Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58086 | −1.11784 | −0.558918 | − | 0.829223i | \(-0.688784\pi\) | ||||
−0.558918 | + | 0.829223i | \(0.688784\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.499118 | 0.249559 | ||||||||
\(5\) | −3.53760 | −1.58206 | −0.791032 | − | 0.611775i | \(-0.790456\pi\) | ||||
−0.791032 | + | 0.611775i | \(0.790456\pi\) | |||||||
\(6\) | −1.58086 | −0.645383 | ||||||||
\(7\) | −3.85230 | −1.45603 | −0.728016 | − | 0.685560i | \(-0.759558\pi\) | ||||
−0.728016 | + | 0.685560i | \(0.759558\pi\) | |||||||
\(8\) | 2.37268 | 0.838870 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.59245 | 1.76849 | ||||||||
\(11\) | −4.80037 | −1.44737 | −0.723683 | − | 0.690133i | \(-0.757552\pi\) | ||||
−0.723683 | + | 0.690133i | \(0.757552\pi\) | |||||||
\(12\) | 0.499118 | 0.144083 | ||||||||
\(13\) | 2.42528 | 0.672651 | 0.336326 | − | 0.941746i | \(-0.390816\pi\) | ||||
0.336326 | + | 0.941746i | \(0.390816\pi\) | |||||||
\(14\) | 6.08995 | 1.62761 | ||||||||
\(15\) | −3.53760 | −0.913405 | ||||||||
\(16\) | −4.74912 | −1.18728 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.58086 | −0.372612 | ||||||||
\(19\) | 1.75486 | 0.402591 | 0.201296 | − | 0.979531i | \(-0.435485\pi\) | ||||
0.201296 | + | 0.979531i | \(0.435485\pi\) | |||||||
\(20\) | −1.76568 | −0.394818 | ||||||||
\(21\) | −3.85230 | −0.840641 | ||||||||
\(22\) | 7.58871 | 1.61792 | ||||||||
\(23\) | −7.27500 | −1.51694 | −0.758471 | − | 0.651707i | \(-0.774053\pi\) | ||||
−0.758471 | + | 0.651707i | \(0.774053\pi\) | |||||||
\(24\) | 2.37268 | 0.484322 | ||||||||
\(25\) | 7.51462 | 1.50292 | ||||||||
\(26\) | −3.83402 | −0.751914 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.92275 | −0.363366 | ||||||||
\(29\) | −1.01319 | −0.188145 | −0.0940725 | − | 0.995565i | \(-0.529989\pi\) | ||||
−0.0940725 | + | 0.995565i | \(0.529989\pi\) | |||||||
\(30\) | 5.59245 | 1.02104 | ||||||||
\(31\) | −0.736752 | −0.132325 | −0.0661623 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661623 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(32\) | 2.76232 | 0.488314 | ||||||||
\(33\) | −4.80037 | −0.835637 | ||||||||
\(34\) | 1.58086 | 0.271115 | ||||||||
\(35\) | 13.6279 | 2.30354 | ||||||||
\(36\) | 0.499118 | 0.0831864 | ||||||||
\(37\) | 0.762412 | 0.125340 | 0.0626699 | − | 0.998034i | \(-0.480038\pi\) | ||||
0.0626699 | + | 0.998034i | \(0.480038\pi\) | |||||||
\(38\) | −2.77418 | −0.450031 | ||||||||
\(39\) | 2.42528 | 0.388355 | ||||||||
\(40\) | −8.39361 | −1.32715 | ||||||||
\(41\) | 4.24448 | 0.662876 | 0.331438 | − | 0.943477i | \(-0.392466\pi\) | ||||
0.331438 | + | 0.943477i | \(0.392466\pi\) | |||||||
\(42\) | 6.08995 | 0.939699 | ||||||||
\(43\) | 7.99270 | 1.21888 | 0.609438 | − | 0.792834i | \(-0.291395\pi\) | ||||
0.609438 | + | 0.792834i | \(0.291395\pi\) | |||||||
\(44\) | −2.39595 | −0.361203 | ||||||||
\(45\) | −3.53760 | −0.527354 | ||||||||
\(46\) | 11.5007 | 1.69569 | ||||||||
\(47\) | 11.0591 | 1.61314 | 0.806571 | − | 0.591137i | \(-0.201321\pi\) | ||||
0.806571 | + | 0.591137i | \(0.201321\pi\) | |||||||
\(48\) | −4.74912 | −0.685476 | ||||||||
\(49\) | 7.84022 | 1.12003 | ||||||||
\(50\) | −11.8796 | −1.68002 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 1.21050 | 0.167866 | ||||||||
\(53\) | −7.96423 | −1.09397 | −0.546985 | − | 0.837142i | \(-0.684225\pi\) | ||||
−0.546985 | + | 0.837142i | \(0.684225\pi\) | |||||||
\(54\) | −1.58086 | −0.215128 | ||||||||
\(55\) | 16.9818 | 2.28982 | ||||||||
\(56\) | −9.14029 | −1.22142 | ||||||||
\(57\) | 1.75486 | 0.232436 | ||||||||
\(58\) | 1.60171 | 0.210315 | ||||||||
\(59\) | 0.229221 | 0.0298421 | 0.0149210 | − | 0.999889i | \(-0.495250\pi\) | ||||
0.0149210 | + | 0.999889i | \(0.495250\pi\) | |||||||
\(60\) | −1.76568 | −0.227948 | ||||||||
\(61\) | 7.63803 | 0.977950 | 0.488975 | − | 0.872298i | \(-0.337371\pi\) | ||||
0.488975 | + | 0.872298i | \(0.337371\pi\) | |||||||
\(62\) | 1.16470 | 0.147917 | ||||||||
\(63\) | −3.85230 | −0.485344 | ||||||||
\(64\) | 5.13139 | 0.641424 | ||||||||
\(65\) | −8.57966 | −1.06418 | ||||||||
\(66\) | 7.58871 | 0.934106 | ||||||||
\(67\) | 2.68683 | 0.328249 | 0.164124 | − | 0.986440i | \(-0.447520\pi\) | ||||
0.164124 | + | 0.986440i | \(0.447520\pi\) | |||||||
\(68\) | −0.499118 | −0.0605270 | ||||||||
\(69\) | −7.27500 | −0.875807 | ||||||||
\(70\) | −21.5438 | −2.57498 | ||||||||
\(71\) | 5.96838 | 0.708317 | 0.354158 | − | 0.935185i | \(-0.384767\pi\) | ||||
0.354158 | + | 0.935185i | \(0.384767\pi\) | |||||||
\(72\) | 2.37268 | 0.279623 | ||||||||
\(73\) | −5.15619 | −0.603487 | −0.301743 | − | 0.953389i | \(-0.597569\pi\) | ||||
−0.301743 | + | 0.953389i | \(0.597569\pi\) | |||||||
\(74\) | −1.20527 | −0.140109 | ||||||||
\(75\) | 7.51462 | 0.867713 | ||||||||
\(76\) | 0.875880 | 0.100470 | ||||||||
\(77\) | 18.4925 | 2.10741 | ||||||||
\(78\) | −3.83402 | −0.434118 | ||||||||
\(79\) | 3.52278 | 0.396343 | 0.198172 | − | 0.980167i | \(-0.436500\pi\) | ||||
0.198172 | + | 0.980167i | \(0.436500\pi\) | |||||||
\(80\) | 16.8005 | 1.87835 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.70993 | −0.740988 | ||||||||
\(83\) | −3.41706 | −0.375071 | −0.187535 | − | 0.982258i | \(-0.560050\pi\) | ||||
−0.187535 | + | 0.982258i | \(0.560050\pi\) | |||||||
\(84\) | −1.92275 | −0.209790 | ||||||||
\(85\) | 3.53760 | 0.383707 | ||||||||
\(86\) | −12.6353 | −1.36250 | ||||||||
\(87\) | −1.01319 | −0.108626 | ||||||||
\(88\) | −11.3898 | −1.21415 | ||||||||
\(89\) | 5.27093 | 0.558717 | 0.279359 | − | 0.960187i | \(-0.409878\pi\) | ||||
0.279359 | + | 0.960187i | \(0.409878\pi\) | |||||||
\(90\) | 5.59245 | 0.589496 | ||||||||
\(91\) | −9.34290 | −0.979402 | ||||||||
\(92\) | −3.63108 | −0.378567 | ||||||||
\(93\) | −0.736752 | −0.0763976 | ||||||||
\(94\) | −17.4830 | −1.80323 | ||||||||
\(95\) | −6.20798 | −0.636925 | ||||||||
\(96\) | 2.76232 | 0.281928 | ||||||||
\(97\) | −9.65063 | −0.979873 | −0.489937 | − | 0.871758i | \(-0.662980\pi\) | ||||
−0.489937 | + | 0.871758i | \(0.662980\pi\) | |||||||
\(98\) | −12.3943 | −1.25201 | ||||||||
\(99\) | −4.80037 | −0.482455 | ||||||||
\(100\) | 3.75068 | 0.375068 | ||||||||
\(101\) | 15.7385 | 1.56604 | 0.783021 | − | 0.621995i | \(-0.213678\pi\) | ||||
0.783021 | + | 0.621995i | \(0.213678\pi\) | |||||||
\(102\) | 1.58086 | 0.156528 | ||||||||
\(103\) | −9.19924 | −0.906428 | −0.453214 | − | 0.891402i | \(-0.649723\pi\) | ||||
−0.453214 | + | 0.891402i | \(0.649723\pi\) | |||||||
\(104\) | 5.75442 | 0.564267 | ||||||||
\(105\) | 13.6279 | 1.32995 | ||||||||
\(106\) | 12.5903 | 1.22288 | ||||||||
\(107\) | −5.65567 | −0.546754 | −0.273377 | − | 0.961907i | \(-0.588141\pi\) | ||||
−0.273377 | + | 0.961907i | \(0.588141\pi\) | |||||||
\(108\) | 0.499118 | 0.0480277 | ||||||||
\(109\) | 0.761443 | 0.0729330 | 0.0364665 | − | 0.999335i | \(-0.488390\pi\) | ||||
0.0364665 | + | 0.999335i | \(0.488390\pi\) | |||||||
\(110\) | −26.8458 | −2.55965 | ||||||||
\(111\) | 0.762412 | 0.0723650 | ||||||||
\(112\) | 18.2950 | 1.72872 | ||||||||
\(113\) | −5.95512 | −0.560210 | −0.280105 | − | 0.959969i | \(-0.590369\pi\) | ||||
−0.280105 | + | 0.959969i | \(0.590369\pi\) | |||||||
\(114\) | −2.77418 | −0.259826 | ||||||||
\(115\) | 25.7360 | 2.39990 | ||||||||
\(116\) | −0.505703 | −0.0469533 | ||||||||
\(117\) | 2.42528 | 0.224217 | ||||||||
\(118\) | −0.362367 | −0.0333586 | ||||||||
\(119\) | 3.85230 | 0.353140 | ||||||||
\(120\) | −8.39361 | −0.766228 | ||||||||
\(121\) | 12.0435 | 1.09487 | ||||||||
\(122\) | −12.0747 | −1.09319 | ||||||||
\(123\) | 4.24448 | 0.382712 | ||||||||
\(124\) | −0.367726 | −0.0330228 | ||||||||
\(125\) | −8.89571 | −0.795657 | ||||||||
\(126\) | 6.08995 | 0.542536 | ||||||||
\(127\) | 10.5579 | 0.936862 | 0.468431 | − | 0.883500i | \(-0.344819\pi\) | ||||
0.468431 | + | 0.883500i | \(0.344819\pi\) | |||||||
\(128\) | −13.6367 | −1.20532 | ||||||||
\(129\) | 7.99270 | 0.703718 | ||||||||
\(130\) | 13.5632 | 1.18958 | ||||||||
\(131\) | −13.8248 | −1.20788 | −0.603941 | − | 0.797029i | \(-0.706404\pi\) | ||||
−0.603941 | + | 0.797029i | \(0.706404\pi\) | |||||||
\(132\) | −2.39595 | −0.208541 | ||||||||
\(133\) | −6.76023 | −0.586186 | ||||||||
\(134\) | −4.24750 | −0.366928 | ||||||||
\(135\) | −3.53760 | −0.304468 | ||||||||
\(136\) | −2.37268 | −0.203456 | ||||||||
\(137\) | 15.3289 | 1.30964 | 0.654819 | − | 0.755786i | \(-0.272745\pi\) | ||||
0.654819 | + | 0.755786i | \(0.272745\pi\) | |||||||
\(138\) | 11.5007 | 0.979009 | ||||||||
\(139\) | −8.01914 | −0.680175 | −0.340087 | − | 0.940394i | \(-0.610457\pi\) | ||||
−0.340087 | + | 0.940394i | \(0.610457\pi\) | |||||||
\(140\) | 6.80194 | 0.574869 | ||||||||
\(141\) | 11.0591 | 0.931348 | ||||||||
\(142\) | −9.43518 | −0.791782 | ||||||||
\(143\) | −11.6422 | −0.973572 | ||||||||
\(144\) | −4.74912 | −0.395760 | ||||||||
\(145\) | 3.58427 | 0.297657 | ||||||||
\(146\) | 8.15122 | 0.674600 | ||||||||
\(147\) | 7.84022 | 0.646651 | ||||||||
\(148\) | 0.380534 | 0.0312797 | ||||||||
\(149\) | −4.63856 | −0.380006 | −0.190003 | − | 0.981784i | \(-0.560850\pi\) | ||||
−0.190003 | + | 0.981784i | \(0.560850\pi\) | |||||||
\(150\) | −11.8796 | −0.969962 | ||||||||
\(151\) | 11.1849 | 0.910216 | 0.455108 | − | 0.890436i | \(-0.349601\pi\) | ||||
0.455108 | + | 0.890436i | \(0.349601\pi\) | |||||||
\(152\) | 4.16372 | 0.337722 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −29.2340 | −2.35574 | ||||||||
\(155\) | 2.60633 | 0.209346 | ||||||||
\(156\) | 1.21050 | 0.0969176 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −5.56902 | −0.443047 | ||||||||
\(159\) | −7.96423 | −0.631604 | ||||||||
\(160\) | −9.77199 | −0.772544 | ||||||||
\(161\) | 28.0255 | 2.20872 | ||||||||
\(162\) | −1.58086 | −0.124204 | ||||||||
\(163\) | 12.6969 | 0.994499 | 0.497249 | − | 0.867608i | \(-0.334343\pi\) | ||||
0.497249 | + | 0.867608i | \(0.334343\pi\) | |||||||
\(164\) | 2.11850 | 0.165427 | ||||||||
\(165\) | 16.9818 | 1.32203 | ||||||||
\(166\) | 5.40189 | 0.419268 | ||||||||
\(167\) | 12.7587 | 0.987299 | 0.493649 | − | 0.869661i | \(-0.335663\pi\) | ||||
0.493649 | + | 0.869661i | \(0.335663\pi\) | |||||||
\(168\) | −9.14029 | −0.705189 | ||||||||
\(169\) | −7.11803 | −0.547541 | ||||||||
\(170\) | −5.59245 | −0.428921 | ||||||||
\(171\) | 1.75486 | 0.134197 | ||||||||
\(172\) | 3.98930 | 0.304182 | ||||||||
\(173\) | −18.0809 | −1.37467 | −0.687333 | − | 0.726342i | \(-0.741219\pi\) | ||||
−0.687333 | + | 0.726342i | \(0.741219\pi\) | |||||||
\(174\) | 1.60171 | 0.121426 | ||||||||
\(175\) | −28.9486 | −2.18831 | ||||||||
\(176\) | 22.7975 | 1.71843 | ||||||||
\(177\) | 0.229221 | 0.0172293 | ||||||||
\(178\) | −8.33260 | −0.624555 | ||||||||
\(179\) | −8.85007 | −0.661485 | −0.330743 | − | 0.943721i | \(-0.607299\pi\) | ||||
−0.330743 | + | 0.943721i | \(0.607299\pi\) | |||||||
\(180\) | −1.76568 | −0.131606 | ||||||||
\(181\) | 20.5968 | 1.53095 | 0.765473 | − | 0.643468i | \(-0.222505\pi\) | ||||
0.765473 | + | 0.643468i | \(0.222505\pi\) | |||||||
\(182\) | 14.7698 | 1.09481 | ||||||||
\(183\) | 7.63803 | 0.564620 | ||||||||
\(184\) | −17.2613 | −1.27252 | ||||||||
\(185\) | −2.69711 | −0.198295 | ||||||||
\(186\) | 1.16470 | 0.0854001 | ||||||||
\(187\) | 4.80037 | 0.351038 | ||||||||
\(188\) | 5.51982 | 0.402574 | ||||||||
\(189\) | −3.85230 | −0.280214 | ||||||||
\(190\) | 9.81394 | 0.711978 | ||||||||
\(191\) | −14.1872 | −1.02655 | −0.513275 | − | 0.858224i | \(-0.671568\pi\) | ||||
−0.513275 | + | 0.858224i | \(0.671568\pi\) | |||||||
\(192\) | 5.13139 | 0.370326 | ||||||||
\(193\) | 1.19405 | 0.0859493 | 0.0429747 | − | 0.999076i | \(-0.486317\pi\) | ||||
0.0429747 | + | 0.999076i | \(0.486317\pi\) | |||||||
\(194\) | 15.2563 | 1.09534 | ||||||||
\(195\) | −8.57966 | −0.614402 | ||||||||
\(196\) | 3.91320 | 0.279514 | ||||||||
\(197\) | 11.6432 | 0.829542 | 0.414771 | − | 0.909926i | \(-0.363862\pi\) | ||||
0.414771 | + | 0.909926i | \(0.363862\pi\) | |||||||
\(198\) | 7.58871 | 0.539306 | ||||||||
\(199\) | 12.0052 | 0.851028 | 0.425514 | − | 0.904952i | \(-0.360093\pi\) | ||||
0.425514 | + | 0.904952i | \(0.360093\pi\) | |||||||
\(200\) | 17.8298 | 1.26076 | ||||||||
\(201\) | 2.68683 | 0.189514 | ||||||||
\(202\) | −24.8804 | −1.75058 | ||||||||
\(203\) | 3.90312 | 0.273945 | ||||||||
\(204\) | −0.499118 | −0.0349453 | ||||||||
\(205\) | −15.0153 | −1.04871 | ||||||||
\(206\) | 14.5427 | 1.01324 | ||||||||
\(207\) | −7.27500 | −0.505647 | ||||||||
\(208\) | −11.5179 | −0.798625 | ||||||||
\(209\) | −8.42395 | −0.582697 | ||||||||
\(210\) | −21.5438 | −1.48666 | ||||||||
\(211\) | −13.8510 | −0.953544 | −0.476772 | − | 0.879027i | \(-0.658193\pi\) | ||||
−0.476772 | + | 0.879027i | \(0.658193\pi\) | |||||||
\(212\) | −3.97509 | −0.273010 | ||||||||
\(213\) | 5.96838 | 0.408947 | ||||||||
\(214\) | 8.94082 | 0.611182 | ||||||||
\(215\) | −28.2750 | −1.92834 | ||||||||
\(216\) | 2.37268 | 0.161441 | ||||||||
\(217\) | 2.83819 | 0.192669 | ||||||||
\(218\) | −1.20373 | −0.0815272 | ||||||||
\(219\) | −5.15619 | −0.348423 | ||||||||
\(220\) | 8.47592 | 0.571446 | ||||||||
\(221\) | −2.42528 | −0.163142 | ||||||||
\(222\) | −1.20527 | −0.0808922 | ||||||||
\(223\) | 21.5425 | 1.44259 | 0.721297 | − | 0.692626i | \(-0.243546\pi\) | ||||
0.721297 | + | 0.692626i | \(0.243546\pi\) | |||||||
\(224\) | −10.6413 | −0.711002 | ||||||||
\(225\) | 7.51462 | 0.500975 | ||||||||
\(226\) | 9.41421 | 0.626224 | ||||||||
\(227\) | −3.89994 | −0.258848 | −0.129424 | − | 0.991589i | \(-0.541313\pi\) | ||||
−0.129424 | + | 0.991589i | \(0.541313\pi\) | |||||||
\(228\) | 0.875880 | 0.0580066 | ||||||||
\(229\) | 28.8788 | 1.90837 | 0.954183 | − | 0.299224i | \(-0.0967278\pi\) | ||||
0.954183 | + | 0.299224i | \(0.0967278\pi\) | |||||||
\(230\) | −40.6851 | −2.68269 | ||||||||
\(231\) | 18.4925 | 1.21671 | ||||||||
\(232\) | −2.40398 | −0.157829 | ||||||||
\(233\) | 3.82664 | 0.250691 | 0.125346 | − | 0.992113i | \(-0.459996\pi\) | ||||
0.125346 | + | 0.992113i | \(0.459996\pi\) | |||||||
\(234\) | −3.83402 | −0.250638 | ||||||||
\(235\) | −39.1228 | −2.55209 | ||||||||
\(236\) | 0.114409 | 0.00744736 | ||||||||
\(237\) | 3.52278 | 0.228829 | ||||||||
\(238\) | −6.08995 | −0.394753 | ||||||||
\(239\) | 16.4165 | 1.06190 | 0.530949 | − | 0.847404i | \(-0.321836\pi\) | ||||
0.530949 | + | 0.847404i | \(0.321836\pi\) | |||||||
\(240\) | 16.8005 | 1.08447 | ||||||||
\(241\) | −27.8172 | −1.79186 | −0.895932 | − | 0.444190i | \(-0.853491\pi\) | ||||
−0.895932 | + | 0.444190i | \(0.853491\pi\) | |||||||
\(242\) | −19.0391 | −1.22388 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.81228 | 0.244056 | ||||||||
\(245\) | −27.7356 | −1.77196 | ||||||||
\(246\) | −6.70993 | −0.427809 | ||||||||
\(247\) | 4.25601 | 0.270804 | ||||||||
\(248\) | −1.74808 | −0.111003 | ||||||||
\(249\) | −3.41706 | −0.216547 | ||||||||
\(250\) | 14.0629 | 0.889414 | ||||||||
\(251\) | 24.7440 | 1.56183 | 0.780913 | − | 0.624640i | \(-0.214754\pi\) | ||||
0.780913 | + | 0.624640i | \(0.214754\pi\) | |||||||
\(252\) | −1.92275 | −0.121122 | ||||||||
\(253\) | 34.9227 | 2.19557 | ||||||||
\(254\) | −16.6906 | −1.04726 | ||||||||
\(255\) | 3.53760 | 0.221533 | ||||||||
\(256\) | 11.2949 | 0.705929 | ||||||||
\(257\) | −18.2528 | −1.13858 | −0.569289 | − | 0.822137i | \(-0.692781\pi\) | ||||
−0.569289 | + | 0.822137i | \(0.692781\pi\) | |||||||
\(258\) | −12.6353 | −0.786642 | ||||||||
\(259\) | −2.93704 | −0.182499 | ||||||||
\(260\) | −4.28227 | −0.265575 | ||||||||
\(261\) | −1.01319 | −0.0627150 | ||||||||
\(262\) | 21.8551 | 1.35021 | ||||||||
\(263\) | 29.8867 | 1.84289 | 0.921445 | − | 0.388508i | \(-0.127010\pi\) | ||||
0.921445 | + | 0.388508i | \(0.127010\pi\) | |||||||
\(264\) | −11.3898 | −0.700991 | ||||||||
\(265\) | 28.1743 | 1.73073 | ||||||||
\(266\) | 10.6870 | 0.655261 | ||||||||
\(267\) | 5.27093 | 0.322576 | ||||||||
\(268\) | 1.34105 | 0.0819175 | ||||||||
\(269\) | −6.43186 | −0.392157 | −0.196079 | − | 0.980588i | \(-0.562821\pi\) | ||||
−0.196079 | + | 0.980588i | \(0.562821\pi\) | |||||||
\(270\) | 5.59245 | 0.340346 | ||||||||
\(271\) | 10.0760 | 0.612076 | 0.306038 | − | 0.952019i | \(-0.400997\pi\) | ||||
0.306038 | + | 0.952019i | \(0.400997\pi\) | |||||||
\(272\) | 4.74912 | 0.287958 | ||||||||
\(273\) | −9.34290 | −0.565458 | ||||||||
\(274\) | −24.2329 | −1.46396 | ||||||||
\(275\) | −36.0729 | −2.17528 | ||||||||
\(276\) | −3.63108 | −0.218566 | ||||||||
\(277\) | 14.1352 | 0.849301 | 0.424650 | − | 0.905357i | \(-0.360397\pi\) | ||||
0.424650 | + | 0.905357i | \(0.360397\pi\) | |||||||
\(278\) | 12.6771 | 0.760324 | ||||||||
\(279\) | −0.736752 | −0.0441082 | ||||||||
\(280\) | 32.3347 | 1.93237 | ||||||||
\(281\) | −30.2938 | −1.80718 | −0.903589 | − | 0.428401i | \(-0.859077\pi\) | ||||
−0.903589 | + | 0.428401i | \(0.859077\pi\) | |||||||
\(282\) | −17.4830 | −1.04110 | ||||||||
\(283\) | 22.8584 | 1.35879 | 0.679395 | − | 0.733773i | \(-0.262242\pi\) | ||||
0.679395 | + | 0.733773i | \(0.262242\pi\) | |||||||
\(284\) | 2.97893 | 0.176767 | ||||||||
\(285\) | −6.20798 | −0.367729 | ||||||||
\(286\) | 18.4047 | 1.08829 | ||||||||
\(287\) | −16.3510 | −0.965170 | ||||||||
\(288\) | 2.76232 | 0.162771 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.66623 | −0.332732 | ||||||||
\(291\) | −9.65063 | −0.565730 | ||||||||
\(292\) | −2.57355 | −0.150606 | ||||||||
\(293\) | −18.5166 | −1.08175 | −0.540877 | − | 0.841102i | \(-0.681908\pi\) | ||||
−0.540877 | + | 0.841102i | \(0.681908\pi\) | |||||||
\(294\) | −12.3943 | −0.722850 | ||||||||
\(295\) | −0.810893 | −0.0472120 | ||||||||
\(296\) | 1.80896 | 0.105144 | ||||||||
\(297\) | −4.80037 | −0.278546 | ||||||||
\(298\) | 7.33292 | 0.424785 | ||||||||
\(299\) | −17.6439 | −1.02037 | ||||||||
\(300\) | 3.75068 | 0.216546 | ||||||||
\(301\) | −30.7903 | −1.77472 | ||||||||
\(302\) | −17.6818 | −1.01747 | ||||||||
\(303\) | 15.7385 | 0.904155 | ||||||||
\(304\) | −8.33401 | −0.477988 | ||||||||
\(305\) | −27.0203 | −1.54718 | ||||||||
\(306\) | 1.58086 | 0.0903718 | ||||||||
\(307\) | −7.26341 | −0.414545 | −0.207272 | − | 0.978283i | \(-0.566459\pi\) | ||||
−0.207272 | + | 0.978283i | \(0.566459\pi\) | |||||||
\(308\) | 9.22993 | 0.525924 | ||||||||
\(309\) | −9.19924 | −0.523327 | ||||||||
\(310\) | −4.12025 | −0.234014 | ||||||||
\(311\) | −25.0635 | −1.42122 | −0.710611 | − | 0.703585i | \(-0.751581\pi\) | ||||
−0.710611 | + | 0.703585i | \(0.751581\pi\) | |||||||
\(312\) | 5.75442 | 0.325780 | ||||||||
\(313\) | −11.8317 | −0.668767 | −0.334384 | − | 0.942437i | \(-0.608528\pi\) | ||||
−0.334384 | + | 0.942437i | \(0.608528\pi\) | |||||||
\(314\) | −1.58086 | −0.0892131 | ||||||||
\(315\) | 13.6279 | 0.767845 | ||||||||
\(316\) | 1.75828 | 0.0989111 | ||||||||
\(317\) | 3.63674 | 0.204260 | 0.102130 | − | 0.994771i | \(-0.467434\pi\) | ||||
0.102130 | + | 0.994771i | \(0.467434\pi\) | |||||||
\(318\) | 12.5903 | 0.706031 | ||||||||
\(319\) | 4.86369 | 0.272315 | ||||||||
\(320\) | −18.1528 | −1.01477 | ||||||||
\(321\) | −5.65567 | −0.315669 | ||||||||
\(322\) | −44.3043 | −2.46898 | ||||||||
\(323\) | −1.75486 | −0.0976428 | ||||||||
\(324\) | 0.499118 | 0.0277288 | ||||||||
\(325\) | 18.2250 | 1.01094 | ||||||||
\(326\) | −20.0720 | −1.11169 | ||||||||
\(327\) | 0.761443 | 0.0421079 | ||||||||
\(328\) | 10.0708 | 0.556067 | ||||||||
\(329\) | −42.6032 | −2.34879 | ||||||||
\(330\) | −26.8458 | −1.47781 | ||||||||
\(331\) | −17.6453 | −0.969874 | −0.484937 | − | 0.874549i | \(-0.661157\pi\) | ||||
−0.484937 | + | 0.874549i | \(0.661157\pi\) | |||||||
\(332\) | −1.70552 | −0.0936023 | ||||||||
\(333\) | 0.762412 | 0.0417799 | ||||||||
\(334\) | −20.1697 | −1.10364 | ||||||||
\(335\) | −9.50493 | −0.519310 | ||||||||
\(336\) | 18.2950 | 0.998076 | ||||||||
\(337\) | −17.4892 | −0.952695 | −0.476348 | − | 0.879257i | \(-0.658040\pi\) | ||||
−0.476348 | + | 0.879257i | \(0.658040\pi\) | |||||||
\(338\) | 11.2526 | 0.612061 | ||||||||
\(339\) | −5.95512 | −0.323438 | ||||||||
\(340\) | 1.76568 | 0.0957575 | ||||||||
\(341\) | 3.53668 | 0.191522 | ||||||||
\(342\) | −2.77418 | −0.150010 | ||||||||
\(343\) | −3.23679 | −0.174770 | ||||||||
\(344\) | 18.9642 | 1.02248 | ||||||||
\(345\) | 25.7360 | 1.38558 | ||||||||
\(346\) | 28.5834 | 1.53665 | ||||||||
\(347\) | −11.4729 | −0.615898 | −0.307949 | − | 0.951403i | \(-0.599643\pi\) | ||||
−0.307949 | + | 0.951403i | \(0.599643\pi\) | |||||||
\(348\) | −0.505703 | −0.0271085 | ||||||||
\(349\) | −28.9256 | −1.54835 | −0.774176 | − | 0.632971i | \(-0.781835\pi\) | ||||
−0.774176 | + | 0.632971i | \(0.781835\pi\) | |||||||
\(350\) | 45.7636 | 2.44617 | ||||||||
\(351\) | 2.42528 | 0.129452 | ||||||||
\(352\) | −13.2602 | −0.706769 | ||||||||
\(353\) | −24.9696 | −1.32900 | −0.664499 | − | 0.747289i | \(-0.731355\pi\) | ||||
−0.664499 | + | 0.747289i | \(0.731355\pi\) | |||||||
\(354\) | −0.362367 | −0.0192596 | ||||||||
\(355\) | −21.1137 | −1.12060 | ||||||||
\(356\) | 2.63082 | 0.139433 | ||||||||
\(357\) | 3.85230 | 0.203885 | ||||||||
\(358\) | 13.9907 | 0.739432 | ||||||||
\(359\) | 10.3710 | 0.547358 | 0.273679 | − | 0.961821i | \(-0.411759\pi\) | ||||
0.273679 | + | 0.961821i | \(0.411759\pi\) | |||||||
\(360\) | −8.39361 | −0.442382 | ||||||||
\(361\) | −15.9205 | −0.837920 | ||||||||
\(362\) | −32.5606 | −1.71135 | ||||||||
\(363\) | 12.0435 | 0.632122 | ||||||||
\(364\) | −4.66321 | −0.244419 | ||||||||
\(365\) | 18.2406 | 0.954754 | ||||||||
\(366\) | −12.0747 | −0.631153 | ||||||||
\(367\) | −24.3395 | −1.27051 | −0.635255 | − | 0.772303i | \(-0.719105\pi\) | ||||
−0.635255 | + | 0.772303i | \(0.719105\pi\) | |||||||
\(368\) | 34.5498 | 1.80103 | ||||||||
\(369\) | 4.24448 | 0.220959 | ||||||||
\(370\) | 4.26375 | 0.221662 | ||||||||
\(371\) | 30.6806 | 1.59286 | ||||||||
\(372\) | −0.367726 | −0.0190657 | ||||||||
\(373\) | 4.47354 | 0.231631 | 0.115816 | − | 0.993271i | \(-0.463052\pi\) | ||||
0.115816 | + | 0.993271i | \(0.463052\pi\) | |||||||
\(374\) | −7.58871 | −0.392403 | ||||||||
\(375\) | −8.89571 | −0.459373 | ||||||||
\(376\) | 26.2399 | 1.35322 | ||||||||
\(377\) | −2.45727 | −0.126556 | ||||||||
\(378\) | 6.08995 | 0.313233 | ||||||||
\(379\) | 0.986729 | 0.0506849 | 0.0253424 | − | 0.999679i | \(-0.491932\pi\) | ||||
0.0253424 | + | 0.999679i | \(0.491932\pi\) | |||||||
\(380\) | −3.09852 | −0.158950 | ||||||||
\(381\) | 10.5579 | 0.540898 | ||||||||
\(382\) | 22.4280 | 1.14751 | ||||||||
\(383\) | 16.1312 | 0.824266 | 0.412133 | − | 0.911124i | \(-0.364784\pi\) | ||||
0.412133 | + | 0.911124i | \(0.364784\pi\) | |||||||
\(384\) | −13.6367 | −0.695893 | ||||||||
\(385\) | −65.4189 | −3.33406 | ||||||||
\(386\) | −1.88762 | −0.0960773 | ||||||||
\(387\) | 7.99270 | 0.406292 | ||||||||
\(388\) | −4.81681 | −0.244536 | ||||||||
\(389\) | −26.5216 | −1.34470 | −0.672348 | − | 0.740235i | \(-0.734714\pi\) | ||||
−0.672348 | + | 0.740235i | \(0.734714\pi\) | |||||||
\(390\) | 13.5632 | 0.686802 | ||||||||
\(391\) | 7.27500 | 0.367912 | ||||||||
\(392\) | 18.6024 | 0.939561 | ||||||||
\(393\) | −13.8248 | −0.697371 | ||||||||
\(394\) | −18.4062 | −0.927292 | ||||||||
\(395\) | −12.4622 | −0.627040 | ||||||||
\(396\) | −2.39595 | −0.120401 | ||||||||
\(397\) | −1.06167 | −0.0532835 | −0.0266417 | − | 0.999645i | \(-0.508481\pi\) | ||||
−0.0266417 | + | 0.999645i | \(0.508481\pi\) | |||||||
\(398\) | −18.9786 | −0.951310 | ||||||||
\(399\) | −6.76023 | −0.338435 | ||||||||
\(400\) | −35.6878 | −1.78439 | ||||||||
\(401\) | −12.6139 | −0.629907 | −0.314953 | − | 0.949107i | \(-0.601989\pi\) | ||||
−0.314953 | + | 0.949107i | \(0.601989\pi\) | |||||||
\(402\) | −4.24750 | −0.211846 | ||||||||
\(403\) | −1.78683 | −0.0890083 | ||||||||
\(404\) | 7.85539 | 0.390820 | ||||||||
\(405\) | −3.53760 | −0.175785 | ||||||||
\(406\) | −6.17029 | −0.306226 | ||||||||
\(407\) | −3.65986 | −0.181412 | ||||||||
\(408\) | −2.37268 | −0.117465 | ||||||||
\(409\) | −10.4223 | −0.515351 | −0.257675 | − | 0.966232i | \(-0.582957\pi\) | ||||
−0.257675 | + | 0.966232i | \(0.582957\pi\) | |||||||
\(410\) | 23.7370 | 1.17229 | ||||||||
\(411\) | 15.3289 | 0.756120 | ||||||||
\(412\) | −4.59151 | −0.226208 | ||||||||
\(413\) | −0.883029 | −0.0434510 | ||||||||
\(414\) | 11.5007 | 0.565231 | ||||||||
\(415\) | 12.0882 | 0.593385 | ||||||||
\(416\) | 6.69940 | 0.328465 | ||||||||
\(417\) | −8.01914 | −0.392699 | ||||||||
\(418\) | 13.3171 | 0.651360 | ||||||||
\(419\) | 2.42233 | 0.118338 | 0.0591692 | − | 0.998248i | \(-0.481155\pi\) | ||||
0.0591692 | + | 0.998248i | \(0.481155\pi\) | |||||||
\(420\) | 6.80194 | 0.331900 | ||||||||
\(421\) | 4.98654 | 0.243029 | 0.121515 | − | 0.992590i | \(-0.461225\pi\) | ||||
0.121515 | + | 0.992590i | \(0.461225\pi\) | |||||||
\(422\) | 21.8965 | 1.06591 | ||||||||
\(423\) | 11.0591 | 0.537714 | ||||||||
\(424\) | −18.8966 | −0.917700 | ||||||||
\(425\) | −7.51462 | −0.364513 | ||||||||
\(426\) | −9.43518 | −0.457136 | ||||||||
\(427\) | −29.4240 | −1.42393 | ||||||||
\(428\) | −2.82285 | −0.136448 | ||||||||
\(429\) | −11.6422 | −0.562092 | ||||||||
\(430\) | 44.6988 | 2.15557 | ||||||||
\(431\) | −8.26742 | −0.398228 | −0.199114 | − | 0.979976i | \(-0.563806\pi\) | ||||
−0.199114 | + | 0.979976i | \(0.563806\pi\) | |||||||
\(432\) | −4.74912 | −0.228492 | ||||||||
\(433\) | 2.46995 | 0.118698 | 0.0593490 | − | 0.998237i | \(-0.481098\pi\) | ||||
0.0593490 | + | 0.998237i | \(0.481098\pi\) | |||||||
\(434\) | −4.48678 | −0.215372 | ||||||||
\(435\) | 3.58427 | 0.171853 | ||||||||
\(436\) | 0.380050 | 0.0182011 | ||||||||
\(437\) | −12.7666 | −0.610708 | ||||||||
\(438\) | 8.15122 | 0.389480 | ||||||||
\(439\) | 15.7951 | 0.753861 | 0.376930 | − | 0.926242i | \(-0.376980\pi\) | ||||
0.376930 | + | 0.926242i | \(0.376980\pi\) | |||||||
\(440\) | 40.2924 | 1.92087 | ||||||||
\(441\) | 7.84022 | 0.373344 | ||||||||
\(442\) | 3.83402 | 0.182366 | ||||||||
\(443\) | 10.3206 | 0.490347 | 0.245174 | − | 0.969479i | \(-0.421155\pi\) | ||||
0.245174 | + | 0.969479i | \(0.421155\pi\) | |||||||
\(444\) | 0.380534 | 0.0180593 | ||||||||
\(445\) | −18.6464 | −0.883926 | ||||||||
\(446\) | −34.0557 | −1.61259 | ||||||||
\(447\) | −4.63856 | −0.219396 | ||||||||
\(448\) | −19.7677 | −0.933934 | ||||||||
\(449\) | 25.0616 | 1.18273 | 0.591364 | − | 0.806405i | \(-0.298590\pi\) | ||||
0.591364 | + | 0.806405i | \(0.298590\pi\) | |||||||
\(450\) | −11.8796 | −0.560008 | ||||||||
\(451\) | −20.3751 | −0.959424 | ||||||||
\(452\) | −2.97231 | −0.139806 | ||||||||
\(453\) | 11.1849 | 0.525514 | ||||||||
\(454\) | 6.16527 | 0.289350 | ||||||||
\(455\) | 33.0514 | 1.54948 | ||||||||
\(456\) | 4.16372 | 0.194984 | ||||||||
\(457\) | −23.3835 | −1.09383 | −0.546916 | − | 0.837187i | \(-0.684198\pi\) | ||||
−0.546916 | + | 0.837187i | \(0.684198\pi\) | |||||||
\(458\) | −45.6534 | −2.13324 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 12.8453 | 0.598916 | ||||||||
\(461\) | −17.9057 | −0.833952 | −0.416976 | − | 0.908917i | \(-0.636910\pi\) | ||||
−0.416976 | + | 0.908917i | \(0.636910\pi\) | |||||||
\(462\) | −29.2340 | −1.36009 | ||||||||
\(463\) | 21.4086 | 0.994943 | 0.497471 | − | 0.867480i | \(-0.334262\pi\) | ||||
0.497471 | + | 0.867480i | \(0.334262\pi\) | |||||||
\(464\) | 4.81177 | 0.223381 | ||||||||
\(465\) | 2.60633 | 0.120866 | ||||||||
\(466\) | −6.04937 | −0.280232 | ||||||||
\(467\) | −32.4640 | −1.50225 | −0.751127 | − | 0.660158i | \(-0.770489\pi\) | ||||
−0.751127 | + | 0.660158i | \(0.770489\pi\) | |||||||
\(468\) | 1.21050 | 0.0559554 | ||||||||
\(469\) | −10.3505 | −0.477941 | ||||||||
\(470\) | 61.8477 | 2.85282 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 0.543870 | 0.0250336 | ||||||||
\(473\) | −38.3679 | −1.76416 | ||||||||
\(474\) | −5.56902 | −0.255793 | ||||||||
\(475\) | 13.1871 | 0.605064 | ||||||||
\(476\) | 1.92275 | 0.0881293 | ||||||||
\(477\) | −7.96423 | −0.364657 | ||||||||
\(478\) | −25.9522 | −1.18703 | ||||||||
\(479\) | −23.7640 | −1.08580 | −0.542901 | − | 0.839796i | \(-0.682674\pi\) | ||||
−0.542901 | + | 0.839796i | \(0.682674\pi\) | |||||||
\(480\) | −9.77199 | −0.446028 | ||||||||
\(481\) | 1.84906 | 0.0843099 | ||||||||
\(482\) | 43.9751 | 2.00301 | ||||||||
\(483\) | 28.0255 | 1.27520 | ||||||||
\(484\) | 6.01115 | 0.273234 | ||||||||
\(485\) | 34.1401 | 1.55022 | ||||||||
\(486\) | −1.58086 | −0.0717093 | ||||||||
\(487\) | 14.2473 | 0.645608 | 0.322804 | − | 0.946466i | \(-0.395375\pi\) | ||||
0.322804 | + | 0.946466i | \(0.395375\pi\) | |||||||
\(488\) | 18.1226 | 0.820373 | ||||||||
\(489\) | 12.6969 | 0.574174 | ||||||||
\(490\) | 43.8461 | 1.98076 | ||||||||
\(491\) | −13.8647 | −0.625704 | −0.312852 | − | 0.949802i | \(-0.601284\pi\) | ||||
−0.312852 | + | 0.949802i | \(0.601284\pi\) | |||||||
\(492\) | 2.11850 | 0.0955092 | ||||||||
\(493\) | 1.01319 | 0.0456319 | ||||||||
\(494\) | −6.72816 | −0.302714 | ||||||||
\(495\) | 16.9818 | 0.763275 | ||||||||
\(496\) | 3.49892 | 0.157106 | ||||||||
\(497\) | −22.9920 | −1.03133 | ||||||||
\(498\) | 5.40189 | 0.242064 | ||||||||
\(499\) | −28.3173 | −1.26766 | −0.633829 | − | 0.773473i | \(-0.718518\pi\) | ||||
−0.633829 | + | 0.773473i | \(0.718518\pi\) | |||||||
\(500\) | −4.44001 | −0.198563 | ||||||||
\(501\) | 12.7587 | 0.570017 | ||||||||
\(502\) | −39.1167 | −1.74587 | ||||||||
\(503\) | −22.3818 | −0.997953 | −0.498977 | − | 0.866615i | \(-0.666291\pi\) | ||||
−0.498977 | + | 0.866615i | \(0.666291\pi\) | |||||||
\(504\) | −9.14029 | −0.407141 | ||||||||
\(505\) | −55.6766 | −2.47758 | ||||||||
\(506\) | −55.2078 | −2.45429 | ||||||||
\(507\) | −7.11803 | −0.316123 | ||||||||
\(508\) | 5.26964 | 0.233803 | ||||||||
\(509\) | −23.7814 | −1.05409 | −0.527047 | − | 0.849836i | \(-0.676701\pi\) | ||||
−0.527047 | + | 0.849836i | \(0.676701\pi\) | |||||||
\(510\) | −5.59245 | −0.247638 | ||||||||
\(511\) | 19.8632 | 0.878697 | ||||||||
\(512\) | 9.41771 | 0.416208 | ||||||||
\(513\) | 1.75486 | 0.0774788 | ||||||||
\(514\) | 28.8551 | 1.27274 | ||||||||
\(515\) | 32.5433 | 1.43403 | ||||||||
\(516\) | 3.98930 | 0.175619 | ||||||||
\(517\) | −53.0880 | −2.33481 | ||||||||
\(518\) | 4.64305 | 0.204004 | ||||||||
\(519\) | −18.0809 | −0.793664 | ||||||||
\(520\) | −20.3568 | −0.892706 | ||||||||
\(521\) | 30.9013 | 1.35381 | 0.676906 | − | 0.736070i | \(-0.263321\pi\) | ||||
0.676906 | + | 0.736070i | \(0.263321\pi\) | |||||||
\(522\) | 1.60171 | 0.0701051 | ||||||||
\(523\) | 21.0092 | 0.918668 | 0.459334 | − | 0.888264i | \(-0.348088\pi\) | ||||
0.459334 | + | 0.888264i | \(0.348088\pi\) | |||||||
\(524\) | −6.90023 | −0.301438 | ||||||||
\(525\) | −28.9486 | −1.26342 | ||||||||
\(526\) | −47.2466 | −2.06005 | ||||||||
\(527\) | 0.736752 | 0.0320934 | ||||||||
\(528\) | 22.7975 | 0.992134 | ||||||||
\(529\) | 29.9256 | 1.30111 | ||||||||
\(530\) | −44.5396 | −1.93467 | ||||||||
\(531\) | 0.229221 | 0.00994736 | ||||||||
\(532\) | −3.37416 | −0.146288 | ||||||||
\(533\) | 10.2940 | 0.445884 | ||||||||
\(534\) | −8.33260 | −0.360587 | ||||||||
\(535\) | 20.0075 | 0.865000 | ||||||||
\(536\) | 6.37500 | 0.275358 | ||||||||
\(537\) | −8.85007 | −0.381909 | ||||||||
\(538\) | 10.1679 | 0.438368 | ||||||||
\(539\) | −37.6360 | −1.62110 | ||||||||
\(540\) | −1.76568 | −0.0759828 | ||||||||
\(541\) | 12.6476 | 0.543762 | 0.271881 | − | 0.962331i | \(-0.412354\pi\) | ||||
0.271881 | + | 0.962331i | \(0.412354\pi\) | |||||||
\(542\) | −15.9288 | −0.684201 | ||||||||
\(543\) | 20.5968 | 0.883892 | ||||||||
\(544\) | −2.76232 | −0.118434 | ||||||||
\(545\) | −2.69368 | −0.115385 | ||||||||
\(546\) | 14.7698 | 0.632090 | ||||||||
\(547\) | 27.0303 | 1.15573 | 0.577867 | − | 0.816131i | \(-0.303885\pi\) | ||||
0.577867 | + | 0.816131i | \(0.303885\pi\) | |||||||
\(548\) | 7.65095 | 0.326832 | ||||||||
\(549\) | 7.63803 | 0.325983 | ||||||||
\(550\) | 57.0263 | 2.43161 | ||||||||
\(551\) | −1.77801 | −0.0757456 | ||||||||
\(552\) | −17.2613 | −0.734688 | ||||||||
\(553\) | −13.5708 | −0.577089 | ||||||||
\(554\) | −22.3457 | −0.949379 | ||||||||
\(555\) | −2.69711 | −0.114486 | ||||||||
\(556\) | −4.00250 | −0.169744 | ||||||||
\(557\) | 30.6429 | 1.29838 | 0.649191 | − | 0.760626i | \(-0.275108\pi\) | ||||
0.649191 | + | 0.760626i | \(0.275108\pi\) | |||||||
\(558\) | 1.16470 | 0.0493058 | ||||||||
\(559\) | 19.3845 | 0.819878 | ||||||||
\(560\) | −64.7205 | −2.73494 | ||||||||
\(561\) | 4.80037 | 0.202672 | ||||||||
\(562\) | 47.8903 | 2.02013 | ||||||||
\(563\) | −34.0002 | −1.43294 | −0.716469 | − | 0.697619i | \(-0.754243\pi\) | ||||
−0.716469 | + | 0.697619i | \(0.754243\pi\) | |||||||
\(564\) | 5.51982 | 0.232426 | ||||||||
\(565\) | 21.0668 | 0.886288 | ||||||||
\(566\) | −36.1359 | −1.51891 | ||||||||
\(567\) | −3.85230 | −0.161781 | ||||||||
\(568\) | 14.1611 | 0.594186 | ||||||||
\(569\) | −31.7725 | −1.33197 | −0.665986 | − | 0.745964i | \(-0.731989\pi\) | ||||
−0.665986 | + | 0.745964i | \(0.731989\pi\) | |||||||
\(570\) | 9.81394 | 0.411061 | ||||||||
\(571\) | 26.3491 | 1.10267 | 0.551337 | − | 0.834283i | \(-0.314118\pi\) | ||||
0.551337 | + | 0.834283i | \(0.314118\pi\) | |||||||
\(572\) | −5.81085 | −0.242964 | ||||||||
\(573\) | −14.1872 | −0.592678 | ||||||||
\(574\) | 25.8487 | 1.07890 | ||||||||
\(575\) | −54.6688 | −2.27985 | ||||||||
\(576\) | 5.13139 | 0.213808 | ||||||||
\(577\) | 6.91871 | 0.288030 | 0.144015 | − | 0.989576i | \(-0.453999\pi\) | ||||
0.144015 | + | 0.989576i | \(0.453999\pi\) | |||||||
\(578\) | −1.58086 | −0.0657551 | ||||||||
\(579\) | 1.19405 | 0.0496229 | ||||||||
\(580\) | 1.78897 | 0.0742831 | ||||||||
\(581\) | 13.1635 | 0.546115 | ||||||||
\(582\) | 15.2563 | 0.632394 | ||||||||
\(583\) | 38.2312 | 1.58338 | ||||||||
\(584\) | −12.2340 | −0.506247 | ||||||||
\(585\) | −8.57966 | −0.354725 | ||||||||
\(586\) | 29.2722 | 1.20922 | ||||||||
\(587\) | 7.67877 | 0.316937 | 0.158468 | − | 0.987364i | \(-0.449344\pi\) | ||||
0.158468 | + | 0.987364i | \(0.449344\pi\) | |||||||
\(588\) | 3.91320 | 0.161378 | ||||||||
\(589\) | −1.29289 | −0.0532727 | ||||||||
\(590\) | 1.28191 | 0.0527753 | ||||||||
\(591\) | 11.6432 | 0.478936 | ||||||||
\(592\) | −3.62078 | −0.148813 | ||||||||
\(593\) | −17.8218 | −0.731855 | −0.365927 | − | 0.930643i | \(-0.619248\pi\) | ||||
−0.365927 | + | 0.930643i | \(0.619248\pi\) | |||||||
\(594\) | 7.58871 | 0.311369 | ||||||||
\(595\) | −13.6279 | −0.558690 | ||||||||
\(596\) | −2.31519 | −0.0948340 | ||||||||
\(597\) | 12.0052 | 0.491341 | ||||||||
\(598\) | 27.8925 | 1.14061 | ||||||||
\(599\) | −9.41239 | −0.384580 | −0.192290 | − | 0.981338i | \(-0.561591\pi\) | ||||
−0.192290 | + | 0.981338i | \(0.561591\pi\) | |||||||
\(600\) | 17.8298 | 0.727899 | ||||||||
\(601\) | 26.7330 | 1.09046 | 0.545231 | − | 0.838286i | \(-0.316442\pi\) | ||||
0.545231 | + | 0.838286i | \(0.316442\pi\) | |||||||
\(602\) | 48.6751 | 1.98385 | ||||||||
\(603\) | 2.68683 | 0.109416 | ||||||||
\(604\) | 5.58260 | 0.227153 | ||||||||
\(605\) | −42.6052 | −1.73215 | ||||||||
\(606\) | −24.8804 | −1.01070 | ||||||||
\(607\) | −41.0397 | −1.66575 | −0.832875 | − | 0.553461i | \(-0.813307\pi\) | ||||
−0.832875 | + | 0.553461i | \(0.813307\pi\) | |||||||
\(608\) | 4.84748 | 0.196591 | ||||||||
\(609\) | 3.90312 | 0.158162 | ||||||||
\(610\) | 42.7153 | 1.72949 | ||||||||
\(611\) | 26.8215 | 1.08508 | ||||||||
\(612\) | −0.499118 | −0.0201757 | ||||||||
\(613\) | −45.4730 | −1.83664 | −0.918319 | − | 0.395841i | \(-0.870453\pi\) | ||||
−0.918319 | + | 0.395841i | \(0.870453\pi\) | |||||||
\(614\) | 11.4824 | 0.463394 | ||||||||
\(615\) | −15.0153 | −0.605474 | ||||||||
\(616\) | 43.8768 | 1.76785 | ||||||||
\(617\) | 2.09276 | 0.0842514 | 0.0421257 | − | 0.999112i | \(-0.486587\pi\) | ||||
0.0421257 | + | 0.999112i | \(0.486587\pi\) | |||||||
\(618\) | 14.5427 | 0.584994 | ||||||||
\(619\) | 17.4035 | 0.699505 | 0.349752 | − | 0.936842i | \(-0.386266\pi\) | ||||
0.349752 | + | 0.936842i | \(0.386266\pi\) | |||||||
\(620\) | 1.30087 | 0.0522442 | ||||||||
\(621\) | −7.27500 | −0.291936 | ||||||||
\(622\) | 39.6219 | 1.58869 | ||||||||
\(623\) | −20.3052 | −0.813511 | ||||||||
\(624\) | −11.5179 | −0.461086 | ||||||||
\(625\) | −6.10361 | −0.244144 | ||||||||
\(626\) | 18.7043 | 0.747573 | ||||||||
\(627\) | −8.42395 | −0.336420 | ||||||||
\(628\) | 0.499118 | 0.0199170 | ||||||||
\(629\) | −0.762412 | −0.0303994 | ||||||||
\(630\) | −21.5438 | −0.858326 | ||||||||
\(631\) | 34.0744 | 1.35648 | 0.678240 | − | 0.734840i | \(-0.262743\pi\) | ||||
0.678240 | + | 0.734840i | \(0.262743\pi\) | |||||||
\(632\) | 8.35843 | 0.332481 | ||||||||
\(633\) | −13.8510 | −0.550529 | ||||||||
\(634\) | −5.74918 | −0.228329 | ||||||||
\(635\) | −37.3496 | −1.48218 | ||||||||
\(636\) | −3.97509 | −0.157623 | ||||||||
\(637\) | 19.0147 | 0.753390 | ||||||||
\(638\) | −7.68882 | −0.304403 | ||||||||
\(639\) | 5.96838 | 0.236106 | ||||||||
\(640\) | 48.2410 | 1.90689 | ||||||||
\(641\) | 25.3528 | 1.00137 | 0.500687 | − | 0.865628i | \(-0.333081\pi\) | ||||
0.500687 | + | 0.865628i | \(0.333081\pi\) | |||||||
\(642\) | 8.94082 | 0.352866 | ||||||||
\(643\) | 28.8439 | 1.13749 | 0.568747 | − | 0.822513i | \(-0.307428\pi\) | ||||
0.568747 | + | 0.822513i | \(0.307428\pi\) | |||||||
\(644\) | 13.9880 | 0.551205 | ||||||||
\(645\) | −28.2750 | −1.11333 | ||||||||
\(646\) | 2.77418 | 0.109149 | ||||||||
\(647\) | −30.0805 | −1.18259 | −0.591294 | − | 0.806456i | \(-0.701383\pi\) | ||||
−0.591294 | + | 0.806456i | \(0.701383\pi\) | |||||||
\(648\) | 2.37268 | 0.0932078 | ||||||||
\(649\) | −1.10035 | −0.0431924 | ||||||||
\(650\) | −28.8112 | −1.13007 | ||||||||
\(651\) | 2.83819 | 0.111237 | ||||||||
\(652\) | 6.33726 | 0.248186 | ||||||||
\(653\) | −5.84435 | −0.228707 | −0.114354 | − | 0.993440i | \(-0.536480\pi\) | ||||
−0.114354 | + | 0.993440i | \(0.536480\pi\) | |||||||
\(654\) | −1.20373 | −0.0470697 | ||||||||
\(655\) | 48.9068 | 1.91095 | ||||||||
\(656\) | −20.1575 | −0.787019 | ||||||||
\(657\) | −5.15619 | −0.201162 | ||||||||
\(658\) | 67.3496 | 2.62556 | ||||||||
\(659\) | −5.79259 | −0.225647 | −0.112824 | − | 0.993615i | \(-0.535990\pi\) | ||||
−0.112824 | + | 0.993615i | \(0.535990\pi\) | |||||||
\(660\) | 8.47592 | 0.329925 | ||||||||
\(661\) | 10.1149 | 0.393424 | 0.196712 | − | 0.980461i | \(-0.436974\pi\) | ||||
0.196712 | + | 0.980461i | \(0.436974\pi\) | |||||||
\(662\) | 27.8948 | 1.08416 | ||||||||
\(663\) | −2.42528 | −0.0941900 | ||||||||
\(664\) | −8.10759 | −0.314636 | ||||||||
\(665\) | 23.9150 | 0.927384 | ||||||||
\(666\) | −1.20527 | −0.0467031 | ||||||||
\(667\) | 7.37097 | 0.285405 | ||||||||
\(668\) | 6.36811 | 0.246389 | ||||||||
\(669\) | 21.5425 | 0.832882 | ||||||||
\(670\) | 15.0260 | 0.580504 | ||||||||
\(671\) | −36.6654 | −1.41545 | ||||||||
\(672\) | −10.6413 | −0.410497 | ||||||||
\(673\) | −41.0567 | −1.58262 | −0.791309 | − | 0.611416i | \(-0.790600\pi\) | ||||
−0.791309 | + | 0.611416i | \(0.790600\pi\) | |||||||
\(674\) | 27.6479 | 1.06496 | ||||||||
\(675\) | 7.51462 | 0.289238 | ||||||||
\(676\) | −3.55274 | −0.136644 | ||||||||
\(677\) | −0.224724 | −0.00863685 | −0.00431843 | − | 0.999991i | \(-0.501375\pi\) | ||||
−0.00431843 | + | 0.999991i | \(0.501375\pi\) | |||||||
\(678\) | 9.41421 | 0.361550 | ||||||||
\(679\) | 37.1771 | 1.42673 | ||||||||
\(680\) | 8.39361 | 0.321880 | ||||||||
\(681\) | −3.89994 | −0.149446 | ||||||||
\(682\) | −5.59100 | −0.214090 | ||||||||
\(683\) | 26.8739 | 1.02830 | 0.514151 | − | 0.857699i | \(-0.328107\pi\) | ||||
0.514151 | + | 0.857699i | \(0.328107\pi\) | |||||||
\(684\) | 0.875880 | 0.0334901 | ||||||||
\(685\) | −54.2276 | −2.07193 | ||||||||
\(686\) | 5.11691 | 0.195364 | ||||||||
\(687\) | 28.8788 | 1.10180 | ||||||||
\(688\) | −37.9583 | −1.44715 | ||||||||
\(689\) | −19.3155 | −0.735861 | ||||||||
\(690\) | −40.6851 | −1.54885 | ||||||||
\(691\) | 37.4828 | 1.42591 | 0.712956 | − | 0.701209i | \(-0.247356\pi\) | ||||
0.712956 | + | 0.701209i | \(0.247356\pi\) | |||||||
\(692\) | −9.02451 | −0.343061 | ||||||||
\(693\) | 18.4925 | 0.702471 | ||||||||
\(694\) | 18.1371 | 0.688473 | ||||||||
\(695\) | 28.3685 | 1.07608 | ||||||||
\(696\) | −2.40398 | −0.0911228 | ||||||||
\(697\) | −4.24448 | −0.160771 | ||||||||
\(698\) | 45.7273 | 1.73080 | ||||||||
\(699\) | 3.82664 | 0.144737 | ||||||||
\(700\) | −14.4488 | −0.546112 | ||||||||
\(701\) | −25.0402 | −0.945756 | −0.472878 | − | 0.881128i | \(-0.656785\pi\) | ||||
−0.472878 | + | 0.881128i | \(0.656785\pi\) | |||||||
\(702\) | −3.83402 | −0.144706 | ||||||||
\(703\) | 1.33792 | 0.0504607 | ||||||||
\(704\) | −24.6326 | −0.928375 | ||||||||
\(705\) | −39.1228 | −1.47345 | ||||||||
\(706\) | 39.4735 | 1.48560 | ||||||||
\(707\) | −60.6295 | −2.28021 | ||||||||
\(708\) | 0.114409 | 0.00429974 | ||||||||
\(709\) | −8.84718 | −0.332263 | −0.166131 | − | 0.986104i | \(-0.553128\pi\) | ||||
−0.166131 | + | 0.986104i | \(0.553128\pi\) | |||||||
\(710\) | 33.3779 | 1.25265 | ||||||||
\(711\) | 3.52278 | 0.132114 | ||||||||
\(712\) | 12.5062 | 0.468691 | ||||||||
\(713\) | 5.35987 | 0.200729 | ||||||||
\(714\) | −6.08995 | −0.227911 | ||||||||
\(715\) | 41.1855 | 1.54025 | ||||||||
\(716\) | −4.41723 | −0.165080 | ||||||||
\(717\) | 16.4165 | 0.613087 | ||||||||
\(718\) | −16.3950 | −0.611857 | ||||||||
\(719\) | 15.6770 | 0.584655 | 0.292327 | − | 0.956318i | \(-0.405570\pi\) | ||||
0.292327 | + | 0.956318i | \(0.405570\pi\) | |||||||
\(720\) | 16.8005 | 0.626117 | ||||||||
\(721\) | 35.4383 | 1.31979 | ||||||||
\(722\) | 25.1681 | 0.936658 | ||||||||
\(723\) | −27.8172 | −1.03453 | ||||||||
\(724\) | 10.2802 | 0.382061 | ||||||||
\(725\) | −7.61375 | −0.282768 | ||||||||
\(726\) | −19.0391 | −0.706609 | ||||||||
\(727\) | 26.7565 | 0.992343 | 0.496172 | − | 0.868225i | \(-0.334739\pi\) | ||||
0.496172 | + | 0.868225i | \(0.334739\pi\) | |||||||
\(728\) | −22.1677 | −0.821591 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −28.8358 | −1.06726 | ||||||||
\(731\) | −7.99270 | −0.295621 | ||||||||
\(732\) | 3.81228 | 0.140906 | ||||||||
\(733\) | 4.26635 | 0.157581 | 0.0787906 | − | 0.996891i | \(-0.474894\pi\) | ||||
0.0787906 | + | 0.996891i | \(0.474894\pi\) | |||||||
\(734\) | 38.4773 | 1.42022 | ||||||||
\(735\) | −27.7356 | −1.02304 | ||||||||
\(736\) | −20.0959 | −0.740744 | ||||||||
\(737\) | −12.8978 | −0.475096 | ||||||||
\(738\) | −6.70993 | −0.246996 | ||||||||
\(739\) | −30.5678 | −1.12445 | −0.562227 | − | 0.826983i | \(-0.690055\pi\) | ||||
−0.562227 | + | 0.826983i | \(0.690055\pi\) | |||||||
\(740\) | −1.34618 | −0.0494864 | ||||||||
\(741\) | 4.25601 | 0.156348 | ||||||||
\(742\) | −48.5017 | −1.78055 | ||||||||
\(743\) | 7.08018 | 0.259747 | 0.129873 | − | 0.991531i | \(-0.458543\pi\) | ||||
0.129873 | + | 0.991531i | \(0.458543\pi\) | |||||||
\(744\) | −1.74808 | −0.0640877 | ||||||||
\(745\) | 16.4094 | 0.601193 | ||||||||
\(746\) | −7.07204 | −0.258926 | ||||||||
\(747\) | −3.41706 | −0.125024 | ||||||||
\(748\) | 2.39595 | 0.0876047 | ||||||||
\(749\) | 21.7873 | 0.796092 | ||||||||
\(750\) | 14.0629 | 0.513504 | ||||||||
\(751\) | −16.6583 | −0.607869 | −0.303934 | − | 0.952693i | \(-0.598300\pi\) | ||||
−0.303934 | + | 0.952693i | \(0.598300\pi\) | |||||||
\(752\) | −52.5212 | −1.91525 | ||||||||
\(753\) | 24.7440 | 0.901720 | ||||||||
\(754\) | 3.88460 | 0.141469 | ||||||||
\(755\) | −39.5678 | −1.44002 | ||||||||
\(756\) | −1.92275 | −0.0699299 | ||||||||
\(757\) | −18.1079 | −0.658142 | −0.329071 | − | 0.944305i | \(-0.606736\pi\) | ||||
−0.329071 | + | 0.944305i | \(0.606736\pi\) | |||||||
\(758\) | −1.55988 | −0.0566574 | ||||||||
\(759\) | 34.9227 | 1.26761 | ||||||||
\(760\) | −14.7296 | −0.534298 | ||||||||
\(761\) | −16.4803 | −0.597411 | −0.298706 | − | 0.954345i | \(-0.596555\pi\) | ||||
−0.298706 | + | 0.954345i | \(0.596555\pi\) | |||||||
\(762\) | −16.6906 | −0.604635 | ||||||||
\(763\) | −2.93331 | −0.106193 | ||||||||
\(764\) | −7.08109 | −0.256185 | ||||||||
\(765\) | 3.53760 | 0.127902 | ||||||||
\(766\) | −25.5012 | −0.921395 | ||||||||
\(767\) | 0.555925 | 0.0200733 | ||||||||
\(768\) | 11.2949 | 0.407568 | ||||||||
\(769\) | 33.7503 | 1.21707 | 0.608534 | − | 0.793528i | \(-0.291758\pi\) | ||||
0.608534 | + | 0.793528i | \(0.291758\pi\) | |||||||
\(770\) | 103.418 | 3.72693 | ||||||||
\(771\) | −18.2528 | −0.657358 | ||||||||
\(772\) | 0.595970 | 0.0214494 | ||||||||
\(773\) | 22.7886 | 0.819649 | 0.409824 | − | 0.912164i | \(-0.365590\pi\) | ||||
0.409824 | + | 0.912164i | \(0.365590\pi\) | |||||||
\(774\) | −12.6353 | −0.454168 | ||||||||
\(775\) | −5.53641 | −0.198874 | ||||||||
\(776\) | −22.8979 | −0.821987 | ||||||||
\(777\) | −2.93704 | −0.105366 | ||||||||
\(778\) | 41.9269 | 1.50315 | ||||||||
\(779\) | 7.44845 | 0.266868 | ||||||||
\(780\) | −4.28227 | −0.153330 | ||||||||
\(781\) | −28.6504 | −1.02519 | ||||||||
\(782\) | −11.5007 | −0.411266 | ||||||||
\(783\) | −1.01319 | −0.0362085 | ||||||||
\(784\) | −37.2341 | −1.32979 | ||||||||
\(785\) | −3.53760 | −0.126262 | ||||||||
\(786\) | 21.8551 | 0.779547 | ||||||||
\(787\) | −39.8451 | −1.42032 | −0.710162 | − | 0.704039i | \(-0.751378\pi\) | ||||
−0.710162 | + | 0.704039i | \(0.751378\pi\) | |||||||
\(788\) | 5.81132 | 0.207020 | ||||||||
\(789\) | 29.8867 | 1.06399 | ||||||||
\(790\) | 19.7010 | 0.700929 | ||||||||
\(791\) | 22.9409 | 0.815685 | ||||||||
\(792\) | −11.3898 | −0.404717 | ||||||||
\(793\) | 18.5243 | 0.657819 | ||||||||
\(794\) | 1.67834 | 0.0595622 | ||||||||
\(795\) | 28.1743 | 0.999238 | ||||||||
\(796\) | 5.99203 | 0.212382 | ||||||||
\(797\) | −54.9131 | −1.94512 | −0.972561 | − | 0.232648i | \(-0.925261\pi\) | ||||
−0.972561 | + | 0.232648i | \(0.925261\pi\) | |||||||
\(798\) | 10.6870 | 0.378315 | ||||||||
\(799\) | −11.0591 | −0.391244 | ||||||||
\(800\) | 20.7578 | 0.733899 | ||||||||
\(801\) | 5.27093 | 0.186239 | ||||||||
\(802\) | 19.9408 | 0.704133 | ||||||||
\(803\) | 24.7516 | 0.873466 | ||||||||
\(804\) | 1.34105 | 0.0472951 | ||||||||
\(805\) | −99.1429 | −3.49433 | ||||||||
\(806\) | 2.82473 | 0.0994967 | ||||||||
\(807\) | −6.43186 | −0.226412 | ||||||||
\(808\) | 37.3425 | 1.31371 | ||||||||
\(809\) | 48.0642 | 1.68985 | 0.844923 | − | 0.534887i | \(-0.179646\pi\) | ||||
0.844923 | + | 0.534887i | \(0.179646\pi\) | |||||||
\(810\) | 5.59245 | 0.196499 | ||||||||
\(811\) | 52.4064 | 1.84024 | 0.920119 | − | 0.391638i | \(-0.128092\pi\) | ||||
0.920119 | + | 0.391638i | \(0.128092\pi\) | |||||||
\(812\) | 1.94812 | 0.0683656 | ||||||||
\(813\) | 10.0760 | 0.353382 | ||||||||
\(814\) | 5.78572 | 0.202790 | ||||||||
\(815\) | −44.9166 | −1.57336 | ||||||||
\(816\) | 4.74912 | 0.166252 | ||||||||
\(817\) | 14.0260 | 0.490709 | ||||||||
\(818\) | 16.4762 | 0.576078 | ||||||||
\(819\) | −9.34290 | −0.326467 | ||||||||
\(820\) | −7.49440 | −0.261716 | ||||||||
\(821\) | 27.0103 | 0.942666 | 0.471333 | − | 0.881955i | \(-0.343773\pi\) | ||||
0.471333 | + | 0.881955i | \(0.343773\pi\) | |||||||
\(822\) | −24.2329 | −0.845219 | ||||||||
\(823\) | 21.4070 | 0.746202 | 0.373101 | − | 0.927791i | \(-0.378294\pi\) | ||||
0.373101 | + | 0.927791i | \(0.378294\pi\) | |||||||
\(824\) | −21.8269 | −0.760376 | ||||||||
\(825\) | −36.0729 | −1.25590 | ||||||||
\(826\) | 1.39595 | 0.0485712 | ||||||||
\(827\) | 2.54490 | 0.0884948 | 0.0442474 | − | 0.999021i | \(-0.485911\pi\) | ||||
0.0442474 | + | 0.999021i | \(0.485911\pi\) | |||||||
\(828\) | −3.63108 | −0.126189 | ||||||||
\(829\) | −4.45015 | −0.154560 | −0.0772800 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772800 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(830\) | −19.1097 | −0.663308 | ||||||||
\(831\) | 14.1352 | 0.490344 | ||||||||
\(832\) | 12.4450 | 0.431454 | ||||||||
\(833\) | −7.84022 | −0.271648 | ||||||||
\(834\) | 12.6771 | 0.438973 | ||||||||
\(835\) | −45.1352 | −1.56197 | ||||||||
\(836\) | −4.20455 | −0.145417 | ||||||||
\(837\) | −0.736752 | −0.0254659 | ||||||||
\(838\) | −3.82936 | −0.132283 | ||||||||
\(839\) | −3.53469 | −0.122031 | −0.0610156 | − | 0.998137i | \(-0.519434\pi\) | ||||
−0.0610156 | + | 0.998137i | \(0.519434\pi\) | |||||||
\(840\) | 32.3347 | 1.11565 | ||||||||
\(841\) | −27.9734 | −0.964601 | ||||||||
\(842\) | −7.88303 | −0.271667 | ||||||||
\(843\) | −30.2938 | −1.04337 | ||||||||
\(844\) | −6.91330 | −0.237966 | ||||||||
\(845\) | 25.1807 | 0.866244 | ||||||||
\(846\) | −17.4830 | −0.601077 | ||||||||
\(847\) | −46.3953 | −1.59416 | ||||||||
\(848\) | 37.8231 | 1.29885 | ||||||||
\(849\) | 22.8584 | 0.784498 | ||||||||
\(850\) | 11.8796 | 0.407466 | ||||||||
\(851\) | −5.54654 | −0.190133 | ||||||||
\(852\) | 2.97893 | 0.102056 | ||||||||
\(853\) | −10.1369 | −0.347082 | −0.173541 | − | 0.984827i | \(-0.555521\pi\) | ||||
−0.173541 | + | 0.984827i | \(0.555521\pi\) | |||||||
\(854\) | 46.5152 | 1.59172 | ||||||||
\(855\) | −6.20798 | −0.212308 | ||||||||
\(856\) | −13.4191 | −0.458656 | ||||||||
\(857\) | 12.2463 | 0.418325 | 0.209162 | − | 0.977881i | \(-0.432926\pi\) | ||||
0.209162 | + | 0.977881i | \(0.432926\pi\) | |||||||
\(858\) | 18.4047 | 0.628327 | ||||||||
\(859\) | −24.7164 | −0.843314 | −0.421657 | − | 0.906755i | \(-0.638551\pi\) | ||||
−0.421657 | + | 0.906755i | \(0.638551\pi\) | |||||||
\(860\) | −14.1126 | −0.481234 | ||||||||
\(861\) | −16.3510 | −0.557241 | ||||||||
\(862\) | 13.0696 | 0.445153 | ||||||||
\(863\) | 45.0279 | 1.53277 | 0.766385 | − | 0.642382i | \(-0.222054\pi\) | ||||
0.766385 | + | 0.642382i | \(0.222054\pi\) | |||||||
\(864\) | 2.76232 | 0.0939761 | ||||||||
\(865\) | 63.9630 | 2.17481 | ||||||||
\(866\) | −3.90464 | −0.132685 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 1.41659 | 0.0480823 | ||||||||
\(869\) | −16.9106 | −0.573654 | ||||||||
\(870\) | −5.66623 | −0.192103 | ||||||||
\(871\) | 6.51631 | 0.220797 | ||||||||
\(872\) | 1.80666 | 0.0611813 | ||||||||
\(873\) | −9.65063 | −0.326624 | ||||||||
\(874\) | 20.1822 | 0.682671 | ||||||||
\(875\) | 34.2690 | 1.15850 | ||||||||
\(876\) | −2.57355 | −0.0869522 | ||||||||
\(877\) | −21.4479 | −0.724244 | −0.362122 | − | 0.932131i | \(-0.617948\pi\) | ||||
−0.362122 | + | 0.932131i | \(0.617948\pi\) | |||||||
\(878\) | −24.9699 | −0.842693 | ||||||||
\(879\) | −18.5166 | −0.624551 | ||||||||
\(880\) | −80.6485 | −2.71866 | ||||||||
\(881\) | 3.83436 | 0.129183 | 0.0645915 | − | 0.997912i | \(-0.479426\pi\) | ||||
0.0645915 | + | 0.997912i | \(0.479426\pi\) | |||||||
\(882\) | −12.3943 | −0.417338 | ||||||||
\(883\) | 33.3115 | 1.12102 | 0.560510 | − | 0.828147i | \(-0.310605\pi\) | ||||
0.560510 | + | 0.828147i | \(0.310605\pi\) | |||||||
\(884\) | −1.21050 | −0.0407135 | ||||||||
\(885\) | −0.810893 | −0.0272579 | ||||||||
\(886\) | −16.3154 | −0.548128 | ||||||||
\(887\) | 53.4388 | 1.79430 | 0.897150 | − | 0.441727i | \(-0.145634\pi\) | ||||
0.897150 | + | 0.441727i | \(0.145634\pi\) | |||||||
\(888\) | 1.80896 | 0.0607048 | ||||||||
\(889\) | −40.6722 | −1.36410 | ||||||||
\(890\) | 29.4774 | 0.988085 | ||||||||
\(891\) | −4.80037 | −0.160818 | ||||||||
\(892\) | 10.7523 | 0.360013 | ||||||||
\(893\) | 19.4072 | 0.649437 | ||||||||
\(894\) | 7.33292 | 0.245249 | ||||||||
\(895\) | 31.3080 | 1.04651 | ||||||||
\(896\) | 52.5325 | 1.75499 | ||||||||
\(897\) | −17.6439 | −0.589112 | ||||||||
\(898\) | −39.6188 | −1.32210 | ||||||||
\(899\) | 0.746471 | 0.0248962 | ||||||||
\(900\) | 3.75068 | 0.125023 | ||||||||
\(901\) | 7.96423 | 0.265327 | ||||||||
\(902\) | 32.2101 | 1.07248 | ||||||||
\(903\) | −30.7903 | −1.02464 | ||||||||
\(904\) | −14.1296 | −0.469944 | ||||||||
\(905\) | −72.8631 | −2.42205 | ||||||||
\(906\) | −17.6818 | −0.587439 | ||||||||
\(907\) | 26.7813 | 0.889258 | 0.444629 | − | 0.895715i | \(-0.353336\pi\) | ||||
0.444629 | + | 0.895715i | \(0.353336\pi\) | |||||||
\(908\) | −1.94653 | −0.0645980 | ||||||||
\(909\) | 15.7385 | 0.522014 | ||||||||
\(910\) | −52.2497 | −1.73206 | ||||||||
\(911\) | 53.1814 | 1.76198 | 0.880989 | − | 0.473138i | \(-0.156879\pi\) | ||||
0.880989 | + | 0.473138i | \(0.156879\pi\) | |||||||
\(912\) | −8.33401 | −0.275967 | ||||||||
\(913\) | 16.4031 | 0.542864 | ||||||||
\(914\) | 36.9660 | 1.22273 | ||||||||
\(915\) | −27.0203 | −0.893264 | ||||||||
\(916\) | 14.4139 | 0.476250 | ||||||||
\(917\) | 53.2574 | 1.75872 | ||||||||
\(918\) | 1.58086 | 0.0521762 | ||||||||
\(919\) | −24.2882 | −0.801194 | −0.400597 | − | 0.916254i | \(-0.631197\pi\) | ||||
−0.400597 | + | 0.916254i | \(0.631197\pi\) | |||||||
\(920\) | 61.0635 | 2.01320 | ||||||||
\(921\) | −7.26341 | −0.239338 | ||||||||
\(922\) | 28.3064 | 0.932222 | ||||||||
\(923\) | 14.4750 | 0.476450 | ||||||||
\(924\) | 9.22993 | 0.303642 | ||||||||
\(925\) | 5.72924 | 0.188376 | ||||||||
\(926\) | −33.8440 | −1.11218 | ||||||||
\(927\) | −9.19924 | −0.302143 | ||||||||
\(928\) | −2.79876 | −0.0918739 | ||||||||
\(929\) | −21.3849 | −0.701615 | −0.350807 | − | 0.936448i | \(-0.614093\pi\) | ||||
−0.350807 | + | 0.936448i | \(0.614093\pi\) | |||||||
\(930\) | −4.12025 | −0.135108 | ||||||||
\(931\) | 13.7585 | 0.450915 | ||||||||
\(932\) | 1.90994 | 0.0625623 | ||||||||
\(933\) | −25.0635 | −0.820543 | ||||||||
\(934\) | 51.3210 | 1.67927 | ||||||||
\(935\) | −16.9818 | −0.555364 | ||||||||
\(936\) | 5.75442 | 0.188089 | ||||||||
\(937\) | −40.6432 | −1.32776 | −0.663878 | − | 0.747841i | \(-0.731090\pi\) | ||||
−0.663878 | + | 0.747841i | \(0.731090\pi\) | |||||||
\(938\) | 16.3627 | 0.534260 | ||||||||
\(939\) | −11.8317 | −0.386113 | ||||||||
\(940\) | −19.5269 | −0.636898 | ||||||||
\(941\) | 44.7569 | 1.45903 | 0.729517 | − | 0.683963i | \(-0.239745\pi\) | ||||
0.729517 | + | 0.683963i | \(0.239745\pi\) | |||||||
\(942\) | −1.58086 | −0.0515072 | ||||||||
\(943\) | −30.8786 | −1.00554 | ||||||||
\(944\) | −1.08860 | −0.0354309 | ||||||||
\(945\) | 13.6279 | 0.443316 | ||||||||
\(946\) | 60.6543 | 1.97204 | ||||||||
\(947\) | −19.5829 | −0.636359 | −0.318180 | − | 0.948030i | \(-0.603072\pi\) | ||||
−0.318180 | + | 0.948030i | \(0.603072\pi\) | |||||||
\(948\) | 1.75828 | 0.0571064 | ||||||||
\(949\) | −12.5052 | −0.405936 | ||||||||
\(950\) | −20.8469 | −0.676363 | ||||||||
\(951\) | 3.63674 | 0.117929 | ||||||||
\(952\) | 9.14029 | 0.296239 | ||||||||
\(953\) | −16.1190 | −0.522146 | −0.261073 | − | 0.965319i | \(-0.584076\pi\) | ||||
−0.261073 | + | 0.965319i | \(0.584076\pi\) | |||||||
\(954\) | 12.5903 | 0.407627 | ||||||||
\(955\) | 50.1886 | 1.62407 | ||||||||
\(956\) | 8.19379 | 0.265006 | ||||||||
\(957\) | 4.86369 | 0.157221 | ||||||||
\(958\) | 37.5675 | 1.21375 | ||||||||
\(959\) | −59.0516 | −1.90688 | ||||||||
\(960\) | −18.1528 | −0.585879 | ||||||||
\(961\) | −30.4572 | −0.982490 | ||||||||
\(962\) | −2.92311 | −0.0942447 | ||||||||
\(963\) | −5.65567 | −0.182251 | ||||||||
\(964\) | −13.8841 | −0.447176 | ||||||||
\(965\) | −4.22406 | −0.135977 | ||||||||
\(966\) | −44.3043 | −1.42547 | ||||||||
\(967\) | 12.3387 | 0.396786 | 0.198393 | − | 0.980123i | \(-0.436428\pi\) | ||||
0.198393 | + | 0.980123i | \(0.436428\pi\) | |||||||
\(968\) | 28.5755 | 0.918451 | ||||||||
\(969\) | −1.75486 | −0.0563741 | ||||||||
\(970\) | −53.9707 | −1.73289 | ||||||||
\(971\) | −24.6652 | −0.791545 | −0.395772 | − | 0.918349i | \(-0.629523\pi\) | ||||
−0.395772 | + | 0.918349i | \(0.629523\pi\) | |||||||
\(972\) | 0.499118 | 0.0160092 | ||||||||
\(973\) | 30.8921 | 0.990357 | ||||||||
\(974\) | −22.5230 | −0.721684 | ||||||||
\(975\) | 18.2250 | 0.583668 | ||||||||
\(976\) | −36.2739 | −1.16110 | ||||||||
\(977\) | −48.4016 | −1.54850 | −0.774252 | − | 0.632878i | \(-0.781873\pi\) | ||||
−0.774252 | + | 0.632878i | \(0.781873\pi\) | |||||||
\(978\) | −20.0720 | −0.641833 | ||||||||
\(979\) | −25.3024 | −0.808668 | ||||||||
\(980\) | −13.8433 | −0.442209 | ||||||||
\(981\) | 0.761443 | 0.0243110 | ||||||||
\(982\) | 21.9181 | 0.699435 | ||||||||
\(983\) | −38.7403 | −1.23562 | −0.617812 | − | 0.786326i | \(-0.711981\pi\) | ||||
−0.617812 | + | 0.786326i | \(0.711981\pi\) | |||||||
\(984\) | 10.0708 | 0.321046 | ||||||||
\(985\) | −41.1889 | −1.31239 | ||||||||
\(986\) | −1.60171 | −0.0510090 | ||||||||
\(987\) | −42.6032 | −1.35607 | ||||||||
\(988\) | 2.12425 | 0.0675815 | ||||||||
\(989\) | −58.1469 | −1.84896 | ||||||||
\(990\) | −26.8458 | −0.853216 | ||||||||
\(991\) | −30.7620 | −0.977187 | −0.488594 | − | 0.872512i | \(-0.662490\pi\) | ||||
−0.488594 | + | 0.872512i | \(0.662490\pi\) | |||||||
\(992\) | −2.03515 | −0.0646160 | ||||||||
\(993\) | −17.6453 | −0.559957 | ||||||||
\(994\) | 36.3471 | 1.15286 | ||||||||
\(995\) | −42.4697 | −1.34638 | ||||||||
\(996\) | −1.70552 | −0.0540413 | ||||||||
\(997\) | −26.0982 | −0.826537 | −0.413269 | − | 0.910609i | \(-0.635613\pi\) | ||||
−0.413269 | + | 0.910609i | \(0.635613\pi\) | |||||||
\(998\) | 44.7658 | 1.41704 | ||||||||
\(999\) | 0.762412 | 0.0241217 |
(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 | 8007.2.a.e.1.12 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.12 | ✓ | 46 | 1.1 | even | 1 | trivial |