Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36585 | −1.67291 | −0.836456 | − | 0.548035i | \(-0.815376\pi\) | ||||
−0.836456 | + | 0.548035i | \(0.815376\pi\) | |||||||
\(3\) | 2.45510 | 1.41745 | 0.708727 | − | 0.705483i | \(-0.249270\pi\) | ||||
0.708727 | + | 0.705483i | \(0.249270\pi\) | |||||||
\(4\) | 3.59727 | 1.79863 | ||||||||
\(5\) | 1.09940 | 0.491667 | 0.245833 | − | 0.969312i | \(-0.420938\pi\) | ||||
0.245833 | + | 0.969312i | \(0.420938\pi\) | |||||||
\(6\) | −5.80841 | −2.37127 | ||||||||
\(7\) | 2.69770 | 1.01963 | 0.509817 | − | 0.860283i | \(-0.329713\pi\) | ||||
0.509817 | + | 0.860283i | \(0.329713\pi\) | |||||||
\(8\) | −3.77890 | −1.33604 | ||||||||
\(9\) | 3.02752 | 1.00917 | ||||||||
\(10\) | −2.60102 | −0.822515 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 8.83165 | 2.54948 | ||||||||
\(13\) | −0.515099 | −0.142863 | −0.0714313 | − | 0.997446i | \(-0.522757\pi\) | ||||
−0.0714313 | + | 0.997446i | \(0.522757\pi\) | |||||||
\(14\) | −6.38237 | −1.70576 | ||||||||
\(15\) | 2.69914 | 0.696915 | ||||||||
\(16\) | 1.74579 | 0.436447 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −7.16267 | −1.68826 | ||||||||
\(19\) | −4.85774 | −1.11444 | −0.557221 | − | 0.830364i | \(-0.688132\pi\) | ||||
−0.557221 | + | 0.830364i | \(0.688132\pi\) | |||||||
\(20\) | 3.95483 | 0.884328 | ||||||||
\(21\) | 6.62313 | 1.44528 | ||||||||
\(22\) | −2.36585 | −0.504402 | ||||||||
\(23\) | −7.58610 | −1.58181 | −0.790906 | − | 0.611938i | \(-0.790390\pi\) | ||||
−0.790906 | + | 0.611938i | \(0.790390\pi\) | |||||||
\(24\) | −9.27757 | −1.89378 | ||||||||
\(25\) | −3.79132 | −0.758264 | ||||||||
\(26\) | 1.21865 | 0.238997 | ||||||||
\(27\) | 0.0675680 | 0.0130035 | ||||||||
\(28\) | 9.70434 | 1.83395 | ||||||||
\(29\) | −5.74572 | −1.06695 | −0.533477 | − | 0.845815i | \(-0.679115\pi\) | ||||
−0.533477 | + | 0.845815i | \(0.679115\pi\) | |||||||
\(30\) | −6.38577 | −1.16588 | ||||||||
\(31\) | −4.06124 | −0.729420 | −0.364710 | − | 0.931121i | \(-0.618832\pi\) | ||||
−0.364710 | + | 0.931121i | \(0.618832\pi\) | |||||||
\(32\) | 3.42751 | 0.605905 | ||||||||
\(33\) | 2.45510 | 0.427378 | ||||||||
\(34\) | 2.36585 | 0.405741 | ||||||||
\(35\) | 2.96585 | 0.501321 | ||||||||
\(36\) | 10.8908 | 1.81513 | ||||||||
\(37\) | −5.18985 | −0.853206 | −0.426603 | − | 0.904439i | \(-0.640290\pi\) | ||||
−0.426603 | + | 0.904439i | \(0.640290\pi\) | |||||||
\(38\) | 11.4927 | 1.86436 | ||||||||
\(39\) | −1.26462 | −0.202501 | ||||||||
\(40\) | −4.15452 | −0.656887 | ||||||||
\(41\) | 5.65407 | 0.883017 | 0.441508 | − | 0.897257i | \(-0.354444\pi\) | ||||
0.441508 | + | 0.897257i | \(0.354444\pi\) | |||||||
\(42\) | −15.6694 | −2.41783 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 3.59727 | 0.542308 | ||||||||
\(45\) | 3.32846 | 0.496177 | ||||||||
\(46\) | 17.9476 | 2.64623 | ||||||||
\(47\) | 4.43739 | 0.647259 | 0.323630 | − | 0.946184i | \(-0.395097\pi\) | ||||
0.323630 | + | 0.946184i | \(0.395097\pi\) | |||||||
\(48\) | 4.28609 | 0.618643 | ||||||||
\(49\) | 0.277587 | 0.0396552 | ||||||||
\(50\) | 8.96971 | 1.26851 | ||||||||
\(51\) | −2.45510 | −0.343783 | ||||||||
\(52\) | −1.85295 | −0.256957 | ||||||||
\(53\) | −1.94057 | −0.266558 | −0.133279 | − | 0.991079i | \(-0.542551\pi\) | ||||
−0.133279 | + | 0.991079i | \(0.542551\pi\) | |||||||
\(54\) | −0.159856 | −0.0217536 | ||||||||
\(55\) | 1.09940 | 0.148243 | ||||||||
\(56\) | −10.1943 | −1.36227 | ||||||||
\(57\) | −11.9262 | −1.57967 | ||||||||
\(58\) | 13.5935 | 1.78492 | ||||||||
\(59\) | 2.90607 | 0.378338 | 0.189169 | − | 0.981945i | \(-0.439421\pi\) | ||||
0.189169 | + | 0.981945i | \(0.439421\pi\) | |||||||
\(60\) | 9.70952 | 1.25349 | ||||||||
\(61\) | −9.75564 | −1.24908 | −0.624541 | − | 0.780992i | \(-0.714714\pi\) | ||||
−0.624541 | + | 0.780992i | \(0.714714\pi\) | |||||||
\(62\) | 9.60830 | 1.22026 | ||||||||
\(63\) | 8.16735 | 1.02899 | ||||||||
\(64\) | −11.6006 | −1.45007 | ||||||||
\(65\) | −0.566300 | −0.0702408 | ||||||||
\(66\) | −5.80841 | −0.714966 | ||||||||
\(67\) | −4.84702 | −0.592158 | −0.296079 | − | 0.955163i | \(-0.595679\pi\) | ||||
−0.296079 | + | 0.955163i | \(0.595679\pi\) | |||||||
\(68\) | −3.59727 | −0.436233 | ||||||||
\(69\) | −18.6246 | −2.24214 | ||||||||
\(70\) | −7.01677 | −0.838665 | ||||||||
\(71\) | −14.9495 | −1.77418 | −0.887091 | − | 0.461594i | \(-0.847278\pi\) | ||||
−0.887091 | + | 0.461594i | \(0.847278\pi\) | |||||||
\(72\) | −11.4407 | −1.34830 | ||||||||
\(73\) | 14.4159 | 1.68725 | 0.843627 | − | 0.536929i | \(-0.180416\pi\) | ||||
0.843627 | + | 0.536929i | \(0.180416\pi\) | |||||||
\(74\) | 12.2784 | 1.42734 | ||||||||
\(75\) | −9.30807 | −1.07480 | ||||||||
\(76\) | −17.4746 | −2.00447 | ||||||||
\(77\) | 2.69770 | 0.307431 | ||||||||
\(78\) | 2.99190 | 0.338766 | ||||||||
\(79\) | 9.29512 | 1.04578 | 0.522891 | − | 0.852399i | \(-0.324853\pi\) | ||||
0.522891 | + | 0.852399i | \(0.324853\pi\) | |||||||
\(80\) | 1.91932 | 0.214586 | ||||||||
\(81\) | −8.91668 | −0.990742 | ||||||||
\(82\) | −13.3767 | −1.47721 | ||||||||
\(83\) | −15.8395 | −1.73861 | −0.869303 | − | 0.494280i | \(-0.835432\pi\) | ||||
−0.869303 | + | 0.494280i | \(0.835432\pi\) | |||||||
\(84\) | 23.8251 | 2.59954 | ||||||||
\(85\) | −1.09940 | −0.119247 | ||||||||
\(86\) | −2.36585 | −0.255117 | ||||||||
\(87\) | −14.1063 | −1.51236 | ||||||||
\(88\) | −3.77890 | −0.402832 | ||||||||
\(89\) | 7.64563 | 0.810435 | 0.405217 | − | 0.914220i | \(-0.367196\pi\) | ||||
0.405217 | + | 0.914220i | \(0.367196\pi\) | |||||||
\(90\) | −7.87465 | −0.830061 | ||||||||
\(91\) | −1.38958 | −0.145668 | ||||||||
\(92\) | −27.2892 | −2.84510 | ||||||||
\(93\) | −9.97076 | −1.03392 | ||||||||
\(94\) | −10.4982 | −1.08281 | ||||||||
\(95\) | −5.34060 | −0.547934 | ||||||||
\(96\) | 8.41490 | 0.858842 | ||||||||
\(97\) | 6.14325 | 0.623753 | 0.311876 | − | 0.950123i | \(-0.399043\pi\) | ||||
0.311876 | + | 0.950123i | \(0.399043\pi\) | |||||||
\(98\) | −0.656729 | −0.0663397 | ||||||||
\(99\) | 3.02752 | 0.304277 | ||||||||
\(100\) | −13.6384 | −1.36384 | ||||||||
\(101\) | 2.68999 | 0.267664 | 0.133832 | − | 0.991004i | \(-0.457272\pi\) | ||||
0.133832 | + | 0.991004i | \(0.457272\pi\) | |||||||
\(102\) | 5.80841 | 0.575118 | ||||||||
\(103\) | −9.72591 | −0.958322 | −0.479161 | − | 0.877727i | \(-0.659059\pi\) | ||||
−0.479161 | + | 0.877727i | \(0.659059\pi\) | |||||||
\(104\) | 1.94650 | 0.190870 | ||||||||
\(105\) | 7.28147 | 0.710598 | ||||||||
\(106\) | 4.59111 | 0.445928 | ||||||||
\(107\) | −18.5163 | −1.79004 | −0.895019 | − | 0.446029i | \(-0.852838\pi\) | ||||
−0.895019 | + | 0.446029i | \(0.852838\pi\) | |||||||
\(108\) | 0.243060 | 0.0233885 | ||||||||
\(109\) | 8.69013 | 0.832364 | 0.416182 | − | 0.909281i | \(-0.363368\pi\) | ||||
0.416182 | + | 0.909281i | \(0.363368\pi\) | |||||||
\(110\) | −2.60102 | −0.247998 | ||||||||
\(111\) | −12.7416 | −1.20938 | ||||||||
\(112\) | 4.70961 | 0.445016 | ||||||||
\(113\) | 0.909959 | 0.0856018 | 0.0428009 | − | 0.999084i | \(-0.486372\pi\) | ||||
0.0428009 | + | 0.999084i | \(0.486372\pi\) | |||||||
\(114\) | 28.2157 | 2.64265 | ||||||||
\(115\) | −8.34016 | −0.777724 | ||||||||
\(116\) | −20.6689 | −1.91906 | ||||||||
\(117\) | −1.55947 | −0.144173 | ||||||||
\(118\) | −6.87533 | −0.632925 | ||||||||
\(119\) | −2.69770 | −0.247298 | ||||||||
\(120\) | −10.1998 | −0.931107 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 23.0804 | 2.08960 | ||||||||
\(123\) | 13.8813 | 1.25163 | ||||||||
\(124\) | −14.6094 | −1.31196 | ||||||||
\(125\) | −9.66518 | −0.864480 | ||||||||
\(126\) | −19.3227 | −1.72141 | ||||||||
\(127\) | −0.696723 | −0.0618242 | −0.0309121 | − | 0.999522i | \(-0.509841\pi\) | ||||
−0.0309121 | + | 0.999522i | \(0.509841\pi\) | |||||||
\(128\) | 20.5902 | 1.81994 | ||||||||
\(129\) | 2.45510 | 0.216160 | ||||||||
\(130\) | 1.33978 | 0.117507 | ||||||||
\(131\) | −1.80562 | −0.157758 | −0.0788789 | − | 0.996884i | \(-0.525134\pi\) | ||||
−0.0788789 | + | 0.996884i | \(0.525134\pi\) | |||||||
\(132\) | 8.83165 | 0.768696 | ||||||||
\(133\) | −13.1047 | −1.13632 | ||||||||
\(134\) | 11.4673 | 0.990628 | ||||||||
\(135\) | 0.0742843 | 0.00639337 | ||||||||
\(136\) | 3.77890 | 0.324038 | ||||||||
\(137\) | −5.52702 | −0.472205 | −0.236103 | − | 0.971728i | \(-0.575870\pi\) | ||||
−0.236103 | + | 0.971728i | \(0.575870\pi\) | |||||||
\(138\) | 44.0632 | 3.75091 | ||||||||
\(139\) | 7.19577 | 0.610337 | 0.305169 | − | 0.952298i | \(-0.401287\pi\) | ||||
0.305169 | + | 0.952298i | \(0.401287\pi\) | |||||||
\(140\) | 10.6690 | 0.901692 | ||||||||
\(141\) | 10.8942 | 0.917460 | ||||||||
\(142\) | 35.3684 | 2.96805 | ||||||||
\(143\) | −0.515099 | −0.0430747 | ||||||||
\(144\) | 5.28541 | 0.440451 | ||||||||
\(145\) | −6.31684 | −0.524585 | ||||||||
\(146\) | −34.1059 | −2.82263 | ||||||||
\(147\) | 0.681503 | 0.0562094 | ||||||||
\(148\) | −18.6693 | −1.53460 | ||||||||
\(149\) | −11.5691 | −0.947781 | −0.473891 | − | 0.880584i | \(-0.657151\pi\) | ||||
−0.473891 | + | 0.880584i | \(0.657151\pi\) | |||||||
\(150\) | 22.0215 | 1.79805 | ||||||||
\(151\) | 8.41378 | 0.684704 | 0.342352 | − | 0.939572i | \(-0.388776\pi\) | ||||
0.342352 | + | 0.939572i | \(0.388776\pi\) | |||||||
\(152\) | 18.3569 | 1.48894 | ||||||||
\(153\) | −3.02752 | −0.244761 | ||||||||
\(154\) | −6.38237 | −0.514306 | ||||||||
\(155\) | −4.46493 | −0.358632 | ||||||||
\(156\) | −4.54917 | −0.364225 | ||||||||
\(157\) | 4.37885 | 0.349471 | 0.174735 | − | 0.984615i | \(-0.444093\pi\) | ||||
0.174735 | + | 0.984615i | \(0.444093\pi\) | |||||||
\(158\) | −21.9909 | −1.74950 | ||||||||
\(159\) | −4.76430 | −0.377833 | ||||||||
\(160\) | 3.76821 | 0.297903 | ||||||||
\(161\) | −20.4650 | −1.61287 | ||||||||
\(162\) | 21.0956 | 1.65742 | ||||||||
\(163\) | 11.6055 | 0.909014 | 0.454507 | − | 0.890743i | \(-0.349816\pi\) | ||||
0.454507 | + | 0.890743i | \(0.349816\pi\) | |||||||
\(164\) | 20.3392 | 1.58822 | ||||||||
\(165\) | 2.69914 | 0.210128 | ||||||||
\(166\) | 37.4738 | 2.90853 | ||||||||
\(167\) | −5.80665 | −0.449332 | −0.224666 | − | 0.974436i | \(-0.572129\pi\) | ||||
−0.224666 | + | 0.974436i | \(0.572129\pi\) | |||||||
\(168\) | −25.0281 | −1.93096 | ||||||||
\(169\) | −12.7347 | −0.979590 | ||||||||
\(170\) | 2.60102 | 0.199489 | ||||||||
\(171\) | −14.7069 | −1.12467 | ||||||||
\(172\) | 3.59727 | 0.274289 | ||||||||
\(173\) | −11.0016 | −0.836436 | −0.418218 | − | 0.908347i | \(-0.637345\pi\) | ||||
−0.418218 | + | 0.908347i | \(0.637345\pi\) | |||||||
\(174\) | 33.3735 | 2.53004 | ||||||||
\(175\) | −10.2278 | −0.773152 | ||||||||
\(176\) | 1.74579 | 0.131594 | ||||||||
\(177\) | 7.13469 | 0.536276 | ||||||||
\(178\) | −18.0884 | −1.35579 | ||||||||
\(179\) | −6.29037 | −0.470165 | −0.235082 | − | 0.971975i | \(-0.575536\pi\) | ||||
−0.235082 | + | 0.971975i | \(0.575536\pi\) | |||||||
\(180\) | 11.9733 | 0.892441 | ||||||||
\(181\) | 1.17111 | 0.0870479 | 0.0435239 | − | 0.999052i | \(-0.486142\pi\) | ||||
0.0435239 | + | 0.999052i | \(0.486142\pi\) | |||||||
\(182\) | 3.28755 | 0.243689 | ||||||||
\(183\) | −23.9511 | −1.77052 | ||||||||
\(184\) | 28.6671 | 2.11337 | ||||||||
\(185\) | −5.70572 | −0.419493 | ||||||||
\(186\) | 23.5894 | 1.72966 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 15.9625 | 1.16418 | ||||||||
\(189\) | 0.182278 | 0.0132588 | ||||||||
\(190\) | 12.6351 | 0.916645 | ||||||||
\(191\) | −11.8307 | −0.856040 | −0.428020 | − | 0.903769i | \(-0.640789\pi\) | ||||
−0.428020 | + | 0.903769i | \(0.640789\pi\) | |||||||
\(192\) | −28.4806 | −2.05541 | ||||||||
\(193\) | 26.1116 | 1.87955 | 0.939777 | − | 0.341787i | \(-0.111032\pi\) | ||||
0.939777 | + | 0.341787i | \(0.111032\pi\) | |||||||
\(194\) | −14.5340 | −1.04348 | ||||||||
\(195\) | −1.39032 | −0.0995631 | ||||||||
\(196\) | 0.998552 | 0.0713252 | ||||||||
\(197\) | −2.34507 | −0.167079 | −0.0835395 | − | 0.996504i | \(-0.526622\pi\) | ||||
−0.0835395 | + | 0.996504i | \(0.526622\pi\) | |||||||
\(198\) | −7.16267 | −0.509029 | ||||||||
\(199\) | 16.5562 | 1.17364 | 0.586819 | − | 0.809718i | \(-0.300380\pi\) | ||||
0.586819 | + | 0.809718i | \(0.300380\pi\) | |||||||
\(200\) | 14.3270 | 1.01307 | ||||||||
\(201\) | −11.8999 | −0.839356 | ||||||||
\(202\) | −6.36412 | −0.447778 | ||||||||
\(203\) | −15.5002 | −1.08790 | ||||||||
\(204\) | −8.83165 | −0.618339 | ||||||||
\(205\) | 6.21608 | 0.434150 | ||||||||
\(206\) | 23.0101 | 1.60319 | ||||||||
\(207\) | −22.9671 | −1.59632 | ||||||||
\(208\) | −0.899253 | −0.0623520 | ||||||||
\(209\) | −4.85774 | −0.336017 | ||||||||
\(210\) | −17.2269 | −1.18877 | ||||||||
\(211\) | 4.07452 | 0.280502 | 0.140251 | − | 0.990116i | \(-0.455209\pi\) | ||||
0.140251 | + | 0.990116i | \(0.455209\pi\) | |||||||
\(212\) | −6.98075 | −0.479440 | ||||||||
\(213\) | −36.7026 | −2.51482 | ||||||||
\(214\) | 43.8068 | 2.99457 | ||||||||
\(215\) | 1.09940 | 0.0749785 | ||||||||
\(216\) | −0.255332 | −0.0173732 | ||||||||
\(217\) | −10.9560 | −0.743742 | ||||||||
\(218\) | −20.5596 | −1.39247 | ||||||||
\(219\) | 35.3925 | 2.39160 | ||||||||
\(220\) | 3.95483 | 0.266635 | ||||||||
\(221\) | 0.515099 | 0.0346493 | ||||||||
\(222\) | 30.1448 | 2.02318 | ||||||||
\(223\) | −15.3677 | −1.02909 | −0.514547 | − | 0.857462i | \(-0.672040\pi\) | ||||
−0.514547 | + | 0.857462i | \(0.672040\pi\) | |||||||
\(224\) | 9.24641 | 0.617802 | ||||||||
\(225\) | −11.4783 | −0.765220 | ||||||||
\(226\) | −2.15283 | −0.143204 | ||||||||
\(227\) | 17.6543 | 1.17176 | 0.585879 | − | 0.810399i | \(-0.300749\pi\) | ||||
0.585879 | + | 0.810399i | \(0.300749\pi\) | |||||||
\(228\) | −42.9018 | −2.84124 | ||||||||
\(229\) | 11.6975 | 0.772995 | 0.386497 | − | 0.922291i | \(-0.373685\pi\) | ||||
0.386497 | + | 0.922291i | \(0.373685\pi\) | |||||||
\(230\) | 19.7316 | 1.30106 | ||||||||
\(231\) | 6.62313 | 0.435770 | ||||||||
\(232\) | 21.7125 | 1.42549 | ||||||||
\(233\) | −7.39715 | −0.484603 | −0.242302 | − | 0.970201i | \(-0.577902\pi\) | ||||
−0.242302 | + | 0.970201i | \(0.577902\pi\) | |||||||
\(234\) | 3.68948 | 0.241189 | ||||||||
\(235\) | 4.87846 | 0.318236 | ||||||||
\(236\) | 10.4539 | 0.680490 | ||||||||
\(237\) | 22.8205 | 1.48235 | ||||||||
\(238\) | 6.38237 | 0.413707 | ||||||||
\(239\) | −5.48879 | −0.355040 | −0.177520 | − | 0.984117i | \(-0.556807\pi\) | ||||
−0.177520 | + | 0.984117i | \(0.556807\pi\) | |||||||
\(240\) | 4.71212 | 0.304166 | ||||||||
\(241\) | 13.2782 | 0.855326 | 0.427663 | − | 0.903938i | \(-0.359337\pi\) | ||||
0.427663 | + | 0.903938i | \(0.359337\pi\) | |||||||
\(242\) | −2.36585 | −0.152083 | ||||||||
\(243\) | −22.0941 | −1.41733 | ||||||||
\(244\) | −35.0936 | −2.24664 | ||||||||
\(245\) | 0.305179 | 0.0194972 | ||||||||
\(246\) | −32.8411 | −2.09387 | ||||||||
\(247\) | 2.50221 | 0.159212 | ||||||||
\(248\) | 15.3470 | 0.974536 | ||||||||
\(249\) | −38.8875 | −2.46439 | ||||||||
\(250\) | 22.8664 | 1.44620 | ||||||||
\(251\) | 6.76490 | 0.426997 | 0.213498 | − | 0.976943i | \(-0.431514\pi\) | ||||
0.213498 | + | 0.976943i | \(0.431514\pi\) | |||||||
\(252\) | 29.3801 | 1.85077 | ||||||||
\(253\) | −7.58610 | −0.476934 | ||||||||
\(254\) | 1.64835 | 0.103426 | ||||||||
\(255\) | −2.69914 | −0.169027 | ||||||||
\(256\) | −25.5123 | −1.59452 | ||||||||
\(257\) | −15.1225 | −0.943316 | −0.471658 | − | 0.881782i | \(-0.656344\pi\) | ||||
−0.471658 | + | 0.881782i | \(0.656344\pi\) | |||||||
\(258\) | −5.80841 | −0.361616 | ||||||||
\(259\) | −14.0007 | −0.869958 | ||||||||
\(260\) | −2.03713 | −0.126337 | ||||||||
\(261\) | −17.3953 | −1.07674 | ||||||||
\(262\) | 4.27183 | 0.263915 | ||||||||
\(263\) | −5.51617 | −0.340142 | −0.170071 | − | 0.985432i | \(-0.554400\pi\) | ||||
−0.170071 | + | 0.985432i | \(0.554400\pi\) | |||||||
\(264\) | −9.27757 | −0.570995 | ||||||||
\(265\) | −2.13346 | −0.131058 | ||||||||
\(266\) | 31.0039 | 1.90097 | ||||||||
\(267\) | 18.7708 | 1.14875 | ||||||||
\(268\) | −17.4360 | −1.06507 | ||||||||
\(269\) | −25.5878 | −1.56011 | −0.780056 | − | 0.625709i | \(-0.784810\pi\) | ||||
−0.780056 | + | 0.625709i | \(0.784810\pi\) | |||||||
\(270\) | −0.175746 | −0.0106955 | ||||||||
\(271\) | 8.35581 | 0.507579 | 0.253790 | − | 0.967259i | \(-0.418323\pi\) | ||||
0.253790 | + | 0.967259i | \(0.418323\pi\) | |||||||
\(272\) | −1.74579 | −0.105854 | ||||||||
\(273\) | −3.41156 | −0.206477 | ||||||||
\(274\) | 13.0761 | 0.789957 | ||||||||
\(275\) | −3.79132 | −0.228625 | ||||||||
\(276\) | −66.9978 | −4.03279 | ||||||||
\(277\) | 6.54336 | 0.393153 | 0.196576 | − | 0.980489i | \(-0.437018\pi\) | ||||
0.196576 | + | 0.980489i | \(0.437018\pi\) | |||||||
\(278\) | −17.0241 | −1.02104 | ||||||||
\(279\) | −12.2955 | −0.736112 | ||||||||
\(280\) | −11.2077 | −0.669785 | ||||||||
\(281\) | 4.85109 | 0.289392 | 0.144696 | − | 0.989476i | \(-0.453780\pi\) | ||||
0.144696 | + | 0.989476i | \(0.453780\pi\) | |||||||
\(282\) | −25.7742 | −1.53483 | ||||||||
\(283\) | −12.9371 | −0.769031 | −0.384515 | − | 0.923119i | \(-0.625631\pi\) | ||||
−0.384515 | + | 0.923119i | \(0.625631\pi\) | |||||||
\(284\) | −53.7774 | −3.19110 | ||||||||
\(285\) | −13.1117 | −0.776671 | ||||||||
\(286\) | 1.21865 | 0.0720602 | ||||||||
\(287\) | 15.2530 | 0.900355 | ||||||||
\(288\) | 10.3769 | 0.611463 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 14.9447 | 0.877585 | ||||||||
\(291\) | 15.0823 | 0.884140 | ||||||||
\(292\) | 51.8578 | 3.03475 | ||||||||
\(293\) | 24.5242 | 1.43272 | 0.716359 | − | 0.697732i | \(-0.245807\pi\) | ||||
0.716359 | + | 0.697732i | \(0.245807\pi\) | |||||||
\(294\) | −1.61234 | −0.0940334 | ||||||||
\(295\) | 3.19493 | 0.186016 | ||||||||
\(296\) | 19.6119 | 1.13992 | ||||||||
\(297\) | 0.0675680 | 0.00392069 | ||||||||
\(298\) | 27.3709 | 1.58555 | ||||||||
\(299\) | 3.90759 | 0.225982 | ||||||||
\(300\) | −33.4836 | −1.93318 | ||||||||
\(301\) | 2.69770 | 0.155493 | ||||||||
\(302\) | −19.9058 | −1.14545 | ||||||||
\(303\) | 6.60420 | 0.379401 | ||||||||
\(304\) | −8.48058 | −0.486395 | ||||||||
\(305\) | −10.7254 | −0.614132 | ||||||||
\(306\) | 7.16267 | 0.409463 | ||||||||
\(307\) | 30.3334 | 1.73122 | 0.865610 | − | 0.500719i | \(-0.166931\pi\) | ||||
0.865610 | + | 0.500719i | \(0.166931\pi\) | |||||||
\(308\) | 9.70434 | 0.552956 | ||||||||
\(309\) | −23.8781 | −1.35838 | ||||||||
\(310\) | 10.5634 | 0.599959 | ||||||||
\(311\) | −2.26764 | −0.128586 | −0.0642931 | − | 0.997931i | \(-0.520479\pi\) | ||||
−0.0642931 | + | 0.997931i | \(0.520479\pi\) | |||||||
\(312\) | 4.77887 | 0.270550 | ||||||||
\(313\) | 5.79665 | 0.327646 | 0.163823 | − | 0.986490i | \(-0.447617\pi\) | ||||
0.163823 | + | 0.986490i | \(0.447617\pi\) | |||||||
\(314\) | −10.3597 | −0.584633 | ||||||||
\(315\) | 8.97918 | 0.505920 | ||||||||
\(316\) | 33.4370 | 1.88098 | ||||||||
\(317\) | −19.2754 | −1.08261 | −0.541307 | − | 0.840825i | \(-0.682070\pi\) | ||||
−0.541307 | + | 0.840825i | \(0.682070\pi\) | |||||||
\(318\) | 11.2716 | 0.632082 | ||||||||
\(319\) | −5.74572 | −0.321698 | ||||||||
\(320\) | −12.7537 | −0.712952 | ||||||||
\(321\) | −45.4594 | −2.53729 | ||||||||
\(322\) | 48.4173 | 2.69819 | ||||||||
\(323\) | 4.85774 | 0.270292 | ||||||||
\(324\) | −32.0757 | −1.78198 | ||||||||
\(325\) | 1.95290 | 0.108328 | ||||||||
\(326\) | −27.4569 | −1.52070 | ||||||||
\(327\) | 21.3352 | 1.17984 | ||||||||
\(328\) | −21.3661 | −1.17975 | ||||||||
\(329\) | 11.9707 | 0.659968 | ||||||||
\(330\) | −6.38577 | −0.351525 | ||||||||
\(331\) | −10.0549 | −0.552667 | −0.276334 | − | 0.961062i | \(-0.589119\pi\) | ||||
−0.276334 | + | 0.961062i | \(0.589119\pi\) | |||||||
\(332\) | −56.9787 | −3.12711 | ||||||||
\(333\) | −15.7124 | −0.861033 | ||||||||
\(334\) | 13.7377 | 0.751692 | ||||||||
\(335\) | −5.32882 | −0.291144 | ||||||||
\(336\) | 11.5626 | 0.630790 | ||||||||
\(337\) | −7.97201 | −0.434263 | −0.217132 | − | 0.976142i | \(-0.569670\pi\) | ||||
−0.217132 | + | 0.976142i | \(0.569670\pi\) | |||||||
\(338\) | 30.1284 | 1.63877 | ||||||||
\(339\) | 2.23404 | 0.121336 | ||||||||
\(340\) | −3.95483 | −0.214481 | ||||||||
\(341\) | −4.06124 | −0.219928 | ||||||||
\(342\) | 34.7944 | 1.88147 | ||||||||
\(343\) | −18.1351 | −0.979201 | ||||||||
\(344\) | −3.77890 | −0.203744 | ||||||||
\(345\) | −20.4759 | −1.10239 | ||||||||
\(346\) | 26.0282 | 1.39928 | ||||||||
\(347\) | 3.16925 | 0.170134 | 0.0850671 | − | 0.996375i | \(-0.472890\pi\) | ||||
0.0850671 | + | 0.996375i | \(0.472890\pi\) | |||||||
\(348\) | −50.7442 | −2.72017 | ||||||||
\(349\) | 7.57402 | 0.405428 | 0.202714 | − | 0.979238i | \(-0.435024\pi\) | ||||
0.202714 | + | 0.979238i | \(0.435024\pi\) | |||||||
\(350\) | 24.1976 | 1.29342 | ||||||||
\(351\) | −0.0348042 | −0.00185771 | ||||||||
\(352\) | 3.42751 | 0.182687 | ||||||||
\(353\) | 30.6821 | 1.63305 | 0.816523 | − | 0.577313i | \(-0.195899\pi\) | ||||
0.816523 | + | 0.577313i | \(0.195899\pi\) | |||||||
\(354\) | −16.8796 | −0.897142 | ||||||||
\(355\) | −16.4355 | −0.872306 | ||||||||
\(356\) | 27.5034 | 1.45767 | ||||||||
\(357\) | −6.62313 | −0.350533 | ||||||||
\(358\) | 14.8821 | 0.786544 | ||||||||
\(359\) | −3.07564 | −0.162326 | −0.0811631 | − | 0.996701i | \(-0.525863\pi\) | ||||
−0.0811631 | + | 0.996701i | \(0.525863\pi\) | |||||||
\(360\) | −12.5779 | −0.662914 | ||||||||
\(361\) | 4.59763 | 0.241980 | ||||||||
\(362\) | −2.77067 | −0.145623 | ||||||||
\(363\) | 2.45510 | 0.128859 | ||||||||
\(364\) | −4.99869 | −0.262003 | ||||||||
\(365\) | 15.8489 | 0.829567 | ||||||||
\(366\) | 56.6648 | 2.96192 | ||||||||
\(367\) | −6.81938 | −0.355969 | −0.177984 | − | 0.984033i | \(-0.556958\pi\) | ||||
−0.177984 | + | 0.984033i | \(0.556958\pi\) | |||||||
\(368\) | −13.2437 | −0.690377 | ||||||||
\(369\) | 17.1178 | 0.891117 | ||||||||
\(370\) | 13.4989 | 0.701774 | ||||||||
\(371\) | −5.23508 | −0.271792 | ||||||||
\(372\) | −35.8675 | −1.85964 | ||||||||
\(373\) | 14.6839 | 0.760303 | 0.380152 | − | 0.924924i | \(-0.375872\pi\) | ||||
0.380152 | + | 0.924924i | \(0.375872\pi\) | |||||||
\(374\) | 2.36585 | 0.122335 | ||||||||
\(375\) | −23.7290 | −1.22536 | ||||||||
\(376\) | −16.7684 | −0.864766 | ||||||||
\(377\) | 2.95961 | 0.152428 | ||||||||
\(378\) | −0.431243 | −0.0221808 | ||||||||
\(379\) | −12.6962 | −0.652161 | −0.326081 | − | 0.945342i | \(-0.605728\pi\) | ||||
−0.326081 | + | 0.945342i | \(0.605728\pi\) | |||||||
\(380\) | −19.2116 | −0.985532 | ||||||||
\(381\) | −1.71053 | −0.0876329 | ||||||||
\(382\) | 27.9897 | 1.43208 | ||||||||
\(383\) | −28.9038 | −1.47691 | −0.738457 | − | 0.674300i | \(-0.764445\pi\) | ||||
−0.738457 | + | 0.674300i | \(0.764445\pi\) | |||||||
\(384\) | 50.5511 | 2.57968 | ||||||||
\(385\) | 2.96585 | 0.151154 | ||||||||
\(386\) | −61.7763 | −3.14433 | ||||||||
\(387\) | 3.02752 | 0.153898 | ||||||||
\(388\) | 22.0989 | 1.12190 | ||||||||
\(389\) | 29.7565 | 1.50872 | 0.754358 | − | 0.656463i | \(-0.227948\pi\) | ||||
0.754358 | + | 0.656463i | \(0.227948\pi\) | |||||||
\(390\) | 3.28930 | 0.166560 | ||||||||
\(391\) | 7.58610 | 0.383646 | ||||||||
\(392\) | −1.04897 | −0.0529810 | ||||||||
\(393\) | −4.43298 | −0.223614 | ||||||||
\(394\) | 5.54809 | 0.279509 | ||||||||
\(395\) | 10.2191 | 0.514177 | ||||||||
\(396\) | 10.8908 | 0.547283 | ||||||||
\(397\) | −21.4070 | −1.07439 | −0.537193 | − | 0.843459i | \(-0.680515\pi\) | ||||
−0.537193 | + | 0.843459i | \(0.680515\pi\) | |||||||
\(398\) | −39.1695 | −1.96339 | ||||||||
\(399\) | −32.1734 | −1.61069 | ||||||||
\(400\) | −6.61884 | −0.330942 | ||||||||
\(401\) | −10.2067 | −0.509700 | −0.254850 | − | 0.966981i | \(-0.582026\pi\) | ||||
−0.254850 | + | 0.966981i | \(0.582026\pi\) | |||||||
\(402\) | 28.1535 | 1.40417 | ||||||||
\(403\) | 2.09194 | 0.104207 | ||||||||
\(404\) | 9.67660 | 0.481429 | ||||||||
\(405\) | −9.80300 | −0.487115 | ||||||||
\(406\) | 36.6713 | 1.81996 | ||||||||
\(407\) | −5.18985 | −0.257251 | ||||||||
\(408\) | 9.27757 | 0.459308 | ||||||||
\(409\) | −29.9332 | −1.48010 | −0.740051 | − | 0.672551i | \(-0.765199\pi\) | ||||
−0.740051 | + | 0.672551i | \(0.765199\pi\) | |||||||
\(410\) | −14.7063 | −0.726294 | ||||||||
\(411\) | −13.5694 | −0.669329 | ||||||||
\(412\) | −34.9867 | −1.72367 | ||||||||
\(413\) | 7.83969 | 0.385766 | ||||||||
\(414\) | 54.3368 | 2.67051 | ||||||||
\(415\) | −17.4139 | −0.854815 | ||||||||
\(416\) | −1.76551 | −0.0865612 | ||||||||
\(417\) | 17.6663 | 0.865124 | ||||||||
\(418\) | 11.4927 | 0.562126 | ||||||||
\(419\) | 23.1330 | 1.13012 | 0.565061 | − | 0.825049i | \(-0.308853\pi\) | ||||
0.565061 | + | 0.825049i | \(0.308853\pi\) | |||||||
\(420\) | 26.1934 | 1.27811 | ||||||||
\(421\) | 10.9290 | 0.532646 | 0.266323 | − | 0.963884i | \(-0.414191\pi\) | ||||
0.266323 | + | 0.963884i | \(0.414191\pi\) | |||||||
\(422\) | −9.63972 | −0.469254 | ||||||||
\(423\) | 13.4343 | 0.653197 | ||||||||
\(424\) | 7.33322 | 0.356132 | ||||||||
\(425\) | 3.79132 | 0.183906 | ||||||||
\(426\) | 86.8330 | 4.20707 | ||||||||
\(427\) | −26.3178 | −1.27361 | ||||||||
\(428\) | −66.6080 | −3.21962 | ||||||||
\(429\) | −1.26462 | −0.0610564 | ||||||||
\(430\) | −2.60102 | −0.125432 | ||||||||
\(431\) | 29.7067 | 1.43092 | 0.715460 | − | 0.698654i | \(-0.246217\pi\) | ||||
0.715460 | + | 0.698654i | \(0.246217\pi\) | |||||||
\(432\) | 0.117959 | 0.00567532 | ||||||||
\(433\) | 29.7726 | 1.43078 | 0.715391 | − | 0.698724i | \(-0.246249\pi\) | ||||
0.715391 | + | 0.698724i | \(0.246249\pi\) | |||||||
\(434\) | 25.9203 | 1.24422 | ||||||||
\(435\) | −15.5085 | −0.743575 | ||||||||
\(436\) | 31.2607 | 1.49712 | ||||||||
\(437\) | 36.8513 | 1.76284 | ||||||||
\(438\) | −83.7335 | −4.00094 | ||||||||
\(439\) | −3.54480 | −0.169184 | −0.0845921 | − | 0.996416i | \(-0.526959\pi\) | ||||
−0.0845921 | + | 0.996416i | \(0.526959\pi\) | |||||||
\(440\) | −4.15452 | −0.198059 | ||||||||
\(441\) | 0.840399 | 0.0400190 | ||||||||
\(442\) | −1.21865 | −0.0579652 | ||||||||
\(443\) | 9.39914 | 0.446567 | 0.223283 | − | 0.974754i | \(-0.428322\pi\) | ||||
0.223283 | + | 0.974754i | \(0.428322\pi\) | |||||||
\(444\) | −45.8349 | −2.17523 | ||||||||
\(445\) | 8.40561 | 0.398464 | ||||||||
\(446\) | 36.3576 | 1.72158 | ||||||||
\(447\) | −28.4034 | −1.34344 | ||||||||
\(448\) | −31.2949 | −1.47854 | ||||||||
\(449\) | −2.29059 | −0.108100 | −0.0540498 | − | 0.998538i | \(-0.517213\pi\) | ||||
−0.0540498 | + | 0.998538i | \(0.517213\pi\) | |||||||
\(450\) | 27.1560 | 1.28015 | ||||||||
\(451\) | 5.65407 | 0.266240 | ||||||||
\(452\) | 3.27336 | 0.153966 | ||||||||
\(453\) | 20.6567 | 0.970536 | ||||||||
\(454\) | −41.7675 | −1.96025 | ||||||||
\(455\) | −1.52771 | −0.0716200 | ||||||||
\(456\) | 45.0680 | 2.11050 | ||||||||
\(457\) | −5.69855 | −0.266567 | −0.133283 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133283 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(458\) | −27.6747 | −1.29315 | ||||||||
\(459\) | −0.0675680 | −0.00315380 | ||||||||
\(460\) | −30.0018 | −1.39884 | ||||||||
\(461\) | 37.7082 | 1.75624 | 0.878122 | − | 0.478436i | \(-0.158796\pi\) | ||||
0.878122 | + | 0.478436i | \(0.158796\pi\) | |||||||
\(462\) | −15.6694 | −0.729004 | ||||||||
\(463\) | 2.73444 | 0.127080 | 0.0635401 | − | 0.997979i | \(-0.479761\pi\) | ||||
0.0635401 | + | 0.997979i | \(0.479761\pi\) | |||||||
\(464\) | −10.0308 | −0.465668 | ||||||||
\(465\) | −10.9619 | −0.508344 | ||||||||
\(466\) | 17.5006 | 0.810699 | ||||||||
\(467\) | −0.612711 | −0.0283529 | −0.0141764 | − | 0.999900i | \(-0.504513\pi\) | ||||
−0.0141764 | + | 0.999900i | \(0.504513\pi\) | |||||||
\(468\) | −5.60984 | −0.259315 | ||||||||
\(469\) | −13.0758 | −0.603785 | ||||||||
\(470\) | −11.5417 | −0.532381 | ||||||||
\(471\) | 10.7505 | 0.495358 | ||||||||
\(472\) | −10.9817 | −0.505475 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −53.9899 | −2.47984 | ||||||||
\(475\) | 18.4172 | 0.845041 | ||||||||
\(476\) | −9.70434 | −0.444798 | ||||||||
\(477\) | −5.87512 | −0.269003 | ||||||||
\(478\) | 12.9857 | 0.593951 | ||||||||
\(479\) | −37.3057 | −1.70454 | −0.852270 | − | 0.523102i | \(-0.824774\pi\) | ||||
−0.852270 | + | 0.523102i | \(0.824774\pi\) | |||||||
\(480\) | 9.25134 | 0.422264 | ||||||||
\(481\) | 2.67328 | 0.121891 | ||||||||
\(482\) | −31.4143 | −1.43088 | ||||||||
\(483\) | −50.2437 | −2.28617 | ||||||||
\(484\) | 3.59727 | 0.163512 | ||||||||
\(485\) | 6.75389 | 0.306678 | ||||||||
\(486\) | 52.2713 | 2.37107 | ||||||||
\(487\) | 20.5030 | 0.929080 | 0.464540 | − | 0.885552i | \(-0.346220\pi\) | ||||
0.464540 | + | 0.885552i | \(0.346220\pi\) | |||||||
\(488\) | 36.8656 | 1.66883 | ||||||||
\(489\) | 28.4927 | 1.28848 | ||||||||
\(490\) | −0.722008 | −0.0326170 | ||||||||
\(491\) | 12.8644 | 0.580564 | 0.290282 | − | 0.956941i | \(-0.406251\pi\) | ||||
0.290282 | + | 0.956941i | \(0.406251\pi\) | |||||||
\(492\) | 49.9347 | 2.25123 | ||||||||
\(493\) | 5.74572 | 0.258774 | ||||||||
\(494\) | −5.91987 | −0.266348 | ||||||||
\(495\) | 3.32846 | 0.149603 | ||||||||
\(496\) | −7.09006 | −0.318353 | ||||||||
\(497\) | −40.3293 | −1.80902 | ||||||||
\(498\) | 92.0021 | 4.12271 | ||||||||
\(499\) | 5.46925 | 0.244837 | 0.122419 | − | 0.992479i | \(-0.460935\pi\) | ||||
0.122419 | + | 0.992479i | \(0.460935\pi\) | |||||||
\(500\) | −34.7682 | −1.55488 | ||||||||
\(501\) | −14.2559 | −0.636907 | ||||||||
\(502\) | −16.0048 | −0.714328 | ||||||||
\(503\) | −20.7481 | −0.925114 | −0.462557 | − | 0.886590i | \(-0.653068\pi\) | ||||
−0.462557 | + | 0.886590i | \(0.653068\pi\) | |||||||
\(504\) | −30.8636 | −1.37477 | ||||||||
\(505\) | 2.95737 | 0.131601 | ||||||||
\(506\) | 17.9476 | 0.797868 | ||||||||
\(507\) | −31.2649 | −1.38852 | ||||||||
\(508\) | −2.50630 | −0.111199 | ||||||||
\(509\) | 22.8313 | 1.01198 | 0.505989 | − | 0.862540i | \(-0.331128\pi\) | ||||
0.505989 | + | 0.862540i | \(0.331128\pi\) | |||||||
\(510\) | 6.38577 | 0.282767 | ||||||||
\(511\) | 38.8898 | 1.72038 | ||||||||
\(512\) | 19.1780 | 0.847557 | ||||||||
\(513\) | −0.328228 | −0.0144916 | ||||||||
\(514\) | 35.7776 | 1.57808 | ||||||||
\(515\) | −10.6927 | −0.471175 | ||||||||
\(516\) | 8.83165 | 0.388792 | ||||||||
\(517\) | 4.43739 | 0.195156 | ||||||||
\(518\) | 33.1235 | 1.45536 | ||||||||
\(519\) | −27.0100 | −1.18561 | ||||||||
\(520\) | 2.13999 | 0.0938447 | ||||||||
\(521\) | −3.59424 | −0.157467 | −0.0787333 | − | 0.996896i | \(-0.525088\pi\) | ||||
−0.0787333 | + | 0.996896i | \(0.525088\pi\) | |||||||
\(522\) | 41.1547 | 1.80129 | ||||||||
\(523\) | −17.0696 | −0.746400 | −0.373200 | − | 0.927751i | \(-0.621740\pi\) | ||||
−0.373200 | + | 0.927751i | \(0.621740\pi\) | |||||||
\(524\) | −6.49530 | −0.283748 | ||||||||
\(525\) | −25.1104 | −1.09591 | ||||||||
\(526\) | 13.0505 | 0.569027 | ||||||||
\(527\) | 4.06124 | 0.176910 | ||||||||
\(528\) | 4.28609 | 0.186528 | ||||||||
\(529\) | 34.5489 | 1.50213 | ||||||||
\(530\) | 5.04746 | 0.219248 | ||||||||
\(531\) | 8.79818 | 0.381808 | ||||||||
\(532\) | −47.1412 | −2.04383 | ||||||||
\(533\) | −2.91240 | −0.126150 | ||||||||
\(534\) | −44.4089 | −1.92176 | ||||||||
\(535\) | −20.3568 | −0.880102 | ||||||||
\(536\) | 18.3164 | 0.791148 | ||||||||
\(537\) | −15.4435 | −0.666436 | ||||||||
\(538\) | 60.5369 | 2.60993 | ||||||||
\(539\) | 0.277587 | 0.0119565 | ||||||||
\(540\) | 0.267220 | 0.0114993 | ||||||||
\(541\) | 15.8809 | 0.682772 | 0.341386 | − | 0.939923i | \(-0.389104\pi\) | ||||
0.341386 | + | 0.939923i | \(0.389104\pi\) | |||||||
\(542\) | −19.7686 | −0.849135 | ||||||||
\(543\) | 2.87519 | 0.123386 | ||||||||
\(544\) | −3.42751 | −0.146953 | ||||||||
\(545\) | 9.55393 | 0.409246 | ||||||||
\(546\) | 8.07126 | 0.345418 | ||||||||
\(547\) | 30.7601 | 1.31521 | 0.657604 | − | 0.753363i | \(-0.271570\pi\) | ||||
0.657604 | + | 0.753363i | \(0.271570\pi\) | |||||||
\(548\) | −19.8822 | −0.849323 | ||||||||
\(549\) | −29.5354 | −1.26054 | ||||||||
\(550\) | 8.96971 | 0.382470 | ||||||||
\(551\) | 27.9112 | 1.18906 | ||||||||
\(552\) | 70.3806 | 2.99560 | ||||||||
\(553\) | 25.0755 | 1.06632 | ||||||||
\(554\) | −15.4806 | −0.657710 | ||||||||
\(555\) | −14.0081 | −0.594612 | ||||||||
\(556\) | 25.8851 | 1.09777 | ||||||||
\(557\) | 37.1957 | 1.57603 | 0.788016 | − | 0.615655i | \(-0.211108\pi\) | ||||
0.788016 | + | 0.615655i | \(0.211108\pi\) | |||||||
\(558\) | 29.0893 | 1.23145 | ||||||||
\(559\) | −0.515099 | −0.0217864 | ||||||||
\(560\) | 5.17775 | 0.218800 | ||||||||
\(561\) | −2.45510 | −0.103654 | ||||||||
\(562\) | −11.4770 | −0.484127 | ||||||||
\(563\) | 32.3657 | 1.36405 | 0.682026 | − | 0.731328i | \(-0.261099\pi\) | ||||
0.682026 | + | 0.731328i | \(0.261099\pi\) | |||||||
\(564\) | 39.1895 | 1.65017 | ||||||||
\(565\) | 1.00041 | 0.0420875 | ||||||||
\(566\) | 30.6073 | 1.28652 | ||||||||
\(567\) | −24.0545 | −1.01020 | ||||||||
\(568\) | 56.4927 | 2.37038 | ||||||||
\(569\) | −47.1163 | −1.97522 | −0.987609 | − | 0.156932i | \(-0.949840\pi\) | ||||
−0.987609 | + | 0.156932i | \(0.949840\pi\) | |||||||
\(570\) | 31.0204 | 1.29930 | ||||||||
\(571\) | 0.292248 | 0.0122302 | 0.00611511 | − | 0.999981i | \(-0.498053\pi\) | ||||
0.00611511 | + | 0.999981i | \(0.498053\pi\) | |||||||
\(572\) | −1.85295 | −0.0774756 | ||||||||
\(573\) | −29.0456 | −1.21340 | ||||||||
\(574\) | −36.0863 | −1.50621 | ||||||||
\(575\) | 28.7613 | 1.19943 | ||||||||
\(576\) | −35.1210 | −1.46337 | ||||||||
\(577\) | 25.4245 | 1.05844 | 0.529219 | − | 0.848485i | \(-0.322485\pi\) | ||||
0.529219 | + | 0.848485i | \(0.322485\pi\) | |||||||
\(578\) | −2.36585 | −0.0984066 | ||||||||
\(579\) | 64.1066 | 2.66418 | ||||||||
\(580\) | −22.7234 | −0.943536 | ||||||||
\(581\) | −42.7301 | −1.77274 | ||||||||
\(582\) | −35.6825 | −1.47909 | ||||||||
\(583\) | −1.94057 | −0.0803702 | ||||||||
\(584\) | −54.4762 | −2.25424 | ||||||||
\(585\) | −1.71448 | −0.0708852 | ||||||||
\(586\) | −58.0206 | −2.39681 | ||||||||
\(587\) | 12.4695 | 0.514671 | 0.257335 | − | 0.966322i | \(-0.417155\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417155\pi\) | |||||||
\(588\) | 2.45155 | 0.101100 | ||||||||
\(589\) | 19.7284 | 0.812896 | ||||||||
\(590\) | −7.55874 | −0.311188 | ||||||||
\(591\) | −5.75738 | −0.236827 | ||||||||
\(592\) | −9.06037 | −0.372379 | ||||||||
\(593\) | 3.15522 | 0.129569 | 0.0647847 | − | 0.997899i | \(-0.479364\pi\) | ||||
0.0647847 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(594\) | −0.159856 | −0.00655897 | ||||||||
\(595\) | −2.96585 | −0.121588 | ||||||||
\(596\) | −41.6173 | −1.70471 | ||||||||
\(597\) | 40.6471 | 1.66358 | ||||||||
\(598\) | −9.24479 | −0.378047 | ||||||||
\(599\) | 15.9386 | 0.651232 | 0.325616 | − | 0.945502i | \(-0.394428\pi\) | ||||
0.325616 | + | 0.945502i | \(0.394428\pi\) | |||||||
\(600\) | 35.1742 | 1.43598 | ||||||||
\(601\) | 27.8894 | 1.13763 | 0.568816 | − | 0.822465i | \(-0.307402\pi\) | ||||
0.568816 | + | 0.822465i | \(0.307402\pi\) | |||||||
\(602\) | −6.38237 | −0.260126 | ||||||||
\(603\) | −14.6745 | −0.597590 | ||||||||
\(604\) | 30.2666 | 1.23153 | ||||||||
\(605\) | 1.09940 | 0.0446970 | ||||||||
\(606\) | −15.6246 | −0.634704 | ||||||||
\(607\) | −26.6709 | −1.08254 | −0.541270 | − | 0.840849i | \(-0.682056\pi\) | ||||
−0.541270 | + | 0.840849i | \(0.682056\pi\) | |||||||
\(608\) | −16.6500 | −0.675246 | ||||||||
\(609\) | −38.0546 | −1.54205 | ||||||||
\(610\) | 25.3746 | 1.02739 | ||||||||
\(611\) | −2.28569 | −0.0924692 | ||||||||
\(612\) | −10.8908 | −0.440234 | ||||||||
\(613\) | −23.7466 | −0.959115 | −0.479557 | − | 0.877511i | \(-0.659203\pi\) | ||||
−0.479557 | + | 0.877511i | \(0.659203\pi\) | |||||||
\(614\) | −71.7644 | −2.89618 | ||||||||
\(615\) | 15.2611 | 0.615387 | ||||||||
\(616\) | −10.1943 | −0.410741 | ||||||||
\(617\) | −18.8314 | −0.758122 | −0.379061 | − | 0.925372i | \(-0.623753\pi\) | ||||
−0.379061 | + | 0.925372i | \(0.623753\pi\) | |||||||
\(618\) | 56.4921 | 2.27244 | ||||||||
\(619\) | 1.36437 | 0.0548388 | 0.0274194 | − | 0.999624i | \(-0.491271\pi\) | ||||
0.0274194 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(620\) | −16.0615 | −0.645047 | ||||||||
\(621\) | −0.512577 | −0.0205690 | ||||||||
\(622\) | 5.36491 | 0.215113 | ||||||||
\(623\) | 20.6256 | 0.826348 | ||||||||
\(624\) | −2.20776 | −0.0883810 | ||||||||
\(625\) | 8.33069 | 0.333228 | ||||||||
\(626\) | −13.7140 | −0.548123 | ||||||||
\(627\) | −11.9262 | −0.476288 | ||||||||
\(628\) | 15.7519 | 0.628569 | ||||||||
\(629\) | 5.18985 | 0.206933 | ||||||||
\(630\) | −21.2434 | −0.846359 | ||||||||
\(631\) | 6.14796 | 0.244746 | 0.122373 | − | 0.992484i | \(-0.460950\pi\) | ||||
0.122373 | + | 0.992484i | \(0.460950\pi\) | |||||||
\(632\) | −35.1253 | −1.39721 | ||||||||
\(633\) | 10.0034 | 0.397598 | ||||||||
\(634\) | 45.6028 | 1.81112 | ||||||||
\(635\) | −0.765978 | −0.0303969 | ||||||||
\(636\) | −17.1384 | −0.679583 | ||||||||
\(637\) | −0.142984 | −0.00566525 | ||||||||
\(638\) | 13.5935 | 0.538173 | ||||||||
\(639\) | −45.2600 | −1.79046 | ||||||||
\(640\) | 22.6369 | 0.894803 | ||||||||
\(641\) | −25.9152 | −1.02359 | −0.511795 | − | 0.859108i | \(-0.671019\pi\) | ||||
−0.511795 | + | 0.859108i | \(0.671019\pi\) | |||||||
\(642\) | 107.550 | 4.24467 | ||||||||
\(643\) | −0.140942 | −0.00555819 | −0.00277910 | − | 0.999996i | \(-0.500885\pi\) | ||||
−0.00277910 | + | 0.999996i | \(0.500885\pi\) | |||||||
\(644\) | −73.6181 | −2.90096 | ||||||||
\(645\) | 2.69914 | 0.106278 | ||||||||
\(646\) | −11.4927 | −0.452174 | ||||||||
\(647\) | −37.9116 | −1.49046 | −0.745228 | − | 0.666809i | \(-0.767660\pi\) | ||||
−0.745228 | + | 0.666809i | \(0.767660\pi\) | |||||||
\(648\) | 33.6952 | 1.32367 | ||||||||
\(649\) | 2.90607 | 0.114073 | ||||||||
\(650\) | −4.62028 | −0.181222 | ||||||||
\(651\) | −26.8981 | −1.05422 | ||||||||
\(652\) | 41.7481 | 1.63498 | ||||||||
\(653\) | 15.4659 | 0.605228 | 0.302614 | − | 0.953113i | \(-0.402141\pi\) | ||||
0.302614 | + | 0.953113i | \(0.402141\pi\) | |||||||
\(654\) | −50.4759 | −1.97376 | ||||||||
\(655\) | −1.98510 | −0.0775643 | ||||||||
\(656\) | 9.87080 | 0.385390 | ||||||||
\(657\) | 43.6445 | 1.70273 | ||||||||
\(658\) | −28.3210 | −1.10407 | ||||||||
\(659\) | 35.5619 | 1.38530 | 0.692648 | − | 0.721276i | \(-0.256444\pi\) | ||||
0.692648 | + | 0.721276i | \(0.256444\pi\) | |||||||
\(660\) | 9.70952 | 0.377943 | ||||||||
\(661\) | 26.3928 | 1.02656 | 0.513281 | − | 0.858221i | \(-0.328430\pi\) | ||||
0.513281 | + | 0.858221i | \(0.328430\pi\) | |||||||
\(662\) | 23.7884 | 0.924563 | ||||||||
\(663\) | 1.26462 | 0.0491137 | ||||||||
\(664\) | 59.8557 | 2.32285 | ||||||||
\(665\) | −14.4073 | −0.558693 | ||||||||
\(666\) | 37.1732 | 1.44043 | ||||||||
\(667\) | 43.5876 | 1.68772 | ||||||||
\(668\) | −20.8880 | −0.808183 | ||||||||
\(669\) | −37.7291 | −1.45869 | ||||||||
\(670\) | 12.6072 | 0.487059 | ||||||||
\(671\) | −9.75564 | −0.376612 | ||||||||
\(672\) | 22.7009 | 0.875705 | ||||||||
\(673\) | −0.823571 | −0.0317463 | −0.0158732 | − | 0.999874i | \(-0.505053\pi\) | ||||
−0.0158732 | + | 0.999874i | \(0.505053\pi\) | |||||||
\(674\) | 18.8606 | 0.726484 | ||||||||
\(675\) | −0.256172 | −0.00986006 | ||||||||
\(676\) | −45.8100 | −1.76192 | ||||||||
\(677\) | 28.1551 | 1.08209 | 0.541045 | − | 0.840994i | \(-0.318029\pi\) | ||||
0.541045 | + | 0.840994i | \(0.318029\pi\) | |||||||
\(678\) | −5.28542 | −0.202985 | ||||||||
\(679\) | 16.5726 | 0.636000 | ||||||||
\(680\) | 4.15452 | 0.159319 | ||||||||
\(681\) | 43.3431 | 1.66091 | ||||||||
\(682\) | 9.60830 | 0.367921 | ||||||||
\(683\) | 4.59032 | 0.175644 | 0.0878219 | − | 0.996136i | \(-0.472009\pi\) | ||||
0.0878219 | + | 0.996136i | \(0.472009\pi\) | |||||||
\(684\) | −52.9047 | −2.02286 | ||||||||
\(685\) | −6.07641 | −0.232168 | ||||||||
\(686\) | 42.9049 | 1.63812 | ||||||||
\(687\) | 28.7186 | 1.09568 | ||||||||
\(688\) | 1.74579 | 0.0665575 | ||||||||
\(689\) | 0.999585 | 0.0380812 | ||||||||
\(690\) | 48.4431 | 1.84420 | ||||||||
\(691\) | −15.5542 | −0.591709 | −0.295854 | − | 0.955233i | \(-0.595604\pi\) | ||||
−0.295854 | + | 0.955233i | \(0.595604\pi\) | |||||||
\(692\) | −39.5756 | −1.50444 | ||||||||
\(693\) | 8.16735 | 0.310252 | ||||||||
\(694\) | −7.49798 | −0.284620 | ||||||||
\(695\) | 7.91103 | 0.300082 | ||||||||
\(696\) | 53.3063 | 2.02057 | ||||||||
\(697\) | −5.65407 | −0.214163 | ||||||||
\(698\) | −17.9190 | −0.678245 | ||||||||
\(699\) | −18.1608 | −0.686903 | ||||||||
\(700\) | −36.7923 | −1.39062 | ||||||||
\(701\) | −19.3849 | −0.732156 | −0.366078 | − | 0.930584i | \(-0.619300\pi\) | ||||
−0.366078 | + | 0.930584i | \(0.619300\pi\) | |||||||
\(702\) | 0.0823416 | 0.00310778 | ||||||||
\(703\) | 25.2109 | 0.950848 | ||||||||
\(704\) | −11.6006 | −0.437213 | ||||||||
\(705\) | 11.9771 | 0.451085 | ||||||||
\(706\) | −72.5895 | −2.73194 | ||||||||
\(707\) | 7.25678 | 0.272919 | ||||||||
\(708\) | 25.6654 | 0.964563 | ||||||||
\(709\) | 12.8044 | 0.480879 | 0.240440 | − | 0.970664i | \(-0.422708\pi\) | ||||
0.240440 | + | 0.970664i | \(0.422708\pi\) | |||||||
\(710\) | 38.8840 | 1.45929 | ||||||||
\(711\) | 28.1412 | 1.05538 | ||||||||
\(712\) | −28.8920 | −1.08277 | ||||||||
\(713\) | 30.8090 | 1.15381 | ||||||||
\(714\) | 15.6694 | 0.586411 | ||||||||
\(715\) | −0.566300 | −0.0211784 | ||||||||
\(716\) | −22.6281 | −0.845654 | ||||||||
\(717\) | −13.4755 | −0.503253 | ||||||||
\(718\) | 7.27652 | 0.271557 | ||||||||
\(719\) | −11.3657 | −0.423868 | −0.211934 | − | 0.977284i | \(-0.567976\pi\) | ||||
−0.211934 | + | 0.977284i | \(0.567976\pi\) | |||||||
\(720\) | 5.81078 | 0.216555 | ||||||||
\(721\) | −26.2376 | −0.977139 | ||||||||
\(722\) | −10.8773 | −0.404812 | ||||||||
\(723\) | 32.5994 | 1.21238 | ||||||||
\(724\) | 4.21279 | 0.156567 | ||||||||
\(725\) | 21.7838 | 0.809032 | ||||||||
\(726\) | −5.80841 | −0.215570 | ||||||||
\(727\) | 11.1880 | 0.414939 | 0.207469 | − | 0.978242i | \(-0.433477\pi\) | ||||
0.207469 | + | 0.978242i | \(0.433477\pi\) | |||||||
\(728\) | 5.25109 | 0.194618 | ||||||||
\(729\) | −27.4931 | −1.01826 | ||||||||
\(730\) | −37.4961 | −1.38779 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | −86.1584 | −3.18451 | ||||||||
\(733\) | −38.4543 | −1.42034 | −0.710171 | − | 0.704030i | \(-0.751382\pi\) | ||||
−0.710171 | + | 0.704030i | \(0.751382\pi\) | |||||||
\(734\) | 16.1337 | 0.595505 | ||||||||
\(735\) | 0.749245 | 0.0276363 | ||||||||
\(736\) | −26.0015 | −0.958427 | ||||||||
\(737\) | −4.84702 | −0.178542 | ||||||||
\(738\) | −40.4982 | −1.49076 | ||||||||
\(739\) | −45.8392 | −1.68622 | −0.843111 | − | 0.537739i | \(-0.819279\pi\) | ||||
−0.843111 | + | 0.537739i | \(0.819279\pi\) | |||||||
\(740\) | −20.5250 | −0.754514 | ||||||||
\(741\) | 6.14319 | 0.225676 | ||||||||
\(742\) | 12.3854 | 0.454683 | ||||||||
\(743\) | −26.9014 | −0.986917 | −0.493458 | − | 0.869769i | \(-0.664267\pi\) | ||||
−0.493458 | + | 0.869769i | \(0.664267\pi\) | |||||||
\(744\) | 37.6785 | 1.38136 | ||||||||
\(745\) | −12.7191 | −0.465993 | ||||||||
\(746\) | −34.7400 | −1.27192 | ||||||||
\(747\) | −47.9543 | −1.75456 | ||||||||
\(748\) | −3.59727 | −0.131529 | ||||||||
\(749\) | −49.9514 | −1.82518 | ||||||||
\(750\) | 56.1393 | 2.04992 | ||||||||
\(751\) | −7.27244 | −0.265375 | −0.132688 | − | 0.991158i | \(-0.542361\pi\) | ||||
−0.132688 | + | 0.991158i | \(0.542361\pi\) | |||||||
\(752\) | 7.74674 | 0.282494 | ||||||||
\(753\) | 16.6085 | 0.605248 | ||||||||
\(754\) | −7.00201 | −0.254998 | ||||||||
\(755\) | 9.25012 | 0.336646 | ||||||||
\(756\) | 0.655703 | 0.0238477 | ||||||||
\(757\) | 27.8741 | 1.01310 | 0.506550 | − | 0.862210i | \(-0.330921\pi\) | ||||
0.506550 | + | 0.862210i | \(0.330921\pi\) | |||||||
\(758\) | 30.0374 | 1.09101 | ||||||||
\(759\) | −18.6246 | −0.676032 | ||||||||
\(760\) | 20.1816 | 0.732063 | ||||||||
\(761\) | −14.2615 | −0.516980 | −0.258490 | − | 0.966014i | \(-0.583225\pi\) | ||||
−0.258490 | + | 0.966014i | \(0.583225\pi\) | |||||||
\(762\) | 4.04685 | 0.146602 | ||||||||
\(763\) | 23.4434 | 0.848707 | ||||||||
\(764\) | −42.5582 | −1.53970 | ||||||||
\(765\) | −3.32846 | −0.120341 | ||||||||
\(766\) | 68.3822 | 2.47075 | ||||||||
\(767\) | −1.49691 | −0.0540503 | ||||||||
\(768\) | −62.6354 | −2.26016 | ||||||||
\(769\) | −16.5906 | −0.598272 | −0.299136 | − | 0.954210i | \(-0.596698\pi\) | ||||
−0.299136 | + | 0.954210i | \(0.596698\pi\) | |||||||
\(770\) | −7.01677 | −0.252867 | ||||||||
\(771\) | −37.1273 | −1.33711 | ||||||||
\(772\) | 93.9304 | 3.38063 | ||||||||
\(773\) | 15.9947 | 0.575290 | 0.287645 | − | 0.957737i | \(-0.407128\pi\) | ||||
0.287645 | + | 0.957737i | \(0.407128\pi\) | |||||||
\(774\) | −7.16267 | −0.257457 | ||||||||
\(775\) | 15.3975 | 0.553093 | ||||||||
\(776\) | −23.2147 | −0.833359 | ||||||||
\(777\) | −34.3730 | −1.23313 | ||||||||
\(778\) | −70.3996 | −2.52395 | ||||||||
\(779\) | −27.4660 | −0.984071 | ||||||||
\(780\) | −5.00136 | −0.179077 | ||||||||
\(781\) | −14.9495 | −0.534936 | ||||||||
\(782\) | −17.9476 | −0.641805 | ||||||||
\(783\) | −0.388227 | −0.0138741 | ||||||||
\(784\) | 0.484607 | 0.0173074 | ||||||||
\(785\) | 4.81411 | 0.171823 | ||||||||
\(786\) | 10.4878 | 0.374087 | ||||||||
\(787\) | −24.2651 | −0.864958 | −0.432479 | − | 0.901644i | \(-0.642361\pi\) | ||||
−0.432479 | + | 0.901644i | \(0.642361\pi\) | |||||||
\(788\) | −8.43583 | −0.300514 | ||||||||
\(789\) | −13.5428 | −0.482135 | ||||||||
\(790\) | −24.1768 | −0.860172 | ||||||||
\(791\) | 2.45480 | 0.0872825 | ||||||||
\(792\) | −11.4407 | −0.406527 | ||||||||
\(793\) | 5.02512 | 0.178447 | ||||||||
\(794\) | 50.6458 | 1.79735 | ||||||||
\(795\) | −5.23787 | −0.185768 | ||||||||
\(796\) | 59.5570 | 2.11094 | ||||||||
\(797\) | −45.6833 | −1.61819 | −0.809093 | − | 0.587680i | \(-0.800041\pi\) | ||||
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(798\) | 76.1176 | 2.69453 | ||||||||
\(799\) | −4.43739 | −0.156983 | ||||||||
\(800\) | −12.9948 | −0.459436 | ||||||||
\(801\) | 23.1473 | 0.817870 | ||||||||
\(802\) | 24.1476 | 0.852683 | ||||||||
\(803\) | 14.4159 | 0.508726 | ||||||||
\(804\) | −42.8072 | −1.50969 | ||||||||
\(805\) | −22.4993 | −0.792994 | ||||||||
\(806\) | −4.94922 | −0.174329 | ||||||||
\(807\) | −62.8205 | −2.21139 | ||||||||
\(808\) | −10.1652 | −0.357610 | ||||||||
\(809\) | 45.0028 | 1.58221 | 0.791107 | − | 0.611677i | \(-0.209505\pi\) | ||||
0.791107 | + | 0.611677i | \(0.209505\pi\) | |||||||
\(810\) | 23.1925 | 0.814900 | ||||||||
\(811\) | 5.42318 | 0.190434 | 0.0952169 | − | 0.995457i | \(-0.469646\pi\) | ||||
0.0952169 | + | 0.995457i | \(0.469646\pi\) | |||||||
\(812\) | −55.7584 | −1.95674 | ||||||||
\(813\) | 20.5144 | 0.719470 | ||||||||
\(814\) | 12.2784 | 0.430358 | ||||||||
\(815\) | 12.7591 | 0.446932 | ||||||||
\(816\) | −4.28609 | −0.150043 | ||||||||
\(817\) | −4.85774 | −0.169951 | ||||||||
\(818\) | 70.8176 | 2.47608 | ||||||||
\(819\) | −4.20699 | −0.147004 | ||||||||
\(820\) | 22.3609 | 0.780876 | ||||||||
\(821\) | −29.3995 | −1.02605 | −0.513024 | − | 0.858374i | \(-0.671475\pi\) | ||||
−0.513024 | + | 0.858374i | \(0.671475\pi\) | |||||||
\(822\) | 32.1032 | 1.11973 | ||||||||
\(823\) | 28.8594 | 1.00597 | 0.502987 | − | 0.864294i | \(-0.332234\pi\) | ||||
0.502987 | + | 0.864294i | \(0.332234\pi\) | |||||||
\(824\) | 36.7532 | 1.28036 | ||||||||
\(825\) | −9.30807 | −0.324065 | ||||||||
\(826\) | −18.5476 | −0.645353 | ||||||||
\(827\) | 5.44279 | 0.189264 | 0.0946322 | − | 0.995512i | \(-0.469832\pi\) | ||||
0.0946322 | + | 0.995512i | \(0.469832\pi\) | |||||||
\(828\) | −82.6187 | −2.87120 | ||||||||
\(829\) | 10.9220 | 0.379336 | 0.189668 | − | 0.981848i | \(-0.439259\pi\) | ||||
0.189668 | + | 0.981848i | \(0.439259\pi\) | |||||||
\(830\) | 41.1987 | 1.43003 | ||||||||
\(831\) | 16.0646 | 0.557276 | ||||||||
\(832\) | 5.97544 | 0.207161 | ||||||||
\(833\) | −0.277587 | −0.00961780 | ||||||||
\(834\) | −41.7960 | −1.44728 | ||||||||
\(835\) | −6.38383 | −0.220921 | ||||||||
\(836\) | −17.4746 | −0.604371 | ||||||||
\(837\) | −0.274410 | −0.00948499 | ||||||||
\(838\) | −54.7293 | −1.89059 | ||||||||
\(839\) | 1.23733 | 0.0427175 | 0.0213588 | − | 0.999772i | \(-0.493201\pi\) | ||||
0.0213588 | + | 0.999772i | \(0.493201\pi\) | |||||||
\(840\) | −27.5159 | −0.949389 | ||||||||
\(841\) | 4.01327 | 0.138389 | ||||||||
\(842\) | −25.8564 | −0.891069 | ||||||||
\(843\) | 11.9099 | 0.410200 | ||||||||
\(844\) | 14.6571 | 0.504519 | ||||||||
\(845\) | −14.0005 | −0.481632 | ||||||||
\(846\) | −31.7836 | −1.09274 | ||||||||
\(847\) | 2.69770 | 0.0926941 | ||||||||
\(848\) | −3.38782 | −0.116338 | ||||||||
\(849\) | −31.7619 | −1.09007 | ||||||||
\(850\) | −8.96971 | −0.307658 | ||||||||
\(851\) | 39.3707 | 1.34961 | ||||||||
\(852\) | −132.029 | −4.52324 | ||||||||
\(853\) | 21.2865 | 0.728837 | 0.364419 | − | 0.931235i | \(-0.381268\pi\) | ||||
0.364419 | + | 0.931235i | \(0.381268\pi\) | |||||||
\(854\) | 62.2641 | 2.13063 | ||||||||
\(855\) | −16.1688 | −0.552961 | ||||||||
\(856\) | 69.9711 | 2.39156 | ||||||||
\(857\) | −38.0727 | −1.30054 | −0.650269 | − | 0.759704i | \(-0.725344\pi\) | ||||
−0.650269 | + | 0.759704i | \(0.725344\pi\) | |||||||
\(858\) | 2.99190 | 0.102142 | ||||||||
\(859\) | −36.9258 | −1.25989 | −0.629946 | − | 0.776639i | \(-0.716923\pi\) | ||||
−0.629946 | + | 0.776639i | \(0.716923\pi\) | |||||||
\(860\) | 3.95483 | 0.134859 | ||||||||
\(861\) | 37.4476 | 1.27621 | ||||||||
\(862\) | −70.2816 | −2.39380 | ||||||||
\(863\) | 0.0207226 | 0.000705406 0 | 0.000352703 | − | 1.00000i | \(-0.499888\pi\) | ||||
0.000352703 | 1.00000i | \(0.499888\pi\) | ||||||||
\(864\) | 0.231590 | 0.00787886 | ||||||||
\(865\) | −12.0952 | −0.411248 | ||||||||
\(866\) | −70.4377 | −2.39357 | ||||||||
\(867\) | 2.45510 | 0.0833796 | ||||||||
\(868\) | −39.4117 | −1.33772 | ||||||||
\(869\) | 9.29512 | 0.315315 | ||||||||
\(870\) | 36.6908 | 1.24394 | ||||||||
\(871\) | 2.49669 | 0.0845973 | ||||||||
\(872\) | −32.8391 | −1.11207 | ||||||||
\(873\) | 18.5988 | 0.629475 | ||||||||
\(874\) | −87.1848 | −2.94907 | ||||||||
\(875\) | −26.0738 | −0.881454 | ||||||||
\(876\) | 127.316 | 4.30162 | ||||||||
\(877\) | 23.2900 | 0.786446 | 0.393223 | − | 0.919443i | \(-0.371360\pi\) | ||||
0.393223 | + | 0.919443i | \(0.371360\pi\) | |||||||
\(878\) | 8.38649 | 0.283030 | ||||||||
\(879\) | 60.2093 | 2.03081 | ||||||||
\(880\) | 1.91932 | 0.0647002 | ||||||||
\(881\) | 6.96971 | 0.234815 | 0.117408 | − | 0.993084i | \(-0.462542\pi\) | ||||
0.117408 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(882\) | −1.98826 | −0.0669483 | ||||||||
\(883\) | 1.91163 | 0.0643315 | 0.0321657 | − | 0.999483i | \(-0.489760\pi\) | ||||
0.0321657 | + | 0.999483i | \(0.489760\pi\) | |||||||
\(884\) | 1.85295 | 0.0623213 | ||||||||
\(885\) | 7.84388 | 0.263669 | ||||||||
\(886\) | −22.2370 | −0.747067 | ||||||||
\(887\) | 2.84615 | 0.0955643 | 0.0477822 | − | 0.998858i | \(-0.484785\pi\) | ||||
0.0477822 | + | 0.998858i | \(0.484785\pi\) | |||||||
\(888\) | 48.1492 | 1.61578 | ||||||||
\(889\) | −1.87955 | −0.0630381 | ||||||||
\(890\) | −19.8864 | −0.666595 | ||||||||
\(891\) | −8.91668 | −0.298720 | ||||||||
\(892\) | −55.2815 | −1.85096 | ||||||||
\(893\) | −21.5557 | −0.721333 | ||||||||
\(894\) | 67.1983 | 2.24745 | ||||||||
\(895\) | −6.91564 | −0.231164 | ||||||||
\(896\) | 55.5463 | 1.85567 | ||||||||
\(897\) | 9.59353 | 0.320319 | ||||||||
\(898\) | 5.41920 | 0.180841 | ||||||||
\(899\) | 23.3347 | 0.778257 | ||||||||
\(900\) | −41.2905 | −1.37635 | ||||||||
\(901\) | 1.94057 | 0.0646498 | ||||||||
\(902\) | −13.3767 | −0.445395 | ||||||||
\(903\) | 6.62313 | 0.220404 | ||||||||
\(904\) | −3.43864 | −0.114368 | ||||||||
\(905\) | 1.28752 | 0.0427986 | ||||||||
\(906\) | −48.8707 | −1.62362 | ||||||||
\(907\) | 34.1374 | 1.13351 | 0.566757 | − | 0.823885i | \(-0.308198\pi\) | ||||
0.566757 | + | 0.823885i | \(0.308198\pi\) | |||||||
\(908\) | 63.5072 | 2.10756 | ||||||||
\(909\) | 8.14400 | 0.270119 | ||||||||
\(910\) | 3.61433 | 0.119814 | ||||||||
\(911\) | 8.49534 | 0.281463 | 0.140732 | − | 0.990048i | \(-0.455055\pi\) | ||||
0.140732 | + | 0.990048i | \(0.455055\pi\) | |||||||
\(912\) | −20.8207 | −0.689442 | ||||||||
\(913\) | −15.8395 | −0.524209 | ||||||||
\(914\) | 13.4819 | 0.445943 | ||||||||
\(915\) | −26.3318 | −0.870503 | ||||||||
\(916\) | 42.0791 | 1.39033 | ||||||||
\(917\) | −4.87102 | −0.160855 | ||||||||
\(918\) | 0.159856 | 0.00527603 | ||||||||
\(919\) | 31.5826 | 1.04181 | 0.520906 | − | 0.853614i | \(-0.325594\pi\) | ||||
0.520906 | + | 0.853614i | \(0.325594\pi\) | |||||||
\(920\) | 31.5166 | 1.03907 | ||||||||
\(921\) | 74.4716 | 2.45392 | ||||||||
\(922\) | −89.2120 | −2.93804 | ||||||||
\(923\) | 7.70048 | 0.253464 | ||||||||
\(924\) | 23.8251 | 0.783790 | ||||||||
\(925\) | 19.6764 | 0.646955 | ||||||||
\(926\) | −6.46929 | −0.212594 | ||||||||
\(927\) | −29.4454 | −0.967114 | ||||||||
\(928\) | −19.6935 | −0.646472 | ||||||||
\(929\) | −0.422315 | −0.0138557 | −0.00692786 | − | 0.999976i | \(-0.502205\pi\) | ||||
−0.00692786 | + | 0.999976i | \(0.502205\pi\) | |||||||
\(930\) | 25.9341 | 0.850414 | ||||||||
\(931\) | −1.34844 | −0.0441934 | ||||||||
\(932\) | −26.6095 | −0.871624 | ||||||||
\(933\) | −5.56729 | −0.182265 | ||||||||
\(934\) | 1.44959 | 0.0474319 | ||||||||
\(935\) | −1.09940 | −0.0359542 | ||||||||
\(936\) | 5.89308 | 0.192621 | ||||||||
\(937\) | −36.9710 | −1.20779 | −0.603896 | − | 0.797063i | \(-0.706386\pi\) | ||||
−0.603896 | + | 0.797063i | \(0.706386\pi\) | |||||||
\(938\) | 30.9355 | 1.01008 | ||||||||
\(939\) | 14.2314 | 0.464423 | ||||||||
\(940\) | 17.5491 | 0.572390 | ||||||||
\(941\) | 24.2905 | 0.791848 | 0.395924 | − | 0.918283i | \(-0.370424\pi\) | ||||
0.395924 | + | 0.918283i | \(0.370424\pi\) | |||||||
\(942\) | −25.4342 | −0.828691 | ||||||||
\(943\) | −42.8923 | −1.39677 | ||||||||
\(944\) | 5.07337 | 0.165124 | ||||||||
\(945\) | 0.200397 | 0.00651890 | ||||||||
\(946\) | −2.36585 | −0.0769206 | ||||||||
\(947\) | −34.3135 | −1.11504 | −0.557519 | − | 0.830164i | \(-0.688247\pi\) | ||||
−0.557519 | + | 0.830164i | \(0.688247\pi\) | |||||||
\(948\) | 82.0913 | 2.66620 | ||||||||
\(949\) | −7.42561 | −0.241046 | ||||||||
\(950\) | −43.5725 | −1.41368 | ||||||||
\(951\) | −47.3230 | −1.53455 | ||||||||
\(952\) | 10.1943 | 0.330400 | ||||||||
\(953\) | −31.5417 | −1.02174 | −0.510869 | − | 0.859659i | \(-0.670676\pi\) | ||||
−0.510869 | + | 0.859659i | \(0.670676\pi\) | |||||||
\(954\) | 13.8997 | 0.450019 | ||||||||
\(955\) | −13.0067 | −0.420886 | ||||||||
\(956\) | −19.7446 | −0.638587 | ||||||||
\(957\) | −14.1063 | −0.455993 | ||||||||
\(958\) | 88.2598 | 2.85154 | ||||||||
\(959\) | −14.9102 | −0.481477 | ||||||||
\(960\) | −31.3116 | −1.01058 | ||||||||
\(961\) | −14.5063 | −0.467946 | ||||||||
\(962\) | −6.32460 | −0.203913 | ||||||||
\(963\) | −56.0585 | −1.80646 | ||||||||
\(964\) | 47.7653 | 1.53842 | ||||||||
\(965\) | 28.7071 | 0.924115 | ||||||||
\(966\) | 118.869 | 3.82456 | ||||||||
\(967\) | −9.67987 | −0.311283 | −0.155642 | − | 0.987814i | \(-0.549745\pi\) | ||||
−0.155642 | + | 0.987814i | \(0.549745\pi\) | |||||||
\(968\) | −3.77890 | −0.121458 | ||||||||
\(969\) | 11.9262 | 0.383126 | ||||||||
\(970\) | −15.9787 | −0.513046 | ||||||||
\(971\) | −52.8570 | −1.69626 | −0.848130 | − | 0.529787i | \(-0.822272\pi\) | ||||
−0.848130 | + | 0.529787i | \(0.822272\pi\) | |||||||
\(972\) | −79.4782 | −2.54926 | ||||||||
\(973\) | 19.4120 | 0.622321 | ||||||||
\(974\) | −48.5072 | −1.55427 | ||||||||
\(975\) | 4.79457 | 0.153549 | ||||||||
\(976\) | −17.0313 | −0.545158 | ||||||||
\(977\) | −22.3812 | −0.716039 | −0.358020 | − | 0.933714i | \(-0.616548\pi\) | ||||
−0.358020 | + | 0.933714i | \(0.616548\pi\) | |||||||
\(978\) | −67.4096 | −2.15552 | ||||||||
\(979\) | 7.64563 | 0.244355 | ||||||||
\(980\) | 1.09781 | 0.0350682 | ||||||||
\(981\) | 26.3096 | 0.840000 | ||||||||
\(982\) | −30.4354 | −0.971232 | ||||||||
\(983\) | −4.22132 | −0.134639 | −0.0673195 | − | 0.997731i | \(-0.521445\pi\) | ||||
−0.0673195 | + | 0.997731i | \(0.521445\pi\) | |||||||
\(984\) | −52.4560 | −1.67224 | ||||||||
\(985\) | −2.57817 | −0.0821472 | ||||||||
\(986\) | −13.5935 | −0.432906 | ||||||||
\(987\) | 29.3894 | 0.935474 | ||||||||
\(988\) | 9.00113 | 0.286364 | ||||||||
\(989\) | −7.58610 | −0.241224 | ||||||||
\(990\) | −7.87465 | −0.250273 | ||||||||
\(991\) | −5.38609 | −0.171095 | −0.0855473 | − | 0.996334i | \(-0.527264\pi\) | ||||
−0.0855473 | + | 0.996334i | \(0.527264\pi\) | |||||||
\(992\) | −13.9200 | −0.441959 | ||||||||
\(993\) | −24.6858 | −0.783380 | ||||||||
\(994\) | 95.4133 | 3.02633 | ||||||||
\(995\) | 18.2019 | 0.577038 | ||||||||
\(996\) | −139.889 | −4.43254 | ||||||||
\(997\) | −43.1298 | −1.36594 | −0.682968 | − | 0.730449i | \(-0.739311\pi\) | ||||
−0.682968 | + | 0.730449i | \(0.739311\pi\) | |||||||
\(998\) | −12.9395 | −0.409591 | ||||||||
\(999\) | −0.350667 | −0.0110946 |
(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 | 8041.2.a.d.1.7 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.d.1.7 | ✓ | 62 | 1.1 | even | 1 | trivial |