Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 16x^{7} + 37x^{6} + 97x^{5} - 72x^{4} - 182x^{3} + 24x^{2} + 70x - 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.12576\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.14251 | −1.40537 | −0.702687 | − | 0.711499i | \(-0.748017\pi\) | ||||
−0.702687 | + | 0.711499i | \(0.748017\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.86106 | −0.703416 | −0.351708 | − | 0.936110i | \(-0.614399\pi\) | ||||
−0.351708 | + | 0.936110i | \(0.614399\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.14251 | 0.993750 | ||||||||
\(11\) | −1.90868 | −0.575488 | −0.287744 | − | 0.957707i | \(-0.592905\pi\) | ||||
−0.287744 | + | 0.957707i | \(0.592905\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.598620 | −0.166027 | −0.0830137 | − | 0.996548i | \(-0.526455\pi\) | ||||
−0.0830137 | + | 0.996548i | \(0.526455\pi\) | |||||||
\(14\) | 1.86106 | 0.497390 | ||||||||
\(15\) | 3.14251 | 0.811393 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.79804 | −0.641914 | −0.320957 | − | 0.947094i | \(-0.604005\pi\) | ||||
−0.320957 | + | 0.947094i | \(0.604005\pi\) | |||||||
\(20\) | −3.14251 | −0.702687 | ||||||||
\(21\) | 1.86106 | 0.406118 | ||||||||
\(22\) | 1.90868 | 0.406931 | ||||||||
\(23\) | 6.06631 | 1.26491 | 0.632456 | − | 0.774596i | \(-0.282047\pi\) | ||||
0.632456 | + | 0.774596i | \(0.282047\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.87539 | 0.975078 | ||||||||
\(26\) | 0.598620 | 0.117399 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.86106 | −0.351708 | ||||||||
\(29\) | −0.0580368 | −0.0107772 | −0.00538858 | − | 0.999985i | \(-0.501715\pi\) | ||||
−0.00538858 | + | 0.999985i | \(0.501715\pi\) | |||||||
\(30\) | −3.14251 | −0.573742 | ||||||||
\(31\) | −9.30117 | −1.67054 | −0.835270 | − | 0.549840i | \(-0.814689\pi\) | ||||
−0.835270 | + | 0.549840i | \(0.814689\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.90868 | 0.332258 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 5.84842 | 0.988564 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.53439 | −0.252252 | −0.126126 | − | 0.992014i | \(-0.540254\pi\) | ||||
−0.126126 | + | 0.992014i | \(0.540254\pi\) | |||||||
\(38\) | 2.79804 | 0.453902 | ||||||||
\(39\) | 0.598620 | 0.0958559 | ||||||||
\(40\) | 3.14251 | 0.496875 | ||||||||
\(41\) | 12.3401 | 1.92721 | 0.963603 | − | 0.267336i | \(-0.0861434\pi\) | ||||
0.963603 | + | 0.267336i | \(0.0861434\pi\) | |||||||
\(42\) | −1.86106 | −0.287169 | ||||||||
\(43\) | 1.47691 | 0.225227 | 0.112613 | − | 0.993639i | \(-0.464078\pi\) | ||||
0.112613 | + | 0.993639i | \(0.464078\pi\) | |||||||
\(44\) | −1.90868 | −0.287744 | ||||||||
\(45\) | −3.14251 | −0.468458 | ||||||||
\(46\) | −6.06631 | −0.894428 | ||||||||
\(47\) | 2.09247 | 0.305218 | 0.152609 | − | 0.988287i | \(-0.451232\pi\) | ||||
0.152609 | + | 0.988287i | \(0.451232\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.53644 | −0.505205 | ||||||||
\(50\) | −4.87539 | −0.689484 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −0.598620 | −0.0830137 | ||||||||
\(53\) | −7.58796 | −1.04229 | −0.521143 | − | 0.853469i | \(-0.674494\pi\) | ||||
−0.521143 | + | 0.853469i | \(0.674494\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 5.99804 | 0.808776 | ||||||||
\(56\) | 1.86106 | 0.248695 | ||||||||
\(57\) | 2.79804 | 0.370609 | ||||||||
\(58\) | 0.0580368 | 0.00762060 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 3.14251 | 0.405697 | ||||||||
\(61\) | 15.1201 | 1.93593 | 0.967964 | − | 0.251090i | \(-0.0807891\pi\) | ||||
0.967964 | + | 0.251090i | \(0.0807891\pi\) | |||||||
\(62\) | 9.30117 | 1.18125 | ||||||||
\(63\) | −1.86106 | −0.234472 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.88117 | 0.233331 | ||||||||
\(66\) | −1.90868 | −0.234942 | ||||||||
\(67\) | 10.7010 | 1.30734 | 0.653669 | − | 0.756781i | \(-0.273229\pi\) | ||||
0.653669 | + | 0.756781i | \(0.273229\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −6.06631 | −0.730298 | ||||||||
\(70\) | −5.84842 | −0.699020 | ||||||||
\(71\) | 1.96132 | 0.232765 | 0.116383 | − | 0.993204i | \(-0.462870\pi\) | ||||
0.116383 | + | 0.993204i | \(0.462870\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.82049 | 0.213072 | 0.106536 | − | 0.994309i | \(-0.466024\pi\) | ||||
0.106536 | + | 0.994309i | \(0.466024\pi\) | |||||||
\(74\) | 1.53439 | 0.178369 | ||||||||
\(75\) | −4.87539 | −0.562962 | ||||||||
\(76\) | −2.79804 | −0.320957 | ||||||||
\(77\) | 3.55217 | 0.404807 | ||||||||
\(78\) | −0.598620 | −0.0677804 | ||||||||
\(79\) | −11.9342 | −1.34271 | −0.671353 | − | 0.741138i | \(-0.734286\pi\) | ||||
−0.671353 | + | 0.741138i | \(0.734286\pi\) | |||||||
\(80\) | −3.14251 | −0.351344 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.3401 | −1.36274 | ||||||||
\(83\) | 16.2029 | 1.77850 | 0.889250 | − | 0.457422i | \(-0.151227\pi\) | ||||
0.889250 | + | 0.457422i | \(0.151227\pi\) | |||||||
\(84\) | 1.86106 | 0.203059 | ||||||||
\(85\) | −3.14251 | −0.340853 | ||||||||
\(86\) | −1.47691 | −0.159259 | ||||||||
\(87\) | 0.0580368 | 0.00622220 | ||||||||
\(88\) | 1.90868 | 0.203466 | ||||||||
\(89\) | 5.45500 | 0.578229 | 0.289115 | − | 0.957295i | \(-0.406639\pi\) | ||||
0.289115 | + | 0.957295i | \(0.406639\pi\) | |||||||
\(90\) | 3.14251 | 0.331250 | ||||||||
\(91\) | 1.11407 | 0.116786 | ||||||||
\(92\) | 6.06631 | 0.632456 | ||||||||
\(93\) | 9.30117 | 0.964487 | ||||||||
\(94\) | −2.09247 | −0.215822 | ||||||||
\(95\) | 8.79288 | 0.902130 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.87586 | 0.190465 | 0.0952323 | − | 0.995455i | \(-0.469641\pi\) | ||||
0.0952323 | + | 0.995455i | \(0.469641\pi\) | |||||||
\(98\) | 3.53644 | 0.357234 | ||||||||
\(99\) | −1.90868 | −0.191829 | ||||||||
\(100\) | 4.87539 | 0.487539 | ||||||||
\(101\) | −0.354613 | −0.0352853 | −0.0176427 | − | 0.999844i | \(-0.505616\pi\) | ||||
−0.0176427 | + | 0.999844i | \(0.505616\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −14.9092 | −1.46905 | −0.734525 | − | 0.678581i | \(-0.762595\pi\) | ||||
−0.734525 | + | 0.678581i | \(0.762595\pi\) | |||||||
\(104\) | 0.598620 | 0.0586995 | ||||||||
\(105\) | −5.84842 | −0.570747 | ||||||||
\(106\) | 7.58796 | 0.737008 | ||||||||
\(107\) | 8.18027 | 0.790817 | 0.395408 | − | 0.918505i | \(-0.370603\pi\) | ||||
0.395408 | + | 0.918505i | \(0.370603\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 16.3901 | 1.56989 | 0.784943 | − | 0.619568i | \(-0.212692\pi\) | ||||
0.784943 | + | 0.619568i | \(0.212692\pi\) | |||||||
\(110\) | −5.99804 | −0.571891 | ||||||||
\(111\) | 1.53439 | 0.145638 | ||||||||
\(112\) | −1.86106 | −0.175854 | ||||||||
\(113\) | 0.272035 | 0.0255909 | 0.0127954 | − | 0.999918i | \(-0.495927\pi\) | ||||
0.0127954 | + | 0.999918i | \(0.495927\pi\) | |||||||
\(114\) | −2.79804 | −0.262060 | ||||||||
\(115\) | −19.0635 | −1.77768 | ||||||||
\(116\) | −0.0580368 | −0.00538858 | ||||||||
\(117\) | −0.598620 | −0.0553425 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −1.86106 | −0.170604 | ||||||||
\(120\) | −3.14251 | −0.286871 | ||||||||
\(121\) | −7.35695 | −0.668814 | ||||||||
\(122\) | −15.1201 | −1.36891 | ||||||||
\(123\) | −12.3401 | −1.11267 | ||||||||
\(124\) | −9.30117 | −0.835270 | ||||||||
\(125\) | 0.391588 | 0.0350247 | ||||||||
\(126\) | 1.86106 | 0.165797 | ||||||||
\(127\) | −16.3022 | −1.44659 | −0.723294 | − | 0.690540i | \(-0.757373\pi\) | ||||
−0.723294 | + | 0.690540i | \(0.757373\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.47691 | −0.130035 | ||||||||
\(130\) | −1.88117 | −0.164990 | ||||||||
\(131\) | 21.4814 | 1.87684 | 0.938421 | − | 0.345493i | \(-0.112288\pi\) | ||||
0.938421 | + | 0.345493i | \(0.112288\pi\) | |||||||
\(132\) | 1.90868 | 0.166129 | ||||||||
\(133\) | 5.20733 | 0.451533 | ||||||||
\(134\) | −10.7010 | −0.924427 | ||||||||
\(135\) | 3.14251 | 0.270464 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 6.72615 | 0.574654 | 0.287327 | − | 0.957833i | \(-0.407233\pi\) | ||||
0.287327 | + | 0.957833i | \(0.407233\pi\) | |||||||
\(138\) | 6.06631 | 0.516399 | ||||||||
\(139\) | 5.74712 | 0.487464 | 0.243732 | − | 0.969843i | \(-0.421628\pi\) | ||||
0.243732 | + | 0.969843i | \(0.421628\pi\) | |||||||
\(140\) | 5.84842 | 0.494282 | ||||||||
\(141\) | −2.09247 | −0.176218 | ||||||||
\(142\) | −1.96132 | −0.164590 | ||||||||
\(143\) | 1.14257 | 0.0955467 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.182381 | 0.0151460 | ||||||||
\(146\) | −1.82049 | −0.150665 | ||||||||
\(147\) | 3.53644 | 0.291680 | ||||||||
\(148\) | −1.53439 | −0.126126 | ||||||||
\(149\) | −4.15571 | −0.340449 | −0.170224 | − | 0.985405i | \(-0.554449\pi\) | ||||
−0.170224 | + | 0.985405i | \(0.554449\pi\) | |||||||
\(150\) | 4.87539 | 0.398074 | ||||||||
\(151\) | 3.76515 | 0.306403 | 0.153202 | − | 0.988195i | \(-0.451042\pi\) | ||||
0.153202 | + | 0.988195i | \(0.451042\pi\) | |||||||
\(152\) | 2.79804 | 0.226951 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −3.55217 | −0.286242 | ||||||||
\(155\) | 29.2291 | 2.34773 | ||||||||
\(156\) | 0.598620 | 0.0479280 | ||||||||
\(157\) | −11.4685 | −0.915284 | −0.457642 | − | 0.889136i | \(-0.651306\pi\) | ||||
−0.457642 | + | 0.889136i | \(0.651306\pi\) | |||||||
\(158\) | 11.9342 | 0.949436 | ||||||||
\(159\) | 7.58796 | 0.601764 | ||||||||
\(160\) | 3.14251 | 0.248437 | ||||||||
\(161\) | −11.2898 | −0.889760 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.29454 | −0.571352 | −0.285676 | − | 0.958326i | \(-0.592218\pi\) | ||||
−0.285676 | + | 0.958326i | \(0.592218\pi\) | |||||||
\(164\) | 12.3401 | 0.963603 | ||||||||
\(165\) | −5.99804 | −0.466947 | ||||||||
\(166\) | −16.2029 | −1.25759 | ||||||||
\(167\) | −17.7398 | −1.37275 | −0.686374 | − | 0.727249i | \(-0.740799\pi\) | ||||
−0.686374 | + | 0.727249i | \(0.740799\pi\) | |||||||
\(168\) | −1.86106 | −0.143584 | ||||||||
\(169\) | −12.6417 | −0.972435 | ||||||||
\(170\) | 3.14251 | 0.241020 | ||||||||
\(171\) | −2.79804 | −0.213971 | ||||||||
\(172\) | 1.47691 | 0.112613 | ||||||||
\(173\) | 6.87128 | 0.522414 | 0.261207 | − | 0.965283i | \(-0.415879\pi\) | ||||
0.261207 | + | 0.965283i | \(0.415879\pi\) | |||||||
\(174\) | −0.0580368 | −0.00439976 | ||||||||
\(175\) | −9.07342 | −0.685886 | ||||||||
\(176\) | −1.90868 | −0.143872 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −5.45500 | −0.408870 | ||||||||
\(179\) | −19.6437 | −1.46824 | −0.734121 | − | 0.679018i | \(-0.762406\pi\) | ||||
−0.734121 | + | 0.679018i | \(0.762406\pi\) | |||||||
\(180\) | −3.14251 | −0.234229 | ||||||||
\(181\) | 1.41315 | 0.105039 | 0.0525193 | − | 0.998620i | \(-0.483275\pi\) | ||||
0.0525193 | + | 0.998620i | \(0.483275\pi\) | |||||||
\(182\) | −1.11407 | −0.0825804 | ||||||||
\(183\) | −15.1201 | −1.11771 | ||||||||
\(184\) | −6.06631 | −0.447214 | ||||||||
\(185\) | 4.82184 | 0.354509 | ||||||||
\(186\) | −9.30117 | −0.681995 | ||||||||
\(187\) | −1.90868 | −0.139576 | ||||||||
\(188\) | 2.09247 | 0.152609 | ||||||||
\(189\) | 1.86106 | 0.135373 | ||||||||
\(190\) | −8.79288 | −0.637902 | ||||||||
\(191\) | 4.57387 | 0.330953 | 0.165477 | − | 0.986214i | \(-0.447084\pi\) | ||||
0.165477 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 24.6726 | 1.77598 | 0.887988 | − | 0.459867i | \(-0.152103\pi\) | ||||
0.887988 | + | 0.459867i | \(0.152103\pi\) | |||||||
\(194\) | −1.87586 | −0.134679 | ||||||||
\(195\) | −1.88117 | −0.134714 | ||||||||
\(196\) | −3.53644 | −0.252603 | ||||||||
\(197\) | 3.81498 | 0.271806 | 0.135903 | − | 0.990722i | \(-0.456606\pi\) | ||||
0.135903 | + | 0.990722i | \(0.456606\pi\) | |||||||
\(198\) | 1.90868 | 0.135644 | ||||||||
\(199\) | 1.86102 | 0.131924 | 0.0659621 | − | 0.997822i | \(-0.478988\pi\) | ||||
0.0659621 | + | 0.997822i | \(0.478988\pi\) | |||||||
\(200\) | −4.87539 | −0.344742 | ||||||||
\(201\) | −10.7010 | −0.754792 | ||||||||
\(202\) | 0.354613 | 0.0249505 | ||||||||
\(203\) | 0.108010 | 0.00758083 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −38.7791 | −2.70845 | ||||||||
\(206\) | 14.9092 | 1.03878 | ||||||||
\(207\) | 6.06631 | 0.421638 | ||||||||
\(208\) | −0.598620 | −0.0415068 | ||||||||
\(209\) | 5.34055 | 0.369414 | ||||||||
\(210\) | 5.84842 | 0.403579 | ||||||||
\(211\) | 7.91425 | 0.544839 | 0.272420 | − | 0.962179i | \(-0.412176\pi\) | ||||
0.272420 | + | 0.962179i | \(0.412176\pi\) | |||||||
\(212\) | −7.58796 | −0.521143 | ||||||||
\(213\) | −1.96132 | −0.134387 | ||||||||
\(214\) | −8.18027 | −0.559192 | ||||||||
\(215\) | −4.64121 | −0.316528 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 17.3101 | 1.17508 | ||||||||
\(218\) | −16.3901 | −1.11008 | ||||||||
\(219\) | −1.82049 | −0.123017 | ||||||||
\(220\) | 5.99804 | 0.404388 | ||||||||
\(221\) | −0.598620 | −0.0402675 | ||||||||
\(222\) | −1.53439 | −0.102982 | ||||||||
\(223\) | −18.3666 | −1.22992 | −0.614959 | − | 0.788559i | \(-0.710827\pi\) | ||||
−0.614959 | + | 0.788559i | \(0.710827\pi\) | |||||||
\(224\) | 1.86106 | 0.124348 | ||||||||
\(225\) | 4.87539 | 0.325026 | ||||||||
\(226\) | −0.272035 | −0.0180955 | ||||||||
\(227\) | −4.93993 | −0.327875 | −0.163937 | − | 0.986471i | \(-0.552419\pi\) | ||||
−0.163937 | + | 0.986471i | \(0.552419\pi\) | |||||||
\(228\) | 2.79804 | 0.185305 | ||||||||
\(229\) | −5.78391 | −0.382212 | −0.191106 | − | 0.981569i | \(-0.561207\pi\) | ||||
−0.191106 | + | 0.981569i | \(0.561207\pi\) | |||||||
\(230\) | 19.0635 | 1.25701 | ||||||||
\(231\) | −3.55217 | −0.233716 | ||||||||
\(232\) | 0.0580368 | 0.00381030 | ||||||||
\(233\) | −16.2536 | −1.06481 | −0.532405 | − | 0.846490i | \(-0.678712\pi\) | ||||
−0.532405 | + | 0.846490i | \(0.678712\pi\) | |||||||
\(234\) | 0.598620 | 0.0391330 | ||||||||
\(235\) | −6.57561 | −0.428946 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | 11.9342 | 0.775211 | ||||||||
\(238\) | 1.86106 | 0.120635 | ||||||||
\(239\) | 7.83325 | 0.506691 | 0.253345 | − | 0.967376i | \(-0.418469\pi\) | ||||
0.253345 | + | 0.967376i | \(0.418469\pi\) | |||||||
\(240\) | 3.14251 | 0.202848 | ||||||||
\(241\) | −5.49476 | −0.353949 | −0.176974 | − | 0.984215i | \(-0.556631\pi\) | ||||
−0.176974 | + | 0.984215i | \(0.556631\pi\) | |||||||
\(242\) | 7.35695 | 0.472923 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 15.1201 | 0.967964 | ||||||||
\(245\) | 11.1133 | 0.710003 | ||||||||
\(246\) | 12.3401 | 0.786779 | ||||||||
\(247\) | 1.67496 | 0.106575 | ||||||||
\(248\) | 9.30117 | 0.590625 | ||||||||
\(249\) | −16.2029 | −1.02682 | ||||||||
\(250\) | −0.391588 | −0.0247662 | ||||||||
\(251\) | −11.2099 | −0.707560 | −0.353780 | − | 0.935329i | \(-0.615104\pi\) | ||||
−0.353780 | + | 0.935329i | \(0.615104\pi\) | |||||||
\(252\) | −1.86106 | −0.117236 | ||||||||
\(253\) | −11.5786 | −0.727942 | ||||||||
\(254\) | 16.3022 | 1.02289 | ||||||||
\(255\) | 3.14251 | 0.196792 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.6981 | −0.854466 | −0.427233 | − | 0.904142i | \(-0.640512\pi\) | ||||
−0.427233 | + | 0.904142i | \(0.640512\pi\) | |||||||
\(258\) | 1.47691 | 0.0919485 | ||||||||
\(259\) | 2.85560 | 0.177438 | ||||||||
\(260\) | 1.88117 | 0.116665 | ||||||||
\(261\) | −0.0580368 | −0.00359239 | ||||||||
\(262\) | −21.4814 | −1.32713 | ||||||||
\(263\) | −18.5784 | −1.14560 | −0.572798 | − | 0.819697i | \(-0.694142\pi\) | ||||
−0.572798 | + | 0.819697i | \(0.694142\pi\) | |||||||
\(264\) | −1.90868 | −0.117471 | ||||||||
\(265\) | 23.8453 | 1.46480 | ||||||||
\(266\) | −5.20733 | −0.319282 | ||||||||
\(267\) | −5.45500 | −0.333841 | ||||||||
\(268\) | 10.7010 | 0.653669 | ||||||||
\(269\) | 28.1773 | 1.71800 | 0.859001 | − | 0.511973i | \(-0.171085\pi\) | ||||
0.859001 | + | 0.511973i | \(0.171085\pi\) | |||||||
\(270\) | −3.14251 | −0.191247 | ||||||||
\(271\) | 15.3524 | 0.932590 | 0.466295 | − | 0.884629i | \(-0.345589\pi\) | ||||
0.466295 | + | 0.884629i | \(0.345589\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −1.11407 | −0.0674266 | ||||||||
\(274\) | −6.72615 | −0.406342 | ||||||||
\(275\) | −9.30554 | −0.561145 | ||||||||
\(276\) | −6.06631 | −0.365149 | ||||||||
\(277\) | −7.29924 | −0.438569 | −0.219284 | − | 0.975661i | \(-0.570372\pi\) | ||||
−0.219284 | + | 0.975661i | \(0.570372\pi\) | |||||||
\(278\) | −5.74712 | −0.344689 | ||||||||
\(279\) | −9.30117 | −0.556847 | ||||||||
\(280\) | −5.84842 | −0.349510 | ||||||||
\(281\) | −10.2946 | −0.614126 | −0.307063 | − | 0.951689i | \(-0.599346\pi\) | ||||
−0.307063 | + | 0.951689i | \(0.599346\pi\) | |||||||
\(282\) | 2.09247 | 0.124605 | ||||||||
\(283\) | −11.1593 | −0.663350 | −0.331675 | − | 0.943394i | \(-0.607614\pi\) | ||||
−0.331675 | + | 0.943394i | \(0.607614\pi\) | |||||||
\(284\) | 1.96132 | 0.116383 | ||||||||
\(285\) | −8.79288 | −0.520845 | ||||||||
\(286\) | −1.14257 | −0.0675617 | ||||||||
\(287\) | −22.9658 | −1.35563 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.182381 | −0.0107098 | ||||||||
\(291\) | −1.87586 | −0.109965 | ||||||||
\(292\) | 1.82049 | 0.106536 | ||||||||
\(293\) | −3.53990 | −0.206803 | −0.103401 | − | 0.994640i | \(-0.532973\pi\) | ||||
−0.103401 | + | 0.994640i | \(0.532973\pi\) | |||||||
\(294\) | −3.53644 | −0.206249 | ||||||||
\(295\) | −3.14251 | −0.182964 | ||||||||
\(296\) | 1.53439 | 0.0891846 | ||||||||
\(297\) | 1.90868 | 0.110753 | ||||||||
\(298\) | 4.15571 | 0.240734 | ||||||||
\(299\) | −3.63141 | −0.210010 | ||||||||
\(300\) | −4.87539 | −0.281481 | ||||||||
\(301\) | −2.74863 | −0.158428 | ||||||||
\(302\) | −3.76515 | −0.216660 | ||||||||
\(303\) | 0.354613 | 0.0203720 | ||||||||
\(304\) | −2.79804 | −0.160479 | ||||||||
\(305\) | −47.5150 | −2.72070 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | 15.1451 | 0.864378 | 0.432189 | − | 0.901783i | \(-0.357741\pi\) | ||||
0.432189 | + | 0.901783i | \(0.357741\pi\) | |||||||
\(308\) | 3.55217 | 0.202404 | ||||||||
\(309\) | 14.9092 | 0.848157 | ||||||||
\(310\) | −29.2291 | −1.66010 | ||||||||
\(311\) | −27.9857 | −1.58692 | −0.793461 | − | 0.608621i | \(-0.791723\pi\) | ||||
−0.793461 | + | 0.608621i | \(0.791723\pi\) | |||||||
\(312\) | −0.598620 | −0.0338902 | ||||||||
\(313\) | −18.6629 | −1.05489 | −0.527444 | − | 0.849590i | \(-0.676850\pi\) | ||||
−0.527444 | + | 0.849590i | \(0.676850\pi\) | |||||||
\(314\) | 11.4685 | 0.647204 | ||||||||
\(315\) | 5.84842 | 0.329521 | ||||||||
\(316\) | −11.9342 | −0.671353 | ||||||||
\(317\) | −5.33071 | −0.299403 | −0.149701 | − | 0.988731i | \(-0.547831\pi\) | ||||
−0.149701 | + | 0.988731i | \(0.547831\pi\) | |||||||
\(318\) | −7.58796 | −0.425512 | ||||||||
\(319\) | 0.110773 | 0.00620212 | ||||||||
\(320\) | −3.14251 | −0.175672 | ||||||||
\(321\) | −8.18027 | −0.456578 | ||||||||
\(322\) | 11.2898 | 0.629156 | ||||||||
\(323\) | −2.79804 | −0.155687 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.91851 | −0.161890 | ||||||||
\(326\) | 7.29454 | 0.404007 | ||||||||
\(327\) | −16.3901 | −0.906374 | ||||||||
\(328\) | −12.3401 | −0.681370 | ||||||||
\(329\) | −3.89422 | −0.214695 | ||||||||
\(330\) | 5.99804 | 0.330181 | ||||||||
\(331\) | −6.46188 | −0.355177 | −0.177588 | − | 0.984105i | \(-0.556830\pi\) | ||||
−0.177588 | + | 0.984105i | \(0.556830\pi\) | |||||||
\(332\) | 16.2029 | 0.889250 | ||||||||
\(333\) | −1.53439 | −0.0840841 | ||||||||
\(334\) | 17.7398 | 0.970680 | ||||||||
\(335\) | −33.6281 | −1.83730 | ||||||||
\(336\) | 1.86106 | 0.101529 | ||||||||
\(337\) | 9.86479 | 0.537370 | 0.268685 | − | 0.963228i | \(-0.413411\pi\) | ||||
0.268685 | + | 0.963228i | \(0.413411\pi\) | |||||||
\(338\) | 12.6417 | 0.687615 | ||||||||
\(339\) | −0.272035 | −0.0147749 | ||||||||
\(340\) | −3.14251 | −0.170427 | ||||||||
\(341\) | 17.7529 | 0.961375 | ||||||||
\(342\) | 2.79804 | 0.151301 | ||||||||
\(343\) | 19.6090 | 1.05879 | ||||||||
\(344\) | −1.47691 | −0.0796297 | ||||||||
\(345\) | 19.0635 | 1.02634 | ||||||||
\(346\) | −6.87128 | −0.369403 | ||||||||
\(347\) | 9.75055 | 0.523437 | 0.261718 | − | 0.965144i | \(-0.415711\pi\) | ||||
0.261718 | + | 0.965144i | \(0.415711\pi\) | |||||||
\(348\) | 0.0580368 | 0.00311110 | ||||||||
\(349\) | 2.64990 | 0.141846 | 0.0709230 | − | 0.997482i | \(-0.477406\pi\) | ||||
0.0709230 | + | 0.997482i | \(0.477406\pi\) | |||||||
\(350\) | 9.07342 | 0.484995 | ||||||||
\(351\) | 0.598620 | 0.0319520 | ||||||||
\(352\) | 1.90868 | 0.101733 | ||||||||
\(353\) | 0.895285 | 0.0476512 | 0.0238256 | − | 0.999716i | \(-0.492415\pi\) | ||||
0.0238256 | + | 0.999716i | \(0.492415\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | −6.16346 | −0.327123 | ||||||||
\(356\) | 5.45500 | 0.289115 | ||||||||
\(357\) | 1.86106 | 0.0984980 | ||||||||
\(358\) | 19.6437 | 1.03820 | ||||||||
\(359\) | 24.1820 | 1.27627 | 0.638137 | − | 0.769923i | \(-0.279705\pi\) | ||||
0.638137 | + | 0.769923i | \(0.279705\pi\) | |||||||
\(360\) | 3.14251 | 0.165625 | ||||||||
\(361\) | −11.1710 | −0.587946 | ||||||||
\(362\) | −1.41315 | −0.0742735 | ||||||||
\(363\) | 7.35695 | 0.386140 | ||||||||
\(364\) | 1.11407 | 0.0583932 | ||||||||
\(365\) | −5.72091 | −0.299446 | ||||||||
\(366\) | 15.1201 | 0.790339 | ||||||||
\(367\) | −7.64468 | −0.399049 | −0.199525 | − | 0.979893i | \(-0.563940\pi\) | ||||
−0.199525 | + | 0.979893i | \(0.563940\pi\) | |||||||
\(368\) | 6.06631 | 0.316228 | ||||||||
\(369\) | 12.3401 | 0.642402 | ||||||||
\(370\) | −4.82184 | −0.250676 | ||||||||
\(371\) | 14.1217 | 0.733161 | ||||||||
\(372\) | 9.30117 | 0.482243 | ||||||||
\(373\) | 0.359609 | 0.0186199 | 0.00930993 | − | 0.999957i | \(-0.497037\pi\) | ||||
0.00930993 | + | 0.999957i | \(0.497037\pi\) | |||||||
\(374\) | 1.90868 | 0.0986953 | ||||||||
\(375\) | −0.391588 | −0.0202215 | ||||||||
\(376\) | −2.09247 | −0.107911 | ||||||||
\(377\) | 0.0347420 | 0.00178930 | ||||||||
\(378\) | −1.86106 | −0.0957228 | ||||||||
\(379\) | 26.7145 | 1.37223 | 0.686117 | − | 0.727491i | \(-0.259314\pi\) | ||||
0.686117 | + | 0.727491i | \(0.259314\pi\) | |||||||
\(380\) | 8.79288 | 0.451065 | ||||||||
\(381\) | 16.3022 | 0.835188 | ||||||||
\(382\) | −4.57387 | −0.234019 | ||||||||
\(383\) | −6.58131 | −0.336289 | −0.168145 | − | 0.985762i | \(-0.553778\pi\) | ||||
−0.168145 | + | 0.985762i | \(0.553778\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −11.1627 | −0.568906 | ||||||||
\(386\) | −24.6726 | −1.25580 | ||||||||
\(387\) | 1.47691 | 0.0750756 | ||||||||
\(388\) | 1.87586 | 0.0952323 | ||||||||
\(389\) | −39.1368 | −1.98432 | −0.992158 | − | 0.124990i | \(-0.960110\pi\) | ||||
−0.992158 | + | 0.124990i | \(0.960110\pi\) | |||||||
\(390\) | 1.88117 | 0.0952568 | ||||||||
\(391\) | 6.06631 | 0.306786 | ||||||||
\(392\) | 3.53644 | 0.178617 | ||||||||
\(393\) | −21.4814 | −1.08360 | ||||||||
\(394\) | −3.81498 | −0.192196 | ||||||||
\(395\) | 37.5035 | 1.88700 | ||||||||
\(396\) | −1.90868 | −0.0959146 | ||||||||
\(397\) | 19.8735 | 0.997420 | 0.498710 | − | 0.866769i | \(-0.333807\pi\) | ||||
0.498710 | + | 0.866769i | \(0.333807\pi\) | |||||||
\(398\) | −1.86102 | −0.0932845 | ||||||||
\(399\) | −5.20733 | −0.260693 | ||||||||
\(400\) | 4.87539 | 0.243770 | ||||||||
\(401\) | −23.6493 | −1.18099 | −0.590495 | − | 0.807041i | \(-0.701067\pi\) | ||||
−0.590495 | + | 0.807041i | \(0.701067\pi\) | |||||||
\(402\) | 10.7010 | 0.533718 | ||||||||
\(403\) | 5.56787 | 0.277355 | ||||||||
\(404\) | −0.354613 | −0.0176427 | ||||||||
\(405\) | −3.14251 | −0.156153 | ||||||||
\(406\) | −0.108010 | −0.00536046 | ||||||||
\(407\) | 2.92865 | 0.145168 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −11.5307 | −0.570158 | −0.285079 | − | 0.958504i | \(-0.592020\pi\) | ||||
−0.285079 | + | 0.958504i | \(0.592020\pi\) | |||||||
\(410\) | 38.7791 | 1.91516 | ||||||||
\(411\) | −6.72615 | −0.331777 | ||||||||
\(412\) | −14.9092 | −0.734525 | ||||||||
\(413\) | −1.86106 | −0.0915770 | ||||||||
\(414\) | −6.06631 | −0.298143 | ||||||||
\(415\) | −50.9178 | −2.49946 | ||||||||
\(416\) | 0.598620 | 0.0293498 | ||||||||
\(417\) | −5.74712 | −0.281438 | ||||||||
\(418\) | −5.34055 | −0.261215 | ||||||||
\(419\) | −6.47921 | −0.316530 | −0.158265 | − | 0.987397i | \(-0.550590\pi\) | ||||
−0.158265 | + | 0.987397i | \(0.550590\pi\) | |||||||
\(420\) | −5.84842 | −0.285374 | ||||||||
\(421\) | −1.57699 | −0.0768580 | −0.0384290 | − | 0.999261i | \(-0.512235\pi\) | ||||
−0.0384290 | + | 0.999261i | \(0.512235\pi\) | |||||||
\(422\) | −7.91425 | −0.385259 | ||||||||
\(423\) | 2.09247 | 0.101739 | ||||||||
\(424\) | 7.58796 | 0.368504 | ||||||||
\(425\) | 4.87539 | 0.236491 | ||||||||
\(426\) | 1.96132 | 0.0950261 | ||||||||
\(427\) | −28.1394 | −1.36176 | ||||||||
\(428\) | 8.18027 | 0.395408 | ||||||||
\(429\) | −1.14257 | −0.0551639 | ||||||||
\(430\) | 4.64121 | 0.223819 | ||||||||
\(431\) | 19.5195 | 0.940222 | 0.470111 | − | 0.882607i | \(-0.344214\pi\) | ||||
0.470111 | + | 0.882607i | \(0.344214\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −23.7483 | −1.14127 | −0.570636 | − | 0.821203i | \(-0.693303\pi\) | ||||
−0.570636 | + | 0.821203i | \(0.693303\pi\) | |||||||
\(434\) | −17.3101 | −0.830911 | ||||||||
\(435\) | −0.182381 | −0.00874452 | ||||||||
\(436\) | 16.3901 | 0.784943 | ||||||||
\(437\) | −16.9738 | −0.811966 | ||||||||
\(438\) | 1.82049 | 0.0869863 | ||||||||
\(439\) | −35.8678 | −1.71188 | −0.855938 | − | 0.517079i | \(-0.827019\pi\) | ||||
−0.855938 | + | 0.517079i | \(0.827019\pi\) | |||||||
\(440\) | −5.99804 | −0.285945 | ||||||||
\(441\) | −3.53644 | −0.168402 | ||||||||
\(442\) | 0.598620 | 0.0284735 | ||||||||
\(443\) | −30.7025 | −1.45872 | −0.729360 | − | 0.684131i | \(-0.760182\pi\) | ||||
−0.729360 | + | 0.684131i | \(0.760182\pi\) | |||||||
\(444\) | 1.53439 | 0.0728189 | ||||||||
\(445\) | −17.1424 | −0.812628 | ||||||||
\(446\) | 18.3666 | 0.869683 | ||||||||
\(447\) | 4.15571 | 0.196558 | ||||||||
\(448\) | −1.86106 | −0.0879270 | ||||||||
\(449\) | −3.86029 | −0.182178 | −0.0910892 | − | 0.995843i | \(-0.529035\pi\) | ||||
−0.0910892 | + | 0.995843i | \(0.529035\pi\) | |||||||
\(450\) | −4.87539 | −0.229828 | ||||||||
\(451\) | −23.5533 | −1.10908 | ||||||||
\(452\) | 0.272035 | 0.0127954 | ||||||||
\(453\) | −3.76515 | −0.176902 | ||||||||
\(454\) | 4.93993 | 0.231842 | ||||||||
\(455\) | −3.50098 | −0.164129 | ||||||||
\(456\) | −2.79804 | −0.131030 | ||||||||
\(457\) | −30.6656 | −1.43447 | −0.717237 | − | 0.696829i | \(-0.754594\pi\) | ||||
−0.717237 | + | 0.696829i | \(0.754594\pi\) | |||||||
\(458\) | 5.78391 | 0.270264 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −19.0635 | −0.888838 | ||||||||
\(461\) | 33.1352 | 1.54326 | 0.771630 | − | 0.636072i | \(-0.219442\pi\) | ||||
0.771630 | + | 0.636072i | \(0.219442\pi\) | |||||||
\(462\) | 3.55217 | 0.165262 | ||||||||
\(463\) | −26.9844 | −1.25407 | −0.627036 | − | 0.778990i | \(-0.715732\pi\) | ||||
−0.627036 | + | 0.778990i | \(0.715732\pi\) | |||||||
\(464\) | −0.0580368 | −0.00269429 | ||||||||
\(465\) | −29.2291 | −1.35546 | ||||||||
\(466\) | 16.2536 | 0.752935 | ||||||||
\(467\) | 19.8835 | 0.920098 | 0.460049 | − | 0.887894i | \(-0.347832\pi\) | ||||
0.460049 | + | 0.887894i | \(0.347832\pi\) | |||||||
\(468\) | −0.598620 | −0.0276712 | ||||||||
\(469\) | −19.9153 | −0.919603 | ||||||||
\(470\) | 6.57561 | 0.303310 | ||||||||
\(471\) | 11.4685 | 0.528440 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −2.81895 | −0.129615 | ||||||||
\(474\) | −11.9342 | −0.548157 | ||||||||
\(475\) | −13.6415 | −0.625917 | ||||||||
\(476\) | −1.86106 | −0.0853018 | ||||||||
\(477\) | −7.58796 | −0.347429 | ||||||||
\(478\) | −7.83325 | −0.358284 | ||||||||
\(479\) | 3.62156 | 0.165473 | 0.0827366 | − | 0.996571i | \(-0.473634\pi\) | ||||
0.0827366 | + | 0.996571i | \(0.473634\pi\) | |||||||
\(480\) | −3.14251 | −0.143435 | ||||||||
\(481\) | 0.918517 | 0.0418808 | ||||||||
\(482\) | 5.49476 | 0.250280 | ||||||||
\(483\) | 11.2898 | 0.513703 | ||||||||
\(484\) | −7.35695 | −0.334407 | ||||||||
\(485\) | −5.89491 | −0.267674 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −3.29761 | −0.149429 | −0.0747145 | − | 0.997205i | \(-0.523805\pi\) | ||||
−0.0747145 | + | 0.997205i | \(0.523805\pi\) | |||||||
\(488\) | −15.1201 | −0.684454 | ||||||||
\(489\) | 7.29454 | 0.329870 | ||||||||
\(490\) | −11.1133 | −0.502048 | ||||||||
\(491\) | 3.68978 | 0.166518 | 0.0832588 | − | 0.996528i | \(-0.473467\pi\) | ||||
0.0832588 | + | 0.996528i | \(0.473467\pi\) | |||||||
\(492\) | −12.3401 | −0.556337 | ||||||||
\(493\) | −0.0580368 | −0.00261385 | ||||||||
\(494\) | −1.67496 | −0.0753601 | ||||||||
\(495\) | 5.99804 | 0.269592 | ||||||||
\(496\) | −9.30117 | −0.417635 | ||||||||
\(497\) | −3.65014 | −0.163731 | ||||||||
\(498\) | 16.2029 | 0.726069 | ||||||||
\(499\) | 20.7578 | 0.929246 | 0.464623 | − | 0.885508i | \(-0.346190\pi\) | ||||
0.464623 | + | 0.885508i | \(0.346190\pi\) | |||||||
\(500\) | 0.391588 | 0.0175123 | ||||||||
\(501\) | 17.7398 | 0.792557 | ||||||||
\(502\) | 11.2099 | 0.500321 | ||||||||
\(503\) | −35.7200 | −1.59268 | −0.796338 | − | 0.604852i | \(-0.793232\pi\) | ||||
−0.796338 | + | 0.604852i | \(0.793232\pi\) | |||||||
\(504\) | 1.86106 | 0.0828984 | ||||||||
\(505\) | 1.11438 | 0.0495891 | ||||||||
\(506\) | 11.5786 | 0.514733 | ||||||||
\(507\) | 12.6417 | 0.561436 | ||||||||
\(508\) | −16.3022 | −0.723294 | ||||||||
\(509\) | 36.2571 | 1.60707 | 0.803533 | − | 0.595260i | \(-0.202951\pi\) | ||||
0.803533 | + | 0.595260i | \(0.202951\pi\) | |||||||
\(510\) | −3.14251 | −0.139153 | ||||||||
\(511\) | −3.38805 | −0.149878 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.79804 | 0.123536 | ||||||||
\(514\) | 13.6981 | 0.604198 | ||||||||
\(515\) | 46.8525 | 2.06457 | ||||||||
\(516\) | −1.47691 | −0.0650174 | ||||||||
\(517\) | −3.99385 | −0.175649 | ||||||||
\(518\) | −2.85560 | −0.125468 | ||||||||
\(519\) | −6.87128 | −0.301616 | ||||||||
\(520\) | −1.88117 | −0.0824948 | ||||||||
\(521\) | 3.29763 | 0.144472 | 0.0722360 | − | 0.997388i | \(-0.476987\pi\) | ||||
0.0722360 | + | 0.997388i | \(0.476987\pi\) | |||||||
\(522\) | 0.0580368 | 0.00254020 | ||||||||
\(523\) | −0.897541 | −0.0392467 | −0.0196234 | − | 0.999807i | \(-0.506247\pi\) | ||||
−0.0196234 | + | 0.999807i | \(0.506247\pi\) | |||||||
\(524\) | 21.4814 | 0.938421 | ||||||||
\(525\) | 9.07342 | 0.395996 | ||||||||
\(526\) | 18.5784 | 0.810059 | ||||||||
\(527\) | −9.30117 | −0.405165 | ||||||||
\(528\) | 1.90868 | 0.0830645 | ||||||||
\(529\) | 13.8001 | 0.600005 | ||||||||
\(530\) | −23.8453 | −1.03577 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 5.20733 | 0.225767 | ||||||||
\(533\) | −7.38706 | −0.319969 | ||||||||
\(534\) | 5.45500 | 0.236061 | ||||||||
\(535\) | −25.7066 | −1.11139 | ||||||||
\(536\) | −10.7010 | −0.462214 | ||||||||
\(537\) | 19.6437 | 0.847690 | ||||||||
\(538\) | −28.1773 | −1.21481 | ||||||||
\(539\) | 6.74992 | 0.290740 | ||||||||
\(540\) | 3.14251 | 0.135232 | ||||||||
\(541\) | 1.03530 | 0.0445110 | 0.0222555 | − | 0.999752i | \(-0.492915\pi\) | ||||
0.0222555 | + | 0.999752i | \(0.492915\pi\) | |||||||
\(542\) | −15.3524 | −0.659441 | ||||||||
\(543\) | −1.41315 | −0.0606440 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −51.5061 | −2.20628 | ||||||||
\(546\) | 1.11407 | 0.0476778 | ||||||||
\(547\) | 10.3399 | 0.442104 | 0.221052 | − | 0.975262i | \(-0.429051\pi\) | ||||
0.221052 | + | 0.975262i | \(0.429051\pi\) | |||||||
\(548\) | 6.72615 | 0.287327 | ||||||||
\(549\) | 15.1201 | 0.645309 | ||||||||
\(550\) | 9.30554 | 0.396790 | ||||||||
\(551\) | 0.162389 | 0.00691802 | ||||||||
\(552\) | 6.06631 | 0.258199 | ||||||||
\(553\) | 22.2104 | 0.944481 | ||||||||
\(554\) | 7.29924 | 0.310115 | ||||||||
\(555\) | −4.82184 | −0.204676 | ||||||||
\(556\) | 5.74712 | 0.243732 | ||||||||
\(557\) | 3.20934 | 0.135984 | 0.0679920 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679920 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(558\) | 9.30117 | 0.393750 | ||||||||
\(559\) | −0.884109 | −0.0373938 | ||||||||
\(560\) | 5.84842 | 0.247141 | ||||||||
\(561\) | 1.90868 | 0.0805844 | ||||||||
\(562\) | 10.2946 | 0.434252 | ||||||||
\(563\) | 41.9631 | 1.76853 | 0.884267 | − | 0.466982i | \(-0.154659\pi\) | ||||
0.884267 | + | 0.466982i | \(0.154659\pi\) | |||||||
\(564\) | −2.09247 | −0.0881089 | ||||||||
\(565\) | −0.854872 | −0.0359648 | ||||||||
\(566\) | 11.1593 | 0.469060 | ||||||||
\(567\) | −1.86106 | −0.0781574 | ||||||||
\(568\) | −1.96132 | −0.0822950 | ||||||||
\(569\) | −1.36078 | −0.0570467 | −0.0285233 | − | 0.999593i | \(-0.509080\pi\) | ||||
−0.0285233 | + | 0.999593i | \(0.509080\pi\) | |||||||
\(570\) | 8.79288 | 0.368293 | ||||||||
\(571\) | −25.8025 | −1.07980 | −0.539901 | − | 0.841728i | \(-0.681538\pi\) | ||||
−0.539901 | + | 0.841728i | \(0.681538\pi\) | |||||||
\(572\) | 1.14257 | 0.0477733 | ||||||||
\(573\) | −4.57387 | −0.191076 | ||||||||
\(574\) | 22.9658 | 0.958574 | ||||||||
\(575\) | 29.5756 | 1.23339 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 24.2000 | 1.00746 | 0.503730 | − | 0.863861i | \(-0.331961\pi\) | ||||
0.503730 | + | 0.863861i | \(0.331961\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −24.6726 | −1.02536 | ||||||||
\(580\) | 0.182381 | 0.00757298 | ||||||||
\(581\) | −30.1546 | −1.25103 | ||||||||
\(582\) | 1.87586 | 0.0777569 | ||||||||
\(583\) | 14.4830 | 0.599823 | ||||||||
\(584\) | −1.82049 | −0.0753324 | ||||||||
\(585\) | 1.88117 | 0.0777769 | ||||||||
\(586\) | 3.53990 | 0.146232 | ||||||||
\(587\) | −4.68153 | −0.193228 | −0.0966138 | − | 0.995322i | \(-0.530801\pi\) | ||||
−0.0966138 | + | 0.995322i | \(0.530801\pi\) | |||||||
\(588\) | 3.53644 | 0.145840 | ||||||||
\(589\) | 26.0250 | 1.07234 | ||||||||
\(590\) | 3.14251 | 0.129375 | ||||||||
\(591\) | −3.81498 | −0.156927 | ||||||||
\(592\) | −1.53439 | −0.0630630 | ||||||||
\(593\) | −3.54913 | −0.145745 | −0.0728727 | − | 0.997341i | \(-0.523217\pi\) | ||||
−0.0728727 | + | 0.997341i | \(0.523217\pi\) | |||||||
\(594\) | −1.90868 | −0.0783140 | ||||||||
\(595\) | 5.84842 | 0.239762 | ||||||||
\(596\) | −4.15571 | −0.170224 | ||||||||
\(597\) | −1.86102 | −0.0761665 | ||||||||
\(598\) | 3.63141 | 0.148500 | ||||||||
\(599\) | −9.71087 | −0.396775 | −0.198388 | − | 0.980124i | \(-0.563570\pi\) | ||||
−0.198388 | + | 0.980124i | \(0.563570\pi\) | |||||||
\(600\) | 4.87539 | 0.199037 | ||||||||
\(601\) | 41.2484 | 1.68256 | 0.841280 | − | 0.540600i | \(-0.181803\pi\) | ||||
0.841280 | + | 0.540600i | \(0.181803\pi\) | |||||||
\(602\) | 2.74863 | 0.112026 | ||||||||
\(603\) | 10.7010 | 0.435779 | ||||||||
\(604\) | 3.76515 | 0.153202 | ||||||||
\(605\) | 23.1193 | 0.939934 | ||||||||
\(606\) | −0.354613 | −0.0144052 | ||||||||
\(607\) | 10.7455 | 0.436148 | 0.218074 | − | 0.975932i | \(-0.430023\pi\) | ||||
0.218074 | + | 0.975932i | \(0.430023\pi\) | |||||||
\(608\) | 2.79804 | 0.113476 | ||||||||
\(609\) | −0.108010 | −0.00437680 | ||||||||
\(610\) | 47.5150 | 1.92383 | ||||||||
\(611\) | −1.25259 | −0.0506745 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −42.8545 | −1.73088 | −0.865439 | − | 0.501015i | \(-0.832960\pi\) | ||||
−0.865439 | + | 0.501015i | \(0.832960\pi\) | |||||||
\(614\) | −15.1451 | −0.611207 | ||||||||
\(615\) | 38.7791 | 1.56372 | ||||||||
\(616\) | −3.55217 | −0.143121 | ||||||||
\(617\) | 12.5734 | 0.506186 | 0.253093 | − | 0.967442i | \(-0.418552\pi\) | ||||
0.253093 | + | 0.967442i | \(0.418552\pi\) | |||||||
\(618\) | −14.9092 | −0.599737 | ||||||||
\(619\) | −30.9707 | −1.24482 | −0.622409 | − | 0.782692i | \(-0.713846\pi\) | ||||
−0.622409 | + | 0.782692i | \(0.713846\pi\) | |||||||
\(620\) | 29.2291 | 1.17387 | ||||||||
\(621\) | −6.06631 | −0.243433 | ||||||||
\(622\) | 27.9857 | 1.12212 | ||||||||
\(623\) | −10.1521 | −0.406736 | ||||||||
\(624\) | 0.598620 | 0.0239640 | ||||||||
\(625\) | −25.6075 | −1.02430 | ||||||||
\(626\) | 18.6629 | 0.745918 | ||||||||
\(627\) | −5.34055 | −0.213281 | ||||||||
\(628\) | −11.4685 | −0.457642 | ||||||||
\(629\) | −1.53439 | −0.0611801 | ||||||||
\(630\) | −5.84842 | −0.233007 | ||||||||
\(631\) | 36.5580 | 1.45535 | 0.727676 | − | 0.685921i | \(-0.240601\pi\) | ||||
0.727676 | + | 0.685921i | \(0.240601\pi\) | |||||||
\(632\) | 11.9342 | 0.474718 | ||||||||
\(633\) | −7.91425 | −0.314563 | ||||||||
\(634\) | 5.33071 | 0.211710 | ||||||||
\(635\) | 51.2299 | 2.03300 | ||||||||
\(636\) | 7.58796 | 0.300882 | ||||||||
\(637\) | 2.11698 | 0.0838779 | ||||||||
\(638\) | −0.110773 | −0.00438556 | ||||||||
\(639\) | 1.96132 | 0.0775885 | ||||||||
\(640\) | 3.14251 | 0.124219 | ||||||||
\(641\) | −48.2160 | −1.90442 | −0.952208 | − | 0.305451i | \(-0.901193\pi\) | ||||
−0.952208 | + | 0.305451i | \(0.901193\pi\) | |||||||
\(642\) | 8.18027 | 0.322850 | ||||||||
\(643\) | −5.90006 | −0.232675 | −0.116338 | − | 0.993210i | \(-0.537115\pi\) | ||||
−0.116338 | + | 0.993210i | \(0.537115\pi\) | |||||||
\(644\) | −11.2898 | −0.444880 | ||||||||
\(645\) | 4.64121 | 0.182748 | ||||||||
\(646\) | 2.79804 | 0.110087 | ||||||||
\(647\) | −41.2781 | −1.62281 | −0.811406 | − | 0.584483i | \(-0.801297\pi\) | ||||
−0.811406 | + | 0.584483i | \(0.801297\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −1.90868 | −0.0749221 | ||||||||
\(650\) | 2.91851 | 0.114473 | ||||||||
\(651\) | −17.3101 | −0.678436 | ||||||||
\(652\) | −7.29454 | −0.285676 | ||||||||
\(653\) | 41.0822 | 1.60767 | 0.803834 | − | 0.594853i | \(-0.202790\pi\) | ||||
0.803834 | + | 0.594853i | \(0.202790\pi\) | |||||||
\(654\) | 16.3901 | 0.640903 | ||||||||
\(655\) | −67.5057 | −2.63767 | ||||||||
\(656\) | 12.3401 | 0.481802 | ||||||||
\(657\) | 1.82049 | 0.0710240 | ||||||||
\(658\) | 3.89422 | 0.151813 | ||||||||
\(659\) | −9.72224 | −0.378725 | −0.189362 | − | 0.981907i | \(-0.560642\pi\) | ||||
−0.189362 | + | 0.981907i | \(0.560642\pi\) | |||||||
\(660\) | −5.99804 | −0.233473 | ||||||||
\(661\) | 48.5684 | 1.88909 | 0.944547 | − | 0.328377i | \(-0.106502\pi\) | ||||
0.944547 | + | 0.328377i | \(0.106502\pi\) | |||||||
\(662\) | 6.46188 | 0.251148 | ||||||||
\(663\) | 0.598620 | 0.0232485 | ||||||||
\(664\) | −16.2029 | −0.628795 | ||||||||
\(665\) | −16.3641 | −0.634573 | ||||||||
\(666\) | 1.53439 | 0.0594564 | ||||||||
\(667\) | −0.352069 | −0.0136322 | ||||||||
\(668\) | −17.7398 | −0.686374 | ||||||||
\(669\) | 18.3666 | 0.710094 | ||||||||
\(670\) | 33.6281 | 1.29917 | ||||||||
\(671\) | −28.8593 | −1.11410 | ||||||||
\(672\) | −1.86106 | −0.0717921 | ||||||||
\(673\) | 30.9484 | 1.19297 | 0.596486 | − | 0.802624i | \(-0.296563\pi\) | ||||
0.596486 | + | 0.802624i | \(0.296563\pi\) | |||||||
\(674\) | −9.86479 | −0.379978 | ||||||||
\(675\) | −4.87539 | −0.187654 | ||||||||
\(676\) | −12.6417 | −0.486217 | ||||||||
\(677\) | −21.5578 | −0.828533 | −0.414267 | − | 0.910156i | \(-0.635962\pi\) | ||||
−0.414267 | + | 0.910156i | \(0.635962\pi\) | |||||||
\(678\) | 0.272035 | 0.0104474 | ||||||||
\(679\) | −3.49110 | −0.133976 | ||||||||
\(680\) | 3.14251 | 0.120510 | ||||||||
\(681\) | 4.93993 | 0.189299 | ||||||||
\(682\) | −17.7529 | −0.679795 | ||||||||
\(683\) | −48.8989 | −1.87107 | −0.935533 | − | 0.353240i | \(-0.885080\pi\) | ||||
−0.935533 | + | 0.353240i | \(0.885080\pi\) | |||||||
\(684\) | −2.79804 | −0.106986 | ||||||||
\(685\) | −21.1370 | −0.807604 | ||||||||
\(686\) | −19.6090 | −0.748675 | ||||||||
\(687\) | 5.78391 | 0.220670 | ||||||||
\(688\) | 1.47691 | 0.0563067 | ||||||||
\(689\) | 4.54230 | 0.173048 | ||||||||
\(690\) | −19.0635 | −0.725733 | ||||||||
\(691\) | −41.5151 | −1.57931 | −0.789654 | − | 0.613552i | \(-0.789740\pi\) | ||||
−0.789654 | + | 0.613552i | \(0.789740\pi\) | |||||||
\(692\) | 6.87128 | 0.261207 | ||||||||
\(693\) | 3.55217 | 0.134936 | ||||||||
\(694\) | −9.75055 | −0.370126 | ||||||||
\(695\) | −18.0604 | −0.685070 | ||||||||
\(696\) | −0.0580368 | −0.00219988 | ||||||||
\(697\) | 12.3401 | 0.467416 | ||||||||
\(698\) | −2.64990 | −0.100300 | ||||||||
\(699\) | 16.2536 | 0.614769 | ||||||||
\(700\) | −9.07342 | −0.342943 | ||||||||
\(701\) | 15.8052 | 0.596953 | 0.298476 | − | 0.954417i | \(-0.403522\pi\) | ||||
0.298476 | + | 0.954417i | \(0.403522\pi\) | |||||||
\(702\) | −0.598620 | −0.0225935 | ||||||||
\(703\) | 4.29329 | 0.161924 | ||||||||
\(704\) | −1.90868 | −0.0719360 | ||||||||
\(705\) | 6.57561 | 0.247652 | ||||||||
\(706\) | −0.895285 | −0.0336945 | ||||||||
\(707\) | 0.659958 | 0.0248203 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 2.50063 | 0.0939130 | 0.0469565 | − | 0.998897i | \(-0.485048\pi\) | ||||
0.0469565 | + | 0.998897i | \(0.485048\pi\) | |||||||
\(710\) | 6.16346 | 0.231311 | ||||||||
\(711\) | −11.9342 | −0.447568 | ||||||||
\(712\) | −5.45500 | −0.204435 | ||||||||
\(713\) | −56.4238 | −2.11309 | ||||||||
\(714\) | −1.86106 | −0.0696486 | ||||||||
\(715\) | −3.59055 | −0.134279 | ||||||||
\(716\) | −19.6437 | −0.734121 | ||||||||
\(717\) | −7.83325 | −0.292538 | ||||||||
\(718\) | −24.1820 | −0.902462 | ||||||||
\(719\) | 1.43858 | 0.0536500 | 0.0268250 | − | 0.999640i | \(-0.491460\pi\) | ||||
0.0268250 | + | 0.999640i | \(0.491460\pi\) | |||||||
\(720\) | −3.14251 | −0.117115 | ||||||||
\(721\) | 27.7471 | 1.03335 | ||||||||
\(722\) | 11.1710 | 0.415741 | ||||||||
\(723\) | 5.49476 | 0.204352 | ||||||||
\(724\) | 1.41315 | 0.0525193 | ||||||||
\(725\) | −0.282952 | −0.0105086 | ||||||||
\(726\) | −7.35695 | −0.273042 | ||||||||
\(727\) | −25.5769 | −0.948595 | −0.474297 | − | 0.880365i | \(-0.657298\pi\) | ||||
−0.474297 | + | 0.880365i | \(0.657298\pi\) | |||||||
\(728\) | −1.11407 | −0.0412902 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.72091 | 0.211740 | ||||||||
\(731\) | 1.47691 | 0.0546255 | ||||||||
\(732\) | −15.1201 | −0.558854 | ||||||||
\(733\) | −33.2668 | −1.22874 | −0.614368 | − | 0.789020i | \(-0.710589\pi\) | ||||
−0.614368 | + | 0.789020i | \(0.710589\pi\) | |||||||
\(734\) | 7.64468 | 0.282170 | ||||||||
\(735\) | −11.1133 | −0.409920 | ||||||||
\(736\) | −6.06631 | −0.223607 | ||||||||
\(737\) | −20.4248 | −0.752357 | ||||||||
\(738\) | −12.3401 | −0.454247 | ||||||||
\(739\) | 40.7673 | 1.49965 | 0.749824 | − | 0.661637i | \(-0.230138\pi\) | ||||
0.749824 | + | 0.661637i | \(0.230138\pi\) | |||||||
\(740\) | 4.82184 | 0.177254 | ||||||||
\(741\) | −1.67496 | −0.0615313 | ||||||||
\(742\) | −14.1217 | −0.518423 | ||||||||
\(743\) | −10.3232 | −0.378723 | −0.189362 | − | 0.981907i | \(-0.560642\pi\) | ||||
−0.189362 | + | 0.981907i | \(0.560642\pi\) | |||||||
\(744\) | −9.30117 | −0.340997 | ||||||||
\(745\) | 13.0594 | 0.478458 | ||||||||
\(746\) | −0.359609 | −0.0131662 | ||||||||
\(747\) | 16.2029 | 0.592833 | ||||||||
\(748\) | −1.90868 | −0.0697881 | ||||||||
\(749\) | −15.2240 | −0.556274 | ||||||||
\(750\) | 0.391588 | 0.0142988 | ||||||||
\(751\) | 13.2524 | 0.483585 | 0.241793 | − | 0.970328i | \(-0.422265\pi\) | ||||
0.241793 | + | 0.970328i | \(0.422265\pi\) | |||||||
\(752\) | 2.09247 | 0.0763045 | ||||||||
\(753\) | 11.2099 | 0.408510 | ||||||||
\(754\) | −0.0347420 | −0.00126523 | ||||||||
\(755\) | −11.8320 | −0.430612 | ||||||||
\(756\) | 1.86106 | 0.0676863 | ||||||||
\(757\) | −35.5662 | −1.29268 | −0.646338 | − | 0.763051i | \(-0.723700\pi\) | ||||
−0.646338 | + | 0.763051i | \(0.723700\pi\) | |||||||
\(758\) | −26.7145 | −0.970316 | ||||||||
\(759\) | 11.5786 | 0.420277 | ||||||||
\(760\) | −8.79288 | −0.318951 | ||||||||
\(761\) | 6.12212 | 0.221927 | 0.110963 | − | 0.993825i | \(-0.464606\pi\) | ||||
0.110963 | + | 0.993825i | \(0.464606\pi\) | |||||||
\(762\) | −16.3022 | −0.590567 | ||||||||
\(763\) | −30.5030 | −1.10428 | ||||||||
\(764\) | 4.57387 | 0.165477 | ||||||||
\(765\) | −3.14251 | −0.113618 | ||||||||
\(766\) | 6.58131 | 0.237792 | ||||||||
\(767\) | −0.598620 | −0.0216149 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 20.7532 | 0.748380 | 0.374190 | − | 0.927352i | \(-0.377921\pi\) | ||||
0.374190 | + | 0.927352i | \(0.377921\pi\) | |||||||
\(770\) | 11.1627 | 0.402277 | ||||||||
\(771\) | 13.6981 | 0.493326 | ||||||||
\(772\) | 24.6726 | 0.887988 | ||||||||
\(773\) | −11.0940 | −0.399022 | −0.199511 | − | 0.979896i | \(-0.563935\pi\) | ||||
−0.199511 | + | 0.979896i | \(0.563935\pi\) | |||||||
\(774\) | −1.47691 | −0.0530865 | ||||||||
\(775\) | −45.3468 | −1.62891 | ||||||||
\(776\) | −1.87586 | −0.0673394 | ||||||||
\(777\) | −2.85560 | −0.102444 | ||||||||
\(778\) | 39.1368 | 1.40312 | ||||||||
\(779\) | −34.5282 | −1.23710 | ||||||||
\(780\) | −1.88117 | −0.0673568 | ||||||||
\(781\) | −3.74352 | −0.133954 | ||||||||
\(782\) | −6.06631 | −0.216931 | ||||||||
\(783\) | 0.0580368 | 0.00207407 | ||||||||
\(784\) | −3.53644 | −0.126301 | ||||||||
\(785\) | 36.0399 | 1.28632 | ||||||||
\(786\) | 21.4814 | 0.766218 | ||||||||
\(787\) | −43.6838 | −1.55716 | −0.778579 | − | 0.627546i | \(-0.784059\pi\) | ||||
−0.778579 | + | 0.627546i | \(0.784059\pi\) | |||||||
\(788\) | 3.81498 | 0.135903 | ||||||||
\(789\) | 18.5784 | 0.661410 | ||||||||
\(790\) | −37.5035 | −1.33431 | ||||||||
\(791\) | −0.506274 | −0.0180010 | ||||||||
\(792\) | 1.90868 | 0.0678219 | ||||||||
\(793\) | −9.05118 | −0.321417 | ||||||||
\(794\) | −19.8735 | −0.705283 | ||||||||
\(795\) | −23.8453 | −0.845704 | ||||||||
\(796\) | 1.86102 | 0.0659621 | ||||||||
\(797\) | 30.6357 | 1.08517 | 0.542586 | − | 0.840001i | \(-0.317445\pi\) | ||||
0.542586 | + | 0.840001i | \(0.317445\pi\) | |||||||
\(798\) | 5.20733 | 0.184338 | ||||||||
\(799\) | 2.09247 | 0.0740262 | ||||||||
\(800\) | −4.87539 | −0.172371 | ||||||||
\(801\) | 5.45500 | 0.192743 | ||||||||
\(802\) | 23.6493 | 0.835086 | ||||||||
\(803\) | −3.47472 | −0.122620 | ||||||||
\(804\) | −10.7010 | −0.377396 | ||||||||
\(805\) | 35.4783 | 1.25045 | ||||||||
\(806\) | −5.56787 | −0.196120 | ||||||||
\(807\) | −28.1773 | −0.991889 | ||||||||
\(808\) | 0.354613 | 0.0124752 | ||||||||
\(809\) | −34.8608 | −1.22564 | −0.612820 | − | 0.790222i | \(-0.709965\pi\) | ||||
−0.612820 | + | 0.790222i | \(0.709965\pi\) | |||||||
\(810\) | 3.14251 | 0.110417 | ||||||||
\(811\) | −44.8939 | −1.57644 | −0.788220 | − | 0.615394i | \(-0.788997\pi\) | ||||
−0.788220 | + | 0.615394i | \(0.788997\pi\) | |||||||
\(812\) | 0.108010 | 0.00379042 | ||||||||
\(813\) | −15.3524 | −0.538431 | ||||||||
\(814\) | −2.92865 | −0.102649 | ||||||||
\(815\) | 22.9232 | 0.802964 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −4.13246 | −0.144576 | ||||||||
\(818\) | 11.5307 | 0.403162 | ||||||||
\(819\) | 1.11407 | 0.0389288 | ||||||||
\(820\) | −38.7791 | −1.35422 | ||||||||
\(821\) | −30.2437 | −1.05551 | −0.527756 | − | 0.849396i | \(-0.676967\pi\) | ||||
−0.527756 | + | 0.849396i | \(0.676967\pi\) | |||||||
\(822\) | 6.72615 | 0.234602 | ||||||||
\(823\) | 5.02773 | 0.175256 | 0.0876279 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876279 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(824\) | 14.9092 | 0.519388 | ||||||||
\(825\) | 9.30554 | 0.323977 | ||||||||
\(826\) | 1.86106 | 0.0647547 | ||||||||
\(827\) | −15.8411 | −0.550848 | −0.275424 | − | 0.961323i | \(-0.588818\pi\) | ||||
−0.275424 | + | 0.961323i | \(0.588818\pi\) | |||||||
\(828\) | 6.06631 | 0.210819 | ||||||||
\(829\) | 35.0633 | 1.21780 | 0.608899 | − | 0.793248i | \(-0.291612\pi\) | ||||
0.608899 | + | 0.793248i | \(0.291612\pi\) | |||||||
\(830\) | 50.9178 | 1.76738 | ||||||||
\(831\) | 7.29924 | 0.253208 | ||||||||
\(832\) | −0.598620 | −0.0207534 | ||||||||
\(833\) | −3.53644 | −0.122530 | ||||||||
\(834\) | 5.74712 | 0.199006 | ||||||||
\(835\) | 55.7476 | 1.92923 | ||||||||
\(836\) | 5.34055 | 0.184707 | ||||||||
\(837\) | 9.30117 | 0.321496 | ||||||||
\(838\) | 6.47921 | 0.223821 | ||||||||
\(839\) | 28.9036 | 0.997863 | 0.498931 | − | 0.866641i | \(-0.333726\pi\) | ||||
0.498931 | + | 0.866641i | \(0.333726\pi\) | |||||||
\(840\) | 5.84842 | 0.201790 | ||||||||
\(841\) | −28.9966 | −0.999884 | ||||||||
\(842\) | 1.57699 | 0.0543468 | ||||||||
\(843\) | 10.2946 | 0.354566 | ||||||||
\(844\) | 7.91425 | 0.272420 | ||||||||
\(845\) | 39.7266 | 1.36664 | ||||||||
\(846\) | −2.09247 | −0.0719406 | ||||||||
\(847\) | 13.6918 | 0.470455 | ||||||||
\(848\) | −7.58796 | −0.260572 | ||||||||
\(849\) | 11.1593 | 0.382986 | ||||||||
\(850\) | −4.87539 | −0.167225 | ||||||||
\(851\) | −9.30809 | −0.319077 | ||||||||
\(852\) | −1.96132 | −0.0671936 | ||||||||
\(853\) | −51.9757 | −1.77961 | −0.889807 | − | 0.456337i | \(-0.849161\pi\) | ||||
−0.889807 | + | 0.456337i | \(0.849161\pi\) | |||||||
\(854\) | 28.1394 | 0.962912 | ||||||||
\(855\) | 8.79288 | 0.300710 | ||||||||
\(856\) | −8.18027 | −0.279596 | ||||||||
\(857\) | −15.1236 | −0.516612 | −0.258306 | − | 0.966063i | \(-0.583164\pi\) | ||||
−0.258306 | + | 0.966063i | \(0.583164\pi\) | |||||||
\(858\) | 1.14257 | 0.0390068 | ||||||||
\(859\) | −23.2044 | −0.791724 | −0.395862 | − | 0.918310i | \(-0.629554\pi\) | ||||
−0.395862 | + | 0.918310i | \(0.629554\pi\) | |||||||
\(860\) | −4.64121 | −0.158264 | ||||||||
\(861\) | 22.9658 | 0.782673 | ||||||||
\(862\) | −19.5195 | −0.664837 | ||||||||
\(863\) | −6.78838 | −0.231079 | −0.115540 | − | 0.993303i | \(-0.536860\pi\) | ||||
−0.115540 | + | 0.993303i | \(0.536860\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −21.5931 | −0.734188 | ||||||||
\(866\) | 23.7483 | 0.807001 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 17.3101 | 0.587542 | ||||||||
\(869\) | 22.7786 | 0.772710 | ||||||||
\(870\) | 0.182381 | 0.00618331 | ||||||||
\(871\) | −6.40585 | −0.217054 | ||||||||
\(872\) | −16.3901 | −0.555039 | ||||||||
\(873\) | 1.87586 | 0.0634882 | ||||||||
\(874\) | 16.9738 | 0.574147 | ||||||||
\(875\) | −0.728770 | −0.0246369 | ||||||||
\(876\) | −1.82049 | −0.0615086 | ||||||||
\(877\) | 22.4067 | 0.756621 | 0.378310 | − | 0.925679i | \(-0.376505\pi\) | ||||
0.378310 | + | 0.925679i | \(0.376505\pi\) | |||||||
\(878\) | 35.8678 | 1.21048 | ||||||||
\(879\) | 3.53990 | 0.119398 | ||||||||
\(880\) | 5.99804 | 0.202194 | ||||||||
\(881\) | 34.1130 | 1.14930 | 0.574649 | − | 0.818400i | \(-0.305139\pi\) | ||||
0.574649 | + | 0.818400i | \(0.305139\pi\) | |||||||
\(882\) | 3.53644 | 0.119078 | ||||||||
\(883\) | −22.8326 | −0.768378 | −0.384189 | − | 0.923254i | \(-0.625519\pi\) | ||||
−0.384189 | + | 0.923254i | \(0.625519\pi\) | |||||||
\(884\) | −0.598620 | −0.0201338 | ||||||||
\(885\) | 3.14251 | 0.105634 | ||||||||
\(886\) | 30.7025 | 1.03147 | ||||||||
\(887\) | 12.2213 | 0.410350 | 0.205175 | − | 0.978725i | \(-0.434224\pi\) | ||||
0.205175 | + | 0.978725i | \(0.434224\pi\) | |||||||
\(888\) | −1.53439 | −0.0514908 | ||||||||
\(889\) | 30.3395 | 1.01755 | ||||||||
\(890\) | 17.1424 | 0.574615 | ||||||||
\(891\) | −1.90868 | −0.0639431 | ||||||||
\(892\) | −18.3666 | −0.614959 | ||||||||
\(893\) | −5.85481 | −0.195924 | ||||||||
\(894\) | −4.15571 | −0.138988 | ||||||||
\(895\) | 61.7307 | 2.06343 | ||||||||
\(896\) | 1.86106 | 0.0621738 | ||||||||
\(897\) | 3.63141 | 0.121249 | ||||||||
\(898\) | 3.86029 | 0.128820 | ||||||||
\(899\) | 0.539810 | 0.0180037 | ||||||||
\(900\) | 4.87539 | 0.162513 | ||||||||
\(901\) | −7.58796 | −0.252792 | ||||||||
\(902\) | 23.5533 | 0.784241 | ||||||||
\(903\) | 2.74863 | 0.0914686 | ||||||||
\(904\) | −0.272035 | −0.00904774 | ||||||||
\(905\) | −4.44084 | −0.147619 | ||||||||
\(906\) | 3.76515 | 0.125089 | ||||||||
\(907\) | −4.63566 | −0.153925 | −0.0769623 | − | 0.997034i | \(-0.524522\pi\) | ||||
−0.0769623 | + | 0.997034i | \(0.524522\pi\) | |||||||
\(908\) | −4.93993 | −0.163937 | ||||||||
\(909\) | −0.354613 | −0.0117618 | ||||||||
\(910\) | 3.50098 | 0.116056 | ||||||||
\(911\) | −41.8449 | −1.38638 | −0.693192 | − | 0.720753i | \(-0.743796\pi\) | ||||
−0.693192 | + | 0.720753i | \(0.743796\pi\) | |||||||
\(912\) | 2.79804 | 0.0926524 | ||||||||
\(913\) | −30.9261 | −1.02350 | ||||||||
\(914\) | 30.6656 | 1.01433 | ||||||||
\(915\) | 47.5150 | 1.57080 | ||||||||
\(916\) | −5.78391 | −0.191106 | ||||||||
\(917\) | −39.9784 | −1.32020 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 14.9079 | 0.491765 | 0.245882 | − | 0.969300i | \(-0.420922\pi\) | ||||
0.245882 | + | 0.969300i | \(0.420922\pi\) | |||||||
\(920\) | 19.0635 | 0.628504 | ||||||||
\(921\) | −15.1451 | −0.499049 | ||||||||
\(922\) | −33.1352 | −1.09125 | ||||||||
\(923\) | −1.17408 | −0.0386454 | ||||||||
\(924\) | −3.55217 | −0.116858 | ||||||||
\(925\) | −7.48075 | −0.245966 | ||||||||
\(926\) | 26.9844 | 0.886763 | ||||||||
\(927\) | −14.9092 | −0.489684 | ||||||||
\(928\) | 0.0580368 | 0.00190515 | ||||||||
\(929\) | 7.90774 | 0.259444 | 0.129722 | − | 0.991550i | \(-0.458591\pi\) | ||||
0.129722 | + | 0.991550i | \(0.458591\pi\) | |||||||
\(930\) | 29.2291 | 0.958458 | ||||||||
\(931\) | 9.89509 | 0.324299 | ||||||||
\(932\) | −16.2536 | −0.532405 | ||||||||
\(933\) | 27.9857 | 0.916210 | ||||||||
\(934\) | −19.8835 | −0.650607 | ||||||||
\(935\) | 5.99804 | 0.196157 | ||||||||
\(936\) | 0.598620 | 0.0195665 | ||||||||
\(937\) | 18.9798 | 0.620041 | 0.310021 | − | 0.950730i | \(-0.399664\pi\) | ||||
0.310021 | + | 0.950730i | \(0.399664\pi\) | |||||||
\(938\) | 19.9153 | 0.650257 | ||||||||
\(939\) | 18.6629 | 0.609040 | ||||||||
\(940\) | −6.57561 | −0.214473 | ||||||||
\(941\) | 7.83769 | 0.255501 | 0.127751 | − | 0.991806i | \(-0.459224\pi\) | ||||
0.127751 | + | 0.991806i | \(0.459224\pi\) | |||||||
\(942\) | −11.4685 | −0.373663 | ||||||||
\(943\) | 74.8591 | 2.43775 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | −5.84842 | −0.190249 | ||||||||
\(946\) | 2.81895 | 0.0916518 | ||||||||
\(947\) | 46.2923 | 1.50430 | 0.752150 | − | 0.658993i | \(-0.229017\pi\) | ||||
0.752150 | + | 0.658993i | \(0.229017\pi\) | |||||||
\(948\) | 11.9342 | 0.387606 | ||||||||
\(949\) | −1.08978 | −0.0353758 | ||||||||
\(950\) | 13.6415 | 0.442590 | ||||||||
\(951\) | 5.33071 | 0.172860 | ||||||||
\(952\) | 1.86106 | 0.0603175 | ||||||||
\(953\) | 13.3168 | 0.431373 | 0.215687 | − | 0.976463i | \(-0.430801\pi\) | ||||
0.215687 | + | 0.976463i | \(0.430801\pi\) | |||||||
\(954\) | 7.58796 | 0.245669 | ||||||||
\(955\) | −14.3734 | −0.465113 | ||||||||
\(956\) | 7.83325 | 0.253345 | ||||||||
\(957\) | −0.110773 | −0.00358080 | ||||||||
\(958\) | −3.62156 | −0.117007 | ||||||||
\(959\) | −12.5178 | −0.404221 | ||||||||
\(960\) | 3.14251 | 0.101424 | ||||||||
\(961\) | 55.5118 | 1.79070 | ||||||||
\(962\) | −0.918517 | −0.0296142 | ||||||||
\(963\) | 8.18027 | 0.263606 | ||||||||
\(964\) | −5.49476 | −0.176974 | ||||||||
\(965\) | −77.5341 | −2.49591 | ||||||||
\(966\) | −11.2898 | −0.363243 | ||||||||
\(967\) | −37.2363 | −1.19744 | −0.598719 | − | 0.800959i | \(-0.704324\pi\) | ||||
−0.598719 | + | 0.800959i | \(0.704324\pi\) | |||||||
\(968\) | 7.35695 | 0.236461 | ||||||||
\(969\) | 2.79804 | 0.0898860 | ||||||||
\(970\) | 5.89491 | 0.189274 | ||||||||
\(971\) | 43.0354 | 1.38107 | 0.690536 | − | 0.723298i | \(-0.257375\pi\) | ||||
0.690536 | + | 0.723298i | \(0.257375\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −10.6958 | −0.342890 | ||||||||
\(974\) | 3.29761 | 0.105662 | ||||||||
\(975\) | 2.91851 | 0.0934670 | ||||||||
\(976\) | 15.1201 | 0.483982 | ||||||||
\(977\) | −24.7135 | −0.790653 | −0.395327 | − | 0.918541i | \(-0.629369\pi\) | ||||
−0.395327 | + | 0.918541i | \(0.629369\pi\) | |||||||
\(978\) | −7.29454 | −0.233254 | ||||||||
\(979\) | −10.4118 | −0.332764 | ||||||||
\(980\) | 11.1133 | 0.355001 | ||||||||
\(981\) | 16.3901 | 0.523295 | ||||||||
\(982\) | −3.68978 | −0.117746 | ||||||||
\(983\) | −4.57592 | −0.145949 | −0.0729745 | − | 0.997334i | \(-0.523249\pi\) | ||||
−0.0729745 | + | 0.997334i | \(0.523249\pi\) | |||||||
\(984\) | 12.3401 | 0.393389 | ||||||||
\(985\) | −11.9886 | −0.381989 | ||||||||
\(986\) | 0.0580368 | 0.00184827 | ||||||||
\(987\) | 3.89422 | 0.123954 | ||||||||
\(988\) | 1.67496 | 0.0532877 | ||||||||
\(989\) | 8.95940 | 0.284892 | ||||||||
\(990\) | −5.99804 | −0.190630 | ||||||||
\(991\) | −35.6719 | −1.13315 | −0.566577 | − | 0.824009i | \(-0.691733\pi\) | ||||
−0.566577 | + | 0.824009i | \(0.691733\pi\) | |||||||
\(992\) | 9.30117 | 0.295312 | ||||||||
\(993\) | 6.46188 | 0.205061 | ||||||||
\(994\) | 3.65014 | 0.115775 | ||||||||
\(995\) | −5.84828 | −0.185403 | ||||||||
\(996\) | −16.2029 | −0.513409 | ||||||||
\(997\) | −17.3650 | −0.549956 | −0.274978 | − | 0.961451i | \(-0.588671\pi\) | ||||
−0.274978 | + | 0.961451i | \(0.588671\pi\) | |||||||
\(998\) | −20.7578 | −0.657076 | ||||||||
\(999\) | 1.53439 | 0.0485460 |
(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 | 6018.2.a.u.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.u.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |