Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, 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("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.87996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.29417 | −1.47320 | −0.736600 | − | 0.676329i | \(-0.763570\pi\) | ||||
−0.736600 | + | 0.676329i | \(0.763570\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.46575 | 0.931965 | 0.465982 | − | 0.884794i | \(-0.345701\pi\) | ||||
0.465982 | + | 0.884794i | \(0.345701\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.29417 | 1.04171 | ||||||||
\(11\) | 5.48709 | 1.65442 | 0.827210 | − | 0.561892i | \(-0.189926\pi\) | ||||
0.827210 | + | 0.561892i | \(0.189926\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.169761 | −0.0470832 | −0.0235416 | − | 0.999723i | \(-0.507494\pi\) | ||||
−0.0235416 | + | 0.999723i | \(0.507494\pi\) | |||||||
\(14\) | −2.46575 | −0.658999 | ||||||||
\(15\) | 3.29417 | 0.850552 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.362680 | 0.0879628 | 0.0439814 | − | 0.999032i | \(-0.485996\pi\) | ||||
0.0439814 | + | 0.999032i | \(0.485996\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.85158 | 1.11303 | 0.556515 | − | 0.830838i | \(-0.312138\pi\) | ||||
0.556515 | + | 0.830838i | \(0.312138\pi\) | |||||||
\(20\) | −3.29417 | −0.736600 | ||||||||
\(21\) | −2.46575 | −0.538070 | ||||||||
\(22\) | −5.48709 | −1.16985 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 5.85158 | 1.17032 | ||||||||
\(26\) | 0.169761 | 0.0332929 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.46575 | 0.465982 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −3.29417 | −0.601431 | ||||||||
\(31\) | −3.48709 | −0.626300 | −0.313150 | − | 0.949704i | \(-0.601384\pi\) | ||||
−0.313150 | + | 0.949704i | \(0.601384\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.48709 | −0.955180 | ||||||||
\(34\) | −0.362680 | −0.0621991 | ||||||||
\(35\) | −8.12260 | −1.37297 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.8843 | 1.78937 | 0.894687 | − | 0.446694i | \(-0.147399\pi\) | ||||
0.894687 | + | 0.446694i | \(0.147399\pi\) | |||||||
\(38\) | −4.85158 | −0.787031 | ||||||||
\(39\) | 0.169761 | 0.0271835 | ||||||||
\(40\) | 3.29417 | 0.520855 | ||||||||
\(41\) | 7.95284 | 1.24203 | 0.621013 | − | 0.783801i | \(-0.286722\pi\) | ||||
0.621013 | + | 0.783801i | \(0.286722\pi\) | |||||||
\(42\) | 2.46575 | 0.380473 | ||||||||
\(43\) | 10.1226 | 1.54368 | 0.771841 | − | 0.635815i | \(-0.219336\pi\) | ||||
0.771841 | + | 0.635815i | \(0.219336\pi\) | |||||||
\(44\) | 5.48709 | 0.827210 | ||||||||
\(45\) | −3.29417 | −0.491067 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 1.53425 | 0.223794 | 0.111897 | − | 0.993720i | \(-0.464307\pi\) | ||||
0.111897 | + | 0.993720i | \(0.464307\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −0.920090 | −0.131441 | ||||||||
\(50\) | −5.85158 | −0.827539 | ||||||||
\(51\) | −0.362680 | −0.0507853 | ||||||||
\(52\) | −0.169761 | −0.0235416 | ||||||||
\(53\) | −5.21426 | −0.716234 | −0.358117 | − | 0.933677i | \(-0.616581\pi\) | ||||
−0.358117 | + | 0.933677i | \(0.616581\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −18.0754 | −2.43729 | ||||||||
\(56\) | −2.46575 | −0.329499 | ||||||||
\(57\) | −4.85158 | −0.642608 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −12.1226 | −1.57823 | −0.789114 | − | 0.614247i | \(-0.789460\pi\) | ||||
−0.789114 | + | 0.614247i | \(0.789460\pi\) | |||||||
\(60\) | 3.29417 | 0.425276 | ||||||||
\(61\) | 9.27102 | 1.18703 | 0.593516 | − | 0.804822i | \(-0.297739\pi\) | ||||
0.593516 | + | 0.804822i | \(0.297739\pi\) | |||||||
\(62\) | 3.48709 | 0.442861 | ||||||||
\(63\) | 2.46575 | 0.310655 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.559222 | 0.0693630 | ||||||||
\(66\) | 5.48709 | 0.675414 | ||||||||
\(67\) | −6.34827 | −0.775565 | −0.387782 | − | 0.921751i | \(-0.626759\pi\) | ||||
−0.387782 | + | 0.921751i | \(0.626759\pi\) | |||||||
\(68\) | 0.362680 | 0.0439814 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 8.12260 | 0.970837 | ||||||||
\(71\) | −6.07544 | −0.721022 | −0.360511 | − | 0.932755i | \(-0.617398\pi\) | ||||
−0.360511 | + | 0.932755i | \(0.617398\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −3.86299 | −0.452129 | −0.226064 | − | 0.974112i | \(-0.572586\pi\) | ||||
−0.226064 | + | 0.974112i | \(0.572586\pi\) | |||||||
\(74\) | −10.8843 | −1.26528 | ||||||||
\(75\) | −5.85158 | −0.675683 | ||||||||
\(76\) | 4.85158 | 0.556515 | ||||||||
\(77\) | 13.5298 | 1.54186 | ||||||||
\(78\) | −0.169761 | −0.0192217 | ||||||||
\(79\) | −3.38403 | −0.380733 | −0.190366 | − | 0.981713i | \(-0.560968\pi\) | ||||
−0.190366 | + | 0.981713i | \(0.560968\pi\) | |||||||
\(80\) | −3.29417 | −0.368300 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.95284 | −0.878244 | ||||||||
\(83\) | 5.55741 | 0.610005 | 0.305003 | − | 0.952352i | \(-0.401343\pi\) | ||||
0.305003 | + | 0.952352i | \(0.401343\pi\) | |||||||
\(84\) | −2.46575 | −0.269035 | ||||||||
\(85\) | −1.19473 | −0.129587 | ||||||||
\(86\) | −10.1226 | −1.09155 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | −5.48709 | −0.584926 | ||||||||
\(89\) | −10.2828 | −1.08997 | −0.544986 | − | 0.838445i | \(-0.683465\pi\) | ||||
−0.544986 | + | 0.838445i | \(0.683465\pi\) | |||||||
\(90\) | 3.29417 | 0.347236 | ||||||||
\(91\) | −0.418588 | −0.0438799 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 3.48709 | 0.361595 | ||||||||
\(94\) | −1.53425 | −0.158246 | ||||||||
\(95\) | −15.9820 | −1.63972 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −16.1458 | −1.63935 | −0.819677 | − | 0.572826i | \(-0.805847\pi\) | ||||
−0.819677 | + | 0.572826i | \(0.805847\pi\) | |||||||
\(98\) | 0.920090 | 0.0929432 | ||||||||
\(99\) | 5.48709 | 0.551474 | ||||||||
\(100\) | 5.85158 | 0.585158 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0.362680 | 0.0359107 | ||||||||
\(103\) | 12.8480 | 1.26595 | 0.632974 | − | 0.774173i | \(-0.281834\pi\) | ||||
0.632974 | + | 0.774173i | \(0.281834\pi\) | |||||||
\(104\) | 0.169761 | 0.0166464 | ||||||||
\(105\) | 8.12260 | 0.792685 | ||||||||
\(106\) | 5.21426 | 0.506454 | ||||||||
\(107\) | −10.0986 | −0.976268 | −0.488134 | − | 0.872769i | \(-0.662322\pi\) | ||||
−0.488134 | + | 0.872769i | \(0.662322\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.442589 | 0.0423924 | 0.0211962 | − | 0.999775i | \(-0.493253\pi\) | ||||
0.0211962 | + | 0.999775i | \(0.493253\pi\) | |||||||
\(110\) | 18.0754 | 1.72343 | ||||||||
\(111\) | −10.8843 | −1.03310 | ||||||||
\(112\) | 2.46575 | 0.232991 | ||||||||
\(113\) | 10.5652 | 0.993890 | 0.496945 | − | 0.867782i | \(-0.334455\pi\) | ||||
0.496945 | + | 0.867782i | \(0.334455\pi\) | |||||||
\(114\) | 4.85158 | 0.454393 | ||||||||
\(115\) | −3.29417 | −0.307183 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −0.169761 | −0.0156944 | ||||||||
\(118\) | 12.1226 | 1.11598 | ||||||||
\(119\) | 0.894277 | 0.0819782 | ||||||||
\(120\) | −3.29417 | −0.300716 | ||||||||
\(121\) | 19.1082 | 1.73711 | ||||||||
\(122\) | −9.27102 | −0.839358 | ||||||||
\(123\) | −7.95284 | −0.717083 | ||||||||
\(124\) | −3.48709 | −0.313150 | ||||||||
\(125\) | −2.80527 | −0.250911 | ||||||||
\(126\) | −2.46575 | −0.219666 | ||||||||
\(127\) | 6.72898 | 0.597101 | 0.298550 | − | 0.954394i | \(-0.403497\pi\) | ||||
0.298550 | + | 0.954394i | \(0.403497\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.1226 | −0.891245 | ||||||||
\(130\) | −0.559222 | −0.0490470 | ||||||||
\(131\) | −21.1903 | −1.85140 | −0.925701 | − | 0.378256i | \(-0.876524\pi\) | ||||
−0.925701 | + | 0.378256i | \(0.876524\pi\) | |||||||
\(132\) | −5.48709 | −0.477590 | ||||||||
\(133\) | 11.9628 | 1.03730 | ||||||||
\(134\) | 6.34827 | 0.548407 | ||||||||
\(135\) | 3.29417 | 0.283517 | ||||||||
\(136\) | −0.362680 | −0.0310995 | ||||||||
\(137\) | 19.6193 | 1.67619 | 0.838094 | − | 0.545525i | \(-0.183670\pi\) | ||||
0.838094 | + | 0.545525i | \(0.183670\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −7.06851 | −0.599543 | −0.299771 | − | 0.954011i | \(-0.596910\pi\) | ||||
−0.299771 | + | 0.954011i | \(0.596910\pi\) | |||||||
\(140\) | −8.12260 | −0.686485 | ||||||||
\(141\) | −1.53425 | −0.129207 | ||||||||
\(142\) | 6.07544 | 0.509840 | ||||||||
\(143\) | −0.931495 | −0.0778955 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.29417 | 0.273566 | ||||||||
\(146\) | 3.86299 | 0.319703 | ||||||||
\(147\) | 0.920090 | 0.0758878 | ||||||||
\(148\) | 10.8843 | 0.894687 | ||||||||
\(149\) | 13.9288 | 1.14109 | 0.570547 | − | 0.821265i | \(-0.306731\pi\) | ||||
0.570547 | + | 0.821265i | \(0.306731\pi\) | |||||||
\(150\) | 5.85158 | 0.477780 | ||||||||
\(151\) | 10.8380 | 0.881986 | 0.440993 | − | 0.897511i | \(-0.354626\pi\) | ||||
0.440993 | + | 0.897511i | \(0.354626\pi\) | |||||||
\(152\) | −4.85158 | −0.393516 | ||||||||
\(153\) | 0.362680 | 0.0293209 | ||||||||
\(154\) | −13.5298 | −1.09026 | ||||||||
\(155\) | 11.4871 | 0.922666 | ||||||||
\(156\) | 0.169761 | 0.0135918 | ||||||||
\(157\) | 13.9528 | 1.11356 | 0.556779 | − | 0.830661i | \(-0.312037\pi\) | ||||
0.556779 | + | 0.830661i | \(0.312037\pi\) | |||||||
\(158\) | 3.38403 | 0.269219 | ||||||||
\(159\) | 5.21426 | 0.413518 | ||||||||
\(160\) | 3.29417 | 0.260427 | ||||||||
\(161\) | 2.46575 | 0.194328 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 15.2702 | 1.19605 | 0.598026 | − | 0.801477i | \(-0.295952\pi\) | ||||
0.598026 | + | 0.801477i | \(0.295952\pi\) | |||||||
\(164\) | 7.95284 | 0.621013 | ||||||||
\(165\) | 18.0754 | 1.40717 | ||||||||
\(166\) | −5.55741 | −0.431339 | ||||||||
\(167\) | −15.5662 | −1.20455 | −0.602273 | − | 0.798290i | \(-0.705738\pi\) | ||||
−0.602273 | + | 0.798290i | \(0.705738\pi\) | |||||||
\(168\) | 2.46575 | 0.190237 | ||||||||
\(169\) | −12.9712 | −0.997783 | ||||||||
\(170\) | 1.19473 | 0.0916317 | ||||||||
\(171\) | 4.85158 | 0.371010 | ||||||||
\(172\) | 10.1226 | 0.771841 | ||||||||
\(173\) | −4.29236 | −0.326342 | −0.163171 | − | 0.986598i | \(-0.552172\pi\) | ||||
−0.163171 | + | 0.986598i | \(0.552172\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 14.4285 | 1.09069 | ||||||||
\(176\) | 5.48709 | 0.413605 | ||||||||
\(177\) | 12.1226 | 0.911191 | ||||||||
\(178\) | 10.2828 | 0.770726 | ||||||||
\(179\) | −23.3600 | −1.74601 | −0.873005 | − | 0.487711i | \(-0.837832\pi\) | ||||
−0.873005 | + | 0.487711i | \(0.837832\pi\) | |||||||
\(180\) | −3.29417 | −0.245533 | ||||||||
\(181\) | 3.04450 | 0.226296 | 0.113148 | − | 0.993578i | \(-0.463907\pi\) | ||||
0.113148 | + | 0.993578i | \(0.463907\pi\) | |||||||
\(182\) | 0.418588 | 0.0310278 | ||||||||
\(183\) | −9.27102 | −0.685333 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −35.8549 | −2.63610 | ||||||||
\(186\) | −3.48709 | −0.255686 | ||||||||
\(187\) | 1.99006 | 0.145527 | ||||||||
\(188\) | 1.53425 | 0.111897 | ||||||||
\(189\) | −2.46575 | −0.179357 | ||||||||
\(190\) | 15.9820 | 1.15945 | ||||||||
\(191\) | 18.3011 | 1.32422 | 0.662111 | − | 0.749406i | \(-0.269661\pi\) | ||||
0.662111 | + | 0.749406i | \(0.269661\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 22.7909 | 1.64052 | 0.820261 | − | 0.571989i | \(-0.193828\pi\) | ||||
0.820261 | + | 0.571989i | \(0.193828\pi\) | |||||||
\(194\) | 16.1458 | 1.15920 | ||||||||
\(195\) | −0.559222 | −0.0400467 | ||||||||
\(196\) | −0.920090 | −0.0657207 | ||||||||
\(197\) | 15.0213 | 1.07023 | 0.535113 | − | 0.844780i | \(-0.320269\pi\) | ||||
0.535113 | + | 0.844780i | \(0.320269\pi\) | |||||||
\(198\) | −5.48709 | −0.389951 | ||||||||
\(199\) | 22.1082 | 1.56721 | 0.783604 | − | 0.621261i | \(-0.213379\pi\) | ||||
0.783604 | + | 0.621261i | \(0.213379\pi\) | |||||||
\(200\) | −5.85158 | −0.413770 | ||||||||
\(201\) | 6.34827 | 0.447772 | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | −2.46575 | −0.173062 | ||||||||
\(204\) | −0.362680 | −0.0253927 | ||||||||
\(205\) | −26.1980 | −1.82975 | ||||||||
\(206\) | −12.8480 | −0.895160 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −0.169761 | −0.0117708 | ||||||||
\(209\) | 26.6211 | 1.84142 | ||||||||
\(210\) | −8.12260 | −0.560513 | ||||||||
\(211\) | −6.49850 | −0.447375 | −0.223688 | − | 0.974661i | \(-0.571810\pi\) | ||||
−0.223688 | + | 0.974661i | \(0.571810\pi\) | |||||||
\(212\) | −5.21426 | −0.358117 | ||||||||
\(213\) | 6.07544 | 0.416282 | ||||||||
\(214\) | 10.0986 | 0.690326 | ||||||||
\(215\) | −33.3456 | −2.27415 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.59829 | −0.583690 | ||||||||
\(218\) | −0.442589 | −0.0299759 | ||||||||
\(219\) | 3.86299 | 0.261037 | ||||||||
\(220\) | −18.0754 | −1.21865 | ||||||||
\(221\) | −0.0615689 | −0.00414157 | ||||||||
\(222\) | 10.8843 | 0.730509 | ||||||||
\(223\) | −2.34315 | −0.156909 | −0.0784543 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784543 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(224\) | −2.46575 | −0.164750 | ||||||||
\(225\) | 5.85158 | 0.390106 | ||||||||
\(226\) | −10.5652 | −0.702786 | ||||||||
\(227\) | 5.80708 | 0.385430 | 0.192715 | − | 0.981255i | \(-0.438271\pi\) | ||||
0.192715 | + | 0.981255i | \(0.438271\pi\) | |||||||
\(228\) | −4.85158 | −0.321304 | ||||||||
\(229\) | −5.08685 | −0.336148 | −0.168074 | − | 0.985774i | \(-0.553755\pi\) | ||||
−0.168074 | + | 0.985774i | \(0.553755\pi\) | |||||||
\(230\) | 3.29417 | 0.217211 | ||||||||
\(231\) | −13.5298 | −0.890195 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 3.95731 | 0.259252 | 0.129626 | − | 0.991563i | \(-0.458622\pi\) | ||||
0.129626 | + | 0.991563i | \(0.458622\pi\) | |||||||
\(234\) | 0.169761 | 0.0110976 | ||||||||
\(235\) | −5.05410 | −0.329693 | ||||||||
\(236\) | −12.1226 | −0.789114 | ||||||||
\(237\) | 3.38403 | 0.219816 | ||||||||
\(238\) | −0.894277 | −0.0579674 | ||||||||
\(239\) | 16.7254 | 1.08187 | 0.540937 | − | 0.841063i | \(-0.318070\pi\) | ||||
0.540937 | + | 0.841063i | \(0.318070\pi\) | |||||||
\(240\) | 3.29417 | 0.212638 | ||||||||
\(241\) | 7.56700 | 0.487434 | 0.243717 | − | 0.969846i | \(-0.421633\pi\) | ||||
0.243717 | + | 0.969846i | \(0.421633\pi\) | |||||||
\(242\) | −19.1082 | −1.22832 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.27102 | 0.593516 | ||||||||
\(245\) | 3.03094 | 0.193640 | ||||||||
\(246\) | 7.95284 | 0.507055 | ||||||||
\(247\) | −0.823610 | −0.0524050 | ||||||||
\(248\) | 3.48709 | 0.221431 | ||||||||
\(249\) | −5.55741 | −0.352187 | ||||||||
\(250\) | 2.80527 | 0.177421 | ||||||||
\(251\) | −6.79086 | −0.428635 | −0.214318 | − | 0.976764i | \(-0.568753\pi\) | ||||
−0.214318 | + | 0.976764i | \(0.568753\pi\) | |||||||
\(252\) | 2.46575 | 0.155327 | ||||||||
\(253\) | 5.48709 | 0.344971 | ||||||||
\(254\) | −6.72898 | −0.422214 | ||||||||
\(255\) | 1.19473 | 0.0748169 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.3670 | 1.51997 | 0.759985 | − | 0.649941i | \(-0.225206\pi\) | ||||
0.759985 | + | 0.649941i | \(0.225206\pi\) | |||||||
\(258\) | 10.1226 | 0.630206 | ||||||||
\(259\) | 26.8380 | 1.66763 | ||||||||
\(260\) | 0.559222 | 0.0346815 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 21.1903 | 1.30914 | ||||||||
\(263\) | 28.2975 | 1.74490 | 0.872449 | − | 0.488705i | \(-0.162531\pi\) | ||||
0.872449 | + | 0.488705i | \(0.162531\pi\) | |||||||
\(264\) | 5.48709 | 0.337707 | ||||||||
\(265\) | 17.1767 | 1.05516 | ||||||||
\(266\) | −11.9628 | −0.733485 | ||||||||
\(267\) | 10.2828 | 0.629295 | ||||||||
\(268\) | −6.34827 | −0.387782 | ||||||||
\(269\) | 14.8044 | 0.902642 | 0.451321 | − | 0.892362i | \(-0.350953\pi\) | ||||
0.451321 | + | 0.892362i | \(0.350953\pi\) | |||||||
\(270\) | −3.29417 | −0.200477 | ||||||||
\(271\) | −7.03969 | −0.427631 | −0.213815 | − | 0.976874i | \(-0.568589\pi\) | ||||
−0.213815 | + | 0.976874i | \(0.568589\pi\) | |||||||
\(272\) | 0.362680 | 0.0219907 | ||||||||
\(273\) | 0.418588 | 0.0253341 | ||||||||
\(274\) | −19.6193 | −1.18524 | ||||||||
\(275\) | 32.1082 | 1.93620 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 29.6843 | 1.78356 | 0.891778 | − | 0.452473i | \(-0.149458\pi\) | ||||
0.891778 | + | 0.452473i | \(0.149458\pi\) | |||||||
\(278\) | 7.06851 | 0.423941 | ||||||||
\(279\) | −3.48709 | −0.208767 | ||||||||
\(280\) | 8.12260 | 0.485418 | ||||||||
\(281\) | −9.66048 | −0.576296 | −0.288148 | − | 0.957586i | \(-0.593039\pi\) | ||||
−0.288148 | + | 0.957586i | \(0.593039\pi\) | |||||||
\(282\) | 1.53425 | 0.0913634 | ||||||||
\(283\) | 6.25002 | 0.371525 | 0.185763 | − | 0.982595i | \(-0.440524\pi\) | ||||
0.185763 | + | 0.982595i | \(0.440524\pi\) | |||||||
\(284\) | −6.07544 | −0.360511 | ||||||||
\(285\) | 15.9820 | 0.946690 | ||||||||
\(286\) | 0.931495 | 0.0550804 | ||||||||
\(287\) | 19.6097 | 1.15752 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.8685 | −0.992263 | ||||||||
\(290\) | −3.29417 | −0.193441 | ||||||||
\(291\) | 16.1458 | 0.946481 | ||||||||
\(292\) | −3.86299 | −0.226064 | ||||||||
\(293\) | 21.1304 | 1.23445 | 0.617225 | − | 0.786787i | \(-0.288257\pi\) | ||||
0.617225 | + | 0.786787i | \(0.288257\pi\) | |||||||
\(294\) | −0.920090 | −0.0536608 | ||||||||
\(295\) | 39.9340 | 2.32505 | ||||||||
\(296\) | −10.8843 | −0.632639 | ||||||||
\(297\) | −5.48709 | −0.318393 | ||||||||
\(298\) | −13.9288 | −0.806876 | ||||||||
\(299\) | −0.169761 | −0.00981753 | ||||||||
\(300\) | −5.85158 | −0.337841 | ||||||||
\(301\) | 24.9598 | 1.43866 | ||||||||
\(302\) | −10.8380 | −0.623658 | ||||||||
\(303\) | 10.0000 | 0.574485 | ||||||||
\(304\) | 4.85158 | 0.278257 | ||||||||
\(305\) | −30.5403 | −1.74874 | ||||||||
\(306\) | −0.362680 | −0.0207330 | ||||||||
\(307\) | −13.1767 | −0.752034 | −0.376017 | − | 0.926613i | \(-0.622707\pi\) | ||||
−0.376017 | + | 0.926613i | \(0.622707\pi\) | |||||||
\(308\) | 13.5298 | 0.770931 | ||||||||
\(309\) | −12.8480 | −0.730895 | ||||||||
\(310\) | −11.4871 | −0.652423 | ||||||||
\(311\) | 20.6683 | 1.17199 | 0.585995 | − | 0.810315i | \(-0.300704\pi\) | ||||
0.585995 | + | 0.810315i | \(0.300704\pi\) | |||||||
\(312\) | −0.169761 | −0.00961083 | ||||||||
\(313\) | 10.8152 | 0.611312 | 0.305656 | − | 0.952142i | \(-0.401124\pi\) | ||||
0.305656 | + | 0.952142i | \(0.401124\pi\) | |||||||
\(314\) | −13.9528 | −0.787404 | ||||||||
\(315\) | −8.12260 | −0.457657 | ||||||||
\(316\) | −3.38403 | −0.190366 | ||||||||
\(317\) | −32.4805 | −1.82428 | −0.912142 | − | 0.409874i | \(-0.865573\pi\) | ||||
−0.912142 | + | 0.409874i | \(0.865573\pi\) | |||||||
\(318\) | −5.21426 | −0.292401 | ||||||||
\(319\) | −5.48709 | −0.307218 | ||||||||
\(320\) | −3.29417 | −0.184150 | ||||||||
\(321\) | 10.0986 | 0.563649 | ||||||||
\(322\) | −2.46575 | −0.137411 | ||||||||
\(323\) | 1.75957 | 0.0979052 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.993371 | −0.0551023 | ||||||||
\(326\) | −15.2702 | −0.845737 | ||||||||
\(327\) | −0.442589 | −0.0244753 | ||||||||
\(328\) | −7.95284 | −0.439122 | ||||||||
\(329\) | 3.78308 | 0.208568 | ||||||||
\(330\) | −18.0754 | −0.995020 | ||||||||
\(331\) | −23.2629 | −1.27865 | −0.639323 | − | 0.768938i | \(-0.720785\pi\) | ||||
−0.639323 | + | 0.768938i | \(0.720785\pi\) | |||||||
\(332\) | 5.55741 | 0.305003 | ||||||||
\(333\) | 10.8843 | 0.596458 | ||||||||
\(334\) | 15.5662 | 0.851742 | ||||||||
\(335\) | 20.9123 | 1.14256 | ||||||||
\(336\) | −2.46575 | −0.134518 | ||||||||
\(337\) | −31.1391 | −1.69626 | −0.848128 | − | 0.529791i | \(-0.822270\pi\) | ||||
−0.848128 | + | 0.529791i | \(0.822270\pi\) | |||||||
\(338\) | 12.9712 | 0.705539 | ||||||||
\(339\) | −10.5652 | −0.573822 | ||||||||
\(340\) | −1.19473 | −0.0647934 | ||||||||
\(341\) | −19.1340 | −1.03616 | ||||||||
\(342\) | −4.85158 | −0.262344 | ||||||||
\(343\) | −19.5289 | −1.05446 | ||||||||
\(344\) | −10.1226 | −0.545774 | ||||||||
\(345\) | 3.29417 | 0.177352 | ||||||||
\(346\) | 4.29236 | 0.230759 | ||||||||
\(347\) | −33.7795 | −1.81338 | −0.906688 | − | 0.421802i | \(-0.861398\pi\) | ||||
−0.906688 | + | 0.421802i | \(0.861398\pi\) | |||||||
\(348\) | 1.00000 | 0.0536056 | ||||||||
\(349\) | −4.08901 | −0.218880 | −0.109440 | − | 0.993993i | \(-0.534906\pi\) | ||||
−0.109440 | + | 0.993993i | \(0.534906\pi\) | |||||||
\(350\) | −14.4285 | −0.771237 | ||||||||
\(351\) | 0.169761 | 0.00906117 | ||||||||
\(352\) | −5.48709 | −0.292463 | ||||||||
\(353\) | 20.2025 | 1.07527 | 0.537636 | − | 0.843177i | \(-0.319318\pi\) | ||||
0.537636 | + | 0.843177i | \(0.319318\pi\) | |||||||
\(354\) | −12.1226 | −0.644309 | ||||||||
\(355\) | 20.0136 | 1.06221 | ||||||||
\(356\) | −10.2828 | −0.544986 | ||||||||
\(357\) | −0.894277 | −0.0473302 | ||||||||
\(358\) | 23.3600 | 1.23462 | ||||||||
\(359\) | 15.2806 | 0.806480 | 0.403240 | − | 0.915094i | \(-0.367884\pi\) | ||||
0.403240 | + | 0.915094i | \(0.367884\pi\) | |||||||
\(360\) | 3.29417 | 0.173618 | ||||||||
\(361\) | 4.53788 | 0.238836 | ||||||||
\(362\) | −3.04450 | −0.160016 | ||||||||
\(363\) | −19.1082 | −1.00292 | ||||||||
\(364\) | −0.418588 | −0.0219400 | ||||||||
\(365\) | 12.7254 | 0.666076 | ||||||||
\(366\) | 9.27102 | 0.484604 | ||||||||
\(367\) | 24.8324 | 1.29624 | 0.648119 | − | 0.761539i | \(-0.275556\pi\) | ||||
0.648119 | + | 0.761539i | \(0.275556\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 7.95284 | 0.414008 | ||||||||
\(370\) | 35.8549 | 1.86401 | ||||||||
\(371\) | −12.8571 | −0.667505 | ||||||||
\(372\) | 3.48709 | 0.180797 | ||||||||
\(373\) | −28.1404 | −1.45706 | −0.728529 | − | 0.685015i | \(-0.759795\pi\) | ||||
−0.728529 | + | 0.685015i | \(0.759795\pi\) | |||||||
\(374\) | −1.99006 | −0.102903 | ||||||||
\(375\) | 2.80527 | 0.144863 | ||||||||
\(376\) | −1.53425 | −0.0791230 | ||||||||
\(377\) | 0.169761 | 0.00874314 | ||||||||
\(378\) | 2.46575 | 0.126824 | ||||||||
\(379\) | −16.2025 | −0.832267 | −0.416134 | − | 0.909304i | \(-0.636615\pi\) | ||||
−0.416134 | + | 0.909304i | \(0.636615\pi\) | |||||||
\(380\) | −15.9820 | −0.819858 | ||||||||
\(381\) | −6.72898 | −0.344736 | ||||||||
\(382\) | −18.3011 | −0.936366 | ||||||||
\(383\) | 15.5063 | 0.792334 | 0.396167 | − | 0.918179i | \(-0.370340\pi\) | ||||
0.396167 | + | 0.918179i | \(0.370340\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −44.5695 | −2.27147 | ||||||||
\(386\) | −22.7909 | −1.16002 | ||||||||
\(387\) | 10.1226 | 0.514561 | ||||||||
\(388\) | −16.1458 | −0.819677 | ||||||||
\(389\) | −14.2680 | −0.723417 | −0.361708 | − | 0.932291i | \(-0.617806\pi\) | ||||
−0.361708 | + | 0.932291i | \(0.617806\pi\) | |||||||
\(390\) | 0.559222 | 0.0283173 | ||||||||
\(391\) | 0.362680 | 0.0183415 | ||||||||
\(392\) | 0.920090 | 0.0464716 | ||||||||
\(393\) | 21.1903 | 1.06891 | ||||||||
\(394\) | −15.0213 | −0.756764 | ||||||||
\(395\) | 11.1476 | 0.560895 | ||||||||
\(396\) | 5.48709 | 0.275737 | ||||||||
\(397\) | −28.8200 | −1.44643 | −0.723217 | − | 0.690621i | \(-0.757337\pi\) | ||||
−0.723217 | + | 0.690621i | \(0.757337\pi\) | |||||||
\(398\) | −22.1082 | −1.10818 | ||||||||
\(399\) | −11.9628 | −0.598888 | ||||||||
\(400\) | 5.85158 | 0.292579 | ||||||||
\(401\) | 26.9706 | 1.34685 | 0.673423 | − | 0.739258i | \(-0.264823\pi\) | ||||
0.673423 | + | 0.739258i | \(0.264823\pi\) | |||||||
\(402\) | −6.34827 | −0.316623 | ||||||||
\(403\) | 0.591973 | 0.0294883 | ||||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | −3.29417 | −0.163689 | ||||||||
\(406\) | 2.46575 | 0.122373 | ||||||||
\(407\) | 59.7234 | 2.96038 | ||||||||
\(408\) | 0.362680 | 0.0179553 | ||||||||
\(409\) | −37.7786 | −1.86803 | −0.934016 | − | 0.357231i | \(-0.883721\pi\) | ||||
−0.934016 | + | 0.357231i | \(0.883721\pi\) | |||||||
\(410\) | 26.1980 | 1.29383 | ||||||||
\(411\) | −19.6193 | −0.967748 | ||||||||
\(412\) | 12.8480 | 0.632974 | ||||||||
\(413\) | −29.8913 | −1.47085 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −18.3071 | −0.898659 | ||||||||
\(416\) | 0.169761 | 0.00832322 | ||||||||
\(417\) | 7.06851 | 0.346146 | ||||||||
\(418\) | −26.6211 | −1.30208 | ||||||||
\(419\) | −10.9838 | −0.536593 | −0.268296 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268296 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(420\) | 8.12260 | 0.396342 | ||||||||
\(421\) | 20.8762 | 1.01745 | 0.508723 | − | 0.860930i | \(-0.330118\pi\) | ||||
0.508723 | + | 0.860930i | \(0.330118\pi\) | |||||||
\(422\) | 6.49850 | 0.316342 | ||||||||
\(423\) | 1.53425 | 0.0745979 | ||||||||
\(424\) | 5.21426 | 0.253227 | ||||||||
\(425\) | 2.12225 | 0.102944 | ||||||||
\(426\) | −6.07544 | −0.294356 | ||||||||
\(427\) | 22.8600 | 1.10627 | ||||||||
\(428\) | −10.0986 | −0.488134 | ||||||||
\(429\) | 0.931495 | 0.0449730 | ||||||||
\(430\) | 33.3456 | 1.60807 | ||||||||
\(431\) | 10.1698 | 0.489860 | 0.244930 | − | 0.969541i | \(-0.421235\pi\) | ||||
0.244930 | + | 0.969541i | \(0.421235\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −20.0842 | −0.965185 | −0.482592 | − | 0.875845i | \(-0.660305\pi\) | ||||
−0.482592 | + | 0.875845i | \(0.660305\pi\) | |||||||
\(434\) | 8.59829 | 0.412731 | ||||||||
\(435\) | −3.29417 | −0.157944 | ||||||||
\(436\) | 0.442589 | 0.0211962 | ||||||||
\(437\) | 4.85158 | 0.232083 | ||||||||
\(438\) | −3.86299 | −0.184581 | ||||||||
\(439\) | 35.6097 | 1.69956 | 0.849779 | − | 0.527139i | \(-0.176735\pi\) | ||||
0.849779 | + | 0.527139i | \(0.176735\pi\) | |||||||
\(440\) | 18.0754 | 0.861713 | ||||||||
\(441\) | −0.920090 | −0.0438138 | ||||||||
\(442\) | 0.0615689 | 0.00292853 | ||||||||
\(443\) | 2.56916 | 0.122065 | 0.0610323 | − | 0.998136i | \(-0.480561\pi\) | ||||
0.0610323 | + | 0.998136i | \(0.480561\pi\) | |||||||
\(444\) | −10.8843 | −0.516548 | ||||||||
\(445\) | 33.8732 | 1.60575 | ||||||||
\(446\) | 2.34315 | 0.110951 | ||||||||
\(447\) | −13.9288 | −0.658811 | ||||||||
\(448\) | 2.46575 | 0.116496 | ||||||||
\(449\) | −15.5207 | −0.732467 | −0.366233 | − | 0.930523i | \(-0.619353\pi\) | ||||
−0.366233 | + | 0.930523i | \(0.619353\pi\) | |||||||
\(450\) | −5.85158 | −0.275846 | ||||||||
\(451\) | 43.6380 | 2.05483 | ||||||||
\(452\) | 10.5652 | 0.496945 | ||||||||
\(453\) | −10.8380 | −0.509215 | ||||||||
\(454\) | −5.80708 | −0.272540 | ||||||||
\(455\) | 1.37890 | 0.0646439 | ||||||||
\(456\) | 4.85158 | 0.227196 | ||||||||
\(457\) | 18.5220 | 0.866423 | 0.433211 | − | 0.901292i | \(-0.357380\pi\) | ||||
0.433211 | + | 0.901292i | \(0.357380\pi\) | |||||||
\(458\) | 5.08685 | 0.237693 | ||||||||
\(459\) | −0.362680 | −0.0169284 | ||||||||
\(460\) | −3.29417 | −0.153592 | ||||||||
\(461\) | −8.76173 | −0.408075 | −0.204037 | − | 0.978963i | \(-0.565406\pi\) | ||||
−0.204037 | + | 0.978963i | \(0.565406\pi\) | |||||||
\(462\) | 13.5298 | 0.629463 | ||||||||
\(463\) | −9.49704 | −0.441365 | −0.220682 | − | 0.975346i | \(-0.570828\pi\) | ||||
−0.220682 | + | 0.975346i | \(0.570828\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −11.4871 | −0.532701 | ||||||||
\(466\) | −3.95731 | −0.183319 | ||||||||
\(467\) | −34.0718 | −1.57666 | −0.788328 | − | 0.615255i | \(-0.789053\pi\) | ||||
−0.788328 | + | 0.615255i | \(0.789053\pi\) | |||||||
\(468\) | −0.169761 | −0.00784721 | ||||||||
\(469\) | −15.6532 | −0.722799 | ||||||||
\(470\) | 5.05410 | 0.233128 | ||||||||
\(471\) | −13.9528 | −0.642913 | ||||||||
\(472\) | 12.1226 | 0.557988 | ||||||||
\(473\) | 55.5437 | 2.55390 | ||||||||
\(474\) | −3.38403 | −0.155433 | ||||||||
\(475\) | 28.3895 | 1.30260 | ||||||||
\(476\) | 0.894277 | 0.0409891 | ||||||||
\(477\) | −5.21426 | −0.238745 | ||||||||
\(478\) | −16.7254 | −0.765000 | ||||||||
\(479\) | 20.7341 | 0.947366 | 0.473683 | − | 0.880696i | \(-0.342924\pi\) | ||||
0.473683 | + | 0.880696i | \(0.342924\pi\) | |||||||
\(480\) | −3.29417 | −0.150358 | ||||||||
\(481\) | −1.84774 | −0.0842495 | ||||||||
\(482\) | −7.56700 | −0.344668 | ||||||||
\(483\) | −2.46575 | −0.112195 | ||||||||
\(484\) | 19.1082 | 0.868554 | ||||||||
\(485\) | 53.1869 | 2.41509 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 42.0111 | 1.90370 | 0.951852 | − | 0.306557i | \(-0.0991771\pi\) | ||||
0.951852 | + | 0.306557i | \(0.0991771\pi\) | |||||||
\(488\) | −9.27102 | −0.419679 | ||||||||
\(489\) | −15.2702 | −0.690541 | ||||||||
\(490\) | −3.03094 | −0.136924 | ||||||||
\(491\) | 21.6896 | 0.978838 | 0.489419 | − | 0.872049i | \(-0.337209\pi\) | ||||
0.489419 | + | 0.872049i | \(0.337209\pi\) | |||||||
\(492\) | −7.95284 | −0.358542 | ||||||||
\(493\) | −0.362680 | −0.0163343 | ||||||||
\(494\) | 0.823610 | 0.0370560 | ||||||||
\(495\) | −18.0754 | −0.812431 | ||||||||
\(496\) | −3.48709 | −0.156575 | ||||||||
\(497\) | −14.9805 | −0.671967 | ||||||||
\(498\) | 5.55741 | 0.249034 | ||||||||
\(499\) | 16.2125 | 0.725769 | 0.362885 | − | 0.931834i | \(-0.381792\pi\) | ||||
0.362885 | + | 0.931834i | \(0.381792\pi\) | |||||||
\(500\) | −2.80527 | −0.125455 | ||||||||
\(501\) | 15.5662 | 0.695445 | ||||||||
\(502\) | 6.79086 | 0.303091 | ||||||||
\(503\) | 4.87028 | 0.217155 | 0.108577 | − | 0.994088i | \(-0.465370\pi\) | ||||
0.108577 | + | 0.994088i | \(0.465370\pi\) | |||||||
\(504\) | −2.46575 | −0.109833 | ||||||||
\(505\) | 32.9417 | 1.46589 | ||||||||
\(506\) | −5.48709 | −0.243931 | ||||||||
\(507\) | 12.9712 | 0.576070 | ||||||||
\(508\) | 6.72898 | 0.298550 | ||||||||
\(509\) | −20.9498 | −0.928585 | −0.464293 | − | 0.885682i | \(-0.653691\pi\) | ||||
−0.464293 | + | 0.885682i | \(0.653691\pi\) | |||||||
\(510\) | −1.19473 | −0.0529036 | ||||||||
\(511\) | −9.52515 | −0.421368 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.85158 | −0.214203 | ||||||||
\(514\) | −24.3670 | −1.07478 | ||||||||
\(515\) | −42.3234 | −1.86499 | ||||||||
\(516\) | −10.1226 | −0.445623 | ||||||||
\(517\) | 8.41859 | 0.370249 | ||||||||
\(518\) | −26.8380 | −1.17919 | ||||||||
\(519\) | 4.29236 | 0.188414 | ||||||||
\(520\) | −0.559222 | −0.0245235 | ||||||||
\(521\) | 33.6188 | 1.47287 | 0.736433 | − | 0.676510i | \(-0.236509\pi\) | ||||
0.736433 | + | 0.676510i | \(0.236509\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | −4.73048 | −0.206850 | −0.103425 | − | 0.994637i | \(-0.532980\pi\) | ||||
−0.103425 | + | 0.994637i | \(0.532980\pi\) | |||||||
\(524\) | −21.1903 | −0.925701 | ||||||||
\(525\) | −14.4285 | −0.629713 | ||||||||
\(526\) | −28.2975 | −1.23383 | ||||||||
\(527\) | −1.26470 | −0.0550911 | ||||||||
\(528\) | −5.48709 | −0.238795 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −17.1767 | −0.746108 | ||||||||
\(531\) | −12.1226 | −0.526076 | ||||||||
\(532\) | 11.9628 | 0.518652 | ||||||||
\(533\) | −1.35008 | −0.0584786 | ||||||||
\(534\) | −10.2828 | −0.444979 | ||||||||
\(535\) | 33.2665 | 1.43824 | ||||||||
\(536\) | 6.34827 | 0.274204 | ||||||||
\(537\) | 23.3600 | 1.00806 | ||||||||
\(538\) | −14.8044 | −0.638264 | ||||||||
\(539\) | −5.04862 | −0.217460 | ||||||||
\(540\) | 3.29417 | 0.141759 | ||||||||
\(541\) | −11.8450 | −0.509254 | −0.254627 | − | 0.967039i | \(-0.581953\pi\) | ||||
−0.254627 | + | 0.967039i | \(0.581953\pi\) | |||||||
\(542\) | 7.03969 | 0.302380 | ||||||||
\(543\) | −3.04450 | −0.130652 | ||||||||
\(544\) | −0.362680 | −0.0155498 | ||||||||
\(545\) | −1.45797 | −0.0624524 | ||||||||
\(546\) | −0.418588 | −0.0179139 | ||||||||
\(547\) | −12.5920 | −0.538394 | −0.269197 | − | 0.963085i | \(-0.586758\pi\) | ||||
−0.269197 | + | 0.963085i | \(0.586758\pi\) | |||||||
\(548\) | 19.6193 | 0.838094 | ||||||||
\(549\) | 9.27102 | 0.395677 | ||||||||
\(550\) | −32.1082 | −1.36910 | ||||||||
\(551\) | −4.85158 | −0.206684 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −8.34415 | −0.354829 | ||||||||
\(554\) | −29.6843 | −1.26116 | ||||||||
\(555\) | 35.8549 | 1.52196 | ||||||||
\(556\) | −7.06851 | −0.299771 | ||||||||
\(557\) | −36.0761 | −1.52859 | −0.764297 | − | 0.644865i | \(-0.776914\pi\) | ||||
−0.764297 | + | 0.644865i | \(0.776914\pi\) | |||||||
\(558\) | 3.48709 | 0.147620 | ||||||||
\(559\) | −1.71842 | −0.0726816 | ||||||||
\(560\) | −8.12260 | −0.343243 | ||||||||
\(561\) | −1.99006 | −0.0840203 | ||||||||
\(562\) | 9.66048 | 0.407503 | ||||||||
\(563\) | 25.1803 | 1.06122 | 0.530612 | − | 0.847615i | \(-0.321962\pi\) | ||||
0.530612 | + | 0.847615i | \(0.321962\pi\) | |||||||
\(564\) | −1.53425 | −0.0646037 | ||||||||
\(565\) | −34.8036 | −1.46420 | ||||||||
\(566\) | −6.25002 | −0.262708 | ||||||||
\(567\) | 2.46575 | 0.103552 | ||||||||
\(568\) | 6.07544 | 0.254920 | ||||||||
\(569\) | 27.4487 | 1.15071 | 0.575354 | − | 0.817904i | \(-0.304864\pi\) | ||||
0.575354 | + | 0.817904i | \(0.304864\pi\) | |||||||
\(570\) | −15.9820 | −0.669411 | ||||||||
\(571\) | −26.8132 | −1.12210 | −0.561048 | − | 0.827783i | \(-0.689602\pi\) | ||||
−0.561048 | + | 0.827783i | \(0.689602\pi\) | |||||||
\(572\) | −0.931495 | −0.0389477 | ||||||||
\(573\) | −18.3011 | −0.764540 | ||||||||
\(574\) | −19.6097 | −0.818493 | ||||||||
\(575\) | 5.85158 | 0.244028 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 4.37590 | 0.182171 | 0.0910855 | − | 0.995843i | \(-0.470966\pi\) | ||||
0.0910855 | + | 0.995843i | \(0.470966\pi\) | |||||||
\(578\) | 16.8685 | 0.701636 | ||||||||
\(579\) | −22.7909 | −0.947156 | ||||||||
\(580\) | 3.29417 | 0.136783 | ||||||||
\(581\) | 13.7032 | 0.568503 | ||||||||
\(582\) | −16.1458 | −0.669263 | ||||||||
\(583\) | −28.6112 | −1.18495 | ||||||||
\(584\) | 3.86299 | 0.159852 | ||||||||
\(585\) | 0.559222 | 0.0231210 | ||||||||
\(586\) | −21.1304 | −0.872888 | ||||||||
\(587\) | 0.808893 | 0.0333866 | 0.0166933 | − | 0.999861i | \(-0.494686\pi\) | ||||
0.0166933 | + | 0.999861i | \(0.494686\pi\) | |||||||
\(588\) | 0.920090 | 0.0379439 | ||||||||
\(589\) | −16.9179 | −0.697091 | ||||||||
\(590\) | −39.9340 | −1.64406 | ||||||||
\(591\) | −15.0213 | −0.617896 | ||||||||
\(592\) | 10.8843 | 0.447343 | ||||||||
\(593\) | 6.59197 | 0.270700 | 0.135350 | − | 0.990798i | \(-0.456784\pi\) | ||||
0.135350 | + | 0.990798i | \(0.456784\pi\) | |||||||
\(594\) | 5.48709 | 0.225138 | ||||||||
\(595\) | −2.94590 | −0.120770 | ||||||||
\(596\) | 13.9288 | 0.570547 | ||||||||
\(597\) | −22.1082 | −0.904828 | ||||||||
\(598\) | 0.169761 | 0.00694204 | ||||||||
\(599\) | 39.8504 | 1.62824 | 0.814122 | − | 0.580694i | \(-0.197219\pi\) | ||||
0.814122 | + | 0.580694i | \(0.197219\pi\) | |||||||
\(600\) | 5.85158 | 0.238890 | ||||||||
\(601\) | 14.6575 | 0.597891 | 0.298945 | − | 0.954270i | \(-0.403365\pi\) | ||||
0.298945 | + | 0.954270i | \(0.403365\pi\) | |||||||
\(602\) | −24.9598 | −1.01728 | ||||||||
\(603\) | −6.34827 | −0.258522 | ||||||||
\(604\) | 10.8380 | 0.440993 | ||||||||
\(605\) | −62.9457 | −2.55911 | ||||||||
\(606\) | −10.0000 | −0.406222 | ||||||||
\(607\) | −35.7714 | −1.45191 | −0.725957 | − | 0.687740i | \(-0.758603\pi\) | ||||
−0.725957 | + | 0.687740i | \(0.758603\pi\) | |||||||
\(608\) | −4.85158 | −0.196758 | ||||||||
\(609\) | 2.46575 | 0.0999171 | ||||||||
\(610\) | 30.5403 | 1.23654 | ||||||||
\(611\) | −0.260456 | −0.0105369 | ||||||||
\(612\) | 0.362680 | 0.0146605 | ||||||||
\(613\) | 24.0087 | 0.969704 | 0.484852 | − | 0.874596i | \(-0.338873\pi\) | ||||
0.484852 | + | 0.874596i | \(0.338873\pi\) | |||||||
\(614\) | 13.1767 | 0.531768 | ||||||||
\(615\) | 26.1980 | 1.05641 | ||||||||
\(616\) | −13.5298 | −0.545131 | ||||||||
\(617\) | 2.81039 | 0.113142 | 0.0565711 | − | 0.998399i | \(-0.481983\pi\) | ||||
0.0565711 | + | 0.998399i | \(0.481983\pi\) | |||||||
\(618\) | 12.8480 | 0.516821 | ||||||||
\(619\) | −15.1659 | −0.609569 | −0.304785 | − | 0.952421i | \(-0.598585\pi\) | ||||
−0.304785 | + | 0.952421i | \(0.598585\pi\) | |||||||
\(620\) | 11.4871 | 0.461333 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −20.6683 | −0.828722 | ||||||||
\(623\) | −25.3547 | −1.01582 | ||||||||
\(624\) | 0.169761 | 0.00679588 | ||||||||
\(625\) | −20.0169 | −0.800675 | ||||||||
\(626\) | −10.8152 | −0.432263 | ||||||||
\(627\) | −26.6211 | −1.06314 | ||||||||
\(628\) | 13.9528 | 0.556779 | ||||||||
\(629\) | 3.94753 | 0.157398 | ||||||||
\(630\) | 8.12260 | 0.323612 | ||||||||
\(631\) | 14.1190 | 0.562068 | 0.281034 | − | 0.959698i | \(-0.409323\pi\) | ||||
0.281034 | + | 0.959698i | \(0.409323\pi\) | |||||||
\(632\) | 3.38403 | 0.134609 | ||||||||
\(633\) | 6.49850 | 0.258292 | ||||||||
\(634\) | 32.4805 | 1.28996 | ||||||||
\(635\) | −22.1664 | −0.879649 | ||||||||
\(636\) | 5.21426 | 0.206759 | ||||||||
\(637\) | 0.156195 | 0.00618869 | ||||||||
\(638\) | 5.48709 | 0.217236 | ||||||||
\(639\) | −6.07544 | −0.240341 | ||||||||
\(640\) | 3.29417 | 0.130214 | ||||||||
\(641\) | −8.45700 | −0.334031 | −0.167016 | − | 0.985954i | \(-0.553413\pi\) | ||||
−0.167016 | + | 0.985954i | \(0.553413\pi\) | |||||||
\(642\) | −10.0986 | −0.398560 | ||||||||
\(643\) | 48.9238 | 1.92936 | 0.964682 | − | 0.263416i | \(-0.0848493\pi\) | ||||
0.964682 | + | 0.263416i | \(0.0848493\pi\) | |||||||
\(644\) | 2.46575 | 0.0971641 | ||||||||
\(645\) | 33.3456 | 1.31298 | ||||||||
\(646\) | −1.75957 | −0.0692294 | ||||||||
\(647\) | 20.5129 | 0.806446 | 0.403223 | − | 0.915102i | \(-0.367890\pi\) | ||||
0.403223 | + | 0.915102i | \(0.367890\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −66.5178 | −2.61105 | ||||||||
\(650\) | 0.993371 | 0.0389632 | ||||||||
\(651\) | 8.59829 | 0.336994 | ||||||||
\(652\) | 15.2702 | 0.598026 | ||||||||
\(653\) | −12.5013 | −0.489213 | −0.244606 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244606 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(654\) | 0.442589 | 0.0173066 | ||||||||
\(655\) | 69.8044 | 2.72748 | ||||||||
\(656\) | 7.95284 | 0.310506 | ||||||||
\(657\) | −3.86299 | −0.150710 | ||||||||
\(658\) | −3.78308 | −0.147480 | ||||||||
\(659\) | 31.1479 | 1.21335 | 0.606675 | − | 0.794950i | \(-0.292503\pi\) | ||||
0.606675 | + | 0.794950i | \(0.292503\pi\) | |||||||
\(660\) | 18.0754 | 0.703586 | ||||||||
\(661\) | 9.98594 | 0.388408 | 0.194204 | − | 0.980961i | \(-0.437788\pi\) | ||||
0.194204 | + | 0.980961i | \(0.437788\pi\) | |||||||
\(662\) | 23.2629 | 0.904139 | ||||||||
\(663\) | 0.0615689 | 0.00239114 | ||||||||
\(664\) | −5.55741 | −0.215669 | ||||||||
\(665\) | −39.4075 | −1.52816 | ||||||||
\(666\) | −10.8843 | −0.421759 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −15.5662 | −0.602273 | ||||||||
\(669\) | 2.34315 | 0.0905912 | ||||||||
\(670\) | −20.9123 | −0.807913 | ||||||||
\(671\) | 50.8709 | 1.96385 | ||||||||
\(672\) | 2.46575 | 0.0951183 | ||||||||
\(673\) | −7.50782 | −0.289405 | −0.144703 | − | 0.989475i | \(-0.546223\pi\) | ||||
−0.144703 | + | 0.989475i | \(0.546223\pi\) | |||||||
\(674\) | 31.1391 | 1.19943 | ||||||||
\(675\) | −5.85158 | −0.225228 | ||||||||
\(676\) | −12.9712 | −0.498892 | ||||||||
\(677\) | 15.7650 | 0.605900 | 0.302950 | − | 0.953006i | \(-0.402028\pi\) | ||||
0.302950 | + | 0.953006i | \(0.402028\pi\) | |||||||
\(678\) | 10.5652 | 0.405754 | ||||||||
\(679\) | −39.8114 | −1.52782 | ||||||||
\(680\) | 1.19473 | 0.0458158 | ||||||||
\(681\) | −5.80708 | −0.222528 | ||||||||
\(682\) | 19.1340 | 0.732679 | ||||||||
\(683\) | 44.1792 | 1.69047 | 0.845234 | − | 0.534396i | \(-0.179461\pi\) | ||||
0.845234 | + | 0.534396i | \(0.179461\pi\) | |||||||
\(684\) | 4.85158 | 0.185505 | ||||||||
\(685\) | −64.6294 | −2.46936 | ||||||||
\(686\) | 19.5289 | 0.745618 | ||||||||
\(687\) | 5.08685 | 0.194075 | ||||||||
\(688\) | 10.1226 | 0.385921 | ||||||||
\(689\) | 0.885179 | 0.0337226 | ||||||||
\(690\) | −3.29417 | −0.125407 | ||||||||
\(691\) | −1.47322 | −0.0560439 | −0.0280220 | − | 0.999607i | \(-0.508921\pi\) | ||||
−0.0280220 | + | 0.999607i | \(0.508921\pi\) | |||||||
\(692\) | −4.29236 | −0.163171 | ||||||||
\(693\) | 13.5298 | 0.513954 | ||||||||
\(694\) | 33.7795 | 1.28225 | ||||||||
\(695\) | 23.2849 | 0.883246 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | 2.88434 | 0.109252 | ||||||||
\(698\) | 4.08901 | 0.154771 | ||||||||
\(699\) | −3.95731 | −0.149679 | ||||||||
\(700\) | 14.4285 | 0.545347 | ||||||||
\(701\) | −9.42950 | −0.356147 | −0.178074 | − | 0.984017i | \(-0.556987\pi\) | ||||
−0.178074 | + | 0.984017i | \(0.556987\pi\) | |||||||
\(702\) | −0.169761 | −0.00640722 | ||||||||
\(703\) | 52.8063 | 1.99163 | ||||||||
\(704\) | 5.48709 | 0.206803 | ||||||||
\(705\) | 5.05410 | 0.190348 | ||||||||
\(706\) | −20.2025 | −0.760332 | ||||||||
\(707\) | −24.6575 | −0.927340 | ||||||||
\(708\) | 12.1226 | 0.455595 | ||||||||
\(709\) | −23.6365 | −0.887686 | −0.443843 | − | 0.896104i | \(-0.646385\pi\) | ||||
−0.443843 | + | 0.896104i | \(0.646385\pi\) | |||||||
\(710\) | −20.0136 | −0.751096 | ||||||||
\(711\) | −3.38403 | −0.126911 | ||||||||
\(712\) | 10.2828 | 0.385363 | ||||||||
\(713\) | −3.48709 | −0.130593 | ||||||||
\(714\) | 0.894277 | 0.0334675 | ||||||||
\(715\) | 3.06851 | 0.114756 | ||||||||
\(716\) | −23.3600 | −0.873005 | ||||||||
\(717\) | −16.7254 | −0.624620 | ||||||||
\(718\) | −15.2806 | −0.570267 | ||||||||
\(719\) | −3.44078 | −0.128319 | −0.0641597 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641597 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(720\) | −3.29417 | −0.122767 | ||||||||
\(721\) | 31.6798 | 1.17982 | ||||||||
\(722\) | −4.53788 | −0.168882 | ||||||||
\(723\) | −7.56700 | −0.281420 | ||||||||
\(724\) | 3.04450 | 0.113148 | ||||||||
\(725\) | −5.85158 | −0.217322 | ||||||||
\(726\) | 19.1082 | 0.709172 | ||||||||
\(727\) | −2.08026 | −0.0771525 | −0.0385763 | − | 0.999256i | \(-0.512282\pi\) | ||||
−0.0385763 | + | 0.999256i | \(0.512282\pi\) | |||||||
\(728\) | 0.418588 | 0.0155139 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.7254 | −0.470987 | ||||||||
\(731\) | 3.67126 | 0.135787 | ||||||||
\(732\) | −9.27102 | −0.342667 | ||||||||
\(733\) | 0.751792 | 0.0277681 | 0.0138840 | − | 0.999904i | \(-0.495580\pi\) | ||||
0.0138840 | + | 0.999904i | \(0.495580\pi\) | |||||||
\(734\) | −24.8324 | −0.916579 | ||||||||
\(735\) | −3.03094 | −0.111798 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −34.8336 | −1.28311 | ||||||||
\(738\) | −7.95284 | −0.292748 | ||||||||
\(739\) | 28.0583 | 1.03214 | 0.516070 | − | 0.856547i | \(-0.327395\pi\) | ||||
0.516070 | + | 0.856547i | \(0.327395\pi\) | |||||||
\(740\) | −35.8549 | −1.31805 | ||||||||
\(741\) | 0.823610 | 0.0302561 | ||||||||
\(742\) | 12.8571 | 0.471997 | ||||||||
\(743\) | 31.7693 | 1.16550 | 0.582752 | − | 0.812650i | \(-0.301976\pi\) | ||||
0.582752 | + | 0.812650i | \(0.301976\pi\) | |||||||
\(744\) | −3.48709 | −0.127843 | ||||||||
\(745\) | −45.8840 | −1.68106 | ||||||||
\(746\) | 28.1404 | 1.03029 | ||||||||
\(747\) | 5.55741 | 0.203335 | ||||||||
\(748\) | 1.99006 | 0.0727637 | ||||||||
\(749\) | −24.9006 | −0.909848 | ||||||||
\(750\) | −2.80527 | −0.102434 | ||||||||
\(751\) | 17.9197 | 0.653901 | 0.326950 | − | 0.945042i | \(-0.393979\pi\) | ||||
0.326950 | + | 0.945042i | \(0.393979\pi\) | |||||||
\(752\) | 1.53425 | 0.0559484 | ||||||||
\(753\) | 6.79086 | 0.247473 | ||||||||
\(754\) | −0.169761 | −0.00618233 | ||||||||
\(755\) | −35.7023 | −1.29934 | ||||||||
\(756\) | −2.46575 | −0.0896784 | ||||||||
\(757\) | 41.8784 | 1.52210 | 0.761048 | − | 0.648695i | \(-0.224685\pi\) | ||||
0.761048 | + | 0.648695i | \(0.224685\pi\) | |||||||
\(758\) | 16.2025 | 0.588502 | ||||||||
\(759\) | −5.48709 | −0.199169 | ||||||||
\(760\) | 15.9820 | 0.579727 | ||||||||
\(761\) | −51.0016 | −1.84881 | −0.924404 | − | 0.381415i | \(-0.875437\pi\) | ||||
−0.924404 | + | 0.381415i | \(0.875437\pi\) | |||||||
\(762\) | 6.72898 | 0.243765 | ||||||||
\(763\) | 1.09131 | 0.0395082 | ||||||||
\(764\) | 18.3011 | 0.662111 | ||||||||
\(765\) | −1.19473 | −0.0431956 | ||||||||
\(766\) | −15.5063 | −0.560265 | ||||||||
\(767\) | 2.05795 | 0.0743081 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −39.7447 | −1.43323 | −0.716615 | − | 0.697469i | \(-0.754309\pi\) | ||||
−0.716615 | + | 0.697469i | \(0.754309\pi\) | |||||||
\(770\) | 44.5695 | 1.60617 | ||||||||
\(771\) | −24.3670 | −0.877555 | ||||||||
\(772\) | 22.7909 | 0.820261 | ||||||||
\(773\) | 51.7714 | 1.86209 | 0.931043 | − | 0.364909i | \(-0.118900\pi\) | ||||
0.931043 | + | 0.364909i | \(0.118900\pi\) | |||||||
\(774\) | −10.1226 | −0.363849 | ||||||||
\(775\) | −20.4050 | −0.732970 | ||||||||
\(776\) | 16.1458 | 0.579599 | ||||||||
\(777\) | −26.8380 | −0.962809 | ||||||||
\(778\) | 14.2680 | 0.511533 | ||||||||
\(779\) | 38.5839 | 1.38241 | ||||||||
\(780\) | −0.559222 | −0.0200234 | ||||||||
\(781\) | −33.3365 | −1.19287 | ||||||||
\(782\) | −0.362680 | −0.0129694 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −0.920090 | −0.0328604 | ||||||||
\(785\) | −45.9631 | −1.64049 | ||||||||
\(786\) | −21.1903 | −0.755832 | ||||||||
\(787\) | −17.7235 | −0.631776 | −0.315888 | − | 0.948796i | \(-0.602302\pi\) | ||||
−0.315888 | + | 0.948796i | \(0.602302\pi\) | |||||||
\(788\) | 15.0213 | 0.535113 | ||||||||
\(789\) | −28.2975 | −1.00742 | ||||||||
\(790\) | −11.1476 | −0.396613 | ||||||||
\(791\) | 26.0511 | 0.926270 | ||||||||
\(792\) | −5.48709 | −0.194975 | ||||||||
\(793\) | −1.57386 | −0.0558893 | ||||||||
\(794\) | 28.8200 | 1.02278 | ||||||||
\(795\) | −17.1767 | −0.609195 | ||||||||
\(796\) | 22.1082 | 0.783604 | ||||||||
\(797\) | 45.1079 | 1.59780 | 0.798902 | − | 0.601462i | \(-0.205415\pi\) | ||||
0.798902 | + | 0.601462i | \(0.205415\pi\) | |||||||
\(798\) | 11.9628 | 0.423478 | ||||||||
\(799\) | 0.556443 | 0.0196855 | ||||||||
\(800\) | −5.85158 | −0.206885 | ||||||||
\(801\) | −10.2828 | −0.363324 | ||||||||
\(802\) | −26.9706 | −0.952364 | ||||||||
\(803\) | −21.1966 | −0.748011 | ||||||||
\(804\) | 6.34827 | 0.223886 | ||||||||
\(805\) | −8.12260 | −0.286284 | ||||||||
\(806\) | −0.591973 | −0.0208513 | ||||||||
\(807\) | −14.8044 | −0.521140 | ||||||||
\(808\) | 10.0000 | 0.351799 | ||||||||
\(809\) | 17.2458 | 0.606331 | 0.303165 | − | 0.952938i | \(-0.401957\pi\) | ||||
0.303165 | + | 0.952938i | \(0.401957\pi\) | |||||||
\(810\) | 3.29417 | 0.115745 | ||||||||
\(811\) | −26.0410 | −0.914423 | −0.457212 | − | 0.889358i | \(-0.651152\pi\) | ||||
−0.457212 | + | 0.889358i | \(0.651152\pi\) | |||||||
\(812\) | −2.46575 | −0.0865308 | ||||||||
\(813\) | 7.03969 | 0.246893 | ||||||||
\(814\) | −59.7234 | −2.09330 | ||||||||
\(815\) | −50.3026 | −1.76202 | ||||||||
\(816\) | −0.362680 | −0.0126963 | ||||||||
\(817\) | 49.1107 | 1.71816 | ||||||||
\(818\) | 37.7786 | 1.32090 | ||||||||
\(819\) | −0.418588 | −0.0146266 | ||||||||
\(820\) | −26.1980 | −0.914875 | ||||||||
\(821\) | 15.7224 | 0.548714 | 0.274357 | − | 0.961628i | \(-0.411535\pi\) | ||||
0.274357 | + | 0.961628i | \(0.411535\pi\) | |||||||
\(822\) | 19.6193 | 0.684301 | ||||||||
\(823\) | −33.8213 | −1.17894 | −0.589468 | − | 0.807792i | \(-0.700663\pi\) | ||||
−0.589468 | + | 0.807792i | \(0.700663\pi\) | |||||||
\(824\) | −12.8480 | −0.447580 | ||||||||
\(825\) | −32.1082 | −1.11786 | ||||||||
\(826\) | 29.8913 | 1.04005 | ||||||||
\(827\) | −48.8726 | −1.69947 | −0.849734 | − | 0.527212i | \(-0.823237\pi\) | ||||
−0.849734 | + | 0.527212i | \(0.823237\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −43.6461 | −1.51589 | −0.757945 | − | 0.652318i | \(-0.773797\pi\) | ||||
−0.757945 | + | 0.652318i | \(0.773797\pi\) | |||||||
\(830\) | 18.3071 | 0.635448 | ||||||||
\(831\) | −29.6843 | −1.02974 | ||||||||
\(832\) | −0.169761 | −0.00588540 | ||||||||
\(833\) | −0.333698 | −0.0115620 | ||||||||
\(834\) | −7.06851 | −0.244762 | ||||||||
\(835\) | 51.2776 | 1.77454 | ||||||||
\(836\) | 26.6211 | 0.920710 | ||||||||
\(837\) | 3.48709 | 0.120532 | ||||||||
\(838\) | 10.9838 | 0.379428 | ||||||||
\(839\) | −40.4844 | −1.39768 | −0.698839 | − | 0.715279i | \(-0.746300\pi\) | ||||
−0.698839 | + | 0.715279i | \(0.746300\pi\) | |||||||
\(840\) | −8.12260 | −0.280256 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −20.8762 | −0.719443 | ||||||||
\(843\) | 9.66048 | 0.332725 | ||||||||
\(844\) | −6.49850 | −0.223688 | ||||||||
\(845\) | 42.7293 | 1.46993 | ||||||||
\(846\) | −1.53425 | −0.0527487 | ||||||||
\(847\) | 47.1160 | 1.61892 | ||||||||
\(848\) | −5.21426 | −0.179059 | ||||||||
\(849\) | −6.25002 | −0.214500 | ||||||||
\(850\) | −2.12225 | −0.0727926 | ||||||||
\(851\) | 10.8843 | 0.373110 | ||||||||
\(852\) | 6.07544 | 0.208141 | ||||||||
\(853\) | 0.878017 | 0.0300627 | 0.0150314 | − | 0.999887i | \(-0.495215\pi\) | ||||
0.0150314 | + | 0.999887i | \(0.495215\pi\) | |||||||
\(854\) | −22.8600 | −0.782253 | ||||||||
\(855\) | −15.9820 | −0.546572 | ||||||||
\(856\) | 10.0986 | 0.345163 | ||||||||
\(857\) | −41.3838 | −1.41365 | −0.706823 | − | 0.707391i | \(-0.749872\pi\) | ||||
−0.706823 | + | 0.707391i | \(0.749872\pi\) | |||||||
\(858\) | −0.931495 | −0.0318007 | ||||||||
\(859\) | −5.59413 | −0.190869 | −0.0954347 | − | 0.995436i | \(-0.530424\pi\) | ||||
−0.0954347 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(860\) | −33.3456 | −1.13708 | ||||||||
\(861\) | −19.6097 | −0.668297 | ||||||||
\(862\) | −10.1698 | −0.346383 | ||||||||
\(863\) | −52.5142 | −1.78760 | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 14.1398 | 0.480767 | ||||||||
\(866\) | 20.0842 | 0.682489 | ||||||||
\(867\) | 16.8685 | 0.572883 | ||||||||
\(868\) | −8.59829 | −0.291845 | ||||||||
\(869\) | −18.5685 | −0.629892 | ||||||||
\(870\) | 3.29417 | 0.111683 | ||||||||
\(871\) | 1.07769 | 0.0365161 | ||||||||
\(872\) | −0.442589 | −0.0149880 | ||||||||
\(873\) | −16.1458 | −0.546451 | ||||||||
\(874\) | −4.85158 | −0.164107 | ||||||||
\(875\) | −6.91709 | −0.233840 | ||||||||
\(876\) | 3.86299 | 0.130518 | ||||||||
\(877\) | −11.4156 | −0.385477 | −0.192738 | − | 0.981250i | \(-0.561737\pi\) | ||||
−0.192738 | + | 0.981250i | \(0.561737\pi\) | |||||||
\(878\) | −35.6097 | −1.20177 | ||||||||
\(879\) | −21.1304 | −0.712710 | ||||||||
\(880\) | −18.0754 | −0.609323 | ||||||||
\(881\) | −8.39265 | −0.282756 | −0.141378 | − | 0.989956i | \(-0.545153\pi\) | ||||
−0.141378 | + | 0.989956i | \(0.545153\pi\) | |||||||
\(882\) | 0.920090 | 0.0309811 | ||||||||
\(883\) | 4.53279 | 0.152541 | 0.0762703 | − | 0.997087i | \(-0.475699\pi\) | ||||
0.0762703 | + | 0.997087i | \(0.475699\pi\) | |||||||
\(884\) | −0.0615689 | −0.00207079 | ||||||||
\(885\) | −39.9340 | −1.34237 | ||||||||
\(886\) | −2.56916 | −0.0863128 | ||||||||
\(887\) | −47.6443 | −1.59974 | −0.799869 | − | 0.600174i | \(-0.795098\pi\) | ||||
−0.799869 | + | 0.600174i | \(0.795098\pi\) | |||||||
\(888\) | 10.8843 | 0.365254 | ||||||||
\(889\) | 16.5920 | 0.556477 | ||||||||
\(890\) | −33.8732 | −1.13543 | ||||||||
\(891\) | 5.48709 | 0.183825 | ||||||||
\(892\) | −2.34315 | −0.0784543 | ||||||||
\(893\) | 7.44356 | 0.249089 | ||||||||
\(894\) | 13.9288 | 0.465850 | ||||||||
\(895\) | 76.9520 | 2.57222 | ||||||||
\(896\) | −2.46575 | −0.0823748 | ||||||||
\(897\) | 0.169761 | 0.00566816 | ||||||||
\(898\) | 15.5207 | 0.517932 | ||||||||
\(899\) | 3.48709 | 0.116301 | ||||||||
\(900\) | 5.85158 | 0.195053 | ||||||||
\(901\) | −1.89111 | −0.0630020 | ||||||||
\(902\) | −43.6380 | −1.45299 | ||||||||
\(903\) | −24.9598 | −0.830609 | ||||||||
\(904\) | −10.5652 | −0.351393 | ||||||||
\(905\) | −10.0291 | −0.333379 | ||||||||
\(906\) | 10.8380 | 0.360069 | ||||||||
\(907\) | −0.757802 | −0.0251624 | −0.0125812 | − | 0.999921i | \(-0.504005\pi\) | ||||
−0.0125812 | + | 0.999921i | \(0.504005\pi\) | |||||||
\(908\) | 5.80708 | 0.192715 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | −1.37890 | −0.0457101 | ||||||||
\(911\) | −19.8417 | −0.657384 | −0.328692 | − | 0.944437i | \(-0.606608\pi\) | ||||
−0.328692 | + | 0.944437i | \(0.606608\pi\) | |||||||
\(912\) | −4.85158 | −0.160652 | ||||||||
\(913\) | 30.4940 | 1.00921 | ||||||||
\(914\) | −18.5220 | −0.612653 | ||||||||
\(915\) | 30.5403 | 1.00963 | ||||||||
\(916\) | −5.08685 | −0.168074 | ||||||||
\(917\) | −52.2498 | −1.72544 | ||||||||
\(918\) | 0.362680 | 0.0119702 | ||||||||
\(919\) | 4.53557 | 0.149615 | 0.0748073 | − | 0.997198i | \(-0.476166\pi\) | ||||
0.0748073 | + | 0.997198i | \(0.476166\pi\) | |||||||
\(920\) | 3.29417 | 0.108606 | ||||||||
\(921\) | 13.1767 | 0.434187 | ||||||||
\(922\) | 8.76173 | 0.288552 | ||||||||
\(923\) | 1.03137 | 0.0339481 | ||||||||
\(924\) | −13.5298 | −0.445097 | ||||||||
\(925\) | 63.6906 | 2.09413 | ||||||||
\(926\) | 9.49704 | 0.312092 | ||||||||
\(927\) | 12.8480 | 0.421982 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 19.7597 | 0.648296 | 0.324148 | − | 0.946006i | \(-0.394922\pi\) | ||||
0.324148 | + | 0.946006i | \(0.394922\pi\) | |||||||
\(930\) | 11.4871 | 0.376677 | ||||||||
\(931\) | −4.46390 | −0.146298 | ||||||||
\(932\) | 3.95731 | 0.129626 | ||||||||
\(933\) | −20.6683 | −0.676648 | ||||||||
\(934\) | 34.0718 | 1.11486 | ||||||||
\(935\) | −6.55560 | −0.214391 | ||||||||
\(936\) | 0.169761 | 0.00554881 | ||||||||
\(937\) | 3.25630 | 0.106379 | 0.0531893 | − | 0.998584i | \(-0.483061\pi\) | ||||
0.0531893 | + | 0.998584i | \(0.483061\pi\) | |||||||
\(938\) | 15.6532 | 0.511096 | ||||||||
\(939\) | −10.8152 | −0.352941 | ||||||||
\(940\) | −5.05410 | −0.164846 | ||||||||
\(941\) | 28.1404 | 0.917352 | 0.458676 | − | 0.888603i | \(-0.348324\pi\) | ||||
0.458676 | + | 0.888603i | \(0.348324\pi\) | |||||||
\(942\) | 13.9528 | 0.454608 | ||||||||
\(943\) | 7.95284 | 0.258980 | ||||||||
\(944\) | −12.1226 | −0.394557 | ||||||||
\(945\) | 8.12260 | 0.264228 | ||||||||
\(946\) | −55.5437 | −1.80588 | ||||||||
\(947\) | −17.5953 | −0.571770 | −0.285885 | − | 0.958264i | \(-0.592288\pi\) | ||||
−0.285885 | + | 0.958264i | \(0.592288\pi\) | |||||||
\(948\) | 3.38403 | 0.109908 | ||||||||
\(949\) | 0.655785 | 0.0212877 | ||||||||
\(950\) | −28.3895 | −0.921076 | ||||||||
\(951\) | 32.4805 | 1.05325 | ||||||||
\(952\) | −0.894277 | −0.0289837 | ||||||||
\(953\) | 11.7512 | 0.380658 | 0.190329 | − | 0.981720i | \(-0.439045\pi\) | ||||
0.190329 | + | 0.981720i | \(0.439045\pi\) | |||||||
\(954\) | 5.21426 | 0.168818 | ||||||||
\(955\) | −60.2871 | −1.95084 | ||||||||
\(956\) | 16.7254 | 0.540937 | ||||||||
\(957\) | 5.48709 | 0.177373 | ||||||||
\(958\) | −20.7341 | −0.669889 | ||||||||
\(959\) | 48.3762 | 1.56215 | ||||||||
\(960\) | 3.29417 | 0.106319 | ||||||||
\(961\) | −18.8402 | −0.607748 | ||||||||
\(962\) | 1.84774 | 0.0595734 | ||||||||
\(963\) | −10.0986 | −0.325423 | ||||||||
\(964\) | 7.56700 | 0.243717 | ||||||||
\(965\) | −75.0771 | −2.41682 | ||||||||
\(966\) | 2.46575 | 0.0793341 | ||||||||
\(967\) | 2.50928 | 0.0806931 | 0.0403466 | − | 0.999186i | \(-0.487154\pi\) | ||||
0.0403466 | + | 0.999186i | \(0.487154\pi\) | |||||||
\(968\) | −19.1082 | −0.614161 | ||||||||
\(969\) | −1.75957 | −0.0565256 | ||||||||
\(970\) | −53.1869 | −1.70773 | ||||||||
\(971\) | −20.9414 | −0.672043 | −0.336021 | − | 0.941854i | \(-0.609081\pi\) | ||||
−0.336021 | + | 0.941854i | \(0.609081\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −17.4291 | −0.558753 | ||||||||
\(974\) | −42.0111 | −1.34612 | ||||||||
\(975\) | 0.993371 | 0.0318133 | ||||||||
\(976\) | 9.27102 | 0.296758 | ||||||||
\(977\) | −15.3501 | −0.491093 | −0.245546 | − | 0.969385i | \(-0.578967\pi\) | ||||
−0.245546 | + | 0.969385i | \(0.578967\pi\) | |||||||
\(978\) | 15.2702 | 0.488286 | ||||||||
\(979\) | −56.4225 | −1.80327 | ||||||||
\(980\) | 3.03094 | 0.0968198 | ||||||||
\(981\) | 0.442589 | 0.0141308 | ||||||||
\(982\) | −21.6896 | −0.692143 | ||||||||
\(983\) | −29.2533 | −0.933036 | −0.466518 | − | 0.884512i | \(-0.654492\pi\) | ||||
−0.466518 | + | 0.884512i | \(0.654492\pi\) | |||||||
\(984\) | 7.95284 | 0.253527 | ||||||||
\(985\) | −49.4829 | −1.57666 | ||||||||
\(986\) | 0.362680 | 0.0115501 | ||||||||
\(987\) | −3.78308 | −0.120417 | ||||||||
\(988\) | −0.823610 | −0.0262025 | ||||||||
\(989\) | 10.1226 | 0.321880 | ||||||||
\(990\) | 18.0754 | 0.574475 | ||||||||
\(991\) | 35.3747 | 1.12372 | 0.561858 | − | 0.827234i | \(-0.310087\pi\) | ||||
0.561858 | + | 0.827234i | \(0.310087\pi\) | |||||||
\(992\) | 3.48709 | 0.110715 | ||||||||
\(993\) | 23.2629 | 0.738227 | ||||||||
\(994\) | 14.9805 | 0.475153 | ||||||||
\(995\) | −72.8282 | −2.30881 | ||||||||
\(996\) | −5.55741 | −0.176093 | ||||||||
\(997\) | 36.7573 | 1.16411 | 0.582057 | − | 0.813148i | \(-0.302248\pi\) | ||||
0.582057 | + | 0.813148i | \(0.302248\pi\) | |||||||
\(998\) | −16.2125 | −0.513196 | ||||||||
\(999\) | −10.8843 | −0.344365 |
(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 | 4002.2.a.ba.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.ba.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |