Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 | ||||||||
\(3\) | −1.36333 | −0.787118 | −0.393559 | − | 0.919299i | \(-0.628756\pi\) | ||||
−0.393559 | + | 0.919299i | \(0.628756\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.363328 | 0.162485 | 0.0812427 | − | 0.996694i | \(-0.474111\pi\) | ||||
0.0812427 | + | 0.996694i | \(0.474111\pi\) | |||||||
\(6\) | −1.36333 | −0.556576 | ||||||||
\(7\) | 2.14134 | 0.809349 | 0.404674 | − | 0.914461i | \(-0.367385\pi\) | ||||
0.404674 | + | 0.914461i | \(0.367385\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.14134 | −0.380445 | ||||||||
\(10\) | 0.363328 | 0.114894 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.36333 | −0.393559 | ||||||||
\(13\) | −3.14134 | −0.871250 | −0.435625 | − | 0.900128i | \(-0.643473\pi\) | ||||
−0.435625 | + | 0.900128i | \(0.643473\pi\) | |||||||
\(14\) | 2.14134 | 0.572296 | ||||||||
\(15\) | −0.495336 | −0.127895 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.14134 | 0.276815 | 0.138407 | − | 0.990375i | \(-0.455802\pi\) | ||||
0.138407 | + | 0.990375i | \(0.455802\pi\) | |||||||
\(18\) | −1.14134 | −0.269016 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.363328 | 0.0812427 | ||||||||
\(21\) | −2.91934 | −0.637053 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.14134 | −0.446499 | −0.223250 | − | 0.974761i | \(-0.571667\pi\) | ||||
−0.223250 | + | 0.974761i | \(0.571667\pi\) | |||||||
\(24\) | −1.36333 | −0.278288 | ||||||||
\(25\) | −4.86799 | −0.973599 | ||||||||
\(26\) | −3.14134 | −0.616067 | ||||||||
\(27\) | 5.64600 | 1.08657 | ||||||||
\(28\) | 2.14134 | 0.404674 | ||||||||
\(29\) | −1.77801 | −0.330168 | −0.165084 | − | 0.986280i | \(-0.552789\pi\) | ||||
−0.165084 | + | 0.986280i | \(0.552789\pi\) | |||||||
\(30\) | −0.495336 | −0.0904355 | ||||||||
\(31\) | 7.00933 | 1.25891 | 0.629456 | − | 0.777036i | \(-0.283278\pi\) | ||||
0.629456 | + | 0.777036i | \(0.283278\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.14134 | 0.195738 | ||||||||
\(35\) | 0.778008 | 0.131507 | ||||||||
\(36\) | −1.14134 | −0.190223 | ||||||||
\(37\) | −9.77801 | −1.60749 | −0.803747 | − | 0.594971i | \(-0.797164\pi\) | ||||
−0.803747 | + | 0.594971i | \(0.797164\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 4.28267 | 0.685776 | ||||||||
\(40\) | 0.363328 | 0.0574472 | ||||||||
\(41\) | −7.91934 | −1.23679 | −0.618397 | − | 0.785866i | \(-0.712218\pi\) | ||||
−0.618397 | + | 0.785866i | \(0.712218\pi\) | |||||||
\(42\) | −2.91934 | −0.450465 | ||||||||
\(43\) | −4.28267 | −0.653101 | −0.326551 | − | 0.945180i | \(-0.605886\pi\) | ||||
−0.326551 | + | 0.945180i | \(0.605886\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.414680 | −0.0618168 | ||||||||
\(46\) | −2.14134 | −0.315723 | ||||||||
\(47\) | −7.59465 | −1.10779 | −0.553897 | − | 0.832585i | \(-0.686860\pi\) | ||||
−0.553897 | + | 0.832585i | \(0.686860\pi\) | |||||||
\(48\) | −1.36333 | −0.196779 | ||||||||
\(49\) | −2.41468 | −0.344954 | ||||||||
\(50\) | −4.86799 | −0.688438 | ||||||||
\(51\) | −1.55602 | −0.217886 | ||||||||
\(52\) | −3.14134 | −0.435625 | ||||||||
\(53\) | 10.7873 | 1.48175 | 0.740877 | − | 0.671640i | \(-0.234410\pi\) | ||||
0.740877 | + | 0.671640i | \(0.234410\pi\) | |||||||
\(54\) | 5.64600 | 0.768323 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.14134 | 0.286148 | ||||||||
\(57\) | 1.36333 | 0.180577 | ||||||||
\(58\) | −1.77801 | −0.233464 | ||||||||
\(59\) | −1.08066 | −0.140689 | −0.0703447 | − | 0.997523i | \(-0.522410\pi\) | ||||
−0.0703447 | + | 0.997523i | \(0.522410\pi\) | |||||||
\(60\) | −0.495336 | −0.0639476 | ||||||||
\(61\) | −8.51399 | −1.09011 | −0.545053 | − | 0.838402i | \(-0.683490\pi\) | ||||
−0.545053 | + | 0.838402i | \(0.683490\pi\) | |||||||
\(62\) | 7.00933 | 0.890186 | ||||||||
\(63\) | −2.44398 | −0.307913 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.14134 | −0.141565 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.56534 | 1.04642 | 0.523212 | − | 0.852203i | \(-0.324734\pi\) | ||||
0.523212 | + | 0.852203i | \(0.324734\pi\) | |||||||
\(68\) | 1.14134 | 0.138407 | ||||||||
\(69\) | 2.91934 | 0.351448 | ||||||||
\(70\) | 0.778008 | 0.0929897 | ||||||||
\(71\) | 3.50466 | 0.415927 | 0.207964 | − | 0.978137i | \(-0.433316\pi\) | ||||
0.207964 | + | 0.978137i | \(0.433316\pi\) | |||||||
\(72\) | −1.14134 | −0.134508 | ||||||||
\(73\) | 11.7360 | 1.37359 | 0.686797 | − | 0.726850i | \(-0.259016\pi\) | ||||
0.686797 | + | 0.726850i | \(0.259016\pi\) | |||||||
\(74\) | −9.77801 | −1.13667 | ||||||||
\(75\) | 6.63667 | 0.766337 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.28267 | 0.484917 | ||||||||
\(79\) | 0.778008 | 0.0875327 | 0.0437664 | − | 0.999042i | \(-0.486064\pi\) | ||||
0.0437664 | + | 0.999042i | \(0.486064\pi\) | |||||||
\(80\) | 0.363328 | 0.0406213 | ||||||||
\(81\) | −4.27334 | −0.474816 | ||||||||
\(82\) | −7.91934 | −0.874545 | ||||||||
\(83\) | −0.778008 | −0.0853975 | −0.0426987 | − | 0.999088i | \(-0.513596\pi\) | ||||
−0.0426987 | + | 0.999088i | \(0.513596\pi\) | |||||||
\(84\) | −2.91934 | −0.318527 | ||||||||
\(85\) | 0.414680 | 0.0449783 | ||||||||
\(86\) | −4.28267 | −0.461812 | ||||||||
\(87\) | 2.42401 | 0.259881 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.20202 | −0.869412 | −0.434706 | − | 0.900572i | \(-0.643148\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(90\) | −0.414680 | −0.0437111 | ||||||||
\(91\) | −6.72666 | −0.705145 | ||||||||
\(92\) | −2.14134 | −0.223250 | ||||||||
\(93\) | −9.55602 | −0.990913 | ||||||||
\(94\) | −7.59465 | −0.783328 | ||||||||
\(95\) | −0.363328 | −0.0372767 | ||||||||
\(96\) | −1.36333 | −0.139144 | ||||||||
\(97\) | −1.86799 | −0.189666 | −0.0948330 | − | 0.995493i | \(-0.530232\pi\) | ||||
−0.0948330 | + | 0.995493i | \(0.530232\pi\) | |||||||
\(98\) | −2.41468 | −0.243919 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.86799 | −0.486799 | ||||||||
\(101\) | −10.0700 | −1.00200 | −0.501002 | − | 0.865446i | \(-0.667035\pi\) | ||||
−0.501002 | + | 0.865446i | \(0.667035\pi\) | |||||||
\(102\) | −1.55602 | −0.154069 | ||||||||
\(103\) | −17.3434 | −1.70889 | −0.854446 | − | 0.519541i | \(-0.826103\pi\) | ||||
−0.854446 | + | 0.519541i | \(0.826103\pi\) | |||||||
\(104\) | −3.14134 | −0.308033 | ||||||||
\(105\) | −1.06068 | −0.103512 | ||||||||
\(106\) | 10.7873 | 1.04776 | ||||||||
\(107\) | −13.6460 | −1.31921 | −0.659604 | − | 0.751613i | \(-0.729276\pi\) | ||||
−0.659604 | + | 0.751613i | \(0.729276\pi\) | |||||||
\(108\) | 5.64600 | 0.543287 | ||||||||
\(109\) | 5.33402 | 0.510907 | 0.255453 | − | 0.966821i | \(-0.417775\pi\) | ||||
0.255453 | + | 0.966821i | \(0.417775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.3306 | 1.26529 | ||||||||
\(112\) | 2.14134 | 0.202337 | ||||||||
\(113\) | −14.3633 | −1.35119 | −0.675594 | − | 0.737274i | \(-0.736113\pi\) | ||||
−0.675594 | + | 0.737274i | \(0.736113\pi\) | |||||||
\(114\) | 1.36333 | 0.127687 | ||||||||
\(115\) | −0.778008 | −0.0725496 | ||||||||
\(116\) | −1.77801 | −0.165084 | ||||||||
\(117\) | 3.58532 | 0.331463 | ||||||||
\(118\) | −1.08066 | −0.0994824 | ||||||||
\(119\) | 2.44398 | 0.224040 | ||||||||
\(120\) | −0.495336 | −0.0452178 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.51399 | −0.770821 | ||||||||
\(123\) | 10.7967 | 0.973503 | ||||||||
\(124\) | 7.00933 | 0.629456 | ||||||||
\(125\) | −3.58532 | −0.320681 | ||||||||
\(126\) | −2.44398 | −0.217727 | ||||||||
\(127\) | −2.44398 | −0.216869 | −0.108434 | − | 0.994104i | \(-0.534584\pi\) | ||||
−0.108434 | + | 0.994104i | \(0.534584\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.83869 | 0.514068 | ||||||||
\(130\) | −1.14134 | −0.100102 | ||||||||
\(131\) | −0.707999 | −0.0618582 | −0.0309291 | − | 0.999522i | \(-0.509847\pi\) | ||||
−0.0309291 | + | 0.999522i | \(0.509847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.14134 | −0.185677 | ||||||||
\(134\) | 8.56534 | 0.739933 | ||||||||
\(135\) | 2.05135 | 0.176552 | ||||||||
\(136\) | 1.14134 | 0.0978688 | ||||||||
\(137\) | 6.28267 | 0.536765 | 0.268382 | − | 0.963312i | \(-0.413511\pi\) | ||||
0.268382 | + | 0.963312i | \(0.413511\pi\) | |||||||
\(138\) | 2.91934 | 0.248511 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0.778008 | 0.0657537 | ||||||||
\(141\) | 10.3540 | 0.871964 | ||||||||
\(142\) | 3.50466 | 0.294105 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.14134 | −0.0951113 | ||||||||
\(145\) | −0.646000 | −0.0536474 | ||||||||
\(146\) | 11.7360 | 0.971277 | ||||||||
\(147\) | 3.29200 | 0.271520 | ||||||||
\(148\) | −9.77801 | −0.803747 | ||||||||
\(149\) | 11.1600 | 0.914262 | 0.457131 | − | 0.889399i | \(-0.348877\pi\) | ||||
0.457131 | + | 0.889399i | \(0.348877\pi\) | |||||||
\(150\) | 6.63667 | 0.541882 | ||||||||
\(151\) | −13.8060 | −1.12352 | −0.561758 | − | 0.827302i | \(-0.689875\pi\) | ||||
−0.561758 | + | 0.827302i | \(0.689875\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −1.30265 | −0.105313 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.54669 | 0.204555 | ||||||||
\(156\) | 4.28267 | 0.342888 | ||||||||
\(157\) | 15.8060 | 1.26146 | 0.630728 | − | 0.776004i | \(-0.282756\pi\) | ||||
0.630728 | + | 0.776004i | \(0.282756\pi\) | |||||||
\(158\) | 0.778008 | 0.0618950 | ||||||||
\(159\) | −14.7067 | −1.16632 | ||||||||
\(160\) | 0.363328 | 0.0287236 | ||||||||
\(161\) | −4.58532 | −0.361374 | ||||||||
\(162\) | −4.27334 | −0.335746 | ||||||||
\(163\) | −3.71733 | −0.291164 | −0.145582 | − | 0.989346i | \(-0.546505\pi\) | ||||
−0.145582 | + | 0.989346i | \(0.546505\pi\) | |||||||
\(164\) | −7.91934 | −0.618397 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.778008 | −0.0603851 | ||||||||
\(167\) | 5.27334 | 0.408064 | 0.204032 | − | 0.978964i | \(-0.434595\pi\) | ||||
0.204032 | + | 0.978964i | \(0.434595\pi\) | |||||||
\(168\) | −2.91934 | −0.225232 | ||||||||
\(169\) | −3.13201 | −0.240924 | ||||||||
\(170\) | 0.414680 | 0.0318045 | ||||||||
\(171\) | 1.14134 | 0.0872802 | ||||||||
\(172\) | −4.28267 | −0.326551 | ||||||||
\(173\) | 11.4660 | 0.871746 | 0.435873 | − | 0.900008i | \(-0.356440\pi\) | ||||
0.435873 | + | 0.900008i | \(0.356440\pi\) | |||||||
\(174\) | 2.42401 | 0.183764 | ||||||||
\(175\) | −10.4240 | −0.787981 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.47329 | 0.110739 | ||||||||
\(178\) | −8.20202 | −0.614767 | ||||||||
\(179\) | −0.900687 | −0.0673205 | −0.0336602 | − | 0.999433i | \(-0.510716\pi\) | ||||
−0.0336602 | + | 0.999433i | \(0.510716\pi\) | |||||||
\(180\) | −0.414680 | −0.0309084 | ||||||||
\(181\) | −16.6974 | −1.24110 | −0.620552 | − | 0.784165i | \(-0.713091\pi\) | ||||
−0.620552 | + | 0.784165i | \(0.713091\pi\) | |||||||
\(182\) | −6.72666 | −0.498613 | ||||||||
\(183\) | 11.6074 | 0.858041 | ||||||||
\(184\) | −2.14134 | −0.157861 | ||||||||
\(185\) | −3.55263 | −0.261194 | ||||||||
\(186\) | −9.55602 | −0.700681 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.59465 | −0.553897 | ||||||||
\(189\) | 12.0900 | 0.879417 | ||||||||
\(190\) | −0.363328 | −0.0263586 | ||||||||
\(191\) | −3.87732 | −0.280553 | −0.140277 | − | 0.990112i | \(-0.544799\pi\) | ||||
−0.140277 | + | 0.990112i | \(0.544799\pi\) | |||||||
\(192\) | −1.36333 | −0.0983897 | ||||||||
\(193\) | 5.32131 | 0.383036 | 0.191518 | − | 0.981489i | \(-0.438659\pi\) | ||||
0.191518 | + | 0.981489i | \(0.438659\pi\) | |||||||
\(194\) | −1.86799 | −0.134114 | ||||||||
\(195\) | 1.55602 | 0.111429 | ||||||||
\(196\) | −2.41468 | −0.172477 | ||||||||
\(197\) | −14.3306 | −1.02102 | −0.510508 | − | 0.859873i | \(-0.670543\pi\) | ||||
−0.510508 | + | 0.859873i | \(0.670543\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.83869 | 0.413894 | 0.206947 | − | 0.978352i | \(-0.433647\pi\) | ||||
0.206947 | + | 0.978352i | \(0.433647\pi\) | |||||||
\(200\) | −4.86799 | −0.344219 | ||||||||
\(201\) | −11.6774 | −0.823659 | ||||||||
\(202\) | −10.0700 | −0.708523 | ||||||||
\(203\) | −3.80731 | −0.267221 | ||||||||
\(204\) | −1.55602 | −0.108943 | ||||||||
\(205\) | −2.87732 | −0.200961 | ||||||||
\(206\) | −17.3434 | −1.20837 | ||||||||
\(207\) | 2.44398 | 0.169869 | ||||||||
\(208\) | −3.14134 | −0.217812 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.06068 | −0.0731939 | ||||||||
\(211\) | 9.74870 | 0.671128 | 0.335564 | − | 0.942017i | \(-0.391073\pi\) | ||||
0.335564 | + | 0.942017i | \(0.391073\pi\) | |||||||
\(212\) | 10.7873 | 0.740877 | ||||||||
\(213\) | −4.77801 | −0.327384 | ||||||||
\(214\) | −13.6460 | −0.932821 | ||||||||
\(215\) | −1.55602 | −0.106119 | ||||||||
\(216\) | 5.64600 | 0.384162 | ||||||||
\(217\) | 15.0093 | 1.01890 | ||||||||
\(218\) | 5.33402 | 0.361266 | ||||||||
\(219\) | −16.0000 | −1.08118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.58532 | −0.241175 | ||||||||
\(222\) | 13.3306 | 0.894694 | ||||||||
\(223\) | −18.6167 | −1.24667 | −0.623333 | − | 0.781956i | \(-0.714222\pi\) | ||||
−0.623333 | + | 0.781956i | \(0.714222\pi\) | |||||||
\(224\) | 2.14134 | 0.143074 | ||||||||
\(225\) | 5.55602 | 0.370401 | ||||||||
\(226\) | −14.3633 | −0.955434 | ||||||||
\(227\) | −17.9160 | −1.18912 | −0.594562 | − | 0.804050i | \(-0.702674\pi\) | ||||
−0.594562 | + | 0.804050i | \(0.702674\pi\) | |||||||
\(228\) | 1.36333 | 0.0902886 | ||||||||
\(229\) | −8.31198 | −0.549271 | −0.274635 | − | 0.961548i | \(-0.588557\pi\) | ||||
−0.274635 | + | 0.961548i | \(0.588557\pi\) | |||||||
\(230\) | −0.778008 | −0.0513003 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.77801 | −0.116732 | ||||||||
\(233\) | 7.28267 | 0.477104 | 0.238552 | − | 0.971130i | \(-0.423327\pi\) | ||||
0.238552 | + | 0.971130i | \(0.423327\pi\) | |||||||
\(234\) | 3.58532 | 0.234380 | ||||||||
\(235\) | −2.75935 | −0.180000 | ||||||||
\(236\) | −1.08066 | −0.0703447 | ||||||||
\(237\) | −1.06068 | −0.0688986 | ||||||||
\(238\) | 2.44398 | 0.158420 | ||||||||
\(239\) | 11.1693 | 0.722483 | 0.361242 | − | 0.932472i | \(-0.382353\pi\) | ||||
0.361242 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(240\) | −0.495336 | −0.0319738 | ||||||||
\(241\) | 6.39263 | 0.411786 | 0.205893 | − | 0.978575i | \(-0.433990\pi\) | ||||
0.205893 | + | 0.978575i | \(0.433990\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.1120 | −0.712837 | ||||||||
\(244\) | −8.51399 | −0.545053 | ||||||||
\(245\) | −0.877321 | −0.0560500 | ||||||||
\(246\) | 10.7967 | 0.688370 | ||||||||
\(247\) | 3.14134 | 0.199878 | ||||||||
\(248\) | 7.00933 | 0.445093 | ||||||||
\(249\) | 1.06068 | 0.0672179 | ||||||||
\(250\) | −3.58532 | −0.226756 | ||||||||
\(251\) | 8.17997 | 0.516315 | 0.258158 | − | 0.966103i | \(-0.416885\pi\) | ||||
0.258158 | + | 0.966103i | \(0.416885\pi\) | |||||||
\(252\) | −2.44398 | −0.153957 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.44398 | −0.153349 | ||||||||
\(255\) | −0.565344 | −0.0354032 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.8773 | −1.80132 | −0.900659 | − | 0.434527i | \(-0.856916\pi\) | ||||
−0.900659 | + | 0.434527i | \(0.856916\pi\) | |||||||
\(258\) | 5.83869 | 0.363501 | ||||||||
\(259\) | −20.9380 | −1.30102 | ||||||||
\(260\) | −1.14134 | −0.0707827 | ||||||||
\(261\) | 2.02930 | 0.125611 | ||||||||
\(262\) | −0.707999 | −0.0437403 | ||||||||
\(263\) | 0.385375 | 0.0237632 | 0.0118816 | − | 0.999929i | \(-0.496218\pi\) | ||||
0.0118816 | + | 0.999929i | \(0.496218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.91934 | 0.240763 | ||||||||
\(266\) | −2.14134 | −0.131294 | ||||||||
\(267\) | 11.1820 | 0.684330 | ||||||||
\(268\) | 8.56534 | 0.523212 | ||||||||
\(269\) | 13.5140 | 0.823963 | 0.411981 | − | 0.911192i | \(-0.364837\pi\) | ||||
0.411981 | + | 0.911192i | \(0.364837\pi\) | |||||||
\(270\) | 2.05135 | 0.124841 | ||||||||
\(271\) | −9.73599 | −0.591419 | −0.295709 | − | 0.955278i | \(-0.595556\pi\) | ||||
−0.295709 | + | 0.955278i | \(0.595556\pi\) | |||||||
\(272\) | 1.14134 | 0.0692037 | ||||||||
\(273\) | 9.17064 | 0.555032 | ||||||||
\(274\) | 6.28267 | 0.379550 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.91934 | 0.175724 | ||||||||
\(277\) | −6.74870 | −0.405490 | −0.202745 | − | 0.979232i | \(-0.564986\pi\) | ||||
−0.202745 | + | 0.979232i | \(0.564986\pi\) | |||||||
\(278\) | 4.00000 | 0.239904 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0.778008 | 0.0464949 | ||||||||
\(281\) | −7.06068 | −0.421205 | −0.210602 | − | 0.977572i | \(-0.567543\pi\) | ||||
−0.210602 | + | 0.977572i | \(0.567543\pi\) | |||||||
\(282\) | 10.3540 | 0.616572 | ||||||||
\(283\) | −8.46264 | −0.503052 | −0.251526 | − | 0.967851i | \(-0.580932\pi\) | ||||
−0.251526 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(284\) | 3.50466 | 0.207964 | ||||||||
\(285\) | 0.495336 | 0.0293412 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.9580 | −1.00100 | ||||||||
\(288\) | −1.14134 | −0.0672539 | ||||||||
\(289\) | −15.6974 | −0.923374 | ||||||||
\(290\) | −0.646000 | −0.0379345 | ||||||||
\(291\) | 2.54669 | 0.149289 | ||||||||
\(292\) | 11.7360 | 0.686797 | ||||||||
\(293\) | 21.7967 | 1.27337 | 0.636687 | − | 0.771122i | \(-0.280304\pi\) | ||||
0.636687 | + | 0.771122i | \(0.280304\pi\) | |||||||
\(294\) | 3.29200 | 0.191993 | ||||||||
\(295\) | −0.392633 | −0.0228600 | ||||||||
\(296\) | −9.77801 | −0.568335 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.1600 | 0.646481 | ||||||||
\(299\) | 6.72666 | 0.389013 | ||||||||
\(300\) | 6.63667 | 0.383168 | ||||||||
\(301\) | −9.17064 | −0.528587 | ||||||||
\(302\) | −13.8060 | −0.794446 | ||||||||
\(303\) | 13.7287 | 0.788695 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −3.09337 | −0.177126 | ||||||||
\(306\) | −1.30265 | −0.0744674 | ||||||||
\(307\) | −16.5526 | −0.944708 | −0.472354 | − | 0.881409i | \(-0.656596\pi\) | ||||
−0.472354 | + | 0.881409i | \(0.656596\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.6447 | 1.34510 | ||||||||
\(310\) | 2.54669 | 0.144642 | ||||||||
\(311\) | −20.8480 | −1.18218 | −0.591091 | − | 0.806605i | \(-0.701303\pi\) | ||||
−0.591091 | + | 0.806605i | \(0.701303\pi\) | |||||||
\(312\) | 4.28267 | 0.242459 | ||||||||
\(313\) | −2.98134 | −0.168515 | −0.0842577 | − | 0.996444i | \(-0.526852\pi\) | ||||
−0.0842577 | + | 0.996444i | \(0.526852\pi\) | |||||||
\(314\) | 15.8060 | 0.891984 | ||||||||
\(315\) | −0.887968 | −0.0500314 | ||||||||
\(316\) | 0.778008 | 0.0437664 | ||||||||
\(317\) | −11.9160 | −0.669267 | −0.334633 | − | 0.942348i | \(-0.608612\pi\) | ||||
−0.334633 | + | 0.942348i | \(0.608612\pi\) | |||||||
\(318\) | −14.7067 | −0.824710 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.363328 | 0.0203107 | ||||||||
\(321\) | 18.6040 | 1.03837 | ||||||||
\(322\) | −4.58532 | −0.255530 | ||||||||
\(323\) | −1.14134 | −0.0635056 | ||||||||
\(324\) | −4.27334 | −0.237408 | ||||||||
\(325\) | 15.2920 | 0.848248 | ||||||||
\(326\) | −3.71733 | −0.205884 | ||||||||
\(327\) | −7.27203 | −0.402144 | ||||||||
\(328\) | −7.91934 | −0.437273 | ||||||||
\(329\) | −16.2627 | −0.896591 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0127181 | 0.000699049 0 | 0.000349525 | − | 1.00000i | \(-0.499889\pi\) | ||||
0.000349525 | 1.00000i | \(0.499889\pi\) | ||||||||
\(332\) | −0.778008 | −0.0426987 | ||||||||
\(333\) | 11.1600 | 0.611564 | ||||||||
\(334\) | 5.27334 | 0.288545 | ||||||||
\(335\) | 3.11203 | 0.170028 | ||||||||
\(336\) | −2.91934 | −0.159263 | ||||||||
\(337\) | 28.1180 | 1.53168 | 0.765842 | − | 0.643029i | \(-0.222323\pi\) | ||||
0.765842 | + | 0.643029i | \(0.222323\pi\) | |||||||
\(338\) | −3.13201 | −0.170359 | ||||||||
\(339\) | 19.5819 | 1.06354 | ||||||||
\(340\) | 0.414680 | 0.0224892 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.14134 | 0.0617164 | ||||||||
\(343\) | −20.1600 | −1.08854 | ||||||||
\(344\) | −4.28267 | −0.230906 | ||||||||
\(345\) | 1.06068 | 0.0571051 | ||||||||
\(346\) | 11.4660 | 0.616418 | ||||||||
\(347\) | 5.66598 | 0.304166 | 0.152083 | − | 0.988368i | \(-0.451402\pi\) | ||||
0.152083 | + | 0.988368i | \(0.451402\pi\) | |||||||
\(348\) | 2.42401 | 0.129940 | ||||||||
\(349\) | 24.3306 | 1.30239 | 0.651194 | − | 0.758911i | \(-0.274268\pi\) | ||||
0.651194 | + | 0.758911i | \(0.274268\pi\) | |||||||
\(350\) | −10.4240 | −0.557187 | ||||||||
\(351\) | −17.7360 | −0.946677 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.11203 | 0.112412 | 0.0562060 | − | 0.998419i | \(-0.482100\pi\) | ||||
0.0562060 | + | 0.998419i | \(0.482100\pi\) | |||||||
\(354\) | 1.47329 | 0.0783044 | ||||||||
\(355\) | 1.27334 | 0.0675821 | ||||||||
\(356\) | −8.20202 | −0.434706 | ||||||||
\(357\) | −3.33195 | −0.176346 | ||||||||
\(358\) | −0.900687 | −0.0476028 | ||||||||
\(359\) | −34.6613 | −1.82935 | −0.914676 | − | 0.404188i | \(-0.867554\pi\) | ||||
−0.914676 | + | 0.404188i | \(0.867554\pi\) | |||||||
\(360\) | −0.414680 | −0.0218555 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −16.6974 | −0.877593 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.72666 | −0.352573 | ||||||||
\(365\) | 4.26401 | 0.223189 | ||||||||
\(366\) | 11.6074 | 0.606727 | ||||||||
\(367\) | −36.3400 | −1.89693 | −0.948465 | − | 0.316881i | \(-0.897364\pi\) | ||||
−0.948465 | + | 0.316881i | \(0.897364\pi\) | |||||||
\(368\) | −2.14134 | −0.111625 | ||||||||
\(369\) | 9.03863 | 0.470532 | ||||||||
\(370\) | −3.55263 | −0.184692 | ||||||||
\(371\) | 23.0993 | 1.19926 | ||||||||
\(372\) | −9.55602 | −0.495456 | ||||||||
\(373\) | 30.1273 | 1.55993 | 0.779966 | − | 0.625822i | \(-0.215236\pi\) | ||||
0.779966 | + | 0.625822i | \(0.215236\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.88797 | 0.252414 | ||||||||
\(376\) | −7.59465 | −0.391664 | ||||||||
\(377\) | 5.58532 | 0.287659 | ||||||||
\(378\) | 12.0900 | 0.621842 | ||||||||
\(379\) | 3.06200 | 0.157284 | 0.0786422 | − | 0.996903i | \(-0.474942\pi\) | ||||
0.0786422 | + | 0.996903i | \(0.474942\pi\) | |||||||
\(380\) | −0.363328 | −0.0186383 | ||||||||
\(381\) | 3.33195 | 0.170701 | ||||||||
\(382\) | −3.87732 | −0.198381 | ||||||||
\(383\) | 33.1307 | 1.69290 | 0.846450 | − | 0.532469i | \(-0.178736\pi\) | ||||
0.846450 | + | 0.532469i | \(0.178736\pi\) | |||||||
\(384\) | −1.36333 | −0.0695721 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.32131 | 0.270847 | ||||||||
\(387\) | 4.88797 | 0.248469 | ||||||||
\(388\) | −1.86799 | −0.0948330 | ||||||||
\(389\) | −3.81664 | −0.193511 | −0.0967557 | − | 0.995308i | \(-0.530847\pi\) | ||||
−0.0967557 | + | 0.995308i | \(0.530847\pi\) | |||||||
\(390\) | 1.55602 | 0.0787919 | ||||||||
\(391\) | −2.44398 | −0.123598 | ||||||||
\(392\) | −2.41468 | −0.121960 | ||||||||
\(393\) | 0.965235 | 0.0486897 | ||||||||
\(394\) | −14.3306 | −0.721967 | ||||||||
\(395\) | 0.282672 | 0.0142228 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.0573 | −1.25759 | −0.628795 | − | 0.777571i | \(-0.716451\pi\) | ||||
−0.628795 | + | 0.777571i | \(0.716451\pi\) | |||||||
\(398\) | 5.83869 | 0.292667 | ||||||||
\(399\) | 2.91934 | 0.146150 | ||||||||
\(400\) | −4.86799 | −0.243400 | ||||||||
\(401\) | −31.9567 | −1.59584 | −0.797920 | − | 0.602764i | \(-0.794066\pi\) | ||||
−0.797920 | + | 0.602764i | \(0.794066\pi\) | |||||||
\(402\) | −11.6774 | −0.582415 | ||||||||
\(403\) | −22.0187 | −1.09683 | ||||||||
\(404\) | −10.0700 | −0.501002 | ||||||||
\(405\) | −1.55263 | −0.0771506 | ||||||||
\(406\) | −3.80731 | −0.188954 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.55602 | −0.0770343 | ||||||||
\(409\) | 27.8280 | 1.37601 | 0.688004 | − | 0.725707i | \(-0.258487\pi\) | ||||
0.688004 | + | 0.725707i | \(0.258487\pi\) | |||||||
\(410\) | −2.87732 | −0.142101 | ||||||||
\(411\) | −8.56534 | −0.422497 | ||||||||
\(412\) | −17.3434 | −0.854446 | ||||||||
\(413\) | −2.31405 | −0.113867 | ||||||||
\(414\) | 2.44398 | 0.120115 | ||||||||
\(415\) | −0.282672 | −0.0138758 | ||||||||
\(416\) | −3.14134 | −0.154017 | ||||||||
\(417\) | −5.45331 | −0.267050 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.24065 | −0.256022 | −0.128011 | − | 0.991773i | \(-0.540859\pi\) | ||||
−0.128011 | + | 0.991773i | \(0.540859\pi\) | |||||||
\(420\) | −1.06068 | −0.0517559 | ||||||||
\(421\) | −15.3340 | −0.747335 | −0.373667 | − | 0.927563i | \(-0.621900\pi\) | ||||
−0.373667 | + | 0.927563i | \(0.621900\pi\) | |||||||
\(422\) | 9.74870 | 0.474559 | ||||||||
\(423\) | 8.66805 | 0.421455 | ||||||||
\(424\) | 10.7873 | 0.523879 | ||||||||
\(425\) | −5.55602 | −0.269506 | ||||||||
\(426\) | −4.77801 | −0.231495 | ||||||||
\(427\) | −18.2313 | −0.882275 | ||||||||
\(428\) | −13.6460 | −0.659604 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.55602 | −0.0750377 | ||||||||
\(431\) | 18.8994 | 0.910351 | 0.455175 | − | 0.890402i | \(-0.349577\pi\) | ||||
0.455175 | + | 0.890402i | \(0.349577\pi\) | |||||||
\(432\) | 5.64600 | 0.271643 | ||||||||
\(433\) | −11.1787 | −0.537212 | −0.268606 | − | 0.963250i | \(-0.586563\pi\) | ||||
−0.268606 | + | 0.963250i | \(0.586563\pi\) | |||||||
\(434\) | 15.0093 | 0.720471 | ||||||||
\(435\) | 0.880711 | 0.0422268 | ||||||||
\(436\) | 5.33402 | 0.255453 | ||||||||
\(437\) | 2.14134 | 0.102434 | ||||||||
\(438\) | −16.0000 | −0.764510 | ||||||||
\(439\) | 23.4720 | 1.12026 | 0.560128 | − | 0.828406i | \(-0.310752\pi\) | ||||
0.560128 | + | 0.828406i | \(0.310752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.75596 | 0.131236 | ||||||||
\(442\) | −3.58532 | −0.170536 | ||||||||
\(443\) | −29.8387 | −1.41768 | −0.708839 | − | 0.705370i | \(-0.750781\pi\) | ||||
−0.708839 | + | 0.705370i | \(0.750781\pi\) | |||||||
\(444\) | 13.3306 | 0.632644 | ||||||||
\(445\) | −2.98002 | −0.141267 | ||||||||
\(446\) | −18.6167 | −0.881526 | ||||||||
\(447\) | −15.2147 | −0.719632 | ||||||||
\(448\) | 2.14134 | 0.101169 | ||||||||
\(449\) | −10.6133 | −0.500873 | −0.250436 | − | 0.968133i | \(-0.580574\pi\) | ||||
−0.250436 | + | 0.968133i | \(0.580574\pi\) | |||||||
\(450\) | 5.55602 | 0.261913 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −14.3633 | −0.675594 | ||||||||
\(453\) | 18.8221 | 0.884339 | ||||||||
\(454\) | −17.9160 | −0.840837 | ||||||||
\(455\) | −2.44398 | −0.114576 | ||||||||
\(456\) | 1.36333 | 0.0638437 | ||||||||
\(457\) | −7.82936 | −0.366242 | −0.183121 | − | 0.983090i | \(-0.558620\pi\) | ||||
−0.183121 | + | 0.983090i | \(0.558620\pi\) | |||||||
\(458\) | −8.31198 | −0.388393 | ||||||||
\(459\) | 6.44398 | 0.300779 | ||||||||
\(460\) | −0.778008 | −0.0362748 | ||||||||
\(461\) | −2.54330 | −0.118453 | −0.0592266 | − | 0.998245i | \(-0.518863\pi\) | ||||
−0.0592266 | + | 0.998245i | \(0.518863\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.6519 | −1.47099 | −0.735495 | − | 0.677530i | \(-0.763050\pi\) | ||||
−0.735495 | + | 0.677530i | \(0.763050\pi\) | |||||||
\(464\) | −1.77801 | −0.0825419 | ||||||||
\(465\) | −3.47197 | −0.161009 | ||||||||
\(466\) | 7.28267 | 0.337363 | ||||||||
\(467\) | −7.85735 | −0.363595 | −0.181797 | − | 0.983336i | \(-0.558191\pi\) | ||||
−0.181797 | + | 0.983336i | \(0.558191\pi\) | |||||||
\(468\) | 3.58532 | 0.165731 | ||||||||
\(469\) | 18.3413 | 0.846922 | ||||||||
\(470\) | −2.75935 | −0.127279 | ||||||||
\(471\) | −21.5488 | −0.992914 | ||||||||
\(472\) | −1.08066 | −0.0497412 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.06068 | −0.0487187 | ||||||||
\(475\) | 4.86799 | 0.223359 | ||||||||
\(476\) | 2.44398 | 0.112020 | ||||||||
\(477\) | −12.3120 | −0.563727 | ||||||||
\(478\) | 11.1693 | 0.510873 | ||||||||
\(479\) | 13.9614 | 0.637911 | 0.318956 | − | 0.947770i | \(-0.396668\pi\) | ||||
0.318956 | + | 0.947770i | \(0.396668\pi\) | |||||||
\(480\) | −0.495336 | −0.0226089 | ||||||||
\(481\) | 30.7160 | 1.40053 | ||||||||
\(482\) | 6.39263 | 0.291176 | ||||||||
\(483\) | 6.25130 | 0.284444 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.678694 | −0.0308179 | ||||||||
\(486\) | −11.1120 | −0.504052 | ||||||||
\(487\) | 1.83869 | 0.0833189 | 0.0416595 | − | 0.999132i | \(-0.486736\pi\) | ||||
0.0416595 | + | 0.999132i | \(0.486736\pi\) | |||||||
\(488\) | −8.51399 | −0.385410 | ||||||||
\(489\) | 5.06794 | 0.229180 | ||||||||
\(490\) | −0.877321 | −0.0396333 | ||||||||
\(491\) | 27.5747 | 1.24443 | 0.622214 | − | 0.782847i | \(-0.286233\pi\) | ||||
0.622214 | + | 0.782847i | \(0.286233\pi\) | |||||||
\(492\) | 10.7967 | 0.486751 | ||||||||
\(493\) | −2.02930 | −0.0913953 | ||||||||
\(494\) | 3.14134 | 0.141335 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.00933 | 0.314728 | ||||||||
\(497\) | 7.50466 | 0.336630 | ||||||||
\(498\) | 1.06068 | 0.0475302 | ||||||||
\(499\) | 26.4113 | 1.18233 | 0.591166 | − | 0.806550i | \(-0.298668\pi\) | ||||
0.591166 | + | 0.806550i | \(0.298668\pi\) | |||||||
\(500\) | −3.58532 | −0.160340 | ||||||||
\(501\) | −7.18930 | −0.321194 | ||||||||
\(502\) | 8.17997 | 0.365090 | ||||||||
\(503\) | 12.5853 | 0.561152 | 0.280576 | − | 0.959832i | \(-0.409475\pi\) | ||||
0.280576 | + | 0.959832i | \(0.409475\pi\) | |||||||
\(504\) | −2.44398 | −0.108864 | ||||||||
\(505\) | −3.65872 | −0.162811 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.26995 | 0.189635 | ||||||||
\(508\) | −2.44398 | −0.108434 | ||||||||
\(509\) | 28.8166 | 1.27728 | 0.638638 | − | 0.769508i | \(-0.279498\pi\) | ||||
0.638638 | + | 0.769508i | \(0.279498\pi\) | |||||||
\(510\) | −0.565344 | −0.0250339 | ||||||||
\(511\) | 25.1307 | 1.11172 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.64600 | −0.249277 | ||||||||
\(514\) | −28.8773 | −1.27372 | ||||||||
\(515\) | −6.30133 | −0.277670 | ||||||||
\(516\) | 5.83869 | 0.257034 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −20.9380 | −0.919963 | ||||||||
\(519\) | −15.6320 | −0.686167 | ||||||||
\(520\) | −1.14134 | −0.0500509 | ||||||||
\(521\) | 32.5840 | 1.42753 | 0.713766 | − | 0.700385i | \(-0.246988\pi\) | ||||
0.713766 | + | 0.700385i | \(0.246988\pi\) | |||||||
\(522\) | 2.02930 | 0.0888202 | ||||||||
\(523\) | 43.3820 | 1.89696 | 0.948481 | − | 0.316834i | \(-0.102620\pi\) | ||||
0.948481 | + | 0.316834i | \(0.102620\pi\) | |||||||
\(524\) | −0.707999 | −0.0309291 | ||||||||
\(525\) | 14.2113 | 0.620234 | ||||||||
\(526\) | 0.385375 | 0.0168032 | ||||||||
\(527\) | 8.00000 | 0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.4147 | −0.800638 | ||||||||
\(530\) | 3.91934 | 0.170245 | ||||||||
\(531\) | 1.23339 | 0.0535246 | ||||||||
\(532\) | −2.14134 | −0.0928387 | ||||||||
\(533\) | 24.8773 | 1.07756 | ||||||||
\(534\) | 11.1820 | 0.483894 | ||||||||
\(535\) | −4.95798 | −0.214352 | ||||||||
\(536\) | 8.56534 | 0.369967 | ||||||||
\(537\) | 1.22793 | 0.0529892 | ||||||||
\(538\) | 13.5140 | 0.582630 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.05135 | 0.0882761 | ||||||||
\(541\) | −28.6867 | −1.23334 | −0.616669 | − | 0.787223i | \(-0.711518\pi\) | ||||
−0.616669 | + | 0.787223i | \(0.711518\pi\) | |||||||
\(542\) | −9.73599 | −0.418196 | ||||||||
\(543\) | 22.7640 | 0.976896 | ||||||||
\(544\) | 1.14134 | 0.0489344 | ||||||||
\(545\) | 1.93800 | 0.0830149 | ||||||||
\(546\) | 9.17064 | 0.392467 | ||||||||
\(547\) | −3.09931 | −0.132517 | −0.0662585 | − | 0.997802i | \(-0.521106\pi\) | ||||
−0.0662585 | + | 0.997802i | \(0.521106\pi\) | |||||||
\(548\) | 6.28267 | 0.268382 | ||||||||
\(549\) | 9.71733 | 0.414725 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.77801 | 0.0757457 | ||||||||
\(552\) | 2.91934 | 0.124256 | ||||||||
\(553\) | 1.66598 | 0.0708445 | ||||||||
\(554\) | −6.74870 | −0.286725 | ||||||||
\(555\) | 4.84340 | 0.205591 | ||||||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 23.9160 | 1.01335 | 0.506676 | − | 0.862137i | \(-0.330874\pi\) | ||||
0.506676 | + | 0.862137i | \(0.330874\pi\) | |||||||
\(558\) | −8.00000 | −0.338667 | ||||||||
\(559\) | 13.4533 | 0.569015 | ||||||||
\(560\) | 0.778008 | 0.0328768 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.06068 | −0.297837 | ||||||||
\(563\) | 35.7674 | 1.50741 | 0.753707 | − | 0.657210i | \(-0.228264\pi\) | ||||
0.753707 | + | 0.657210i | \(0.228264\pi\) | |||||||
\(564\) | 10.3540 | 0.435982 | ||||||||
\(565\) | −5.21860 | −0.219548 | ||||||||
\(566\) | −8.46264 | −0.355711 | ||||||||
\(567\) | −9.15066 | −0.384292 | ||||||||
\(568\) | 3.50466 | 0.147052 | ||||||||
\(569\) | −9.71733 | −0.407372 | −0.203686 | − | 0.979036i | \(-0.565292\pi\) | ||||
−0.203686 | + | 0.979036i | \(0.565292\pi\) | |||||||
\(570\) | 0.495336 | 0.0207473 | ||||||||
\(571\) | −37.6260 | −1.57460 | −0.787300 | − | 0.616570i | \(-0.788522\pi\) | ||||
−0.787300 | + | 0.616570i | \(0.788522\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.28606 | 0.220828 | ||||||||
\(574\) | −16.9580 | −0.707812 | ||||||||
\(575\) | 10.4240 | 0.434711 | ||||||||
\(576\) | −1.14134 | −0.0475557 | ||||||||
\(577\) | 9.60398 | 0.399819 | 0.199909 | − | 0.979814i | \(-0.435935\pi\) | ||||
0.199909 | + | 0.979814i | \(0.435935\pi\) | |||||||
\(578\) | −15.6974 | −0.652924 | ||||||||
\(579\) | −7.25469 | −0.301494 | ||||||||
\(580\) | −0.646000 | −0.0268237 | ||||||||
\(581\) | −1.66598 | −0.0691163 | ||||||||
\(582\) | 2.54669 | 0.105564 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.7360 | 0.485639 | ||||||||
\(585\) | 1.30265 | 0.0538579 | ||||||||
\(586\) | 21.7967 | 0.900412 | ||||||||
\(587\) | 40.8153 | 1.68463 | 0.842314 | − | 0.538987i | \(-0.181193\pi\) | ||||
0.842314 | + | 0.538987i | \(0.181193\pi\) | |||||||
\(588\) | 3.29200 | 0.135760 | ||||||||
\(589\) | −7.00933 | −0.288814 | ||||||||
\(590\) | −0.392633 | −0.0161644 | ||||||||
\(591\) | 19.5374 | 0.803660 | ||||||||
\(592\) | −9.77801 | −0.401874 | ||||||||
\(593\) | 47.8853 | 1.96641 | 0.983207 | − | 0.182491i | \(-0.0584162\pi\) | ||||
0.983207 | + | 0.182491i | \(0.0584162\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.887968 | 0.0364032 | ||||||||
\(596\) | 11.1600 | 0.457131 | ||||||||
\(597\) | −7.96005 | −0.325783 | ||||||||
\(598\) | 6.72666 | 0.275073 | ||||||||
\(599\) | 24.9253 | 1.01842 | 0.509210 | − | 0.860642i | \(-0.329938\pi\) | ||||
0.509210 | + | 0.860642i | \(0.329938\pi\) | |||||||
\(600\) | 6.63667 | 0.270941 | ||||||||
\(601\) | 8.29332 | 0.338292 | 0.169146 | − | 0.985591i | \(-0.445899\pi\) | ||||
0.169146 | + | 0.985591i | \(0.445899\pi\) | |||||||
\(602\) | −9.17064 | −0.373767 | ||||||||
\(603\) | −9.77594 | −0.398107 | ||||||||
\(604\) | −13.8060 | −0.561758 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.7287 | 0.557691 | ||||||||
\(607\) | 5.13795 | 0.208543 | 0.104271 | − | 0.994549i | \(-0.466749\pi\) | ||||
0.104271 | + | 0.994549i | \(0.466749\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 5.19062 | 0.210334 | ||||||||
\(610\) | −3.09337 | −0.125247 | ||||||||
\(611\) | 23.8573 | 0.965165 | ||||||||
\(612\) | −1.30265 | −0.0526564 | ||||||||
\(613\) | 1.63667 | 0.0661045 | 0.0330523 | − | 0.999454i | \(-0.489477\pi\) | ||||
0.0330523 | + | 0.999454i | \(0.489477\pi\) | |||||||
\(614\) | −16.5526 | −0.668010 | ||||||||
\(615\) | 3.92273 | 0.158180 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8973 | −0.680260 | −0.340130 | − | 0.940379i | \(-0.610471\pi\) | ||||
−0.340130 | + | 0.940379i | \(0.610471\pi\) | |||||||
\(618\) | 23.6447 | 0.951129 | ||||||||
\(619\) | −28.8480 | −1.15950 | −0.579750 | − | 0.814795i | \(-0.696850\pi\) | ||||
−0.579750 | + | 0.814795i | \(0.696850\pi\) | |||||||
\(620\) | 2.54669 | 0.102277 | ||||||||
\(621\) | −12.0900 | −0.485154 | ||||||||
\(622\) | −20.8480 | −0.835929 | ||||||||
\(623\) | −17.5633 | −0.703658 | ||||||||
\(624\) | 4.28267 | 0.171444 | ||||||||
\(625\) | 23.0373 | 0.921493 | ||||||||
\(626\) | −2.98134 | −0.119158 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.8060 | 0.630728 | ||||||||
\(629\) | −11.1600 | −0.444978 | ||||||||
\(630\) | −0.887968 | −0.0353775 | ||||||||
\(631\) | −2.24404 | −0.0893338 | −0.0446669 | − | 0.999002i | \(-0.514223\pi\) | ||||
−0.0446669 | + | 0.999002i | \(0.514223\pi\) | |||||||
\(632\) | 0.778008 | 0.0309475 | ||||||||
\(633\) | −13.2907 | −0.528257 | ||||||||
\(634\) | −11.9160 | −0.473243 | ||||||||
\(635\) | −0.887968 | −0.0352380 | ||||||||
\(636\) | −14.7067 | −0.583158 | ||||||||
\(637\) | 7.58532 | 0.300541 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.00000 | −0.158238 | ||||||||
\(640\) | 0.363328 | 0.0143618 | ||||||||
\(641\) | 43.2300 | 1.70748 | 0.853741 | − | 0.520698i | \(-0.174328\pi\) | ||||
0.853741 | + | 0.520698i | \(0.174328\pi\) | |||||||
\(642\) | 18.6040 | 0.734240 | ||||||||
\(643\) | 9.69867 | 0.382478 | 0.191239 | − | 0.981543i | \(-0.438749\pi\) | ||||
0.191239 | + | 0.981543i | \(0.438749\pi\) | |||||||
\(644\) | −4.58532 | −0.180687 | ||||||||
\(645\) | 2.12136 | 0.0835285 | ||||||||
\(646\) | −1.14134 | −0.0449053 | ||||||||
\(647\) | 3.59465 | 0.141320 | 0.0706601 | − | 0.997500i | \(-0.477489\pi\) | ||||
0.0706601 | + | 0.997500i | \(0.477489\pi\) | |||||||
\(648\) | −4.27334 | −0.167873 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 15.2920 | 0.599802 | ||||||||
\(651\) | −20.4626 | −0.801994 | ||||||||
\(652\) | −3.71733 | −0.145582 | ||||||||
\(653\) | 18.8226 | 0.736584 | 0.368292 | − | 0.929710i | \(-0.379943\pi\) | ||||
0.368292 | + | 0.929710i | \(0.379943\pi\) | |||||||
\(654\) | −7.27203 | −0.284359 | ||||||||
\(655\) | −0.257236 | −0.0100510 | ||||||||
\(656\) | −7.91934 | −0.309198 | ||||||||
\(657\) | −13.3947 | −0.522577 | ||||||||
\(658\) | −16.2627 | −0.633986 | ||||||||
\(659\) | 46.6613 | 1.81766 | 0.908832 | − | 0.417161i | \(-0.136975\pi\) | ||||
0.908832 | + | 0.417161i | \(0.136975\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.4554 | −0.990100 | −0.495050 | − | 0.868865i | \(-0.664850\pi\) | ||||
−0.495050 | + | 0.868865i | \(0.664850\pi\) | |||||||
\(662\) | 0.0127181 | 0.000494303 0 | ||||||||
\(663\) | 4.88797 | 0.189833 | ||||||||
\(664\) | −0.778008 | −0.0301926 | ||||||||
\(665\) | −0.778008 | −0.0301699 | ||||||||
\(666\) | 11.1600 | 0.432441 | ||||||||
\(667\) | 3.80731 | 0.147420 | ||||||||
\(668\) | 5.27334 | 0.204032 | ||||||||
\(669\) | 25.3807 | 0.981273 | ||||||||
\(670\) | 3.11203 | 0.120228 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.91934 | −0.112616 | ||||||||
\(673\) | −2.03269 | −0.0783546 | −0.0391773 | − | 0.999232i | \(-0.512474\pi\) | ||||
−0.0391773 | + | 0.999232i | \(0.512474\pi\) | |||||||
\(674\) | 28.1180 | 1.08306 | ||||||||
\(675\) | −27.4847 | −1.05789 | ||||||||
\(676\) | −3.13201 | −0.120462 | ||||||||
\(677\) | 15.1727 | 0.583135 | 0.291567 | − | 0.956550i | \(-0.405823\pi\) | ||||
0.291567 | + | 0.956550i | \(0.405823\pi\) | |||||||
\(678\) | 19.5819 | 0.752040 | ||||||||
\(679\) | −4.00000 | −0.153506 | ||||||||
\(680\) | 0.414680 | 0.0159022 | ||||||||
\(681\) | 24.4253 | 0.935981 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.2241 | 0.544269 | 0.272134 | − | 0.962259i | \(-0.412270\pi\) | ||||
0.272134 | + | 0.962259i | \(0.412270\pi\) | |||||||
\(684\) | 1.14134 | 0.0436401 | ||||||||
\(685\) | 2.28267 | 0.0872164 | ||||||||
\(686\) | −20.1600 | −0.769712 | ||||||||
\(687\) | 11.3320 | 0.432341 | ||||||||
\(688\) | −4.28267 | −0.163275 | ||||||||
\(689\) | −33.8867 | −1.29098 | ||||||||
\(690\) | 1.06068 | 0.0403794 | ||||||||
\(691\) | 13.1379 | 0.499791 | 0.249896 | − | 0.968273i | \(-0.419604\pi\) | ||||
0.249896 | + | 0.968273i | \(0.419604\pi\) | |||||||
\(692\) | 11.4660 | 0.435873 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.66598 | 0.215078 | ||||||||
\(695\) | 1.45331 | 0.0551273 | ||||||||
\(696\) | 2.42401 | 0.0918818 | ||||||||
\(697\) | −9.03863 | −0.342363 | ||||||||
\(698\) | 24.3306 | 0.920928 | ||||||||
\(699\) | −9.92867 | −0.375537 | ||||||||
\(700\) | −10.4240 | −0.393990 | ||||||||
\(701\) | −25.2373 | −0.953198 | −0.476599 | − | 0.879121i | \(-0.658131\pi\) | ||||
−0.476599 | + | 0.879121i | \(0.658131\pi\) | |||||||
\(702\) | −17.7360 | −0.669402 | ||||||||
\(703\) | 9.77801 | 0.368785 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.76190 | 0.141681 | ||||||||
\(706\) | 2.11203 | 0.0794874 | ||||||||
\(707\) | −21.5633 | −0.810970 | ||||||||
\(708\) | 1.47329 | 0.0553696 | ||||||||
\(709\) | 23.3760 | 0.877906 | 0.438953 | − | 0.898510i | \(-0.355349\pi\) | ||||
0.438953 | + | 0.898510i | \(0.355349\pi\) | |||||||
\(710\) | 1.27334 | 0.0477877 | ||||||||
\(711\) | −0.887968 | −0.0333014 | ||||||||
\(712\) | −8.20202 | −0.307384 | ||||||||
\(713\) | −15.0093 | −0.562104 | ||||||||
\(714\) | −3.33195 | −0.124695 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.900687 | −0.0336602 | ||||||||
\(717\) | −15.2275 | −0.568680 | ||||||||
\(718\) | −34.6613 | −1.29355 | ||||||||
\(719\) | 31.6774 | 1.18137 | 0.590683 | − | 0.806903i | \(-0.298858\pi\) | ||||
0.590683 | + | 0.806903i | \(0.298858\pi\) | |||||||
\(720\) | −0.414680 | −0.0154542 | ||||||||
\(721\) | −37.1379 | −1.38309 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −8.71526 | −0.324124 | ||||||||
\(724\) | −16.6974 | −0.620552 | ||||||||
\(725\) | 8.65533 | 0.321451 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.5199 | −1.35445 | −0.677225 | − | 0.735776i | \(-0.736817\pi\) | ||||
−0.677225 | + | 0.735776i | \(0.736817\pi\) | |||||||
\(728\) | −6.72666 | −0.249306 | ||||||||
\(729\) | 27.9694 | 1.03590 | ||||||||
\(730\) | 4.26401 | 0.157818 | ||||||||
\(731\) | −4.88797 | −0.180788 | ||||||||
\(732\) | 11.6074 | 0.429021 | ||||||||
\(733\) | 36.1880 | 1.33663 | 0.668317 | − | 0.743877i | \(-0.267015\pi\) | ||||
0.668317 | + | 0.743877i | \(0.267015\pi\) | |||||||
\(734\) | −36.3400 | −1.34133 | ||||||||
\(735\) | 1.19608 | 0.0441180 | ||||||||
\(736\) | −2.14134 | −0.0789307 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 9.03863 | 0.332717 | ||||||||
\(739\) | −15.1447 | −0.557108 | −0.278554 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278554 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(740\) | −3.55263 | −0.130597 | ||||||||
\(741\) | −4.28267 | −0.157328 | ||||||||
\(742\) | 23.0993 | 0.848002 | ||||||||
\(743\) | −3.85735 | −0.141512 | −0.0707561 | − | 0.997494i | \(-0.522541\pi\) | ||||
−0.0707561 | + | 0.997494i | \(0.522541\pi\) | |||||||
\(744\) | −9.55602 | −0.350341 | ||||||||
\(745\) | 4.05474 | 0.148554 | ||||||||
\(746\) | 30.1273 | 1.10304 | ||||||||
\(747\) | 0.887968 | 0.0324891 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.2207 | −1.06770 | ||||||||
\(750\) | 4.88797 | 0.178483 | ||||||||
\(751\) | 15.9346 | 0.581462 | 0.290731 | − | 0.956805i | \(-0.406101\pi\) | ||||
0.290731 | + | 0.956805i | \(0.406101\pi\) | |||||||
\(752\) | −7.59465 | −0.276948 | ||||||||
\(753\) | −11.1520 | −0.406401 | ||||||||
\(754\) | 5.58532 | 0.203405 | ||||||||
\(755\) | −5.01611 | −0.182555 | ||||||||
\(756\) | 12.0900 | 0.439708 | ||||||||
\(757\) | 25.7767 | 0.936870 | 0.468435 | − | 0.883498i | \(-0.344818\pi\) | ||||
0.468435 | + | 0.883498i | \(0.344818\pi\) | |||||||
\(758\) | 3.06200 | 0.111217 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.363328 | −0.0131793 | ||||||||
\(761\) | −24.5747 | −0.890831 | −0.445416 | − | 0.895324i | \(-0.646944\pi\) | ||||
−0.445416 | + | 0.895324i | \(0.646944\pi\) | |||||||
\(762\) | 3.33195 | 0.120704 | ||||||||
\(763\) | 11.4219 | 0.413502 | ||||||||
\(764\) | −3.87732 | −0.140277 | ||||||||
\(765\) | −0.473289 | −0.0171118 | ||||||||
\(766\) | 33.1307 | 1.19706 | ||||||||
\(767\) | 3.39470 | 0.122576 | ||||||||
\(768\) | −1.36333 | −0.0491949 | ||||||||
\(769\) | 51.3200 | 1.85065 | 0.925323 | − | 0.379180i | \(-0.123794\pi\) | ||||
0.925323 | + | 0.379180i | \(0.123794\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.3693 | 1.41785 | ||||||||
\(772\) | 5.32131 | 0.191518 | ||||||||
\(773\) | 27.0153 | 0.971672 | 0.485836 | − | 0.874050i | \(-0.338515\pi\) | ||||
0.485836 | + | 0.874050i | \(0.338515\pi\) | |||||||
\(774\) | 4.88797 | 0.175694 | ||||||||
\(775\) | −34.1214 | −1.22568 | ||||||||
\(776\) | −1.86799 | −0.0670570 | ||||||||
\(777\) | 28.5454 | 1.02406 | ||||||||
\(778\) | −3.81664 | −0.136833 | ||||||||
\(779\) | 7.91934 | 0.283740 | ||||||||
\(780\) | 1.55602 | 0.0557143 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.44398 | −0.0873967 | ||||||||
\(783\) | −10.0386 | −0.358751 | ||||||||
\(784\) | −2.41468 | −0.0862386 | ||||||||
\(785\) | 5.74276 | 0.204968 | ||||||||
\(786\) | 0.965235 | 0.0344288 | ||||||||
\(787\) | −22.8794 | −0.815562 | −0.407781 | − | 0.913080i | \(-0.633697\pi\) | ||||
−0.407781 | + | 0.913080i | \(0.633697\pi\) | |||||||
\(788\) | −14.3306 | −0.510508 | ||||||||
\(789\) | −0.525393 | −0.0187045 | ||||||||
\(790\) | 0.282672 | 0.0100570 | ||||||||
\(791\) | −30.7567 | −1.09358 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.7453 | 0.949754 | ||||||||
\(794\) | −25.0573 | −0.889250 | ||||||||
\(795\) | −5.34335 | −0.189509 | ||||||||
\(796\) | 5.83869 | 0.206947 | ||||||||
\(797\) | 41.6774 | 1.47629 | 0.738144 | − | 0.674643i | \(-0.235702\pi\) | ||||
0.738144 | + | 0.674643i | \(0.235702\pi\) | |||||||
\(798\) | 2.91934 | 0.103344 | ||||||||
\(799\) | −8.66805 | −0.306653 | ||||||||
\(800\) | −4.86799 | −0.172110 | ||||||||
\(801\) | 9.36126 | 0.330764 | ||||||||
\(802\) | −31.9567 | −1.12843 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −11.6774 | −0.411829 | ||||||||
\(805\) | −1.66598 | −0.0587180 | ||||||||
\(806\) | −22.0187 | −0.775574 | ||||||||
\(807\) | −18.4240 | −0.648556 | ||||||||
\(808\) | −10.0700 | −0.354262 | ||||||||
\(809\) | 29.7347 | 1.04542 | 0.522708 | − | 0.852512i | \(-0.324922\pi\) | ||||
0.522708 | + | 0.852512i | \(0.324922\pi\) | |||||||
\(810\) | −1.55263 | −0.0545537 | ||||||||
\(811\) | 17.6460 | 0.619635 | 0.309817 | − | 0.950796i | \(-0.399732\pi\) | ||||
0.309817 | + | 0.950796i | \(0.399732\pi\) | |||||||
\(812\) | −3.80731 | −0.133610 | ||||||||
\(813\) | 13.2733 | 0.465516 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.35061 | −0.0473098 | ||||||||
\(816\) | −1.55602 | −0.0544714 | ||||||||
\(817\) | 4.28267 | 0.149832 | ||||||||
\(818\) | 27.8280 | 0.972985 | ||||||||
\(819\) | 7.67738 | 0.268269 | ||||||||
\(820\) | −2.87732 | −0.100480 | ||||||||
\(821\) | −36.9766 | −1.29049 | −0.645247 | − | 0.763974i | \(-0.723245\pi\) | ||||
−0.645247 | + | 0.763974i | \(0.723245\pi\) | |||||||
\(822\) | −8.56534 | −0.298751 | ||||||||
\(823\) | −38.8094 | −1.35281 | −0.676405 | − | 0.736530i | \(-0.736463\pi\) | ||||
−0.676405 | + | 0.736530i | \(0.736463\pi\) | |||||||
\(824\) | −17.3434 | −0.604184 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.31405 | −0.0805160 | ||||||||
\(827\) | −29.0534 | −1.01029 | −0.505143 | − | 0.863036i | \(-0.668560\pi\) | ||||
−0.505143 | + | 0.863036i | \(0.668560\pi\) | |||||||
\(828\) | 2.44398 | 0.0849343 | ||||||||
\(829\) | 44.9333 | 1.56060 | 0.780299 | − | 0.625407i | \(-0.215067\pi\) | ||||
0.780299 | + | 0.625407i | \(0.215067\pi\) | |||||||
\(830\) | −0.282672 | −0.00981170 | ||||||||
\(831\) | 9.20070 | 0.319169 | ||||||||
\(832\) | −3.14134 | −0.108906 | ||||||||
\(833\) | −2.75596 | −0.0954884 | ||||||||
\(834\) | −5.45331 | −0.188833 | ||||||||
\(835\) | 1.91595 | 0.0663043 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.5747 | 1.36790 | ||||||||
\(838\) | −5.24065 | −0.181035 | ||||||||
\(839\) | 10.5140 | 0.362983 | 0.181492 | − | 0.983392i | \(-0.441907\pi\) | ||||
0.181492 | + | 0.983392i | \(0.441907\pi\) | |||||||
\(840\) | −1.06068 | −0.0365969 | ||||||||
\(841\) | −25.8387 | −0.890989 | ||||||||
\(842\) | −15.3340 | −0.528445 | ||||||||
\(843\) | 9.62602 | 0.331538 | ||||||||
\(844\) | 9.74870 | 0.335564 | ||||||||
\(845\) | −1.13795 | −0.0391466 | ||||||||
\(846\) | 8.66805 | 0.298014 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.7873 | 0.370439 | ||||||||
\(849\) | 11.5374 | 0.395961 | ||||||||
\(850\) | −5.55602 | −0.190570 | ||||||||
\(851\) | 20.9380 | 0.717745 | ||||||||
\(852\) | −4.77801 | −0.163692 | ||||||||
\(853\) | −8.55733 | −0.292998 | −0.146499 | − | 0.989211i | \(-0.546800\pi\) | ||||
−0.146499 | + | 0.989211i | \(0.546800\pi\) | |||||||
\(854\) | −18.2313 | −0.623863 | ||||||||
\(855\) | 0.414680 | 0.0141817 | ||||||||
\(856\) | −13.6460 | −0.466411 | ||||||||
\(857\) | 19.5560 | 0.668021 | 0.334010 | − | 0.942569i | \(-0.391598\pi\) | ||||
0.334010 | + | 0.942569i | \(0.391598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.7873 | 1.08457 | 0.542285 | − | 0.840195i | \(-0.317559\pi\) | ||||
0.542285 | + | 0.840195i | \(0.317559\pi\) | |||||||
\(860\) | −1.55602 | −0.0530597 | ||||||||
\(861\) | 23.1193 | 0.787903 | ||||||||
\(862\) | 18.8994 | 0.643715 | ||||||||
\(863\) | 28.8226 | 0.981132 | 0.490566 | − | 0.871404i | \(-0.336790\pi\) | ||||
0.490566 | + | 0.871404i | \(0.336790\pi\) | |||||||
\(864\) | 5.64600 | 0.192081 | ||||||||
\(865\) | 4.16593 | 0.141646 | ||||||||
\(866\) | −11.1787 | −0.379866 | ||||||||
\(867\) | 21.4006 | 0.726804 | ||||||||
\(868\) | 15.0093 | 0.509450 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.880711 | 0.0298589 | ||||||||
\(871\) | −26.9066 | −0.911696 | ||||||||
\(872\) | 5.33402 | 0.180633 | ||||||||
\(873\) | 2.13201 | 0.0721575 | ||||||||
\(874\) | 2.14134 | 0.0724318 | ||||||||
\(875\) | −7.67738 | −0.259543 | ||||||||
\(876\) | −16.0000 | −0.540590 | ||||||||
\(877\) | −11.4613 | −0.387021 | −0.193511 | − | 0.981098i | \(-0.561987\pi\) | ||||
−0.193511 | + | 0.981098i | \(0.561987\pi\) | |||||||
\(878\) | 23.4720 | 0.792141 | ||||||||
\(879\) | −29.7160 | −1.00230 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.7826 | −1.54246 | −0.771228 | − | 0.636559i | \(-0.780357\pi\) | ||||
−0.771228 | + | 0.636559i | \(0.780357\pi\) | |||||||
\(882\) | 2.75596 | 0.0927980 | ||||||||
\(883\) | −39.9673 | −1.34501 | −0.672503 | − | 0.740094i | \(-0.734781\pi\) | ||||
−0.672503 | + | 0.740094i | \(0.734781\pi\) | |||||||
\(884\) | −3.58532 | −0.120587 | ||||||||
\(885\) | 0.535287 | 0.0179935 | ||||||||
\(886\) | −29.8387 | −1.00245 | ||||||||
\(887\) | 37.8833 | 1.27200 | 0.635998 | − | 0.771691i | \(-0.280589\pi\) | ||||
0.635998 | + | 0.771691i | \(0.280589\pi\) | |||||||
\(888\) | 13.3306 | 0.447347 | ||||||||
\(889\) | −5.23339 | −0.175522 | ||||||||
\(890\) | −2.98002 | −0.0998906 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.6167 | −0.623333 | ||||||||
\(893\) | 7.59465 | 0.254145 | ||||||||
\(894\) | −15.2147 | −0.508857 | ||||||||
\(895\) | −0.327245 | −0.0109386 | ||||||||
\(896\) | 2.14134 | 0.0715370 | ||||||||
\(897\) | −9.17064 | −0.306199 | ||||||||
\(898\) | −10.6133 | −0.354171 | ||||||||
\(899\) | −12.4626 | −0.415652 | ||||||||
\(900\) | 5.55602 | 0.185201 | ||||||||
\(901\) | 12.3120 | 0.410171 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.5026 | 0.416060 | ||||||||
\(904\) | −14.3633 | −0.477717 | ||||||||
\(905\) | −6.06662 | −0.201661 | ||||||||
\(906\) | 18.8221 | 0.625322 | ||||||||
\(907\) | 9.11797 | 0.302757 | 0.151379 | − | 0.988476i | \(-0.451629\pi\) | ||||
0.151379 | + | 0.988476i | \(0.451629\pi\) | |||||||
\(908\) | −17.9160 | −0.594562 | ||||||||
\(909\) | 11.4933 | 0.381208 | ||||||||
\(910\) | −2.44398 | −0.0810173 | ||||||||
\(911\) | −13.9087 | −0.460816 | −0.230408 | − | 0.973094i | \(-0.574006\pi\) | ||||
−0.230408 | + | 0.973094i | \(0.574006\pi\) | |||||||
\(912\) | 1.36333 | 0.0451443 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −7.82936 | −0.258972 | ||||||||
\(915\) | 4.21728 | 0.139419 | ||||||||
\(916\) | −8.31198 | −0.274635 | ||||||||
\(917\) | −1.51606 | −0.0500648 | ||||||||
\(918\) | 6.44398 | 0.212683 | ||||||||
\(919\) | −35.1120 | −1.15824 | −0.579120 | − | 0.815243i | \(-0.696604\pi\) | ||||
−0.579120 | + | 0.815243i | \(0.696604\pi\) | |||||||
\(920\) | −0.778008 | −0.0256502 | ||||||||
\(921\) | 22.5667 | 0.743597 | ||||||||
\(922\) | −2.54330 | −0.0837590 | ||||||||
\(923\) | −11.0093 | −0.362376 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.5993 | 1.56505 | ||||||||
\(926\) | −31.6519 | −1.04015 | ||||||||
\(927\) | 19.7946 | 0.650140 | ||||||||
\(928\) | −1.77801 | −0.0583660 | ||||||||
\(929\) | −2.47875 | −0.0813251 | −0.0406626 | − | 0.999173i | \(-0.512947\pi\) | ||||
−0.0406626 | + | 0.999173i | \(0.512947\pi\) | |||||||
\(930\) | −3.47197 | −0.113850 | ||||||||
\(931\) | 2.41468 | 0.0791379 | ||||||||
\(932\) | 7.28267 | 0.238552 | ||||||||
\(933\) | 28.4227 | 0.930517 | ||||||||
\(934\) | −7.85735 | −0.257100 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.58532 | 0.117190 | ||||||||
\(937\) | −6.41600 | −0.209602 | −0.104801 | − | 0.994493i | \(-0.533420\pi\) | ||||
−0.104801 | + | 0.994493i | \(0.533420\pi\) | |||||||
\(938\) | 18.3413 | 0.598864 | ||||||||
\(939\) | 4.06455 | 0.132642 | ||||||||
\(940\) | −2.75935 | −0.0900001 | ||||||||
\(941\) | 19.2373 | 0.627117 | 0.313558 | − | 0.949569i | \(-0.398479\pi\) | ||||
0.313558 | + | 0.949569i | \(0.398479\pi\) | |||||||
\(942\) | −21.5488 | −0.702096 | ||||||||
\(943\) | 16.9580 | 0.552228 | ||||||||
\(944\) | −1.08066 | −0.0351724 | ||||||||
\(945\) | 4.39263 | 0.142892 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.2614 | 1.50329 | 0.751646 | − | 0.659566i | \(-0.229260\pi\) | ||||
0.751646 | + | 0.659566i | \(0.229260\pi\) | |||||||
\(948\) | −1.06068 | −0.0344493 | ||||||||
\(949\) | −36.8667 | −1.19674 | ||||||||
\(950\) | 4.86799 | 0.157939 | ||||||||
\(951\) | 16.2454 | 0.526792 | ||||||||
\(952\) | 2.44398 | 0.0792100 | ||||||||
\(953\) | −55.4541 | −1.79633 | −0.898167 | − | 0.439655i | \(-0.855101\pi\) | ||||
−0.898167 | + | 0.439655i | \(0.855101\pi\) | |||||||
\(954\) | −12.3120 | −0.398615 | ||||||||
\(955\) | −1.40874 | −0.0455858 | ||||||||
\(956\) | 11.1693 | 0.361242 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.9614 | 0.451071 | ||||||||
\(959\) | 13.4533 | 0.434430 | ||||||||
\(960\) | −0.495336 | −0.0159869 | ||||||||
\(961\) | 18.1307 | 0.584861 | ||||||||
\(962\) | 30.7160 | 0.990324 | ||||||||
\(963\) | 15.5747 | 0.501887 | ||||||||
\(964\) | 6.39263 | 0.205893 | ||||||||
\(965\) | 1.93338 | 0.0622377 | ||||||||
\(966\) | 6.25130 | 0.201132 | ||||||||
\(967\) | −14.4240 | −0.463845 | −0.231922 | − | 0.972734i | \(-0.574502\pi\) | ||||
−0.231922 | + | 0.972734i | \(0.574502\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.55602 | 0.0499864 | ||||||||
\(970\) | −0.678694 | −0.0217916 | ||||||||
\(971\) | 46.3140 | 1.48629 | 0.743144 | − | 0.669131i | \(-0.233334\pi\) | ||||
0.743144 | + | 0.669131i | \(0.233334\pi\) | |||||||
\(972\) | −11.1120 | −0.356419 | ||||||||
\(973\) | 8.56534 | 0.274592 | ||||||||
\(974\) | 1.83869 | 0.0589154 | ||||||||
\(975\) | −20.8480 | −0.667671 | ||||||||
\(976\) | −8.51399 | −0.272526 | ||||||||
\(977\) | 47.8680 | 1.53143 | 0.765716 | − | 0.643178i | \(-0.222385\pi\) | ||||
0.765716 | + | 0.643178i | \(0.222385\pi\) | |||||||
\(978\) | 5.06794 | 0.162055 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.877321 | −0.0280250 | ||||||||
\(981\) | −6.08791 | −0.194372 | ||||||||
\(982\) | 27.5747 | 0.879943 | ||||||||
\(983\) | −3.54198 | −0.112972 | −0.0564858 | − | 0.998403i | \(-0.517990\pi\) | ||||
−0.0564858 | + | 0.998403i | \(0.517990\pi\) | |||||||
\(984\) | 10.7967 | 0.344185 | ||||||||
\(985\) | −5.20672 | −0.165900 | ||||||||
\(986\) | −2.02930 | −0.0646262 | ||||||||
\(987\) | 22.1714 | 0.705723 | ||||||||
\(988\) | 3.14134 | 0.0999392 | ||||||||
\(989\) | 9.17064 | 0.291609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4113 | −0.330726 | −0.165363 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165363 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(992\) | 7.00933 | 0.222546 | ||||||||
\(993\) | −0.0173389 | −0.000550234 0 | ||||||||
\(994\) | 7.50466 | 0.238033 | ||||||||
\(995\) | 2.12136 | 0.0672516 | ||||||||
\(996\) | 1.06068 | 0.0336089 | ||||||||
\(997\) | −10.1834 | −0.322510 | −0.161255 | − | 0.986913i | \(-0.551554\pi\) | ||||
−0.161255 | + | 0.986913i | \(0.551554\pi\) | |||||||
\(998\) | 26.4113 | 0.836035 | ||||||||
\(999\) | −55.2066 | −1.74666 |
(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 | 4598.2.a.bn.1.2 | yes | 3 | |
11.10 | odd | 2 | 4598.2.a.bk.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.bk.1.2 | ✓ | 3 | 11.10 | odd | 2 | ||
4598.2.a.bn.1.2 | yes | 3 | 1.1 | even | 1 | trivial |