Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} + \cdots - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.76837\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | −1.76837 | −1.02097 | −0.510483 | − | 0.859888i | \(-0.670534\pi\) | ||||
−0.510483 | + | 0.859888i | \(0.670534\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.49209 | 0.667281 | 0.333641 | − | 0.942700i | \(-0.391723\pi\) | ||||
0.333641 | + | 0.942700i | \(0.391723\pi\) | |||||||
\(6\) | −1.76837 | −0.721933 | ||||||||
\(7\) | 3.65436 | 1.38122 | 0.690608 | − | 0.723229i | \(-0.257343\pi\) | ||||
0.690608 | + | 0.723229i | \(0.257343\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.127121 | 0.0423736 | ||||||||
\(10\) | 1.49209 | 0.471839 | ||||||||
\(11\) | −3.80342 | −1.14677 | −0.573387 | − | 0.819285i | \(-0.694371\pi\) | ||||
−0.573387 | + | 0.819285i | \(0.694371\pi\) | |||||||
\(12\) | −1.76837 | −0.510483 | ||||||||
\(13\) | 1.15241 | 0.319621 | 0.159811 | − | 0.987148i | \(-0.448912\pi\) | ||||
0.159811 | + | 0.987148i | \(0.448912\pi\) | |||||||
\(14\) | 3.65436 | 0.976668 | ||||||||
\(15\) | −2.63855 | −0.681272 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.90897 | −1.67567 | −0.837836 | − | 0.545922i | \(-0.816179\pi\) | ||||
−0.837836 | + | 0.545922i | \(0.816179\pi\) | |||||||
\(18\) | 0.127121 | 0.0299626 | ||||||||
\(19\) | −1.36683 | −0.313573 | −0.156786 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156786 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(20\) | 1.49209 | 0.333641 | ||||||||
\(21\) | −6.46224 | −1.41018 | ||||||||
\(22\) | −3.80342 | −0.810891 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.76837 | −0.360966 | ||||||||
\(25\) | −2.77368 | −0.554736 | ||||||||
\(26\) | 1.15241 | 0.226006 | ||||||||
\(27\) | 5.08030 | 0.977705 | ||||||||
\(28\) | 3.65436 | 0.690608 | ||||||||
\(29\) | 10.2612 | 1.90546 | 0.952729 | − | 0.303821i | \(-0.0982625\pi\) | ||||
0.952729 | + | 0.303821i | \(0.0982625\pi\) | |||||||
\(30\) | −2.63855 | −0.481732 | ||||||||
\(31\) | −4.85848 | −0.872609 | −0.436305 | − | 0.899799i | \(-0.643713\pi\) | ||||
−0.436305 | + | 0.899799i | \(0.643713\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.72584 | 1.17082 | ||||||||
\(34\) | −6.90897 | −1.18488 | ||||||||
\(35\) | 5.45261 | 0.921660 | ||||||||
\(36\) | 0.127121 | 0.0211868 | ||||||||
\(37\) | −3.49596 | −0.574733 | −0.287367 | − | 0.957821i | \(-0.592780\pi\) | ||||
−0.287367 | + | 0.957821i | \(0.592780\pi\) | |||||||
\(38\) | −1.36683 | −0.221729 | ||||||||
\(39\) | −2.03788 | −0.326323 | ||||||||
\(40\) | 1.49209 | 0.235919 | ||||||||
\(41\) | −4.95721 | −0.774186 | −0.387093 | − | 0.922041i | \(-0.626521\pi\) | ||||
−0.387093 | + | 0.922041i | \(0.626521\pi\) | |||||||
\(42\) | −6.46224 | −0.997146 | ||||||||
\(43\) | −11.4310 | −1.74321 | −0.871604 | − | 0.490211i | \(-0.836920\pi\) | ||||
−0.871604 | + | 0.490211i | \(0.836920\pi\) | |||||||
\(44\) | −3.80342 | −0.573387 | ||||||||
\(45\) | 0.189675 | 0.0282751 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 1.92948 | 0.281444 | 0.140722 | − | 0.990049i | \(-0.455058\pi\) | ||||
0.140722 | + | 0.990049i | \(0.455058\pi\) | |||||||
\(48\) | −1.76837 | −0.255242 | ||||||||
\(49\) | 6.35432 | 0.907760 | ||||||||
\(50\) | −2.77368 | −0.392258 | ||||||||
\(51\) | 12.2176 | 1.71081 | ||||||||
\(52\) | 1.15241 | 0.159811 | ||||||||
\(53\) | −11.6074 | −1.59440 | −0.797202 | − | 0.603712i | \(-0.793688\pi\) | ||||
−0.797202 | + | 0.603712i | \(0.793688\pi\) | |||||||
\(54\) | 5.08030 | 0.691342 | ||||||||
\(55\) | −5.67503 | −0.765220 | ||||||||
\(56\) | 3.65436 | 0.488334 | ||||||||
\(57\) | 2.41706 | 0.320147 | ||||||||
\(58\) | 10.2612 | 1.34736 | ||||||||
\(59\) | −6.12808 | −0.797808 | −0.398904 | − | 0.916993i | \(-0.630609\pi\) | ||||
−0.398904 | + | 0.916993i | \(0.630609\pi\) | |||||||
\(60\) | −2.63855 | −0.340636 | ||||||||
\(61\) | −10.6230 | −1.36014 | −0.680068 | − | 0.733149i | \(-0.738050\pi\) | ||||
−0.680068 | + | 0.733149i | \(0.738050\pi\) | |||||||
\(62\) | −4.85848 | −0.617028 | ||||||||
\(63\) | 0.464544 | 0.0585271 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.71949 | 0.213277 | ||||||||
\(66\) | 6.72584 | 0.827893 | ||||||||
\(67\) | −1.94680 | −0.237839 | −0.118920 | − | 0.992904i | \(-0.537943\pi\) | ||||
−0.118920 | + | 0.992904i | \(0.537943\pi\) | |||||||
\(68\) | −6.90897 | −0.837836 | ||||||||
\(69\) | −1.76837 | −0.212886 | ||||||||
\(70\) | 5.45261 | 0.651712 | ||||||||
\(71\) | −9.55777 | −1.13430 | −0.567150 | − | 0.823615i | \(-0.691954\pi\) | ||||
−0.567150 | + | 0.823615i | \(0.691954\pi\) | |||||||
\(72\) | 0.127121 | 0.0149813 | ||||||||
\(73\) | 0.982039 | 0.114939 | 0.0574695 | − | 0.998347i | \(-0.481697\pi\) | ||||
0.0574695 | + | 0.998347i | \(0.481697\pi\) | |||||||
\(74\) | −3.49596 | −0.406398 | ||||||||
\(75\) | 4.90488 | 0.566367 | ||||||||
\(76\) | −1.36683 | −0.156786 | ||||||||
\(77\) | −13.8990 | −1.58394 | ||||||||
\(78\) | −2.03788 | −0.230745 | ||||||||
\(79\) | 5.33190 | 0.599886 | 0.299943 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299943 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(80\) | 1.49209 | 0.166820 | ||||||||
\(81\) | −9.36520 | −1.04058 | ||||||||
\(82\) | −4.95721 | −0.547432 | ||||||||
\(83\) | 3.48726 | 0.382776 | 0.191388 | − | 0.981514i | \(-0.438701\pi\) | ||||
0.191388 | + | 0.981514i | \(0.438701\pi\) | |||||||
\(84\) | −6.46224 | −0.705088 | ||||||||
\(85\) | −10.3088 | −1.11814 | ||||||||
\(86\) | −11.4310 | −1.23263 | ||||||||
\(87\) | −18.1456 | −1.94541 | ||||||||
\(88\) | −3.80342 | −0.405446 | ||||||||
\(89\) | 12.5179 | 1.32690 | 0.663448 | − | 0.748223i | \(-0.269093\pi\) | ||||
0.663448 | + | 0.748223i | \(0.269093\pi\) | |||||||
\(90\) | 0.189675 | 0.0199935 | ||||||||
\(91\) | 4.21132 | 0.441466 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 8.59158 | 0.890905 | ||||||||
\(94\) | 1.92948 | 0.199011 | ||||||||
\(95\) | −2.03943 | −0.209241 | ||||||||
\(96\) | −1.76837 | −0.180483 | ||||||||
\(97\) | 12.5598 | 1.27526 | 0.637629 | − | 0.770343i | \(-0.279915\pi\) | ||||
0.637629 | + | 0.770343i | \(0.279915\pi\) | |||||||
\(98\) | 6.35432 | 0.641883 | ||||||||
\(99\) | −0.483493 | −0.0485929 | ||||||||
\(100\) | −2.77368 | −0.277368 | ||||||||
\(101\) | −4.07669 | −0.405646 | −0.202823 | − | 0.979215i | \(-0.565012\pi\) | ||||
−0.202823 | + | 0.979215i | \(0.565012\pi\) | |||||||
\(102\) | 12.2176 | 1.20972 | ||||||||
\(103\) | −11.2455 | −1.10805 | −0.554026 | − | 0.832500i | \(-0.686909\pi\) | ||||
−0.554026 | + | 0.832500i | \(0.686909\pi\) | |||||||
\(104\) | 1.15241 | 0.113003 | ||||||||
\(105\) | −9.64222 | −0.940984 | ||||||||
\(106\) | −11.6074 | −1.12741 | ||||||||
\(107\) | 13.1940 | 1.27551 | 0.637755 | − | 0.770239i | \(-0.279863\pi\) | ||||
0.637755 | + | 0.770239i | \(0.279863\pi\) | |||||||
\(108\) | 5.08030 | 0.488852 | ||||||||
\(109\) | −1.49354 | −0.143055 | −0.0715276 | − | 0.997439i | \(-0.522787\pi\) | ||||
−0.0715276 | + | 0.997439i | \(0.522787\pi\) | |||||||
\(110\) | −5.67503 | −0.541092 | ||||||||
\(111\) | 6.18215 | 0.586784 | ||||||||
\(112\) | 3.65436 | 0.345304 | ||||||||
\(113\) | 4.90373 | 0.461304 | 0.230652 | − | 0.973036i | \(-0.425914\pi\) | ||||
0.230652 | + | 0.973036i | \(0.425914\pi\) | |||||||
\(114\) | 2.41706 | 0.226378 | ||||||||
\(115\) | 1.49209 | 0.139138 | ||||||||
\(116\) | 10.2612 | 0.952729 | ||||||||
\(117\) | 0.146495 | 0.0135435 | ||||||||
\(118\) | −6.12808 | −0.564135 | ||||||||
\(119\) | −25.2478 | −2.31447 | ||||||||
\(120\) | −2.63855 | −0.240866 | ||||||||
\(121\) | 3.46599 | 0.315090 | ||||||||
\(122\) | −10.6230 | −0.961761 | ||||||||
\(123\) | 8.76617 | 0.790419 | ||||||||
\(124\) | −4.85848 | −0.436305 | ||||||||
\(125\) | −11.5990 | −1.03745 | ||||||||
\(126\) | 0.464544 | 0.0413849 | ||||||||
\(127\) | 3.66865 | 0.325540 | 0.162770 | − | 0.986664i | \(-0.447957\pi\) | ||||
0.162770 | + | 0.986664i | \(0.447957\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 20.2142 | 1.77976 | ||||||||
\(130\) | 1.71949 | 0.150810 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | 6.72584 | 0.585409 | ||||||||
\(133\) | −4.99489 | −0.433112 | ||||||||
\(134\) | −1.94680 | −0.168178 | ||||||||
\(135\) | 7.58025 | 0.652404 | ||||||||
\(136\) | −6.90897 | −0.592439 | ||||||||
\(137\) | −6.11041 | −0.522048 | −0.261024 | − | 0.965332i | \(-0.584060\pi\) | ||||
−0.261024 | + | 0.965332i | \(0.584060\pi\) | |||||||
\(138\) | −1.76837 | −0.150533 | ||||||||
\(139\) | 6.89890 | 0.585157 | 0.292579 | − | 0.956241i | \(-0.405487\pi\) | ||||
0.292579 | + | 0.956241i | \(0.405487\pi\) | |||||||
\(140\) | 5.45261 | 0.460830 | ||||||||
\(141\) | −3.41203 | −0.287345 | ||||||||
\(142\) | −9.55777 | −0.802071 | ||||||||
\(143\) | −4.38310 | −0.366533 | ||||||||
\(144\) | 0.127121 | 0.0105934 | ||||||||
\(145\) | 15.3106 | 1.27148 | ||||||||
\(146\) | 0.982039 | 0.0812741 | ||||||||
\(147\) | −11.2368 | −0.926793 | ||||||||
\(148\) | −3.49596 | −0.287367 | ||||||||
\(149\) | 9.97008 | 0.816781 | 0.408390 | − | 0.912807i | \(-0.366090\pi\) | ||||
0.408390 | + | 0.912807i | \(0.366090\pi\) | |||||||
\(150\) | 4.90488 | 0.400482 | ||||||||
\(151\) | −7.46498 | −0.607491 | −0.303746 | − | 0.952753i | \(-0.598237\pi\) | ||||
−0.303746 | + | 0.952753i | \(0.598237\pi\) | |||||||
\(152\) | −1.36683 | −0.110865 | ||||||||
\(153\) | −0.878273 | −0.0710042 | ||||||||
\(154\) | −13.8990 | −1.12002 | ||||||||
\(155\) | −7.24927 | −0.582276 | ||||||||
\(156\) | −2.03788 | −0.163161 | ||||||||
\(157\) | −0.950697 | −0.0758739 | −0.0379369 | − | 0.999280i | \(-0.512079\pi\) | ||||
−0.0379369 | + | 0.999280i | \(0.512079\pi\) | |||||||
\(158\) | 5.33190 | 0.424183 | ||||||||
\(159\) | 20.5262 | 1.62783 | ||||||||
\(160\) | 1.49209 | 0.117960 | ||||||||
\(161\) | 3.65436 | 0.288004 | ||||||||
\(162\) | −9.36520 | −0.735800 | ||||||||
\(163\) | 15.2119 | 1.19149 | 0.595745 | − | 0.803174i | \(-0.296857\pi\) | ||||
0.595745 | + | 0.803174i | \(0.296857\pi\) | |||||||
\(164\) | −4.95721 | −0.387093 | ||||||||
\(165\) | 10.0355 | 0.781265 | ||||||||
\(166\) | 3.48726 | 0.270664 | ||||||||
\(167\) | 2.51551 | 0.194656 | 0.0973280 | − | 0.995252i | \(-0.468970\pi\) | ||||
0.0973280 | + | 0.995252i | \(0.468970\pi\) | |||||||
\(168\) | −6.46224 | −0.498573 | ||||||||
\(169\) | −11.6720 | −0.897842 | ||||||||
\(170\) | −10.3088 | −0.790647 | ||||||||
\(171\) | −0.173753 | −0.0132872 | ||||||||
\(172\) | −11.4310 | −0.871604 | ||||||||
\(173\) | −11.3846 | −0.865556 | −0.432778 | − | 0.901500i | \(-0.642467\pi\) | ||||
−0.432778 | + | 0.901500i | \(0.642467\pi\) | |||||||
\(174\) | −18.1456 | −1.37561 | ||||||||
\(175\) | −10.1360 | −0.766211 | ||||||||
\(176\) | −3.80342 | −0.286693 | ||||||||
\(177\) | 10.8367 | 0.814536 | ||||||||
\(178\) | 12.5179 | 0.938257 | ||||||||
\(179\) | −7.42749 | −0.555157 | −0.277579 | − | 0.960703i | \(-0.589532\pi\) | ||||
−0.277579 | + | 0.960703i | \(0.589532\pi\) | |||||||
\(180\) | 0.189675 | 0.0141375 | ||||||||
\(181\) | −6.58423 | −0.489402 | −0.244701 | − | 0.969599i | \(-0.578690\pi\) | ||||
−0.244701 | + | 0.969599i | \(0.578690\pi\) | |||||||
\(182\) | 4.21132 | 0.312164 | ||||||||
\(183\) | 18.7854 | 1.38865 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −5.21628 | −0.383508 | ||||||||
\(186\) | 8.59158 | 0.629965 | ||||||||
\(187\) | 26.2777 | 1.92162 | ||||||||
\(188\) | 1.92948 | 0.140722 | ||||||||
\(189\) | 18.5652 | 1.35042 | ||||||||
\(190\) | −2.03943 | −0.147956 | ||||||||
\(191\) | 19.7052 | 1.42582 | 0.712910 | − | 0.701255i | \(-0.247377\pi\) | ||||
0.712910 | + | 0.701255i | \(0.247377\pi\) | |||||||
\(192\) | −1.76837 | −0.127621 | ||||||||
\(193\) | −13.0842 | −0.941818 | −0.470909 | − | 0.882182i | \(-0.656074\pi\) | ||||
−0.470909 | + | 0.882182i | \(0.656074\pi\) | |||||||
\(194\) | 12.5598 | 0.901744 | ||||||||
\(195\) | −3.04070 | −0.217749 | ||||||||
\(196\) | 6.35432 | 0.453880 | ||||||||
\(197\) | 2.45311 | 0.174777 | 0.0873884 | − | 0.996174i | \(-0.472148\pi\) | ||||
0.0873884 | + | 0.996174i | \(0.472148\pi\) | |||||||
\(198\) | −0.483493 | −0.0343604 | ||||||||
\(199\) | −9.16778 | −0.649887 | −0.324943 | − | 0.945733i | \(-0.605345\pi\) | ||||
−0.324943 | + | 0.945733i | \(0.605345\pi\) | |||||||
\(200\) | −2.77368 | −0.196129 | ||||||||
\(201\) | 3.44265 | 0.242826 | ||||||||
\(202\) | −4.07669 | −0.286835 | ||||||||
\(203\) | 37.4981 | 2.63185 | ||||||||
\(204\) | 12.2176 | 0.855403 | ||||||||
\(205\) | −7.39658 | −0.516600 | ||||||||
\(206\) | −11.2455 | −0.783511 | ||||||||
\(207\) | 0.127121 | 0.00883550 | ||||||||
\(208\) | 1.15241 | 0.0799053 | ||||||||
\(209\) | 5.19863 | 0.359597 | ||||||||
\(210\) | −9.64222 | −0.665376 | ||||||||
\(211\) | −10.3828 | −0.714780 | −0.357390 | − | 0.933955i | \(-0.616333\pi\) | ||||
−0.357390 | + | 0.933955i | \(0.616333\pi\) | |||||||
\(212\) | −11.6074 | −0.797202 | ||||||||
\(213\) | 16.9016 | 1.15808 | ||||||||
\(214\) | 13.1940 | 0.901922 | ||||||||
\(215\) | −17.0560 | −1.16321 | ||||||||
\(216\) | 5.08030 | 0.345671 | ||||||||
\(217\) | −17.7546 | −1.20526 | ||||||||
\(218\) | −1.49354 | −0.101155 | ||||||||
\(219\) | −1.73660 | −0.117349 | ||||||||
\(220\) | −5.67503 | −0.382610 | ||||||||
\(221\) | −7.96197 | −0.535580 | ||||||||
\(222\) | 6.18215 | 0.414919 | ||||||||
\(223\) | 19.9461 | 1.33569 | 0.667844 | − | 0.744302i | \(-0.267217\pi\) | ||||
0.667844 | + | 0.744302i | \(0.267217\pi\) | |||||||
\(224\) | 3.65436 | 0.244167 | ||||||||
\(225\) | −0.352592 | −0.0235062 | ||||||||
\(226\) | 4.90373 | 0.326192 | ||||||||
\(227\) | 4.12615 | 0.273862 | 0.136931 | − | 0.990581i | \(-0.456276\pi\) | ||||
0.136931 | + | 0.990581i | \(0.456276\pi\) | |||||||
\(228\) | 2.41706 | 0.160074 | ||||||||
\(229\) | 19.7304 | 1.30382 | 0.651911 | − | 0.758295i | \(-0.273967\pi\) | ||||
0.651911 | + | 0.758295i | \(0.273967\pi\) | |||||||
\(230\) | 1.49209 | 0.0983852 | ||||||||
\(231\) | 24.5786 | 1.61715 | ||||||||
\(232\) | 10.2612 | 0.673681 | ||||||||
\(233\) | −20.4976 | −1.34284 | −0.671421 | − | 0.741076i | \(-0.734316\pi\) | ||||
−0.671421 | + | 0.741076i | \(0.734316\pi\) | |||||||
\(234\) | 0.146495 | 0.00957669 | ||||||||
\(235\) | 2.87895 | 0.187802 | ||||||||
\(236\) | −6.12808 | −0.398904 | ||||||||
\(237\) | −9.42875 | −0.612463 | ||||||||
\(238\) | −25.2478 | −1.63657 | ||||||||
\(239\) | −24.7053 | −1.59805 | −0.799025 | − | 0.601298i | \(-0.794651\pi\) | ||||
−0.799025 | + | 0.601298i | \(0.794651\pi\) | |||||||
\(240\) | −2.63855 | −0.170318 | ||||||||
\(241\) | −0.352041 | −0.0226770 | −0.0113385 | − | 0.999936i | \(-0.503609\pi\) | ||||
−0.0113385 | + | 0.999936i | \(0.503609\pi\) | |||||||
\(242\) | 3.46599 | 0.222802 | ||||||||
\(243\) | 1.32020 | 0.0846909 | ||||||||
\(244\) | −10.6230 | −0.680068 | ||||||||
\(245\) | 9.48119 | 0.605731 | ||||||||
\(246\) | 8.76617 | 0.558910 | ||||||||
\(247\) | −1.57515 | −0.100224 | ||||||||
\(248\) | −4.85848 | −0.308514 | ||||||||
\(249\) | −6.16675 | −0.390802 | ||||||||
\(250\) | −11.5990 | −0.733585 | ||||||||
\(251\) | 15.9077 | 1.00408 | 0.502042 | − | 0.864844i | \(-0.332582\pi\) | ||||
0.502042 | + | 0.864844i | \(0.332582\pi\) | |||||||
\(252\) | 0.464544 | 0.0292636 | ||||||||
\(253\) | −3.80342 | −0.239119 | ||||||||
\(254\) | 3.66865 | 0.230191 | ||||||||
\(255\) | 18.2297 | 1.14159 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.558890 | −0.0348626 | −0.0174313 | − | 0.999848i | \(-0.505549\pi\) | ||||
−0.0174313 | + | 0.999848i | \(0.505549\pi\) | |||||||
\(258\) | 20.2142 | 1.25848 | ||||||||
\(259\) | −12.7755 | −0.793831 | ||||||||
\(260\) | 1.71949 | 0.106639 | ||||||||
\(261\) | 1.30441 | 0.0807411 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 17.8238 | 1.09906 | 0.549531 | − | 0.835473i | \(-0.314806\pi\) | ||||
0.549531 | + | 0.835473i | \(0.314806\pi\) | |||||||
\(264\) | 6.72584 | 0.413947 | ||||||||
\(265\) | −17.3193 | −1.06392 | ||||||||
\(266\) | −4.99489 | −0.306256 | ||||||||
\(267\) | −22.1362 | −1.35472 | ||||||||
\(268\) | −1.94680 | −0.118920 | ||||||||
\(269\) | −7.74721 | −0.472356 | −0.236178 | − | 0.971710i | \(-0.575895\pi\) | ||||
−0.236178 | + | 0.971710i | \(0.575895\pi\) | |||||||
\(270\) | 7.58025 | 0.461319 | ||||||||
\(271\) | −5.30801 | −0.322438 | −0.161219 | − | 0.986919i | \(-0.551543\pi\) | ||||
−0.161219 | + | 0.986919i | \(0.551543\pi\) | |||||||
\(272\) | −6.90897 | −0.418918 | ||||||||
\(273\) | −7.44715 | −0.450722 | ||||||||
\(274\) | −6.11041 | −0.369143 | ||||||||
\(275\) | 10.5495 | 0.636157 | ||||||||
\(276\) | −1.76837 | −0.106443 | ||||||||
\(277\) | −3.63363 | −0.218324 | −0.109162 | − | 0.994024i | \(-0.534817\pi\) | ||||
−0.109162 | + | 0.994024i | \(0.534817\pi\) | |||||||
\(278\) | 6.89890 | 0.413769 | ||||||||
\(279\) | −0.617614 | −0.0369756 | ||||||||
\(280\) | 5.45261 | 0.325856 | ||||||||
\(281\) | −16.9276 | −1.00981 | −0.504906 | − | 0.863174i | \(-0.668473\pi\) | ||||
−0.504906 | + | 0.863174i | \(0.668473\pi\) | |||||||
\(282\) | −3.41203 | −0.203183 | ||||||||
\(283\) | −31.8013 | −1.89039 | −0.945195 | − | 0.326506i | \(-0.894129\pi\) | ||||
−0.945195 | + | 0.326506i | \(0.894129\pi\) | |||||||
\(284\) | −9.55777 | −0.567150 | ||||||||
\(285\) | 3.60646 | 0.213628 | ||||||||
\(286\) | −4.38310 | −0.259178 | ||||||||
\(287\) | −18.1154 | −1.06932 | ||||||||
\(288\) | 0.127121 | 0.00749066 | ||||||||
\(289\) | 30.7339 | 1.80787 | ||||||||
\(290\) | 15.3106 | 0.899069 | ||||||||
\(291\) | −22.2104 | −1.30200 | ||||||||
\(292\) | 0.982039 | 0.0574695 | ||||||||
\(293\) | 4.80599 | 0.280769 | 0.140384 | − | 0.990097i | \(-0.455166\pi\) | ||||
0.140384 | + | 0.990097i | \(0.455166\pi\) | |||||||
\(294\) | −11.2368 | −0.655342 | ||||||||
\(295\) | −9.14362 | −0.532362 | ||||||||
\(296\) | −3.49596 | −0.203199 | ||||||||
\(297\) | −19.3225 | −1.12121 | ||||||||
\(298\) | 9.97008 | 0.577551 | ||||||||
\(299\) | 1.15241 | 0.0666456 | ||||||||
\(300\) | 4.90488 | 0.283184 | ||||||||
\(301\) | −41.7729 | −2.40775 | ||||||||
\(302\) | −7.46498 | −0.429561 | ||||||||
\(303\) | 7.20908 | 0.414151 | ||||||||
\(304\) | −1.36683 | −0.0783932 | ||||||||
\(305\) | −15.8504 | −0.907593 | ||||||||
\(306\) | −0.878273 | −0.0502075 | ||||||||
\(307\) | −19.8325 | −1.13190 | −0.565950 | − | 0.824440i | \(-0.691490\pi\) | ||||
−0.565950 | + | 0.824440i | \(0.691490\pi\) | |||||||
\(308\) | −13.8990 | −0.791972 | ||||||||
\(309\) | 19.8862 | 1.13128 | ||||||||
\(310\) | −7.24927 | −0.411731 | ||||||||
\(311\) | −23.5442 | −1.33507 | −0.667535 | − | 0.744578i | \(-0.732651\pi\) | ||||
−0.667535 | + | 0.744578i | \(0.732651\pi\) | |||||||
\(312\) | −2.03788 | −0.115372 | ||||||||
\(313\) | −19.8159 | −1.12006 | −0.560030 | − | 0.828472i | \(-0.689210\pi\) | ||||
−0.560030 | + | 0.828472i | \(0.689210\pi\) | |||||||
\(314\) | −0.950697 | −0.0536509 | ||||||||
\(315\) | 0.693140 | 0.0390540 | ||||||||
\(316\) | 5.33190 | 0.299943 | ||||||||
\(317\) | −6.59785 | −0.370572 | −0.185286 | − | 0.982685i | \(-0.559321\pi\) | ||||
−0.185286 | + | 0.982685i | \(0.559321\pi\) | |||||||
\(318\) | 20.5262 | 1.15105 | ||||||||
\(319\) | −39.0277 | −2.18513 | ||||||||
\(320\) | 1.49209 | 0.0834101 | ||||||||
\(321\) | −23.3318 | −1.30225 | ||||||||
\(322\) | 3.65436 | 0.203649 | ||||||||
\(323\) | 9.44340 | 0.525445 | ||||||||
\(324\) | −9.36520 | −0.520289 | ||||||||
\(325\) | −3.19642 | −0.177305 | ||||||||
\(326\) | 15.2119 | 0.842510 | ||||||||
\(327\) | 2.64113 | 0.146055 | ||||||||
\(328\) | −4.95721 | −0.273716 | ||||||||
\(329\) | 7.05101 | 0.388735 | ||||||||
\(330\) | 10.0355 | 0.552438 | ||||||||
\(331\) | −21.6708 | −1.19113 | −0.595567 | − | 0.803306i | \(-0.703073\pi\) | ||||
−0.595567 | + | 0.803306i | \(0.703073\pi\) | |||||||
\(332\) | 3.48726 | 0.191388 | ||||||||
\(333\) | −0.444410 | −0.0243535 | ||||||||
\(334\) | 2.51551 | 0.137643 | ||||||||
\(335\) | −2.90479 | −0.158706 | ||||||||
\(336\) | −6.46224 | −0.352544 | ||||||||
\(337\) | −1.89195 | −0.103061 | −0.0515307 | − | 0.998671i | \(-0.516410\pi\) | ||||
−0.0515307 | + | 0.998671i | \(0.516410\pi\) | |||||||
\(338\) | −11.6720 | −0.634870 | ||||||||
\(339\) | −8.67160 | −0.470977 | ||||||||
\(340\) | −10.3088 | −0.559072 | ||||||||
\(341\) | 18.4788 | 1.00069 | ||||||||
\(342\) | −0.173753 | −0.00939547 | ||||||||
\(343\) | −2.35954 | −0.127403 | ||||||||
\(344\) | −11.4310 | −0.616317 | ||||||||
\(345\) | −2.63855 | −0.142055 | ||||||||
\(346\) | −11.3846 | −0.612041 | ||||||||
\(347\) | 7.18382 | 0.385648 | 0.192824 | − | 0.981233i | \(-0.438235\pi\) | ||||
0.192824 | + | 0.981233i | \(0.438235\pi\) | |||||||
\(348\) | −18.1456 | −0.972705 | ||||||||
\(349\) | 11.8172 | 0.632560 | 0.316280 | − | 0.948666i | \(-0.397566\pi\) | ||||
0.316280 | + | 0.948666i | \(0.397566\pi\) | |||||||
\(350\) | −10.1360 | −0.541793 | ||||||||
\(351\) | 5.85459 | 0.312495 | ||||||||
\(352\) | −3.80342 | −0.202723 | ||||||||
\(353\) | −19.9397 | −1.06128 | −0.530642 | − | 0.847596i | \(-0.678049\pi\) | ||||
−0.530642 | + | 0.847596i | \(0.678049\pi\) | |||||||
\(354\) | 10.8367 | 0.575964 | ||||||||
\(355\) | −14.2610 | −0.756896 | ||||||||
\(356\) | 12.5179 | 0.663448 | ||||||||
\(357\) | 44.6474 | 2.36299 | ||||||||
\(358\) | −7.42749 | −0.392555 | ||||||||
\(359\) | 31.0530 | 1.63891 | 0.819457 | − | 0.573141i | \(-0.194275\pi\) | ||||
0.819457 | + | 0.573141i | \(0.194275\pi\) | |||||||
\(360\) | 0.189675 | 0.00999675 | ||||||||
\(361\) | −17.1318 | −0.901672 | ||||||||
\(362\) | −6.58423 | −0.346059 | ||||||||
\(363\) | −6.12914 | −0.321696 | ||||||||
\(364\) | 4.21132 | 0.220733 | ||||||||
\(365\) | 1.46529 | 0.0766966 | ||||||||
\(366\) | 18.7854 | 0.981926 | ||||||||
\(367\) | 13.2547 | 0.691887 | 0.345944 | − | 0.938255i | \(-0.387559\pi\) | ||||
0.345944 | + | 0.938255i | \(0.387559\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −0.630164 | −0.0328050 | ||||||||
\(370\) | −5.21628 | −0.271181 | ||||||||
\(371\) | −42.4177 | −2.20222 | ||||||||
\(372\) | 8.59158 | 0.445453 | ||||||||
\(373\) | −33.2382 | −1.72101 | −0.860505 | − | 0.509442i | \(-0.829852\pi\) | ||||
−0.860505 | + | 0.509442i | \(0.829852\pi\) | |||||||
\(374\) | 26.2777 | 1.35879 | ||||||||
\(375\) | 20.5113 | 1.05920 | ||||||||
\(376\) | 1.92948 | 0.0995054 | ||||||||
\(377\) | 11.8251 | 0.609025 | ||||||||
\(378\) | 18.5652 | 0.954893 | ||||||||
\(379\) | −4.97231 | −0.255410 | −0.127705 | − | 0.991812i | \(-0.540761\pi\) | ||||
−0.127705 | + | 0.991812i | \(0.540761\pi\) | |||||||
\(380\) | −2.03943 | −0.104621 | ||||||||
\(381\) | −6.48751 | −0.332365 | ||||||||
\(382\) | 19.7052 | 1.00821 | ||||||||
\(383\) | 30.2486 | 1.54563 | 0.772814 | − | 0.634632i | \(-0.218848\pi\) | ||||
0.772814 | + | 0.634632i | \(0.218848\pi\) | |||||||
\(384\) | −1.76837 | −0.0902416 | ||||||||
\(385\) | −20.7386 | −1.05694 | ||||||||
\(386\) | −13.0842 | −0.665966 | ||||||||
\(387\) | −1.45311 | −0.0738659 | ||||||||
\(388\) | 12.5598 | 0.637629 | ||||||||
\(389\) | 13.7779 | 0.698566 | 0.349283 | − | 0.937017i | \(-0.386425\pi\) | ||||
0.349283 | + | 0.937017i | \(0.386425\pi\) | |||||||
\(390\) | −3.04070 | −0.153972 | ||||||||
\(391\) | −6.90897 | −0.349402 | ||||||||
\(392\) | 6.35432 | 0.320942 | ||||||||
\(393\) | 1.76837 | 0.0892023 | ||||||||
\(394\) | 2.45311 | 0.123586 | ||||||||
\(395\) | 7.95565 | 0.400292 | ||||||||
\(396\) | −0.483493 | −0.0242965 | ||||||||
\(397\) | −23.3680 | −1.17281 | −0.586403 | − | 0.810020i | \(-0.699456\pi\) | ||||
−0.586403 | + | 0.810020i | \(0.699456\pi\) | |||||||
\(398\) | −9.16778 | −0.459539 | ||||||||
\(399\) | 8.83280 | 0.442193 | ||||||||
\(400\) | −2.77368 | −0.138684 | ||||||||
\(401\) | −0.577445 | −0.0288362 | −0.0144181 | − | 0.999896i | \(-0.504590\pi\) | ||||
−0.0144181 | + | 0.999896i | \(0.504590\pi\) | |||||||
\(402\) | 3.44265 | 0.171704 | ||||||||
\(403\) | −5.59896 | −0.278904 | ||||||||
\(404\) | −4.07669 | −0.202823 | ||||||||
\(405\) | −13.9737 | −0.694358 | ||||||||
\(406\) | 37.4981 | 1.86100 | ||||||||
\(407\) | 13.2966 | 0.659089 | ||||||||
\(408\) | 12.2176 | 0.604861 | ||||||||
\(409\) | 32.9261 | 1.62809 | 0.814045 | − | 0.580802i | \(-0.197261\pi\) | ||||
0.814045 | + | 0.580802i | \(0.197261\pi\) | |||||||
\(410\) | −7.39658 | −0.365291 | ||||||||
\(411\) | 10.8054 | 0.532993 | ||||||||
\(412\) | −11.2455 | −0.554026 | ||||||||
\(413\) | −22.3942 | −1.10195 | ||||||||
\(414\) | 0.127121 | 0.00624764 | ||||||||
\(415\) | 5.20329 | 0.255419 | ||||||||
\(416\) | 1.15241 | 0.0565015 | ||||||||
\(417\) | −12.1998 | −0.597426 | ||||||||
\(418\) | 5.19863 | 0.254273 | ||||||||
\(419\) | 9.40549 | 0.459488 | 0.229744 | − | 0.973251i | \(-0.426211\pi\) | ||||
0.229744 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(420\) | −9.64222 | −0.470492 | ||||||||
\(421\) | −2.40395 | −0.117161 | −0.0585806 | − | 0.998283i | \(-0.518657\pi\) | ||||
−0.0585806 | + | 0.998283i | \(0.518657\pi\) | |||||||
\(422\) | −10.3828 | −0.505426 | ||||||||
\(423\) | 0.245277 | 0.0119258 | ||||||||
\(424\) | −11.6074 | −0.563707 | ||||||||
\(425\) | 19.1633 | 0.929555 | ||||||||
\(426\) | 16.9016 | 0.818888 | ||||||||
\(427\) | −38.8202 | −1.87864 | ||||||||
\(428\) | 13.1940 | 0.637755 | ||||||||
\(429\) | 7.75092 | 0.374218 | ||||||||
\(430\) | −17.0560 | −0.822513 | ||||||||
\(431\) | 11.7801 | 0.567428 | 0.283714 | − | 0.958909i | \(-0.408433\pi\) | ||||
0.283714 | + | 0.958909i | \(0.408433\pi\) | |||||||
\(432\) | 5.08030 | 0.244426 | ||||||||
\(433\) | −18.0802 | −0.868881 | −0.434440 | − | 0.900701i | \(-0.643054\pi\) | ||||
−0.434440 | + | 0.900701i | \(0.643054\pi\) | |||||||
\(434\) | −17.7546 | −0.852249 | ||||||||
\(435\) | −27.0748 | −1.29814 | ||||||||
\(436\) | −1.49354 | −0.0715276 | ||||||||
\(437\) | −1.36683 | −0.0653844 | ||||||||
\(438\) | −1.73660 | −0.0829782 | ||||||||
\(439\) | −3.48237 | −0.166204 | −0.0831022 | − | 0.996541i | \(-0.526483\pi\) | ||||
−0.0831022 | + | 0.996541i | \(0.526483\pi\) | |||||||
\(440\) | −5.67503 | −0.270546 | ||||||||
\(441\) | 0.807766 | 0.0384650 | ||||||||
\(442\) | −7.96197 | −0.378712 | ||||||||
\(443\) | −21.5689 | −1.02477 | −0.512384 | − | 0.858756i | \(-0.671238\pi\) | ||||
−0.512384 | + | 0.858756i | \(0.671238\pi\) | |||||||
\(444\) | 6.18215 | 0.293392 | ||||||||
\(445\) | 18.6778 | 0.885412 | ||||||||
\(446\) | 19.9461 | 0.944474 | ||||||||
\(447\) | −17.6308 | −0.833906 | ||||||||
\(448\) | 3.65436 | 0.172652 | ||||||||
\(449\) | −16.8096 | −0.793296 | −0.396648 | − | 0.917971i | \(-0.629827\pi\) | ||||
−0.396648 | + | 0.917971i | \(0.629827\pi\) | |||||||
\(450\) | −0.352592 | −0.0166214 | ||||||||
\(451\) | 18.8543 | 0.887816 | ||||||||
\(452\) | 4.90373 | 0.230652 | ||||||||
\(453\) | 13.2008 | 0.620228 | ||||||||
\(454\) | 4.12615 | 0.193650 | ||||||||
\(455\) | 6.28365 | 0.294582 | ||||||||
\(456\) | 2.41706 | 0.113189 | ||||||||
\(457\) | −34.5898 | −1.61804 | −0.809021 | − | 0.587780i | \(-0.800002\pi\) | ||||
−0.809021 | + | 0.587780i | \(0.800002\pi\) | |||||||
\(458\) | 19.7304 | 0.921942 | ||||||||
\(459\) | −35.0997 | −1.63831 | ||||||||
\(460\) | 1.49209 | 0.0695689 | ||||||||
\(461\) | 39.4992 | 1.83966 | 0.919831 | − | 0.392315i | \(-0.128326\pi\) | ||||
0.919831 | + | 0.392315i | \(0.128326\pi\) | |||||||
\(462\) | 24.5786 | 1.14350 | ||||||||
\(463\) | 26.6234 | 1.23730 | 0.618648 | − | 0.785668i | \(-0.287681\pi\) | ||||
0.618648 | + | 0.785668i | \(0.287681\pi\) | |||||||
\(464\) | 10.2612 | 0.476365 | ||||||||
\(465\) | 12.8194 | 0.594484 | ||||||||
\(466\) | −20.4976 | −0.949533 | ||||||||
\(467\) | 24.1096 | 1.11566 | 0.557831 | − | 0.829955i | \(-0.311634\pi\) | ||||
0.557831 | + | 0.829955i | \(0.311634\pi\) | |||||||
\(468\) | 0.146495 | 0.00677174 | ||||||||
\(469\) | −7.11430 | −0.328508 | ||||||||
\(470\) | 2.87895 | 0.132796 | ||||||||
\(471\) | 1.68118 | 0.0774647 | ||||||||
\(472\) | −6.12808 | −0.282068 | ||||||||
\(473\) | 43.4768 | 1.99906 | ||||||||
\(474\) | −9.42875 | −0.433077 | ||||||||
\(475\) | 3.79116 | 0.173950 | ||||||||
\(476\) | −25.2478 | −1.15723 | ||||||||
\(477\) | −1.47555 | −0.0675606 | ||||||||
\(478\) | −24.7053 | −1.12999 | ||||||||
\(479\) | 31.6140 | 1.44448 | 0.722239 | − | 0.691643i | \(-0.243113\pi\) | ||||
0.722239 | + | 0.691643i | \(0.243113\pi\) | |||||||
\(480\) | −2.63855 | −0.120433 | ||||||||
\(481\) | −4.02878 | −0.183697 | ||||||||
\(482\) | −0.352041 | −0.0160350 | ||||||||
\(483\) | −6.46224 | −0.294042 | ||||||||
\(484\) | 3.46599 | 0.157545 | ||||||||
\(485\) | 18.7404 | 0.850956 | ||||||||
\(486\) | 1.32020 | 0.0598855 | ||||||||
\(487\) | 27.4000 | 1.24161 | 0.620805 | − | 0.783965i | \(-0.286806\pi\) | ||||
0.620805 | + | 0.783965i | \(0.286806\pi\) | |||||||
\(488\) | −10.6230 | −0.480881 | ||||||||
\(489\) | −26.9002 | −1.21647 | ||||||||
\(490\) | 9.48119 | 0.428317 | ||||||||
\(491\) | 38.5933 | 1.74169 | 0.870846 | − | 0.491556i | \(-0.163572\pi\) | ||||
0.870846 | + | 0.491556i | \(0.163572\pi\) | |||||||
\(492\) | 8.76617 | 0.395209 | ||||||||
\(493\) | −70.8944 | −3.19292 | ||||||||
\(494\) | −1.57515 | −0.0708694 | ||||||||
\(495\) | −0.721413 | −0.0324251 | ||||||||
\(496\) | −4.85848 | −0.218152 | ||||||||
\(497\) | −34.9275 | −1.56671 | ||||||||
\(498\) | −6.16675 | −0.276339 | ||||||||
\(499\) | 18.9661 | 0.849040 | 0.424520 | − | 0.905419i | \(-0.360443\pi\) | ||||
0.424520 | + | 0.905419i | \(0.360443\pi\) | |||||||
\(500\) | −11.5990 | −0.518723 | ||||||||
\(501\) | −4.44835 | −0.198737 | ||||||||
\(502\) | 15.9077 | 0.709994 | ||||||||
\(503\) | −36.2209 | −1.61501 | −0.807504 | − | 0.589862i | \(-0.799182\pi\) | ||||
−0.807504 | + | 0.589862i | \(0.799182\pi\) | |||||||
\(504\) | 0.464544 | 0.0206925 | ||||||||
\(505\) | −6.08277 | −0.270680 | ||||||||
\(506\) | −3.80342 | −0.169083 | ||||||||
\(507\) | 20.6403 | 0.916667 | ||||||||
\(508\) | 3.66865 | 0.162770 | ||||||||
\(509\) | −17.5489 | −0.777842 | −0.388921 | − | 0.921271i | \(-0.627152\pi\) | ||||
−0.388921 | + | 0.921271i | \(0.627152\pi\) | |||||||
\(510\) | 18.2297 | 0.807224 | ||||||||
\(511\) | 3.58872 | 0.158756 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.94392 | −0.306582 | ||||||||
\(514\) | −0.558890 | −0.0246516 | ||||||||
\(515\) | −16.7792 | −0.739382 | ||||||||
\(516\) | 20.2142 | 0.889879 | ||||||||
\(517\) | −7.33862 | −0.322752 | ||||||||
\(518\) | −12.7755 | −0.561323 | ||||||||
\(519\) | 20.1322 | 0.883704 | ||||||||
\(520\) | 1.71949 | 0.0754048 | ||||||||
\(521\) | −0.369981 | −0.0162091 | −0.00810457 | − | 0.999967i | \(-0.502580\pi\) | ||||
−0.00810457 | + | 0.999967i | \(0.502580\pi\) | |||||||
\(522\) | 1.30441 | 0.0570926 | ||||||||
\(523\) | 20.3547 | 0.890049 | 0.445025 | − | 0.895518i | \(-0.353195\pi\) | ||||
0.445025 | + | 0.895518i | \(0.353195\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 17.9242 | 0.782276 | ||||||||
\(526\) | 17.8238 | 0.777155 | ||||||||
\(527\) | 33.5671 | 1.46221 | ||||||||
\(528\) | 6.72584 | 0.292705 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −17.3193 | −0.752302 | ||||||||
\(531\) | −0.779006 | −0.0338060 | ||||||||
\(532\) | −4.99489 | −0.216556 | ||||||||
\(533\) | −5.71274 | −0.247446 | ||||||||
\(534\) | −22.1362 | −0.957929 | ||||||||
\(535\) | 19.6866 | 0.851124 | ||||||||
\(536\) | −1.94680 | −0.0840889 | ||||||||
\(537\) | 13.1345 | 0.566797 | ||||||||
\(538\) | −7.74721 | −0.334006 | ||||||||
\(539\) | −24.1681 | −1.04100 | ||||||||
\(540\) | 7.58025 | 0.326202 | ||||||||
\(541\) | −1.06724 | −0.0458843 | −0.0229422 | − | 0.999737i | \(-0.507303\pi\) | ||||
−0.0229422 | + | 0.999737i | \(0.507303\pi\) | |||||||
\(542\) | −5.30801 | −0.227998 | ||||||||
\(543\) | 11.6433 | 0.499663 | ||||||||
\(544\) | −6.90897 | −0.296220 | ||||||||
\(545\) | −2.22849 | −0.0954580 | ||||||||
\(546\) | −7.44715 | −0.318709 | ||||||||
\(547\) | −41.9510 | −1.79370 | −0.896848 | − | 0.442338i | \(-0.854149\pi\) | ||||
−0.896848 | + | 0.442338i | \(0.854149\pi\) | |||||||
\(548\) | −6.11041 | −0.261024 | ||||||||
\(549\) | −1.35040 | −0.0576338 | ||||||||
\(550\) | 10.5495 | 0.449831 | ||||||||
\(551\) | −14.0253 | −0.597500 | ||||||||
\(552\) | −1.76837 | −0.0752667 | ||||||||
\(553\) | 19.4847 | 0.828572 | ||||||||
\(554\) | −3.63363 | −0.154378 | ||||||||
\(555\) | 9.22429 | 0.391549 | ||||||||
\(556\) | 6.89890 | 0.292579 | ||||||||
\(557\) | 22.2132 | 0.941204 | 0.470602 | − | 0.882346i | \(-0.344037\pi\) | ||||
0.470602 | + | 0.882346i | \(0.344037\pi\) | |||||||
\(558\) | −0.617614 | −0.0261457 | ||||||||
\(559\) | −13.1732 | −0.557166 | ||||||||
\(560\) | 5.45261 | 0.230415 | ||||||||
\(561\) | −46.4686 | −1.96191 | ||||||||
\(562\) | −16.9276 | −0.714046 | ||||||||
\(563\) | 41.1487 | 1.73421 | 0.867104 | − | 0.498126i | \(-0.165978\pi\) | ||||
0.867104 | + | 0.498126i | \(0.165978\pi\) | |||||||
\(564\) | −3.41203 | −0.143672 | ||||||||
\(565\) | 7.31679 | 0.307820 | ||||||||
\(566\) | −31.8013 | −1.33671 | ||||||||
\(567\) | −34.2238 | −1.43726 | ||||||||
\(568\) | −9.55777 | −0.401035 | ||||||||
\(569\) | −7.53567 | −0.315912 | −0.157956 | − | 0.987446i | \(-0.550490\pi\) | ||||
−0.157956 | + | 0.987446i | \(0.550490\pi\) | |||||||
\(570\) | 3.60646 | 0.151058 | ||||||||
\(571\) | −34.2929 | −1.43511 | −0.717557 | − | 0.696500i | \(-0.754740\pi\) | ||||
−0.717557 | + | 0.696500i | \(0.754740\pi\) | |||||||
\(572\) | −4.38310 | −0.183266 | ||||||||
\(573\) | −34.8461 | −1.45572 | ||||||||
\(574\) | −18.1154 | −0.756123 | ||||||||
\(575\) | −2.77368 | −0.115670 | ||||||||
\(576\) | 0.127121 | 0.00529670 | ||||||||
\(577\) | −20.0143 | −0.833208 | −0.416604 | − | 0.909088i | \(-0.636780\pi\) | ||||
−0.416604 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(578\) | 30.7339 | 1.27836 | ||||||||
\(579\) | 23.1376 | 0.961565 | ||||||||
\(580\) | 15.3106 | 0.635738 | ||||||||
\(581\) | 12.7437 | 0.528697 | ||||||||
\(582\) | −22.2104 | −0.920651 | ||||||||
\(583\) | 44.1479 | 1.82842 | ||||||||
\(584\) | 0.982039 | 0.0406371 | ||||||||
\(585\) | 0.218583 | 0.00903731 | ||||||||
\(586\) | 4.80599 | 0.198534 | ||||||||
\(587\) | 6.48741 | 0.267764 | 0.133882 | − | 0.990997i | \(-0.457256\pi\) | ||||
0.133882 | + | 0.990997i | \(0.457256\pi\) | |||||||
\(588\) | −11.2368 | −0.463397 | ||||||||
\(589\) | 6.64073 | 0.273627 | ||||||||
\(590\) | −9.14362 | −0.376437 | ||||||||
\(591\) | −4.33800 | −0.178441 | ||||||||
\(592\) | −3.49596 | −0.143683 | ||||||||
\(593\) | 14.0991 | 0.578981 | 0.289490 | − | 0.957181i | \(-0.406514\pi\) | ||||
0.289490 | + | 0.957181i | \(0.406514\pi\) | |||||||
\(594\) | −19.3225 | −0.792813 | ||||||||
\(595\) | −37.6719 | −1.54440 | ||||||||
\(596\) | 9.97008 | 0.408390 | ||||||||
\(597\) | 16.2120 | 0.663513 | ||||||||
\(598\) | 1.15241 | 0.0471255 | ||||||||
\(599\) | 3.65675 | 0.149411 | 0.0747054 | − | 0.997206i | \(-0.476198\pi\) | ||||
0.0747054 | + | 0.997206i | \(0.476198\pi\) | |||||||
\(600\) | 4.90488 | 0.200241 | ||||||||
\(601\) | −24.3062 | −0.991471 | −0.495735 | − | 0.868474i | \(-0.665101\pi\) | ||||
−0.495735 | + | 0.868474i | \(0.665101\pi\) | |||||||
\(602\) | −41.7729 | −1.70253 | ||||||||
\(603\) | −0.247478 | −0.0100781 | ||||||||
\(604\) | −7.46498 | −0.303746 | ||||||||
\(605\) | 5.17155 | 0.210253 | ||||||||
\(606\) | 7.20908 | 0.292849 | ||||||||
\(607\) | −31.4760 | −1.27757 | −0.638785 | − | 0.769385i | \(-0.720563\pi\) | ||||
−0.638785 | + | 0.769385i | \(0.720563\pi\) | |||||||
\(608\) | −1.36683 | −0.0554324 | ||||||||
\(609\) | −66.3104 | −2.68703 | ||||||||
\(610\) | −15.8504 | −0.641765 | ||||||||
\(611\) | 2.22355 | 0.0899554 | ||||||||
\(612\) | −0.878273 | −0.0355021 | ||||||||
\(613\) | 31.3452 | 1.26602 | 0.633011 | − | 0.774143i | \(-0.281819\pi\) | ||||
0.633011 | + | 0.774143i | \(0.281819\pi\) | |||||||
\(614\) | −19.8325 | −0.800374 | ||||||||
\(615\) | 13.0799 | 0.527431 | ||||||||
\(616\) | −13.8990 | −0.560008 | ||||||||
\(617\) | −12.2805 | −0.494396 | −0.247198 | − | 0.968965i | \(-0.579510\pi\) | ||||
−0.247198 | + | 0.968965i | \(0.579510\pi\) | |||||||
\(618\) | 19.8862 | 0.799939 | ||||||||
\(619\) | 24.3545 | 0.978892 | 0.489446 | − | 0.872034i | \(-0.337199\pi\) | ||||
0.489446 | + | 0.872034i | \(0.337199\pi\) | |||||||
\(620\) | −7.24927 | −0.291138 | ||||||||
\(621\) | 5.08030 | 0.203866 | ||||||||
\(622\) | −23.5442 | −0.944037 | ||||||||
\(623\) | 45.7449 | 1.83273 | ||||||||
\(624\) | −2.03788 | −0.0815806 | ||||||||
\(625\) | −3.43830 | −0.137532 | ||||||||
\(626\) | −19.8159 | −0.792002 | ||||||||
\(627\) | −9.19309 | −0.367137 | ||||||||
\(628\) | −0.950697 | −0.0379369 | ||||||||
\(629\) | 24.1535 | 0.963064 | ||||||||
\(630\) | 0.693140 | 0.0276154 | ||||||||
\(631\) | 14.4076 | 0.573556 | 0.286778 | − | 0.957997i | \(-0.407416\pi\) | ||||
0.286778 | + | 0.957997i | \(0.407416\pi\) | |||||||
\(632\) | 5.33190 | 0.212092 | ||||||||
\(633\) | 18.3606 | 0.729767 | ||||||||
\(634\) | −6.59785 | −0.262034 | ||||||||
\(635\) | 5.47393 | 0.217226 | ||||||||
\(636\) | 20.5262 | 0.813917 | ||||||||
\(637\) | 7.32278 | 0.290139 | ||||||||
\(638\) | −39.0277 | −1.54512 | ||||||||
\(639\) | −1.21499 | −0.0480643 | ||||||||
\(640\) | 1.49209 | 0.0589799 | ||||||||
\(641\) | −1.04081 | −0.0411094 | −0.0205547 | − | 0.999789i | \(-0.506543\pi\) | ||||
−0.0205547 | + | 0.999789i | \(0.506543\pi\) | |||||||
\(642\) | −23.3318 | −0.920833 | ||||||||
\(643\) | −13.2422 | −0.522219 | −0.261110 | − | 0.965309i | \(-0.584088\pi\) | ||||
−0.261110 | + | 0.965309i | \(0.584088\pi\) | |||||||
\(644\) | 3.65436 | 0.144002 | ||||||||
\(645\) | 30.1613 | 1.18760 | ||||||||
\(646\) | 9.44340 | 0.371546 | ||||||||
\(647\) | −11.4589 | −0.450496 | −0.225248 | − | 0.974301i | \(-0.572319\pi\) | ||||
−0.225248 | + | 0.974301i | \(0.572319\pi\) | |||||||
\(648\) | −9.36520 | −0.367900 | ||||||||
\(649\) | 23.3076 | 0.914905 | ||||||||
\(650\) | −3.19642 | −0.125374 | ||||||||
\(651\) | 31.3967 | 1.23053 | ||||||||
\(652\) | 15.2119 | 0.595745 | ||||||||
\(653\) | −20.0278 | −0.783750 | −0.391875 | − | 0.920019i | \(-0.628173\pi\) | ||||
−0.391875 | + | 0.920019i | \(0.628173\pi\) | |||||||
\(654\) | 2.64113 | 0.103276 | ||||||||
\(655\) | −1.49209 | −0.0583006 | ||||||||
\(656\) | −4.95721 | −0.193547 | ||||||||
\(657\) | 0.124837 | 0.00487037 | ||||||||
\(658\) | 7.05101 | 0.274877 | ||||||||
\(659\) | 1.88462 | 0.0734143 | 0.0367072 | − | 0.999326i | \(-0.488313\pi\) | ||||
0.0367072 | + | 0.999326i | \(0.488313\pi\) | |||||||
\(660\) | 10.0355 | 0.390632 | ||||||||
\(661\) | −34.7164 | −1.35031 | −0.675155 | − | 0.737676i | \(-0.735923\pi\) | ||||
−0.675155 | + | 0.737676i | \(0.735923\pi\) | |||||||
\(662\) | −21.6708 | −0.842259 | ||||||||
\(663\) | 14.0797 | 0.546809 | ||||||||
\(664\) | 3.48726 | 0.135332 | ||||||||
\(665\) | −7.45281 | −0.289007 | ||||||||
\(666\) | −0.444410 | −0.0172205 | ||||||||
\(667\) | 10.2612 | 0.397315 | ||||||||
\(668\) | 2.51551 | 0.0973280 | ||||||||
\(669\) | −35.2720 | −1.36369 | ||||||||
\(670\) | −2.90479 | −0.112222 | ||||||||
\(671\) | 40.4037 | 1.55977 | ||||||||
\(672\) | −6.46224 | −0.249286 | ||||||||
\(673\) | 3.79605 | 0.146327 | 0.0731634 | − | 0.997320i | \(-0.476691\pi\) | ||||
0.0731634 | + | 0.997320i | \(0.476691\pi\) | |||||||
\(674\) | −1.89195 | −0.0728754 | ||||||||
\(675\) | −14.0911 | −0.542368 | ||||||||
\(676\) | −11.6720 | −0.448921 | ||||||||
\(677\) | −16.5157 | −0.634750 | −0.317375 | − | 0.948300i | \(-0.602801\pi\) | ||||
−0.317375 | + | 0.948300i | \(0.602801\pi\) | |||||||
\(678\) | −8.67160 | −0.333031 | ||||||||
\(679\) | 45.8981 | 1.76141 | ||||||||
\(680\) | −10.3088 | −0.395323 | ||||||||
\(681\) | −7.29654 | −0.279604 | ||||||||
\(682\) | 18.4788 | 0.707591 | ||||||||
\(683\) | −20.8222 | −0.796740 | −0.398370 | − | 0.917225i | \(-0.630424\pi\) | ||||
−0.398370 | + | 0.917225i | \(0.630424\pi\) | |||||||
\(684\) | −0.173753 | −0.00664360 | ||||||||
\(685\) | −9.11726 | −0.348353 | ||||||||
\(686\) | −2.35954 | −0.0900878 | ||||||||
\(687\) | −34.8906 | −1.33116 | ||||||||
\(688\) | −11.4310 | −0.435802 | ||||||||
\(689\) | −13.3765 | −0.509605 | ||||||||
\(690\) | −2.63855 | −0.100448 | ||||||||
\(691\) | 31.0286 | 1.18038 | 0.590191 | − | 0.807263i | \(-0.299052\pi\) | ||||
0.590191 | + | 0.807263i | \(0.299052\pi\) | |||||||
\(692\) | −11.3846 | −0.432778 | ||||||||
\(693\) | −1.76686 | −0.0671173 | ||||||||
\(694\) | 7.18382 | 0.272694 | ||||||||
\(695\) | 10.2938 | 0.390464 | ||||||||
\(696\) | −18.1456 | −0.687806 | ||||||||
\(697\) | 34.2492 | 1.29728 | ||||||||
\(698\) | 11.8172 | 0.447287 | ||||||||
\(699\) | 36.2473 | 1.37100 | ||||||||
\(700\) | −10.1360 | −0.383105 | ||||||||
\(701\) | 32.5687 | 1.23010 | 0.615052 | − | 0.788486i | \(-0.289135\pi\) | ||||
0.615052 | + | 0.788486i | \(0.289135\pi\) | |||||||
\(702\) | 5.85459 | 0.220967 | ||||||||
\(703\) | 4.77840 | 0.180221 | ||||||||
\(704\) | −3.80342 | −0.143347 | ||||||||
\(705\) | −5.09104 | −0.191740 | ||||||||
\(706\) | −19.9397 | −0.750441 | ||||||||
\(707\) | −14.8977 | −0.560284 | ||||||||
\(708\) | 10.8367 | 0.407268 | ||||||||
\(709\) | 51.5471 | 1.93589 | 0.967946 | − | 0.251159i | \(-0.0808118\pi\) | ||||
0.967946 | + | 0.251159i | \(0.0808118\pi\) | |||||||
\(710\) | −14.2610 | −0.535206 | ||||||||
\(711\) | 0.677795 | 0.0254193 | ||||||||
\(712\) | 12.5179 | 0.469128 | ||||||||
\(713\) | −4.85848 | −0.181952 | ||||||||
\(714\) | 44.6474 | 1.67089 | ||||||||
\(715\) | −6.53996 | −0.244580 | ||||||||
\(716\) | −7.42749 | −0.277579 | ||||||||
\(717\) | 43.6880 | 1.63156 | ||||||||
\(718\) | 31.0530 | 1.15889 | ||||||||
\(719\) | 14.2049 | 0.529755 | 0.264877 | − | 0.964282i | \(-0.414669\pi\) | ||||
0.264877 | + | 0.964282i | \(0.414669\pi\) | |||||||
\(720\) | 0.189675 | 0.00706877 | ||||||||
\(721\) | −41.0950 | −1.53046 | ||||||||
\(722\) | −17.1318 | −0.637578 | ||||||||
\(723\) | 0.622538 | 0.0231524 | ||||||||
\(724\) | −6.58423 | −0.244701 | ||||||||
\(725\) | −28.4613 | −1.05703 | ||||||||
\(726\) | −6.12914 | −0.227474 | ||||||||
\(727\) | −45.7525 | −1.69687 | −0.848433 | − | 0.529303i | \(-0.822454\pi\) | ||||
−0.848433 | + | 0.529303i | \(0.822454\pi\) | |||||||
\(728\) | 4.21132 | 0.156082 | ||||||||
\(729\) | 25.7610 | 0.954111 | ||||||||
\(730\) | 1.46529 | 0.0542327 | ||||||||
\(731\) | 78.9763 | 2.92104 | ||||||||
\(732\) | 18.7854 | 0.694327 | ||||||||
\(733\) | 37.5072 | 1.38536 | 0.692680 | − | 0.721245i | \(-0.256430\pi\) | ||||
0.692680 | + | 0.721245i | \(0.256430\pi\) | |||||||
\(734\) | 13.2547 | 0.489238 | ||||||||
\(735\) | −16.7662 | −0.618431 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 7.40449 | 0.272748 | ||||||||
\(738\) | −0.630164 | −0.0231967 | ||||||||
\(739\) | 45.7613 | 1.68336 | 0.841678 | − | 0.539979i | \(-0.181568\pi\) | ||||
0.841678 | + | 0.539979i | \(0.181568\pi\) | |||||||
\(740\) | −5.21628 | −0.191754 | ||||||||
\(741\) | 2.78544 | 0.102326 | ||||||||
\(742\) | −42.4177 | −1.55720 | ||||||||
\(743\) | 8.96576 | 0.328922 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(744\) | 8.59158 | 0.314983 | ||||||||
\(745\) | 14.8762 | 0.545022 | ||||||||
\(746\) | −33.2382 | −1.21694 | ||||||||
\(747\) | 0.443303 | 0.0162196 | ||||||||
\(748\) | 26.2777 | 0.960808 | ||||||||
\(749\) | 48.2155 | 1.76176 | ||||||||
\(750\) | 20.5113 | 0.748966 | ||||||||
\(751\) | 5.17286 | 0.188760 | 0.0943801 | − | 0.995536i | \(-0.469913\pi\) | ||||
0.0943801 | + | 0.995536i | \(0.469913\pi\) | |||||||
\(752\) | 1.92948 | 0.0703609 | ||||||||
\(753\) | −28.1306 | −1.02514 | ||||||||
\(754\) | 11.8251 | 0.430645 | ||||||||
\(755\) | −11.1384 | −0.405367 | ||||||||
\(756\) | 18.5652 | 0.675211 | ||||||||
\(757\) | 33.4756 | 1.21669 | 0.608347 | − | 0.793671i | \(-0.291833\pi\) | ||||
0.608347 | + | 0.793671i | \(0.291833\pi\) | |||||||
\(758\) | −4.97231 | −0.180602 | ||||||||
\(759\) | 6.72584 | 0.244132 | ||||||||
\(760\) | −2.03943 | −0.0739779 | ||||||||
\(761\) | −14.2812 | −0.517694 | −0.258847 | − | 0.965918i | \(-0.583343\pi\) | ||||
−0.258847 | + | 0.965918i | \(0.583343\pi\) | |||||||
\(762\) | −6.48751 | −0.235018 | ||||||||
\(763\) | −5.45793 | −0.197590 | ||||||||
\(764\) | 19.7052 | 0.712910 | ||||||||
\(765\) | −1.31046 | −0.0473797 | ||||||||
\(766\) | 30.2486 | 1.09292 | ||||||||
\(767\) | −7.06206 | −0.254996 | ||||||||
\(768\) | −1.76837 | −0.0638104 | ||||||||
\(769\) | 5.87258 | 0.211771 | 0.105885 | − | 0.994378i | \(-0.466232\pi\) | ||||
0.105885 | + | 0.994378i | \(0.466232\pi\) | |||||||
\(770\) | −20.7386 | −0.747366 | ||||||||
\(771\) | 0.988323 | 0.0355936 | ||||||||
\(772\) | −13.0842 | −0.470909 | ||||||||
\(773\) | 0.706883 | 0.0254248 | 0.0127124 | − | 0.999919i | \(-0.495953\pi\) | ||||
0.0127124 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(774\) | −1.45311 | −0.0522311 | ||||||||
\(775\) | 13.4759 | 0.484068 | ||||||||
\(776\) | 12.5598 | 0.450872 | ||||||||
\(777\) | 22.5918 | 0.810475 | ||||||||
\(778\) | 13.7779 | 0.493961 | ||||||||
\(779\) | 6.77567 | 0.242764 | ||||||||
\(780\) | −3.04070 | −0.108874 | ||||||||
\(781\) | 36.3522 | 1.30078 | ||||||||
\(782\) | −6.90897 | −0.247064 | ||||||||
\(783\) | 52.1300 | 1.86298 | ||||||||
\(784\) | 6.35432 | 0.226940 | ||||||||
\(785\) | −1.41852 | −0.0506292 | ||||||||
\(786\) | 1.76837 | 0.0630756 | ||||||||
\(787\) | 11.4425 | 0.407880 | 0.203940 | − | 0.978983i | \(-0.434625\pi\) | ||||
0.203940 | + | 0.978983i | \(0.434625\pi\) | |||||||
\(788\) | 2.45311 | 0.0873884 | ||||||||
\(789\) | −31.5190 | −1.12211 | ||||||||
\(790\) | 7.95565 | 0.283049 | ||||||||
\(791\) | 17.9200 | 0.637162 | ||||||||
\(792\) | −0.483493 | −0.0171802 | ||||||||
\(793\) | −12.2421 | −0.434728 | ||||||||
\(794\) | −23.3680 | −0.829298 | ||||||||
\(795\) | 30.6269 | 1.08622 | ||||||||
\(796\) | −9.16778 | −0.324943 | ||||||||
\(797\) | −26.3884 | −0.934724 | −0.467362 | − | 0.884066i | \(-0.654796\pi\) | ||||
−0.467362 | + | 0.884066i | \(0.654796\pi\) | |||||||
\(798\) | 8.83280 | 0.312678 | ||||||||
\(799\) | −13.3307 | −0.471607 | ||||||||
\(800\) | −2.77368 | −0.0980644 | ||||||||
\(801\) | 1.59129 | 0.0562253 | ||||||||
\(802\) | −0.577445 | −0.0203903 | ||||||||
\(803\) | −3.73510 | −0.131809 | ||||||||
\(804\) | 3.44265 | 0.121413 | ||||||||
\(805\) | 5.45261 | 0.192179 | ||||||||
\(806\) | −5.59896 | −0.197215 | ||||||||
\(807\) | 13.6999 | 0.482260 | ||||||||
\(808\) | −4.07669 | −0.143417 | ||||||||
\(809\) | −2.12707 | −0.0747839 | −0.0373919 | − | 0.999301i | \(-0.511905\pi\) | ||||
−0.0373919 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(810\) | −13.9737 | −0.490985 | ||||||||
\(811\) | 37.2203 | 1.30698 | 0.653492 | − | 0.756934i | \(-0.273303\pi\) | ||||
0.653492 | + | 0.756934i | \(0.273303\pi\) | |||||||
\(812\) | 37.4981 | 1.31593 | ||||||||
\(813\) | 9.38650 | 0.329199 | ||||||||
\(814\) | 13.2966 | 0.466046 | ||||||||
\(815\) | 22.6975 | 0.795058 | ||||||||
\(816\) | 12.2176 | 0.427701 | ||||||||
\(817\) | 15.6242 | 0.546622 | ||||||||
\(818\) | 32.9261 | 1.15123 | ||||||||
\(819\) | 0.535346 | 0.0187065 | ||||||||
\(820\) | −7.39658 | −0.258300 | ||||||||
\(821\) | −23.9603 | −0.836219 | −0.418109 | − | 0.908397i | \(-0.637307\pi\) | ||||
−0.418109 | + | 0.908397i | \(0.637307\pi\) | |||||||
\(822\) | 10.8054 | 0.376883 | ||||||||
\(823\) | −4.50535 | −0.157047 | −0.0785234 | − | 0.996912i | \(-0.525021\pi\) | ||||
−0.0785234 | + | 0.996912i | \(0.525021\pi\) | |||||||
\(824\) | −11.2455 | −0.391755 | ||||||||
\(825\) | −18.6553 | −0.649495 | ||||||||
\(826\) | −22.3942 | −0.779193 | ||||||||
\(827\) | 14.9884 | 0.521196 | 0.260598 | − | 0.965447i | \(-0.416080\pi\) | ||||
0.260598 | + | 0.965447i | \(0.416080\pi\) | |||||||
\(828\) | 0.127121 | 0.00441775 | ||||||||
\(829\) | −39.2151 | −1.36200 | −0.680999 | − | 0.732284i | \(-0.738454\pi\) | ||||
−0.680999 | + | 0.732284i | \(0.738454\pi\) | |||||||
\(830\) | 5.20329 | 0.180609 | ||||||||
\(831\) | 6.42560 | 0.222902 | ||||||||
\(832\) | 1.15241 | 0.0399526 | ||||||||
\(833\) | −43.9018 | −1.52111 | ||||||||
\(834\) | −12.1998 | −0.422444 | ||||||||
\(835\) | 3.75336 | 0.129890 | ||||||||
\(836\) | 5.19863 | 0.179798 | ||||||||
\(837\) | −24.6826 | −0.853154 | ||||||||
\(838\) | 9.40549 | 0.324907 | ||||||||
\(839\) | 18.3997 | 0.635227 | 0.317614 | − | 0.948220i | \(-0.397119\pi\) | ||||
0.317614 | + | 0.948220i | \(0.397119\pi\) | |||||||
\(840\) | −9.64222 | −0.332688 | ||||||||
\(841\) | 76.2924 | 2.63077 | ||||||||
\(842\) | −2.40395 | −0.0828454 | ||||||||
\(843\) | 29.9341 | 1.03099 | ||||||||
\(844\) | −10.3828 | −0.357390 | ||||||||
\(845\) | −17.4156 | −0.599113 | ||||||||
\(846\) | 0.245277 | 0.00843280 | ||||||||
\(847\) | 12.6660 | 0.435207 | ||||||||
\(848\) | −11.6074 | −0.398601 | ||||||||
\(849\) | 56.2363 | 1.93003 | ||||||||
\(850\) | 19.1633 | 0.657295 | ||||||||
\(851\) | −3.49596 | −0.119840 | ||||||||
\(852\) | 16.9016 | 0.579041 | ||||||||
\(853\) | −19.1200 | −0.654655 | −0.327328 | − | 0.944911i | \(-0.606148\pi\) | ||||
−0.327328 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(854\) | −38.8202 | −1.32840 | ||||||||
\(855\) | −0.259254 | −0.00886630 | ||||||||
\(856\) | 13.1940 | 0.450961 | ||||||||
\(857\) | 4.98827 | 0.170396 | 0.0851980 | − | 0.996364i | \(-0.472848\pi\) | ||||
0.0851980 | + | 0.996364i | \(0.472848\pi\) | |||||||
\(858\) | 7.75092 | 0.264612 | ||||||||
\(859\) | 15.0504 | 0.513512 | 0.256756 | − | 0.966476i | \(-0.417346\pi\) | ||||
0.256756 | + | 0.966476i | \(0.417346\pi\) | |||||||
\(860\) | −17.0560 | −0.581605 | ||||||||
\(861\) | 32.0347 | 1.09174 | ||||||||
\(862\) | 11.7801 | 0.401232 | ||||||||
\(863\) | −42.9207 | −1.46104 | −0.730520 | − | 0.682892i | \(-0.760722\pi\) | ||||
−0.730520 | + | 0.682892i | \(0.760722\pi\) | |||||||
\(864\) | 5.08030 | 0.172835 | ||||||||
\(865\) | −16.9868 | −0.577569 | ||||||||
\(866\) | −18.0802 | −0.614392 | ||||||||
\(867\) | −54.3488 | −1.84578 | ||||||||
\(868\) | −17.7546 | −0.602631 | ||||||||
\(869\) | −20.2794 | −0.687933 | ||||||||
\(870\) | −27.0748 | −0.917920 | ||||||||
\(871\) | −2.24351 | −0.0760185 | ||||||||
\(872\) | −1.49354 | −0.0505777 | ||||||||
\(873\) | 1.59662 | 0.0540373 | ||||||||
\(874\) | −1.36683 | −0.0462338 | ||||||||
\(875\) | −42.3869 | −1.43294 | ||||||||
\(876\) | −1.73660 | −0.0586744 | ||||||||
\(877\) | −53.8301 | −1.81771 | −0.908856 | − | 0.417110i | \(-0.863043\pi\) | ||||
−0.908856 | + | 0.417110i | \(0.863043\pi\) | |||||||
\(878\) | −3.48237 | −0.117524 | ||||||||
\(879\) | −8.49875 | −0.286656 | ||||||||
\(880\) | −5.67503 | −0.191305 | ||||||||
\(881\) | −42.0254 | −1.41587 | −0.707936 | − | 0.706276i | \(-0.750374\pi\) | ||||
−0.707936 | + | 0.706276i | \(0.750374\pi\) | |||||||
\(882\) | 0.807766 | 0.0271989 | ||||||||
\(883\) | −23.2560 | −0.782626 | −0.391313 | − | 0.920258i | \(-0.627979\pi\) | ||||
−0.391313 | + | 0.920258i | \(0.627979\pi\) | |||||||
\(884\) | −7.96197 | −0.267790 | ||||||||
\(885\) | 16.1693 | 0.543524 | ||||||||
\(886\) | −21.5689 | −0.724621 | ||||||||
\(887\) | 34.6868 | 1.16467 | 0.582334 | − | 0.812950i | \(-0.302140\pi\) | ||||
0.582334 | + | 0.812950i | \(0.302140\pi\) | |||||||
\(888\) | 6.18215 | 0.207459 | ||||||||
\(889\) | 13.4065 | 0.449641 | ||||||||
\(890\) | 18.6778 | 0.626081 | ||||||||
\(891\) | 35.6198 | 1.19331 | ||||||||
\(892\) | 19.9461 | 0.667844 | ||||||||
\(893\) | −2.63728 | −0.0882531 | ||||||||
\(894\) | −17.6308 | −0.589661 | ||||||||
\(895\) | −11.0825 | −0.370446 | ||||||||
\(896\) | 3.65436 | 0.122083 | ||||||||
\(897\) | −2.03788 | −0.0680429 | ||||||||
\(898\) | −16.8096 | −0.560945 | ||||||||
\(899\) | −49.8539 | −1.66272 | ||||||||
\(900\) | −0.352592 | −0.0117531 | ||||||||
\(901\) | 80.1955 | 2.67170 | ||||||||
\(902\) | 18.8543 | 0.627781 | ||||||||
\(903\) | 73.8697 | 2.45823 | ||||||||
\(904\) | 4.90373 | 0.163096 | ||||||||
\(905\) | −9.82423 | −0.326568 | ||||||||
\(906\) | 13.2008 | 0.438568 | ||||||||
\(907\) | −8.03171 | −0.266688 | −0.133344 | − | 0.991070i | \(-0.542572\pi\) | ||||
−0.133344 | + | 0.991070i | \(0.542572\pi\) | |||||||
\(908\) | 4.12615 | 0.136931 | ||||||||
\(909\) | −0.518231 | −0.0171887 | ||||||||
\(910\) | 6.28365 | 0.208301 | ||||||||
\(911\) | −33.3845 | −1.10608 | −0.553039 | − | 0.833155i | \(-0.686532\pi\) | ||||
−0.553039 | + | 0.833155i | \(0.686532\pi\) | |||||||
\(912\) | 2.41706 | 0.0800369 | ||||||||
\(913\) | −13.2635 | −0.438958 | ||||||||
\(914\) | −34.5898 | −1.14413 | ||||||||
\(915\) | 28.0294 | 0.926622 | ||||||||
\(916\) | 19.7304 | 0.651911 | ||||||||
\(917\) | −3.65436 | −0.120677 | ||||||||
\(918\) | −35.0997 | −1.15846 | ||||||||
\(919\) | −8.18635 | −0.270043 | −0.135021 | − | 0.990843i | \(-0.543110\pi\) | ||||
−0.135021 | + | 0.990843i | \(0.543110\pi\) | |||||||
\(920\) | 1.49209 | 0.0491926 | ||||||||
\(921\) | 35.0711 | 1.15563 | ||||||||
\(922\) | 39.4992 | 1.30084 | ||||||||
\(923\) | −11.0145 | −0.362546 | ||||||||
\(924\) | 24.5786 | 0.808577 | ||||||||
\(925\) | 9.69669 | 0.318825 | ||||||||
\(926\) | 26.6234 | 0.874900 | ||||||||
\(927\) | −1.42954 | −0.0469521 | ||||||||
\(928\) | 10.2612 | 0.336841 | ||||||||
\(929\) | −11.5590 | −0.379237 | −0.189619 | − | 0.981858i | \(-0.560725\pi\) | ||||
−0.189619 | + | 0.981858i | \(0.560725\pi\) | |||||||
\(930\) | 12.8194 | 0.420364 | ||||||||
\(931\) | −8.68529 | −0.284649 | ||||||||
\(932\) | −20.4976 | −0.671421 | ||||||||
\(933\) | 41.6348 | 1.36306 | ||||||||
\(934\) | 24.1096 | 0.788892 | ||||||||
\(935\) | 39.2086 | 1.28226 | ||||||||
\(936\) | 0.146495 | 0.00478835 | ||||||||
\(937\) | −31.0546 | −1.01451 | −0.507254 | − | 0.861797i | \(-0.669339\pi\) | ||||
−0.507254 | + | 0.861797i | \(0.669339\pi\) | |||||||
\(938\) | −7.11430 | −0.232290 | ||||||||
\(939\) | 35.0417 | 1.14354 | ||||||||
\(940\) | 2.87895 | 0.0939010 | ||||||||
\(941\) | −2.41102 | −0.0785970 | −0.0392985 | − | 0.999228i | \(-0.512512\pi\) | ||||
−0.0392985 | + | 0.999228i | \(0.512512\pi\) | |||||||
\(942\) | 1.68118 | 0.0547758 | ||||||||
\(943\) | −4.95721 | −0.161429 | ||||||||
\(944\) | −6.12808 | −0.199452 | ||||||||
\(945\) | 27.7009 | 0.901111 | ||||||||
\(946\) | 43.4768 | 1.41355 | ||||||||
\(947\) | 29.4598 | 0.957314 | 0.478657 | − | 0.878002i | \(-0.341124\pi\) | ||||
0.478657 | + | 0.878002i | \(0.341124\pi\) | |||||||
\(948\) | −9.42875 | −0.306232 | ||||||||
\(949\) | 1.13171 | 0.0367369 | ||||||||
\(950\) | 3.79116 | 0.123001 | ||||||||
\(951\) | 11.6674 | 0.378342 | ||||||||
\(952\) | −25.2478 | −0.818287 | ||||||||
\(953\) | −17.5497 | −0.568490 | −0.284245 | − | 0.958752i | \(-0.591743\pi\) | ||||
−0.284245 | + | 0.958752i | \(0.591743\pi\) | |||||||
\(954\) | −1.47555 | −0.0477726 | ||||||||
\(955\) | 29.4019 | 0.951423 | ||||||||
\(956\) | −24.7053 | −0.799025 | ||||||||
\(957\) | 69.0152 | 2.23094 | ||||||||
\(958\) | 31.6140 | 1.02140 | ||||||||
\(959\) | −22.3296 | −0.721061 | ||||||||
\(960\) | −2.63855 | −0.0851590 | ||||||||
\(961\) | −7.39514 | −0.238553 | ||||||||
\(962\) | −4.02878 | −0.129893 | ||||||||
\(963\) | 1.67723 | 0.0540479 | ||||||||
\(964\) | −0.352041 | −0.0113385 | ||||||||
\(965\) | −19.5227 | −0.628457 | ||||||||
\(966\) | −6.46224 | −0.207919 | ||||||||
\(967\) | 34.5653 | 1.11155 | 0.555773 | − | 0.831334i | \(-0.312423\pi\) | ||||
0.555773 | + | 0.831334i | \(0.312423\pi\) | |||||||
\(968\) | 3.46599 | 0.111401 | ||||||||
\(969\) | −16.6994 | −0.536462 | ||||||||
\(970\) | 18.7404 | 0.601717 | ||||||||
\(971\) | −17.5609 | −0.563556 | −0.281778 | − | 0.959480i | \(-0.590924\pi\) | ||||
−0.281778 | + | 0.959480i | \(0.590924\pi\) | |||||||
\(972\) | 1.32020 | 0.0423454 | ||||||||
\(973\) | 25.2111 | 0.808229 | ||||||||
\(974\) | 27.4000 | 0.877951 | ||||||||
\(975\) | 5.65244 | 0.181023 | ||||||||
\(976\) | −10.6230 | −0.340034 | ||||||||
\(977\) | −18.6995 | −0.598249 | −0.299125 | − | 0.954214i | \(-0.596695\pi\) | ||||
−0.299125 | + | 0.954214i | \(0.596695\pi\) | |||||||
\(978\) | −26.9002 | −0.860175 | ||||||||
\(979\) | −47.6108 | −1.52165 | ||||||||
\(980\) | 9.48119 | 0.302866 | ||||||||
\(981\) | −0.189860 | −0.00606176 | ||||||||
\(982\) | 38.5933 | 1.23156 | ||||||||
\(983\) | 33.1212 | 1.05640 | 0.528201 | − | 0.849119i | \(-0.322867\pi\) | ||||
0.528201 | + | 0.849119i | \(0.322867\pi\) | |||||||
\(984\) | 8.76617 | 0.279455 | ||||||||
\(985\) | 3.66025 | 0.116625 | ||||||||
\(986\) | −70.8944 | −2.25774 | ||||||||
\(987\) | −12.4688 | −0.396886 | ||||||||
\(988\) | −1.57515 | −0.0501122 | ||||||||
\(989\) | −11.4310 | −0.363484 | ||||||||
\(990\) | −0.721413 | −0.0229280 | ||||||||
\(991\) | −6.54358 | −0.207864 | −0.103932 | − | 0.994584i | \(-0.533142\pi\) | ||||
−0.103932 | + | 0.994584i | \(0.533142\pi\) | |||||||
\(992\) | −4.85848 | −0.154257 | ||||||||
\(993\) | 38.3219 | 1.21611 | ||||||||
\(994\) | −34.9275 | −1.10783 | ||||||||
\(995\) | −13.6791 | −0.433657 | ||||||||
\(996\) | −6.16675 | −0.195401 | ||||||||
\(997\) | 20.4934 | 0.649034 | 0.324517 | − | 0.945880i | \(-0.394798\pi\) | ||||
0.324517 | + | 0.945880i | \(0.394798\pi\) | |||||||
\(998\) | 18.9661 | 0.600362 | ||||||||
\(999\) | −17.7606 | −0.561919 |
(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 | 6026.2.a.f.1.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.f.1.5 | ✓ | 20 | 1.1 | even | 1 | trivial |