Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.7457527933.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.978012\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13860 | −0.805109 | −0.402554 | − | 0.915396i | \(-0.631878\pi\) | ||||
−0.402554 | + | 0.915396i | \(0.631878\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.703600 | −0.351800 | ||||||||
\(5\) | −2.27123 | −1.01572 | −0.507862 | − | 0.861438i | \(-0.669564\pi\) | ||||
−0.507862 | + | 0.861438i | \(0.669564\pi\) | |||||||
\(6\) | 1.13860 | 0.464830 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07831 | 1.08835 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.58601 | 0.817769 | ||||||||
\(11\) | 4.11356 | 1.24029 | 0.620143 | − | 0.784489i | \(-0.287075\pi\) | ||||
0.620143 | + | 0.784489i | \(0.287075\pi\) | |||||||
\(12\) | 0.703600 | 0.203112 | ||||||||
\(13\) | 1.02235 | 0.283548 | 0.141774 | − | 0.989899i | \(-0.454719\pi\) | ||||
0.141774 | + | 0.989899i | \(0.454719\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.27123 | 0.586429 | ||||||||
\(16\) | −2.09775 | −0.524437 | ||||||||
\(17\) | −1.01936 | −0.247232 | −0.123616 | − | 0.992330i | \(-0.539449\pi\) | ||||
−0.123616 | + | 0.992330i | \(0.539449\pi\) | |||||||
\(18\) | −1.13860 | −0.268370 | ||||||||
\(19\) | −0.361035 | −0.0828271 | −0.0414135 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414135 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(20\) | 1.59804 | 0.357332 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.68368 | −0.998564 | ||||||||
\(23\) | −4.61988 | −0.963312 | −0.481656 | − | 0.876360i | \(-0.659965\pi\) | ||||
−0.481656 | + | 0.876360i | \(0.659965\pi\) | |||||||
\(24\) | −3.07831 | −0.628357 | ||||||||
\(25\) | 0.158481 | 0.0316963 | ||||||||
\(26\) | −1.16404 | −0.228287 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50587 | −0.279633 | −0.139816 | − | 0.990177i | \(-0.544651\pi\) | ||||
−0.139816 | + | 0.990177i | \(0.544651\pi\) | |||||||
\(30\) | −2.58601 | −0.472139 | ||||||||
\(31\) | −3.87299 | −0.695610 | −0.347805 | − | 0.937567i | \(-0.613073\pi\) | ||||
−0.347805 | + | 0.937567i | \(0.613073\pi\) | |||||||
\(32\) | −3.76813 | −0.666117 | ||||||||
\(33\) | −4.11356 | −0.716079 | ||||||||
\(34\) | 1.16064 | 0.199049 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.703600 | −0.117267 | ||||||||
\(37\) | 9.23719 | 1.51858 | 0.759292 | − | 0.650750i | \(-0.225545\pi\) | ||||
0.759292 | + | 0.650750i | \(0.225545\pi\) | |||||||
\(38\) | 0.411073 | 0.0666848 | ||||||||
\(39\) | −1.02235 | −0.163706 | ||||||||
\(40\) | −6.99154 | −1.10546 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.19077 | −0.334089 | −0.167045 | − | 0.985949i | \(-0.553422\pi\) | ||||
−0.167045 | + | 0.985949i | \(0.553422\pi\) | |||||||
\(44\) | −2.89430 | −0.436332 | ||||||||
\(45\) | −2.27123 | −0.338575 | ||||||||
\(46\) | 5.26018 | 0.775571 | ||||||||
\(47\) | 1.32485 | 0.193249 | 0.0966245 | − | 0.995321i | \(-0.469195\pi\) | ||||
0.0966245 | + | 0.995321i | \(0.469195\pi\) | |||||||
\(48\) | 2.09775 | 0.302784 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.180446 | −0.0255190 | ||||||||
\(51\) | 1.01936 | 0.142739 | ||||||||
\(52\) | −0.719323 | −0.0997522 | ||||||||
\(53\) | 7.53796 | 1.03542 | 0.517709 | − | 0.855557i | \(-0.326785\pi\) | ||||
0.517709 | + | 0.855557i | \(0.326785\pi\) | |||||||
\(54\) | 1.13860 | 0.154943 | ||||||||
\(55\) | −9.34284 | −1.25979 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.361035 | 0.0478202 | ||||||||
\(58\) | 1.71458 | 0.225135 | ||||||||
\(59\) | 1.63497 | 0.212855 | 0.106427 | − | 0.994320i | \(-0.466059\pi\) | ||||
0.106427 | + | 0.994320i | \(0.466059\pi\) | |||||||
\(60\) | −1.59804 | −0.206306 | ||||||||
\(61\) | −14.8701 | −1.90392 | −0.951961 | − | 0.306218i | \(-0.900936\pi\) | ||||
−0.951961 | + | 0.306218i | \(0.900936\pi\) | |||||||
\(62\) | 4.40977 | 0.560042 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.48587 | 1.06073 | ||||||||
\(65\) | −2.32198 | −0.288007 | ||||||||
\(66\) | 4.68368 | 0.576521 | ||||||||
\(67\) | 5.38619 | 0.658027 | 0.329014 | − | 0.944325i | \(-0.393284\pi\) | ||||
0.329014 | + | 0.944325i | \(0.393284\pi\) | |||||||
\(68\) | 0.717224 | 0.0869762 | ||||||||
\(69\) | 4.61988 | 0.556169 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.61302 | −0.191430 | −0.0957149 | − | 0.995409i | \(-0.530514\pi\) | ||||
−0.0957149 | + | 0.995409i | \(0.530514\pi\) | |||||||
\(72\) | 3.07831 | 0.362782 | ||||||||
\(73\) | −2.22290 | −0.260171 | −0.130086 | − | 0.991503i | \(-0.541525\pi\) | ||||
−0.130086 | + | 0.991503i | \(0.541525\pi\) | |||||||
\(74\) | −10.5174 | −1.22263 | ||||||||
\(75\) | −0.158481 | −0.0182999 | ||||||||
\(76\) | 0.254024 | 0.0291386 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.16404 | 0.131801 | ||||||||
\(79\) | −4.15827 | −0.467842 | −0.233921 | − | 0.972256i | \(-0.575156\pi\) | ||||
−0.233921 | + | 0.972256i | \(0.575156\pi\) | |||||||
\(80\) | 4.76446 | 0.532683 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.13860 | 0.125737 | ||||||||
\(83\) | −1.53726 | −0.168736 | −0.0843679 | − | 0.996435i | \(-0.526887\pi\) | ||||
−0.0843679 | + | 0.996435i | \(0.526887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.31521 | 0.251119 | ||||||||
\(86\) | 2.49440 | 0.268978 | ||||||||
\(87\) | 1.50587 | 0.161446 | ||||||||
\(88\) | 12.6628 | 1.34986 | ||||||||
\(89\) | −1.06059 | −0.112422 | −0.0562111 | − | 0.998419i | \(-0.517902\pi\) | ||||
−0.0562111 | + | 0.998419i | \(0.517902\pi\) | |||||||
\(90\) | 2.58601 | 0.272590 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.25055 | 0.338893 | ||||||||
\(93\) | 3.87299 | 0.401611 | ||||||||
\(94\) | −1.50847 | −0.155586 | ||||||||
\(95\) | 0.819993 | 0.0841295 | ||||||||
\(96\) | 3.76813 | 0.384583 | ||||||||
\(97\) | −0.418003 | −0.0424418 | −0.0212209 | − | 0.999775i | \(-0.506755\pi\) | ||||
−0.0212209 | + | 0.999775i | \(0.506755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.11356 | 0.413428 | ||||||||
\(100\) | −0.111508 | −0.0111508 | ||||||||
\(101\) | −3.97091 | −0.395121 | −0.197560 | − | 0.980291i | \(-0.563302\pi\) | ||||
−0.197560 | + | 0.980291i | \(0.563302\pi\) | |||||||
\(102\) | −1.16064 | −0.114921 | ||||||||
\(103\) | 10.9705 | 1.08096 | 0.540479 | − | 0.841358i | \(-0.318243\pi\) | ||||
0.540479 | + | 0.841358i | \(0.318243\pi\) | |||||||
\(104\) | 3.14710 | 0.308598 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.58268 | −0.833624 | ||||||||
\(107\) | 19.5498 | 1.88995 | 0.944974 | − | 0.327146i | \(-0.106087\pi\) | ||||
0.944974 | + | 0.327146i | \(0.106087\pi\) | |||||||
\(108\) | 0.703600 | 0.0677039 | ||||||||
\(109\) | 17.4207 | 1.66860 | 0.834299 | − | 0.551313i | \(-0.185873\pi\) | ||||
0.834299 | + | 0.551313i | \(0.185873\pi\) | |||||||
\(110\) | 10.6377 | 1.01427 | ||||||||
\(111\) | −9.23719 | −0.876755 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.78704 | −0.920687 | −0.460344 | − | 0.887741i | \(-0.652274\pi\) | ||||
−0.460344 | + | 0.887741i | \(0.652274\pi\) | |||||||
\(114\) | −0.411073 | −0.0385005 | ||||||||
\(115\) | 10.4928 | 0.978460 | ||||||||
\(116\) | 1.05953 | 0.0983748 | ||||||||
\(117\) | 1.02235 | 0.0945160 | ||||||||
\(118\) | −1.86157 | −0.171371 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.99154 | 0.638237 | ||||||||
\(121\) | 5.92138 | 0.538307 | ||||||||
\(122\) | 16.9310 | 1.53286 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 2.72504 | 0.244716 | ||||||||
\(125\) | 10.9962 | 0.983530 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9152 | −1.50098 | −0.750489 | − | 0.660883i | \(-0.770182\pi\) | ||||
−0.750489 | + | 0.660883i | \(0.770182\pi\) | |||||||
\(128\) | −2.12572 | −0.187888 | ||||||||
\(129\) | 2.19077 | 0.192887 | ||||||||
\(130\) | 2.64380 | 0.231877 | ||||||||
\(131\) | 20.7104 | 1.80948 | 0.904738 | − | 0.425969i | \(-0.140067\pi\) | ||||
0.904738 | + | 0.425969i | \(0.140067\pi\) | |||||||
\(132\) | 2.89430 | 0.251917 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.13269 | −0.529784 | ||||||||
\(135\) | 2.27123 | 0.195476 | ||||||||
\(136\) | −3.13791 | −0.269074 | ||||||||
\(137\) | 6.27873 | 0.536428 | 0.268214 | − | 0.963359i | \(-0.413567\pi\) | ||||
0.268214 | + | 0.963359i | \(0.413567\pi\) | |||||||
\(138\) | −5.26018 | −0.447776 | ||||||||
\(139\) | 3.27698 | 0.277950 | 0.138975 | − | 0.990296i | \(-0.455619\pi\) | ||||
0.138975 | + | 0.990296i | \(0.455619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.32485 | −0.111572 | ||||||||
\(142\) | 1.83657 | 0.154122 | ||||||||
\(143\) | 4.20548 | 0.351680 | ||||||||
\(144\) | −2.09775 | −0.174812 | ||||||||
\(145\) | 3.42017 | 0.284030 | ||||||||
\(146\) | 2.53099 | 0.209466 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.49929 | −0.534238 | ||||||||
\(149\) | −12.5636 | −1.02925 | −0.514624 | − | 0.857416i | \(-0.672068\pi\) | ||||
−0.514624 | + | 0.857416i | \(0.672068\pi\) | |||||||
\(150\) | 0.180446 | 0.0147334 | ||||||||
\(151\) | 9.45156 | 0.769157 | 0.384578 | − | 0.923092i | \(-0.374347\pi\) | ||||
0.384578 | + | 0.923092i | \(0.374347\pi\) | |||||||
\(152\) | −1.11138 | −0.0901445 | ||||||||
\(153\) | −1.01936 | −0.0824106 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.79646 | 0.706548 | ||||||||
\(156\) | 0.719323 | 0.0575919 | ||||||||
\(157\) | −11.1900 | −0.893061 | −0.446530 | − | 0.894768i | \(-0.647341\pi\) | ||||
−0.446530 | + | 0.894768i | \(0.647341\pi\) | |||||||
\(158\) | 4.73459 | 0.376664 | ||||||||
\(159\) | −7.53796 | −0.597799 | ||||||||
\(160\) | 8.55828 | 0.676592 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.13860 | −0.0894565 | ||||||||
\(163\) | −5.24847 | −0.411092 | −0.205546 | − | 0.978647i | \(-0.565897\pi\) | ||||
−0.205546 | + | 0.978647i | \(0.565897\pi\) | |||||||
\(164\) | 0.703600 | 0.0549419 | ||||||||
\(165\) | 9.34284 | 0.727339 | ||||||||
\(166\) | 1.75031 | 0.135851 | ||||||||
\(167\) | −13.1078 | −1.01432 | −0.507158 | − | 0.861853i | \(-0.669304\pi\) | ||||
−0.507158 | + | 0.861853i | \(0.669304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9548 | −0.919601 | ||||||||
\(170\) | −2.63608 | −0.202178 | ||||||||
\(171\) | −0.361035 | −0.0276090 | ||||||||
\(172\) | 1.54143 | 0.117533 | ||||||||
\(173\) | −2.61929 | −0.199141 | −0.0995704 | − | 0.995031i | \(-0.531747\pi\) | ||||
−0.0995704 | + | 0.995031i | \(0.531747\pi\) | |||||||
\(174\) | −1.71458 | −0.129982 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.62921 | −0.650451 | ||||||||
\(177\) | −1.63497 | −0.122892 | ||||||||
\(178\) | 1.20758 | 0.0905121 | ||||||||
\(179\) | 20.0966 | 1.50209 | 0.751044 | − | 0.660252i | \(-0.229550\pi\) | ||||
0.751044 | + | 0.660252i | \(0.229550\pi\) | |||||||
\(180\) | 1.59804 | 0.119111 | ||||||||
\(181\) | 13.9771 | 1.03891 | 0.519456 | − | 0.854497i | \(-0.326135\pi\) | ||||
0.519456 | + | 0.854497i | \(0.326135\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.8701 | 1.09923 | ||||||||
\(184\) | −14.2214 | −1.04842 | ||||||||
\(185\) | −20.9798 | −1.54246 | ||||||||
\(186\) | −4.40977 | −0.323340 | ||||||||
\(187\) | −4.19321 | −0.306638 | ||||||||
\(188\) | −0.932164 | −0.0679850 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.933640 | −0.0677334 | ||||||||
\(191\) | 11.8333 | 0.856230 | 0.428115 | − | 0.903724i | \(-0.359178\pi\) | ||||
0.428115 | + | 0.903724i | \(0.359178\pi\) | |||||||
\(192\) | −8.48587 | −0.612415 | ||||||||
\(193\) | 9.09972 | 0.655012 | 0.327506 | − | 0.944849i | \(-0.393792\pi\) | ||||
0.327506 | + | 0.944849i | \(0.393792\pi\) | |||||||
\(194\) | 0.475937 | 0.0341703 | ||||||||
\(195\) | 2.32198 | 0.166281 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.846122 | 0.0602837 | 0.0301418 | − | 0.999546i | \(-0.490404\pi\) | ||||
0.0301418 | + | 0.999546i | \(0.490404\pi\) | |||||||
\(198\) | −4.68368 | −0.332855 | ||||||||
\(199\) | −3.86730 | −0.274146 | −0.137073 | − | 0.990561i | \(-0.543769\pi\) | ||||
−0.137073 | + | 0.990561i | \(0.543769\pi\) | |||||||
\(200\) | 0.487855 | 0.0344965 | ||||||||
\(201\) | −5.38619 | −0.379912 | ||||||||
\(202\) | 4.52126 | 0.318115 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.717224 | −0.0502157 | ||||||||
\(205\) | 2.27123 | 0.158630 | ||||||||
\(206\) | −12.4910 | −0.870288 | ||||||||
\(207\) | −4.61988 | −0.321104 | ||||||||
\(208\) | −2.14462 | −0.148703 | ||||||||
\(209\) | −1.48514 | −0.102729 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6238 | −1.62633 | −0.813166 | − | 0.582032i | \(-0.802258\pi\) | ||||
−0.813166 | + | 0.582032i | \(0.802258\pi\) | |||||||
\(212\) | −5.30371 | −0.364260 | ||||||||
\(213\) | 1.61302 | 0.110522 | ||||||||
\(214\) | −22.2593 | −1.52161 | ||||||||
\(215\) | 4.97574 | 0.339343 | ||||||||
\(216\) | −3.07831 | −0.209452 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −19.8351 | −1.34340 | ||||||||
\(219\) | 2.22290 | 0.150210 | ||||||||
\(220\) | 6.57362 | 0.443193 | ||||||||
\(221\) | −1.04214 | −0.0701021 | ||||||||
\(222\) | 10.5174 | 0.705883 | ||||||||
\(223\) | −14.5761 | −0.976089 | −0.488044 | − | 0.872819i | \(-0.662290\pi\) | ||||
−0.488044 | + | 0.872819i | \(0.662290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.158481 | 0.0105654 | ||||||||
\(226\) | 11.1435 | 0.741253 | ||||||||
\(227\) | −5.42919 | −0.360348 | −0.180174 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180174 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(228\) | −0.254024 | −0.0168232 | ||||||||
\(229\) | 8.50896 | 0.562288 | 0.281144 | − | 0.959666i | \(-0.409286\pi\) | ||||
0.281144 | + | 0.959666i | \(0.409286\pi\) | |||||||
\(230\) | −11.9471 | −0.787767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.63553 | −0.304337 | ||||||||
\(233\) | 18.1099 | 1.18642 | 0.593210 | − | 0.805048i | \(-0.297861\pi\) | ||||
0.593210 | + | 0.805048i | \(0.297861\pi\) | |||||||
\(234\) | −1.16404 | −0.0760956 | ||||||||
\(235\) | −3.00903 | −0.196288 | ||||||||
\(236\) | −1.15036 | −0.0748823 | ||||||||
\(237\) | 4.15827 | 0.270109 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.22639 | 0.144013 | 0.0720066 | − | 0.997404i | \(-0.477060\pi\) | ||||
0.0720066 | + | 0.997404i | \(0.477060\pi\) | |||||||
\(240\) | −4.76446 | −0.307545 | ||||||||
\(241\) | −14.2272 | −0.916456 | −0.458228 | − | 0.888835i | \(-0.651516\pi\) | ||||
−0.458228 | + | 0.888835i | \(0.651516\pi\) | |||||||
\(242\) | −6.74206 | −0.433396 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.4626 | 0.669800 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.13860 | −0.0725942 | ||||||||
\(247\) | −0.369103 | −0.0234854 | ||||||||
\(248\) | −11.9223 | −0.757064 | ||||||||
\(249\) | 1.53726 | 0.0974197 | ||||||||
\(250\) | −12.5202 | −0.791848 | ||||||||
\(251\) | 6.81117 | 0.429918 | 0.214959 | − | 0.976623i | \(-0.431038\pi\) | ||||
0.214959 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.0042 | −1.19478 | ||||||||
\(254\) | 19.2595 | 1.20845 | ||||||||
\(255\) | −2.31521 | −0.144984 | ||||||||
\(256\) | −14.5514 | −0.909463 | ||||||||
\(257\) | −4.87985 | −0.304397 | −0.152198 | − | 0.988350i | \(-0.548635\pi\) | ||||
−0.152198 | + | 0.988350i | \(0.548635\pi\) | |||||||
\(258\) | −2.49440 | −0.155295 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.63375 | 0.101321 | ||||||||
\(261\) | −1.50587 | −0.0932109 | ||||||||
\(262\) | −23.5808 | −1.45682 | ||||||||
\(263\) | −16.5774 | −1.02221 | −0.511104 | − | 0.859519i | \(-0.670763\pi\) | ||||
−0.511104 | + | 0.859519i | \(0.670763\pi\) | |||||||
\(264\) | −12.6628 | −0.779342 | ||||||||
\(265\) | −17.1204 | −1.05170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.06059 | 0.0649070 | ||||||||
\(268\) | −3.78972 | −0.231494 | ||||||||
\(269\) | 7.34953 | 0.448109 | 0.224054 | − | 0.974577i | \(-0.428071\pi\) | ||||
0.224054 | + | 0.974577i | \(0.428071\pi\) | |||||||
\(270\) | −2.58601 | −0.157380 | ||||||||
\(271\) | −14.2752 | −0.867158 | −0.433579 | − | 0.901116i | \(-0.642750\pi\) | ||||
−0.433579 | + | 0.901116i | \(0.642750\pi\) | |||||||
\(272\) | 2.13837 | 0.129657 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.14893 | −0.431883 | ||||||||
\(275\) | 0.651923 | 0.0393124 | ||||||||
\(276\) | −3.25055 | −0.195660 | ||||||||
\(277\) | −11.6467 | −0.699781 | −0.349891 | − | 0.936791i | \(-0.613781\pi\) | ||||
−0.349891 | + | 0.936791i | \(0.613781\pi\) | |||||||
\(278\) | −3.73116 | −0.223780 | ||||||||
\(279\) | −3.87299 | −0.231870 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.4871 | 1.04319 | 0.521595 | − | 0.853193i | \(-0.325337\pi\) | ||||
0.521595 | + | 0.853193i | \(0.325337\pi\) | |||||||
\(282\) | 1.50847 | 0.0898279 | ||||||||
\(283\) | −15.6673 | −0.931327 | −0.465663 | − | 0.884962i | \(-0.654184\pi\) | ||||
−0.465663 | + | 0.884962i | \(0.654184\pi\) | |||||||
\(284\) | 1.13492 | 0.0673450 | ||||||||
\(285\) | −0.819993 | −0.0485722 | ||||||||
\(286\) | −4.78835 | −0.283141 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.76813 | −0.222039 | ||||||||
\(289\) | −15.9609 | −0.938876 | ||||||||
\(290\) | −3.89419 | −0.228675 | ||||||||
\(291\) | 0.418003 | 0.0245038 | ||||||||
\(292\) | 1.56404 | 0.0915282 | ||||||||
\(293\) | 20.8334 | 1.21710 | 0.608550 | − | 0.793516i | \(-0.291751\pi\) | ||||
0.608550 | + | 0.793516i | \(0.291751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.71339 | −0.216202 | ||||||||
\(296\) | 28.4349 | 1.65274 | ||||||||
\(297\) | −4.11356 | −0.238693 | ||||||||
\(298\) | 14.3048 | 0.828656 | ||||||||
\(299\) | −4.72312 | −0.273145 | ||||||||
\(300\) | 0.111508 | 0.00643789 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −10.7615 | −0.619255 | ||||||||
\(303\) | 3.97091 | 0.228123 | ||||||||
\(304\) | 0.757360 | 0.0434376 | ||||||||
\(305\) | 33.7734 | 1.93386 | ||||||||
\(306\) | 1.16064 | 0.0663495 | ||||||||
\(307\) | −4.35015 | −0.248276 | −0.124138 | − | 0.992265i | \(-0.539617\pi\) | ||||
−0.124138 | + | 0.992265i | \(0.539617\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.9705 | −0.624091 | ||||||||
\(310\) | −10.0156 | −0.568848 | ||||||||
\(311\) | −17.4860 | −0.991540 | −0.495770 | − | 0.868454i | \(-0.665114\pi\) | ||||
−0.495770 | + | 0.868454i | \(0.665114\pi\) | |||||||
\(312\) | −3.14710 | −0.178169 | ||||||||
\(313\) | −27.3870 | −1.54800 | −0.774001 | − | 0.633184i | \(-0.781748\pi\) | ||||
−0.774001 | + | 0.633184i | \(0.781748\pi\) | |||||||
\(314\) | 12.7409 | 0.719011 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.92576 | 0.164587 | ||||||||
\(317\) | −31.8861 | −1.79090 | −0.895451 | − | 0.445161i | \(-0.853147\pi\) | ||||
−0.895451 | + | 0.445161i | \(0.853147\pi\) | |||||||
\(318\) | 8.58268 | 0.481293 | ||||||||
\(319\) | −6.19448 | −0.346824 | ||||||||
\(320\) | −19.2734 | −1.07741 | ||||||||
\(321\) | −19.5498 | −1.09116 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.368026 | 0.0204775 | ||||||||
\(324\) | −0.703600 | −0.0390889 | ||||||||
\(325\) | 0.162023 | 0.00898742 | ||||||||
\(326\) | 5.97589 | 0.330974 | ||||||||
\(327\) | −17.4207 | −0.963365 | ||||||||
\(328\) | −3.07831 | −0.169971 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.6377 | −0.585587 | ||||||||
\(331\) | −16.1121 | −0.885601 | −0.442801 | − | 0.896620i | \(-0.646015\pi\) | ||||
−0.442801 | + | 0.896620i | \(0.646015\pi\) | |||||||
\(332\) | 1.08161 | 0.0593613 | ||||||||
\(333\) | 9.23719 | 0.506195 | ||||||||
\(334\) | 14.9245 | 0.816634 | ||||||||
\(335\) | −12.2333 | −0.668375 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.6380 | 0.906331 | 0.453166 | − | 0.891426i | \(-0.350295\pi\) | ||||
0.453166 | + | 0.891426i | \(0.350295\pi\) | |||||||
\(338\) | 13.6117 | 0.740378 | ||||||||
\(339\) | 9.78704 | 0.531559 | ||||||||
\(340\) | −1.62898 | −0.0883438 | ||||||||
\(341\) | −15.9318 | −0.862755 | ||||||||
\(342\) | 0.411073 | 0.0222283 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.74386 | −0.363605 | ||||||||
\(345\) | −10.4928 | −0.564914 | ||||||||
\(346\) | 2.98231 | 0.160330 | ||||||||
\(347\) | 25.4621 | 1.36688 | 0.683440 | − | 0.730007i | \(-0.260483\pi\) | ||||
0.683440 | + | 0.730007i | \(0.260483\pi\) | |||||||
\(348\) | −1.05953 | −0.0567967 | ||||||||
\(349\) | 15.6721 | 0.838911 | 0.419455 | − | 0.907776i | \(-0.362221\pi\) | ||||
0.419455 | + | 0.907776i | \(0.362221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.02235 | −0.0545688 | ||||||||
\(352\) | −15.5004 | −0.826175 | ||||||||
\(353\) | −10.9229 | −0.581366 | −0.290683 | − | 0.956819i | \(-0.593883\pi\) | ||||
−0.290683 | + | 0.956819i | \(0.593883\pi\) | |||||||
\(354\) | 1.86157 | 0.0989413 | ||||||||
\(355\) | 3.66353 | 0.194440 | ||||||||
\(356\) | 0.746231 | 0.0395501 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.8819 | −1.20934 | ||||||||
\(359\) | −1.37014 | −0.0723134 | −0.0361567 | − | 0.999346i | \(-0.511512\pi\) | ||||
−0.0361567 | + | 0.999346i | \(0.511512\pi\) | |||||||
\(360\) | −6.99154 | −0.368487 | ||||||||
\(361\) | −18.8697 | −0.993140 | ||||||||
\(362\) | −15.9143 | −0.836437 | ||||||||
\(363\) | −5.92138 | −0.310792 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.04872 | 0.264262 | ||||||||
\(366\) | −16.9310 | −0.885000 | ||||||||
\(367\) | −33.2866 | −1.73755 | −0.868774 | − | 0.495209i | \(-0.835092\pi\) | ||||
−0.868774 | + | 0.495209i | \(0.835092\pi\) | |||||||
\(368\) | 9.69135 | 0.505196 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 23.8875 | 1.24185 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.72504 | −0.141287 | ||||||||
\(373\) | −13.8615 | −0.717719 | −0.358859 | − | 0.933392i | \(-0.616834\pi\) | ||||
−0.358859 | + | 0.933392i | \(0.616834\pi\) | |||||||
\(374\) | 4.77437 | 0.246877 | ||||||||
\(375\) | −10.9962 | −0.567841 | ||||||||
\(376\) | 4.07829 | 0.210322 | ||||||||
\(377\) | −1.53952 | −0.0792893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.47300 | 0.0756628 | 0.0378314 | − | 0.999284i | \(-0.487955\pi\) | ||||
0.0378314 | + | 0.999284i | \(0.487955\pi\) | |||||||
\(380\) | −0.576947 | −0.0295968 | ||||||||
\(381\) | 16.9152 | 0.866590 | ||||||||
\(382\) | −13.4734 | −0.689359 | ||||||||
\(383\) | 1.29949 | 0.0664006 | 0.0332003 | − | 0.999449i | \(-0.489430\pi\) | ||||
0.0332003 | + | 0.999449i | \(0.489430\pi\) | |||||||
\(384\) | 2.12572 | 0.108477 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.3609 | −0.527356 | ||||||||
\(387\) | −2.19077 | −0.111363 | ||||||||
\(388\) | 0.294107 | 0.0149310 | ||||||||
\(389\) | 16.8058 | 0.852089 | 0.426045 | − | 0.904702i | \(-0.359907\pi\) | ||||
0.426045 | + | 0.904702i | \(0.359907\pi\) | |||||||
\(390\) | −2.64380 | −0.133874 | ||||||||
\(391\) | 4.70934 | 0.238162 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.7104 | −1.04470 | ||||||||
\(394\) | −0.963390 | −0.0485349 | ||||||||
\(395\) | 9.44438 | 0.475198 | ||||||||
\(396\) | −2.89430 | −0.145444 | ||||||||
\(397\) | −17.7317 | −0.889930 | −0.444965 | − | 0.895548i | \(-0.646784\pi\) | ||||
−0.444965 | + | 0.895548i | \(0.646784\pi\) | |||||||
\(398\) | 4.40329 | 0.220717 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.332454 | −0.0166227 | ||||||||
\(401\) | 26.9691 | 1.34677 | 0.673387 | − | 0.739290i | \(-0.264839\pi\) | ||||
0.673387 | + | 0.739290i | \(0.264839\pi\) | |||||||
\(402\) | 6.13269 | 0.305871 | ||||||||
\(403\) | −3.95954 | −0.197239 | ||||||||
\(404\) | 2.79393 | 0.139003 | ||||||||
\(405\) | −2.27123 | −0.112858 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 37.9977 | 1.88348 | ||||||||
\(408\) | 3.13791 | 0.155350 | ||||||||
\(409\) | 22.8930 | 1.13199 | 0.565993 | − | 0.824410i | \(-0.308493\pi\) | ||||
0.565993 | + | 0.824410i | \(0.308493\pi\) | |||||||
\(410\) | −2.58601 | −0.127714 | ||||||||
\(411\) | −6.27873 | −0.309707 | ||||||||
\(412\) | −7.71886 | −0.380281 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.26018 | 0.258524 | ||||||||
\(415\) | 3.49146 | 0.171389 | ||||||||
\(416\) | −3.85233 | −0.188876 | ||||||||
\(417\) | −3.27698 | −0.160474 | ||||||||
\(418\) | 1.69097 | 0.0827082 | ||||||||
\(419\) | −38.2790 | −1.87005 | −0.935026 | − | 0.354579i | \(-0.884624\pi\) | ||||
−0.935026 | + | 0.354579i | \(0.884624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.0730 | −1.41693 | −0.708465 | − | 0.705746i | \(-0.750612\pi\) | ||||
−0.708465 | + | 0.705746i | \(0.750612\pi\) | |||||||
\(422\) | 26.8980 | 1.30937 | ||||||||
\(423\) | 1.32485 | 0.0644164 | ||||||||
\(424\) | 23.2041 | 1.12689 | ||||||||
\(425\) | −0.161550 | −0.00783633 | ||||||||
\(426\) | −1.83657 | −0.0889823 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −13.7552 | −0.664884 | ||||||||
\(429\) | −4.20548 | −0.203043 | ||||||||
\(430\) | −5.66536 | −0.273208 | ||||||||
\(431\) | −28.5861 | −1.37694 | −0.688472 | − | 0.725263i | \(-0.741718\pi\) | ||||
−0.688472 | + | 0.725263i | \(0.741718\pi\) | |||||||
\(432\) | 2.09775 | 0.100928 | ||||||||
\(433\) | 25.3115 | 1.21639 | 0.608196 | − | 0.793787i | \(-0.291894\pi\) | ||||
0.608196 | + | 0.793787i | \(0.291894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.42017 | −0.163985 | ||||||||
\(436\) | −12.2572 | −0.587012 | ||||||||
\(437\) | 1.66794 | 0.0797884 | ||||||||
\(438\) | −2.53099 | −0.120935 | ||||||||
\(439\) | −11.4408 | −0.546042 | −0.273021 | − | 0.962008i | \(-0.588023\pi\) | ||||
−0.273021 | + | 0.962008i | \(0.588023\pi\) | |||||||
\(440\) | −28.7601 | −1.37109 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.18658 | 0.0564398 | ||||||||
\(443\) | −28.2157 | −1.34057 | −0.670285 | − | 0.742104i | \(-0.733828\pi\) | ||||
−0.670285 | + | 0.742104i | \(0.733828\pi\) | |||||||
\(444\) | 6.49929 | 0.308442 | ||||||||
\(445\) | 2.40884 | 0.114190 | ||||||||
\(446\) | 16.5963 | 0.785858 | ||||||||
\(447\) | 12.5636 | 0.594237 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.0482 | 1.74841 | 0.874207 | − | 0.485553i | \(-0.161382\pi\) | ||||
0.874207 | + | 0.485553i | \(0.161382\pi\) | |||||||
\(450\) | −0.180446 | −0.00850632 | ||||||||
\(451\) | −4.11356 | −0.193700 | ||||||||
\(452\) | 6.88616 | 0.323898 | ||||||||
\(453\) | −9.45156 | −0.444073 | ||||||||
\(454\) | 6.18165 | 0.290119 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.11138 | 0.0520450 | ||||||||
\(457\) | −3.13021 | −0.146425 | −0.0732126 | − | 0.997316i | \(-0.523325\pi\) | ||||
−0.0732126 | + | 0.997316i | \(0.523325\pi\) | |||||||
\(458\) | −9.68826 | −0.452703 | ||||||||
\(459\) | 1.01936 | 0.0475798 | ||||||||
\(460\) | −7.38274 | −0.344222 | ||||||||
\(461\) | −32.8502 | −1.52998 | −0.764992 | − | 0.644040i | \(-0.777257\pi\) | ||||
−0.764992 | + | 0.644040i | \(0.777257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8140 | 0.734937 | 0.367468 | − | 0.930036i | \(-0.380225\pi\) | ||||
0.367468 | + | 0.930036i | \(0.380225\pi\) | |||||||
\(464\) | 3.15893 | 0.146650 | ||||||||
\(465\) | −8.79646 | −0.407926 | ||||||||
\(466\) | −20.6199 | −0.955197 | ||||||||
\(467\) | −36.7438 | −1.70030 | −0.850151 | − | 0.526539i | \(-0.823489\pi\) | ||||
−0.850151 | + | 0.526539i | \(0.823489\pi\) | |||||||
\(468\) | −0.719323 | −0.0332507 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.42607 | 0.158033 | ||||||||
\(471\) | 11.1900 | 0.515609 | ||||||||
\(472\) | 5.03294 | 0.231660 | ||||||||
\(473\) | −9.01186 | −0.414366 | ||||||||
\(474\) | −4.73459 | −0.217467 | ||||||||
\(475\) | −0.0572173 | −0.00262531 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.53796 | 0.345139 | ||||||||
\(478\) | −2.53496 | −0.115946 | ||||||||
\(479\) | 34.6662 | 1.58394 | 0.791969 | − | 0.610561i | \(-0.209056\pi\) | ||||
0.791969 | + | 0.610561i | \(0.209056\pi\) | |||||||
\(480\) | −8.55828 | −0.390630 | ||||||||
\(481\) | 9.44361 | 0.430591 | ||||||||
\(482\) | 16.1991 | 0.737847 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.16628 | −0.189376 | ||||||||
\(485\) | 0.949381 | 0.0431092 | ||||||||
\(486\) | 1.13860 | 0.0516477 | ||||||||
\(487\) | −24.3473 | −1.10328 | −0.551640 | − | 0.834082i | \(-0.685998\pi\) | ||||
−0.551640 | + | 0.834082i | \(0.685998\pi\) | |||||||
\(488\) | −45.7748 | −2.07213 | ||||||||
\(489\) | 5.24847 | 0.237344 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.6572 | −1.06764 | −0.533818 | − | 0.845600i | \(-0.679243\pi\) | ||||
−0.533818 | + | 0.845600i | \(0.679243\pi\) | |||||||
\(492\) | −0.703600 | −0.0317207 | ||||||||
\(493\) | 1.53503 | 0.0691341 | ||||||||
\(494\) | 0.420259 | 0.0189083 | ||||||||
\(495\) | −9.34284 | −0.419929 | ||||||||
\(496\) | 8.12456 | 0.364804 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.75031 | −0.0784335 | ||||||||
\(499\) | 31.4749 | 1.40901 | 0.704505 | − | 0.709699i | \(-0.251169\pi\) | ||||
0.704505 | + | 0.709699i | \(0.251169\pi\) | |||||||
\(500\) | −7.73692 | −0.346006 | ||||||||
\(501\) | 13.1078 | 0.585615 | ||||||||
\(502\) | −7.75517 | −0.346130 | ||||||||
\(503\) | 17.3605 | 0.774067 | 0.387034 | − | 0.922066i | \(-0.373500\pi\) | ||||
0.387034 | + | 0.922066i | \(0.373500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.01885 | 0.401334 | ||||||||
\(506\) | 21.6381 | 0.961929 | ||||||||
\(507\) | 11.9548 | 0.530932 | ||||||||
\(508\) | 11.9015 | 0.528044 | ||||||||
\(509\) | 2.68874 | 0.119176 | 0.0595881 | − | 0.998223i | \(-0.481021\pi\) | ||||
0.0595881 | + | 0.998223i | \(0.481021\pi\) | |||||||
\(510\) | 2.63608 | 0.116728 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.8196 | 0.920105 | ||||||||
\(513\) | 0.361035 | 0.0159401 | ||||||||
\(514\) | 5.55618 | 0.245072 | ||||||||
\(515\) | −24.9166 | −1.09795 | ||||||||
\(516\) | −1.54143 | −0.0678575 | ||||||||
\(517\) | 5.44985 | 0.239684 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.61929 | 0.114974 | ||||||||
\(520\) | −7.14778 | −0.313451 | ||||||||
\(521\) | 39.2979 | 1.72167 | 0.860835 | − | 0.508884i | \(-0.169942\pi\) | ||||
0.860835 | + | 0.508884i | \(0.169942\pi\) | |||||||
\(522\) | 1.71458 | 0.0750449 | ||||||||
\(523\) | −6.63116 | −0.289961 | −0.144980 | − | 0.989435i | \(-0.546312\pi\) | ||||
−0.144980 | + | 0.989435i | \(0.546312\pi\) | |||||||
\(524\) | −14.5718 | −0.636573 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.8750 | 0.822988 | ||||||||
\(527\) | 3.94799 | 0.171977 | ||||||||
\(528\) | 8.62921 | 0.375538 | ||||||||
\(529\) | −1.65667 | −0.0720292 | ||||||||
\(530\) | 19.4932 | 0.846732 | ||||||||
\(531\) | 1.63497 | 0.0709516 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.02235 | −0.0442827 | ||||||||
\(534\) | −1.20758 | −0.0522572 | ||||||||
\(535\) | −44.4020 | −1.91967 | ||||||||
\(536\) | 16.5803 | 0.716162 | ||||||||
\(537\) | −20.0966 | −0.867231 | ||||||||
\(538\) | −8.36814 | −0.360776 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.59804 | −0.0687686 | ||||||||
\(541\) | 32.2640 | 1.38714 | 0.693568 | − | 0.720391i | \(-0.256038\pi\) | ||||
0.693568 | + | 0.720391i | \(0.256038\pi\) | |||||||
\(542\) | 16.2537 | 0.698157 | ||||||||
\(543\) | −13.9771 | −0.599816 | ||||||||
\(544\) | 3.84109 | 0.164685 | ||||||||
\(545\) | −39.5663 | −1.69484 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.23994 | −0.309558 | −0.154779 | − | 0.987949i | \(-0.549466\pi\) | ||||
−0.154779 | + | 0.987949i | \(0.549466\pi\) | |||||||
\(548\) | −4.41771 | −0.188715 | ||||||||
\(549\) | −14.8701 | −0.634641 | ||||||||
\(550\) | −0.742277 | −0.0316508 | ||||||||
\(551\) | 0.543671 | 0.0231612 | ||||||||
\(552\) | 14.2214 | 0.605304 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.2609 | 0.563400 | ||||||||
\(555\) | 20.9798 | 0.890542 | ||||||||
\(556\) | −2.30568 | −0.0977828 | ||||||||
\(557\) | −0.594345 | −0.0251832 | −0.0125916 | − | 0.999921i | \(-0.504008\pi\) | ||||
−0.0125916 | + | 0.999921i | \(0.504008\pi\) | |||||||
\(558\) | 4.40977 | 0.186681 | ||||||||
\(559\) | −2.23973 | −0.0947303 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.19321 | 0.177038 | ||||||||
\(562\) | −19.9107 | −0.839882 | ||||||||
\(563\) | −5.25348 | −0.221408 | −0.110704 | − | 0.993853i | \(-0.535310\pi\) | ||||
−0.110704 | + | 0.993853i | \(0.535310\pi\) | |||||||
\(564\) | 0.932164 | 0.0392512 | ||||||||
\(565\) | 22.2286 | 0.935165 | ||||||||
\(566\) | 17.8388 | 0.749819 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.96536 | −0.208342 | ||||||||
\(569\) | −19.6362 | −0.823194 | −0.411597 | − | 0.911366i | \(-0.635029\pi\) | ||||
−0.411597 | + | 0.911366i | \(0.635029\pi\) | |||||||
\(570\) | 0.933640 | 0.0391059 | ||||||||
\(571\) | −35.2958 | −1.47708 | −0.738542 | − | 0.674207i | \(-0.764485\pi\) | ||||
−0.738542 | + | 0.674207i | \(0.764485\pi\) | |||||||
\(572\) | −2.95898 | −0.123721 | ||||||||
\(573\) | −11.8333 | −0.494345 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.732166 | −0.0305334 | ||||||||
\(576\) | 8.48587 | 0.353578 | ||||||||
\(577\) | −34.3114 | −1.42840 | −0.714200 | − | 0.699941i | \(-0.753210\pi\) | ||||
−0.714200 | + | 0.699941i | \(0.753210\pi\) | |||||||
\(578\) | 18.1730 | 0.755898 | ||||||||
\(579\) | −9.09972 | −0.378172 | ||||||||
\(580\) | −2.40643 | −0.0999217 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.475937 | −0.0197282 | ||||||||
\(583\) | 31.0078 | 1.28421 | ||||||||
\(584\) | −6.84278 | −0.283156 | ||||||||
\(585\) | −2.32198 | −0.0960022 | ||||||||
\(586\) | −23.7208 | −0.979898 | ||||||||
\(587\) | 18.7338 | 0.773228 | 0.386614 | − | 0.922242i | \(-0.373645\pi\) | ||||
0.386614 | + | 0.922242i | \(0.373645\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.39829 | 0.0576154 | ||||||||
\(590\) | 4.22805 | 0.174066 | ||||||||
\(591\) | −0.846122 | −0.0348048 | ||||||||
\(592\) | −19.3773 | −0.796401 | ||||||||
\(593\) | 5.35369 | 0.219850 | 0.109925 | − | 0.993940i | \(-0.464939\pi\) | ||||
0.109925 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(594\) | 4.68368 | 0.192174 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.83973 | 0.362089 | ||||||||
\(597\) | 3.86730 | 0.158278 | ||||||||
\(598\) | 5.37773 | 0.219912 | ||||||||
\(599\) | 38.4103 | 1.56940 | 0.784701 | − | 0.619874i | \(-0.212816\pi\) | ||||
0.784701 | + | 0.619874i | \(0.212816\pi\) | |||||||
\(600\) | −0.487855 | −0.0199166 | ||||||||
\(601\) | 2.61417 | 0.106634 | 0.0533172 | − | 0.998578i | \(-0.483021\pi\) | ||||
0.0533172 | + | 0.998578i | \(0.483021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.38619 | 0.219342 | ||||||||
\(604\) | −6.65011 | −0.270589 | ||||||||
\(605\) | −13.4488 | −0.546772 | ||||||||
\(606\) | −4.52126 | −0.183664 | ||||||||
\(607\) | 34.7661 | 1.41111 | 0.705556 | − | 0.708654i | \(-0.250697\pi\) | ||||
0.705556 | + | 0.708654i | \(0.250697\pi\) | |||||||
\(608\) | 1.36043 | 0.0551726 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −38.4543 | −1.55697 | ||||||||
\(611\) | 1.35445 | 0.0547954 | ||||||||
\(612\) | 0.717224 | 0.0289921 | ||||||||
\(613\) | −7.23499 | −0.292219 | −0.146109 | − | 0.989268i | \(-0.546675\pi\) | ||||
−0.146109 | + | 0.989268i | \(0.546675\pi\) | |||||||
\(614\) | 4.95306 | 0.199889 | ||||||||
\(615\) | −2.27123 | −0.0915848 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.70944 | 0.149337 | 0.0746683 | − | 0.997208i | \(-0.476210\pi\) | ||||
0.0746683 | + | 0.997208i | \(0.476210\pi\) | |||||||
\(618\) | 12.4910 | 0.502461 | ||||||||
\(619\) | 21.8562 | 0.878473 | 0.439237 | − | 0.898371i | \(-0.355249\pi\) | ||||
0.439237 | + | 0.898371i | \(0.355249\pi\) | |||||||
\(620\) | −6.18919 | −0.248564 | ||||||||
\(621\) | 4.61988 | 0.185390 | ||||||||
\(622\) | 19.9095 | 0.798298 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.14462 | 0.0858537 | ||||||||
\(625\) | −25.7673 | −1.03069 | ||||||||
\(626\) | 31.1827 | 1.24631 | ||||||||
\(627\) | 1.48514 | 0.0593107 | ||||||||
\(628\) | 7.87330 | 0.314179 | ||||||||
\(629\) | −9.41605 | −0.375442 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7931 | 0.867569 | 0.433784 | − | 0.901017i | \(-0.357178\pi\) | ||||
0.433784 | + | 0.901017i | \(0.357178\pi\) | |||||||
\(632\) | −12.8004 | −0.509174 | ||||||||
\(633\) | 23.6238 | 0.938963 | ||||||||
\(634\) | 36.3054 | 1.44187 | ||||||||
\(635\) | 38.4182 | 1.52458 | ||||||||
\(636\) | 5.30371 | 0.210306 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.05301 | 0.279231 | ||||||||
\(639\) | −1.61302 | −0.0638099 | ||||||||
\(640\) | 4.82799 | 0.190843 | ||||||||
\(641\) | −27.4415 | −1.08388 | −0.541938 | − | 0.840419i | \(-0.682309\pi\) | ||||
−0.541938 | + | 0.840419i | \(0.682309\pi\) | |||||||
\(642\) | 22.2593 | 0.878504 | ||||||||
\(643\) | −0.581325 | −0.0229252 | −0.0114626 | − | 0.999934i | \(-0.503649\pi\) | ||||
−0.0114626 | + | 0.999934i | \(0.503649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.97574 | −0.195920 | ||||||||
\(646\) | −0.419032 | −0.0164866 | ||||||||
\(647\) | −29.9596 | −1.17783 | −0.588917 | − | 0.808194i | \(-0.700445\pi\) | ||||
−0.588917 | + | 0.808194i | \(0.700445\pi\) | |||||||
\(648\) | 3.07831 | 0.120927 | ||||||||
\(649\) | 6.72554 | 0.264001 | ||||||||
\(650\) | −0.184479 | −0.00723585 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.69283 | 0.144622 | ||||||||
\(653\) | 8.27365 | 0.323773 | 0.161886 | − | 0.986809i | \(-0.448242\pi\) | ||||
0.161886 | + | 0.986809i | \(0.448242\pi\) | |||||||
\(654\) | 19.8351 | 0.775614 | ||||||||
\(655\) | −47.0380 | −1.83793 | ||||||||
\(656\) | 2.09775 | 0.0819033 | ||||||||
\(657\) | −2.22290 | −0.0867237 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.3248 | 1.37606 | 0.688030 | − | 0.725682i | \(-0.258476\pi\) | ||||
0.688030 | + | 0.725682i | \(0.258476\pi\) | |||||||
\(660\) | −6.57362 | −0.255878 | ||||||||
\(661\) | −32.2603 | −1.25478 | −0.627390 | − | 0.778705i | \(-0.715877\pi\) | ||||
−0.627390 | + | 0.778705i | \(0.715877\pi\) | |||||||
\(662\) | 18.3452 | 0.713005 | ||||||||
\(663\) | 1.04214 | 0.0404735 | ||||||||
\(664\) | −4.73215 | −0.183643 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.5174 | −0.407542 | ||||||||
\(667\) | 6.95694 | 0.269374 | ||||||||
\(668\) | 9.22268 | 0.356836 | ||||||||
\(669\) | 14.5761 | 0.563545 | ||||||||
\(670\) | 13.9287 | 0.538114 | ||||||||
\(671\) | −61.1691 | −2.36141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.72480 | −0.220675 | −0.110337 | − | 0.993894i | \(-0.535193\pi\) | ||||
−0.110337 | + | 0.993894i | \(0.535193\pi\) | |||||||
\(674\) | −18.9440 | −0.729695 | ||||||||
\(675\) | −0.158481 | −0.00609995 | ||||||||
\(676\) | 8.41140 | 0.323515 | ||||||||
\(677\) | −51.3825 | −1.97479 | −0.987396 | − | 0.158270i | \(-0.949408\pi\) | ||||
−0.987396 | + | 0.158270i | \(0.949408\pi\) | |||||||
\(678\) | −11.1435 | −0.427963 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.12692 | 0.273305 | ||||||||
\(681\) | 5.42919 | 0.208047 | ||||||||
\(682\) | 18.1399 | 0.694611 | ||||||||
\(683\) | −12.9225 | −0.494465 | −0.247232 | − | 0.968956i | \(-0.579521\pi\) | ||||
−0.247232 | + | 0.968956i | \(0.579521\pi\) | |||||||
\(684\) | 0.254024 | 0.00971286 | ||||||||
\(685\) | −14.2604 | −0.544863 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.50896 | −0.324637 | ||||||||
\(688\) | 4.59568 | 0.175209 | ||||||||
\(689\) | 7.70640 | 0.293591 | ||||||||
\(690\) | 11.9471 | 0.454817 | ||||||||
\(691\) | −7.98422 | −0.303734 | −0.151867 | − | 0.988401i | \(-0.548529\pi\) | ||||
−0.151867 | + | 0.988401i | \(0.548529\pi\) | |||||||
\(692\) | 1.84293 | 0.0700577 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.9911 | −1.10049 | ||||||||
\(695\) | −7.44278 | −0.282321 | ||||||||
\(696\) | 4.63553 | 0.175709 | ||||||||
\(697\) | 1.01936 | 0.0386111 | ||||||||
\(698\) | −17.8442 | −0.675414 | ||||||||
\(699\) | −18.1099 | −0.684980 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.14530 | −0.156566 | −0.0782829 | − | 0.996931i | \(-0.524944\pi\) | ||||
−0.0782829 | + | 0.996931i | \(0.524944\pi\) | |||||||
\(702\) | 1.16404 | 0.0439338 | ||||||||
\(703\) | −3.33495 | −0.125780 | ||||||||
\(704\) | 34.9071 | 1.31561 | ||||||||
\(705\) | 3.00903 | 0.113327 | ||||||||
\(706\) | 12.4367 | 0.468063 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.15036 | 0.0432333 | ||||||||
\(709\) | 22.3009 | 0.837527 | 0.418764 | − | 0.908095i | \(-0.362464\pi\) | ||||
0.418764 | + | 0.908095i | \(0.362464\pi\) | |||||||
\(710\) | −4.17128 | −0.156545 | ||||||||
\(711\) | −4.15827 | −0.155947 | ||||||||
\(712\) | −3.26482 | −0.122354 | ||||||||
\(713\) | 17.8928 | 0.670090 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.55162 | −0.357210 | ||||||||
\(716\) | −14.1400 | −0.528435 | ||||||||
\(717\) | −2.22639 | −0.0831461 | ||||||||
\(718\) | 1.56004 | 0.0582201 | ||||||||
\(719\) | 11.8846 | 0.443221 | 0.221610 | − | 0.975135i | \(-0.428869\pi\) | ||||
0.221610 | + | 0.975135i | \(0.428869\pi\) | |||||||
\(720\) | 4.76446 | 0.177561 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.4849 | 0.799585 | ||||||||
\(723\) | 14.2272 | 0.529116 | ||||||||
\(724\) | −9.83431 | −0.365489 | ||||||||
\(725\) | −0.238652 | −0.00886332 | ||||||||
\(726\) | 6.74206 | 0.250221 | ||||||||
\(727\) | −52.7921 | −1.95795 | −0.978976 | − | 0.203977i | \(-0.934613\pi\) | ||||
−0.978976 | + | 0.203977i | \(0.934613\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.74846 | −0.212760 | ||||||||
\(731\) | 2.23319 | 0.0825975 | ||||||||
\(732\) | −10.4626 | −0.386709 | ||||||||
\(733\) | 8.77886 | 0.324255 | 0.162127 | − | 0.986770i | \(-0.448164\pi\) | ||||
0.162127 | + | 0.986770i | \(0.448164\pi\) | |||||||
\(734\) | 37.9000 | 1.39892 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.4083 | 0.641679 | ||||||||
\(737\) | 22.1564 | 0.816142 | ||||||||
\(738\) | 1.13860 | 0.0419123 | ||||||||
\(739\) | −49.4832 | −1.82027 | −0.910135 | − | 0.414311i | \(-0.864023\pi\) | ||||
−0.910135 | + | 0.414311i | \(0.864023\pi\) | |||||||
\(740\) | 14.7614 | 0.542639 | ||||||||
\(741\) | 0.369103 | 0.0135593 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.5917 | 0.975554 | 0.487777 | − | 0.872968i | \(-0.337808\pi\) | ||||
0.487777 | + | 0.872968i | \(0.337808\pi\) | |||||||
\(744\) | 11.9223 | 0.437091 | ||||||||
\(745\) | 28.5348 | 1.04543 | ||||||||
\(746\) | 15.7826 | 0.577842 | ||||||||
\(747\) | −1.53726 | −0.0562453 | ||||||||
\(748\) | 2.95034 | 0.107875 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.5202 | 0.457174 | ||||||||
\(751\) | 7.81219 | 0.285071 | 0.142535 | − | 0.989790i | \(-0.454475\pi\) | ||||
0.142535 | + | 0.989790i | \(0.454475\pi\) | |||||||
\(752\) | −2.77920 | −0.101347 | ||||||||
\(753\) | −6.81117 | −0.248213 | ||||||||
\(754\) | 1.75289 | 0.0638365 | ||||||||
\(755\) | −21.4666 | −0.781251 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.6870 | 1.07899 | 0.539497 | − | 0.841988i | \(-0.318614\pi\) | ||||
0.539497 | + | 0.841988i | \(0.318614\pi\) | |||||||
\(758\) | −1.67715 | −0.0609167 | ||||||||
\(759\) | 19.0042 | 0.689808 | ||||||||
\(760\) | 2.52419 | 0.0915620 | ||||||||
\(761\) | −12.7647 | −0.462720 | −0.231360 | − | 0.972868i | \(-0.574317\pi\) | ||||
−0.231360 | + | 0.972868i | \(0.574317\pi\) | |||||||
\(762\) | −19.2595 | −0.697699 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.32594 | −0.301222 | ||||||||
\(765\) | 2.31521 | 0.0837065 | ||||||||
\(766\) | −1.47959 | −0.0534597 | ||||||||
\(767\) | 1.67151 | 0.0603546 | ||||||||
\(768\) | 14.5514 | 0.525079 | ||||||||
\(769\) | 26.8186 | 0.967104 | 0.483552 | − | 0.875316i | \(-0.339346\pi\) | ||||
0.483552 | + | 0.875316i | \(0.339346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.87985 | 0.175744 | ||||||||
\(772\) | −6.40257 | −0.230433 | ||||||||
\(773\) | 19.7548 | 0.710531 | 0.355265 | − | 0.934766i | \(-0.384391\pi\) | ||||
0.355265 | + | 0.934766i | \(0.384391\pi\) | |||||||
\(774\) | 2.49440 | 0.0896594 | ||||||||
\(775\) | −0.613798 | −0.0220483 | ||||||||
\(776\) | −1.28674 | −0.0461914 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.1350 | −0.686024 | ||||||||
\(779\) | 0.361035 | 0.0129354 | ||||||||
\(780\) | −1.63375 | −0.0584975 | ||||||||
\(781\) | −6.63524 | −0.237428 | ||||||||
\(782\) | −5.36203 | −0.191746 | ||||||||
\(783\) | 1.50587 | 0.0538153 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.4151 | 0.907104 | ||||||||
\(786\) | 23.5808 | 0.841098 | ||||||||
\(787\) | −38.0595 | −1.35667 | −0.678337 | − | 0.734751i | \(-0.737299\pi\) | ||||
−0.678337 | + | 0.734751i | \(0.737299\pi\) | |||||||
\(788\) | −0.595331 | −0.0212078 | ||||||||
\(789\) | 16.5774 | 0.590172 | ||||||||
\(790\) | −10.7533 | −0.382586 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.6628 | 0.449953 | ||||||||
\(793\) | −15.2024 | −0.539853 | ||||||||
\(794\) | 20.1893 | 0.716490 | ||||||||
\(795\) | 17.1204 | 0.607199 | ||||||||
\(796\) | 2.72103 | 0.0964444 | ||||||||
\(797\) | −42.5173 | −1.50604 | −0.753019 | − | 0.657998i | \(-0.771403\pi\) | ||||
−0.753019 | + | 0.657998i | \(0.771403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.35050 | −0.0477773 | ||||||||
\(800\) | −0.597179 | −0.0211135 | ||||||||
\(801\) | −1.06059 | −0.0374741 | ||||||||
\(802\) | −30.7069 | −1.08430 | ||||||||
\(803\) | −9.14405 | −0.322687 | ||||||||
\(804\) | 3.78972 | 0.133653 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.50832 | 0.158799 | ||||||||
\(807\) | −7.34953 | −0.258716 | ||||||||
\(808\) | −12.2237 | −0.430028 | ||||||||
\(809\) | −38.2867 | −1.34609 | −0.673044 | − | 0.739603i | \(-0.735013\pi\) | ||||
−0.673044 | + | 0.739603i | \(0.735013\pi\) | |||||||
\(810\) | 2.58601 | 0.0908632 | ||||||||
\(811\) | 35.9502 | 1.26238 | 0.631191 | − | 0.775628i | \(-0.282566\pi\) | ||||
0.631191 | + | 0.775628i | \(0.282566\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.2752 | 0.500654 | ||||||||
\(814\) | −43.2640 | −1.51640 | ||||||||
\(815\) | 11.9205 | 0.417556 | ||||||||
\(816\) | −2.13837 | −0.0748578 | ||||||||
\(817\) | 0.790944 | 0.0276716 | ||||||||
\(818\) | −26.0659 | −0.911372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.59804 | −0.0558059 | ||||||||
\(821\) | −18.3527 | −0.640514 | −0.320257 | − | 0.947331i | \(-0.603769\pi\) | ||||
−0.320257 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(822\) | 7.14893 | 0.249348 | ||||||||
\(823\) | −41.0862 | −1.43218 | −0.716088 | − | 0.698010i | \(-0.754069\pi\) | ||||
−0.716088 | + | 0.698010i | \(0.754069\pi\) | |||||||
\(824\) | 33.7706 | 1.17646 | ||||||||
\(825\) | −0.651923 | −0.0226970 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.0152 | 0.800316 | 0.400158 | − | 0.916446i | \(-0.368955\pi\) | ||||
0.400158 | + | 0.916446i | \(0.368955\pi\) | |||||||
\(828\) | 3.25055 | 0.112964 | ||||||||
\(829\) | −24.1424 | −0.838499 | −0.419249 | − | 0.907871i | \(-0.637707\pi\) | ||||
−0.419249 | + | 0.907871i | \(0.637707\pi\) | |||||||
\(830\) | −3.97536 | −0.137987 | ||||||||
\(831\) | 11.6467 | 0.404019 | ||||||||
\(832\) | 8.67550 | 0.300769 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.73116 | 0.129199 | ||||||||
\(835\) | 29.7709 | 1.03027 | ||||||||
\(836\) | 1.04494 | 0.0361401 | ||||||||
\(837\) | 3.87299 | 0.133870 | ||||||||
\(838\) | 43.5843 | 1.50559 | ||||||||
\(839\) | 15.6154 | 0.539105 | 0.269552 | − | 0.962986i | \(-0.413124\pi\) | ||||
0.269552 | + | 0.962986i | \(0.413124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7324 | −0.921806 | ||||||||
\(842\) | 33.1024 | 1.14078 | ||||||||
\(843\) | −17.4871 | −0.602286 | ||||||||
\(844\) | 16.6217 | 0.572144 | ||||||||
\(845\) | 27.1521 | 0.934061 | ||||||||
\(846\) | −1.50847 | −0.0518622 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.8127 | −0.543011 | ||||||||
\(849\) | 15.6673 | 0.537702 | ||||||||
\(850\) | 0.183940 | 0.00630910 | ||||||||
\(851\) | −42.6747 | −1.46287 | ||||||||
\(852\) | −1.13492 | −0.0388817 | ||||||||
\(853\) | 16.3069 | 0.558338 | 0.279169 | − | 0.960242i | \(-0.409941\pi\) | ||||
0.279169 | + | 0.960242i | \(0.409941\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.819993 | 0.0280432 | ||||||||
\(856\) | 60.1802 | 2.05692 | ||||||||
\(857\) | −10.4701 | −0.357653 | −0.178827 | − | 0.983881i | \(-0.557230\pi\) | ||||
−0.178827 | + | 0.983881i | \(0.557230\pi\) | |||||||
\(858\) | 4.78835 | 0.163471 | ||||||||
\(859\) | −29.4060 | −1.00332 | −0.501659 | − | 0.865065i | \(-0.667277\pi\) | ||||
−0.501659 | + | 0.865065i | \(0.667277\pi\) | |||||||
\(860\) | −3.50093 | −0.119381 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.5480 | 1.10859 | ||||||||
\(863\) | −11.8231 | −0.402463 | −0.201231 | − | 0.979544i | \(-0.564494\pi\) | ||||
−0.201231 | + | 0.979544i | \(0.564494\pi\) | |||||||
\(864\) | 3.76813 | 0.128194 | ||||||||
\(865\) | 5.94900 | 0.202272 | ||||||||
\(866\) | −28.8195 | −0.979327 | ||||||||
\(867\) | 15.9609 | 0.542061 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.1053 | −0.580257 | ||||||||
\(870\) | 3.89419 | 0.132026 | ||||||||
\(871\) | 5.50655 | 0.186582 | ||||||||
\(872\) | 53.6262 | 1.81601 | ||||||||
\(873\) | −0.418003 | −0.0141473 | ||||||||
\(874\) | −1.89911 | −0.0642383 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.56404 | −0.0528439 | ||||||||
\(877\) | −35.9145 | −1.21275 | −0.606373 | − | 0.795181i | \(-0.707376\pi\) | ||||
−0.606373 | + | 0.795181i | \(0.707376\pi\) | |||||||
\(878\) | 13.0265 | 0.439623 | ||||||||
\(879\) | −20.8334 | −0.702693 | ||||||||
\(880\) | 19.5989 | 0.660679 | ||||||||
\(881\) | −41.3275 | −1.39236 | −0.696180 | − | 0.717868i | \(-0.745118\pi\) | ||||
−0.696180 | + | 0.717868i | \(0.745118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.3608 | −0.988068 | −0.494034 | − | 0.869443i | \(-0.664478\pi\) | ||||
−0.494034 | + | 0.869443i | \(0.664478\pi\) | |||||||
\(884\) | 0.733251 | 0.0246619 | ||||||||
\(885\) | 3.71339 | 0.124824 | ||||||||
\(886\) | 32.1263 | 1.07930 | ||||||||
\(887\) | 25.4418 | 0.854253 | 0.427126 | − | 0.904192i | \(-0.359526\pi\) | ||||
0.427126 | + | 0.904192i | \(0.359526\pi\) | |||||||
\(888\) | −28.4349 | −0.954213 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.74270 | −0.0919354 | ||||||||
\(891\) | 4.11356 | 0.137809 | ||||||||
\(892\) | 10.2558 | 0.343388 | ||||||||
\(893\) | −0.478317 | −0.0160063 | ||||||||
\(894\) | −14.3048 | −0.478425 | ||||||||
\(895\) | −45.6439 | −1.52571 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.72312 | 0.157700 | ||||||||
\(898\) | −42.1830 | −1.40766 | ||||||||
\(899\) | 5.83222 | 0.194515 | ||||||||
\(900\) | −0.111508 | −0.00371692 | ||||||||
\(901\) | −7.68391 | −0.255988 | ||||||||
\(902\) | 4.68368 | 0.155950 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.1275 | −1.00203 | ||||||||
\(905\) | −31.7453 | −1.05525 | ||||||||
\(906\) | 10.7615 | 0.357527 | ||||||||
\(907\) | −21.3485 | −0.708864 | −0.354432 | − | 0.935082i | \(-0.615326\pi\) | ||||
−0.354432 | + | 0.935082i | \(0.615326\pi\) | |||||||
\(908\) | 3.81998 | 0.126770 | ||||||||
\(909\) | −3.97091 | −0.131707 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.8400 | −0.922381 | −0.461190 | − | 0.887301i | \(-0.652577\pi\) | ||||
−0.461190 | + | 0.887301i | \(0.652577\pi\) | |||||||
\(912\) | −0.757360 | −0.0250787 | ||||||||
\(913\) | −6.32360 | −0.209281 | ||||||||
\(914\) | 3.56405 | 0.117888 | ||||||||
\(915\) | −33.7734 | −1.11652 | ||||||||
\(916\) | −5.98690 | −0.197813 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.16064 | −0.0383069 | ||||||||
\(919\) | −0.843163 | −0.0278134 | −0.0139067 | − | 0.999903i | \(-0.504427\pi\) | ||||
−0.0139067 | + | 0.999903i | \(0.504427\pi\) | |||||||
\(920\) | 32.3001 | 1.06490 | ||||||||
\(921\) | 4.35015 | 0.143342 | ||||||||
\(922\) | 37.4030 | 1.23180 | ||||||||
\(923\) | −1.64906 | −0.0542795 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.46392 | 0.0481335 | ||||||||
\(926\) | −18.0057 | −0.591704 | ||||||||
\(927\) | 10.9705 | 0.360319 | ||||||||
\(928\) | 5.67431 | 0.186268 | ||||||||
\(929\) | 3.50232 | 0.114907 | 0.0574537 | − | 0.998348i | \(-0.481702\pi\) | ||||
0.0574537 | + | 0.998348i | \(0.481702\pi\) | |||||||
\(930\) | 10.0156 | 0.328425 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.7421 | −0.417382 | ||||||||
\(933\) | 17.4860 | 0.572466 | ||||||||
\(934\) | 41.8364 | 1.36893 | ||||||||
\(935\) | 9.52375 | 0.311460 | ||||||||
\(936\) | 3.14710 | 0.102866 | ||||||||
\(937\) | 31.5255 | 1.02989 | 0.514946 | − | 0.857222i | \(-0.327812\pi\) | ||||
0.514946 | + | 0.857222i | \(0.327812\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.3870 | 0.893740 | ||||||||
\(940\) | 2.11716 | 0.0690540 | ||||||||
\(941\) | −38.5977 | −1.25825 | −0.629124 | − | 0.777305i | \(-0.716586\pi\) | ||||
−0.629124 | + | 0.777305i | \(0.716586\pi\) | |||||||
\(942\) | −12.7409 | −0.415121 | ||||||||
\(943\) | 4.61988 | 0.150444 | ||||||||
\(944\) | −3.42975 | −0.111629 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.2609 | 0.333610 | ||||||||
\(947\) | −23.0815 | −0.750047 | −0.375023 | − | 0.927015i | \(-0.622365\pi\) | ||||
−0.375023 | + | 0.927015i | \(0.622365\pi\) | |||||||
\(948\) | −2.92576 | −0.0950242 | ||||||||
\(949\) | −2.27258 | −0.0737710 | ||||||||
\(950\) | 0.0651474 | 0.00211366 | ||||||||
\(951\) | 31.8861 | 1.03398 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.506172 | −0.0163965 | −0.00819826 | − | 0.999966i | \(-0.502610\pi\) | ||||
−0.00819826 | + | 0.999966i | \(0.502610\pi\) | |||||||
\(954\) | −8.58268 | −0.277875 | ||||||||
\(955\) | −26.8762 | −0.869694 | ||||||||
\(956\) | −1.56649 | −0.0506638 | ||||||||
\(957\) | 6.19448 | 0.200239 | ||||||||
\(958\) | −39.4707 | −1.27524 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 19.2734 | 0.622045 | ||||||||
\(961\) | −15.9999 | −0.516127 | ||||||||
\(962\) | −10.7524 | −0.346673 | ||||||||
\(963\) | 19.5498 | 0.629983 | ||||||||
\(964\) | 10.0103 | 0.322409 | ||||||||
\(965\) | −20.6676 | −0.665312 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.6196 | −1.56350 | −0.781750 | − | 0.623592i | \(-0.785673\pi\) | ||||
−0.781750 | + | 0.623592i | \(0.785673\pi\) | |||||||
\(968\) | 18.2278 | 0.585864 | ||||||||
\(969\) | −0.368026 | −0.0118227 | ||||||||
\(970\) | −1.08096 | −0.0347076 | ||||||||
\(971\) | 3.29543 | 0.105755 | 0.0528777 | − | 0.998601i | \(-0.483161\pi\) | ||||
0.0528777 | + | 0.998601i | \(0.483161\pi\) | |||||||
\(972\) | 0.703600 | 0.0225680 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 27.7217 | 0.888260 | ||||||||
\(975\) | −0.162023 | −0.00518889 | ||||||||
\(976\) | 31.1937 | 0.998487 | ||||||||
\(977\) | −3.50798 | −0.112230 | −0.0561151 | − | 0.998424i | \(-0.517871\pi\) | ||||
−0.0561151 | + | 0.998424i | \(0.517871\pi\) | |||||||
\(978\) | −5.97589 | −0.191088 | ||||||||
\(979\) | −4.36280 | −0.139436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4207 | 0.556199 | ||||||||
\(982\) | 26.9360 | 0.859562 | ||||||||
\(983\) | 22.3364 | 0.712422 | 0.356211 | − | 0.934406i | \(-0.384068\pi\) | ||||
0.356211 | + | 0.934406i | \(0.384068\pi\) | |||||||
\(984\) | 3.07831 | 0.0981328 | ||||||||
\(985\) | −1.92174 | −0.0612316 | ||||||||
\(986\) | −1.74777 | −0.0556605 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.259701 | 0.00826218 | ||||||||
\(989\) | 10.1211 | 0.321832 | ||||||||
\(990\) | 10.6377 | 0.338089 | ||||||||
\(991\) | 53.4713 | 1.69857 | 0.849286 | − | 0.527933i | \(-0.177033\pi\) | ||||
0.849286 | + | 0.527933i | \(0.177033\pi\) | |||||||
\(992\) | 14.5939 | 0.463358 | ||||||||
\(993\) | 16.1121 | 0.511302 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.78352 | 0.278456 | ||||||||
\(996\) | −1.08161 | −0.0342723 | ||||||||
\(997\) | −41.4921 | −1.31407 | −0.657033 | − | 0.753862i | \(-0.728189\pi\) | ||||
−0.657033 | + | 0.753862i | \(0.728189\pi\) | |||||||
\(998\) | −35.8372 | −1.13441 | ||||||||
\(999\) | −9.23719 | −0.292252 |
(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 | 6027.2.a.bb.1.4 | 8 | ||
7.2 | even | 3 | 861.2.i.d.739.5 | yes | 16 | ||
7.4 | even | 3 | 861.2.i.d.247.5 | ✓ | 16 | ||
7.6 | odd | 2 | 6027.2.a.bc.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.d.247.5 | ✓ | 16 | 7.4 | even | 3 | ||
861.2.i.d.739.5 | yes | 16 | 7.2 | even | 3 | ||
6027.2.a.bb.1.4 | 8 | 1.1 | even | 1 | trivial | ||
6027.2.a.bc.1.4 | 8 | 7.6 | odd | 2 |