Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.48406561.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.41496\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(5\) | 2.41496 | 1.08000 | 0.540001 | − | 0.841664i | \(-0.318424\pi\) | ||||
0.540001 | + | 0.841664i | \(0.318424\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.41496 | −0.763677 | ||||||||
\(11\) | −3.24698 | −0.979001 | −0.489501 | − | 0.872003i | \(-0.662821\pi\) | ||||
−0.489501 | + | 0.872003i | \(0.662821\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.41496 | 0.623539 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.80194 | 0.437034 | 0.218517 | − | 0.975833i | \(-0.429878\pi\) | ||||
0.218517 | + | 0.975833i | \(0.429878\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 2.73858 | 0.628274 | 0.314137 | − | 0.949378i | \(-0.398285\pi\) | ||||
0.314137 | + | 0.949378i | \(0.398285\pi\) | |||||||
\(20\) | 2.41496 | 0.540001 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.24698 | 0.692258 | ||||||||
\(23\) | −6.58012 | −1.37205 | −0.686025 | − | 0.727578i | \(-0.740646\pi\) | ||||
−0.686025 | + | 0.727578i | \(0.740646\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0.832022 | 0.166404 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 6.22322 | 1.15562 | 0.577812 | − | 0.816170i | \(-0.303907\pi\) | ||||
0.577812 | + | 0.816170i | \(0.303907\pi\) | |||||||
\(30\) | −2.41496 | −0.440909 | ||||||||
\(31\) | −2.72294 | −0.489054 | −0.244527 | − | 0.969643i | \(-0.578633\pi\) | ||||
−0.244527 | + | 0.969643i | \(0.578633\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.24698 | −0.565227 | ||||||||
\(34\) | −1.80194 | −0.309030 | ||||||||
\(35\) | −2.41496 | −0.408202 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.93878 | −1.46953 | −0.734764 | − | 0.678323i | \(-0.762707\pi\) | ||||
−0.734764 | + | 0.678323i | \(0.762707\pi\) | |||||||
\(38\) | −2.73858 | −0.444257 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.41496 | −0.381838 | ||||||||
\(41\) | −9.15862 | −1.43034 | −0.715168 | − | 0.698953i | \(-0.753650\pi\) | ||||
−0.715168 | + | 0.698953i | \(0.753650\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −3.95322 | −0.602861 | −0.301430 | − | 0.953488i | \(-0.597464\pi\) | ||||
−0.301430 | + | 0.953488i | \(0.597464\pi\) | |||||||
\(44\) | −3.24698 | −0.489501 | ||||||||
\(45\) | 2.41496 | 0.360001 | ||||||||
\(46\) | 6.58012 | 0.970186 | ||||||||
\(47\) | −9.77289 | −1.42552 | −0.712761 | − | 0.701407i | \(-0.752556\pi\) | ||||
−0.712761 | + | 0.701407i | \(0.752556\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.832022 | −0.117666 | ||||||||
\(51\) | 1.80194 | 0.252322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3747 | −1.42507 | −0.712536 | − | 0.701636i | \(-0.752453\pi\) | ||||
−0.712536 | + | 0.701636i | \(0.752453\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −7.84132 | −1.05732 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 2.73858 | 0.362734 | ||||||||
\(58\) | −6.22322 | −0.817149 | ||||||||
\(59\) | 4.50007 | 0.585859 | 0.292930 | − | 0.956134i | \(-0.405370\pi\) | ||||
0.292930 | + | 0.956134i | \(0.405370\pi\) | |||||||
\(60\) | 2.41496 | 0.311770 | ||||||||
\(61\) | 6.94297 | 0.888957 | 0.444478 | − | 0.895790i | \(-0.353389\pi\) | ||||
0.444478 | + | 0.895790i | \(0.353389\pi\) | |||||||
\(62\) | 2.72294 | 0.345813 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.24698 | 0.399676 | ||||||||
\(67\) | 2.54486 | 0.310904 | 0.155452 | − | 0.987843i | \(-0.450317\pi\) | ||||
0.155452 | + | 0.987843i | \(0.450317\pi\) | |||||||
\(68\) | 1.80194 | 0.218517 | ||||||||
\(69\) | −6.58012 | −0.792153 | ||||||||
\(70\) | 2.41496 | 0.288643 | ||||||||
\(71\) | 1.50961 | 0.179157 | 0.0895787 | − | 0.995980i | \(-0.471448\pi\) | ||||
0.0895787 | + | 0.995980i | \(0.471448\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.786291 | 0.0920283 | 0.0460142 | − | 0.998941i | \(-0.485348\pi\) | ||||
0.0460142 | + | 0.998941i | \(0.485348\pi\) | |||||||
\(74\) | 8.93878 | 1.03911 | ||||||||
\(75\) | 0.832022 | 0.0960736 | ||||||||
\(76\) | 2.73858 | 0.314137 | ||||||||
\(77\) | 3.24698 | 0.370028 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.41753 | −0.271993 | −0.135997 | − | 0.990709i | \(-0.543424\pi\) | ||||
−0.135997 | + | 0.990709i | \(0.543424\pi\) | |||||||
\(80\) | 2.41496 | 0.270001 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.15862 | 1.01140 | ||||||||
\(83\) | 3.51468 | 0.385786 | 0.192893 | − | 0.981220i | \(-0.438213\pi\) | ||||
0.192893 | + | 0.981220i | \(0.438213\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 4.35160 | 0.471998 | ||||||||
\(86\) | 3.95322 | 0.426287 | ||||||||
\(87\) | 6.22322 | 0.667200 | ||||||||
\(88\) | 3.24698 | 0.346129 | ||||||||
\(89\) | −10.9361 | −1.15922 | −0.579610 | − | 0.814894i | \(-0.696795\pi\) | ||||
−0.579610 | + | 0.814894i | \(0.696795\pi\) | |||||||
\(90\) | −2.41496 | −0.254559 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.58012 | −0.686025 | ||||||||
\(93\) | −2.72294 | −0.282355 | ||||||||
\(94\) | 9.77289 | 1.00800 | ||||||||
\(95\) | 6.61356 | 0.678537 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.2904 | −1.24790 | −0.623950 | − | 0.781464i | \(-0.714473\pi\) | ||||
−0.623950 | + | 0.781464i | \(0.714473\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −3.24698 | −0.326334 | ||||||||
\(100\) | 0.832022 | 0.0832022 | ||||||||
\(101\) | 15.5746 | 1.54973 | 0.774866 | − | 0.632126i | \(-0.217817\pi\) | ||||
0.774866 | + | 0.632126i | \(0.217817\pi\) | |||||||
\(102\) | −1.80194 | −0.178418 | ||||||||
\(103\) | 3.71813 | 0.366358 | 0.183179 | − | 0.983080i | \(-0.441361\pi\) | ||||
0.183179 | + | 0.983080i | \(0.441361\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.41496 | −0.235676 | ||||||||
\(106\) | 10.3747 | 1.00768 | ||||||||
\(107\) | −0.125781 | −0.0121597 | −0.00607983 | − | 0.999982i | \(-0.501935\pi\) | ||||
−0.00607983 | + | 0.999982i | \(0.501935\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.84276 | −0.368070 | −0.184035 | − | 0.982920i | \(-0.558916\pi\) | ||||
−0.184035 | + | 0.982920i | \(0.558916\pi\) | |||||||
\(110\) | 7.84132 | 0.747640 | ||||||||
\(111\) | −8.93878 | −0.848432 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 12.7648 | 1.20082 | 0.600408 | − | 0.799694i | \(-0.295005\pi\) | ||||
0.600408 | + | 0.799694i | \(0.295005\pi\) | |||||||
\(114\) | −2.73858 | −0.256492 | ||||||||
\(115\) | −15.8907 | −1.48182 | ||||||||
\(116\) | 6.22322 | 0.577812 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.50007 | −0.414265 | ||||||||
\(119\) | −1.80194 | −0.165183 | ||||||||
\(120\) | −2.41496 | −0.220454 | ||||||||
\(121\) | −0.457123 | −0.0415567 | ||||||||
\(122\) | −6.94297 | −0.628587 | ||||||||
\(123\) | −9.15862 | −0.825805 | ||||||||
\(124\) | −2.72294 | −0.244527 | ||||||||
\(125\) | −10.0655 | −0.900285 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −11.7970 | −1.04682 | −0.523408 | − | 0.852082i | \(-0.675340\pi\) | ||||
−0.523408 | + | 0.852082i | \(0.675340\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.95322 | −0.348062 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.5193 | −1.44330 | −0.721649 | − | 0.692259i | \(-0.756615\pi\) | ||||
−0.721649 | + | 0.692259i | \(0.756615\pi\) | |||||||
\(132\) | −3.24698 | −0.282613 | ||||||||
\(133\) | −2.73858 | −0.237465 | ||||||||
\(134\) | −2.54486 | −0.219843 | ||||||||
\(135\) | 2.41496 | 0.207846 | ||||||||
\(136\) | −1.80194 | −0.154515 | ||||||||
\(137\) | −11.5650 | −0.988068 | −0.494034 | − | 0.869443i | \(-0.664478\pi\) | ||||
−0.494034 | + | 0.869443i | \(0.664478\pi\) | |||||||
\(138\) | 6.58012 | 0.560137 | ||||||||
\(139\) | −2.63433 | −0.223441 | −0.111720 | − | 0.993740i | \(-0.535636\pi\) | ||||
−0.111720 | + | 0.993740i | \(0.535636\pi\) | |||||||
\(140\) | −2.41496 | −0.204101 | ||||||||
\(141\) | −9.77289 | −0.823026 | ||||||||
\(142\) | −1.50961 | −0.126683 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 15.0288 | 1.24808 | ||||||||
\(146\) | −0.786291 | −0.0650739 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −8.93878 | −0.734764 | ||||||||
\(149\) | 19.3553 | 1.58565 | 0.792825 | − | 0.609450i | \(-0.208609\pi\) | ||||
0.792825 | + | 0.609450i | \(0.208609\pi\) | |||||||
\(150\) | −0.832022 | −0.0679343 | ||||||||
\(151\) | −9.50760 | −0.773717 | −0.386859 | − | 0.922139i | \(-0.626440\pi\) | ||||
−0.386859 | + | 0.922139i | \(0.626440\pi\) | |||||||
\(152\) | −2.73858 | −0.222128 | ||||||||
\(153\) | 1.80194 | 0.145678 | ||||||||
\(154\) | −3.24698 | −0.261649 | ||||||||
\(155\) | −6.57578 | −0.528179 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.70530 | 0.215907 | 0.107953 | − | 0.994156i | \(-0.465570\pi\) | ||||
0.107953 | + | 0.994156i | \(0.465570\pi\) | |||||||
\(158\) | 2.41753 | 0.192328 | ||||||||
\(159\) | −10.3747 | −0.822766 | ||||||||
\(160\) | −2.41496 | −0.190919 | ||||||||
\(161\) | 6.58012 | 0.518586 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 6.79361 | 0.532117 | 0.266058 | − | 0.963957i | \(-0.414279\pi\) | ||||
0.266058 | + | 0.963957i | \(0.414279\pi\) | |||||||
\(164\) | −9.15862 | −0.715168 | ||||||||
\(165\) | −7.84132 | −0.610446 | ||||||||
\(166\) | −3.51468 | −0.272792 | ||||||||
\(167\) | −17.9654 | −1.39020 | −0.695101 | − | 0.718912i | \(-0.744640\pi\) | ||||
−0.695101 | + | 0.718912i | \(0.744640\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.35160 | −0.333753 | ||||||||
\(171\) | 2.73858 | 0.209425 | ||||||||
\(172\) | −3.95322 | −0.301430 | ||||||||
\(173\) | −7.21332 | −0.548418 | −0.274209 | − | 0.961670i | \(-0.588416\pi\) | ||||
−0.274209 | + | 0.961670i | \(0.588416\pi\) | |||||||
\(174\) | −6.22322 | −0.471781 | ||||||||
\(175\) | −0.832022 | −0.0628949 | ||||||||
\(176\) | −3.24698 | −0.244750 | ||||||||
\(177\) | 4.50007 | 0.338246 | ||||||||
\(178\) | 10.9361 | 0.819693 | ||||||||
\(179\) | 3.27893 | 0.245079 | 0.122539 | − | 0.992464i | \(-0.460896\pi\) | ||||
0.122539 | + | 0.992464i | \(0.460896\pi\) | |||||||
\(180\) | 2.41496 | 0.180000 | ||||||||
\(181\) | 21.0091 | 1.56160 | 0.780798 | − | 0.624783i | \(-0.214813\pi\) | ||||
0.780798 | + | 0.624783i | \(0.214813\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.94297 | 0.513239 | ||||||||
\(184\) | 6.58012 | 0.485093 | ||||||||
\(185\) | −21.5868 | −1.58709 | ||||||||
\(186\) | 2.72294 | 0.199655 | ||||||||
\(187\) | −5.85086 | −0.427857 | ||||||||
\(188\) | −9.77289 | −0.712761 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −6.61356 | −0.479798 | ||||||||
\(191\) | −6.15290 | −0.445208 | −0.222604 | − | 0.974909i | \(-0.571456\pi\) | ||||
−0.222604 | + | 0.974909i | \(0.571456\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 18.6232 | 1.34053 | 0.670265 | − | 0.742122i | \(-0.266181\pi\) | ||||
0.670265 | + | 0.742122i | \(0.266181\pi\) | |||||||
\(194\) | 12.2904 | 0.882398 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −16.8553 | −1.20089 | −0.600443 | − | 0.799667i | \(-0.705009\pi\) | ||||
−0.600443 | + | 0.799667i | \(0.705009\pi\) | |||||||
\(198\) | 3.24698 | 0.230753 | ||||||||
\(199\) | 12.3376 | 0.874589 | 0.437295 | − | 0.899318i | \(-0.355937\pi\) | ||||
0.437295 | + | 0.899318i | \(0.355937\pi\) | |||||||
\(200\) | −0.832022 | −0.0588328 | ||||||||
\(201\) | 2.54486 | 0.179501 | ||||||||
\(202\) | −15.5746 | −1.09583 | ||||||||
\(203\) | −6.22322 | −0.436785 | ||||||||
\(204\) | 1.80194 | 0.126161 | ||||||||
\(205\) | −22.1177 | −1.54477 | ||||||||
\(206\) | −3.71813 | −0.259055 | ||||||||
\(207\) | −6.58012 | −0.457350 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.89213 | −0.615081 | ||||||||
\(210\) | 2.41496 | 0.166648 | ||||||||
\(211\) | −15.6160 | −1.07505 | −0.537525 | − | 0.843248i | \(-0.680641\pi\) | ||||
−0.537525 | + | 0.843248i | \(0.680641\pi\) | |||||||
\(212\) | −10.3747 | −0.712536 | ||||||||
\(213\) | 1.50961 | 0.103437 | ||||||||
\(214\) | 0.125781 | 0.00859818 | ||||||||
\(215\) | −9.54686 | −0.651091 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.72294 | 0.184845 | ||||||||
\(218\) | 3.84276 | 0.260264 | ||||||||
\(219\) | 0.786291 | 0.0531326 | ||||||||
\(220\) | −7.84132 | −0.528662 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8.93878 | 0.599932 | ||||||||
\(223\) | −5.53203 | −0.370452 | −0.185226 | − | 0.982696i | \(-0.559302\pi\) | ||||
−0.185226 | + | 0.982696i | \(0.559302\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0.832022 | 0.0554681 | ||||||||
\(226\) | −12.7648 | −0.849105 | ||||||||
\(227\) | −20.4532 | −1.35753 | −0.678763 | − | 0.734357i | \(-0.737484\pi\) | ||||
−0.678763 | + | 0.734357i | \(0.737484\pi\) | |||||||
\(228\) | 2.73858 | 0.181367 | ||||||||
\(229\) | 29.0317 | 1.91847 | 0.959234 | − | 0.282612i | \(-0.0912010\pi\) | ||||
0.959234 | + | 0.282612i | \(0.0912010\pi\) | |||||||
\(230\) | 15.8907 | 1.04780 | ||||||||
\(231\) | 3.24698 | 0.213636 | ||||||||
\(232\) | −6.22322 | −0.408575 | ||||||||
\(233\) | 12.4742 | 0.817211 | 0.408605 | − | 0.912711i | \(-0.366015\pi\) | ||||
0.408605 | + | 0.912711i | \(0.366015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.6011 | −1.53957 | ||||||||
\(236\) | 4.50007 | 0.292930 | ||||||||
\(237\) | −2.41753 | −0.157035 | ||||||||
\(238\) | 1.80194 | 0.116802 | ||||||||
\(239\) | 23.3225 | 1.50861 | 0.754303 | − | 0.656527i | \(-0.227975\pi\) | ||||
0.754303 | + | 0.656527i | \(0.227975\pi\) | |||||||
\(240\) | 2.41496 | 0.155885 | ||||||||
\(241\) | −28.8105 | −1.85584 | −0.927922 | − | 0.372773i | \(-0.878407\pi\) | ||||
−0.927922 | + | 0.372773i | \(0.878407\pi\) | |||||||
\(242\) | 0.457123 | 0.0293850 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.94297 | 0.444478 | ||||||||
\(245\) | 2.41496 | 0.154286 | ||||||||
\(246\) | 9.15862 | 0.583932 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.72294 | 0.172907 | ||||||||
\(249\) | 3.51468 | 0.222734 | ||||||||
\(250\) | 10.0655 | 0.636598 | ||||||||
\(251\) | 1.56870 | 0.0990152 | 0.0495076 | − | 0.998774i | \(-0.484235\pi\) | ||||
0.0495076 | + | 0.998774i | \(0.484235\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 21.3655 | 1.34324 | ||||||||
\(254\) | 11.7970 | 0.740211 | ||||||||
\(255\) | 4.35160 | 0.272508 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.0911 | −0.878981 | −0.439491 | − | 0.898247i | \(-0.644841\pi\) | ||||
−0.439491 | + | 0.898247i | \(0.644841\pi\) | |||||||
\(258\) | 3.95322 | 0.246117 | ||||||||
\(259\) | 8.93878 | 0.555429 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.22322 | 0.385208 | ||||||||
\(262\) | 16.5193 | 1.02057 | ||||||||
\(263\) | −6.63837 | −0.409339 | −0.204670 | − | 0.978831i | \(-0.565612\pi\) | ||||
−0.204670 | + | 0.978831i | \(0.565612\pi\) | |||||||
\(264\) | 3.24698 | 0.199838 | ||||||||
\(265\) | −25.0544 | −1.53908 | ||||||||
\(266\) | 2.73858 | 0.167913 | ||||||||
\(267\) | −10.9361 | −0.669276 | ||||||||
\(268\) | 2.54486 | 0.155452 | ||||||||
\(269\) | 18.0426 | 1.10007 | 0.550037 | − | 0.835140i | \(-0.314614\pi\) | ||||
0.550037 | + | 0.835140i | \(0.314614\pi\) | |||||||
\(270\) | −2.41496 | −0.146970 | ||||||||
\(271\) | −12.0877 | −0.734277 | −0.367139 | − | 0.930166i | \(-0.619663\pi\) | ||||
−0.367139 | + | 0.930166i | \(0.619663\pi\) | |||||||
\(272\) | 1.80194 | 0.109259 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.5650 | 0.698670 | ||||||||
\(275\) | −2.70156 | −0.162910 | ||||||||
\(276\) | −6.58012 | −0.396077 | ||||||||
\(277\) | 30.1936 | 1.81416 | 0.907080 | − | 0.420958i | \(-0.138306\pi\) | ||||
0.907080 | + | 0.420958i | \(0.138306\pi\) | |||||||
\(278\) | 2.63433 | 0.157997 | ||||||||
\(279\) | −2.72294 | −0.163018 | ||||||||
\(280\) | 2.41496 | 0.144321 | ||||||||
\(281\) | −20.4356 | −1.21909 | −0.609543 | − | 0.792753i | \(-0.708647\pi\) | ||||
−0.609543 | + | 0.792753i | \(0.708647\pi\) | |||||||
\(282\) | 9.77289 | 0.581967 | ||||||||
\(283\) | −4.01876 | −0.238890 | −0.119445 | − | 0.992841i | \(-0.538112\pi\) | ||||
−0.119445 | + | 0.992841i | \(0.538112\pi\) | |||||||
\(284\) | 1.50961 | 0.0895787 | ||||||||
\(285\) | 6.61356 | 0.391754 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.15862 | 0.540616 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −13.7530 | −0.809001 | ||||||||
\(290\) | −15.0288 | −0.882523 | ||||||||
\(291\) | −12.2904 | −0.720475 | ||||||||
\(292\) | 0.786291 | 0.0460142 | ||||||||
\(293\) | −19.3490 | −1.13038 | −0.565191 | − | 0.824960i | \(-0.691198\pi\) | ||||
−0.565191 | + | 0.824960i | \(0.691198\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 10.8675 | 0.632729 | ||||||||
\(296\) | 8.93878 | 0.519556 | ||||||||
\(297\) | −3.24698 | −0.188409 | ||||||||
\(298\) | −19.3553 | −1.12122 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.832022 | 0.0480368 | ||||||||
\(301\) | 3.95322 | 0.227860 | ||||||||
\(302\) | 9.50760 | 0.547101 | ||||||||
\(303\) | 15.5746 | 0.894738 | ||||||||
\(304\) | 2.73858 | 0.157069 | ||||||||
\(305\) | 16.7670 | 0.960075 | ||||||||
\(306\) | −1.80194 | −0.103010 | ||||||||
\(307\) | −5.04050 | −0.287677 | −0.143838 | − | 0.989601i | \(-0.545945\pi\) | ||||
−0.143838 | + | 0.989601i | \(0.545945\pi\) | |||||||
\(308\) | 3.24698 | 0.185014 | ||||||||
\(309\) | 3.71813 | 0.211517 | ||||||||
\(310\) | 6.57578 | 0.373479 | ||||||||
\(311\) | −16.2638 | −0.922235 | −0.461117 | − | 0.887339i | \(-0.652551\pi\) | ||||
−0.461117 | + | 0.887339i | \(0.652551\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.80560 | −0.497722 | −0.248861 | − | 0.968539i | \(-0.580056\pi\) | ||||
−0.248861 | + | 0.968539i | \(0.580056\pi\) | |||||||
\(314\) | −2.70530 | −0.152669 | ||||||||
\(315\) | −2.41496 | −0.136067 | ||||||||
\(316\) | −2.41753 | −0.135997 | ||||||||
\(317\) | −20.0495 | −1.12609 | −0.563047 | − | 0.826425i | \(-0.690371\pi\) | ||||
−0.563047 | + | 0.826425i | \(0.690371\pi\) | |||||||
\(318\) | 10.3747 | 0.581783 | ||||||||
\(319\) | −20.2067 | −1.13136 | ||||||||
\(320\) | 2.41496 | 0.135000 | ||||||||
\(321\) | −0.125781 | −0.00702039 | ||||||||
\(322\) | −6.58012 | −0.366696 | ||||||||
\(323\) | 4.93476 | 0.274577 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.79361 | −0.376263 | ||||||||
\(327\) | −3.84276 | −0.212505 | ||||||||
\(328\) | 9.15862 | 0.505700 | ||||||||
\(329\) | 9.77289 | 0.538797 | ||||||||
\(330\) | 7.84132 | 0.431650 | ||||||||
\(331\) | 19.0732 | 1.04836 | 0.524180 | − | 0.851607i | \(-0.324372\pi\) | ||||
0.524180 | + | 0.851607i | \(0.324372\pi\) | |||||||
\(332\) | 3.51468 | 0.192893 | ||||||||
\(333\) | −8.93878 | −0.489842 | ||||||||
\(334\) | 17.9654 | 0.983021 | ||||||||
\(335\) | 6.14573 | 0.335777 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 14.8542 | 0.809159 | 0.404580 | − | 0.914503i | \(-0.367418\pi\) | ||||
0.404580 | + | 0.914503i | \(0.367418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.7648 | 0.693291 | ||||||||
\(340\) | 4.35160 | 0.235999 | ||||||||
\(341\) | 8.84132 | 0.478784 | ||||||||
\(342\) | −2.73858 | −0.148086 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.95322 | 0.213143 | ||||||||
\(345\) | −15.8907 | −0.855527 | ||||||||
\(346\) | 7.21332 | 0.387790 | ||||||||
\(347\) | 26.6896 | 1.43277 | 0.716386 | − | 0.697704i | \(-0.245795\pi\) | ||||
0.716386 | + | 0.697704i | \(0.245795\pi\) | |||||||
\(348\) | 6.22322 | 0.333600 | ||||||||
\(349\) | 31.8560 | 1.70521 | 0.852607 | − | 0.522552i | \(-0.175020\pi\) | ||||
0.852607 | + | 0.522552i | \(0.175020\pi\) | |||||||
\(350\) | 0.832022 | 0.0444734 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.24698 | 0.173065 | ||||||||
\(353\) | 3.52242 | 0.187480 | 0.0937398 | − | 0.995597i | \(-0.470118\pi\) | ||||
0.0937398 | + | 0.995597i | \(0.470118\pi\) | |||||||
\(354\) | −4.50007 | −0.239176 | ||||||||
\(355\) | 3.64564 | 0.193490 | ||||||||
\(356\) | −10.9361 | −0.579610 | ||||||||
\(357\) | −1.80194 | −0.0953687 | ||||||||
\(358\) | −3.27893 | −0.173297 | ||||||||
\(359\) | −24.0153 | −1.26748 | −0.633740 | − | 0.773546i | \(-0.718481\pi\) | ||||
−0.633740 | + | 0.773546i | \(0.718481\pi\) | |||||||
\(360\) | −2.41496 | −0.127279 | ||||||||
\(361\) | −11.5002 | −0.605272 | ||||||||
\(362\) | −21.0091 | −1.10422 | ||||||||
\(363\) | −0.457123 | −0.0239928 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.89886 | 0.0993908 | ||||||||
\(366\) | −6.94297 | −0.362915 | ||||||||
\(367\) | −5.01103 | −0.261574 | −0.130787 | − | 0.991411i | \(-0.541750\pi\) | ||||
−0.130787 | + | 0.991411i | \(0.541750\pi\) | |||||||
\(368\) | −6.58012 | −0.343012 | ||||||||
\(369\) | −9.15862 | −0.476779 | ||||||||
\(370\) | 21.5868 | 1.12224 | ||||||||
\(371\) | 10.3747 | 0.538627 | ||||||||
\(372\) | −2.72294 | −0.141178 | ||||||||
\(373\) | −12.2463 | −0.634092 | −0.317046 | − | 0.948410i | \(-0.602691\pi\) | ||||
−0.317046 | + | 0.948410i | \(0.602691\pi\) | |||||||
\(374\) | 5.85086 | 0.302541 | ||||||||
\(375\) | −10.0655 | −0.519780 | ||||||||
\(376\) | 9.77289 | 0.503998 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 15.3669 | 0.789343 | 0.394672 | − | 0.918822i | \(-0.370858\pi\) | ||||
0.394672 | + | 0.918822i | \(0.370858\pi\) | |||||||
\(380\) | 6.61356 | 0.339269 | ||||||||
\(381\) | −11.7970 | −0.604379 | ||||||||
\(382\) | 6.15290 | 0.314810 | ||||||||
\(383\) | −13.7125 | −0.700675 | −0.350338 | − | 0.936623i | \(-0.613933\pi\) | ||||
−0.350338 | + | 0.936623i | \(0.613933\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 7.84132 | 0.399631 | ||||||||
\(386\) | −18.6232 | −0.947897 | ||||||||
\(387\) | −3.95322 | −0.200954 | ||||||||
\(388\) | −12.2904 | −0.623950 | ||||||||
\(389\) | 9.05551 | 0.459133 | 0.229566 | − | 0.973293i | \(-0.426269\pi\) | ||||
0.229566 | + | 0.973293i | \(0.426269\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.8570 | −0.599633 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −16.5193 | −0.833288 | ||||||||
\(394\) | 16.8553 | 0.849155 | ||||||||
\(395\) | −5.83823 | −0.293753 | ||||||||
\(396\) | −3.24698 | −0.163167 | ||||||||
\(397\) | 20.8502 | 1.04644 | 0.523220 | − | 0.852198i | \(-0.324731\pi\) | ||||
0.523220 | + | 0.852198i | \(0.324731\pi\) | |||||||
\(398\) | −12.3376 | −0.618428 | ||||||||
\(399\) | −2.73858 | −0.137101 | ||||||||
\(400\) | 0.832022 | 0.0416011 | ||||||||
\(401\) | 19.6443 | 0.980988 | 0.490494 | − | 0.871445i | \(-0.336816\pi\) | ||||
0.490494 | + | 0.871445i | \(0.336816\pi\) | |||||||
\(402\) | −2.54486 | −0.126926 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 15.5746 | 0.774866 | ||||||||
\(405\) | 2.41496 | 0.120000 | ||||||||
\(406\) | 6.22322 | 0.308853 | ||||||||
\(407\) | 29.0240 | 1.43867 | ||||||||
\(408\) | −1.80194 | −0.0892092 | ||||||||
\(409\) | 2.96748 | 0.146733 | 0.0733663 | − | 0.997305i | \(-0.476626\pi\) | ||||
0.0733663 | + | 0.997305i | \(0.476626\pi\) | |||||||
\(410\) | 22.1177 | 1.09231 | ||||||||
\(411\) | −11.5650 | −0.570461 | ||||||||
\(412\) | 3.71813 | 0.183179 | ||||||||
\(413\) | −4.50007 | −0.221434 | ||||||||
\(414\) | 6.58012 | 0.323395 | ||||||||
\(415\) | 8.48781 | 0.416650 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.63433 | −0.129004 | ||||||||
\(418\) | 8.89213 | 0.434928 | ||||||||
\(419\) | −0.255356 | −0.0124750 | −0.00623748 | − | 0.999981i | \(-0.501985\pi\) | ||||
−0.00623748 | + | 0.999981i | \(0.501985\pi\) | |||||||
\(420\) | −2.41496 | −0.117838 | ||||||||
\(421\) | 36.2298 | 1.76573 | 0.882867 | − | 0.469623i | \(-0.155610\pi\) | ||||
0.882867 | + | 0.469623i | \(0.155610\pi\) | |||||||
\(422\) | 15.6160 | 0.760176 | ||||||||
\(423\) | −9.77289 | −0.475174 | ||||||||
\(424\) | 10.3747 | 0.503839 | ||||||||
\(425\) | 1.49925 | 0.0727244 | ||||||||
\(426\) | −1.50961 | −0.0731407 | ||||||||
\(427\) | −6.94297 | −0.335994 | ||||||||
\(428\) | −0.125781 | −0.00607983 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.54686 | 0.460391 | ||||||||
\(431\) | −26.6462 | −1.28350 | −0.641752 | − | 0.766913i | \(-0.721792\pi\) | ||||
−0.641752 | + | 0.766913i | \(0.721792\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −30.6061 | −1.47083 | −0.735417 | − | 0.677615i | \(-0.763014\pi\) | ||||
−0.735417 | + | 0.677615i | \(0.763014\pi\) | |||||||
\(434\) | −2.72294 | −0.130705 | ||||||||
\(435\) | 15.0288 | 0.720577 | ||||||||
\(436\) | −3.84276 | −0.184035 | ||||||||
\(437\) | −18.0202 | −0.862023 | ||||||||
\(438\) | −0.786291 | −0.0375704 | ||||||||
\(439\) | −11.4091 | −0.544525 | −0.272262 | − | 0.962223i | \(-0.587772\pi\) | ||||
−0.272262 | + | 0.962223i | \(0.587772\pi\) | |||||||
\(440\) | 7.84132 | 0.373820 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.5387 | 1.83103 | 0.915515 | − | 0.402283i | \(-0.131783\pi\) | ||||
0.915515 | + | 0.402283i | \(0.131783\pi\) | |||||||
\(444\) | −8.93878 | −0.424216 | ||||||||
\(445\) | −26.4101 | −1.25196 | ||||||||
\(446\) | 5.53203 | 0.261949 | ||||||||
\(447\) | 19.3553 | 0.915475 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 2.16519 | 0.102182 | 0.0510908 | − | 0.998694i | \(-0.483730\pi\) | ||||
0.0510908 | + | 0.998694i | \(0.483730\pi\) | |||||||
\(450\) | −0.832022 | −0.0392219 | ||||||||
\(451\) | 29.7378 | 1.40030 | ||||||||
\(452\) | 12.7648 | 0.600408 | ||||||||
\(453\) | −9.50760 | −0.446706 | ||||||||
\(454\) | 20.4532 | 0.959917 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.73858 | −0.128246 | ||||||||
\(457\) | 31.4845 | 1.47278 | 0.736392 | − | 0.676555i | \(-0.236528\pi\) | ||||
0.736392 | + | 0.676555i | \(0.236528\pi\) | |||||||
\(458\) | −29.0317 | −1.35656 | ||||||||
\(459\) | 1.80194 | 0.0841073 | ||||||||
\(460\) | −15.8907 | −0.740908 | ||||||||
\(461\) | −7.94726 | −0.370141 | −0.185070 | − | 0.982725i | \(-0.559251\pi\) | ||||
−0.185070 | + | 0.982725i | \(0.559251\pi\) | |||||||
\(462\) | −3.24698 | −0.151063 | ||||||||
\(463\) | −12.1131 | −0.562943 | −0.281471 | − | 0.959570i | \(-0.590822\pi\) | ||||
−0.281471 | + | 0.959570i | \(0.590822\pi\) | |||||||
\(464\) | 6.22322 | 0.288906 | ||||||||
\(465\) | −6.57578 | −0.304944 | ||||||||
\(466\) | −12.4742 | −0.577855 | ||||||||
\(467\) | −1.69520 | −0.0784446 | −0.0392223 | − | 0.999231i | \(-0.512488\pi\) | ||||
−0.0392223 | + | 0.999231i | \(0.512488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.54486 | −0.117511 | ||||||||
\(470\) | 23.6011 | 1.08864 | ||||||||
\(471\) | 2.70530 | 0.124654 | ||||||||
\(472\) | −4.50007 | −0.207133 | ||||||||
\(473\) | 12.8360 | 0.590201 | ||||||||
\(474\) | 2.41753 | 0.111041 | ||||||||
\(475\) | 2.27856 | 0.104548 | ||||||||
\(476\) | −1.80194 | −0.0825917 | ||||||||
\(477\) | −10.3747 | −0.475024 | ||||||||
\(478\) | −23.3225 | −1.06675 | ||||||||
\(479\) | −3.59340 | −0.164187 | −0.0820933 | − | 0.996625i | \(-0.526161\pi\) | ||||
−0.0820933 | + | 0.996625i | \(0.526161\pi\) | |||||||
\(480\) | −2.41496 | −0.110227 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 28.8105 | 1.31228 | ||||||||
\(483\) | 6.58012 | 0.299406 | ||||||||
\(484\) | −0.457123 | −0.0207783 | ||||||||
\(485\) | −29.6808 | −1.34773 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 4.79109 | 0.217105 | 0.108552 | − | 0.994091i | \(-0.465378\pi\) | ||||
0.108552 | + | 0.994091i | \(0.465378\pi\) | |||||||
\(488\) | −6.94297 | −0.314294 | ||||||||
\(489\) | 6.79361 | 0.307218 | ||||||||
\(490\) | −2.41496 | −0.109097 | ||||||||
\(491\) | −42.3139 | −1.90960 | −0.954800 | − | 0.297250i | \(-0.903931\pi\) | ||||
−0.954800 | + | 0.297250i | \(0.903931\pi\) | |||||||
\(492\) | −9.15862 | −0.412902 | ||||||||
\(493\) | 11.2139 | 0.505047 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.84132 | −0.352441 | ||||||||
\(496\) | −2.72294 | −0.122263 | ||||||||
\(497\) | −1.50961 | −0.0677151 | ||||||||
\(498\) | −3.51468 | −0.157497 | ||||||||
\(499\) | −26.4820 | −1.18550 | −0.592749 | − | 0.805387i | \(-0.701958\pi\) | ||||
−0.592749 | + | 0.805387i | \(0.701958\pi\) | |||||||
\(500\) | −10.0655 | −0.450142 | ||||||||
\(501\) | −17.9654 | −0.802633 | ||||||||
\(502\) | −1.56870 | −0.0700143 | ||||||||
\(503\) | 16.9580 | 0.756121 | 0.378060 | − | 0.925781i | \(-0.376591\pi\) | ||||
0.378060 | + | 0.925781i | \(0.376591\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | 37.6120 | 1.67371 | ||||||||
\(506\) | −21.3655 | −0.949813 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.7970 | −0.523408 | ||||||||
\(509\) | 3.29901 | 0.146226 | 0.0731129 | − | 0.997324i | \(-0.476707\pi\) | ||||
0.0731129 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(510\) | −4.35160 | −0.192692 | ||||||||
\(511\) | −0.786291 | −0.0347834 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.73858 | 0.120911 | ||||||||
\(514\) | 14.0911 | 0.621534 | ||||||||
\(515\) | 8.97913 | 0.395668 | ||||||||
\(516\) | −3.95322 | −0.174031 | ||||||||
\(517\) | 31.7324 | 1.39559 | ||||||||
\(518\) | −8.93878 | −0.392748 | ||||||||
\(519\) | −7.21332 | −0.316630 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.85188 | −0.168754 | −0.0843770 | − | 0.996434i | \(-0.526890\pi\) | ||||
−0.0843770 | + | 0.996434i | \(0.526890\pi\) | |||||||
\(522\) | −6.22322 | −0.272383 | ||||||||
\(523\) | −13.8862 | −0.607201 | −0.303601 | − | 0.952799i | \(-0.598189\pi\) | ||||
−0.303601 | + | 0.952799i | \(0.598189\pi\) | |||||||
\(524\) | −16.5193 | −0.721649 | ||||||||
\(525\) | −0.832022 | −0.0363124 | ||||||||
\(526\) | 6.63837 | 0.289447 | ||||||||
\(527\) | −4.90656 | −0.213733 | ||||||||
\(528\) | −3.24698 | −0.141307 | ||||||||
\(529\) | 20.2980 | 0.882521 | ||||||||
\(530\) | 25.0544 | 1.08829 | ||||||||
\(531\) | 4.50007 | 0.195286 | ||||||||
\(532\) | −2.73858 | −0.118733 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10.9361 | 0.473250 | ||||||||
\(535\) | −0.303755 | −0.0131325 | ||||||||
\(536\) | −2.54486 | −0.109921 | ||||||||
\(537\) | 3.27893 | 0.141496 | ||||||||
\(538\) | −18.0426 | −0.777870 | ||||||||
\(539\) | −3.24698 | −0.139857 | ||||||||
\(540\) | 2.41496 | 0.103923 | ||||||||
\(541\) | −5.36925 | −0.230842 | −0.115421 | − | 0.993317i | \(-0.536822\pi\) | ||||
−0.115421 | + | 0.993317i | \(0.536822\pi\) | |||||||
\(542\) | 12.0877 | 0.519212 | ||||||||
\(543\) | 21.0091 | 0.901588 | ||||||||
\(544\) | −1.80194 | −0.0772574 | ||||||||
\(545\) | −9.28010 | −0.397516 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −46.0980 | −1.97101 | −0.985504 | − | 0.169653i | \(-0.945735\pi\) | ||||
−0.985504 | + | 0.169653i | \(0.945735\pi\) | |||||||
\(548\) | −11.5650 | −0.494034 | ||||||||
\(549\) | 6.94297 | 0.296319 | ||||||||
\(550\) | 2.70156 | 0.115195 | ||||||||
\(551\) | 17.0428 | 0.726049 | ||||||||
\(552\) | 6.58012 | 0.280068 | ||||||||
\(553\) | 2.41753 | 0.102804 | ||||||||
\(554\) | −30.1936 | −1.28281 | ||||||||
\(555\) | −21.5868 | −0.916308 | ||||||||
\(556\) | −2.63433 | −0.111720 | ||||||||
\(557\) | −15.3154 | −0.648936 | −0.324468 | − | 0.945897i | \(-0.605185\pi\) | ||||
−0.324468 | + | 0.945897i | \(0.605185\pi\) | |||||||
\(558\) | 2.72294 | 0.115271 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.41496 | −0.102051 | ||||||||
\(561\) | −5.85086 | −0.247023 | ||||||||
\(562\) | 20.4356 | 0.862023 | ||||||||
\(563\) | −8.13781 | −0.342968 | −0.171484 | − | 0.985187i | \(-0.554856\pi\) | ||||
−0.171484 | + | 0.985187i | \(0.554856\pi\) | |||||||
\(564\) | −9.77289 | −0.411513 | ||||||||
\(565\) | 30.8266 | 1.29688 | ||||||||
\(566\) | 4.01876 | 0.168921 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −1.50961 | −0.0633417 | ||||||||
\(569\) | −15.9128 | −0.667099 | −0.333550 | − | 0.942733i | \(-0.608246\pi\) | ||||
−0.333550 | + | 0.942733i | \(0.608246\pi\) | |||||||
\(570\) | −6.61356 | −0.277012 | ||||||||
\(571\) | 29.3918 | 1.23001 | 0.615004 | − | 0.788524i | \(-0.289154\pi\) | ||||
0.615004 | + | 0.788524i | \(0.289154\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.15290 | −0.257041 | ||||||||
\(574\) | −9.15862 | −0.382273 | ||||||||
\(575\) | −5.47480 | −0.228315 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.0602 | 0.918377 | 0.459188 | − | 0.888339i | \(-0.348140\pi\) | ||||
0.459188 | + | 0.888339i | \(0.348140\pi\) | |||||||
\(578\) | 13.7530 | 0.572050 | ||||||||
\(579\) | 18.6232 | 0.773955 | ||||||||
\(580\) | 15.0288 | 0.624038 | ||||||||
\(581\) | −3.51468 | −0.145814 | ||||||||
\(582\) | 12.2904 | 0.509453 | ||||||||
\(583\) | 33.6864 | 1.39515 | ||||||||
\(584\) | −0.786291 | −0.0325369 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.3490 | 0.799301 | ||||||||
\(587\) | −42.3330 | −1.74727 | −0.873634 | − | 0.486583i | \(-0.838243\pi\) | ||||
−0.873634 | + | 0.486583i | \(0.838243\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −7.45699 | −0.307260 | ||||||||
\(590\) | −10.8675 | −0.447407 | ||||||||
\(591\) | −16.8553 | −0.693332 | ||||||||
\(592\) | −8.93878 | −0.367382 | ||||||||
\(593\) | 13.0257 | 0.534903 | 0.267451 | − | 0.963571i | \(-0.413818\pi\) | ||||
0.267451 | + | 0.963571i | \(0.413818\pi\) | |||||||
\(594\) | 3.24698 | 0.133225 | ||||||||
\(595\) | −4.35160 | −0.178398 | ||||||||
\(596\) | 19.3553 | 0.792825 | ||||||||
\(597\) | 12.3376 | 0.504944 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.1604 | −1.15060 | −0.575301 | − | 0.817941i | \(-0.695115\pi\) | ||||
−0.575301 | + | 0.817941i | \(0.695115\pi\) | |||||||
\(600\) | −0.832022 | −0.0339671 | ||||||||
\(601\) | 26.9245 | 1.09827 | 0.549136 | − | 0.835733i | \(-0.314957\pi\) | ||||
0.549136 | + | 0.835733i | \(0.314957\pi\) | |||||||
\(602\) | −3.95322 | −0.161121 | ||||||||
\(603\) | 2.54486 | 0.103635 | ||||||||
\(604\) | −9.50760 | −0.386859 | ||||||||
\(605\) | −1.10393 | −0.0448813 | ||||||||
\(606\) | −15.5746 | −0.632675 | ||||||||
\(607\) | 19.1584 | 0.777617 | 0.388808 | − | 0.921319i | \(-0.372887\pi\) | ||||
0.388808 | + | 0.921319i | \(0.372887\pi\) | |||||||
\(608\) | −2.73858 | −0.111064 | ||||||||
\(609\) | −6.22322 | −0.252178 | ||||||||
\(610\) | −16.7670 | −0.678876 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.80194 | 0.0728390 | ||||||||
\(613\) | 3.78753 | 0.152977 | 0.0764884 | − | 0.997070i | \(-0.475629\pi\) | ||||
0.0764884 | + | 0.997070i | \(0.475629\pi\) | |||||||
\(614\) | 5.04050 | 0.203418 | ||||||||
\(615\) | −22.1177 | −0.891871 | ||||||||
\(616\) | −3.24698 | −0.130825 | ||||||||
\(617\) | 24.0329 | 0.967527 | 0.483764 | − | 0.875199i | \(-0.339269\pi\) | ||||
0.483764 | + | 0.875199i | \(0.339269\pi\) | |||||||
\(618\) | −3.71813 | −0.149565 | ||||||||
\(619\) | 44.5020 | 1.78869 | 0.894344 | − | 0.447381i | \(-0.147643\pi\) | ||||
0.894344 | + | 0.447381i | \(0.147643\pi\) | |||||||
\(620\) | −6.57578 | −0.264090 | ||||||||
\(621\) | −6.58012 | −0.264051 | ||||||||
\(622\) | 16.2638 | 0.652118 | ||||||||
\(623\) | 10.9361 | 0.438144 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.4678 | −1.13871 | ||||||||
\(626\) | 8.80560 | 0.351943 | ||||||||
\(627\) | −8.89213 | −0.355117 | ||||||||
\(628\) | 2.70530 | 0.107953 | ||||||||
\(629\) | −16.1071 | −0.642233 | ||||||||
\(630\) | 2.41496 | 0.0962142 | ||||||||
\(631\) | 26.0186 | 1.03579 | 0.517893 | − | 0.855446i | \(-0.326717\pi\) | ||||
0.517893 | + | 0.855446i | \(0.326717\pi\) | |||||||
\(632\) | 2.41753 | 0.0961642 | ||||||||
\(633\) | −15.6160 | −0.620681 | ||||||||
\(634\) | 20.0495 | 0.796269 | ||||||||
\(635\) | −28.4893 | −1.13056 | ||||||||
\(636\) | −10.3747 | −0.411383 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.2067 | 0.799990 | ||||||||
\(639\) | 1.50961 | 0.0597191 | ||||||||
\(640\) | −2.41496 | −0.0954596 | ||||||||
\(641\) | −37.8504 | −1.49500 | −0.747500 | − | 0.664261i | \(-0.768746\pi\) | ||||
−0.747500 | + | 0.664261i | \(0.768746\pi\) | |||||||
\(642\) | 0.125781 | 0.00496416 | ||||||||
\(643\) | −26.4910 | −1.04470 | −0.522351 | − | 0.852731i | \(-0.674945\pi\) | ||||
−0.522351 | + | 0.852731i | \(0.674945\pi\) | |||||||
\(644\) | 6.58012 | 0.259293 | ||||||||
\(645\) | −9.54686 | −0.375907 | ||||||||
\(646\) | −4.93476 | −0.194155 | ||||||||
\(647\) | −34.8792 | −1.37124 | −0.685621 | − | 0.727959i | \(-0.740469\pi\) | ||||
−0.685621 | + | 0.727959i | \(0.740469\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −14.6116 | −0.573557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.72294 | 0.106720 | ||||||||
\(652\) | 6.79361 | 0.266058 | ||||||||
\(653\) | 0.351211 | 0.0137439 | 0.00687197 | − | 0.999976i | \(-0.497813\pi\) | ||||
0.00687197 | + | 0.999976i | \(0.497813\pi\) | |||||||
\(654\) | 3.84276 | 0.150264 | ||||||||
\(655\) | −39.8934 | −1.55876 | ||||||||
\(656\) | −9.15862 | −0.357584 | ||||||||
\(657\) | 0.786291 | 0.0306761 | ||||||||
\(658\) | −9.77289 | −0.380987 | ||||||||
\(659\) | 10.6161 | 0.413545 | 0.206773 | − | 0.978389i | \(-0.433704\pi\) | ||||
0.206773 | + | 0.978389i | \(0.433704\pi\) | |||||||
\(660\) | −7.84132 | −0.305223 | ||||||||
\(661\) | 45.2269 | 1.75912 | 0.879561 | − | 0.475786i | \(-0.157836\pi\) | ||||
0.879561 | + | 0.475786i | \(0.157836\pi\) | |||||||
\(662\) | −19.0732 | −0.741303 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.51468 | −0.136396 | ||||||||
\(665\) | −6.61356 | −0.256463 | ||||||||
\(666\) | 8.93878 | 0.346371 | ||||||||
\(667\) | −40.9496 | −1.58557 | ||||||||
\(668\) | −17.9654 | −0.695101 | ||||||||
\(669\) | −5.53203 | −0.213881 | ||||||||
\(670\) | −6.14573 | −0.237430 | ||||||||
\(671\) | −22.5437 | −0.870290 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 16.2910 | 0.627973 | 0.313986 | − | 0.949428i | \(-0.398335\pi\) | ||||
0.313986 | + | 0.949428i | \(0.398335\pi\) | |||||||
\(674\) | −14.8542 | −0.572162 | ||||||||
\(675\) | 0.832022 | 0.0320245 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.8672 | −1.14789 | −0.573946 | − | 0.818893i | \(-0.694588\pi\) | ||||
−0.573946 | + | 0.818893i | \(0.694588\pi\) | |||||||
\(678\) | −12.7648 | −0.490231 | ||||||||
\(679\) | 12.2904 | 0.471662 | ||||||||
\(680\) | −4.35160 | −0.166876 | ||||||||
\(681\) | −20.4532 | −0.783769 | ||||||||
\(682\) | −8.84132 | −0.338552 | ||||||||
\(683\) | 3.26490 | 0.124928 | 0.0624640 | − | 0.998047i | \(-0.480104\pi\) | ||||
0.0624640 | + | 0.998047i | \(0.480104\pi\) | |||||||
\(684\) | 2.73858 | 0.104712 | ||||||||
\(685\) | −27.9291 | −1.06712 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 29.0317 | 1.10763 | ||||||||
\(688\) | −3.95322 | −0.150715 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 15.8907 | 0.604949 | ||||||||
\(691\) | −38.2216 | −1.45402 | −0.727010 | − | 0.686627i | \(-0.759090\pi\) | ||||
−0.727010 | + | 0.686627i | \(0.759090\pi\) | |||||||
\(692\) | −7.21332 | −0.274209 | ||||||||
\(693\) | 3.24698 | 0.123343 | ||||||||
\(694\) | −26.6896 | −1.01312 | ||||||||
\(695\) | −6.36179 | −0.241317 | ||||||||
\(696\) | −6.22322 | −0.235891 | ||||||||
\(697\) | −16.5033 | −0.625105 | ||||||||
\(698\) | −31.8560 | −1.20577 | ||||||||
\(699\) | 12.4742 | 0.471817 | ||||||||
\(700\) | −0.832022 | −0.0314475 | ||||||||
\(701\) | −16.1383 | −0.609535 | −0.304767 | − | 0.952427i | \(-0.598579\pi\) | ||||
−0.304767 | + | 0.952427i | \(0.598579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.4796 | −0.923266 | ||||||||
\(704\) | −3.24698 | −0.122375 | ||||||||
\(705\) | −23.6011 | −0.888870 | ||||||||
\(706\) | −3.52242 | −0.132568 | ||||||||
\(707\) | −15.5746 | −0.585744 | ||||||||
\(708\) | 4.50007 | 0.169123 | ||||||||
\(709\) | −17.2856 | −0.649176 | −0.324588 | − | 0.945856i | \(-0.605226\pi\) | ||||
−0.324588 | + | 0.945856i | \(0.605226\pi\) | |||||||
\(710\) | −3.64564 | −0.136818 | ||||||||
\(711\) | −2.41753 | −0.0906645 | ||||||||
\(712\) | 10.9361 | 0.409846 | ||||||||
\(713\) | 17.9172 | 0.671006 | ||||||||
\(714\) | 1.80194 | 0.0674358 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.27893 | 0.122539 | ||||||||
\(717\) | 23.3225 | 0.870994 | ||||||||
\(718\) | 24.0153 | 0.896244 | ||||||||
\(719\) | −32.0469 | −1.19515 | −0.597574 | − | 0.801814i | \(-0.703868\pi\) | ||||
−0.597574 | + | 0.801814i | \(0.703868\pi\) | |||||||
\(720\) | 2.41496 | 0.0900002 | ||||||||
\(721\) | −3.71813 | −0.138470 | ||||||||
\(722\) | 11.5002 | 0.427992 | ||||||||
\(723\) | −28.8105 | −1.07147 | ||||||||
\(724\) | 21.0091 | 0.780798 | ||||||||
\(725\) | 5.17786 | 0.192301 | ||||||||
\(726\) | 0.457123 | 0.0169654 | ||||||||
\(727\) | −9.14186 | −0.339053 | −0.169526 | − | 0.985526i | \(-0.554224\pi\) | ||||
−0.169526 | + | 0.985526i | \(0.554224\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.89886 | −0.0702799 | ||||||||
\(731\) | −7.12346 | −0.263471 | ||||||||
\(732\) | 6.94297 | 0.256620 | ||||||||
\(733\) | 0.298008 | 0.0110072 | 0.00550359 | − | 0.999985i | \(-0.498248\pi\) | ||||
0.00550359 | + | 0.999985i | \(0.498248\pi\) | |||||||
\(734\) | 5.01103 | 0.184961 | ||||||||
\(735\) | 2.41496 | 0.0890771 | ||||||||
\(736\) | 6.58012 | 0.242546 | ||||||||
\(737\) | −8.26311 | −0.304376 | ||||||||
\(738\) | 9.15862 | 0.337133 | ||||||||
\(739\) | 20.7127 | 0.761931 | 0.380965 | − | 0.924589i | \(-0.375592\pi\) | ||||
0.380965 | + | 0.924589i | \(0.375592\pi\) | |||||||
\(740\) | −21.5868 | −0.793546 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.3747 | −0.380867 | ||||||||
\(743\) | 43.7005 | 1.60322 | 0.801608 | − | 0.597849i | \(-0.203978\pi\) | ||||
0.801608 | + | 0.597849i | \(0.203978\pi\) | |||||||
\(744\) | 2.72294 | 0.0998277 | ||||||||
\(745\) | 46.7423 | 1.71250 | ||||||||
\(746\) | 12.2463 | 0.448371 | ||||||||
\(747\) | 3.51468 | 0.128595 | ||||||||
\(748\) | −5.85086 | −0.213928 | ||||||||
\(749\) | 0.125781 | 0.00459592 | ||||||||
\(750\) | 10.0655 | 0.367540 | ||||||||
\(751\) | −51.8962 | −1.89372 | −0.946860 | − | 0.321646i | \(-0.895764\pi\) | ||||
−0.946860 | + | 0.321646i | \(0.895764\pi\) | |||||||
\(752\) | −9.77289 | −0.356381 | ||||||||
\(753\) | 1.56870 | 0.0571664 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.9604 | −0.835616 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 47.3170 | 1.71977 | 0.859883 | − | 0.510491i | \(-0.170536\pi\) | ||||
0.859883 | + | 0.510491i | \(0.170536\pi\) | |||||||
\(758\) | −15.3669 | −0.558150 | ||||||||
\(759\) | 21.3655 | 0.775519 | ||||||||
\(760\) | −6.61356 | −0.239899 | ||||||||
\(761\) | −13.5638 | −0.491687 | −0.245844 | − | 0.969310i | \(-0.579065\pi\) | ||||
−0.245844 | + | 0.969310i | \(0.579065\pi\) | |||||||
\(762\) | 11.7970 | 0.427361 | ||||||||
\(763\) | 3.84276 | 0.139117 | ||||||||
\(764\) | −6.15290 | −0.222604 | ||||||||
\(765\) | 4.35160 | 0.157333 | ||||||||
\(766\) | 13.7125 | 0.495452 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 32.6689 | 1.17807 | 0.589036 | − | 0.808107i | \(-0.299508\pi\) | ||||
0.589036 | + | 0.808107i | \(0.299508\pi\) | |||||||
\(770\) | −7.84132 | −0.282582 | ||||||||
\(771\) | −14.0911 | −0.507480 | ||||||||
\(772\) | 18.6232 | 0.670265 | ||||||||
\(773\) | −31.1438 | −1.12016 | −0.560082 | − | 0.828437i | \(-0.689230\pi\) | ||||
−0.560082 | + | 0.828437i | \(0.689230\pi\) | |||||||
\(774\) | 3.95322 | 0.142096 | ||||||||
\(775\) | −2.26554 | −0.0813807 | ||||||||
\(776\) | 12.2904 | 0.441199 | ||||||||
\(777\) | 8.93878 | 0.320677 | ||||||||
\(778\) | −9.05551 | −0.324656 | ||||||||
\(779\) | −25.0816 | −0.898643 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.90166 | −0.175395 | ||||||||
\(782\) | 11.8570 | 0.424004 | ||||||||
\(783\) | 6.22322 | 0.222400 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 6.53320 | 0.233180 | ||||||||
\(786\) | 16.5193 | 0.589224 | ||||||||
\(787\) | 32.0019 | 1.14075 | 0.570373 | − | 0.821386i | \(-0.306799\pi\) | ||||
0.570373 | + | 0.821386i | \(0.306799\pi\) | |||||||
\(788\) | −16.8553 | −0.600443 | ||||||||
\(789\) | −6.63837 | −0.236332 | ||||||||
\(790\) | 5.83823 | 0.207715 | ||||||||
\(791\) | −12.7648 | −0.453866 | ||||||||
\(792\) | 3.24698 | 0.115376 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.8502 | −0.739944 | ||||||||
\(795\) | −25.0544 | −0.888589 | ||||||||
\(796\) | 12.3376 | 0.437295 | ||||||||
\(797\) | −23.5034 | −0.832532 | −0.416266 | − | 0.909243i | \(-0.636661\pi\) | ||||
−0.416266 | + | 0.909243i | \(0.636661\pi\) | |||||||
\(798\) | 2.73858 | 0.0969448 | ||||||||
\(799\) | −17.6101 | −0.623002 | ||||||||
\(800\) | −0.832022 | −0.0294164 | ||||||||
\(801\) | −10.9361 | −0.386407 | ||||||||
\(802\) | −19.6443 | −0.693663 | ||||||||
\(803\) | −2.55307 | −0.0900959 | ||||||||
\(804\) | 2.54486 | 0.0897504 | ||||||||
\(805\) | 15.8907 | 0.560074 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0426 | 0.635128 | ||||||||
\(808\) | −15.5746 | −0.547913 | ||||||||
\(809\) | 0.626708 | 0.0220339 | 0.0110169 | − | 0.999939i | \(-0.496493\pi\) | ||||
0.0110169 | + | 0.999939i | \(0.496493\pi\) | |||||||
\(810\) | −2.41496 | −0.0848530 | ||||||||
\(811\) | 2.31714 | 0.0813656 | 0.0406828 | − | 0.999172i | \(-0.487047\pi\) | ||||
0.0406828 | + | 0.999172i | \(0.487047\pi\) | |||||||
\(812\) | −6.22322 | −0.218392 | ||||||||
\(813\) | −12.0877 | −0.423935 | ||||||||
\(814\) | −29.0240 | −1.01729 | ||||||||
\(815\) | 16.4063 | 0.574687 | ||||||||
\(816\) | 1.80194 | 0.0630804 | ||||||||
\(817\) | −10.8262 | −0.378762 | ||||||||
\(818\) | −2.96748 | −0.103756 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.1177 | −0.772383 | ||||||||
\(821\) | −45.6066 | −1.59168 | −0.795841 | − | 0.605505i | \(-0.792971\pi\) | ||||
−0.795841 | + | 0.605505i | \(0.792971\pi\) | |||||||
\(822\) | 11.5650 | 0.403377 | ||||||||
\(823\) | 54.7826 | 1.90960 | 0.954801 | − | 0.297246i | \(-0.0960680\pi\) | ||||
0.954801 | + | 0.297246i | \(0.0960680\pi\) | |||||||
\(824\) | −3.71813 | −0.129527 | ||||||||
\(825\) | −2.70156 | −0.0940562 | ||||||||
\(826\) | 4.50007 | 0.156577 | ||||||||
\(827\) | −5.65372 | −0.196599 | −0.0982995 | − | 0.995157i | \(-0.531340\pi\) | ||||
−0.0982995 | + | 0.995157i | \(0.531340\pi\) | |||||||
\(828\) | −6.58012 | −0.228675 | ||||||||
\(829\) | −8.87143 | −0.308117 | −0.154059 | − | 0.988062i | \(-0.549235\pi\) | ||||
−0.154059 | + | 0.988062i | \(0.549235\pi\) | |||||||
\(830\) | −8.48781 | −0.294616 | ||||||||
\(831\) | 30.1936 | 1.04741 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.80194 | 0.0624334 | ||||||||
\(834\) | 2.63433 | 0.0912194 | ||||||||
\(835\) | −43.3856 | −1.50142 | ||||||||
\(836\) | −8.89213 | −0.307541 | ||||||||
\(837\) | −2.72294 | −0.0941185 | ||||||||
\(838\) | 0.255356 | 0.00882112 | ||||||||
\(839\) | −1.78656 | −0.0616789 | −0.0308394 | − | 0.999524i | \(-0.509818\pi\) | ||||
−0.0308394 | + | 0.999524i | \(0.509818\pi\) | |||||||
\(840\) | 2.41496 | 0.0833240 | ||||||||
\(841\) | 9.72852 | 0.335466 | ||||||||
\(842\) | −36.2298 | −1.24856 | ||||||||
\(843\) | −20.4356 | −0.703839 | ||||||||
\(844\) | −15.6160 | −0.537525 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.77289 | 0.335999 | ||||||||
\(847\) | 0.457123 | 0.0157069 | ||||||||
\(848\) | −10.3747 | −0.356268 | ||||||||
\(849\) | −4.01876 | −0.137923 | ||||||||
\(850\) | −1.49925 | −0.0514239 | ||||||||
\(851\) | 58.8183 | 2.01626 | ||||||||
\(852\) | 1.50961 | 0.0517183 | ||||||||
\(853\) | 33.5043 | 1.14716 | 0.573582 | − | 0.819148i | \(-0.305553\pi\) | ||||
0.573582 | + | 0.819148i | \(0.305553\pi\) | |||||||
\(854\) | 6.94297 | 0.237584 | ||||||||
\(855\) | 6.61356 | 0.226179 | ||||||||
\(856\) | 0.125781 | 0.00429909 | ||||||||
\(857\) | −1.66717 | −0.0569496 | −0.0284748 | − | 0.999595i | \(-0.509065\pi\) | ||||
−0.0284748 | + | 0.999595i | \(0.509065\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.42584 | 0.0827685 | 0.0413842 | − | 0.999143i | \(-0.486823\pi\) | ||||
0.0413842 | + | 0.999143i | \(0.486823\pi\) | |||||||
\(860\) | −9.54686 | −0.325545 | ||||||||
\(861\) | 9.15862 | 0.312125 | ||||||||
\(862\) | 26.6462 | 0.907574 | ||||||||
\(863\) | 25.5617 | 0.870132 | 0.435066 | − | 0.900399i | \(-0.356725\pi\) | ||||
0.435066 | + | 0.900399i | \(0.356725\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −17.4199 | −0.592293 | ||||||||
\(866\) | 30.6061 | 1.04004 | ||||||||
\(867\) | −13.7530 | −0.467077 | ||||||||
\(868\) | 2.72294 | 0.0924225 | ||||||||
\(869\) | 7.84967 | 0.266282 | ||||||||
\(870\) | −15.0288 | −0.509525 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.84276 | 0.130132 | ||||||||
\(873\) | −12.2904 | −0.415967 | ||||||||
\(874\) | 18.0202 | 0.609543 | ||||||||
\(875\) | 10.0655 | 0.340276 | ||||||||
\(876\) | 0.786291 | 0.0265663 | ||||||||
\(877\) | 5.50129 | 0.185765 | 0.0928827 | − | 0.995677i | \(-0.470392\pi\) | ||||
0.0928827 | + | 0.995677i | \(0.470392\pi\) | |||||||
\(878\) | 11.4091 | 0.385037 | ||||||||
\(879\) | −19.3490 | −0.652627 | ||||||||
\(880\) | −7.84132 | −0.264331 | ||||||||
\(881\) | −54.5279 | −1.83709 | −0.918546 | − | 0.395313i | \(-0.870636\pi\) | ||||
−0.918546 | + | 0.395313i | \(0.870636\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −29.0931 | −0.979062 | −0.489531 | − | 0.871986i | \(-0.662832\pi\) | ||||
−0.489531 | + | 0.871986i | \(0.662832\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.8675 | 0.365306 | ||||||||
\(886\) | −38.5387 | −1.29473 | ||||||||
\(887\) | 0.0869906 | 0.00292086 | 0.00146043 | − | 0.999999i | \(-0.499535\pi\) | ||||
0.00146043 | + | 0.999999i | \(0.499535\pi\) | |||||||
\(888\) | 8.93878 | 0.299966 | ||||||||
\(889\) | 11.7970 | 0.395659 | ||||||||
\(890\) | 26.4101 | 0.885270 | ||||||||
\(891\) | −3.24698 | −0.108778 | ||||||||
\(892\) | −5.53203 | −0.185226 | ||||||||
\(893\) | −26.7639 | −0.895619 | ||||||||
\(894\) | −19.3553 | −0.647339 | ||||||||
\(895\) | 7.91848 | 0.264686 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.16519 | −0.0722533 | ||||||||
\(899\) | −16.9454 | −0.565162 | ||||||||
\(900\) | 0.832022 | 0.0277341 | ||||||||
\(901\) | −18.6945 | −0.622805 | ||||||||
\(902\) | −29.7378 | −0.990162 | ||||||||
\(903\) | 3.95322 | 0.131555 | ||||||||
\(904\) | −12.7648 | −0.424552 | ||||||||
\(905\) | 50.7362 | 1.68653 | ||||||||
\(906\) | 9.50760 | 0.315869 | ||||||||
\(907\) | 20.4983 | 0.680634 | 0.340317 | − | 0.940311i | \(-0.389466\pi\) | ||||
0.340317 | + | 0.940311i | \(0.389466\pi\) | |||||||
\(908\) | −20.4532 | −0.678763 | ||||||||
\(909\) | 15.5746 | 0.516577 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.1649 | 1.03254 | 0.516269 | − | 0.856426i | \(-0.327320\pi\) | ||||
0.516269 | + | 0.856426i | \(0.327320\pi\) | |||||||
\(912\) | 2.73858 | 0.0906836 | ||||||||
\(913\) | −11.4121 | −0.377685 | ||||||||
\(914\) | −31.4845 | −1.04142 | ||||||||
\(915\) | 16.7670 | 0.554300 | ||||||||
\(916\) | 29.0317 | 0.959234 | ||||||||
\(917\) | 16.5193 | 0.545515 | ||||||||
\(918\) | −1.80194 | −0.0594728 | ||||||||
\(919\) | −39.9574 | −1.31807 | −0.659037 | − | 0.752110i | \(-0.729036\pi\) | ||||
−0.659037 | + | 0.752110i | \(0.729036\pi\) | |||||||
\(920\) | 15.8907 | 0.523901 | ||||||||
\(921\) | −5.04050 | −0.166090 | ||||||||
\(922\) | 7.94726 | 0.261729 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.24698 | 0.106818 | ||||||||
\(925\) | −7.43726 | −0.244536 | ||||||||
\(926\) | 12.1131 | 0.398061 | ||||||||
\(927\) | 3.71813 | 0.122119 | ||||||||
\(928\) | −6.22322 | −0.204287 | ||||||||
\(929\) | −12.8743 | −0.422393 | −0.211196 | − | 0.977444i | \(-0.567736\pi\) | ||||
−0.211196 | + | 0.977444i | \(0.567736\pi\) | |||||||
\(930\) | 6.57578 | 0.215628 | ||||||||
\(931\) | 2.73858 | 0.0897535 | ||||||||
\(932\) | 12.4742 | 0.408605 | ||||||||
\(933\) | −16.2638 | −0.532452 | ||||||||
\(934\) | 1.69520 | 0.0554687 | ||||||||
\(935\) | −14.1296 | −0.462086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.9053 | −0.486936 | −0.243468 | − | 0.969909i | \(-0.578285\pi\) | ||||
−0.243468 | + | 0.969909i | \(0.578285\pi\) | |||||||
\(938\) | 2.54486 | 0.0830927 | ||||||||
\(939\) | −8.80560 | −0.287360 | ||||||||
\(940\) | −23.6011 | −0.769784 | ||||||||
\(941\) | 41.7852 | 1.36216 | 0.681080 | − | 0.732209i | \(-0.261511\pi\) | ||||
0.681080 | + | 0.732209i | \(0.261511\pi\) | |||||||
\(942\) | −2.70530 | −0.0881436 | ||||||||
\(943\) | 60.2648 | 1.96249 | ||||||||
\(944\) | 4.50007 | 0.146465 | ||||||||
\(945\) | −2.41496 | −0.0785586 | ||||||||
\(946\) | −12.8360 | −0.417335 | ||||||||
\(947\) | 21.9153 | 0.712151 | 0.356076 | − | 0.934457i | \(-0.384115\pi\) | ||||
0.356076 | + | 0.934457i | \(0.384115\pi\) | |||||||
\(948\) | −2.41753 | −0.0785177 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.27856 | −0.0739263 | ||||||||
\(951\) | −20.0495 | −0.650151 | ||||||||
\(952\) | 1.80194 | 0.0584011 | ||||||||
\(953\) | 31.7129 | 1.02728 | 0.513641 | − | 0.858005i | \(-0.328296\pi\) | ||||
0.513641 | + | 0.858005i | \(0.328296\pi\) | |||||||
\(954\) | 10.3747 | 0.335893 | ||||||||
\(955\) | −14.8590 | −0.480826 | ||||||||
\(956\) | 23.3225 | 0.754303 | ||||||||
\(957\) | −20.2067 | −0.653189 | ||||||||
\(958\) | 3.59340 | 0.116097 | ||||||||
\(959\) | 11.5650 | 0.373455 | ||||||||
\(960\) | 2.41496 | 0.0779424 | ||||||||
\(961\) | −23.5856 | −0.760826 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.125781 | −0.00405322 | ||||||||
\(964\) | −28.8105 | −0.927922 | ||||||||
\(965\) | 44.9743 | 1.44777 | ||||||||
\(966\) | −6.58012 | −0.211712 | ||||||||
\(967\) | −9.95706 | −0.320198 | −0.160099 | − | 0.987101i | \(-0.551181\pi\) | ||||
−0.160099 | + | 0.987101i | \(0.551181\pi\) | |||||||
\(968\) | 0.457123 | 0.0146925 | ||||||||
\(969\) | 4.93476 | 0.158527 | ||||||||
\(970\) | 29.6808 | 0.952992 | ||||||||
\(971\) | −7.29014 | −0.233952 | −0.116976 | − | 0.993135i | \(-0.537320\pi\) | ||||
−0.116976 | + | 0.993135i | \(0.537320\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 2.63433 | 0.0844527 | ||||||||
\(974\) | −4.79109 | −0.153516 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.94297 | 0.222239 | ||||||||
\(977\) | 15.2936 | 0.489285 | 0.244643 | − | 0.969613i | \(-0.421329\pi\) | ||||
0.244643 | + | 0.969613i | \(0.421329\pi\) | |||||||
\(978\) | −6.79361 | −0.217236 | ||||||||
\(979\) | 35.5092 | 1.13488 | ||||||||
\(980\) | 2.41496 | 0.0771430 | ||||||||
\(981\) | −3.84276 | −0.122690 | ||||||||
\(982\) | 42.3139 | 1.35029 | ||||||||
\(983\) | 53.3268 | 1.70086 | 0.850430 | − | 0.526089i | \(-0.176342\pi\) | ||||
0.850430 | + | 0.526089i | \(0.176342\pi\) | |||||||
\(984\) | 9.15862 | 0.291966 | ||||||||
\(985\) | −40.7047 | −1.29696 | ||||||||
\(986\) | −11.2139 | −0.357122 | ||||||||
\(987\) | 9.77289 | 0.311075 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.0127 | 0.827155 | ||||||||
\(990\) | 7.84132 | 0.249213 | ||||||||
\(991\) | 31.4834 | 1.00010 | 0.500051 | − | 0.865996i | \(-0.333314\pi\) | ||||
0.500051 | + | 0.865996i | \(0.333314\pi\) | |||||||
\(992\) | 2.72294 | 0.0864533 | ||||||||
\(993\) | 19.0732 | 0.605271 | ||||||||
\(994\) | 1.50961 | 0.0478818 | ||||||||
\(995\) | 29.7948 | 0.944558 | ||||||||
\(996\) | 3.51468 | 0.111367 | ||||||||
\(997\) | −16.4135 | −0.519819 | −0.259910 | − | 0.965633i | \(-0.583693\pi\) | ||||
−0.259910 | + | 0.965633i | \(0.583693\pi\) | |||||||
\(998\) | 26.4820 | 0.838274 | ||||||||
\(999\) | −8.93878 | −0.282811 |
(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 | 7098.2.a.cr.1.6 | ✓ | 6 | |
13.12 | even | 2 | 7098.2.a.ct.1.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cr.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
7098.2.a.ct.1.1 | yes | 6 | 13.12 | even | 2 |