Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.460726 | 0.266000 | 0.133000 | − | 0.991116i | \(-0.457539\pi\) | ||||
0.133000 | + | 0.991116i | \(0.457539\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.645126 | 0.288509 | 0.144255 | − | 0.989541i | \(-0.453922\pi\) | ||||
0.144255 | + | 0.989541i | \(0.453922\pi\) | |||||||
\(6\) | 0.460726 | 0.188091 | ||||||||
\(7\) | 1.69833 | 0.641909 | 0.320954 | − | 0.947095i | \(-0.395996\pi\) | ||||
0.320954 | + | 0.947095i | \(0.395996\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.78773 | −0.929244 | ||||||||
\(10\) | 0.645126 | 0.204007 | ||||||||
\(11\) | 0.878525 | 0.264885 | 0.132443 | − | 0.991191i | \(-0.457718\pi\) | ||||
0.132443 | + | 0.991191i | \(0.457718\pi\) | |||||||
\(12\) | 0.460726 | 0.133000 | ||||||||
\(13\) | −2.21021 | −0.613001 | −0.306500 | − | 0.951871i | \(-0.599158\pi\) | ||||
−0.306500 | + | 0.951871i | \(0.599158\pi\) | |||||||
\(14\) | 1.69833 | 0.453898 | ||||||||
\(15\) | 0.297226 | 0.0767435 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.24512 | −0.787056 | −0.393528 | − | 0.919313i | \(-0.628746\pi\) | ||||
−0.393528 | + | 0.919313i | \(0.628746\pi\) | |||||||
\(18\) | −2.78773 | −0.657075 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0.645126 | 0.144255 | ||||||||
\(21\) | 0.782465 | 0.170748 | ||||||||
\(22\) | 0.878525 | 0.187302 | ||||||||
\(23\) | −0.250785 | −0.0522923 | −0.0261462 | − | 0.999658i | \(-0.508324\pi\) | ||||
−0.0261462 | + | 0.999658i | \(0.508324\pi\) | |||||||
\(24\) | 0.460726 | 0.0940453 | ||||||||
\(25\) | −4.58381 | −0.916762 | ||||||||
\(26\) | −2.21021 | −0.433457 | ||||||||
\(27\) | −2.66656 | −0.513179 | ||||||||
\(28\) | 1.69833 | 0.320954 | ||||||||
\(29\) | −6.95706 | −1.29189 | −0.645947 | − | 0.763383i | \(-0.723537\pi\) | ||||
−0.645947 | + | 0.763383i | \(0.723537\pi\) | |||||||
\(30\) | 0.297226 | 0.0542659 | ||||||||
\(31\) | −5.17048 | −0.928645 | −0.464322 | − | 0.885666i | \(-0.653702\pi\) | ||||
−0.464322 | + | 0.885666i | \(0.653702\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.404759 | 0.0704596 | ||||||||
\(34\) | −3.24512 | −0.556533 | ||||||||
\(35\) | 1.09564 | 0.185197 | ||||||||
\(36\) | −2.78773 | −0.464622 | ||||||||
\(37\) | 4.12685 | 0.678450 | 0.339225 | − | 0.940705i | \(-0.389835\pi\) | ||||
0.339225 | + | 0.940705i | \(0.389835\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −1.01830 | −0.163058 | ||||||||
\(40\) | 0.645126 | 0.102003 | ||||||||
\(41\) | −4.51052 | −0.704424 | −0.352212 | − | 0.935920i | \(-0.614570\pi\) | ||||
−0.352212 | + | 0.935920i | \(0.614570\pi\) | |||||||
\(42\) | 0.782465 | 0.120737 | ||||||||
\(43\) | 0.863349 | 0.131660 | 0.0658298 | − | 0.997831i | \(-0.479031\pi\) | ||||
0.0658298 | + | 0.997831i | \(0.479031\pi\) | |||||||
\(44\) | 0.878525 | 0.132443 | ||||||||
\(45\) | −1.79844 | −0.268095 | ||||||||
\(46\) | −0.250785 | −0.0369763 | ||||||||
\(47\) | −8.45380 | −1.23311 | −0.616557 | − | 0.787311i | \(-0.711473\pi\) | ||||
−0.616557 | + | 0.787311i | \(0.711473\pi\) | |||||||
\(48\) | 0.460726 | 0.0665001 | ||||||||
\(49\) | −4.11567 | −0.587953 | ||||||||
\(50\) | −4.58381 | −0.648249 | ||||||||
\(51\) | −1.49511 | −0.209357 | ||||||||
\(52\) | −2.21021 | −0.306500 | ||||||||
\(53\) | 1.10404 | 0.151652 | 0.0758260 | − | 0.997121i | \(-0.475841\pi\) | ||||
0.0758260 | + | 0.997121i | \(0.475841\pi\) | |||||||
\(54\) | −2.66656 | −0.362873 | ||||||||
\(55\) | 0.566760 | 0.0764218 | ||||||||
\(56\) | 1.69833 | 0.226949 | ||||||||
\(57\) | 0.460726 | 0.0610247 | ||||||||
\(58\) | −6.95706 | −0.913506 | ||||||||
\(59\) | −11.4249 | −1.48739 | −0.743696 | − | 0.668518i | \(-0.766929\pi\) | ||||
−0.743696 | + | 0.668518i | \(0.766929\pi\) | |||||||
\(60\) | 0.297226 | 0.0383718 | ||||||||
\(61\) | 7.83485 | 1.00315 | 0.501575 | − | 0.865114i | \(-0.332754\pi\) | ||||
0.501575 | + | 0.865114i | \(0.332754\pi\) | |||||||
\(62\) | −5.17048 | −0.656651 | ||||||||
\(63\) | −4.73449 | −0.596490 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.42586 | −0.176856 | ||||||||
\(66\) | 0.404759 | 0.0498224 | ||||||||
\(67\) | −4.12175 | −0.503552 | −0.251776 | − | 0.967786i | \(-0.581015\pi\) | ||||
−0.251776 | + | 0.967786i | \(0.581015\pi\) | |||||||
\(68\) | −3.24512 | −0.393528 | ||||||||
\(69\) | −0.115543 | −0.0139098 | ||||||||
\(70\) | 1.09564 | 0.130954 | ||||||||
\(71\) | −6.15084 | −0.729971 | −0.364985 | − | 0.931013i | \(-0.618926\pi\) | ||||
−0.364985 | + | 0.931013i | \(0.618926\pi\) | |||||||
\(72\) | −2.78773 | −0.328537 | ||||||||
\(73\) | −0.0206681 | −0.00241902 | −0.00120951 | − | 0.999999i | \(-0.500385\pi\) | ||||
−0.00120951 | + | 0.999999i | \(0.500385\pi\) | |||||||
\(74\) | 4.12685 | 0.479736 | ||||||||
\(75\) | −2.11188 | −0.243859 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 1.49203 | 0.170032 | ||||||||
\(78\) | −1.01830 | −0.115300 | ||||||||
\(79\) | 3.73317 | 0.420014 | 0.210007 | − | 0.977700i | \(-0.432651\pi\) | ||||
0.210007 | + | 0.977700i | \(0.432651\pi\) | |||||||
\(80\) | 0.645126 | 0.0721273 | ||||||||
\(81\) | 7.13464 | 0.792738 | ||||||||
\(82\) | −4.51052 | −0.498103 | ||||||||
\(83\) | 12.2527 | 1.34491 | 0.672453 | − | 0.740140i | \(-0.265241\pi\) | ||||
0.672453 | + | 0.740140i | \(0.265241\pi\) | |||||||
\(84\) | 0.782465 | 0.0853739 | ||||||||
\(85\) | −2.09351 | −0.227073 | ||||||||
\(86\) | 0.863349 | 0.0930974 | ||||||||
\(87\) | −3.20530 | −0.343644 | ||||||||
\(88\) | 0.878525 | 0.0936511 | ||||||||
\(89\) | 0.944202 | 0.100085 | 0.0500426 | − | 0.998747i | \(-0.484064\pi\) | ||||
0.0500426 | + | 0.998747i | \(0.484064\pi\) | |||||||
\(90\) | −1.79844 | −0.189572 | ||||||||
\(91\) | −3.75366 | −0.393490 | ||||||||
\(92\) | −0.250785 | −0.0261462 | ||||||||
\(93\) | −2.38217 | −0.247020 | ||||||||
\(94\) | −8.45380 | −0.871943 | ||||||||
\(95\) | 0.645126 | 0.0661885 | ||||||||
\(96\) | 0.460726 | 0.0470227 | ||||||||
\(97\) | −8.08209 | −0.820612 | −0.410306 | − | 0.911948i | \(-0.634578\pi\) | ||||
−0.410306 | + | 0.911948i | \(0.634578\pi\) | |||||||
\(98\) | −4.11567 | −0.415746 | ||||||||
\(99\) | −2.44909 | −0.246143 | ||||||||
\(100\) | −4.58381 | −0.458381 | ||||||||
\(101\) | 0.959342 | 0.0954581 | 0.0477290 | − | 0.998860i | \(-0.484802\pi\) | ||||
0.0477290 | + | 0.998860i | \(0.484802\pi\) | |||||||
\(102\) | −1.49511 | −0.148038 | ||||||||
\(103\) | −3.43349 | −0.338312 | −0.169156 | − | 0.985589i | \(-0.554104\pi\) | ||||
−0.169156 | + | 0.985589i | \(0.554104\pi\) | |||||||
\(104\) | −2.21021 | −0.216728 | ||||||||
\(105\) | 0.504789 | 0.0492623 | ||||||||
\(106\) | 1.10404 | 0.107234 | ||||||||
\(107\) | 6.03026 | 0.582967 | 0.291483 | − | 0.956576i | \(-0.405851\pi\) | ||||
0.291483 | + | 0.956576i | \(0.405851\pi\) | |||||||
\(108\) | −2.66656 | −0.256590 | ||||||||
\(109\) | −6.44518 | −0.617337 | −0.308668 | − | 0.951170i | \(-0.599883\pi\) | ||||
−0.308668 | + | 0.951170i | \(0.599883\pi\) | |||||||
\(110\) | 0.566760 | 0.0540384 | ||||||||
\(111\) | 1.90135 | 0.180468 | ||||||||
\(112\) | 1.69833 | 0.160477 | ||||||||
\(113\) | 16.3812 | 1.54101 | 0.770506 | − | 0.637433i | \(-0.220004\pi\) | ||||
0.770506 | + | 0.637433i | \(0.220004\pi\) | |||||||
\(114\) | 0.460726 | 0.0431509 | ||||||||
\(115\) | −0.161788 | −0.0150868 | ||||||||
\(116\) | −6.95706 | −0.645947 | ||||||||
\(117\) | 6.16146 | 0.569627 | ||||||||
\(118\) | −11.4249 | −1.05174 | ||||||||
\(119\) | −5.51128 | −0.505218 | ||||||||
\(120\) | 0.297226 | 0.0271329 | ||||||||
\(121\) | −10.2282 | −0.929836 | ||||||||
\(122\) | 7.83485 | 0.709334 | ||||||||
\(123\) | −2.07811 | −0.187377 | ||||||||
\(124\) | −5.17048 | −0.464322 | ||||||||
\(125\) | −6.18277 | −0.553004 | ||||||||
\(126\) | −4.73449 | −0.421782 | ||||||||
\(127\) | −8.38429 | −0.743985 | −0.371993 | − | 0.928236i | \(-0.621325\pi\) | ||||
−0.371993 | + | 0.928236i | \(0.621325\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.397768 | 0.0350215 | ||||||||
\(130\) | −1.42586 | −0.125056 | ||||||||
\(131\) | 11.5878 | 1.01243 | 0.506215 | − | 0.862408i | \(-0.331044\pi\) | ||||
0.506215 | + | 0.862408i | \(0.331044\pi\) | |||||||
\(132\) | 0.404759 | 0.0352298 | ||||||||
\(133\) | 1.69833 | 0.147264 | ||||||||
\(134\) | −4.12175 | −0.356065 | ||||||||
\(135\) | −1.72027 | −0.148057 | ||||||||
\(136\) | −3.24512 | −0.278266 | ||||||||
\(137\) | 17.7090 | 1.51299 | 0.756493 | − | 0.654002i | \(-0.226911\pi\) | ||||
0.756493 | + | 0.654002i | \(0.226911\pi\) | |||||||
\(138\) | −0.115543 | −0.00983570 | ||||||||
\(139\) | −13.7301 | −1.16457 | −0.582286 | − | 0.812984i | \(-0.697842\pi\) | ||||
−0.582286 | + | 0.812984i | \(0.697842\pi\) | |||||||
\(140\) | 1.09564 | 0.0925983 | ||||||||
\(141\) | −3.89489 | −0.328008 | ||||||||
\(142\) | −6.15084 | −0.516167 | ||||||||
\(143\) | −1.94172 | −0.162375 | ||||||||
\(144\) | −2.78773 | −0.232311 | ||||||||
\(145\) | −4.48818 | −0.372723 | ||||||||
\(146\) | −0.0206681 | −0.00171050 | ||||||||
\(147\) | −1.89620 | −0.156396 | ||||||||
\(148\) | 4.12685 | 0.339225 | ||||||||
\(149\) | −11.9151 | −0.976123 | −0.488061 | − | 0.872809i | \(-0.662296\pi\) | ||||
−0.488061 | + | 0.872809i | \(0.662296\pi\) | |||||||
\(150\) | −2.11188 | −0.172434 | ||||||||
\(151\) | 4.00395 | 0.325837 | 0.162918 | − | 0.986640i | \(-0.447909\pi\) | ||||
0.162918 | + | 0.986640i | \(0.447909\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 9.04651 | 0.731367 | ||||||||
\(154\) | 1.49203 | 0.120231 | ||||||||
\(155\) | −3.33561 | −0.267923 | ||||||||
\(156\) | −1.01830 | −0.0815292 | ||||||||
\(157\) | −21.5010 | −1.71597 | −0.857983 | − | 0.513678i | \(-0.828282\pi\) | ||||
−0.857983 | + | 0.513678i | \(0.828282\pi\) | |||||||
\(158\) | 3.73317 | 0.296995 | ||||||||
\(159\) | 0.508661 | 0.0403395 | ||||||||
\(160\) | 0.645126 | 0.0510017 | ||||||||
\(161\) | −0.425916 | −0.0335669 | ||||||||
\(162\) | 7.13464 | 0.560550 | ||||||||
\(163\) | −17.7351 | −1.38912 | −0.694560 | − | 0.719435i | \(-0.744401\pi\) | ||||
−0.694560 | + | 0.719435i | \(0.744401\pi\) | |||||||
\(164\) | −4.51052 | −0.352212 | ||||||||
\(165\) | 0.261121 | 0.0203282 | ||||||||
\(166\) | 12.2527 | 0.950991 | ||||||||
\(167\) | 9.68545 | 0.749483 | 0.374741 | − | 0.927129i | \(-0.377732\pi\) | ||||
0.374741 | + | 0.927129i | \(0.377732\pi\) | |||||||
\(168\) | 0.782465 | 0.0603685 | ||||||||
\(169\) | −8.11499 | −0.624230 | ||||||||
\(170\) | −2.09351 | −0.160565 | ||||||||
\(171\) | −2.78773 | −0.213183 | ||||||||
\(172\) | 0.863349 | 0.0658298 | ||||||||
\(173\) | 22.6120 | 1.71916 | 0.859579 | − | 0.511003i | \(-0.170726\pi\) | ||||
0.859579 | + | 0.511003i | \(0.170726\pi\) | |||||||
\(174\) | −3.20530 | −0.242993 | ||||||||
\(175\) | −7.78483 | −0.588478 | ||||||||
\(176\) | 0.878525 | 0.0662213 | ||||||||
\(177\) | −5.26374 | −0.395647 | ||||||||
\(178\) | 0.944202 | 0.0707709 | ||||||||
\(179\) | −1.85040 | −0.138306 | −0.0691528 | − | 0.997606i | \(-0.522030\pi\) | ||||
−0.0691528 | + | 0.997606i | \(0.522030\pi\) | |||||||
\(180\) | −1.79844 | −0.134048 | ||||||||
\(181\) | 17.8420 | 1.32619 | 0.663093 | − | 0.748537i | \(-0.269243\pi\) | ||||
0.663093 | + | 0.748537i | \(0.269243\pi\) | |||||||
\(182\) | −3.75366 | −0.278240 | ||||||||
\(183\) | 3.60972 | 0.266838 | ||||||||
\(184\) | −0.250785 | −0.0184881 | ||||||||
\(185\) | 2.66234 | 0.195739 | ||||||||
\(186\) | −2.38217 | −0.174669 | ||||||||
\(187\) | −2.85092 | −0.208480 | ||||||||
\(188\) | −8.45380 | −0.616557 | ||||||||
\(189\) | −4.52870 | −0.329414 | ||||||||
\(190\) | 0.645126 | 0.0468024 | ||||||||
\(191\) | −17.5088 | −1.26689 | −0.633445 | − | 0.773788i | \(-0.718360\pi\) | ||||
−0.633445 | + | 0.773788i | \(0.718360\pi\) | |||||||
\(192\) | 0.460726 | 0.0332500 | ||||||||
\(193\) | 18.8884 | 1.35961 | 0.679807 | − | 0.733391i | \(-0.262064\pi\) | ||||
0.679807 | + | 0.733391i | \(0.262064\pi\) | |||||||
\(194\) | −8.08209 | −0.580260 | ||||||||
\(195\) | −0.656931 | −0.0470438 | ||||||||
\(196\) | −4.11567 | −0.293977 | ||||||||
\(197\) | 16.3478 | 1.16474 | 0.582368 | − | 0.812926i | \(-0.302126\pi\) | ||||
0.582368 | + | 0.812926i | \(0.302126\pi\) | |||||||
\(198\) | −2.44909 | −0.174049 | ||||||||
\(199\) | 6.35334 | 0.450377 | 0.225188 | − | 0.974315i | \(-0.427700\pi\) | ||||
0.225188 | + | 0.974315i | \(0.427700\pi\) | |||||||
\(200\) | −4.58381 | −0.324124 | ||||||||
\(201\) | −1.89900 | −0.133945 | ||||||||
\(202\) | 0.959342 | 0.0674990 | ||||||||
\(203\) | −11.8154 | −0.829277 | ||||||||
\(204\) | −1.49511 | −0.104679 | ||||||||
\(205\) | −2.90985 | −0.203233 | ||||||||
\(206\) | −3.43349 | −0.239223 | ||||||||
\(207\) | 0.699122 | 0.0485923 | ||||||||
\(208\) | −2.21021 | −0.153250 | ||||||||
\(209\) | 0.878525 | 0.0607689 | ||||||||
\(210\) | 0.504789 | 0.0348337 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 1.10404 | 0.0758260 | ||||||||
\(213\) | −2.83385 | −0.194172 | ||||||||
\(214\) | 6.03026 | 0.412220 | ||||||||
\(215\) | 0.556969 | 0.0379850 | ||||||||
\(216\) | −2.66656 | −0.181436 | ||||||||
\(217\) | −8.78118 | −0.596105 | ||||||||
\(218\) | −6.44518 | −0.436523 | ||||||||
\(219\) | −0.00952234 | −0.000643460 0 | ||||||||
\(220\) | 0.566760 | 0.0382109 | ||||||||
\(221\) | 7.17237 | 0.482466 | ||||||||
\(222\) | 1.90135 | 0.127610 | ||||||||
\(223\) | −0.300471 | −0.0201211 | −0.0100605 | − | 0.999949i | \(-0.503202\pi\) | ||||
−0.0100605 | + | 0.999949i | \(0.503202\pi\) | |||||||
\(224\) | 1.69833 | 0.113474 | ||||||||
\(225\) | 12.7784 | 0.851896 | ||||||||
\(226\) | 16.3812 | 1.08966 | ||||||||
\(227\) | 24.1346 | 1.60187 | 0.800934 | − | 0.598753i | \(-0.204337\pi\) | ||||
0.800934 | + | 0.598753i | \(0.204337\pi\) | |||||||
\(228\) | 0.460726 | 0.0305123 | ||||||||
\(229\) | 18.5855 | 1.22816 | 0.614082 | − | 0.789242i | \(-0.289527\pi\) | ||||
0.614082 | + | 0.789242i | \(0.289527\pi\) | |||||||
\(230\) | −0.161788 | −0.0106680 | ||||||||
\(231\) | 0.687415 | 0.0452286 | ||||||||
\(232\) | −6.95706 | −0.456753 | ||||||||
\(233\) | −20.7966 | −1.36243 | −0.681215 | − | 0.732084i | \(-0.738548\pi\) | ||||
−0.681215 | + | 0.732084i | \(0.738548\pi\) | |||||||
\(234\) | 6.16146 | 0.402787 | ||||||||
\(235\) | −5.45377 | −0.355764 | ||||||||
\(236\) | −11.4249 | −0.743696 | ||||||||
\(237\) | 1.71997 | 0.111724 | ||||||||
\(238\) | −5.51128 | −0.357243 | ||||||||
\(239\) | −8.68185 | −0.561582 | −0.280791 | − | 0.959769i | \(-0.590597\pi\) | ||||
−0.280791 | + | 0.959769i | \(0.590597\pi\) | |||||||
\(240\) | 0.297226 | 0.0191859 | ||||||||
\(241\) | −5.50361 | −0.354519 | −0.177259 | − | 0.984164i | \(-0.556723\pi\) | ||||
−0.177259 | + | 0.984164i | \(0.556723\pi\) | |||||||
\(242\) | −10.2282 | −0.657493 | ||||||||
\(243\) | 11.2868 | 0.724048 | ||||||||
\(244\) | 7.83485 | 0.501575 | ||||||||
\(245\) | −2.65513 | −0.169630 | ||||||||
\(246\) | −2.07811 | −0.132496 | ||||||||
\(247\) | −2.21021 | −0.140632 | ||||||||
\(248\) | −5.17048 | −0.328326 | ||||||||
\(249\) | 5.64512 | 0.357745 | ||||||||
\(250\) | −6.18277 | −0.391033 | ||||||||
\(251\) | −13.7081 | −0.865249 | −0.432624 | − | 0.901574i | \(-0.642412\pi\) | ||||
−0.432624 | + | 0.901574i | \(0.642412\pi\) | |||||||
\(252\) | −4.73449 | −0.298245 | ||||||||
\(253\) | −0.220321 | −0.0138515 | ||||||||
\(254\) | −8.38429 | −0.526077 | ||||||||
\(255\) | −0.964534 | −0.0604015 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.3600 | −1.02051 | −0.510255 | − | 0.860023i | \(-0.670449\pi\) | ||||
−0.510255 | + | 0.860023i | \(0.670449\pi\) | |||||||
\(258\) | 0.397768 | 0.0247639 | ||||||||
\(259\) | 7.00875 | 0.435503 | ||||||||
\(260\) | −1.42586 | −0.0884282 | ||||||||
\(261\) | 19.3944 | 1.20048 | ||||||||
\(262\) | 11.5878 | 0.715895 | ||||||||
\(263\) | −15.2573 | −0.940807 | −0.470404 | − | 0.882451i | \(-0.655892\pi\) | ||||
−0.470404 | + | 0.882451i | \(0.655892\pi\) | |||||||
\(264\) | 0.404759 | 0.0249112 | ||||||||
\(265\) | 0.712247 | 0.0437530 | ||||||||
\(266\) | 1.69833 | 0.104131 | ||||||||
\(267\) | 0.435018 | 0.0266227 | ||||||||
\(268\) | −4.12175 | −0.251776 | ||||||||
\(269\) | 2.66337 | 0.162388 | 0.0811942 | − | 0.996698i | \(-0.474127\pi\) | ||||
0.0811942 | + | 0.996698i | \(0.474127\pi\) | |||||||
\(270\) | −1.72027 | −0.104692 | ||||||||
\(271\) | −11.1873 | −0.679578 | −0.339789 | − | 0.940502i | \(-0.610356\pi\) | ||||
−0.339789 | + | 0.940502i | \(0.610356\pi\) | |||||||
\(272\) | −3.24512 | −0.196764 | ||||||||
\(273\) | −1.72941 | −0.104669 | ||||||||
\(274\) | 17.7090 | 1.06984 | ||||||||
\(275\) | −4.02699 | −0.242837 | ||||||||
\(276\) | −0.115543 | −0.00695489 | ||||||||
\(277\) | 13.7972 | 0.828994 | 0.414497 | − | 0.910051i | \(-0.363958\pi\) | ||||
0.414497 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(278\) | −13.7301 | −0.823477 | ||||||||
\(279\) | 14.4139 | 0.862938 | ||||||||
\(280\) | 1.09564 | 0.0654769 | ||||||||
\(281\) | −20.6065 | −1.22928 | −0.614641 | − | 0.788807i | \(-0.710699\pi\) | ||||
−0.614641 | + | 0.788807i | \(0.710699\pi\) | |||||||
\(282\) | −3.89489 | −0.231937 | ||||||||
\(283\) | −15.6785 | −0.931989 | −0.465995 | − | 0.884788i | \(-0.654303\pi\) | ||||
−0.465995 | + | 0.884788i | \(0.654303\pi\) | |||||||
\(284\) | −6.15084 | −0.364985 | ||||||||
\(285\) | 0.297226 | 0.0176062 | ||||||||
\(286\) | −1.94172 | −0.114816 | ||||||||
\(287\) | −7.66035 | −0.452176 | ||||||||
\(288\) | −2.78773 | −0.164269 | ||||||||
\(289\) | −6.46922 | −0.380542 | ||||||||
\(290\) | −4.48818 | −0.263555 | ||||||||
\(291\) | −3.72363 | −0.218283 | ||||||||
\(292\) | −0.0206681 | −0.00120951 | ||||||||
\(293\) | 15.5027 | 0.905677 | 0.452839 | − | 0.891592i | \(-0.350411\pi\) | ||||
0.452839 | + | 0.891592i | \(0.350411\pi\) | |||||||
\(294\) | −1.89620 | −0.110589 | ||||||||
\(295\) | −7.37048 | −0.429126 | ||||||||
\(296\) | 4.12685 | 0.239868 | ||||||||
\(297\) | −2.34264 | −0.135934 | ||||||||
\(298\) | −11.9151 | −0.690223 | ||||||||
\(299\) | 0.554287 | 0.0320552 | ||||||||
\(300\) | −2.11188 | −0.121930 | ||||||||
\(301\) | 1.46625 | 0.0845134 | ||||||||
\(302\) | 4.00395 | 0.230402 | ||||||||
\(303\) | 0.441994 | 0.0253919 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 5.05446 | 0.289418 | ||||||||
\(306\) | 9.04651 | 0.517155 | ||||||||
\(307\) | 1.42294 | 0.0812113 | 0.0406056 | − | 0.999175i | \(-0.487071\pi\) | ||||
0.0406056 | + | 0.999175i | \(0.487071\pi\) | |||||||
\(308\) | 1.49203 | 0.0850161 | ||||||||
\(309\) | −1.58190 | −0.0899910 | ||||||||
\(310\) | −3.33561 | −0.189450 | ||||||||
\(311\) | 1.66714 | 0.0945350 | 0.0472675 | − | 0.998882i | \(-0.484949\pi\) | ||||
0.0472675 | + | 0.998882i | \(0.484949\pi\) | |||||||
\(312\) | −1.01830 | −0.0576498 | ||||||||
\(313\) | 29.0193 | 1.64027 | 0.820134 | − | 0.572172i | \(-0.193899\pi\) | ||||
0.820134 | + | 0.572172i | \(0.193899\pi\) | |||||||
\(314\) | −21.5010 | −1.21337 | ||||||||
\(315\) | −3.05434 | −0.172093 | ||||||||
\(316\) | 3.73317 | 0.210007 | ||||||||
\(317\) | −20.7912 | −1.16775 | −0.583876 | − | 0.811843i | \(-0.698464\pi\) | ||||
−0.583876 | + | 0.811843i | \(0.698464\pi\) | |||||||
\(318\) | 0.508661 | 0.0285243 | ||||||||
\(319\) | −6.11195 | −0.342203 | ||||||||
\(320\) | 0.645126 | 0.0360636 | ||||||||
\(321\) | 2.77830 | 0.155069 | ||||||||
\(322\) | −0.425916 | −0.0237354 | ||||||||
\(323\) | −3.24512 | −0.180563 | ||||||||
\(324\) | 7.13464 | 0.396369 | ||||||||
\(325\) | 10.1312 | 0.561976 | ||||||||
\(326\) | −17.7351 | −0.982256 | ||||||||
\(327\) | −2.96946 | −0.164212 | ||||||||
\(328\) | −4.51052 | −0.249052 | ||||||||
\(329\) | −14.3573 | −0.791546 | ||||||||
\(330\) | 0.261121 | 0.0143742 | ||||||||
\(331\) | 1.45503 | 0.0799757 | 0.0399878 | − | 0.999200i | \(-0.487268\pi\) | ||||
0.0399878 | + | 0.999200i | \(0.487268\pi\) | |||||||
\(332\) | 12.2527 | 0.672453 | ||||||||
\(333\) | −11.5045 | −0.630445 | ||||||||
\(334\) | 9.68545 | 0.529964 | ||||||||
\(335\) | −2.65905 | −0.145279 | ||||||||
\(336\) | 0.782465 | 0.0426870 | ||||||||
\(337\) | −21.9574 | −1.19610 | −0.598048 | − | 0.801461i | \(-0.704057\pi\) | ||||
−0.598048 | + | 0.801461i | \(0.704057\pi\) | |||||||
\(338\) | −8.11499 | −0.441397 | ||||||||
\(339\) | 7.54724 | 0.409910 | ||||||||
\(340\) | −2.09351 | −0.113536 | ||||||||
\(341\) | −4.54239 | −0.245984 | ||||||||
\(342\) | −2.78773 | −0.150743 | ||||||||
\(343\) | −18.8781 | −1.01932 | ||||||||
\(344\) | 0.863349 | 0.0465487 | ||||||||
\(345\) | −0.0745400 | −0.00401310 | ||||||||
\(346\) | 22.6120 | 1.21563 | ||||||||
\(347\) | −16.7802 | −0.900809 | −0.450404 | − | 0.892825i | \(-0.648720\pi\) | ||||
−0.450404 | + | 0.892825i | \(0.648720\pi\) | |||||||
\(348\) | −3.20530 | −0.171822 | ||||||||
\(349\) | 31.6741 | 1.69548 | 0.847738 | − | 0.530415i | \(-0.177964\pi\) | ||||
0.847738 | + | 0.530415i | \(0.177964\pi\) | |||||||
\(350\) | −7.78483 | −0.416117 | ||||||||
\(351\) | 5.89364 | 0.314579 | ||||||||
\(352\) | 0.878525 | 0.0468255 | ||||||||
\(353\) | 8.97346 | 0.477609 | 0.238804 | − | 0.971068i | \(-0.423245\pi\) | ||||
0.238804 | + | 0.971068i | \(0.423245\pi\) | |||||||
\(354\) | −5.26374 | −0.279764 | ||||||||
\(355\) | −3.96807 | −0.210603 | ||||||||
\(356\) | 0.944202 | 0.0500426 | ||||||||
\(357\) | −2.53919 | −0.134388 | ||||||||
\(358\) | −1.85040 | −0.0977968 | ||||||||
\(359\) | −11.1130 | −0.586524 | −0.293262 | − | 0.956032i | \(-0.594741\pi\) | ||||
−0.293262 | + | 0.956032i | \(0.594741\pi\) | |||||||
\(360\) | −1.79844 | −0.0947860 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 17.8420 | 0.937755 | ||||||||
\(363\) | −4.71240 | −0.247337 | ||||||||
\(364\) | −3.75366 | −0.196745 | ||||||||
\(365\) | −0.0133335 | −0.000697909 0 | ||||||||
\(366\) | 3.60972 | 0.188683 | ||||||||
\(367\) | 22.3538 | 1.16686 | 0.583429 | − | 0.812164i | \(-0.301711\pi\) | ||||
0.583429 | + | 0.812164i | \(0.301711\pi\) | |||||||
\(368\) | −0.250785 | −0.0130731 | ||||||||
\(369\) | 12.5741 | 0.654582 | ||||||||
\(370\) | 2.66234 | 0.138408 | ||||||||
\(371\) | 1.87503 | 0.0973467 | ||||||||
\(372\) | −2.38217 | −0.123510 | ||||||||
\(373\) | −0.703120 | −0.0364062 | −0.0182031 | − | 0.999834i | \(-0.505795\pi\) | ||||
−0.0182031 | + | 0.999834i | \(0.505795\pi\) | |||||||
\(374\) | −2.85092 | −0.147417 | ||||||||
\(375\) | −2.84856 | −0.147099 | ||||||||
\(376\) | −8.45380 | −0.435971 | ||||||||
\(377\) | 15.3765 | 0.791931 | ||||||||
\(378\) | −4.52870 | −0.232931 | ||||||||
\(379\) | 4.45597 | 0.228888 | 0.114444 | − | 0.993430i | \(-0.463491\pi\) | ||||
0.114444 | + | 0.993430i | \(0.463491\pi\) | |||||||
\(380\) | 0.645126 | 0.0330943 | ||||||||
\(381\) | −3.86286 | −0.197900 | ||||||||
\(382\) | −17.5088 | −0.895827 | ||||||||
\(383\) | 15.3346 | 0.783560 | 0.391780 | − | 0.920059i | \(-0.371859\pi\) | ||||
0.391780 | + | 0.920059i | \(0.371859\pi\) | |||||||
\(384\) | 0.460726 | 0.0235113 | ||||||||
\(385\) | 0.962545 | 0.0490558 | ||||||||
\(386\) | 18.8884 | 0.961392 | ||||||||
\(387\) | −2.40679 | −0.122344 | ||||||||
\(388\) | −8.08209 | −0.410306 | ||||||||
\(389\) | 0.666043 | 0.0337697 | 0.0168849 | − | 0.999857i | \(-0.494625\pi\) | ||||
0.0168849 | + | 0.999857i | \(0.494625\pi\) | |||||||
\(390\) | −0.656931 | −0.0332650 | ||||||||
\(391\) | 0.813827 | 0.0411570 | ||||||||
\(392\) | −4.11567 | −0.207873 | ||||||||
\(393\) | 5.33879 | 0.269306 | ||||||||
\(394\) | 16.3478 | 0.823592 | ||||||||
\(395\) | 2.40837 | 0.121178 | ||||||||
\(396\) | −2.44909 | −0.123072 | ||||||||
\(397\) | −27.5420 | −1.38230 | −0.691148 | − | 0.722714i | \(-0.742895\pi\) | ||||
−0.691148 | + | 0.722714i | \(0.742895\pi\) | |||||||
\(398\) | 6.35334 | 0.318464 | ||||||||
\(399\) | 0.782465 | 0.0391722 | ||||||||
\(400\) | −4.58381 | −0.229191 | ||||||||
\(401\) | 25.4611 | 1.27146 | 0.635732 | − | 0.771910i | \(-0.280698\pi\) | ||||
0.635732 | + | 0.771910i | \(0.280698\pi\) | |||||||
\(402\) | −1.89900 | −0.0947134 | ||||||||
\(403\) | 11.4278 | 0.569260 | ||||||||
\(404\) | 0.959342 | 0.0477290 | ||||||||
\(405\) | 4.60274 | 0.228712 | ||||||||
\(406\) | −11.8154 | −0.586388 | ||||||||
\(407\) | 3.62554 | 0.179711 | ||||||||
\(408\) | −1.49511 | −0.0740190 | ||||||||
\(409\) | −12.7346 | −0.629685 | −0.314842 | − | 0.949144i | \(-0.601952\pi\) | ||||
−0.314842 | + | 0.949144i | \(0.601952\pi\) | |||||||
\(410\) | −2.90985 | −0.143707 | ||||||||
\(411\) | 8.15902 | 0.402455 | ||||||||
\(412\) | −3.43349 | −0.169156 | ||||||||
\(413\) | −19.4032 | −0.954770 | ||||||||
\(414\) | 0.699122 | 0.0343600 | ||||||||
\(415\) | 7.90452 | 0.388017 | ||||||||
\(416\) | −2.21021 | −0.108364 | ||||||||
\(417\) | −6.32582 | −0.309777 | ||||||||
\(418\) | 0.878525 | 0.0429701 | ||||||||
\(419\) | 35.7455 | 1.74628 | 0.873141 | − | 0.487469i | \(-0.162080\pi\) | ||||
0.873141 | + | 0.487469i | \(0.162080\pi\) | |||||||
\(420\) | 0.504789 | 0.0246312 | ||||||||
\(421\) | 9.41270 | 0.458747 | 0.229374 | − | 0.973338i | \(-0.426332\pi\) | ||||
0.229374 | + | 0.973338i | \(0.426332\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 23.5669 | 1.14586 | ||||||||
\(424\) | 1.10404 | 0.0536171 | ||||||||
\(425\) | 14.8750 | 0.721544 | ||||||||
\(426\) | −2.83385 | −0.137301 | ||||||||
\(427\) | 13.3062 | 0.643930 | ||||||||
\(428\) | 6.03026 | 0.291483 | ||||||||
\(429\) | −0.894601 | −0.0431918 | ||||||||
\(430\) | 0.556969 | 0.0268594 | ||||||||
\(431\) | −26.0702 | −1.25576 | −0.627880 | − | 0.778310i | \(-0.716077\pi\) | ||||
−0.627880 | + | 0.778310i | \(0.716077\pi\) | |||||||
\(432\) | −2.66656 | −0.128295 | ||||||||
\(433\) | 16.2636 | 0.781578 | 0.390789 | − | 0.920480i | \(-0.372202\pi\) | ||||
0.390789 | + | 0.920480i | \(0.372202\pi\) | |||||||
\(434\) | −8.78118 | −0.421510 | ||||||||
\(435\) | −2.06782 | −0.0991444 | ||||||||
\(436\) | −6.44518 | −0.308668 | ||||||||
\(437\) | −0.250785 | −0.0119967 | ||||||||
\(438\) | −0.00952234 | −0.000454995 0 | ||||||||
\(439\) | −31.8460 | −1.51993 | −0.759964 | − | 0.649965i | \(-0.774783\pi\) | ||||
−0.759964 | + | 0.649965i | \(0.774783\pi\) | |||||||
\(440\) | 0.566760 | 0.0270192 | ||||||||
\(441\) | 11.4734 | 0.546352 | ||||||||
\(442\) | 7.17237 | 0.341155 | ||||||||
\(443\) | 33.2149 | 1.57809 | 0.789044 | − | 0.614337i | \(-0.210576\pi\) | ||||
0.789044 | + | 0.614337i | \(0.210576\pi\) | |||||||
\(444\) | 1.90135 | 0.0902339 | ||||||||
\(445\) | 0.609129 | 0.0288755 | ||||||||
\(446\) | −0.300471 | −0.0142277 | ||||||||
\(447\) | −5.48960 | −0.259649 | ||||||||
\(448\) | 1.69833 | 0.0802386 | ||||||||
\(449\) | 31.3215 | 1.47815 | 0.739077 | − | 0.673621i | \(-0.235262\pi\) | ||||
0.739077 | + | 0.673621i | \(0.235262\pi\) | |||||||
\(450\) | 12.7784 | 0.602381 | ||||||||
\(451\) | −3.96260 | −0.186592 | ||||||||
\(452\) | 16.3812 | 0.770506 | ||||||||
\(453\) | 1.84472 | 0.0866727 | ||||||||
\(454\) | 24.1346 | 1.13269 | ||||||||
\(455\) | −2.42158 | −0.113526 | ||||||||
\(456\) | 0.460726 | 0.0215755 | ||||||||
\(457\) | −36.4027 | −1.70285 | −0.851424 | − | 0.524479i | \(-0.824260\pi\) | ||||
−0.851424 | + | 0.524479i | \(0.824260\pi\) | |||||||
\(458\) | 18.5855 | 0.868443 | ||||||||
\(459\) | 8.65329 | 0.403901 | ||||||||
\(460\) | −0.161788 | −0.00754341 | ||||||||
\(461\) | −20.5792 | −0.958467 | −0.479234 | − | 0.877687i | \(-0.659085\pi\) | ||||
−0.479234 | + | 0.877687i | \(0.659085\pi\) | |||||||
\(462\) | 0.687415 | 0.0319815 | ||||||||
\(463\) | 10.6034 | 0.492782 | 0.246391 | − | 0.969170i | \(-0.420755\pi\) | ||||
0.246391 | + | 0.969170i | \(0.420755\pi\) | |||||||
\(464\) | −6.95706 | −0.322973 | ||||||||
\(465\) | −1.53680 | −0.0712675 | ||||||||
\(466\) | −20.7966 | −0.963383 | ||||||||
\(467\) | −2.51857 | −0.116545 | −0.0582727 | − | 0.998301i | \(-0.518559\pi\) | ||||
−0.0582727 | + | 0.998301i | \(0.518559\pi\) | |||||||
\(468\) | 6.16146 | 0.284814 | ||||||||
\(469\) | −7.00010 | −0.323234 | ||||||||
\(470\) | −5.45377 | −0.251563 | ||||||||
\(471\) | −9.90606 | −0.456447 | ||||||||
\(472\) | −11.4249 | −0.525872 | ||||||||
\(473\) | 0.758474 | 0.0348747 | ||||||||
\(474\) | 1.71997 | 0.0790008 | ||||||||
\(475\) | −4.58381 | −0.210320 | ||||||||
\(476\) | −5.51128 | −0.252609 | ||||||||
\(477\) | −3.07777 | −0.140922 | ||||||||
\(478\) | −8.68185 | −0.397099 | ||||||||
\(479\) | −28.5571 | −1.30481 | −0.652405 | − | 0.757871i | \(-0.726240\pi\) | ||||
−0.652405 | + | 0.757871i | \(0.726240\pi\) | |||||||
\(480\) | 0.297226 | 0.0135665 | ||||||||
\(481\) | −9.12118 | −0.415890 | ||||||||
\(482\) | −5.50361 | −0.250683 | ||||||||
\(483\) | −0.196231 | −0.00892880 | ||||||||
\(484\) | −10.2282 | −0.464918 | ||||||||
\(485\) | −5.21397 | −0.236754 | ||||||||
\(486\) | 11.2868 | 0.511979 | ||||||||
\(487\) | 11.9271 | 0.540469 | 0.270235 | − | 0.962795i | \(-0.412899\pi\) | ||||
0.270235 | + | 0.962795i | \(0.412899\pi\) | |||||||
\(488\) | 7.83485 | 0.354667 | ||||||||
\(489\) | −8.17102 | −0.369506 | ||||||||
\(490\) | −2.65513 | −0.119946 | ||||||||
\(491\) | −26.7750 | −1.20834 | −0.604170 | − | 0.796856i | \(-0.706495\pi\) | ||||
−0.604170 | + | 0.796856i | \(0.706495\pi\) | |||||||
\(492\) | −2.07811 | −0.0936886 | ||||||||
\(493\) | 22.5765 | 1.01679 | ||||||||
\(494\) | −2.21021 | −0.0994418 | ||||||||
\(495\) | −1.57997 | −0.0710145 | ||||||||
\(496\) | −5.17048 | −0.232161 | ||||||||
\(497\) | −10.4462 | −0.468575 | ||||||||
\(498\) | 5.64512 | 0.252964 | ||||||||
\(499\) | 34.3714 | 1.53868 | 0.769339 | − | 0.638841i | \(-0.220586\pi\) | ||||
0.769339 | + | 0.638841i | \(0.220586\pi\) | |||||||
\(500\) | −6.18277 | −0.276502 | ||||||||
\(501\) | 4.46234 | 0.199363 | ||||||||
\(502\) | −13.7081 | −0.611823 | ||||||||
\(503\) | −24.1789 | −1.07809 | −0.539043 | − | 0.842278i | \(-0.681214\pi\) | ||||
−0.539043 | + | 0.842278i | \(0.681214\pi\) | |||||||
\(504\) | −4.73449 | −0.210891 | ||||||||
\(505\) | 0.618896 | 0.0275405 | ||||||||
\(506\) | −0.220321 | −0.00979447 | ||||||||
\(507\) | −3.73879 | −0.166045 | ||||||||
\(508\) | −8.38429 | −0.371993 | ||||||||
\(509\) | 4.62230 | 0.204880 | 0.102440 | − | 0.994739i | \(-0.467335\pi\) | ||||
0.102440 | + | 0.994739i | \(0.467335\pi\) | |||||||
\(510\) | −0.964534 | −0.0427103 | ||||||||
\(511\) | −0.0351013 | −0.00155279 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.66656 | −0.117731 | ||||||||
\(514\) | −16.3600 | −0.721610 | ||||||||
\(515\) | −2.21503 | −0.0976061 | ||||||||
\(516\) | 0.397768 | 0.0175107 | ||||||||
\(517\) | −7.42687 | −0.326634 | ||||||||
\(518\) | 7.00875 | 0.307947 | ||||||||
\(519\) | 10.4179 | 0.457297 | ||||||||
\(520\) | −1.42586 | −0.0625281 | ||||||||
\(521\) | −21.2661 | −0.931685 | −0.465842 | − | 0.884868i | \(-0.654249\pi\) | ||||
−0.465842 | + | 0.884868i | \(0.654249\pi\) | |||||||
\(522\) | 19.3944 | 0.848870 | ||||||||
\(523\) | −6.44365 | −0.281761 | −0.140880 | − | 0.990027i | \(-0.544993\pi\) | ||||
−0.140880 | + | 0.990027i | \(0.544993\pi\) | |||||||
\(524\) | 11.5878 | 0.506215 | ||||||||
\(525\) | −3.58667 | −0.156535 | ||||||||
\(526\) | −15.2573 | −0.665251 | ||||||||
\(527\) | 16.7788 | 0.730896 | ||||||||
\(528\) | 0.404759 | 0.0176149 | ||||||||
\(529\) | −22.9371 | −0.997266 | ||||||||
\(530\) | 0.712247 | 0.0309380 | ||||||||
\(531\) | 31.8495 | 1.38215 | ||||||||
\(532\) | 1.69833 | 0.0736320 | ||||||||
\(533\) | 9.96917 | 0.431813 | ||||||||
\(534\) | 0.435018 | 0.0188251 | ||||||||
\(535\) | 3.89028 | 0.168191 | ||||||||
\(536\) | −4.12175 | −0.178033 | ||||||||
\(537\) | −0.852528 | −0.0367893 | ||||||||
\(538\) | 2.66337 | 0.114826 | ||||||||
\(539\) | −3.61572 | −0.155740 | ||||||||
\(540\) | −1.72027 | −0.0740285 | ||||||||
\(541\) | −1.05796 | −0.0454854 | −0.0227427 | − | 0.999741i | \(-0.507240\pi\) | ||||
−0.0227427 | + | 0.999741i | \(0.507240\pi\) | |||||||
\(542\) | −11.1873 | −0.480534 | ||||||||
\(543\) | 8.22028 | 0.352766 | ||||||||
\(544\) | −3.24512 | −0.139133 | ||||||||
\(545\) | −4.15796 | −0.178107 | ||||||||
\(546\) | −1.72941 | −0.0740118 | ||||||||
\(547\) | 16.0363 | 0.685661 | 0.342830 | − | 0.939397i | \(-0.388614\pi\) | ||||
0.342830 | + | 0.939397i | \(0.388614\pi\) | |||||||
\(548\) | 17.7090 | 0.756493 | ||||||||
\(549\) | −21.8414 | −0.932170 | ||||||||
\(550\) | −4.02699 | −0.171712 | ||||||||
\(551\) | −6.95706 | −0.296381 | ||||||||
\(552\) | −0.115543 | −0.00491785 | ||||||||
\(553\) | 6.34016 | 0.269611 | ||||||||
\(554\) | 13.7972 | 0.586187 | ||||||||
\(555\) | 1.22661 | 0.0520666 | ||||||||
\(556\) | −13.7301 | −0.582286 | ||||||||
\(557\) | 2.07876 | 0.0880798 | 0.0440399 | − | 0.999030i | \(-0.485977\pi\) | ||||
0.0440399 | + | 0.999030i | \(0.485977\pi\) | |||||||
\(558\) | 14.4139 | 0.610189 | ||||||||
\(559\) | −1.90818 | −0.0807074 | ||||||||
\(560\) | 1.09564 | 0.0462991 | ||||||||
\(561\) | −1.31349 | −0.0554556 | ||||||||
\(562\) | −20.6065 | −0.869234 | ||||||||
\(563\) | −10.9676 | −0.462231 | −0.231116 | − | 0.972926i | \(-0.574238\pi\) | ||||
−0.231116 | + | 0.972926i | \(0.574238\pi\) | |||||||
\(564\) | −3.89489 | −0.164004 | ||||||||
\(565\) | 10.5679 | 0.444596 | ||||||||
\(566\) | −15.6785 | −0.659016 | ||||||||
\(567\) | 12.1170 | 0.508865 | ||||||||
\(568\) | −6.15084 | −0.258084 | ||||||||
\(569\) | 0.865205 | 0.0362713 | 0.0181356 | − | 0.999836i | \(-0.494227\pi\) | ||||
0.0181356 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(570\) | 0.297226 | 0.0124494 | ||||||||
\(571\) | 24.5838 | 1.02880 | 0.514400 | − | 0.857551i | \(-0.328015\pi\) | ||||
0.514400 | + | 0.857551i | \(0.328015\pi\) | |||||||
\(572\) | −1.94172 | −0.0811874 | ||||||||
\(573\) | −8.06675 | −0.336993 | ||||||||
\(574\) | −7.66035 | −0.319737 | ||||||||
\(575\) | 1.14955 | 0.0479396 | ||||||||
\(576\) | −2.78773 | −0.116155 | ||||||||
\(577\) | 12.1607 | 0.506257 | 0.253128 | − | 0.967433i | \(-0.418541\pi\) | ||||
0.253128 | + | 0.967433i | \(0.418541\pi\) | |||||||
\(578\) | −6.46922 | −0.269084 | ||||||||
\(579\) | 8.70236 | 0.361658 | ||||||||
\(580\) | −4.48818 | −0.186361 | ||||||||
\(581\) | 20.8091 | 0.863306 | ||||||||
\(582\) | −3.72363 | −0.154349 | ||||||||
\(583\) | 0.969929 | 0.0401704 | ||||||||
\(584\) | −0.0206681 | −0.000855252 0 | ||||||||
\(585\) | 3.97492 | 0.164343 | ||||||||
\(586\) | 15.5027 | 0.640411 | ||||||||
\(587\) | 30.0892 | 1.24191 | 0.620957 | − | 0.783845i | \(-0.286744\pi\) | ||||
0.620957 | + | 0.783845i | \(0.286744\pi\) | |||||||
\(588\) | −1.89620 | −0.0781979 | ||||||||
\(589\) | −5.17048 | −0.213046 | ||||||||
\(590\) | −7.37048 | −0.303438 | ||||||||
\(591\) | 7.53187 | 0.309820 | ||||||||
\(592\) | 4.12685 | 0.169612 | ||||||||
\(593\) | −30.8823 | −1.26819 | −0.634093 | − | 0.773257i | \(-0.718626\pi\) | ||||
−0.634093 | + | 0.773257i | \(0.718626\pi\) | |||||||
\(594\) | −2.34264 | −0.0961196 | ||||||||
\(595\) | −3.55547 | −0.145760 | ||||||||
\(596\) | −11.9151 | −0.488061 | ||||||||
\(597\) | 2.92715 | 0.119800 | ||||||||
\(598\) | 0.554287 | 0.0226665 | ||||||||
\(599\) | −28.0460 | −1.14593 | −0.572964 | − | 0.819581i | \(-0.694206\pi\) | ||||
−0.572964 | + | 0.819581i | \(0.694206\pi\) | |||||||
\(600\) | −2.11188 | −0.0862172 | ||||||||
\(601\) | −22.7623 | −0.928493 | −0.464246 | − | 0.885706i | \(-0.653675\pi\) | ||||
−0.464246 | + | 0.885706i | \(0.653675\pi\) | |||||||
\(602\) | 1.46625 | 0.0597600 | ||||||||
\(603\) | 11.4903 | 0.467923 | ||||||||
\(604\) | 4.00395 | 0.162918 | ||||||||
\(605\) | −6.59847 | −0.268266 | ||||||||
\(606\) | 0.441994 | 0.0179548 | ||||||||
\(607\) | −46.9739 | −1.90661 | −0.953306 | − | 0.302005i | \(-0.902344\pi\) | ||||
−0.953306 | + | 0.302005i | \(0.902344\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −5.44365 | −0.220588 | ||||||||
\(610\) | 5.05446 | 0.204649 | ||||||||
\(611\) | 18.6846 | 0.755899 | ||||||||
\(612\) | 9.04651 | 0.365684 | ||||||||
\(613\) | −48.8112 | −1.97147 | −0.985733 | − | 0.168315i | \(-0.946168\pi\) | ||||
−0.985733 | + | 0.168315i | \(0.946168\pi\) | |||||||
\(614\) | 1.42294 | 0.0574250 | ||||||||
\(615\) | −1.34064 | −0.0540600 | ||||||||
\(616\) | 1.49203 | 0.0601154 | ||||||||
\(617\) | 22.6779 | 0.912978 | 0.456489 | − | 0.889729i | \(-0.349107\pi\) | ||||
0.456489 | + | 0.889729i | \(0.349107\pi\) | |||||||
\(618\) | −1.58190 | −0.0636333 | ||||||||
\(619\) | 20.5635 | 0.826518 | 0.413259 | − | 0.910614i | \(-0.364391\pi\) | ||||
0.413259 | + | 0.910614i | \(0.364391\pi\) | |||||||
\(620\) | −3.33561 | −0.133961 | ||||||||
\(621\) | 0.668733 | 0.0268354 | ||||||||
\(622\) | 1.66714 | 0.0668463 | ||||||||
\(623\) | 1.60357 | 0.0642455 | ||||||||
\(624\) | −1.01830 | −0.0407646 | ||||||||
\(625\) | 18.9304 | 0.757216 | ||||||||
\(626\) | 29.0193 | 1.15984 | ||||||||
\(627\) | 0.404759 | 0.0161645 | ||||||||
\(628\) | −21.5010 | −0.857983 | ||||||||
\(629\) | −13.3921 | −0.533978 | ||||||||
\(630\) | −3.05434 | −0.121688 | ||||||||
\(631\) | 19.1828 | 0.763655 | 0.381827 | − | 0.924234i | \(-0.375295\pi\) | ||||
0.381827 | + | 0.924234i | \(0.375295\pi\) | |||||||
\(632\) | 3.73317 | 0.148498 | ||||||||
\(633\) | −0.460726 | −0.0183122 | ||||||||
\(634\) | −20.7912 | −0.825725 | ||||||||
\(635\) | −5.40892 | −0.214647 | ||||||||
\(636\) | 0.508661 | 0.0201697 | ||||||||
\(637\) | 9.09648 | 0.360416 | ||||||||
\(638\) | −6.11195 | −0.241974 | ||||||||
\(639\) | 17.1469 | 0.678321 | ||||||||
\(640\) | 0.645126 | 0.0255008 | ||||||||
\(641\) | 11.3206 | 0.447136 | 0.223568 | − | 0.974688i | \(-0.428230\pi\) | ||||
0.223568 | + | 0.974688i | \(0.428230\pi\) | |||||||
\(642\) | 2.77830 | 0.109651 | ||||||||
\(643\) | −6.07447 | −0.239554 | −0.119777 | − | 0.992801i | \(-0.538218\pi\) | ||||
−0.119777 | + | 0.992801i | \(0.538218\pi\) | |||||||
\(644\) | −0.425916 | −0.0167834 | ||||||||
\(645\) | 0.256610 | 0.0101040 | ||||||||
\(646\) | −3.24512 | −0.127677 | ||||||||
\(647\) | −7.00039 | −0.275214 | −0.137607 | − | 0.990487i | \(-0.543941\pi\) | ||||
−0.137607 | + | 0.990487i | \(0.543941\pi\) | |||||||
\(648\) | 7.13464 | 0.280275 | ||||||||
\(649\) | −10.0370 | −0.393988 | ||||||||
\(650\) | 10.1312 | 0.397377 | ||||||||
\(651\) | −4.04572 | −0.158564 | ||||||||
\(652\) | −17.7351 | −0.694560 | ||||||||
\(653\) | 13.6085 | 0.532540 | 0.266270 | − | 0.963898i | \(-0.414209\pi\) | ||||
0.266270 | + | 0.963898i | \(0.414209\pi\) | |||||||
\(654\) | −2.96946 | −0.116115 | ||||||||
\(655\) | 7.47558 | 0.292095 | ||||||||
\(656\) | −4.51052 | −0.176106 | ||||||||
\(657\) | 0.0576171 | 0.00224786 | ||||||||
\(658\) | −14.3573 | −0.559708 | ||||||||
\(659\) | 8.07413 | 0.314523 | 0.157262 | − | 0.987557i | \(-0.449733\pi\) | ||||
0.157262 | + | 0.987557i | \(0.449733\pi\) | |||||||
\(660\) | 0.261121 | 0.0101641 | ||||||||
\(661\) | −14.9075 | −0.579836 | −0.289918 | − | 0.957052i | \(-0.593628\pi\) | ||||
−0.289918 | + | 0.957052i | \(0.593628\pi\) | |||||||
\(662\) | 1.45503 | 0.0565513 | ||||||||
\(663\) | 3.30450 | 0.128336 | ||||||||
\(664\) | 12.2527 | 0.475496 | ||||||||
\(665\) | 1.09564 | 0.0424870 | ||||||||
\(666\) | −11.5045 | −0.445792 | ||||||||
\(667\) | 1.74473 | 0.0675561 | ||||||||
\(668\) | 9.68545 | 0.374741 | ||||||||
\(669\) | −0.138435 | −0.00535221 | ||||||||
\(670\) | −2.65905 | −0.102728 | ||||||||
\(671\) | 6.88311 | 0.265719 | ||||||||
\(672\) | 0.782465 | 0.0301842 | ||||||||
\(673\) | −9.77470 | −0.376787 | −0.188394 | − | 0.982094i | \(-0.560328\pi\) | ||||
−0.188394 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(674\) | −21.9574 | −0.845767 | ||||||||
\(675\) | 12.2230 | 0.470464 | ||||||||
\(676\) | −8.11499 | −0.312115 | ||||||||
\(677\) | −41.7106 | −1.60307 | −0.801535 | − | 0.597948i | \(-0.795983\pi\) | ||||
−0.801535 | + | 0.597948i | \(0.795983\pi\) | |||||||
\(678\) | 7.54724 | 0.289850 | ||||||||
\(679\) | −13.7261 | −0.526758 | ||||||||
\(680\) | −2.09351 | −0.0802824 | ||||||||
\(681\) | 11.1194 | 0.426097 | ||||||||
\(682\) | −4.54239 | −0.173937 | ||||||||
\(683\) | 45.3543 | 1.73543 | 0.867717 | − | 0.497059i | \(-0.165587\pi\) | ||||
0.867717 | + | 0.497059i | \(0.165587\pi\) | |||||||
\(684\) | −2.78773 | −0.106592 | ||||||||
\(685\) | 11.4246 | 0.436510 | ||||||||
\(686\) | −18.8781 | −0.720769 | ||||||||
\(687\) | 8.56282 | 0.326692 | ||||||||
\(688\) | 0.863349 | 0.0329149 | ||||||||
\(689\) | −2.44016 | −0.0929627 | ||||||||
\(690\) | −0.0745400 | −0.00283769 | ||||||||
\(691\) | −25.0269 | −0.952067 | −0.476034 | − | 0.879427i | \(-0.657926\pi\) | ||||
−0.476034 | + | 0.879427i | \(0.657926\pi\) | |||||||
\(692\) | 22.6120 | 0.859579 | ||||||||
\(693\) | −4.15937 | −0.158001 | ||||||||
\(694\) | −16.7802 | −0.636968 | ||||||||
\(695\) | −8.85765 | −0.335990 | ||||||||
\(696\) | −3.20530 | −0.121496 | ||||||||
\(697\) | 14.6372 | 0.554422 | ||||||||
\(698\) | 31.6741 | 1.19888 | ||||||||
\(699\) | −9.58153 | −0.362407 | ||||||||
\(700\) | −7.78483 | −0.294239 | ||||||||
\(701\) | 5.83789 | 0.220494 | 0.110247 | − | 0.993904i | \(-0.464836\pi\) | ||||
0.110247 | + | 0.993904i | \(0.464836\pi\) | |||||||
\(702\) | 5.89364 | 0.222441 | ||||||||
\(703\) | 4.12685 | 0.155647 | ||||||||
\(704\) | 0.878525 | 0.0331107 | ||||||||
\(705\) | −2.51269 | −0.0946335 | ||||||||
\(706\) | 8.97346 | 0.337721 | ||||||||
\(707\) | 1.62928 | 0.0612753 | ||||||||
\(708\) | −5.26374 | −0.197823 | ||||||||
\(709\) | −7.39188 | −0.277608 | −0.138804 | − | 0.990320i | \(-0.544326\pi\) | ||||
−0.138804 | + | 0.990320i | \(0.544326\pi\) | |||||||
\(710\) | −3.96807 | −0.148919 | ||||||||
\(711\) | −10.4071 | −0.390296 | ||||||||
\(712\) | 0.944202 | 0.0353855 | ||||||||
\(713\) | 1.29668 | 0.0485610 | ||||||||
\(714\) | −2.53919 | −0.0950268 | ||||||||
\(715\) | −1.25265 | −0.0468466 | ||||||||
\(716\) | −1.85040 | −0.0691528 | ||||||||
\(717\) | −3.99996 | −0.149381 | ||||||||
\(718\) | −11.1130 | −0.414735 | ||||||||
\(719\) | −37.4008 | −1.39482 | −0.697408 | − | 0.716675i | \(-0.745663\pi\) | ||||
−0.697408 | + | 0.716675i | \(0.745663\pi\) | |||||||
\(720\) | −1.79844 | −0.0670238 | ||||||||
\(721\) | −5.83120 | −0.217165 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −2.53566 | −0.0943021 | ||||||||
\(724\) | 17.8420 | 0.663093 | ||||||||
\(725\) | 31.8898 | 1.18436 | ||||||||
\(726\) | −4.71240 | −0.174893 | ||||||||
\(727\) | 3.91838 | 0.145325 | 0.0726623 | − | 0.997357i | \(-0.476850\pi\) | ||||
0.0726623 | + | 0.997357i | \(0.476850\pi\) | |||||||
\(728\) | −3.75366 | −0.139120 | ||||||||
\(729\) | −16.2038 | −0.600141 | ||||||||
\(730\) | −0.0133335 | −0.000493496 0 | ||||||||
\(731\) | −2.80167 | −0.103623 | ||||||||
\(732\) | 3.60972 | 0.133419 | ||||||||
\(733\) | 20.3180 | 0.750464 | 0.375232 | − | 0.926931i | \(-0.377563\pi\) | ||||
0.375232 | + | 0.926931i | \(0.377563\pi\) | |||||||
\(734\) | 22.3538 | 0.825094 | ||||||||
\(735\) | −1.22329 | −0.0451216 | ||||||||
\(736\) | −0.250785 | −0.00924407 | ||||||||
\(737\) | −3.62106 | −0.133384 | ||||||||
\(738\) | 12.5741 | 0.462859 | ||||||||
\(739\) | −22.6161 | −0.831946 | −0.415973 | − | 0.909377i | \(-0.636559\pi\) | ||||
−0.415973 | + | 0.909377i | \(0.636559\pi\) | |||||||
\(740\) | 2.66234 | 0.0978695 | ||||||||
\(741\) | −1.01830 | −0.0374082 | ||||||||
\(742\) | 1.87503 | 0.0688345 | ||||||||
\(743\) | 41.6489 | 1.52795 | 0.763975 | − | 0.645246i | \(-0.223245\pi\) | ||||
0.763975 | + | 0.645246i | \(0.223245\pi\) | |||||||
\(744\) | −2.38217 | −0.0873347 | ||||||||
\(745\) | −7.68674 | −0.281620 | ||||||||
\(746\) | −0.703120 | −0.0257431 | ||||||||
\(747\) | −34.1571 | −1.24974 | ||||||||
\(748\) | −2.85092 | −0.104240 | ||||||||
\(749\) | 10.2414 | 0.374212 | ||||||||
\(750\) | −2.84856 | −0.104015 | ||||||||
\(751\) | −3.07181 | −0.112092 | −0.0560460 | − | 0.998428i | \(-0.517849\pi\) | ||||
−0.0560460 | + | 0.998428i | \(0.517849\pi\) | |||||||
\(752\) | −8.45380 | −0.308278 | ||||||||
\(753\) | −6.31569 | −0.230156 | ||||||||
\(754\) | 15.3765 | 0.559980 | ||||||||
\(755\) | 2.58305 | 0.0940069 | ||||||||
\(756\) | −4.52870 | −0.164707 | ||||||||
\(757\) | 11.4073 | 0.414605 | 0.207303 | − | 0.978277i | \(-0.433532\pi\) | ||||
0.207303 | + | 0.978277i | \(0.433532\pi\) | |||||||
\(758\) | 4.45597 | 0.161848 | ||||||||
\(759\) | −0.101508 | −0.00368450 | ||||||||
\(760\) | 0.645126 | 0.0234012 | ||||||||
\(761\) | −3.48416 | −0.126301 | −0.0631503 | − | 0.998004i | \(-0.520115\pi\) | ||||
−0.0631503 | + | 0.998004i | \(0.520115\pi\) | |||||||
\(762\) | −3.86286 | −0.139937 | ||||||||
\(763\) | −10.9461 | −0.396274 | ||||||||
\(764\) | −17.5088 | −0.633445 | ||||||||
\(765\) | 5.83614 | 0.211006 | ||||||||
\(766\) | 15.3346 | 0.554061 | ||||||||
\(767\) | 25.2513 | 0.911772 | ||||||||
\(768\) | 0.460726 | 0.0166250 | ||||||||
\(769\) | −18.2702 | −0.658839 | −0.329419 | − | 0.944184i | \(-0.606853\pi\) | ||||
−0.329419 | + | 0.944184i | \(0.606853\pi\) | |||||||
\(770\) | 0.962545 | 0.0346877 | ||||||||
\(771\) | −7.53749 | −0.271456 | ||||||||
\(772\) | 18.8884 | 0.679807 | ||||||||
\(773\) | −12.8306 | −0.461484 | −0.230742 | − | 0.973015i | \(-0.574115\pi\) | ||||
−0.230742 | + | 0.973015i | \(0.574115\pi\) | |||||||
\(774\) | −2.40679 | −0.0865102 | ||||||||
\(775\) | 23.7005 | 0.851347 | ||||||||
\(776\) | −8.08209 | −0.290130 | ||||||||
\(777\) | 3.22911 | 0.115844 | ||||||||
\(778\) | 0.666043 | 0.0238788 | ||||||||
\(779\) | −4.51052 | −0.161606 | ||||||||
\(780\) | −0.656931 | −0.0235219 | ||||||||
\(781\) | −5.40367 | −0.193359 | ||||||||
\(782\) | 0.813827 | 0.0291024 | ||||||||
\(783\) | 18.5514 | 0.662973 | ||||||||
\(784\) | −4.11567 | −0.146988 | ||||||||
\(785\) | −13.8708 | −0.495072 | ||||||||
\(786\) | 5.33879 | 0.190428 | ||||||||
\(787\) | 15.2580 | 0.543888 | 0.271944 | − | 0.962313i | \(-0.412333\pi\) | ||||
0.271944 | + | 0.962313i | \(0.412333\pi\) | |||||||
\(788\) | 16.3478 | 0.582368 | ||||||||
\(789\) | −7.02945 | −0.250255 | ||||||||
\(790\) | 2.40837 | 0.0856858 | ||||||||
\(791\) | 27.8207 | 0.989189 | ||||||||
\(792\) | −2.44909 | −0.0870247 | ||||||||
\(793\) | −17.3166 | −0.614931 | ||||||||
\(794\) | −27.5420 | −0.977430 | ||||||||
\(795\) | 0.328151 | 0.0116383 | ||||||||
\(796\) | 6.35334 | 0.225188 | ||||||||
\(797\) | −35.9817 | −1.27454 | −0.637269 | − | 0.770641i | \(-0.719936\pi\) | ||||
−0.637269 | + | 0.770641i | \(0.719936\pi\) | |||||||
\(798\) | 0.782465 | 0.0276990 | ||||||||
\(799\) | 27.4336 | 0.970530 | ||||||||
\(800\) | −4.58381 | −0.162062 | ||||||||
\(801\) | −2.63218 | −0.0930035 | ||||||||
\(802\) | 25.4611 | 0.899061 | ||||||||
\(803\) | −0.0181575 | −0.000640763 0 | ||||||||
\(804\) | −1.89900 | −0.0669725 | ||||||||
\(805\) | −0.274770 | −0.00968436 | ||||||||
\(806\) | 11.4278 | 0.402528 | ||||||||
\(807\) | 1.22708 | 0.0431954 | ||||||||
\(808\) | 0.959342 | 0.0337495 | ||||||||
\(809\) | 34.3670 | 1.20828 | 0.604139 | − | 0.796879i | \(-0.293517\pi\) | ||||
0.604139 | + | 0.796879i | \(0.293517\pi\) | |||||||
\(810\) | 4.60274 | 0.161724 | ||||||||
\(811\) | −21.2131 | −0.744892 | −0.372446 | − | 0.928054i | \(-0.621481\pi\) | ||||
−0.372446 | + | 0.928054i | \(0.621481\pi\) | |||||||
\(812\) | −11.8154 | −0.414639 | ||||||||
\(813\) | −5.15426 | −0.180768 | ||||||||
\(814\) | 3.62554 | 0.127075 | ||||||||
\(815\) | −11.4414 | −0.400774 | ||||||||
\(816\) | −1.49511 | −0.0523393 | ||||||||
\(817\) | 0.863349 | 0.0302048 | ||||||||
\(818\) | −12.7346 | −0.445254 | ||||||||
\(819\) | 10.4642 | 0.365649 | ||||||||
\(820\) | −2.90985 | −0.101616 | ||||||||
\(821\) | −35.5049 | −1.23913 | −0.619566 | − | 0.784945i | \(-0.712691\pi\) | ||||
−0.619566 | + | 0.784945i | \(0.712691\pi\) | |||||||
\(822\) | 8.15902 | 0.284578 | ||||||||
\(823\) | −18.7535 | −0.653706 | −0.326853 | − | 0.945075i | \(-0.605988\pi\) | ||||
−0.326853 | + | 0.945075i | \(0.605988\pi\) | |||||||
\(824\) | −3.43349 | −0.119611 | ||||||||
\(825\) | −1.85534 | −0.0645947 | ||||||||
\(826\) | −19.4032 | −0.675124 | ||||||||
\(827\) | −21.5994 | −0.751086 | −0.375543 | − | 0.926805i | \(-0.622544\pi\) | ||||
−0.375543 | + | 0.926805i | \(0.622544\pi\) | |||||||
\(828\) | 0.699122 | 0.0242962 | ||||||||
\(829\) | 20.3139 | 0.705532 | 0.352766 | − | 0.935711i | \(-0.385241\pi\) | ||||
0.352766 | + | 0.935711i | \(0.385241\pi\) | |||||||
\(830\) | 7.90452 | 0.274370 | ||||||||
\(831\) | 6.35673 | 0.220513 | ||||||||
\(832\) | −2.21021 | −0.0766251 | ||||||||
\(833\) | 13.3558 | 0.462752 | ||||||||
\(834\) | −6.32582 | −0.219045 | ||||||||
\(835\) | 6.24834 | 0.216233 | ||||||||
\(836\) | 0.878525 | 0.0303844 | ||||||||
\(837\) | 13.7874 | 0.476561 | ||||||||
\(838\) | 35.7455 | 1.23481 | ||||||||
\(839\) | −18.6544 | −0.644022 | −0.322011 | − | 0.946736i | \(-0.604359\pi\) | ||||
−0.322011 | + | 0.946736i | \(0.604359\pi\) | |||||||
\(840\) | 0.504789 | 0.0174169 | ||||||||
\(841\) | 19.4006 | 0.668988 | ||||||||
\(842\) | 9.41270 | 0.324383 | ||||||||
\(843\) | −9.49396 | −0.326989 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −5.23519 | −0.180096 | ||||||||
\(846\) | 23.5669 | 0.810247 | ||||||||
\(847\) | −17.3709 | −0.596870 | ||||||||
\(848\) | 1.10404 | 0.0379130 | ||||||||
\(849\) | −7.22349 | −0.247909 | ||||||||
\(850\) | 14.8750 | 0.510208 | ||||||||
\(851\) | −1.03495 | −0.0354777 | ||||||||
\(852\) | −2.83385 | −0.0970862 | ||||||||
\(853\) | 49.2044 | 1.68473 | 0.842363 | − | 0.538910i | \(-0.181164\pi\) | ||||
0.842363 | + | 0.538910i | \(0.181164\pi\) | |||||||
\(854\) | 13.3062 | 0.455327 | ||||||||
\(855\) | −1.79844 | −0.0615053 | ||||||||
\(856\) | 6.03026 | 0.206110 | ||||||||
\(857\) | 15.6583 | 0.534876 | 0.267438 | − | 0.963575i | \(-0.413823\pi\) | ||||
0.267438 | + | 0.963575i | \(0.413823\pi\) | |||||||
\(858\) | −0.894601 | −0.0305412 | ||||||||
\(859\) | 12.4783 | 0.425754 | 0.212877 | − | 0.977079i | \(-0.431717\pi\) | ||||
0.212877 | + | 0.977079i | \(0.431717\pi\) | |||||||
\(860\) | 0.556969 | 0.0189925 | ||||||||
\(861\) | −3.52932 | −0.120279 | ||||||||
\(862\) | −26.0702 | −0.887956 | ||||||||
\(863\) | −13.8419 | −0.471183 | −0.235591 | − | 0.971852i | \(-0.575703\pi\) | ||||
−0.235591 | + | 0.971852i | \(0.575703\pi\) | |||||||
\(864\) | −2.66656 | −0.0907182 | ||||||||
\(865\) | 14.5876 | 0.495993 | ||||||||
\(866\) | 16.2636 | 0.552659 | ||||||||
\(867\) | −2.98054 | −0.101224 | ||||||||
\(868\) | −8.78118 | −0.298053 | ||||||||
\(869\) | 3.27968 | 0.111256 | ||||||||
\(870\) | −2.06782 | −0.0701057 | ||||||||
\(871\) | 9.10992 | 0.308678 | ||||||||
\(872\) | −6.44518 | −0.218261 | ||||||||
\(873\) | 22.5307 | 0.762549 | ||||||||
\(874\) | −0.250785 | −0.00848294 | ||||||||
\(875\) | −10.5004 | −0.354978 | ||||||||
\(876\) | −0.00952234 | −0.000321730 0 | ||||||||
\(877\) | 19.5952 | 0.661683 | 0.330841 | − | 0.943686i | \(-0.392667\pi\) | ||||
0.330841 | + | 0.943686i | \(0.392667\pi\) | |||||||
\(878\) | −31.8460 | −1.07475 | ||||||||
\(879\) | 7.14250 | 0.240910 | ||||||||
\(880\) | 0.566760 | 0.0191055 | ||||||||
\(881\) | 5.60531 | 0.188848 | 0.0944239 | − | 0.995532i | \(-0.469899\pi\) | ||||
0.0944239 | + | 0.995532i | \(0.469899\pi\) | |||||||
\(882\) | 11.4734 | 0.386329 | ||||||||
\(883\) | −12.3954 | −0.417139 | −0.208570 | − | 0.978008i | \(-0.566881\pi\) | ||||
−0.208570 | + | 0.978008i | \(0.566881\pi\) | |||||||
\(884\) | 7.17237 | 0.241233 | ||||||||
\(885\) | −3.39577 | −0.114148 | ||||||||
\(886\) | 33.2149 | 1.11588 | ||||||||
\(887\) | 36.5755 | 1.22808 | 0.614042 | − | 0.789273i | \(-0.289542\pi\) | ||||
0.614042 | + | 0.789273i | \(0.289542\pi\) | |||||||
\(888\) | 1.90135 | 0.0638050 | ||||||||
\(889\) | −14.2393 | −0.477571 | ||||||||
\(890\) | 0.609129 | 0.0204181 | ||||||||
\(891\) | 6.26796 | 0.209985 | ||||||||
\(892\) | −0.300471 | −0.0100605 | ||||||||
\(893\) | −8.45380 | −0.282896 | ||||||||
\(894\) | −5.48960 | −0.183600 | ||||||||
\(895\) | −1.19374 | −0.0399024 | ||||||||
\(896\) | 1.69833 | 0.0567372 | ||||||||
\(897\) | 0.255374 | 0.00852670 | ||||||||
\(898\) | 31.3215 | 1.04521 | ||||||||
\(899\) | 35.9713 | 1.19971 | ||||||||
\(900\) | 12.7784 | 0.425948 | ||||||||
\(901\) | −3.58275 | −0.119359 | ||||||||
\(902\) | −3.96260 | −0.131940 | ||||||||
\(903\) | 0.675541 | 0.0224806 | ||||||||
\(904\) | 16.3812 | 0.544830 | ||||||||
\(905\) | 11.5103 | 0.382617 | ||||||||
\(906\) | 1.84472 | 0.0612869 | ||||||||
\(907\) | 5.29724 | 0.175892 | 0.0879459 | − | 0.996125i | \(-0.471970\pi\) | ||||
0.0879459 | + | 0.996125i | \(0.471970\pi\) | |||||||
\(908\) | 24.1346 | 0.800934 | ||||||||
\(909\) | −2.67439 | −0.0887038 | ||||||||
\(910\) | −2.42158 | −0.0802747 | ||||||||
\(911\) | 51.5586 | 1.70821 | 0.854106 | − | 0.520099i | \(-0.174105\pi\) | ||||
0.854106 | + | 0.520099i | \(0.174105\pi\) | |||||||
\(912\) | 0.460726 | 0.0152562 | ||||||||
\(913\) | 10.7643 | 0.356246 | ||||||||
\(914\) | −36.4027 | −1.20409 | ||||||||
\(915\) | 2.32872 | 0.0769852 | ||||||||
\(916\) | 18.5855 | 0.614082 | ||||||||
\(917\) | 19.6799 | 0.649887 | ||||||||
\(918\) | 8.65329 | 0.285601 | ||||||||
\(919\) | −10.7944 | −0.356074 | −0.178037 | − | 0.984024i | \(-0.556975\pi\) | ||||
−0.178037 | + | 0.984024i | \(0.556975\pi\) | |||||||
\(920\) | −0.161788 | −0.00533400 | ||||||||
\(921\) | 0.655584 | 0.0216022 | ||||||||
\(922\) | −20.5792 | −0.677739 | ||||||||
\(923\) | 13.5946 | 0.447473 | ||||||||
\(924\) | 0.687415 | 0.0226143 | ||||||||
\(925\) | −18.9167 | −0.621977 | ||||||||
\(926\) | 10.6034 | 0.348450 | ||||||||
\(927\) | 9.57165 | 0.314374 | ||||||||
\(928\) | −6.95706 | −0.228377 | ||||||||
\(929\) | 42.5967 | 1.39755 | 0.698776 | − | 0.715341i | \(-0.253728\pi\) | ||||
0.698776 | + | 0.715341i | \(0.253728\pi\) | |||||||
\(930\) | −1.53680 | −0.0503937 | ||||||||
\(931\) | −4.11567 | −0.134886 | ||||||||
\(932\) | −20.7966 | −0.681215 | ||||||||
\(933\) | 0.768096 | 0.0251463 | ||||||||
\(934\) | −2.51857 | −0.0824100 | ||||||||
\(935\) | −1.83920 | −0.0601483 | ||||||||
\(936\) | 6.16146 | 0.201394 | ||||||||
\(937\) | −9.40348 | −0.307198 | −0.153599 | − | 0.988133i | \(-0.549086\pi\) | ||||
−0.153599 | + | 0.988133i | \(0.549086\pi\) | |||||||
\(938\) | −7.00010 | −0.228561 | ||||||||
\(939\) | 13.3699 | 0.436312 | ||||||||
\(940\) | −5.45377 | −0.177882 | ||||||||
\(941\) | −14.8997 | −0.485715 | −0.242858 | − | 0.970062i | \(-0.578085\pi\) | ||||
−0.242858 | + | 0.970062i | \(0.578085\pi\) | |||||||
\(942\) | −9.90606 | −0.322757 | ||||||||
\(943\) | 1.13117 | 0.0368360 | ||||||||
\(944\) | −11.4249 | −0.371848 | ||||||||
\(945\) | −2.92158 | −0.0950390 | ||||||||
\(946\) | 0.758474 | 0.0246601 | ||||||||
\(947\) | −34.8195 | −1.13148 | −0.565741 | − | 0.824583i | \(-0.691410\pi\) | ||||
−0.565741 | + | 0.824583i | \(0.691410\pi\) | |||||||
\(948\) | 1.71997 | 0.0558620 | ||||||||
\(949\) | 0.0456808 | 0.00148286 | ||||||||
\(950\) | −4.58381 | −0.148719 | ||||||||
\(951\) | −9.57906 | −0.310622 | ||||||||
\(952\) | −5.51128 | −0.178622 | ||||||||
\(953\) | −23.7351 | −0.768856 | −0.384428 | − | 0.923155i | \(-0.625601\pi\) | ||||
−0.384428 | + | 0.923155i | \(0.625601\pi\) | |||||||
\(954\) | −3.07777 | −0.0996466 | ||||||||
\(955\) | −11.2954 | −0.365509 | ||||||||
\(956\) | −8.68185 | −0.280791 | ||||||||
\(957\) | −2.81593 | −0.0910262 | ||||||||
\(958\) | −28.5571 | −0.922640 | ||||||||
\(959\) | 30.0758 | 0.971198 | ||||||||
\(960\) | 0.297226 | 0.00959294 | ||||||||
\(961\) | −4.26618 | −0.137619 | ||||||||
\(962\) | −9.12118 | −0.294079 | ||||||||
\(963\) | −16.8107 | −0.541718 | ||||||||
\(964\) | −5.50361 | −0.177259 | ||||||||
\(965\) | 12.1854 | 0.392261 | ||||||||
\(966\) | −0.196231 | −0.00631362 | ||||||||
\(967\) | −5.78042 | −0.185886 | −0.0929429 | − | 0.995671i | \(-0.529627\pi\) | ||||
−0.0929429 | + | 0.995671i | \(0.529627\pi\) | |||||||
\(968\) | −10.2282 | −0.328747 | ||||||||
\(969\) | −1.49511 | −0.0480298 | ||||||||
\(970\) | −5.21397 | −0.167410 | ||||||||
\(971\) | −2.26732 | −0.0727617 | −0.0363809 | − | 0.999338i | \(-0.511583\pi\) | ||||
−0.0363809 | + | 0.999338i | \(0.511583\pi\) | |||||||
\(972\) | 11.2868 | 0.362024 | ||||||||
\(973\) | −23.3183 | −0.747549 | ||||||||
\(974\) | 11.9271 | 0.382169 | ||||||||
\(975\) | 4.66769 | 0.149486 | ||||||||
\(976\) | 7.83485 | 0.250787 | ||||||||
\(977\) | −51.3263 | −1.64207 | −0.821036 | − | 0.570876i | \(-0.806604\pi\) | ||||
−0.821036 | + | 0.570876i | \(0.806604\pi\) | |||||||
\(978\) | −8.17102 | −0.261280 | ||||||||
\(979\) | 0.829505 | 0.0265111 | ||||||||
\(980\) | −2.65513 | −0.0848150 | ||||||||
\(981\) | 17.9674 | 0.573656 | ||||||||
\(982\) | −26.7750 | −0.854425 | ||||||||
\(983\) | 47.6101 | 1.51852 | 0.759262 | − | 0.650785i | \(-0.225560\pi\) | ||||
0.759262 | + | 0.650785i | \(0.225560\pi\) | |||||||
\(984\) | −2.07811 | −0.0662478 | ||||||||
\(985\) | 10.5464 | 0.336037 | ||||||||
\(986\) | 22.5765 | 0.718981 | ||||||||
\(987\) | −6.61480 | −0.210551 | ||||||||
\(988\) | −2.21021 | −0.0703160 | ||||||||
\(989\) | −0.216515 | −0.00688479 | ||||||||
\(990\) | −1.57997 | −0.0502148 | ||||||||
\(991\) | 4.39478 | 0.139605 | 0.0698024 | − | 0.997561i | \(-0.477763\pi\) | ||||
0.0698024 | + | 0.997561i | \(0.477763\pi\) | |||||||
\(992\) | −5.17048 | −0.164163 | ||||||||
\(993\) | 0.670370 | 0.0212736 | ||||||||
\(994\) | −10.4462 | −0.331332 | ||||||||
\(995\) | 4.09871 | 0.129938 | ||||||||
\(996\) | 5.64512 | 0.178873 | ||||||||
\(997\) | −18.5491 | −0.587457 | −0.293728 | − | 0.955889i | \(-0.594896\pi\) | ||||
−0.293728 | + | 0.955889i | \(0.594896\pi\) | |||||||
\(998\) | 34.3714 | 1.08801 | ||||||||
\(999\) | −11.0045 | −0.348166 |
(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 | 8018.2.a.d.1.18 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.18 | ✓ | 30 | 1.1 | even | 1 | trivial |