Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.68137\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.68137 | −1.18891 | −0.594455 | − | 0.804129i | \(-0.702632\pi\) | ||||
−0.594455 | + | 0.804129i | \(0.702632\pi\) | |||||||
\(3\) | −2.54941 | −1.47190 | −0.735951 | − | 0.677035i | \(-0.763265\pi\) | ||||
−0.735951 | + | 0.677035i | \(0.763265\pi\) | |||||||
\(4\) | 0.827018 | 0.413509 | ||||||||
\(5\) | −1.60084 | −0.715917 | −0.357958 | − | 0.933738i | \(-0.616527\pi\) | ||||
−0.357958 | + | 0.933738i | \(0.616527\pi\) | |||||||
\(6\) | 4.28651 | 1.74996 | ||||||||
\(7\) | −4.81497 | −1.81989 | −0.909945 | − | 0.414730i | \(-0.863876\pi\) | ||||
−0.909945 | + | 0.414730i | \(0.863876\pi\) | |||||||
\(8\) | 1.97222 | 0.697286 | ||||||||
\(9\) | 3.49949 | 1.16650 | ||||||||
\(10\) | 2.69161 | 0.851161 | ||||||||
\(11\) | 6.43743 | 1.94096 | 0.970480 | − | 0.241184i | \(-0.0775356\pi\) | ||||
0.970480 | + | 0.241184i | \(0.0775356\pi\) | |||||||
\(12\) | −2.10841 | −0.608645 | ||||||||
\(13\) | 3.23728 | 0.897860 | 0.448930 | − | 0.893567i | \(-0.351805\pi\) | ||||
0.448930 | + | 0.893567i | \(0.351805\pi\) | |||||||
\(14\) | 8.09577 | 2.16369 | ||||||||
\(15\) | 4.08119 | 1.05376 | ||||||||
\(16\) | −4.97008 | −1.24252 | ||||||||
\(17\) | −4.60504 | −1.11689 | −0.558444 | − | 0.829543i | \(-0.688601\pi\) | ||||
−0.558444 | + | 0.829543i | \(0.688601\pi\) | |||||||
\(18\) | −5.88395 | −1.38686 | ||||||||
\(19\) | 4.55028 | 1.04391 | 0.521953 | − | 0.852974i | \(-0.325204\pi\) | ||||
0.521953 | + | 0.852974i | \(0.325204\pi\) | |||||||
\(20\) | −1.32392 | −0.296038 | ||||||||
\(21\) | 12.2753 | 2.67870 | ||||||||
\(22\) | −10.8237 | −2.30763 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −5.02800 | −1.02634 | ||||||||
\(25\) | −2.43731 | −0.487463 | ||||||||
\(26\) | −5.44308 | −1.06747 | ||||||||
\(27\) | −1.27340 | −0.245067 | ||||||||
\(28\) | −3.98207 | −0.752540 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −6.86201 | −1.25283 | ||||||||
\(31\) | −1.11371 | −0.200029 | −0.100014 | − | 0.994986i | \(-0.531889\pi\) | ||||
−0.100014 | + | 0.994986i | \(0.531889\pi\) | |||||||
\(32\) | 4.41211 | 0.779959 | ||||||||
\(33\) | −16.4117 | −2.85690 | ||||||||
\(34\) | 7.74280 | 1.32788 | ||||||||
\(35\) | 7.70800 | 1.30289 | ||||||||
\(36\) | 2.89414 | 0.482357 | ||||||||
\(37\) | 4.51518 | 0.742291 | 0.371145 | − | 0.928575i | \(-0.378965\pi\) | ||||
0.371145 | + | 0.928575i | \(0.378965\pi\) | |||||||
\(38\) | −7.65072 | −1.24111 | ||||||||
\(39\) | −8.25315 | −1.32156 | ||||||||
\(40\) | −3.15721 | −0.499199 | ||||||||
\(41\) | −10.0963 | −1.57678 | −0.788389 | − | 0.615177i | \(-0.789085\pi\) | ||||
−0.788389 | + | 0.615177i | \(0.789085\pi\) | |||||||
\(42\) | −20.6394 | −3.18473 | ||||||||
\(43\) | 8.83757 | 1.34772 | 0.673858 | − | 0.738860i | \(-0.264636\pi\) | ||||
0.673858 | + | 0.738860i | \(0.264636\pi\) | |||||||
\(44\) | 5.32387 | 0.802604 | ||||||||
\(45\) | −5.60212 | −0.835115 | ||||||||
\(46\) | −1.68137 | −0.247905 | ||||||||
\(47\) | −5.22064 | −0.761508 | −0.380754 | − | 0.924676i | \(-0.624336\pi\) | ||||
−0.380754 | + | 0.924676i | \(0.624336\pi\) | |||||||
\(48\) | 12.6708 | 1.82887 | ||||||||
\(49\) | 16.1840 | 2.31200 | ||||||||
\(50\) | 4.09804 | 0.579550 | ||||||||
\(51\) | 11.7401 | 1.64395 | ||||||||
\(52\) | 2.67729 | 0.371273 | ||||||||
\(53\) | −7.18320 | −0.986688 | −0.493344 | − | 0.869834i | \(-0.664226\pi\) | ||||
−0.493344 | + | 0.869834i | \(0.664226\pi\) | |||||||
\(54\) | 2.14107 | 0.291362 | ||||||||
\(55\) | −10.3053 | −1.38957 | ||||||||
\(56\) | −9.49620 | −1.26898 | ||||||||
\(57\) | −11.6005 | −1.53653 | ||||||||
\(58\) | −1.68137 | −0.220775 | ||||||||
\(59\) | 4.45792 | 0.580372 | 0.290186 | − | 0.956970i | \(-0.406283\pi\) | ||||
0.290186 | + | 0.956970i | \(0.406283\pi\) | |||||||
\(60\) | 3.37522 | 0.435739 | ||||||||
\(61\) | −3.88029 | −0.496820 | −0.248410 | − | 0.968655i | \(-0.579908\pi\) | ||||
−0.248410 | + | 0.968655i | \(0.579908\pi\) | |||||||
\(62\) | 1.87257 | 0.237817 | ||||||||
\(63\) | −16.8500 | −2.12289 | ||||||||
\(64\) | 2.52174 | 0.315218 | ||||||||
\(65\) | −5.18236 | −0.642793 | ||||||||
\(66\) | 27.5941 | 3.39660 | ||||||||
\(67\) | −12.5392 | −1.53190 | −0.765951 | − | 0.642899i | \(-0.777731\pi\) | ||||
−0.765951 | + | 0.642899i | \(0.777731\pi\) | |||||||
\(68\) | −3.80845 | −0.461843 | ||||||||
\(69\) | −2.54941 | −0.306913 | ||||||||
\(70\) | −12.9600 | −1.54902 | ||||||||
\(71\) | 10.9516 | 1.29972 | 0.649860 | − | 0.760054i | \(-0.274828\pi\) | ||||
0.649860 | + | 0.760054i | \(0.274828\pi\) | |||||||
\(72\) | 6.90177 | 0.813381 | ||||||||
\(73\) | −0.460744 | −0.0539260 | −0.0269630 | − | 0.999636i | \(-0.508584\pi\) | ||||
−0.0269630 | + | 0.999636i | \(0.508584\pi\) | |||||||
\(74\) | −7.59170 | −0.882518 | ||||||||
\(75\) | 6.21371 | 0.717498 | ||||||||
\(76\) | 3.76316 | 0.431664 | ||||||||
\(77\) | −30.9961 | −3.53233 | ||||||||
\(78\) | 13.8766 | 1.57122 | ||||||||
\(79\) | −0.482984 | −0.0543400 | −0.0271700 | − | 0.999631i | \(-0.508650\pi\) | ||||
−0.0271700 | + | 0.999631i | \(0.508650\pi\) | |||||||
\(80\) | 7.95629 | 0.889541 | ||||||||
\(81\) | −7.25204 | −0.805782 | ||||||||
\(82\) | 16.9757 | 1.87465 | ||||||||
\(83\) | −4.96905 | −0.545424 | −0.272712 | − | 0.962096i | \(-0.587921\pi\) | ||||
−0.272712 | + | 0.962096i | \(0.587921\pi\) | |||||||
\(84\) | 10.1519 | 1.10767 | ||||||||
\(85\) | 7.37193 | 0.799598 | ||||||||
\(86\) | −14.8593 | −1.60232 | ||||||||
\(87\) | −2.54941 | −0.273325 | ||||||||
\(88\) | 12.6960 | 1.35340 | ||||||||
\(89\) | −17.2218 | −1.82550 | −0.912752 | − | 0.408513i | \(-0.866047\pi\) | ||||
−0.912752 | + | 0.408513i | \(0.866047\pi\) | |||||||
\(90\) | 9.41926 | 0.992877 | ||||||||
\(91\) | −15.5874 | −1.63400 | ||||||||
\(92\) | 0.827018 | 0.0862226 | ||||||||
\(93\) | 2.83931 | 0.294423 | ||||||||
\(94\) | 8.77784 | 0.905365 | ||||||||
\(95\) | −7.28426 | −0.747350 | ||||||||
\(96\) | −11.2483 | −1.14802 | ||||||||
\(97\) | 1.06047 | 0.107675 | 0.0538373 | − | 0.998550i | \(-0.482855\pi\) | ||||
0.0538373 | + | 0.998550i | \(0.482855\pi\) | |||||||
\(98\) | −27.2113 | −2.74876 | ||||||||
\(99\) | 22.5277 | 2.26412 | ||||||||
\(100\) | −2.01570 | −0.201570 | ||||||||
\(101\) | −5.50199 | −0.547469 | −0.273734 | − | 0.961805i | \(-0.588259\pi\) | ||||
−0.273734 | + | 0.961805i | \(0.588259\pi\) | |||||||
\(102\) | −19.7396 | −1.95451 | ||||||||
\(103\) | 11.3403 | 1.11739 | 0.558695 | − | 0.829373i | \(-0.311302\pi\) | ||||
0.558695 | + | 0.829373i | \(0.311302\pi\) | |||||||
\(104\) | 6.38463 | 0.626065 | ||||||||
\(105\) | −19.6508 | −1.91773 | ||||||||
\(106\) | 12.0776 | 1.17308 | ||||||||
\(107\) | 3.06127 | 0.295944 | 0.147972 | − | 0.988992i | \(-0.452725\pi\) | ||||
0.147972 | + | 0.988992i | \(0.452725\pi\) | |||||||
\(108\) | −1.05313 | −0.101337 | ||||||||
\(109\) | 6.89736 | 0.660647 | 0.330324 | − | 0.943868i | \(-0.392842\pi\) | ||||
0.330324 | + | 0.943868i | \(0.392842\pi\) | |||||||
\(110\) | 17.3270 | 1.65207 | ||||||||
\(111\) | −11.5110 | −1.09258 | ||||||||
\(112\) | 23.9308 | 2.26125 | ||||||||
\(113\) | −1.58895 | −0.149475 | −0.0747377 | − | 0.997203i | \(-0.523812\pi\) | ||||
−0.0747377 | + | 0.997203i | \(0.523812\pi\) | |||||||
\(114\) | 19.5048 | 1.82679 | ||||||||
\(115\) | −1.60084 | −0.149279 | ||||||||
\(116\) | 0.827018 | 0.0767867 | ||||||||
\(117\) | 11.3288 | 1.04735 | ||||||||
\(118\) | −7.49544 | −0.690011 | ||||||||
\(119\) | 22.1732 | 2.03261 | ||||||||
\(120\) | 8.04902 | 0.734772 | ||||||||
\(121\) | 30.4405 | 2.76732 | ||||||||
\(122\) | 6.52422 | 0.590675 | ||||||||
\(123\) | 25.7396 | 2.32086 | ||||||||
\(124\) | −0.921061 | −0.0827138 | ||||||||
\(125\) | 11.9059 | 1.06490 | ||||||||
\(126\) | 28.3311 | 2.52393 | ||||||||
\(127\) | −3.05960 | −0.271496 | −0.135748 | − | 0.990743i | \(-0.543344\pi\) | ||||
−0.135748 | + | 0.990743i | \(0.543344\pi\) | |||||||
\(128\) | −13.0642 | −1.15472 | ||||||||
\(129\) | −22.5306 | −1.98371 | ||||||||
\(130\) | 8.71349 | 0.764223 | ||||||||
\(131\) | −6.01078 | −0.525164 | −0.262582 | − | 0.964910i | \(-0.584574\pi\) | ||||
−0.262582 | + | 0.964910i | \(0.584574\pi\) | |||||||
\(132\) | −13.5727 | −1.18135 | ||||||||
\(133\) | −21.9095 | −1.89979 | ||||||||
\(134\) | 21.0830 | 1.82129 | ||||||||
\(135\) | 2.03851 | 0.175447 | ||||||||
\(136\) | −9.08217 | −0.778789 | ||||||||
\(137\) | 3.47329 | 0.296743 | 0.148372 | − | 0.988932i | \(-0.452597\pi\) | ||||
0.148372 | + | 0.988932i | \(0.452597\pi\) | |||||||
\(138\) | 4.28651 | 0.364892 | ||||||||
\(139\) | 3.17264 | 0.269100 | 0.134550 | − | 0.990907i | \(-0.457041\pi\) | ||||
0.134550 | + | 0.990907i | \(0.457041\pi\) | |||||||
\(140\) | 6.37465 | 0.538756 | ||||||||
\(141\) | 13.3095 | 1.12087 | ||||||||
\(142\) | −18.4138 | −1.54525 | ||||||||
\(143\) | 20.8398 | 1.74271 | ||||||||
\(144\) | −17.3927 | −1.44939 | ||||||||
\(145\) | −1.60084 | −0.132942 | ||||||||
\(146\) | 0.774682 | 0.0641131 | ||||||||
\(147\) | −41.2596 | −3.40303 | ||||||||
\(148\) | 3.73413 | 0.306944 | ||||||||
\(149\) | −6.52252 | −0.534346 | −0.267173 | − | 0.963649i | \(-0.586090\pi\) | ||||
−0.267173 | + | 0.963649i | \(0.586090\pi\) | |||||||
\(150\) | −10.4476 | −0.853041 | ||||||||
\(151\) | −8.50988 | −0.692524 | −0.346262 | − | 0.938138i | \(-0.612549\pi\) | ||||
−0.346262 | + | 0.938138i | \(0.612549\pi\) | |||||||
\(152\) | 8.97416 | 0.727900 | ||||||||
\(153\) | −16.1153 | −1.30284 | ||||||||
\(154\) | 52.1160 | 4.19963 | ||||||||
\(155\) | 1.78288 | 0.143204 | ||||||||
\(156\) | −6.82550 | −0.546477 | ||||||||
\(157\) | 0.655927 | 0.0523487 | 0.0261744 | − | 0.999657i | \(-0.491667\pi\) | ||||
0.0261744 | + | 0.999657i | \(0.491667\pi\) | |||||||
\(158\) | 0.812077 | 0.0646054 | ||||||||
\(159\) | 18.3129 | 1.45231 | ||||||||
\(160\) | −7.06308 | −0.558386 | ||||||||
\(161\) | −4.81497 | −0.379473 | ||||||||
\(162\) | 12.1934 | 0.958003 | ||||||||
\(163\) | 16.1610 | 1.26583 | 0.632914 | − | 0.774222i | \(-0.281859\pi\) | ||||
0.632914 | + | 0.774222i | \(0.281859\pi\) | |||||||
\(164\) | −8.34982 | −0.652012 | ||||||||
\(165\) | 26.2724 | 2.04530 | ||||||||
\(166\) | 8.35482 | 0.648460 | ||||||||
\(167\) | −0.0420128 | −0.00325105 | −0.00162553 | − | 0.999999i | \(-0.500517\pi\) | ||||
−0.00162553 | + | 0.999999i | \(0.500517\pi\) | |||||||
\(168\) | 24.2097 | 1.86782 | ||||||||
\(169\) | −2.52003 | −0.193848 | ||||||||
\(170\) | −12.3950 | −0.950651 | ||||||||
\(171\) | 15.9237 | 1.21771 | ||||||||
\(172\) | 7.30883 | 0.557293 | ||||||||
\(173\) | −21.8701 | −1.66276 | −0.831378 | − | 0.555708i | \(-0.812447\pi\) | ||||
−0.831378 | + | 0.555708i | \(0.812447\pi\) | |||||||
\(174\) | 4.28651 | 0.324960 | ||||||||
\(175\) | 11.7356 | 0.887129 | ||||||||
\(176\) | −31.9945 | −2.41168 | ||||||||
\(177\) | −11.3651 | −0.854251 | ||||||||
\(178\) | 28.9562 | 2.17036 | ||||||||
\(179\) | −19.9950 | −1.49450 | −0.747249 | − | 0.664544i | \(-0.768626\pi\) | ||||
−0.747249 | + | 0.664544i | \(0.768626\pi\) | |||||||
\(180\) | −4.63305 | −0.345327 | ||||||||
\(181\) | −3.65534 | −0.271700 | −0.135850 | − | 0.990729i | \(-0.543376\pi\) | ||||
−0.135850 | + | 0.990729i | \(0.543376\pi\) | |||||||
\(182\) | 26.2083 | 1.94269 | ||||||||
\(183\) | 9.89245 | 0.731271 | ||||||||
\(184\) | 1.97222 | 0.145394 | ||||||||
\(185\) | −7.22807 | −0.531419 | ||||||||
\(186\) | −4.77395 | −0.350043 | ||||||||
\(187\) | −29.6447 | −2.16783 | ||||||||
\(188\) | −4.31756 | −0.314890 | ||||||||
\(189\) | 6.13141 | 0.445994 | ||||||||
\(190\) | 12.2476 | 0.888532 | ||||||||
\(191\) | −22.6912 | −1.64188 | −0.820938 | − | 0.571018i | \(-0.806549\pi\) | ||||
−0.820938 | + | 0.571018i | \(0.806549\pi\) | |||||||
\(192\) | −6.42895 | −0.463970 | ||||||||
\(193\) | −19.2052 | −1.38242 | −0.691212 | − | 0.722652i | \(-0.742923\pi\) | ||||
−0.691212 | + | 0.722652i | \(0.742923\pi\) | |||||||
\(194\) | −1.78305 | −0.128015 | ||||||||
\(195\) | 13.2120 | 0.946128 | ||||||||
\(196\) | 13.3844 | 0.956031 | ||||||||
\(197\) | 1.26964 | 0.0904580 | 0.0452290 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452290 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(198\) | −37.8775 | −2.69184 | ||||||||
\(199\) | 12.0877 | 0.856872 | 0.428436 | − | 0.903572i | \(-0.359065\pi\) | ||||
0.428436 | + | 0.903572i | \(0.359065\pi\) | |||||||
\(200\) | −4.80692 | −0.339901 | ||||||||
\(201\) | 31.9674 | 2.25481 | ||||||||
\(202\) | 9.25090 | 0.650891 | ||||||||
\(203\) | −4.81497 | −0.337945 | ||||||||
\(204\) | 9.70931 | 0.679787 | ||||||||
\(205\) | 16.1626 | 1.12884 | ||||||||
\(206\) | −19.0672 | −1.32848 | ||||||||
\(207\) | 3.49949 | 0.243231 | ||||||||
\(208\) | −16.0895 | −1.11561 | ||||||||
\(209\) | 29.2921 | 2.02618 | ||||||||
\(210\) | 33.0404 | 2.28001 | ||||||||
\(211\) | 2.59871 | 0.178903 | 0.0894515 | − | 0.995991i | \(-0.471489\pi\) | ||||
0.0894515 | + | 0.995991i | \(0.471489\pi\) | |||||||
\(212\) | −5.94063 | −0.408004 | ||||||||
\(213\) | −27.9202 | −1.91306 | ||||||||
\(214\) | −5.14714 | −0.351852 | ||||||||
\(215\) | −14.1475 | −0.964853 | ||||||||
\(216\) | −2.51143 | −0.170881 | ||||||||
\(217\) | 5.36251 | 0.364031 | ||||||||
\(218\) | −11.5970 | −0.785451 | ||||||||
\(219\) | 1.17462 | 0.0793737 | ||||||||
\(220\) | −8.52266 | −0.574598 | ||||||||
\(221\) | −14.9078 | −1.00281 | ||||||||
\(222\) | 19.3544 | 1.29898 | ||||||||
\(223\) | −21.3712 | −1.43112 | −0.715561 | − | 0.698550i | \(-0.753829\pi\) | ||||
−0.715561 | + | 0.698550i | \(0.753829\pi\) | |||||||
\(224\) | −21.2442 | −1.41944 | ||||||||
\(225\) | −8.52936 | −0.568624 | ||||||||
\(226\) | 2.67161 | 0.177713 | ||||||||
\(227\) | 21.5679 | 1.43151 | 0.715757 | − | 0.698349i | \(-0.246082\pi\) | ||||
0.715757 | + | 0.698349i | \(0.246082\pi\) | |||||||
\(228\) | −9.59384 | −0.635367 | ||||||||
\(229\) | −20.6885 | −1.36713 | −0.683566 | − | 0.729888i | \(-0.739572\pi\) | ||||
−0.683566 | + | 0.729888i | \(0.739572\pi\) | |||||||
\(230\) | 2.69161 | 0.177479 | ||||||||
\(231\) | 79.0217 | 5.19925 | ||||||||
\(232\) | 1.97222 | 0.129483 | ||||||||
\(233\) | 24.1369 | 1.58126 | 0.790630 | − | 0.612295i | \(-0.209753\pi\) | ||||
0.790630 | + | 0.612295i | \(0.209753\pi\) | |||||||
\(234\) | −19.0480 | −1.24521 | ||||||||
\(235\) | 8.35740 | 0.545177 | ||||||||
\(236\) | 3.68678 | 0.239989 | ||||||||
\(237\) | 1.23132 | 0.0799831 | ||||||||
\(238\) | −37.2814 | −2.41659 | ||||||||
\(239\) | −22.5135 | −1.45628 | −0.728140 | − | 0.685429i | \(-0.759615\pi\) | ||||
−0.728140 | + | 0.685429i | \(0.759615\pi\) | |||||||
\(240\) | −20.2839 | −1.30932 | ||||||||
\(241\) | −21.1023 | −1.35932 | −0.679659 | − | 0.733528i | \(-0.737872\pi\) | ||||
−0.679659 | + | 0.733528i | \(0.737872\pi\) | |||||||
\(242\) | −51.1819 | −3.29010 | ||||||||
\(243\) | 22.3086 | 1.43110 | ||||||||
\(244\) | −3.20907 | −0.205440 | ||||||||
\(245\) | −25.9079 | −1.65520 | ||||||||
\(246\) | −43.2779 | −2.75930 | ||||||||
\(247\) | 14.7305 | 0.937280 | ||||||||
\(248\) | −2.19649 | −0.139477 | ||||||||
\(249\) | 12.6681 | 0.802810 | ||||||||
\(250\) | −20.0183 | −1.26607 | ||||||||
\(251\) | 5.52800 | 0.348924 | 0.174462 | − | 0.984664i | \(-0.444181\pi\) | ||||
0.174462 | + | 0.984664i | \(0.444181\pi\) | |||||||
\(252\) | −13.9352 | −0.877836 | ||||||||
\(253\) | 6.43743 | 0.404718 | ||||||||
\(254\) | 5.14433 | 0.322784 | ||||||||
\(255\) | −18.7941 | −1.17693 | ||||||||
\(256\) | 16.9223 | 1.05765 | ||||||||
\(257\) | 10.2732 | 0.640823 | 0.320412 | − | 0.947278i | \(-0.396179\pi\) | ||||
0.320412 | + | 0.947278i | \(0.396179\pi\) | |||||||
\(258\) | 37.8823 | 2.35845 | ||||||||
\(259\) | −21.7405 | −1.35089 | ||||||||
\(260\) | −4.28590 | −0.265801 | ||||||||
\(261\) | 3.49949 | 0.216613 | ||||||||
\(262\) | 10.1064 | 0.624373 | ||||||||
\(263\) | −16.0225 | −0.987993 | −0.493996 | − | 0.869464i | \(-0.664464\pi\) | ||||
−0.493996 | + | 0.869464i | \(0.664464\pi\) | |||||||
\(264\) | −32.3674 | −1.99208 | ||||||||
\(265\) | 11.4991 | 0.706387 | ||||||||
\(266\) | 36.8380 | 2.25868 | ||||||||
\(267\) | 43.9054 | 2.68696 | ||||||||
\(268\) | −10.3701 | −0.633455 | ||||||||
\(269\) | −9.31782 | −0.568118 | −0.284059 | − | 0.958807i | \(-0.591681\pi\) | ||||
−0.284059 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(270\) | −3.42750 | −0.208591 | ||||||||
\(271\) | 7.27051 | 0.441652 | 0.220826 | − | 0.975313i | \(-0.429125\pi\) | ||||
0.220826 | + | 0.975313i | \(0.429125\pi\) | |||||||
\(272\) | 22.8874 | 1.38775 | ||||||||
\(273\) | 39.7387 | 2.40510 | ||||||||
\(274\) | −5.83990 | −0.352801 | ||||||||
\(275\) | −15.6900 | −0.946146 | ||||||||
\(276\) | −2.10841 | −0.126911 | ||||||||
\(277\) | −11.2055 | −0.673272 | −0.336636 | − | 0.941635i | \(-0.609289\pi\) | ||||
−0.336636 | + | 0.941635i | \(0.609289\pi\) | |||||||
\(278\) | −5.33440 | −0.319936 | ||||||||
\(279\) | −3.89743 | −0.233333 | ||||||||
\(280\) | 15.2019 | 0.908486 | ||||||||
\(281\) | 3.15279 | 0.188079 | 0.0940397 | − | 0.995568i | \(-0.470022\pi\) | ||||
0.0940397 | + | 0.995568i | \(0.470022\pi\) | |||||||
\(282\) | −22.3783 | −1.33261 | ||||||||
\(283\) | −1.81112 | −0.107660 | −0.0538299 | − | 0.998550i | \(-0.517143\pi\) | ||||
−0.0538299 | + | 0.998550i | \(0.517143\pi\) | |||||||
\(284\) | 9.05719 | 0.537445 | ||||||||
\(285\) | 18.5706 | 1.10003 | ||||||||
\(286\) | −35.0394 | −2.07192 | ||||||||
\(287\) | 48.6135 | 2.86956 | ||||||||
\(288\) | 15.4401 | 0.909819 | ||||||||
\(289\) | 4.20643 | 0.247437 | ||||||||
\(290\) | 2.69161 | 0.158057 | ||||||||
\(291\) | −2.70358 | −0.158486 | ||||||||
\(292\) | −0.381043 | −0.0222989 | ||||||||
\(293\) | −23.6297 | −1.38046 | −0.690232 | − | 0.723588i | \(-0.742492\pi\) | ||||
−0.690232 | + | 0.723588i | \(0.742492\pi\) | |||||||
\(294\) | 69.3728 | 4.04590 | ||||||||
\(295\) | −7.13642 | −0.415498 | ||||||||
\(296\) | 8.90493 | 0.517589 | ||||||||
\(297\) | −8.19745 | −0.475664 | ||||||||
\(298\) | 10.9668 | 0.635290 | ||||||||
\(299\) | 3.23728 | 0.187217 | ||||||||
\(300\) | 5.13885 | 0.296692 | ||||||||
\(301\) | −42.5527 | −2.45270 | ||||||||
\(302\) | 14.3083 | 0.823349 | ||||||||
\(303\) | 14.0268 | 0.805820 | ||||||||
\(304\) | −22.6152 | −1.29707 | ||||||||
\(305\) | 6.21172 | 0.355682 | ||||||||
\(306\) | 27.0958 | 1.54897 | ||||||||
\(307\) | −1.18611 | −0.0676947 | −0.0338474 | − | 0.999427i | \(-0.510776\pi\) | ||||
−0.0338474 | + | 0.999427i | \(0.510776\pi\) | |||||||
\(308\) | −25.6343 | −1.46065 | ||||||||
\(309\) | −28.9110 | −1.64469 | ||||||||
\(310\) | −2.99768 | −0.170257 | ||||||||
\(311\) | −13.3026 | −0.754324 | −0.377162 | − | 0.926147i | \(-0.623100\pi\) | ||||
−0.377162 | + | 0.926147i | \(0.623100\pi\) | |||||||
\(312\) | −16.2770 | −0.921506 | ||||||||
\(313\) | 0.504365 | 0.0285084 | 0.0142542 | − | 0.999898i | \(-0.495463\pi\) | ||||
0.0142542 | + | 0.999898i | \(0.495463\pi\) | |||||||
\(314\) | −1.10286 | −0.0622379 | ||||||||
\(315\) | 26.9741 | 1.51982 | ||||||||
\(316\) | −0.399437 | −0.0224701 | ||||||||
\(317\) | 0.455841 | 0.0256026 | 0.0128013 | − | 0.999918i | \(-0.495925\pi\) | ||||
0.0128013 | + | 0.999918i | \(0.495925\pi\) | |||||||
\(318\) | −30.7909 | −1.72667 | ||||||||
\(319\) | 6.43743 | 0.360427 | ||||||||
\(320\) | −4.03690 | −0.225670 | ||||||||
\(321\) | −7.80444 | −0.435601 | ||||||||
\(322\) | 8.09577 | 0.451160 | ||||||||
\(323\) | −20.9542 | −1.16592 | ||||||||
\(324\) | −5.99757 | −0.333198 | ||||||||
\(325\) | −7.89027 | −0.437673 | ||||||||
\(326\) | −27.1727 | −1.50496 | ||||||||
\(327\) | −17.5842 | −0.972408 | ||||||||
\(328\) | −19.9122 | −1.09946 | ||||||||
\(329\) | 25.1372 | 1.38586 | ||||||||
\(330\) | −44.1737 | −2.43168 | ||||||||
\(331\) | −26.8153 | −1.47390 | −0.736951 | − | 0.675946i | \(-0.763735\pi\) | ||||
−0.736951 | + | 0.675946i | \(0.763735\pi\) | |||||||
\(332\) | −4.10949 | −0.225537 | ||||||||
\(333\) | 15.8008 | 0.865880 | ||||||||
\(334\) | 0.0706393 | 0.00386521 | ||||||||
\(335\) | 20.0732 | 1.09671 | ||||||||
\(336\) | −61.0094 | −3.32834 | ||||||||
\(337\) | 18.8374 | 1.02614 | 0.513069 | − | 0.858347i | \(-0.328508\pi\) | ||||
0.513069 | + | 0.858347i | \(0.328508\pi\) | |||||||
\(338\) | 4.23711 | 0.230468 | ||||||||
\(339\) | 4.05087 | 0.220013 | ||||||||
\(340\) | 6.09672 | 0.330641 | ||||||||
\(341\) | −7.16946 | −0.388248 | ||||||||
\(342\) | −26.7736 | −1.44775 | ||||||||
\(343\) | −44.2206 | −2.38769 | ||||||||
\(344\) | 17.4296 | 0.939744 | ||||||||
\(345\) | 4.08119 | 0.219724 | ||||||||
\(346\) | 36.7719 | 1.97687 | ||||||||
\(347\) | −13.1589 | −0.706408 | −0.353204 | − | 0.935546i | \(-0.614908\pi\) | ||||
−0.353204 | + | 0.935546i | \(0.614908\pi\) | |||||||
\(348\) | −2.10841 | −0.113022 | ||||||||
\(349\) | 2.97143 | 0.159057 | 0.0795285 | − | 0.996833i | \(-0.474659\pi\) | ||||
0.0795285 | + | 0.996833i | \(0.474659\pi\) | |||||||
\(350\) | −19.7319 | −1.05472 | ||||||||
\(351\) | −4.12236 | −0.220035 | ||||||||
\(352\) | 28.4027 | 1.51387 | ||||||||
\(353\) | 0.498800 | 0.0265484 | 0.0132742 | − | 0.999912i | \(-0.495775\pi\) | ||||
0.0132742 | + | 0.999912i | \(0.495775\pi\) | |||||||
\(354\) | 19.1089 | 1.01563 | ||||||||
\(355\) | −17.5318 | −0.930491 | ||||||||
\(356\) | −14.2427 | −0.754862 | ||||||||
\(357\) | −56.5285 | −2.99180 | ||||||||
\(358\) | 33.6191 | 1.77683 | ||||||||
\(359\) | −9.16521 | −0.483721 | −0.241861 | − | 0.970311i | \(-0.577758\pi\) | ||||
−0.241861 | + | 0.970311i | \(0.577758\pi\) | |||||||
\(360\) | −11.0486 | −0.582313 | ||||||||
\(361\) | 1.70503 | 0.0897383 | ||||||||
\(362\) | 6.14600 | 0.323026 | ||||||||
\(363\) | −77.6054 | −4.07323 | ||||||||
\(364\) | −12.8911 | −0.675675 | ||||||||
\(365\) | 0.737576 | 0.0386065 | ||||||||
\(366\) | −16.6329 | −0.869416 | ||||||||
\(367\) | −14.6305 | −0.763706 | −0.381853 | − | 0.924223i | \(-0.624714\pi\) | ||||
−0.381853 | + | 0.924223i | \(0.624714\pi\) | |||||||
\(368\) | −4.97008 | −0.259083 | ||||||||
\(369\) | −35.3319 | −1.83931 | ||||||||
\(370\) | 12.1531 | 0.631809 | ||||||||
\(371\) | 34.5869 | 1.79566 | ||||||||
\(372\) | 2.34816 | 0.121747 | ||||||||
\(373\) | 2.29578 | 0.118871 | 0.0594356 | − | 0.998232i | \(-0.481070\pi\) | ||||
0.0594356 | + | 0.998232i | \(0.481070\pi\) | |||||||
\(374\) | 49.8437 | 2.57736 | ||||||||
\(375\) | −30.3531 | −1.56743 | ||||||||
\(376\) | −10.2963 | −0.530989 | ||||||||
\(377\) | 3.23728 | 0.166728 | ||||||||
\(378\) | −10.3092 | −0.530247 | ||||||||
\(379\) | 37.1473 | 1.90813 | 0.954064 | − | 0.299604i | \(-0.0968545\pi\) | ||||
0.954064 | + | 0.299604i | \(0.0968545\pi\) | |||||||
\(380\) | −6.02421 | −0.309036 | ||||||||
\(381\) | 7.80018 | 0.399615 | ||||||||
\(382\) | 38.1523 | 1.95204 | ||||||||
\(383\) | −33.8199 | −1.72812 | −0.864059 | − | 0.503390i | \(-0.832086\pi\) | ||||
−0.864059 | + | 0.503390i | \(0.832086\pi\) | |||||||
\(384\) | 33.3060 | 1.69964 | ||||||||
\(385\) | 49.6197 | 2.52886 | ||||||||
\(386\) | 32.2912 | 1.64358 | ||||||||
\(387\) | 30.9270 | 1.57211 | ||||||||
\(388\) | 0.877028 | 0.0445244 | ||||||||
\(389\) | 12.9460 | 0.656390 | 0.328195 | − | 0.944610i | \(-0.393560\pi\) | ||||
0.328195 | + | 0.944610i | \(0.393560\pi\) | |||||||
\(390\) | −22.2142 | −1.12486 | ||||||||
\(391\) | −4.60504 | −0.232887 | ||||||||
\(392\) | 31.9184 | 1.61212 | ||||||||
\(393\) | 15.3239 | 0.772990 | ||||||||
\(394\) | −2.13474 | −0.107546 | ||||||||
\(395\) | 0.773180 | 0.0389029 | ||||||||
\(396\) | 18.6308 | 0.936234 | ||||||||
\(397\) | −22.8143 | −1.14502 | −0.572508 | − | 0.819899i | \(-0.694029\pi\) | ||||
−0.572508 | + | 0.819899i | \(0.694029\pi\) | |||||||
\(398\) | −20.3239 | −1.01874 | ||||||||
\(399\) | 55.8562 | 2.79631 | ||||||||
\(400\) | 12.1136 | 0.605682 | ||||||||
\(401\) | −3.51519 | −0.175540 | −0.0877702 | − | 0.996141i | \(-0.527974\pi\) | ||||
−0.0877702 | + | 0.996141i | \(0.527974\pi\) | |||||||
\(402\) | −53.7492 | −2.68077 | ||||||||
\(403\) | −3.60540 | −0.179598 | ||||||||
\(404\) | −4.55024 | −0.226383 | ||||||||
\(405\) | 11.6093 | 0.576873 | ||||||||
\(406\) | 8.09577 | 0.401786 | ||||||||
\(407\) | 29.0662 | 1.44076 | ||||||||
\(408\) | 23.1542 | 1.14630 | ||||||||
\(409\) | 23.9897 | 1.18621 | 0.593107 | − | 0.805124i | \(-0.297901\pi\) | ||||
0.593107 | + | 0.805124i | \(0.297901\pi\) | |||||||
\(410\) | −27.1753 | −1.34209 | ||||||||
\(411\) | −8.85484 | −0.436777 | ||||||||
\(412\) | 9.37860 | 0.462051 | ||||||||
\(413\) | −21.4648 | −1.05621 | ||||||||
\(414\) | −5.88395 | −0.289180 | ||||||||
\(415\) | 7.95464 | 0.390478 | ||||||||
\(416\) | 14.2832 | 0.700293 | ||||||||
\(417\) | −8.08837 | −0.396089 | ||||||||
\(418\) | −49.2510 | −2.40894 | ||||||||
\(419\) | 27.2826 | 1.33284 | 0.666421 | − | 0.745575i | \(-0.267825\pi\) | ||||
0.666421 | + | 0.745575i | \(0.267825\pi\) | |||||||
\(420\) | −16.2516 | −0.792997 | ||||||||
\(421\) | −1.37060 | −0.0667992 | −0.0333996 | − | 0.999442i | \(-0.510633\pi\) | ||||
−0.0333996 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(422\) | −4.36941 | −0.212700 | ||||||||
\(423\) | −18.2696 | −0.888297 | ||||||||
\(424\) | −14.1669 | −0.688004 | ||||||||
\(425\) | 11.2239 | 0.544441 | ||||||||
\(426\) | 46.9443 | 2.27446 | ||||||||
\(427\) | 18.6835 | 0.904158 | ||||||||
\(428\) | 2.53173 | 0.122376 | ||||||||
\(429\) | −53.1291 | −2.56510 | ||||||||
\(430\) | 23.7873 | 1.14712 | ||||||||
\(431\) | 12.0532 | 0.580581 | 0.290291 | − | 0.956939i | \(-0.406248\pi\) | ||||
0.290291 | + | 0.956939i | \(0.406248\pi\) | |||||||
\(432\) | 6.32892 | 0.304500 | ||||||||
\(433\) | −13.8279 | −0.664528 | −0.332264 | − | 0.943186i | \(-0.607813\pi\) | ||||
−0.332264 | + | 0.943186i | \(0.607813\pi\) | |||||||
\(434\) | −9.01638 | −0.432800 | ||||||||
\(435\) | 4.08119 | 0.195678 | ||||||||
\(436\) | 5.70424 | 0.273183 | ||||||||
\(437\) | 4.55028 | 0.217669 | ||||||||
\(438\) | −1.97498 | −0.0943683 | ||||||||
\(439\) | −27.8167 | −1.32762 | −0.663809 | − | 0.747902i | \(-0.731061\pi\) | ||||
−0.663809 | + | 0.747902i | \(0.731061\pi\) | |||||||
\(440\) | −20.3243 | −0.968924 | ||||||||
\(441\) | 56.6357 | 2.69694 | ||||||||
\(442\) | 25.0656 | 1.19225 | ||||||||
\(443\) | −8.80616 | −0.418393 | −0.209197 | − | 0.977874i | \(-0.567085\pi\) | ||||
−0.209197 | + | 0.977874i | \(0.567085\pi\) | |||||||
\(444\) | −9.51983 | −0.451791 | ||||||||
\(445\) | 27.5693 | 1.30691 | ||||||||
\(446\) | 35.9330 | 1.70148 | ||||||||
\(447\) | 16.6286 | 0.786505 | ||||||||
\(448\) | −12.1421 | −0.573661 | ||||||||
\(449\) | 24.5577 | 1.15895 | 0.579475 | − | 0.814990i | \(-0.303258\pi\) | ||||
0.579475 | + | 0.814990i | \(0.303258\pi\) | |||||||
\(450\) | 14.3410 | 0.676043 | ||||||||
\(451\) | −64.9943 | −3.06046 | ||||||||
\(452\) | −1.31409 | −0.0618094 | ||||||||
\(453\) | 21.6952 | 1.01933 | ||||||||
\(454\) | −36.2638 | −1.70194 | ||||||||
\(455\) | 24.9529 | 1.16981 | ||||||||
\(456\) | −22.8788 | −1.07140 | ||||||||
\(457\) | 10.1612 | 0.475320 | 0.237660 | − | 0.971348i | \(-0.423620\pi\) | ||||
0.237660 | + | 0.971348i | \(0.423620\pi\) | |||||||
\(458\) | 34.7851 | 1.62540 | ||||||||
\(459\) | 5.86408 | 0.273712 | ||||||||
\(460\) | −1.32392 | −0.0617282 | ||||||||
\(461\) | 0.775304 | 0.0361095 | 0.0180548 | − | 0.999837i | \(-0.494253\pi\) | ||||
0.0180548 | + | 0.999837i | \(0.494253\pi\) | |||||||
\(462\) | −132.865 | −6.18144 | ||||||||
\(463\) | 26.1512 | 1.21535 | 0.607676 | − | 0.794185i | \(-0.292102\pi\) | ||||
0.607676 | + | 0.794185i | \(0.292102\pi\) | |||||||
\(464\) | −4.97008 | −0.230730 | ||||||||
\(465\) | −4.54528 | −0.210783 | ||||||||
\(466\) | −40.5831 | −1.87998 | ||||||||
\(467\) | −10.9205 | −0.505340 | −0.252670 | − | 0.967553i | \(-0.581309\pi\) | ||||
−0.252670 | + | 0.967553i | \(0.581309\pi\) | |||||||
\(468\) | 9.36914 | 0.433088 | ||||||||
\(469\) | 60.3757 | 2.78789 | ||||||||
\(470\) | −14.0519 | −0.648166 | ||||||||
\(471\) | −1.67223 | −0.0770522 | ||||||||
\(472\) | 8.79201 | 0.404685 | ||||||||
\(473\) | 56.8913 | 2.61586 | ||||||||
\(474\) | −2.07032 | −0.0950928 | ||||||||
\(475\) | −11.0905 | −0.508865 | ||||||||
\(476\) | 18.3376 | 0.840503 | ||||||||
\(477\) | −25.1375 | −1.15097 | ||||||||
\(478\) | 37.8537 | 1.73139 | ||||||||
\(479\) | −32.2575 | −1.47388 | −0.736940 | − | 0.675958i | \(-0.763730\pi\) | ||||
−0.736940 | + | 0.675958i | \(0.763730\pi\) | |||||||
\(480\) | 18.0067 | 0.821889 | ||||||||
\(481\) | 14.6169 | 0.666473 | ||||||||
\(482\) | 35.4808 | 1.61611 | ||||||||
\(483\) | 12.2753 | 0.558547 | ||||||||
\(484\) | 25.1749 | 1.14431 | ||||||||
\(485\) | −1.69764 | −0.0770860 | ||||||||
\(486\) | −37.5092 | −1.70145 | ||||||||
\(487\) | −33.7336 | −1.52862 | −0.764308 | − | 0.644852i | \(-0.776919\pi\) | ||||
−0.764308 | + | 0.644852i | \(0.776919\pi\) | |||||||
\(488\) | −7.65279 | −0.346426 | ||||||||
\(489\) | −41.2011 | −1.86318 | ||||||||
\(490\) | 43.5609 | 1.96788 | ||||||||
\(491\) | 6.13372 | 0.276811 | 0.138406 | − | 0.990376i | \(-0.455802\pi\) | ||||
0.138406 | + | 0.990376i | \(0.455802\pi\) | |||||||
\(492\) | 21.2871 | 0.959697 | ||||||||
\(493\) | −4.60504 | −0.207401 | ||||||||
\(494\) | −24.7675 | −1.11434 | ||||||||
\(495\) | −36.0633 | −1.62092 | ||||||||
\(496\) | 5.53525 | 0.248540 | ||||||||
\(497\) | −52.7318 | −2.36535 | ||||||||
\(498\) | −21.2999 | −0.954470 | ||||||||
\(499\) | −20.6952 | −0.926443 | −0.463222 | − | 0.886242i | \(-0.653307\pi\) | ||||
−0.463222 | + | 0.886242i | \(0.653307\pi\) | |||||||
\(500\) | 9.84643 | 0.440346 | ||||||||
\(501\) | 0.107108 | 0.00478523 | ||||||||
\(502\) | −9.29463 | −0.414840 | ||||||||
\(503\) | −26.7545 | −1.19293 | −0.596463 | − | 0.802641i | \(-0.703428\pi\) | ||||
−0.596463 | + | 0.802641i | \(0.703428\pi\) | |||||||
\(504\) | −33.2318 | −1.48026 | ||||||||
\(505\) | 8.80780 | 0.391942 | ||||||||
\(506\) | −10.8237 | −0.481174 | ||||||||
\(507\) | 6.42458 | 0.285326 | ||||||||
\(508\) | −2.53034 | −0.112266 | ||||||||
\(509\) | −12.8632 | −0.570149 | −0.285075 | − | 0.958505i | \(-0.592018\pi\) | ||||
−0.285075 | + | 0.958505i | \(0.592018\pi\) | |||||||
\(510\) | 31.5999 | 1.39927 | ||||||||
\(511\) | 2.21847 | 0.0981393 | ||||||||
\(512\) | −2.32436 | −0.102723 | ||||||||
\(513\) | −5.79434 | −0.255826 | ||||||||
\(514\) | −17.2730 | −0.761882 | ||||||||
\(515\) | −18.1539 | −0.799958 | ||||||||
\(516\) | −18.6332 | −0.820281 | ||||||||
\(517\) | −33.6075 | −1.47806 | ||||||||
\(518\) | 36.5539 | 1.60608 | ||||||||
\(519\) | 55.7559 | 2.44741 | ||||||||
\(520\) | −10.2208 | −0.448210 | ||||||||
\(521\) | 29.9380 | 1.31161 | 0.655805 | − | 0.754931i | \(-0.272329\pi\) | ||||
0.655805 | + | 0.754931i | \(0.272329\pi\) | |||||||
\(522\) | −5.88395 | −0.257534 | ||||||||
\(523\) | 43.3872 | 1.89719 | 0.948596 | − | 0.316490i | \(-0.102504\pi\) | ||||
0.948596 | + | 0.316490i | \(0.102504\pi\) | |||||||
\(524\) | −4.97102 | −0.217160 | ||||||||
\(525\) | −29.9189 | −1.30577 | ||||||||
\(526\) | 26.9399 | 1.17464 | ||||||||
\(527\) | 5.12870 | 0.223410 | ||||||||
\(528\) | 81.5672 | 3.54976 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −19.3344 | −0.839831 | ||||||||
\(531\) | 15.6005 | 0.677002 | ||||||||
\(532\) | −18.1195 | −0.785581 | ||||||||
\(533\) | −32.6846 | −1.41573 | ||||||||
\(534\) | −73.8213 | −3.19456 | ||||||||
\(535\) | −4.90061 | −0.211872 | ||||||||
\(536\) | −24.7300 | −1.06817 | ||||||||
\(537\) | 50.9755 | 2.19976 | ||||||||
\(538\) | 15.6667 | 0.675441 | ||||||||
\(539\) | 104.183 | 4.48749 | ||||||||
\(540\) | 1.68589 | 0.0725490 | ||||||||
\(541\) | 21.9289 | 0.942798 | 0.471399 | − | 0.881920i | \(-0.343749\pi\) | ||||
0.471399 | + | 0.881920i | \(0.343749\pi\) | |||||||
\(542\) | −12.2244 | −0.525085 | ||||||||
\(543\) | 9.31897 | 0.399915 | ||||||||
\(544\) | −20.3180 | −0.871126 | ||||||||
\(545\) | −11.0416 | −0.472968 | ||||||||
\(546\) | −66.8156 | −2.85944 | ||||||||
\(547\) | 8.25534 | 0.352973 | 0.176486 | − | 0.984303i | \(-0.443527\pi\) | ||||
0.176486 | + | 0.984303i | \(0.443527\pi\) | |||||||
\(548\) | 2.87247 | 0.122706 | ||||||||
\(549\) | −13.5790 | −0.579539 | ||||||||
\(550\) | 26.3808 | 1.12488 | ||||||||
\(551\) | 4.55028 | 0.193848 | ||||||||
\(552\) | −5.02800 | −0.214006 | ||||||||
\(553\) | 2.32556 | 0.0988927 | ||||||||
\(554\) | 18.8406 | 0.800460 | ||||||||
\(555\) | 18.4273 | 0.782196 | ||||||||
\(556\) | 2.62383 | 0.111275 | ||||||||
\(557\) | −6.92176 | −0.293284 | −0.146642 | − | 0.989190i | \(-0.546847\pi\) | ||||
−0.146642 | + | 0.989190i | \(0.546847\pi\) | |||||||
\(558\) | 6.55304 | 0.277412 | ||||||||
\(559\) | 28.6097 | 1.21006 | ||||||||
\(560\) | −38.3093 | −1.61887 | ||||||||
\(561\) | 75.5764 | 3.19084 | ||||||||
\(562\) | −5.30101 | −0.223610 | ||||||||
\(563\) | 8.22790 | 0.346765 | 0.173382 | − | 0.984855i | \(-0.444530\pi\) | ||||
0.173382 | + | 0.984855i | \(0.444530\pi\) | |||||||
\(564\) | 11.0072 | 0.463488 | ||||||||
\(565\) | 2.54365 | 0.107012 | ||||||||
\(566\) | 3.04516 | 0.127998 | ||||||||
\(567\) | 34.9184 | 1.46643 | ||||||||
\(568\) | 21.5990 | 0.906276 | ||||||||
\(569\) | −46.5493 | −1.95145 | −0.975723 | − | 0.219006i | \(-0.929719\pi\) | ||||
−0.975723 | + | 0.219006i | \(0.929719\pi\) | |||||||
\(570\) | −31.2241 | −1.30783 | ||||||||
\(571\) | 26.8952 | 1.12553 | 0.562765 | − | 0.826617i | \(-0.309738\pi\) | ||||
0.562765 | + | 0.826617i | \(0.309738\pi\) | |||||||
\(572\) | 17.2349 | 0.720625 | ||||||||
\(573\) | 57.8491 | 2.41668 | ||||||||
\(574\) | −81.7374 | −3.41165 | ||||||||
\(575\) | −2.43731 | −0.101643 | ||||||||
\(576\) | 8.82481 | 0.367700 | ||||||||
\(577\) | −41.4087 | −1.72387 | −0.861933 | − | 0.507022i | \(-0.830746\pi\) | ||||
−0.861933 | + | 0.507022i | \(0.830746\pi\) | |||||||
\(578\) | −7.07257 | −0.294180 | ||||||||
\(579\) | 48.9620 | 2.03479 | ||||||||
\(580\) | −1.32392 | −0.0549729 | ||||||||
\(581\) | 23.9258 | 0.992611 | ||||||||
\(582\) | 4.54572 | 0.188426 | ||||||||
\(583\) | −46.2414 | −1.91512 | ||||||||
\(584\) | −0.908688 | −0.0376018 | ||||||||
\(585\) | −18.1356 | −0.749816 | ||||||||
\(586\) | 39.7304 | 1.64125 | ||||||||
\(587\) | 19.8813 | 0.820588 | 0.410294 | − | 0.911953i | \(-0.365426\pi\) | ||||
0.410294 | + | 0.911953i | \(0.365426\pi\) | |||||||
\(588\) | −34.1224 | −1.40718 | ||||||||
\(589\) | −5.06771 | −0.208811 | ||||||||
\(590\) | 11.9990 | 0.493990 | ||||||||
\(591\) | −3.23683 | −0.133145 | ||||||||
\(592\) | −22.4408 | −0.922311 | ||||||||
\(593\) | −19.4211 | −0.797527 | −0.398764 | − | 0.917054i | \(-0.630561\pi\) | ||||
−0.398764 | + | 0.917054i | \(0.630561\pi\) | |||||||
\(594\) | 13.7830 | 0.565523 | ||||||||
\(595\) | −35.4957 | −1.45518 | ||||||||
\(596\) | −5.39424 | −0.220957 | ||||||||
\(597\) | −30.8164 | −1.26123 | ||||||||
\(598\) | −5.44308 | −0.222584 | ||||||||
\(599\) | 10.4692 | 0.427758 | 0.213879 | − | 0.976860i | \(-0.431390\pi\) | ||||
0.213879 | + | 0.976860i | \(0.431390\pi\) | |||||||
\(600\) | 12.2548 | 0.500301 | ||||||||
\(601\) | 22.2282 | 0.906707 | 0.453354 | − | 0.891331i | \(-0.350228\pi\) | ||||
0.453354 | + | 0.891331i | \(0.350228\pi\) | |||||||
\(602\) | 71.5470 | 2.91604 | ||||||||
\(603\) | −43.8806 | −1.78696 | ||||||||
\(604\) | −7.03782 | −0.286365 | ||||||||
\(605\) | −48.7304 | −1.98117 | ||||||||
\(606\) | −23.5843 | −0.958048 | ||||||||
\(607\) | −16.8715 | −0.684793 | −0.342396 | − | 0.939556i | \(-0.611239\pi\) | ||||
−0.342396 | + | 0.939556i | \(0.611239\pi\) | |||||||
\(608\) | 20.0763 | 0.814203 | ||||||||
\(609\) | 12.2753 | 0.497422 | ||||||||
\(610\) | −10.4442 | −0.422874 | ||||||||
\(611\) | −16.9007 | −0.683727 | ||||||||
\(612\) | −13.3276 | −0.538738 | ||||||||
\(613\) | 10.0024 | 0.403995 | 0.201997 | − | 0.979386i | \(-0.435257\pi\) | ||||
0.201997 | + | 0.979386i | \(0.435257\pi\) | |||||||
\(614\) | 1.99429 | 0.0804830 | ||||||||
\(615\) | −41.2050 | −1.66155 | ||||||||
\(616\) | −61.1311 | −2.46304 | ||||||||
\(617\) | −21.5133 | −0.866091 | −0.433046 | − | 0.901372i | \(-0.642561\pi\) | ||||
−0.433046 | + | 0.901372i | \(0.642561\pi\) | |||||||
\(618\) | 48.6102 | 1.95539 | ||||||||
\(619\) | 38.6298 | 1.55266 | 0.776330 | − | 0.630326i | \(-0.217079\pi\) | ||||
0.776330 | + | 0.630326i | \(0.217079\pi\) | |||||||
\(620\) | 1.47447 | 0.0592162 | ||||||||
\(621\) | −1.27340 | −0.0510999 | ||||||||
\(622\) | 22.3667 | 0.896824 | ||||||||
\(623\) | 82.9224 | 3.32222 | ||||||||
\(624\) | 41.0188 | 1.64207 | ||||||||
\(625\) | −6.87292 | −0.274917 | ||||||||
\(626\) | −0.848026 | −0.0338939 | ||||||||
\(627\) | −74.6776 | −2.98234 | ||||||||
\(628\) | 0.542464 | 0.0216467 | ||||||||
\(629\) | −20.7926 | −0.829055 | ||||||||
\(630\) | −45.3535 | −1.80693 | ||||||||
\(631\) | 23.0317 | 0.916877 | 0.458439 | − | 0.888726i | \(-0.348409\pi\) | ||||
0.458439 | + | 0.888726i | \(0.348409\pi\) | |||||||
\(632\) | −0.952552 | −0.0378905 | ||||||||
\(633\) | −6.62519 | −0.263328 | ||||||||
\(634\) | −0.766439 | −0.0304392 | ||||||||
\(635\) | 4.89793 | 0.194368 | ||||||||
\(636\) | 15.1451 | 0.600543 | ||||||||
\(637\) | 52.3920 | 2.07585 | ||||||||
\(638\) | −10.8237 | −0.428516 | ||||||||
\(639\) | 38.3251 | 1.51612 | ||||||||
\(640\) | 20.9137 | 0.826687 | ||||||||
\(641\) | −20.0523 | −0.792019 | −0.396010 | − | 0.918246i | \(-0.629605\pi\) | ||||
−0.396010 | + | 0.918246i | \(0.629605\pi\) | |||||||
\(642\) | 13.1222 | 0.517891 | ||||||||
\(643\) | 44.7864 | 1.76620 | 0.883101 | − | 0.469182i | \(-0.155451\pi\) | ||||
0.883101 | + | 0.469182i | \(0.155451\pi\) | |||||||
\(644\) | −3.98207 | −0.156915 | ||||||||
\(645\) | 36.0678 | 1.42017 | ||||||||
\(646\) | 35.2319 | 1.38618 | ||||||||
\(647\) | −27.4834 | −1.08049 | −0.540243 | − | 0.841509i | \(-0.681668\pi\) | ||||
−0.540243 | + | 0.841509i | \(0.681668\pi\) | |||||||
\(648\) | −14.3026 | −0.561860 | ||||||||
\(649\) | 28.6976 | 1.12648 | ||||||||
\(650\) | 13.2665 | 0.520354 | ||||||||
\(651\) | −13.6712 | −0.535818 | ||||||||
\(652\) | 13.3654 | 0.523431 | ||||||||
\(653\) | 15.3774 | 0.601764 | 0.300882 | − | 0.953661i | \(-0.402719\pi\) | ||||
0.300882 | + | 0.953661i | \(0.402719\pi\) | |||||||
\(654\) | 29.5656 | 1.15611 | ||||||||
\(655\) | 9.62228 | 0.375974 | ||||||||
\(656\) | 50.1794 | 1.95918 | ||||||||
\(657\) | −1.61237 | −0.0629044 | ||||||||
\(658\) | −42.2651 | −1.64766 | ||||||||
\(659\) | −37.7949 | −1.47228 | −0.736141 | − | 0.676829i | \(-0.763354\pi\) | ||||
−0.736141 | + | 0.676829i | \(0.763354\pi\) | |||||||
\(660\) | 21.7278 | 0.845752 | ||||||||
\(661\) | −26.1249 | −1.01614 | −0.508070 | − | 0.861316i | \(-0.669641\pi\) | ||||
−0.508070 | + | 0.861316i | \(0.669641\pi\) | |||||||
\(662\) | 45.0865 | 1.75234 | ||||||||
\(663\) | 38.0061 | 1.47604 | ||||||||
\(664\) | −9.80006 | −0.380316 | ||||||||
\(665\) | 35.0735 | 1.36009 | ||||||||
\(666\) | −26.5671 | −1.02945 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −0.0347454 | −0.00134434 | ||||||||
\(669\) | 54.4840 | 2.10647 | ||||||||
\(670\) | −33.7505 | −1.30390 | ||||||||
\(671\) | −24.9791 | −0.964308 | ||||||||
\(672\) | 54.1602 | 2.08928 | ||||||||
\(673\) | −3.68363 | −0.141994 | −0.0709968 | − | 0.997477i | \(-0.522618\pi\) | ||||
−0.0709968 | + | 0.997477i | \(0.522618\pi\) | |||||||
\(674\) | −31.6727 | −1.21999 | ||||||||
\(675\) | 3.10369 | 0.119461 | ||||||||
\(676\) | −2.08411 | −0.0801580 | ||||||||
\(677\) | 32.9920 | 1.26798 | 0.633992 | − | 0.773340i | \(-0.281415\pi\) | ||||
0.633992 | + | 0.773340i | \(0.281415\pi\) | |||||||
\(678\) | −6.81103 | −0.261576 | ||||||||
\(679\) | −5.10614 | −0.195956 | ||||||||
\(680\) | 14.5391 | 0.557549 | ||||||||
\(681\) | −54.9855 | −2.10705 | ||||||||
\(682\) | 12.0545 | 0.461592 | ||||||||
\(683\) | 38.3314 | 1.46671 | 0.733355 | − | 0.679846i | \(-0.237953\pi\) | ||||
0.733355 | + | 0.679846i | \(0.237953\pi\) | |||||||
\(684\) | 13.1691 | 0.503535 | ||||||||
\(685\) | −5.56018 | −0.212444 | ||||||||
\(686\) | 74.3514 | 2.83875 | ||||||||
\(687\) | 52.7434 | 2.01229 | ||||||||
\(688\) | −43.9234 | −1.67456 | ||||||||
\(689\) | −23.2540 | −0.885907 | ||||||||
\(690\) | −6.86201 | −0.261232 | ||||||||
\(691\) | −17.5734 | −0.668524 | −0.334262 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334262 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(692\) | −18.0870 | −0.687564 | ||||||||
\(693\) | −108.470 | −4.12045 | ||||||||
\(694\) | 22.1251 | 0.839856 | ||||||||
\(695\) | −5.07889 | −0.192653 | ||||||||
\(696\) | −5.02800 | −0.190586 | ||||||||
\(697\) | 46.4939 | 1.76108 | ||||||||
\(698\) | −4.99608 | −0.189105 | ||||||||
\(699\) | −61.5348 | −2.32746 | ||||||||
\(700\) | 9.70555 | 0.366835 | ||||||||
\(701\) | −33.7148 | −1.27339 | −0.636696 | − | 0.771115i | \(-0.719699\pi\) | ||||
−0.636696 | + | 0.771115i | \(0.719699\pi\) | |||||||
\(702\) | 6.93123 | 0.261603 | ||||||||
\(703\) | 20.5453 | 0.774881 | ||||||||
\(704\) | 16.2335 | 0.611825 | ||||||||
\(705\) | −21.3064 | −0.802447 | ||||||||
\(706\) | −0.838669 | −0.0315637 | ||||||||
\(707\) | 26.4919 | 0.996332 | ||||||||
\(708\) | −9.39912 | −0.353240 | ||||||||
\(709\) | 28.8835 | 1.08474 | 0.542371 | − | 0.840139i | \(-0.317527\pi\) | ||||
0.542371 | + | 0.840139i | \(0.317527\pi\) | |||||||
\(710\) | 29.4775 | 1.10627 | ||||||||
\(711\) | −1.69020 | −0.0633874 | ||||||||
\(712\) | −33.9652 | −1.27290 | ||||||||
\(713\) | −1.11371 | −0.0417089 | ||||||||
\(714\) | 95.0455 | 3.55699 | ||||||||
\(715\) | −33.3611 | −1.24763 | ||||||||
\(716\) | −16.5362 | −0.617988 | ||||||||
\(717\) | 57.3962 | 2.14350 | ||||||||
\(718\) | 15.4101 | 0.575102 | ||||||||
\(719\) | 12.8825 | 0.480434 | 0.240217 | − | 0.970719i | \(-0.422781\pi\) | ||||
0.240217 | + | 0.970719i | \(0.422781\pi\) | |||||||
\(720\) | 27.8430 | 1.03765 | ||||||||
\(721\) | −54.6031 | −2.03353 | ||||||||
\(722\) | −2.86679 | −0.106691 | ||||||||
\(723\) | 53.7984 | 2.00078 | ||||||||
\(724\) | −3.02303 | −0.112350 | ||||||||
\(725\) | −2.43731 | −0.0905196 | ||||||||
\(726\) | 130.484 | 4.84270 | ||||||||
\(727\) | 23.3004 | 0.864165 | 0.432083 | − | 0.901834i | \(-0.357779\pi\) | ||||
0.432083 | + | 0.901834i | \(0.357779\pi\) | |||||||
\(728\) | −30.7418 | −1.13937 | ||||||||
\(729\) | −35.1177 | −1.30066 | ||||||||
\(730\) | −1.24014 | −0.0458997 | ||||||||
\(731\) | −40.6974 | −1.50525 | ||||||||
\(732\) | 8.18123 | 0.302387 | ||||||||
\(733\) | −21.1360 | −0.780676 | −0.390338 | − | 0.920672i | \(-0.627642\pi\) | ||||
−0.390338 | + | 0.920672i | \(0.627642\pi\) | |||||||
\(734\) | 24.5993 | 0.907978 | ||||||||
\(735\) | 66.0500 | 2.43629 | ||||||||
\(736\) | 4.41211 | 0.162633 | ||||||||
\(737\) | −80.7200 | −2.97336 | ||||||||
\(738\) | 59.4062 | 2.18677 | ||||||||
\(739\) | 10.7981 | 0.397214 | 0.198607 | − | 0.980079i | \(-0.436358\pi\) | ||||
0.198607 | + | 0.980079i | \(0.436358\pi\) | |||||||
\(740\) | −5.97775 | −0.219746 | ||||||||
\(741\) | −37.5541 | −1.37959 | ||||||||
\(742\) | −58.1535 | −2.13488 | ||||||||
\(743\) | 14.3921 | 0.527996 | 0.263998 | − | 0.964523i | \(-0.414959\pi\) | ||||
0.263998 | + | 0.964523i | \(0.414959\pi\) | |||||||
\(744\) | 5.59976 | 0.205297 | ||||||||
\(745\) | 10.4415 | 0.382547 | ||||||||
\(746\) | −3.86007 | −0.141327 | ||||||||
\(747\) | −17.3891 | −0.636235 | ||||||||
\(748\) | −24.5167 | −0.896418 | ||||||||
\(749\) | −14.7400 | −0.538586 | ||||||||
\(750\) | 51.0349 | 1.86353 | ||||||||
\(751\) | 33.1386 | 1.20924 | 0.604622 | − | 0.796512i | \(-0.293324\pi\) | ||||
0.604622 | + | 0.796512i | \(0.293324\pi\) | |||||||
\(752\) | 25.9470 | 0.946189 | ||||||||
\(753\) | −14.0931 | −0.513582 | ||||||||
\(754\) | −5.44308 | −0.198225 | ||||||||
\(755\) | 13.6229 | 0.495790 | ||||||||
\(756\) | 5.07078 | 0.184423 | ||||||||
\(757\) | −40.6036 | −1.47576 | −0.737881 | − | 0.674930i | \(-0.764174\pi\) | ||||
−0.737881 | + | 0.674930i | \(0.764174\pi\) | |||||||
\(758\) | −62.4585 | −2.26859 | ||||||||
\(759\) | −16.4117 | −0.595705 | ||||||||
\(760\) | −14.3662 | −0.521116 | ||||||||
\(761\) | 34.5658 | 1.25301 | 0.626505 | − | 0.779417i | \(-0.284485\pi\) | ||||
0.626505 | + | 0.779417i | \(0.284485\pi\) | |||||||
\(762\) | −13.1150 | −0.475107 | ||||||||
\(763\) | −33.2106 | −1.20230 | ||||||||
\(764\) | −18.7660 | −0.678930 | ||||||||
\(765\) | 25.7980 | 0.932729 | ||||||||
\(766\) | 56.8640 | 2.05458 | ||||||||
\(767\) | 14.4315 | 0.521093 | ||||||||
\(768\) | −43.1420 | −1.55675 | ||||||||
\(769\) | −1.16752 | −0.0421018 | −0.0210509 | − | 0.999778i | \(-0.506701\pi\) | ||||
−0.0210509 | + | 0.999778i | \(0.506701\pi\) | |||||||
\(770\) | −83.4293 | −3.00658 | ||||||||
\(771\) | −26.1905 | −0.943229 | ||||||||
\(772\) | −15.8831 | −0.571645 | ||||||||
\(773\) | 46.0245 | 1.65539 | 0.827693 | − | 0.561182i | \(-0.189653\pi\) | ||||
0.827693 | + | 0.561182i | \(0.189653\pi\) | |||||||
\(774\) | −51.9998 | −1.86910 | ||||||||
\(775\) | 2.71447 | 0.0975067 | ||||||||
\(776\) | 2.09148 | 0.0750799 | ||||||||
\(777\) | 55.4254 | 1.98837 | ||||||||
\(778\) | −21.7671 | −0.780389 | ||||||||
\(779\) | −45.9410 | −1.64601 | ||||||||
\(780\) | 10.9265 | 0.391232 | ||||||||
\(781\) | 70.5004 | 2.52270 | ||||||||
\(782\) | 7.74280 | 0.276882 | ||||||||
\(783\) | −1.27340 | −0.0455077 | ||||||||
\(784\) | −80.4356 | −2.87270 | ||||||||
\(785\) | −1.05003 | −0.0374773 | ||||||||
\(786\) | −25.7653 | −0.919016 | ||||||||
\(787\) | −10.7137 | −0.381901 | −0.190950 | − | 0.981600i | \(-0.561157\pi\) | ||||
−0.190950 | + | 0.981600i | \(0.561157\pi\) | |||||||
\(788\) | 1.05001 | 0.0374052 | ||||||||
\(789\) | 40.8480 | 1.45423 | ||||||||
\(790\) | −1.30000 | −0.0462521 | ||||||||
\(791\) | 7.65073 | 0.272029 | ||||||||
\(792\) | 44.4297 | 1.57874 | ||||||||
\(793\) | −12.5616 | −0.446075 | ||||||||
\(794\) | 38.3593 | 1.36132 | ||||||||
\(795\) | −29.3160 | −1.03973 | ||||||||
\(796\) | 9.99671 | 0.354324 | ||||||||
\(797\) | −50.3132 | −1.78219 | −0.891093 | − | 0.453821i | \(-0.850061\pi\) | ||||
−0.891093 | + | 0.453821i | \(0.850061\pi\) | |||||||
\(798\) | −93.9152 | −3.32456 | ||||||||
\(799\) | 24.0413 | 0.850519 | ||||||||
\(800\) | −10.7537 | −0.380201 | ||||||||
\(801\) | −60.2674 | −2.12944 | ||||||||
\(802\) | 5.91035 | 0.208702 | ||||||||
\(803\) | −2.96601 | −0.104668 | ||||||||
\(804\) | 26.4376 | 0.932384 | ||||||||
\(805\) | 7.70800 | 0.271671 | ||||||||
\(806\) | 6.06203 | 0.213526 | ||||||||
\(807\) | 23.7549 | 0.836214 | ||||||||
\(808\) | −10.8511 | −0.381742 | ||||||||
\(809\) | −36.1726 | −1.27176 | −0.635880 | − | 0.771788i | \(-0.719363\pi\) | ||||
−0.635880 | + | 0.771788i | \(0.719363\pi\) | |||||||
\(810\) | −19.5197 | −0.685851 | ||||||||
\(811\) | −15.5935 | −0.547561 | −0.273781 | − | 0.961792i | \(-0.588274\pi\) | ||||
−0.273781 | + | 0.961792i | \(0.588274\pi\) | |||||||
\(812\) | −3.98207 | −0.139743 | ||||||||
\(813\) | −18.5355 | −0.650069 | ||||||||
\(814\) | −48.8711 | −1.71293 | ||||||||
\(815\) | −25.8712 | −0.906228 | ||||||||
\(816\) | −58.3494 | −2.04264 | ||||||||
\(817\) | 40.2134 | 1.40689 | ||||||||
\(818\) | −40.3357 | −1.41030 | ||||||||
\(819\) | −54.5480 | −1.90606 | ||||||||
\(820\) | 13.3667 | 0.466786 | ||||||||
\(821\) | −17.0501 | −0.595054 | −0.297527 | − | 0.954713i | \(-0.596162\pi\) | ||||
−0.297527 | + | 0.954713i | \(0.596162\pi\) | |||||||
\(822\) | 14.8883 | 0.519289 | ||||||||
\(823\) | −2.67938 | −0.0933974 | −0.0466987 | − | 0.998909i | \(-0.514870\pi\) | ||||
−0.0466987 | + | 0.998909i | \(0.514870\pi\) | |||||||
\(824\) | 22.3655 | 0.779140 | ||||||||
\(825\) | 40.0004 | 1.39263 | ||||||||
\(826\) | 36.0903 | 1.25574 | ||||||||
\(827\) | 6.85300 | 0.238302 | 0.119151 | − | 0.992876i | \(-0.461983\pi\) | ||||
0.119151 | + | 0.992876i | \(0.461983\pi\) | |||||||
\(828\) | 2.89414 | 0.100578 | ||||||||
\(829\) | −16.0498 | −0.557433 | −0.278717 | − | 0.960373i | \(-0.589909\pi\) | ||||
−0.278717 | + | 0.960373i | \(0.589909\pi\) | |||||||
\(830\) | −13.3747 | −0.464243 | ||||||||
\(831\) | 28.5674 | 0.990990 | ||||||||
\(832\) | 8.16358 | 0.283021 | ||||||||
\(833\) | −74.5279 | −2.58224 | ||||||||
\(834\) | 13.5996 | 0.470915 | ||||||||
\(835\) | 0.0672558 | 0.00232748 | ||||||||
\(836\) | 24.2251 | 0.837842 | ||||||||
\(837\) | 1.41821 | 0.0490204 | ||||||||
\(838\) | −45.8723 | −1.58463 | ||||||||
\(839\) | −16.0979 | −0.555761 | −0.277880 | − | 0.960616i | \(-0.589632\pi\) | ||||
−0.277880 | + | 0.960616i | \(0.589632\pi\) | |||||||
\(840\) | −38.7558 | −1.33720 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 2.30450 | 0.0794183 | ||||||||
\(843\) | −8.03774 | −0.276835 | ||||||||
\(844\) | 2.14918 | 0.0739779 | ||||||||
\(845\) | 4.03416 | 0.138779 | ||||||||
\(846\) | 30.7180 | 1.05611 | ||||||||
\(847\) | −146.570 | −5.03622 | ||||||||
\(848\) | 35.7011 | 1.22598 | ||||||||
\(849\) | 4.61728 | 0.158465 | ||||||||
\(850\) | −18.8716 | −0.647292 | ||||||||
\(851\) | 4.51518 | 0.154778 | ||||||||
\(852\) | −23.0905 | −0.791067 | ||||||||
\(853\) | −24.2573 | −0.830552 | −0.415276 | − | 0.909695i | \(-0.636315\pi\) | ||||
−0.415276 | + | 0.909695i | \(0.636315\pi\) | |||||||
\(854\) | −31.4139 | −1.07496 | ||||||||
\(855\) | −25.4912 | −0.871781 | ||||||||
\(856\) | 6.03751 | 0.206358 | ||||||||
\(857\) | −50.4923 | −1.72478 | −0.862391 | − | 0.506242i | \(-0.831034\pi\) | ||||
−0.862391 | + | 0.506242i | \(0.831034\pi\) | |||||||
\(858\) | 89.3299 | 3.04967 | ||||||||
\(859\) | −15.5299 | −0.529873 | −0.264937 | − | 0.964266i | \(-0.585351\pi\) | ||||
−0.264937 | + | 0.964266i | \(0.585351\pi\) | |||||||
\(860\) | −11.7003 | −0.398975 | ||||||||
\(861\) | −123.936 | −4.22371 | ||||||||
\(862\) | −20.2659 | −0.690259 | ||||||||
\(863\) | 13.8161 | 0.470306 | 0.235153 | − | 0.971958i | \(-0.424441\pi\) | ||||
0.235153 | + | 0.971958i | \(0.424441\pi\) | |||||||
\(864\) | −5.61840 | −0.191142 | ||||||||
\(865\) | 35.0106 | 1.19039 | ||||||||
\(866\) | 23.2499 | 0.790065 | ||||||||
\(867\) | −10.7239 | −0.364203 | ||||||||
\(868\) | 4.43489 | 0.150530 | ||||||||
\(869\) | −3.10918 | −0.105472 | ||||||||
\(870\) | −6.86201 | −0.232644 | ||||||||
\(871\) | −40.5927 | −1.37543 | ||||||||
\(872\) | 13.6031 | 0.460660 | ||||||||
\(873\) | 3.71111 | 0.125602 | ||||||||
\(874\) | −7.65072 | −0.258789 | ||||||||
\(875\) | −57.3268 | −1.93800 | ||||||||
\(876\) | 0.971435 | 0.0328217 | ||||||||
\(877\) | 23.5097 | 0.793866 | 0.396933 | − | 0.917848i | \(-0.370075\pi\) | ||||
0.396933 | + | 0.917848i | \(0.370075\pi\) | |||||||
\(878\) | 46.7703 | 1.57842 | ||||||||
\(879\) | 60.2419 | 2.03191 | ||||||||
\(880\) | 51.2181 | 1.72656 | ||||||||
\(881\) | −34.4420 | −1.16038 | −0.580191 | − | 0.814481i | \(-0.697022\pi\) | ||||
−0.580191 | + | 0.814481i | \(0.697022\pi\) | |||||||
\(882\) | −95.2257 | −3.20642 | ||||||||
\(883\) | 15.0881 | 0.507755 | 0.253878 | − | 0.967236i | \(-0.418294\pi\) | ||||
0.253878 | + | 0.967236i | \(0.418294\pi\) | |||||||
\(884\) | −12.3290 | −0.414670 | ||||||||
\(885\) | 18.1937 | 0.611573 | ||||||||
\(886\) | 14.8064 | 0.497432 | ||||||||
\(887\) | −27.1965 | −0.913169 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(888\) | −22.7023 | −0.761840 | ||||||||
\(889\) | 14.7319 | 0.494092 | ||||||||
\(890\) | −46.3543 | −1.55380 | ||||||||
\(891\) | −46.6845 | −1.56399 | ||||||||
\(892\) | −17.6744 | −0.591782 | ||||||||
\(893\) | −23.7554 | −0.794943 | ||||||||
\(894\) | −27.9589 | −0.935085 | ||||||||
\(895\) | 32.0088 | 1.06994 | ||||||||
\(896\) | 62.9039 | 2.10147 | ||||||||
\(897\) | −8.25315 | −0.275565 | ||||||||
\(898\) | −41.2907 | −1.37789 | ||||||||
\(899\) | −1.11371 | −0.0371445 | ||||||||
\(900\) | −7.05393 | −0.235131 | ||||||||
\(901\) | 33.0789 | 1.10202 | ||||||||
\(902\) | 109.280 | 3.63862 | ||||||||
\(903\) | 108.484 | 3.61013 | ||||||||
\(904\) | −3.13375 | −0.104227 | ||||||||
\(905\) | 5.85162 | 0.194514 | ||||||||
\(906\) | −36.4777 | −1.21189 | ||||||||
\(907\) | −32.7246 | −1.08660 | −0.543301 | − | 0.839538i | \(-0.682826\pi\) | ||||
−0.543301 | + | 0.839538i | \(0.682826\pi\) | |||||||
\(908\) | 17.8371 | 0.591944 | ||||||||
\(909\) | −19.2542 | −0.638620 | ||||||||
\(910\) | −41.9552 | −1.39080 | ||||||||
\(911\) | −6.31180 | −0.209119 | −0.104560 | − | 0.994519i | \(-0.533343\pi\) | ||||
−0.104560 | + | 0.994519i | \(0.533343\pi\) | |||||||
\(912\) | 57.6555 | 1.90916 | ||||||||
\(913\) | −31.9879 | −1.05864 | ||||||||
\(914\) | −17.0848 | −0.565114 | ||||||||
\(915\) | −15.8362 | −0.523529 | ||||||||
\(916\) | −17.1097 | −0.565321 | ||||||||
\(917\) | 28.9417 | 0.955740 | ||||||||
\(918\) | −9.85971 | −0.325419 | ||||||||
\(919\) | 27.6020 | 0.910507 | 0.455254 | − | 0.890362i | \(-0.349549\pi\) | ||||
0.455254 | + | 0.890362i | \(0.349549\pi\) | |||||||
\(920\) | −3.15721 | −0.104090 | ||||||||
\(921\) | 3.02387 | 0.0996400 | ||||||||
\(922\) | −1.30358 | −0.0429310 | ||||||||
\(923\) | 35.4535 | 1.16697 | ||||||||
\(924\) | 65.3523 | 2.14993 | ||||||||
\(925\) | −11.0049 | −0.361839 | ||||||||
\(926\) | −43.9700 | −1.44494 | ||||||||
\(927\) | 39.6852 | 1.30343 | ||||||||
\(928\) | 4.41211 | 0.144835 | ||||||||
\(929\) | 12.6957 | 0.416533 | 0.208266 | − | 0.978072i | \(-0.433218\pi\) | ||||
0.208266 | + | 0.978072i | \(0.433218\pi\) | |||||||
\(930\) | 7.64232 | 0.250602 | ||||||||
\(931\) | 73.6416 | 2.41351 | ||||||||
\(932\) | 19.9616 | 0.653865 | ||||||||
\(933\) | 33.9139 | 1.11029 | ||||||||
\(934\) | 18.3614 | 0.600804 | ||||||||
\(935\) | 47.4563 | 1.55199 | ||||||||
\(936\) | 22.3430 | 0.730302 | ||||||||
\(937\) | 19.3527 | 0.632225 | 0.316112 | − | 0.948722i | \(-0.397622\pi\) | ||||
0.316112 | + | 0.948722i | \(0.397622\pi\) | |||||||
\(938\) | −101.514 | −3.31455 | ||||||||
\(939\) | −1.28583 | −0.0419616 | ||||||||
\(940\) | 6.91172 | 0.225435 | ||||||||
\(941\) | 2.26837 | 0.0739467 | 0.0369733 | − | 0.999316i | \(-0.488228\pi\) | ||||
0.0369733 | + | 0.999316i | \(0.488228\pi\) | |||||||
\(942\) | 2.81164 | 0.0916082 | ||||||||
\(943\) | −10.0963 | −0.328781 | ||||||||
\(944\) | −22.1562 | −0.721124 | ||||||||
\(945\) | −9.81540 | −0.319295 | ||||||||
\(946\) | −95.6555 | −3.11003 | ||||||||
\(947\) | −59.7576 | −1.94186 | −0.970930 | − | 0.239364i | \(-0.923061\pi\) | ||||
−0.970930 | + | 0.239364i | \(0.923061\pi\) | |||||||
\(948\) | 1.01833 | 0.0330737 | ||||||||
\(949\) | −1.49156 | −0.0484179 | ||||||||
\(950\) | 18.6472 | 0.604995 | ||||||||
\(951\) | −1.16213 | −0.0376845 | ||||||||
\(952\) | 43.7304 | 1.41731 | ||||||||
\(953\) | 57.0944 | 1.84947 | 0.924734 | − | 0.380615i | \(-0.124288\pi\) | ||||
0.924734 | + | 0.380615i | \(0.124288\pi\) | |||||||
\(954\) | 42.2656 | 1.36840 | ||||||||
\(955\) | 36.3249 | 1.17545 | ||||||||
\(956\) | −18.6191 | −0.602184 | ||||||||
\(957\) | −16.4117 | −0.530513 | ||||||||
\(958\) | 54.2368 | 1.75231 | ||||||||
\(959\) | −16.7238 | −0.540040 | ||||||||
\(960\) | 10.2917 | 0.332164 | ||||||||
\(961\) | −29.7596 | −0.959988 | ||||||||
\(962\) | −24.5765 | −0.792377 | ||||||||
\(963\) | 10.7129 | 0.345218 | ||||||||
\(964\) | −17.4520 | −0.562090 | ||||||||
\(965\) | 30.7445 | 0.989701 | ||||||||
\(966\) | −20.6394 | −0.664063 | ||||||||
\(967\) | 8.21507 | 0.264179 | 0.132089 | − | 0.991238i | \(-0.457831\pi\) | ||||
0.132089 | + | 0.991238i | \(0.457831\pi\) | |||||||
\(968\) | 60.0355 | 1.92961 | ||||||||
\(969\) | 53.4209 | 1.71613 | ||||||||
\(970\) | 2.85437 | 0.0916484 | ||||||||
\(971\) | −27.4049 | −0.879464 | −0.439732 | − | 0.898129i | \(-0.644927\pi\) | ||||
−0.439732 | + | 0.898129i | \(0.644927\pi\) | |||||||
\(972\) | 18.4496 | 0.591772 | ||||||||
\(973\) | −15.2762 | −0.489733 | ||||||||
\(974\) | 56.7188 | 1.81739 | ||||||||
\(975\) | 20.1155 | 0.644212 | ||||||||
\(976\) | 19.2853 | 0.617309 | ||||||||
\(977\) | 55.7031 | 1.78210 | 0.891050 | − | 0.453905i | \(-0.149969\pi\) | ||||
0.891050 | + | 0.453905i | \(0.149969\pi\) | |||||||
\(978\) | 69.2744 | 2.21515 | ||||||||
\(979\) | −110.864 | −3.54323 | ||||||||
\(980\) | −21.4263 | −0.684439 | ||||||||
\(981\) | 24.1372 | 0.770643 | ||||||||
\(982\) | −10.3131 | −0.329104 | ||||||||
\(983\) | 32.4589 | 1.03528 | 0.517639 | − | 0.855599i | \(-0.326811\pi\) | ||||
0.517639 | + | 0.855599i | \(0.326811\pi\) | |||||||
\(984\) | 50.7642 | 1.61830 | ||||||||
\(985\) | −2.03249 | −0.0647604 | ||||||||
\(986\) | 7.74280 | 0.246581 | ||||||||
\(987\) | −64.0851 | −2.03985 | ||||||||
\(988\) | 12.1824 | 0.387574 | ||||||||
\(989\) | 8.83757 | 0.281018 | ||||||||
\(990\) | 60.6358 | 1.92713 | ||||||||
\(991\) | −22.4212 | −0.712234 | −0.356117 | − | 0.934441i | \(-0.615900\pi\) | ||||
−0.356117 | + | 0.934441i | \(0.615900\pi\) | |||||||
\(992\) | −4.91383 | −0.156014 | ||||||||
\(993\) | 68.3632 | 2.16944 | ||||||||
\(994\) | 88.6619 | 2.81218 | ||||||||
\(995\) | −19.3504 | −0.613449 | ||||||||
\(996\) | 10.4768 | 0.331969 | ||||||||
\(997\) | 57.9261 | 1.83454 | 0.917269 | − | 0.398268i | \(-0.130389\pi\) | ||||
0.917269 | + | 0.398268i | \(0.130389\pi\) | |||||||
\(998\) | 34.7963 | 1.10146 | ||||||||
\(999\) | −5.74965 | −0.181911 |
(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 | 667.2.a.a.1.3 | ✓ | 10 | |
3.2 | odd | 2 | 6003.2.a.l.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.a.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6003.2.a.l.1.8 | 10 | 3.2 | odd | 2 |