0.781428 | 0.390714 | − | 0.920512i | \(-0.372228\pi\) | ||||
0.390714 | + | 0.920512i | \(0.372228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.91174 | 0.520554 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.8656 | 1.10490 | 0.552452 | − | 0.833544i | \(-0.313692\pi\) | ||||
0.552452 | + | 0.833544i | \(0.313692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.597940 | −0.0390053 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.57375 | −0.427011 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.70053 | 0.627475 | 0.313737 | − | 0.949510i | \(-0.398419\pi\) | ||||
0.313737 | + | 0.949510i | \(0.398419\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.3108 | −1.56599 | −0.782997 | − | 0.622026i | \(-0.786310\pi\) | ||||
−0.782997 | + | 0.622026i | \(0.786310\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.5957 | −0.936315 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.1766 | −0.905711 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.83629 | 0.180469 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.5861 | −0.987726 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9062 | 1.50894 | 0.754472 | − | 0.656332i | \(-0.227893\pi\) | ||||
0.754472 | + | 0.656332i | \(0.227893\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.2181 | 2.33988 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.385957 | −0.0241696 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.4942 | −0.779364 | −0.389682 | − | 0.920949i | \(-0.627415\pi\) | ||||
−0.389682 | + | 0.920949i | \(0.627415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.23185 | 0.0765432 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.6956 | 0.909636 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.33772 | −0.267475 | −0.133738 | − | 0.991017i | \(-0.542698\pi\) | ||||
−0.133738 | + | 0.991017i | \(0.542698\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.1683 | −1.23893 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.9163 | 1.09646 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.7394 | −1.02062 | −0.510309 | − | 0.859991i | \(-0.670469\pi\) | ||||
−0.510309 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.4434 | 0.938121 | 0.469061 | − | 0.883166i | \(-0.344593\pi\) | ||||
0.469061 | + | 0.883166i | \(0.344593\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.604985 | −0.0366154 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0210 | 0.724891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.1626 | −1.63205 | −0.816023 | − | 0.578020i | \(-0.803826\pi\) | ||||
−0.816023 | + | 0.578020i | \(0.803826\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.1055 | 0.664866 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7885 | 1.12083 | 0.560413 | − | 0.828213i | \(-0.310642\pi\) | ||||
0.560413 | + | 0.828213i | \(0.310642\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.37619 | 0.200694 | 0.100347 | − | 0.994953i | \(-0.468005\pi\) | ||||
0.100347 | + | 0.994953i | \(0.468005\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.1063 | 1.36870 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.51631 | −0.207561 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9852 | −0.999127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.32688 | −0.136404 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.0808 | −1.11471 | −0.557355 | − | 0.830274i | \(-0.688184\pi\) | ||||
−0.557355 | + | 0.830274i | \(0.688184\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.65562 | 0.212838 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.5309 | 1.59751 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.84595 | −0.164585 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.49621 | −0.0862400 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.88617 | −0.395600 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.8945 | −1.31094 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.86952 | −0.506210 | −0.253105 | − | 0.967439i | \(-0.581452\pi\) | ||||
−0.253105 | + | 0.967439i | \(0.581452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.3224 | −0.700994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.06654 | 0.117183 | 0.0585913 | − | 0.998282i | \(-0.481339\pi\) | ||||
0.0585913 | + | 0.998282i | \(0.481339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.69218 | 0.491311 | 0.245656 | − | 0.969357i | \(-0.420997\pi\) | ||||
0.245656 | + | 0.969357i | \(0.420997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.91969 | 0.333537 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.52454 | −0.422620 | −0.211310 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211310 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.6529 | −2.55607 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.4929 | 0.753100 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.888558 | −0.0494407 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.919204 | −0.0509883 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.02067 | −0.443544 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.293630 | 0.0161883 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.396297 | −0.0217825 | −0.0108912 | − | 0.999941i | \(-0.503467\pi\) | ||||
−0.0108912 | + | 0.999941i | \(0.503467\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.51329 | 0.0829279 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.90547 | 0.104107 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.4203 | −1.16684 | −0.583418 | − | 0.812172i | \(-0.698285\pi\) | ||||
−0.583418 | + | 0.812172i | \(0.698285\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.5517 | 1.27915 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.4998 | −1.86827 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.2897 | 0.879562 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.1850 | −1.24824 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.2531 | −1.08725 | −0.543623 | − | 0.839330i | \(-0.682948\pi\) | ||||
−0.543623 | + | 0.839330i | \(0.682948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2589 | −1.08444 | −0.542218 | − | 0.840238i | \(-0.682415\pi\) | ||||
−0.542218 | + | 0.840238i | \(0.682415\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.10520 | −0.112367 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.7266 | −1.52896 | −0.764482 | − | 0.644645i | \(-0.777005\pi\) | ||||
−0.764482 | + | 0.644645i | \(0.777005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.6580 | −1.46794 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.189531 | 0.0100311 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.4920 | 1.02875 | 0.514375 | − | 0.857565i | \(-0.328024\pi\) | ||||
0.514375 | + | 0.857565i | \(0.328024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.1959 | 1.79978 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.3518 | −0.910733 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.3616 | 1.06577 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2145 | −1.00299 | −0.501496 | − | 0.865160i | \(-0.667217\pi\) | ||||
−0.501496 | + | 0.865160i | \(0.667217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.31970 | −0.224875 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.90404 | 0.514192 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.3774 | −0.847992 | −0.423996 | − | 0.905664i | \(-0.639373\pi\) | ||||
−0.423996 | + | 0.905664i | \(0.639373\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.35178 | 0.431284 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.49093 | 0.179792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.6952 | −1.78217 | −0.891087 | − | 0.453832i | \(-0.850057\pi\) | ||||
−0.891087 | + | 0.453832i | \(0.850057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.6479 | 0.699205 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.93157 | 0.200894 | 0.100447 | − | 0.994942i | \(-0.467973\pi\) | ||||
0.100447 | + | 0.994942i | \(0.467973\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.3899 | −0.937236 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.83805 | −0.0934336 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.3137 | −0.624327 | −0.312163 | − | 0.950028i | \(-0.601054\pi\) | ||||
−0.312163 | + | 0.950028i | \(0.601054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.891584 | 0.0450894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.70630 | 0.287845 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.2799 | 0.768815 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.01879 | 0.352263 | 0.176132 | − | 0.984367i | \(-0.443642\pi\) | ||||
0.176132 | + | 0.984367i | \(0.443642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.3468 | −0.568050 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.7726 | −1.88627 | −0.943137 | − | 0.332404i | \(-0.892140\pi\) | ||||
−0.943137 | + | 0.332404i | \(0.892140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.63809 | 0.131413 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.82353 | −0.189993 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.70114 | −0.233027 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5818 | 0.819917 | 0.409958 | − | 0.912104i | \(-0.365543\pi\) | ||||
0.409958 | + | 0.912104i | \(0.365543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.1968 | 0.749604 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.79516 | −0.0883340 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.2279 | 1.77836 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.6425 | −0.619105 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.1367 | 0.983741 | 0.491871 | − | 0.870668i | \(-0.336313\pi\) | ||||
0.491871 | + | 0.870668i | \(0.336313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2091 | −0.643774 | −0.321887 | − | 0.946778i | \(-0.604317\pi\) | ||||
−0.321887 | + | 0.946778i | \(0.604317\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.360717 | 0.0175386 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.287970 | 0.0139686 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.2428 | 0.544076 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.30883 | 0.111471 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6942 | −1.38215 | −0.691076 | − | 0.722782i | \(-0.742863\pi\) | ||||
−0.691076 | + | 0.722782i | \(0.742863\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.2483 | 0.780845 | 0.390422 | − | 0.920636i | \(-0.372329\pi\) | ||||
0.390422 | + | 0.920636i | \(0.372329\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.4395 | 1.36357 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −53.3771 | −2.55337 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.8121 | −1.47058 | −0.735291 | − | 0.677752i | \(-0.762954\pi\) | ||||
−0.735291 | + | 0.677752i | \(0.762954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.55227 | 0.407251 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.9987 | −1.52031 | −0.760153 | − | 0.649744i | \(-0.774876\pi\) | ||||
−0.760153 | + | 0.649744i | \(0.774876\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.6444 | −1.97413 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.17855 | 0.0557435 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.25216 | 0.436637 | 0.218318 | − | 0.975878i | \(-0.429943\pi\) | ||||
0.218318 | + | 0.975878i | \(0.429943\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.4194 | 0.631897 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.8169 | 1.30695 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.40622 | 0.0659244 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1559 | 1.22352 | 0.611761 | − | 0.791043i | \(-0.290462\pi\) | ||||
0.611761 | + | 0.791043i | \(0.290462\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.659523 | 0.0307839 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.7843 | 0.688576 | 0.344288 | − | 0.938864i | \(-0.388120\pi\) | ||||
0.344288 | + | 0.938864i | \(0.388120\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.2989 | 1.73343 | 0.866713 | − | 0.498807i | \(-0.166228\pi\) | ||||
0.866713 | + | 0.498807i | \(0.166228\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.4917 | 0.996652 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.4504 | −1.03888 | −0.519440 | − | 0.854507i | \(-0.673860\pi\) | ||||
−0.519440 | + | 0.854507i | \(0.673860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.935717 | −0.0432074 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9151 | −0.502941 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.71003 | 0.262548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.2401 | −0.791030 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.1669 | 0.557082 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7391 | 0.627754 | 0.313877 | − | 0.949464i | \(-0.398372\pi\) | ||||
0.313877 | + | 0.949464i | \(0.398372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.359481 | 0.0163909 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3854 | 0.518055 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.40856 | 0.245590 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.65353 | −0.301500 | −0.150750 | − | 0.988572i | \(-0.548169\pi\) | ||||
−0.150750 | + | 0.988572i | \(0.548169\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.57249 | −0.432883 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.2371 | −1.27432 | −0.637162 | − | 0.770730i | \(-0.719892\pi\) | ||||
−0.637162 | + | 0.770730i | \(0.719892\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.09365 | −0.0492553 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.5915 | −1.01541 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.5820 | 0.609235 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.31213 | 0.193038 | 0.0965188 | − | 0.995331i | \(-0.469229\pi\) | ||||
0.0965188 | + | 0.995331i | \(0.469229\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.647901 | 0.0289461 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.0344 | −0.581176 | −0.290588 | − | 0.956848i | \(-0.593851\pi\) | ||||
−0.290588 | + | 0.956848i | \(0.593851\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0061 | 0.712261 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.0004 | 0.666193 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.880835 | −0.0390423 | −0.0195212 | − | 0.999809i | \(-0.506214\pi\) | ||||
−0.0195212 | + | 0.999809i | \(0.506214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.99892 | −0.442326 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −39.4841 | −1.74326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.6418 | 1.26211 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.12059 | −0.0492834 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.8831 | 1.04835 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3881 | 0.761787 | 0.380893 | − | 0.924619i | \(-0.375616\pi\) | ||||
0.380893 | + | 0.924619i | \(0.375616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.70828 | −0.118425 | −0.0592123 | − | 0.998245i | \(-0.518859\pi\) | ||||
−0.0592123 | + | 0.998245i | \(0.518859\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.67735 | 0.160493 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.826466 | −0.0360014 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.5588 | 1.32865 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.20531 | −0.0957022 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.02614 | −0.0444471 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.3626 | −1.35592 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.2807 | −0.875177 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.5682 | −1.14437 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.9672 | 1.84730 | 0.923652 | − | 0.383233i | \(-0.125189\pi\) | ||||
0.923652 | + | 0.383233i | \(0.125189\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.31830 | −0.0994878 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.6431 | 0.798582 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9413 | 1.10917 | 0.554585 | − | 0.832127i | \(-0.312877\pi\) | ||||
0.554585 | + | 0.832127i | \(0.312877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.8115 | 0.589459 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.4740 | 2.78929 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.50348 | −0.319080 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.92858 | 0.124311 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.63049 | 0.196200 | 0.0981001 | − | 0.995177i | \(-0.468723\pi\) | ||||
0.0981001 | + | 0.995177i | \(0.468723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.436628 | −0.0184674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.723315 | −0.0305384 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.9346 | −1.80948 | −0.904739 | − | 0.425967i | \(-0.859934\pi\) | ||||
−0.904739 | + | 0.425967i | \(0.859934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.7431 | −2.30306 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.87761 | 0.0788524 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5418 | −0.567701 | −0.283850 | − | 0.958869i | \(-0.591612\pi\) | ||||
−0.283850 | + | 0.958869i | \(0.591612\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.0898 | 1.92880 | 0.964398 | − | 0.264454i | \(-0.0851917\pi\) | ||||
0.964398 | + | 0.264454i | \(0.0851917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.3220 | −0.640084 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.2988 | 0.721411 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3950 | −1.51514 | −0.757571 | − | 0.652753i | \(-0.773614\pi\) | ||||
−0.757571 | + | 0.652753i | \(0.773614\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.6071 | −0.897960 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.7904 | −0.738070 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.7971 | −1.56540 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.72750 | 0.0714234 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.36832 | −0.345397 | −0.172699 | − | 0.984975i | \(-0.555249\pi\) | ||||
−0.172699 | + | 0.984975i | \(0.555249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.4786 | 2.03873 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.3642 | −0.673133 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.5531 | 1.58319 | 0.791594 | − | 0.611048i | \(-0.209252\pi\) | ||||
0.791594 | + | 0.611048i | \(0.209252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.440543 | −0.0180605 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.9085 | 0.692021 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.7029 | 1.21363 | 0.606813 | − | 0.794845i | \(-0.292448\pi\) | ||||
0.606813 | + | 0.794845i | \(0.292448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.9283 | −1.05764 | −0.528818 | − | 0.848735i | \(-0.677365\pi\) | ||||
−0.528818 | + | 0.848735i | \(0.677365\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.14951 | −0.0468115 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40.3322 | 1.63974 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.769395 | 0.0312288 | 0.0156144 | − | 0.999878i | \(-0.495030\pi\) | ||||
0.0156144 | + | 0.999878i | \(0.495030\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.9657 | −0.565920 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0856878 | 0.00346656 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.4941 | 0.827747 | 0.413874 | − | 0.910334i | \(-0.364176\pi\) | ||||
0.413874 | + | 0.910334i | \(0.364176\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.35965 | −0.337093 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8472 | 0.436691 | 0.218345 | − | 0.975872i | \(-0.429934\pi\) | ||||
0.218345 | + | 0.975872i | \(0.429934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.8663 | −1.84352 | −0.921761 | − | 0.387758i | \(-0.873249\pi\) | ||||
−0.921761 | + | 0.387758i | \(0.873249\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.6185 | 1.58984 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.4502 | 0.819322 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2314 | −1.24926 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 43.3032 | 1.72936 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.112619 | −0.00449042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0051 | 0.438107 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.61330 | 0.0641228 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −31.7230 | −1.25889 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.03158 | 0.0804942 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.6851 | 0.660054 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.7224 | 1.72693 | 0.863465 | − | 0.504409i | \(-0.168289\pi\) | ||||
0.863465 | + | 0.504409i | \(0.168289\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.8257 | −0.663542 | −0.331771 | − | 0.943360i | \(-0.607646\pi\) | ||||
−0.331771 | + | 0.943360i | \(0.607646\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.55707 | −0.140059 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.0181 | −1.02288 | −0.511439 | − | 0.859320i | \(-0.670887\pi\) | ||||
−0.511439 | + | 0.859320i | \(0.670887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.85093 | 0.268923 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5539 | −0.413639 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.29081 | 0.285312 | 0.142656 | − | 0.989772i | \(-0.454436\pi\) | ||||
0.142656 | + | 0.989772i | \(0.454436\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2636 | −0.518252 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.2834 | −0.479222 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.949968 | −0.0370055 | −0.0185027 | − | 0.999829i | \(-0.505890\pi\) | ||||
−0.0185027 | + | 0.999829i | \(0.505890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.5999 | 1.65694 | 0.828472 | − | 0.560030i | \(-0.189210\pi\) | ||||
0.828472 | + | 0.560030i | \(0.189210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0553096 | 0.00214805 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.3742 | 1.02275 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −65.6970 | −2.54380 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.23787 | 0.125183 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.9062 | −1.65638 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.94684 | −0.152140 | −0.0760698 | − | 0.997102i | \(-0.524237\pi\) | ||||
−0.0760698 | + | 0.997102i | \(0.524237\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.7963 | 0.492529 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.4304 | −0.516174 | −0.258087 | − | 0.966122i | \(-0.583092\pi\) | ||||
−0.258087 | + | 0.966122i | \(0.583092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.65597 | −0.101927 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.7825 | 0.566468 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.4002 | −1.01017 | −0.505087 | − | 0.863068i | \(-0.668540\pi\) | ||||
−0.505087 | + | 0.863068i | \(0.668540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.3232 | −1.34963 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8054 | −0.526709 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.89023 | 0.110109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.53805 | 0.0965519 | 0.0482760 | − | 0.998834i | \(-0.484627\pi\) | ||||
0.0482760 | + | 0.998834i | \(0.484627\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.0940 | 0.421426 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.3859 | 1.11467 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.321472 | 0.0121766 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.6900 | −0.744743 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.13196 | −0.307140 | −0.153570 | − | 0.988138i | \(-0.549077\pi\) | ||||
−0.153570 | + | 0.988138i | \(0.549077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.74224 | 0.254288 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.698072 | 0.0262909 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.86008 | −0.295609 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.635274 | 0.0238582 | 0.0119291 | − | 0.999929i | \(-0.496203\pi\) | ||||
0.0119291 | + | 0.999929i | \(0.496203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.21783 | −0.345696 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −49.6471 | −1.85930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.36659 | −0.200699 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.3250 | −0.422939 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.4664 | −1.91937 | −0.959687 | − | 0.281072i | \(-0.909310\pi\) | ||||
−0.959687 | + | 0.281072i | \(0.909310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0651 | −0.523812 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.3819 | 1.05553 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.2193 | −0.788064 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2966 | −0.826933 | −0.413467 | − | 0.910519i | \(-0.635682\pi\) | ||||
−0.413467 | + | 0.910519i | \(0.635682\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.2670 | 0.787665 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.136788 | 0.00505928 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.7564 | −1.65311 | −0.826557 | − | 0.562853i | \(-0.809704\pi\) | ||||
−0.826557 | + | 0.562853i | \(0.809704\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.5507 | 0.610480 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.57101 | 0.131540 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.87352 | −0.363203 | −0.181602 | − | 0.983372i | \(-0.558128\pi\) | ||||
−0.181602 | + | 0.983372i | \(0.558128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.31125 | −0.121642 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.0393 | −0.955291 | −0.477645 | − | 0.878553i | \(-0.658510\pi\) | ||||
−0.477645 | + | 0.878553i | \(0.658510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.73940 | −0.100364 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.8550 | −0.799634 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.4012 | 0.562748 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.9095 | −1.01708 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −64.6569 | −2.35311 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.8717 | −0.831286 | −0.415643 | − | 0.909528i | \(-0.636443\pi\) | ||||
−0.415643 | + | 0.909528i | \(0.636443\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −43.4506 | −1.57716 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.3492 | 0.520158 | 0.260079 | − | 0.965587i | \(-0.416251\pi\) | ||||
0.260079 | + | 0.965587i | \(0.416251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.15504 | −0.331435 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.541196 | −0.0195670 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.523869 | −0.0189158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.30693 | −0.335617 | −0.167808 | − | 0.985820i | \(-0.553669\pi\) | ||||
−0.167808 | + | 0.985820i | \(0.553669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.5864 | 0.525318 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.5213 | 1.45745 | 0.728725 | − | 0.684807i | \(-0.240113\pi\) | ||||
0.728725 | + | 0.684807i | \(0.240113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.0354 | −0.576008 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.43813 | −0.0515927 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.2458 | −0.689551 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.8334 | −1.85475 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.5973 | −1.73673 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.3708 | 0.905523 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.1951 | −1.53974 | −0.769870 | − | 0.638201i | \(-0.779679\pi\) | ||||
−0.769870 | + | 0.638201i | \(0.779679\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.06411 | 0.180287 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.8826 | 0.955836 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.28090 | 0.116508 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.5458 | 0.835082 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.985432 | −0.0349058 | −0.0174529 | − | 0.999848i | \(-0.505556\pi\) | ||||
−0.0174529 | + | 0.999848i | \(0.505556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0268445 | −0.000949689 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.1226 | 0.887664 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.1592 | 1.34661 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.4641 | −0.932736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.5426 | 0.687931 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.2227 | −0.675834 | −0.337917 | − | 0.941176i | \(-0.609722\pi\) | ||||
−0.337917 | + | 0.941176i | \(0.609722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.6025 | 1.07460 | 0.537300 | − | 0.843391i | \(-0.319444\pi\) | ||||
0.537300 | + | 0.843391i | \(0.319444\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0296 | −0.632325 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.2501 | 0.779387 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.18916 | −0.286502 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.848322 | −0.0296428 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.590203 | −0.0205982 | −0.0102991 | − | 0.999947i | \(-0.503278\pi\) | ||||
−0.0102991 | + | 0.999947i | \(0.503278\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00610 | 0.139644 | 0.0698220 | − | 0.997559i | \(-0.477757\pi\) | ||||
0.0698220 | + | 0.997559i | \(0.477757\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.0340 | −0.488601 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.0294 | 1.80924 | 0.904619 | − | 0.426221i | \(-0.140155\pi\) | ||||
0.904619 | + | 0.426221i | \(0.140155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.1834 | −1.43036 | −0.715179 | − | 0.698941i | \(-0.753655\pi\) | ||||
−0.715179 | + | 0.698941i | \(0.753655\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.7113 | 1.10005 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.636459 | −0.0220520 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50597 | −0.0521162 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.7249 | −1.26940 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.2524 | −0.353951 | −0.176976 | − | 0.984215i | \(-0.556631\pi\) | ||||
−0.176976 | + | 0.984215i | \(0.556631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.5860 | 1.77883 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.9348 | −0.755475 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34.8667 | −1.19945 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.8059 | −0.680537 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.94157 | −0.135274 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.76520 | −0.231908 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2705 | 0.454372 | 0.227186 | − | 0.973851i | \(-0.427047\pi\) | ||||
0.227186 | + | 0.973851i | \(0.427047\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.4001 | 1.10806 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.5362 | −1.00894 | −0.504469 | − | 0.863430i | \(-0.668312\pi\) | ||||
−0.504469 | + | 0.863430i | \(0.668312\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.8936 | 1.32703 | 0.663516 | − | 0.748162i | \(-0.269063\pi\) | ||||
0.663516 | + | 0.748162i | \(0.269063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.10516 | 0.139903 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.7129 | 1.79437 | 0.897184 | − | 0.441658i | \(-0.145609\pi\) | ||||
0.897184 | + | 0.441658i | \(0.145609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −55.5133 | −1.88751 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.8295 | 0.673445 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.6358 | 0.971402 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.273064 | −0.00925241 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.26280 | −0.110429 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.53297 | 0.322273 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.8366 | 0.872441 | 0.436221 | − | 0.899840i | \(-0.356317\pi\) | ||||
0.436221 | + | 0.899840i | \(0.356317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.2761 | 0.751353 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.58855 | 0.154592 | 0.0772961 | − | 0.997008i | \(-0.475371\pi\) | ||||
0.0772961 | + | 0.997008i | \(0.475371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.6061 | −0.861713 | −0.430856 | − | 0.902421i | \(-0.641788\pi\) | ||||
−0.430856 | + | 0.902421i | \(0.641788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.26779 | −0.143460 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.8061 | 1.10152 | 0.550761 | − | 0.834663i | \(-0.314338\pi\) | ||||
0.550761 | + | 0.834663i | \(0.314338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.5782 | 0.522475 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.16561 | −0.240057 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.60712 | 0.0537801 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.1400 | 1.57572 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.32253 | 0.110936 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 60.8987 | 2.03109 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.905457 | −0.0301651 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.74676 | 0.0581287 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.38861 | 0.179123 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.6029 | 1.84627 | 0.923133 | − | 0.384482i | \(-0.125620\pi\) | ||||
0.923133 | + | 0.384482i | \(0.125620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.65591 | −0.320266 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.2271 | 1.26652 | 0.633261 | − | 0.773938i | \(-0.281716\pi\) | ||||
0.633261 | + | 0.773938i | \(0.281716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 67.8941 | 2.24697 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.7285 | 0.883616 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.51334 | 0.215089 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.5273 | 1.00700 | 0.503501 | − | 0.863995i | \(-0.332045\pi\) | ||||
0.503501 | + | 0.863995i | \(0.332045\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.3548 | 0.341203 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.96353 | 0.130461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.18507 | −0.0718448 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.2786 | −0.567504 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.80821 | −0.223370 | −0.111685 | − | 0.993744i | \(-0.535625\pi\) | ||||
−0.111685 | + | 0.993744i | \(0.535625\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.1033 | 1.24878 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.41260 | −0.0789850 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.68126 | 0.0549830 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.02547 | −0.0335008 | −0.0167504 | − | 0.999860i | \(-0.505332\pi\) | ||||
−0.0167504 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.1478 | −0.331160 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.67038 | 0.315245 | 0.157623 | − | 0.987499i | \(-0.449617\pi\) | ||||
0.157623 | + | 0.987499i | \(0.449617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.3113 | 0.628863 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19.5760 | −0.636807 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.5575 | 1.12297 | 0.561485 | − | 0.827487i | \(-0.310230\pi\) | ||||
0.561485 | + | 0.827487i | \(0.310230\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.91791 | −0.0947195 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.78461 | 0.284860 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.16843 | 0.232208 | 0.116104 | − | 0.993237i | \(-0.462959\pi\) | ||||
0.116104 | + | 0.993237i | \(0.462959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.6140 | 1.15244 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 53.2979 | 1.72288 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.3461 | 0.560135 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0211 | 0.484550 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.9200 | 0.609688 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.2231 | 1.61674 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.14216 | −0.0367294 | −0.0183647 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183647 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.03736 | 0.0333247 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.4721 | −1.39509 | −0.697543 | − | 0.716543i | \(-0.745723\pi\) | ||||
−0.697543 | + | 0.716543i | \(0.745723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.4305 | −0.462621 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.07313 | 0.0343678 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.2697 | −0.744464 | −0.372232 | − | 0.928140i | \(-0.621407\pi\) | ||||
−0.372232 | + | 0.928140i | \(0.621407\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78.0450 | −2.49433 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.2467 | −0.359081 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.81080 | 0.217231 | 0.108615 | − | 0.994084i | \(-0.465358\pi\) | ||||
0.108615 | + | 0.994084i | \(0.465358\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.0366 | 1.21195 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.342801 | −0.0109115 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.21705 | 0.261287 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.5372 | 1.95479 | 0.977397 | − | 0.211411i | \(-0.0678059\pi\) | ||||
0.977397 | + | 0.211411i | \(0.0678059\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.462662 | 0.0146821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.3019 | −1.24595 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.6985 | 0.592187 | 0.296093 | − | 0.955159i | \(-0.404316\pi\) | ||||
0.296093 | + | 0.955159i | \(0.404316\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.00435 | −0.158331 |
(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 | 6008.2.a.c.1.17 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.c.1.17 | ✓ | 44 | 1.1 | even | 1 | trivial |