Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | −0.222181 | −0.128276 | −0.0641382 | − | 0.997941i | \(-0.520430\pi\) | ||||
−0.0641382 | + | 0.997941i | \(0.520430\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.181430 | 0.0811381 | 0.0405690 | − | 0.999177i | \(-0.487083\pi\) | ||||
0.0405690 | + | 0.999177i | \(0.487083\pi\) | |||||||
\(6\) | 0.222181 | 0.0907050 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.95064 | −0.983545 | ||||||||
\(10\) | −0.181430 | −0.0573733 | ||||||||
\(11\) | −1.69115 | −0.509901 | −0.254951 | − | 0.966954i | \(-0.582059\pi\) | ||||
−0.254951 | + | 0.966954i | \(0.582059\pi\) | |||||||
\(12\) | −0.222181 | −0.0641382 | ||||||||
\(13\) | −0.764574 | −0.212055 | −0.106027 | − | 0.994363i | \(-0.533813\pi\) | ||||
−0.106027 | + | 0.994363i | \(0.533813\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.0403104 | −0.0104081 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.26296 | −0.791384 | −0.395692 | − | 0.918383i | \(-0.629495\pi\) | ||||
−0.395692 | + | 0.918383i | \(0.629495\pi\) | |||||||
\(18\) | 2.95064 | 0.695471 | ||||||||
\(19\) | −0.180812 | −0.0414811 | −0.0207405 | − | 0.999785i | \(-0.506602\pi\) | ||||
−0.0207405 | + | 0.999785i | \(0.506602\pi\) | |||||||
\(20\) | 0.181430 | 0.0405690 | ||||||||
\(21\) | −0.222181 | −0.0484839 | ||||||||
\(22\) | 1.69115 | 0.360555 | ||||||||
\(23\) | −9.07368 | −1.89199 | −0.945996 | − | 0.324178i | \(-0.894912\pi\) | ||||
−0.945996 | + | 0.324178i | \(0.894912\pi\) | |||||||
\(24\) | 0.222181 | 0.0453525 | ||||||||
\(25\) | −4.96708 | −0.993417 | ||||||||
\(26\) | 0.764574 | 0.149945 | ||||||||
\(27\) | 1.32212 | 0.254442 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 2.26843 | 0.421238 | 0.210619 | − | 0.977568i | \(-0.432452\pi\) | ||||
0.210619 | + | 0.977568i | \(0.432452\pi\) | |||||||
\(30\) | 0.0403104 | 0.00735963 | ||||||||
\(31\) | 6.23761 | 1.12031 | 0.560154 | − | 0.828389i | \(-0.310742\pi\) | ||||
0.560154 | + | 0.828389i | \(0.310742\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.375742 | 0.0654083 | ||||||||
\(34\) | 3.26296 | 0.559593 | ||||||||
\(35\) | 0.181430 | 0.0306673 | ||||||||
\(36\) | −2.95064 | −0.491773 | ||||||||
\(37\) | −6.61975 | −1.08828 | −0.544140 | − | 0.838994i | \(-0.683144\pi\) | ||||
−0.544140 | + | 0.838994i | \(0.683144\pi\) | |||||||
\(38\) | 0.180812 | 0.0293316 | ||||||||
\(39\) | 0.169874 | 0.0272016 | ||||||||
\(40\) | −0.181430 | −0.0286866 | ||||||||
\(41\) | 9.18400 | 1.43430 | 0.717150 | − | 0.696919i | \(-0.245446\pi\) | ||||
0.717150 | + | 0.696919i | \(0.245446\pi\) | |||||||
\(42\) | 0.222181 | 0.0342833 | ||||||||
\(43\) | −10.7521 | −1.63968 | −0.819842 | − | 0.572590i | \(-0.805939\pi\) | ||||
−0.819842 | + | 0.572590i | \(0.805939\pi\) | |||||||
\(44\) | −1.69115 | −0.254951 | ||||||||
\(45\) | −0.535335 | −0.0798030 | ||||||||
\(46\) | 9.07368 | 1.33784 | ||||||||
\(47\) | 0.872479 | 0.127264 | 0.0636321 | − | 0.997973i | \(-0.479732\pi\) | ||||
0.0636321 | + | 0.997973i | \(0.479732\pi\) | |||||||
\(48\) | −0.222181 | −0.0320691 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.96708 | 0.702452 | ||||||||
\(51\) | 0.724968 | 0.101516 | ||||||||
\(52\) | −0.764574 | −0.106027 | ||||||||
\(53\) | 4.44835 | 0.611028 | 0.305514 | − | 0.952188i | \(-0.401172\pi\) | ||||
0.305514 | + | 0.952188i | \(0.401172\pi\) | |||||||
\(54\) | −1.32212 | −0.179918 | ||||||||
\(55\) | −0.306826 | −0.0413724 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0.0401730 | 0.00532104 | ||||||||
\(58\) | −2.26843 | −0.297860 | ||||||||
\(59\) | 8.43820 | 1.09856 | 0.549280 | − | 0.835638i | \(-0.314902\pi\) | ||||
0.549280 | + | 0.835638i | \(0.314902\pi\) | |||||||
\(60\) | −0.0403104 | −0.00520405 | ||||||||
\(61\) | −1.44890 | −0.185513 | −0.0927564 | − | 0.995689i | \(-0.529568\pi\) | ||||
−0.0927564 | + | 0.995689i | \(0.529568\pi\) | |||||||
\(62\) | −6.23761 | −0.792177 | ||||||||
\(63\) | −2.95064 | −0.371745 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.138717 | −0.0172057 | ||||||||
\(66\) | −0.375742 | −0.0462506 | ||||||||
\(67\) | −6.30903 | −0.770771 | −0.385385 | − | 0.922756i | \(-0.625931\pi\) | ||||
−0.385385 | + | 0.922756i | \(0.625931\pi\) | |||||||
\(68\) | −3.26296 | −0.395692 | ||||||||
\(69\) | 2.01600 | 0.242698 | ||||||||
\(70\) | −0.181430 | −0.0216851 | ||||||||
\(71\) | 3.51206 | 0.416805 | 0.208402 | − | 0.978043i | \(-0.433174\pi\) | ||||
0.208402 | + | 0.978043i | \(0.433174\pi\) | |||||||
\(72\) | 2.95064 | 0.347736 | ||||||||
\(73\) | −0.619658 | −0.0725255 | −0.0362628 | − | 0.999342i | \(-0.511545\pi\) | ||||
−0.0362628 | + | 0.999342i | \(0.511545\pi\) | |||||||
\(74\) | 6.61975 | 0.769530 | ||||||||
\(75\) | 1.10359 | 0.127432 | ||||||||
\(76\) | −0.180812 | −0.0207405 | ||||||||
\(77\) | −1.69115 | −0.192725 | ||||||||
\(78\) | −0.169874 | −0.0192344 | ||||||||
\(79\) | 8.64934 | 0.973127 | 0.486563 | − | 0.873645i | \(-0.338250\pi\) | ||||
0.486563 | + | 0.873645i | \(0.338250\pi\) | |||||||
\(80\) | 0.181430 | 0.0202845 | ||||||||
\(81\) | 8.55816 | 0.950906 | ||||||||
\(82\) | −9.18400 | −1.01420 | ||||||||
\(83\) | 12.5383 | 1.37625 | 0.688126 | − | 0.725591i | \(-0.258434\pi\) | ||||
0.688126 | + | 0.725591i | \(0.258434\pi\) | |||||||
\(84\) | −0.222181 | −0.0242419 | ||||||||
\(85\) | −0.591999 | −0.0642114 | ||||||||
\(86\) | 10.7521 | 1.15943 | ||||||||
\(87\) | −0.504003 | −0.0540348 | ||||||||
\(88\) | 1.69115 | 0.180277 | ||||||||
\(89\) | −0.954562 | −0.101183 | −0.0505917 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505917 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(90\) | 0.535335 | 0.0564292 | ||||||||
\(91\) | −0.764574 | −0.0801492 | ||||||||
\(92\) | −9.07368 | −0.945996 | ||||||||
\(93\) | −1.38588 | −0.143709 | ||||||||
\(94\) | −0.872479 | −0.0899893 | ||||||||
\(95\) | −0.0328047 | −0.00336570 | ||||||||
\(96\) | 0.222181 | 0.0226763 | ||||||||
\(97\) | 11.6487 | 1.18274 | 0.591372 | − | 0.806399i | \(-0.298586\pi\) | ||||
0.591372 | + | 0.806399i | \(0.298586\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.98997 | 0.501511 | ||||||||
\(100\) | −4.96708 | −0.496708 | ||||||||
\(101\) | 7.60806 | 0.757030 | 0.378515 | − | 0.925595i | \(-0.376435\pi\) | ||||
0.378515 | + | 0.925595i | \(0.376435\pi\) | |||||||
\(102\) | −0.724968 | −0.0717825 | ||||||||
\(103\) | −2.29684 | −0.226315 | −0.113157 | − | 0.993577i | \(-0.536096\pi\) | ||||
−0.113157 | + | 0.993577i | \(0.536096\pi\) | |||||||
\(104\) | 0.764574 | 0.0749727 | ||||||||
\(105\) | −0.0403104 | −0.00393389 | ||||||||
\(106\) | −4.44835 | −0.432062 | ||||||||
\(107\) | 3.11241 | 0.300888 | 0.150444 | − | 0.988619i | \(-0.451930\pi\) | ||||
0.150444 | + | 0.988619i | \(0.451930\pi\) | |||||||
\(108\) | 1.32212 | 0.127221 | ||||||||
\(109\) | 7.52106 | 0.720387 | 0.360193 | − | 0.932878i | \(-0.382711\pi\) | ||||
0.360193 | + | 0.932878i | \(0.382711\pi\) | |||||||
\(110\) | 0.306826 | 0.0292547 | ||||||||
\(111\) | 1.47078 | 0.139601 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −12.4522 | −1.17141 | −0.585703 | − | 0.810526i | \(-0.699182\pi\) | ||||
−0.585703 | + | 0.810526i | \(0.699182\pi\) | |||||||
\(114\) | −0.0401730 | −0.00376254 | ||||||||
\(115\) | −1.64624 | −0.153513 | ||||||||
\(116\) | 2.26843 | 0.210619 | ||||||||
\(117\) | 2.25598 | 0.208565 | ||||||||
\(118\) | −8.43820 | −0.776800 | ||||||||
\(119\) | −3.26296 | −0.299115 | ||||||||
\(120\) | 0.0403104 | 0.00367982 | ||||||||
\(121\) | −8.14001 | −0.740001 | ||||||||
\(122\) | 1.44890 | 0.131177 | ||||||||
\(123\) | −2.04051 | −0.183987 | ||||||||
\(124\) | 6.23761 | 0.560154 | ||||||||
\(125\) | −1.80833 | −0.161742 | ||||||||
\(126\) | 2.95064 | 0.262864 | ||||||||
\(127\) | −7.59123 | −0.673613 | −0.336807 | − | 0.941574i | \(-0.609347\pi\) | ||||
−0.336807 | + | 0.941574i | \(0.609347\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.38892 | 0.210333 | ||||||||
\(130\) | 0.138717 | 0.0121663 | ||||||||
\(131\) | 14.5569 | 1.27184 | 0.635921 | − | 0.771754i | \(-0.280620\pi\) | ||||
0.635921 | + | 0.771754i | \(0.280620\pi\) | |||||||
\(132\) | 0.375742 | 0.0327041 | ||||||||
\(133\) | −0.180812 | −0.0156784 | ||||||||
\(134\) | 6.30903 | 0.545017 | ||||||||
\(135\) | 0.239872 | 0.0206449 | ||||||||
\(136\) | 3.26296 | 0.279796 | ||||||||
\(137\) | 17.6146 | 1.50491 | 0.752457 | − | 0.658642i | \(-0.228869\pi\) | ||||
0.752457 | + | 0.658642i | \(0.228869\pi\) | |||||||
\(138\) | −2.01600 | −0.171613 | ||||||||
\(139\) | 12.9671 | 1.09986 | 0.549929 | − | 0.835212i | \(-0.314655\pi\) | ||||
0.549929 | + | 0.835212i | \(0.314655\pi\) | |||||||
\(140\) | 0.181430 | 0.0153337 | ||||||||
\(141\) | −0.193848 | −0.0163250 | ||||||||
\(142\) | −3.51206 | −0.294725 | ||||||||
\(143\) | 1.29301 | 0.108127 | ||||||||
\(144\) | −2.95064 | −0.245886 | ||||||||
\(145\) | 0.411563 | 0.0341784 | ||||||||
\(146\) | 0.619658 | 0.0512833 | ||||||||
\(147\) | −0.222181 | −0.0183252 | ||||||||
\(148\) | −6.61975 | −0.544140 | ||||||||
\(149\) | 8.65495 | 0.709041 | 0.354521 | − | 0.935048i | \(-0.384644\pi\) | ||||
0.354521 | + | 0.935048i | \(0.384644\pi\) | |||||||
\(150\) | −1.10359 | −0.0901079 | ||||||||
\(151\) | 0.864486 | 0.0703509 | 0.0351755 | − | 0.999381i | \(-0.488801\pi\) | ||||
0.0351755 | + | 0.999381i | \(0.488801\pi\) | |||||||
\(152\) | 0.180812 | 0.0146658 | ||||||||
\(153\) | 9.62780 | 0.778362 | ||||||||
\(154\) | 1.69115 | 0.136277 | ||||||||
\(155\) | 1.13169 | 0.0908996 | ||||||||
\(156\) | 0.169874 | 0.0136008 | ||||||||
\(157\) | −10.4682 | −0.835455 | −0.417727 | − | 0.908572i | \(-0.637173\pi\) | ||||
−0.417727 | + | 0.908572i | \(0.637173\pi\) | |||||||
\(158\) | −8.64934 | −0.688104 | ||||||||
\(159\) | −0.988340 | −0.0783804 | ||||||||
\(160\) | −0.181430 | −0.0143433 | ||||||||
\(161\) | −9.07368 | −0.715106 | ||||||||
\(162\) | −8.55816 | −0.672392 | ||||||||
\(163\) | −21.5570 | −1.68847 | −0.844237 | − | 0.535970i | \(-0.819946\pi\) | ||||
−0.844237 | + | 0.535970i | \(0.819946\pi\) | |||||||
\(164\) | 9.18400 | 0.717150 | ||||||||
\(165\) | 0.0681710 | 0.00530710 | ||||||||
\(166\) | −12.5383 | −0.973157 | ||||||||
\(167\) | 11.1046 | 0.859302 | 0.429651 | − | 0.902995i | \(-0.358637\pi\) | ||||
0.429651 | + | 0.902995i | \(0.358637\pi\) | |||||||
\(168\) | 0.222181 | 0.0171416 | ||||||||
\(169\) | −12.4154 | −0.955033 | ||||||||
\(170\) | 0.591999 | 0.0454043 | ||||||||
\(171\) | 0.533510 | 0.0407985 | ||||||||
\(172\) | −10.7521 | −0.819842 | ||||||||
\(173\) | 15.8285 | 1.20342 | 0.601709 | − | 0.798715i | \(-0.294487\pi\) | ||||
0.601709 | + | 0.798715i | \(0.294487\pi\) | |||||||
\(174\) | 0.504003 | 0.0382084 | ||||||||
\(175\) | −4.96708 | −0.375476 | ||||||||
\(176\) | −1.69115 | −0.127475 | ||||||||
\(177\) | −1.87481 | −0.140919 | ||||||||
\(178\) | 0.954562 | 0.0715474 | ||||||||
\(179\) | −15.6984 | −1.17336 | −0.586678 | − | 0.809820i | \(-0.699565\pi\) | ||||
−0.586678 | + | 0.809820i | \(0.699565\pi\) | |||||||
\(180\) | −0.535335 | −0.0399015 | ||||||||
\(181\) | 2.21669 | 0.164765 | 0.0823827 | − | 0.996601i | \(-0.473747\pi\) | ||||
0.0823827 | + | 0.996601i | \(0.473747\pi\) | |||||||
\(182\) | 0.764574 | 0.0566740 | ||||||||
\(183\) | 0.321919 | 0.0237969 | ||||||||
\(184\) | 9.07368 | 0.668920 | ||||||||
\(185\) | −1.20102 | −0.0883010 | ||||||||
\(186\) | 1.38588 | 0.101618 | ||||||||
\(187\) | 5.51816 | 0.403528 | ||||||||
\(188\) | 0.872479 | 0.0636321 | ||||||||
\(189\) | 1.32212 | 0.0961700 | ||||||||
\(190\) | 0.0328047 | 0.00237991 | ||||||||
\(191\) | 9.50153 | 0.687507 | 0.343753 | − | 0.939060i | \(-0.388302\pi\) | ||||
0.343753 | + | 0.939060i | \(0.388302\pi\) | |||||||
\(192\) | −0.222181 | −0.0160345 | ||||||||
\(193\) | 14.9199 | 1.07396 | 0.536980 | − | 0.843595i | \(-0.319565\pi\) | ||||
0.536980 | + | 0.843595i | \(0.319565\pi\) | |||||||
\(194\) | −11.6487 | −0.836327 | ||||||||
\(195\) | 0.0308203 | 0.00220709 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.0386 | 0.715224 | 0.357612 | − | 0.933870i | \(-0.383591\pi\) | ||||
0.357612 | + | 0.933870i | \(0.383591\pi\) | |||||||
\(198\) | −4.98997 | −0.354622 | ||||||||
\(199\) | 12.6335 | 0.895562 | 0.447781 | − | 0.894143i | \(-0.352214\pi\) | ||||
0.447781 | + | 0.894143i | \(0.352214\pi\) | |||||||
\(200\) | 4.96708 | 0.351226 | ||||||||
\(201\) | 1.40175 | 0.0988716 | ||||||||
\(202\) | −7.60806 | −0.535301 | ||||||||
\(203\) | 2.26843 | 0.159213 | ||||||||
\(204\) | 0.724968 | 0.0507579 | ||||||||
\(205\) | 1.66626 | 0.116376 | ||||||||
\(206\) | 2.29684 | 0.160029 | ||||||||
\(207\) | 26.7731 | 1.86086 | ||||||||
\(208\) | −0.764574 | −0.0530137 | ||||||||
\(209\) | 0.305780 | 0.0211513 | ||||||||
\(210\) | 0.0403104 | 0.00278168 | ||||||||
\(211\) | 10.0923 | 0.694780 | 0.347390 | − | 0.937721i | \(-0.387068\pi\) | ||||
0.347390 | + | 0.937721i | \(0.387068\pi\) | |||||||
\(212\) | 4.44835 | 0.305514 | ||||||||
\(213\) | −0.780313 | −0.0534661 | ||||||||
\(214\) | −3.11241 | −0.212760 | ||||||||
\(215\) | −1.95076 | −0.133041 | ||||||||
\(216\) | −1.32212 | −0.0899588 | ||||||||
\(217\) | 6.23761 | 0.423436 | ||||||||
\(218\) | −7.52106 | −0.509390 | ||||||||
\(219\) | 0.137676 | 0.00930330 | ||||||||
\(220\) | −0.306826 | −0.0206862 | ||||||||
\(221\) | 2.49477 | 0.167817 | ||||||||
\(222\) | −1.47078 | −0.0987125 | ||||||||
\(223\) | −22.5213 | −1.50814 | −0.754070 | − | 0.656795i | \(-0.771912\pi\) | ||||
−0.754070 | + | 0.656795i | \(0.771912\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 14.6561 | 0.977070 | ||||||||
\(226\) | 12.4522 | 0.828309 | ||||||||
\(227\) | −18.5599 | −1.23186 | −0.615930 | − | 0.787801i | \(-0.711220\pi\) | ||||
−0.615930 | + | 0.787801i | \(0.711220\pi\) | |||||||
\(228\) | 0.0401730 | 0.00266052 | ||||||||
\(229\) | −14.5860 | −0.963868 | −0.481934 | − | 0.876207i | \(-0.660066\pi\) | ||||
−0.481934 | + | 0.876207i | \(0.660066\pi\) | |||||||
\(230\) | 1.64624 | 0.108550 | ||||||||
\(231\) | 0.375742 | 0.0247220 | ||||||||
\(232\) | −2.26843 | −0.148930 | ||||||||
\(233\) | 12.5957 | 0.825171 | 0.412586 | − | 0.910919i | \(-0.364626\pi\) | ||||
0.412586 | + | 0.910919i | \(0.364626\pi\) | |||||||
\(234\) | −2.25598 | −0.147478 | ||||||||
\(235\) | 0.158294 | 0.0103260 | ||||||||
\(236\) | 8.43820 | 0.549280 | ||||||||
\(237\) | −1.92172 | −0.124829 | ||||||||
\(238\) | 3.26296 | 0.211506 | ||||||||
\(239\) | 8.42651 | 0.545066 | 0.272533 | − | 0.962146i | \(-0.412139\pi\) | ||||
0.272533 | + | 0.962146i | \(0.412139\pi\) | |||||||
\(240\) | −0.0403104 | −0.00260202 | ||||||||
\(241\) | −13.6211 | −0.877411 | −0.438705 | − | 0.898631i | \(-0.644563\pi\) | ||||
−0.438705 | + | 0.898631i | \(0.644563\pi\) | |||||||
\(242\) | 8.14001 | 0.523259 | ||||||||
\(243\) | −5.86782 | −0.376421 | ||||||||
\(244\) | −1.44890 | −0.0927564 | ||||||||
\(245\) | 0.181430 | 0.0115912 | ||||||||
\(246\) | 2.04051 | 0.130098 | ||||||||
\(247\) | 0.138244 | 0.00879626 | ||||||||
\(248\) | −6.23761 | −0.396088 | ||||||||
\(249\) | −2.78576 | −0.176541 | ||||||||
\(250\) | 1.80833 | 0.114369 | ||||||||
\(251\) | 16.2758 | 1.02732 | 0.513661 | − | 0.857993i | \(-0.328289\pi\) | ||||
0.513661 | + | 0.857993i | \(0.328289\pi\) | |||||||
\(252\) | −2.95064 | −0.185873 | ||||||||
\(253\) | 15.3450 | 0.964730 | ||||||||
\(254\) | 7.59123 | 0.476316 | ||||||||
\(255\) | 0.131531 | 0.00823680 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.687165 | −0.0428642 | −0.0214321 | − | 0.999770i | \(-0.506823\pi\) | ||||
−0.0214321 | + | 0.999770i | \(0.506823\pi\) | |||||||
\(258\) | −2.38892 | −0.148728 | ||||||||
\(259\) | −6.61975 | −0.411331 | ||||||||
\(260\) | −0.138717 | −0.00860286 | ||||||||
\(261\) | −6.69332 | −0.414306 | ||||||||
\(262\) | −14.5569 | −0.899328 | ||||||||
\(263\) | −7.31477 | −0.451048 | −0.225524 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225524 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(264\) | −0.375742 | −0.0231253 | ||||||||
\(265\) | 0.807066 | 0.0495776 | ||||||||
\(266\) | 0.180812 | 0.0110863 | ||||||||
\(267\) | 0.212086 | 0.0129794 | ||||||||
\(268\) | −6.30903 | −0.385385 | ||||||||
\(269\) | 1.01353 | 0.0617958 | 0.0308979 | − | 0.999523i | \(-0.490163\pi\) | ||||
0.0308979 | + | 0.999523i | \(0.490163\pi\) | |||||||
\(270\) | −0.239872 | −0.0145982 | ||||||||
\(271\) | −11.3333 | −0.688451 | −0.344225 | − | 0.938887i | \(-0.611858\pi\) | ||||
−0.344225 | + | 0.938887i | \(0.611858\pi\) | |||||||
\(272\) | −3.26296 | −0.197846 | ||||||||
\(273\) | 0.169874 | 0.0102812 | ||||||||
\(274\) | −17.6146 | −1.06413 | ||||||||
\(275\) | 8.40009 | 0.506545 | ||||||||
\(276\) | 2.01600 | 0.121349 | ||||||||
\(277\) | 10.1251 | 0.608358 | 0.304179 | − | 0.952615i | \(-0.401618\pi\) | ||||
0.304179 | + | 0.952615i | \(0.401618\pi\) | |||||||
\(278\) | −12.9671 | −0.777717 | ||||||||
\(279\) | −18.4049 | −1.10187 | ||||||||
\(280\) | −0.181430 | −0.0108425 | ||||||||
\(281\) | −10.4542 | −0.623645 | −0.311823 | − | 0.950140i | \(-0.600939\pi\) | ||||
−0.311823 | + | 0.950140i | \(0.600939\pi\) | |||||||
\(282\) | 0.193848 | 0.0115435 | ||||||||
\(283\) | −4.85289 | −0.288475 | −0.144237 | − | 0.989543i | \(-0.546073\pi\) | ||||
−0.144237 | + | 0.989543i | \(0.546073\pi\) | |||||||
\(284\) | 3.51206 | 0.208402 | ||||||||
\(285\) | 0.00728859 | 0.000431739 0 | ||||||||
\(286\) | −1.29301 | −0.0764574 | ||||||||
\(287\) | 9.18400 | 0.542115 | ||||||||
\(288\) | 2.95064 | 0.173868 | ||||||||
\(289\) | −6.35310 | −0.373712 | ||||||||
\(290\) | −0.411563 | −0.0241678 | ||||||||
\(291\) | −2.58812 | −0.151718 | ||||||||
\(292\) | −0.619658 | −0.0362628 | ||||||||
\(293\) | −16.7739 | −0.979939 | −0.489970 | − | 0.871740i | \(-0.662992\pi\) | ||||
−0.489970 | + | 0.871740i | \(0.662992\pi\) | |||||||
\(294\) | 0.222181 | 0.0129579 | ||||||||
\(295\) | 1.53095 | 0.0891351 | ||||||||
\(296\) | 6.61975 | 0.384765 | ||||||||
\(297\) | −2.23590 | −0.129740 | ||||||||
\(298\) | −8.65495 | −0.501368 | ||||||||
\(299\) | 6.93750 | 0.401206 | ||||||||
\(300\) | 1.10359 | 0.0637159 | ||||||||
\(301\) | −10.7521 | −0.619742 | ||||||||
\(302\) | −0.864486 | −0.0497456 | ||||||||
\(303\) | −1.69037 | −0.0971090 | ||||||||
\(304\) | −0.180812 | −0.0103703 | ||||||||
\(305\) | −0.262875 | −0.0150522 | ||||||||
\(306\) | −9.62780 | −0.550385 | ||||||||
\(307\) | 2.02016 | 0.115296 | 0.0576482 | − | 0.998337i | \(-0.481640\pi\) | ||||
0.0576482 | + | 0.998337i | \(0.481640\pi\) | |||||||
\(308\) | −1.69115 | −0.0963623 | ||||||||
\(309\) | 0.510315 | 0.0290308 | ||||||||
\(310\) | −1.13169 | −0.0642757 | ||||||||
\(311\) | 22.6040 | 1.28176 | 0.640878 | − | 0.767643i | \(-0.278570\pi\) | ||||
0.640878 | + | 0.767643i | \(0.278570\pi\) | |||||||
\(312\) | −0.169874 | −0.00961722 | ||||||||
\(313\) | 27.6395 | 1.56228 | 0.781140 | − | 0.624356i | \(-0.214639\pi\) | ||||
0.781140 | + | 0.624356i | \(0.214639\pi\) | |||||||
\(314\) | 10.4682 | 0.590756 | ||||||||
\(315\) | −0.535335 | −0.0301627 | ||||||||
\(316\) | 8.64934 | 0.486563 | ||||||||
\(317\) | 2.82069 | 0.158426 | 0.0792129 | − | 0.996858i | \(-0.474759\pi\) | ||||
0.0792129 | + | 0.996858i | \(0.474759\pi\) | |||||||
\(318\) | 0.988340 | 0.0554233 | ||||||||
\(319\) | −3.83627 | −0.214790 | ||||||||
\(320\) | 0.181430 | 0.0101423 | ||||||||
\(321\) | −0.691518 | −0.0385968 | ||||||||
\(322\) | 9.07368 | 0.505656 | ||||||||
\(323\) | 0.589982 | 0.0328275 | ||||||||
\(324\) | 8.55816 | 0.475453 | ||||||||
\(325\) | 3.79770 | 0.210659 | ||||||||
\(326\) | 21.5570 | 1.19393 | ||||||||
\(327\) | −1.67104 | −0.0924086 | ||||||||
\(328\) | −9.18400 | −0.507102 | ||||||||
\(329\) | 0.872479 | 0.0481013 | ||||||||
\(330\) | −0.0681710 | −0.00375269 | ||||||||
\(331\) | 2.57504 | 0.141537 | 0.0707684 | − | 0.997493i | \(-0.477455\pi\) | ||||
0.0707684 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(332\) | 12.5383 | 0.688126 | ||||||||
\(333\) | 19.5325 | 1.07037 | ||||||||
\(334\) | −11.1046 | −0.607618 | ||||||||
\(335\) | −1.14465 | −0.0625389 | ||||||||
\(336\) | −0.222181 | −0.0121210 | ||||||||
\(337\) | 25.6528 | 1.39740 | 0.698700 | − | 0.715415i | \(-0.253762\pi\) | ||||
0.698700 | + | 0.715415i | \(0.253762\pi\) | |||||||
\(338\) | 12.4154 | 0.675310 | ||||||||
\(339\) | 2.76665 | 0.150264 | ||||||||
\(340\) | −0.591999 | −0.0321057 | ||||||||
\(341\) | −10.5487 | −0.571246 | ||||||||
\(342\) | −0.533510 | −0.0288489 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 10.7521 | 0.579716 | ||||||||
\(345\) | 0.365763 | 0.0196920 | ||||||||
\(346\) | −15.8285 | −0.850945 | ||||||||
\(347\) | 7.27047 | 0.390299 | 0.195150 | − | 0.980773i | \(-0.437481\pi\) | ||||
0.195150 | + | 0.980773i | \(0.437481\pi\) | |||||||
\(348\) | −0.504003 | −0.0270174 | ||||||||
\(349\) | −2.62662 | −0.140600 | −0.0702998 | − | 0.997526i | \(-0.522396\pi\) | ||||
−0.0702998 | + | 0.997526i | \(0.522396\pi\) | |||||||
\(350\) | 4.96708 | 0.265502 | ||||||||
\(351\) | −1.01086 | −0.0539556 | ||||||||
\(352\) | 1.69115 | 0.0901387 | ||||||||
\(353\) | 3.01229 | 0.160328 | 0.0801641 | − | 0.996782i | \(-0.474456\pi\) | ||||
0.0801641 | + | 0.996782i | \(0.474456\pi\) | |||||||
\(354\) | 1.87481 | 0.0996450 | ||||||||
\(355\) | 0.637194 | 0.0338187 | ||||||||
\(356\) | −0.954562 | −0.0505917 | ||||||||
\(357\) | 0.724968 | 0.0383694 | ||||||||
\(358\) | 15.6984 | 0.829688 | ||||||||
\(359\) | −22.6329 | −1.19452 | −0.597260 | − | 0.802048i | \(-0.703744\pi\) | ||||
−0.597260 | + | 0.802048i | \(0.703744\pi\) | |||||||
\(360\) | 0.535335 | 0.0282146 | ||||||||
\(361\) | −18.9673 | −0.998279 | ||||||||
\(362\) | −2.21669 | −0.116507 | ||||||||
\(363\) | 1.80856 | 0.0949245 | ||||||||
\(364\) | −0.764574 | −0.0400746 | ||||||||
\(365\) | −0.112425 | −0.00588458 | ||||||||
\(366\) | −0.321919 | −0.0168270 | ||||||||
\(367\) | −21.7500 | −1.13534 | −0.567670 | − | 0.823256i | \(-0.692155\pi\) | ||||
−0.567670 | + | 0.823256i | \(0.692155\pi\) | |||||||
\(368\) | −9.07368 | −0.472998 | ||||||||
\(369\) | −27.0986 | −1.41070 | ||||||||
\(370\) | 1.20102 | 0.0624382 | ||||||||
\(371\) | 4.44835 | 0.230947 | ||||||||
\(372\) | −1.38588 | −0.0718544 | ||||||||
\(373\) | −19.4177 | −1.00541 | −0.502706 | − | 0.864457i | \(-0.667662\pi\) | ||||
−0.502706 | + | 0.864457i | \(0.667662\pi\) | |||||||
\(374\) | −5.51816 | −0.285337 | ||||||||
\(375\) | 0.401777 | 0.0207477 | ||||||||
\(376\) | −0.872479 | −0.0449947 | ||||||||
\(377\) | −1.73439 | −0.0893254 | ||||||||
\(378\) | −1.32212 | −0.0680024 | ||||||||
\(379\) | −7.48114 | −0.384280 | −0.192140 | − | 0.981367i | \(-0.561543\pi\) | ||||
−0.192140 | + | 0.981367i | \(0.561543\pi\) | |||||||
\(380\) | −0.0328047 | −0.00168285 | ||||||||
\(381\) | 1.68663 | 0.0864086 | ||||||||
\(382\) | −9.50153 | −0.486141 | ||||||||
\(383\) | −20.9325 | −1.06960 | −0.534800 | − | 0.844978i | \(-0.679613\pi\) | ||||
−0.534800 | + | 0.844978i | \(0.679613\pi\) | |||||||
\(384\) | 0.222181 | 0.0113381 | ||||||||
\(385\) | −0.306826 | −0.0156373 | ||||||||
\(386\) | −14.9199 | −0.759404 | ||||||||
\(387\) | 31.7256 | 1.61270 | ||||||||
\(388\) | 11.6487 | 0.591372 | ||||||||
\(389\) | 21.6585 | 1.09813 | 0.549066 | − | 0.835779i | \(-0.314984\pi\) | ||||
0.549066 | + | 0.835779i | \(0.314984\pi\) | |||||||
\(390\) | −0.0308203 | −0.00156065 | ||||||||
\(391\) | 29.6070 | 1.49729 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −3.23427 | −0.163147 | ||||||||
\(394\) | −10.0386 | −0.505740 | ||||||||
\(395\) | 1.56925 | 0.0789576 | ||||||||
\(396\) | 4.98997 | 0.250756 | ||||||||
\(397\) | −7.88730 | −0.395852 | −0.197926 | − | 0.980217i | \(-0.563421\pi\) | ||||
−0.197926 | + | 0.980217i | \(0.563421\pi\) | |||||||
\(398\) | −12.6335 | −0.633258 | ||||||||
\(399\) | 0.0401730 | 0.00201116 | ||||||||
\(400\) | −4.96708 | −0.248354 | ||||||||
\(401\) | 4.85539 | 0.242466 | 0.121233 | − | 0.992624i | \(-0.461315\pi\) | ||||
0.121233 | + | 0.992624i | \(0.461315\pi\) | |||||||
\(402\) | −1.40175 | −0.0699128 | ||||||||
\(403\) | −4.76911 | −0.237566 | ||||||||
\(404\) | 7.60806 | 0.378515 | ||||||||
\(405\) | 1.55271 | 0.0771547 | ||||||||
\(406\) | −2.26843 | −0.112580 | ||||||||
\(407\) | 11.1950 | 0.554916 | ||||||||
\(408\) | −0.724968 | −0.0358912 | ||||||||
\(409\) | 8.40627 | 0.415663 | 0.207832 | − | 0.978165i | \(-0.433359\pi\) | ||||
0.207832 | + | 0.978165i | \(0.433359\pi\) | |||||||
\(410\) | −1.66626 | −0.0822905 | ||||||||
\(411\) | −3.91362 | −0.193045 | ||||||||
\(412\) | −2.29684 | −0.113157 | ||||||||
\(413\) | 8.43820 | 0.415217 | ||||||||
\(414\) | −26.7731 | −1.31583 | ||||||||
\(415\) | 2.27482 | 0.111666 | ||||||||
\(416\) | 0.764574 | 0.0374863 | ||||||||
\(417\) | −2.88105 | −0.141086 | ||||||||
\(418\) | −0.305780 | −0.0149562 | ||||||||
\(419\) | 28.7383 | 1.40396 | 0.701979 | − | 0.712197i | \(-0.252300\pi\) | ||||
0.701979 | + | 0.712197i | \(0.252300\pi\) | |||||||
\(420\) | −0.0403104 | −0.00196694 | ||||||||
\(421\) | 13.7606 | 0.670652 | 0.335326 | − | 0.942102i | \(-0.391153\pi\) | ||||
0.335326 | + | 0.942102i | \(0.391153\pi\) | |||||||
\(422\) | −10.0923 | −0.491284 | ||||||||
\(423\) | −2.57437 | −0.125170 | ||||||||
\(424\) | −4.44835 | −0.216031 | ||||||||
\(425\) | 16.2074 | 0.786174 | ||||||||
\(426\) | 0.780313 | 0.0378063 | ||||||||
\(427\) | −1.44890 | −0.0701173 | ||||||||
\(428\) | 3.11241 | 0.150444 | ||||||||
\(429\) | −0.287283 | −0.0138701 | ||||||||
\(430\) | 1.95076 | 0.0940740 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | 1.32212 | 0.0636105 | ||||||||
\(433\) | 26.5821 | 1.27745 | 0.638726 | − | 0.769434i | \(-0.279462\pi\) | ||||
0.638726 | + | 0.769434i | \(0.279462\pi\) | |||||||
\(434\) | −6.23761 | −0.299415 | ||||||||
\(435\) | −0.0914414 | −0.00438428 | ||||||||
\(436\) | 7.52106 | 0.360193 | ||||||||
\(437\) | 1.64063 | 0.0784819 | ||||||||
\(438\) | −0.137676 | −0.00657843 | ||||||||
\(439\) | 29.1398 | 1.39077 | 0.695383 | − | 0.718639i | \(-0.255235\pi\) | ||||
0.695383 | + | 0.718639i | \(0.255235\pi\) | |||||||
\(440\) | 0.306826 | 0.0146274 | ||||||||
\(441\) | −2.95064 | −0.140506 | ||||||||
\(442\) | −2.49477 | −0.118664 | ||||||||
\(443\) | −3.97756 | −0.188980 | −0.0944898 | − | 0.995526i | \(-0.530122\pi\) | ||||
−0.0944898 | + | 0.995526i | \(0.530122\pi\) | |||||||
\(444\) | 1.47078 | 0.0698003 | ||||||||
\(445\) | −0.173186 | −0.00820982 | ||||||||
\(446\) | 22.5213 | 1.06642 | ||||||||
\(447\) | −1.92297 | −0.0909532 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −37.6928 | −1.77883 | −0.889416 | − | 0.457098i | \(-0.848889\pi\) | ||||
−0.889416 | + | 0.457098i | \(0.848889\pi\) | |||||||
\(450\) | −14.6561 | −0.690893 | ||||||||
\(451\) | −15.5315 | −0.731352 | ||||||||
\(452\) | −12.4522 | −0.585703 | ||||||||
\(453\) | −0.192073 | −0.00902435 | ||||||||
\(454\) | 18.5599 | 0.871057 | ||||||||
\(455\) | −0.138717 | −0.00650315 | ||||||||
\(456\) | −0.0401730 | −0.00188127 | ||||||||
\(457\) | −15.5137 | −0.725701 | −0.362850 | − | 0.931847i | \(-0.618196\pi\) | ||||
−0.362850 | + | 0.931847i | \(0.618196\pi\) | |||||||
\(458\) | 14.5860 | 0.681558 | ||||||||
\(459\) | −4.31402 | −0.201361 | ||||||||
\(460\) | −1.64624 | −0.0767563 | ||||||||
\(461\) | −8.71695 | −0.405989 | −0.202995 | − | 0.979180i | \(-0.565067\pi\) | ||||
−0.202995 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(462\) | −0.375742 | −0.0174811 | ||||||||
\(463\) | 2.18324 | 0.101464 | 0.0507319 | − | 0.998712i | \(-0.483845\pi\) | ||||
0.0507319 | + | 0.998712i | \(0.483845\pi\) | |||||||
\(464\) | 2.26843 | 0.105309 | ||||||||
\(465\) | −0.251440 | −0.0116603 | ||||||||
\(466\) | −12.5957 | −0.583484 | ||||||||
\(467\) | 10.4903 | 0.485434 | 0.242717 | − | 0.970097i | \(-0.421961\pi\) | ||||
0.242717 | + | 0.970097i | \(0.421961\pi\) | |||||||
\(468\) | 2.25598 | 0.104283 | ||||||||
\(469\) | −6.30903 | −0.291324 | ||||||||
\(470\) | −0.158294 | −0.00730156 | ||||||||
\(471\) | 2.32584 | 0.107169 | ||||||||
\(472\) | −8.43820 | −0.388400 | ||||||||
\(473\) | 18.1835 | 0.836077 | ||||||||
\(474\) | 1.92172 | 0.0882675 | ||||||||
\(475\) | 0.898108 | 0.0412080 | ||||||||
\(476\) | −3.26296 | −0.149557 | ||||||||
\(477\) | −13.1255 | −0.600974 | ||||||||
\(478\) | −8.42651 | −0.385420 | ||||||||
\(479\) | −15.1276 | −0.691199 | −0.345600 | − | 0.938382i | \(-0.612324\pi\) | ||||
−0.345600 | + | 0.938382i | \(0.612324\pi\) | |||||||
\(480\) | 0.0403104 | 0.00183991 | ||||||||
\(481\) | 5.06129 | 0.230775 | ||||||||
\(482\) | 13.6211 | 0.620423 | ||||||||
\(483\) | 2.01600 | 0.0917311 | ||||||||
\(484\) | −8.14001 | −0.370000 | ||||||||
\(485\) | 2.11342 | 0.0959656 | ||||||||
\(486\) | 5.86782 | 0.266170 | ||||||||
\(487\) | 38.1697 | 1.72963 | 0.864816 | − | 0.502089i | \(-0.167435\pi\) | ||||
0.864816 | + | 0.502089i | \(0.167435\pi\) | |||||||
\(488\) | 1.44890 | 0.0655887 | ||||||||
\(489\) | 4.78956 | 0.216591 | ||||||||
\(490\) | −0.181430 | −0.00819618 | ||||||||
\(491\) | 23.6915 | 1.06918 | 0.534592 | − | 0.845110i | \(-0.320465\pi\) | ||||
0.534592 | + | 0.845110i | \(0.320465\pi\) | |||||||
\(492\) | −2.04051 | −0.0919934 | ||||||||
\(493\) | −7.40180 | −0.333361 | ||||||||
\(494\) | −0.138244 | −0.00621990 | ||||||||
\(495\) | 0.905332 | 0.0406917 | ||||||||
\(496\) | 6.23761 | 0.280077 | ||||||||
\(497\) | 3.51206 | 0.157537 | ||||||||
\(498\) | 2.78576 | 0.124833 | ||||||||
\(499\) | −4.81388 | −0.215499 | −0.107749 | − | 0.994178i | \(-0.534364\pi\) | ||||
−0.107749 | + | 0.994178i | \(0.534364\pi\) | |||||||
\(500\) | −1.80833 | −0.0808710 | ||||||||
\(501\) | −2.46724 | −0.110228 | ||||||||
\(502\) | −16.2758 | −0.726426 | ||||||||
\(503\) | 17.9650 | 0.801022 | 0.400511 | − | 0.916292i | \(-0.368833\pi\) | ||||
0.400511 | + | 0.916292i | \(0.368833\pi\) | |||||||
\(504\) | 2.95064 | 0.131432 | ||||||||
\(505\) | 1.38033 | 0.0614239 | ||||||||
\(506\) | −15.3450 | −0.682167 | ||||||||
\(507\) | 2.75847 | 0.122508 | ||||||||
\(508\) | −7.59123 | −0.336807 | ||||||||
\(509\) | −39.3976 | −1.74627 | −0.873133 | − | 0.487481i | \(-0.837916\pi\) | ||||
−0.873133 | + | 0.487481i | \(0.837916\pi\) | |||||||
\(510\) | −0.131531 | −0.00582429 | ||||||||
\(511\) | −0.619658 | −0.0274121 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.239055 | −0.0105545 | ||||||||
\(514\) | 0.687165 | 0.0303095 | ||||||||
\(515\) | −0.416717 | −0.0183627 | ||||||||
\(516\) | 2.38892 | 0.105166 | ||||||||
\(517\) | −1.47549 | −0.0648922 | ||||||||
\(518\) | 6.61975 | 0.290855 | ||||||||
\(519\) | −3.51679 | −0.154370 | ||||||||
\(520\) | 0.138717 | 0.00608314 | ||||||||
\(521\) | 0.589027 | 0.0258057 | 0.0129029 | − | 0.999917i | \(-0.495893\pi\) | ||||
0.0129029 | + | 0.999917i | \(0.495893\pi\) | |||||||
\(522\) | 6.69332 | 0.292959 | ||||||||
\(523\) | 31.0425 | 1.35739 | 0.678697 | − | 0.734419i | \(-0.262545\pi\) | ||||
0.678697 | + | 0.734419i | \(0.262545\pi\) | |||||||
\(524\) | 14.5569 | 0.635921 | ||||||||
\(525\) | 1.10359 | 0.0481647 | ||||||||
\(526\) | 7.31477 | 0.318939 | ||||||||
\(527\) | −20.3531 | −0.886593 | ||||||||
\(528\) | 0.375742 | 0.0163521 | ||||||||
\(529\) | 59.3316 | 2.57963 | ||||||||
\(530\) | −0.807066 | −0.0350567 | ||||||||
\(531\) | −24.8981 | −1.08048 | ||||||||
\(532\) | −0.180812 | −0.00783919 | ||||||||
\(533\) | −7.02185 | −0.304150 | ||||||||
\(534\) | −0.212086 | −0.00917784 | ||||||||
\(535\) | 0.564685 | 0.0244135 | ||||||||
\(536\) | 6.30903 | 0.272509 | ||||||||
\(537\) | 3.48790 | 0.150514 | ||||||||
\(538\) | −1.01353 | −0.0436962 | ||||||||
\(539\) | −1.69115 | −0.0728431 | ||||||||
\(540\) | 0.239872 | 0.0103225 | ||||||||
\(541\) | 22.1239 | 0.951182 | 0.475591 | − | 0.879667i | \(-0.342234\pi\) | ||||
0.475591 | + | 0.879667i | \(0.342234\pi\) | |||||||
\(542\) | 11.3333 | 0.486808 | ||||||||
\(543\) | −0.492507 | −0.0211355 | ||||||||
\(544\) | 3.26296 | 0.139898 | ||||||||
\(545\) | 1.36455 | 0.0584508 | ||||||||
\(546\) | −0.169874 | −0.00726993 | ||||||||
\(547\) | 25.6048 | 1.09478 | 0.547391 | − | 0.836877i | \(-0.315621\pi\) | ||||
0.547391 | + | 0.836877i | \(0.315621\pi\) | |||||||
\(548\) | 17.6146 | 0.752457 | ||||||||
\(549\) | 4.27518 | 0.182460 | ||||||||
\(550\) | −8.40009 | −0.358181 | ||||||||
\(551\) | −0.410160 | −0.0174734 | ||||||||
\(552\) | −2.01600 | −0.0858066 | ||||||||
\(553\) | 8.64934 | 0.367807 | ||||||||
\(554\) | −10.1251 | −0.430174 | ||||||||
\(555\) | 0.266845 | 0.0113269 | ||||||||
\(556\) | 12.9671 | 0.549929 | ||||||||
\(557\) | −1.26146 | −0.0534496 | −0.0267248 | − | 0.999643i | \(-0.508508\pi\) | ||||
−0.0267248 | + | 0.999643i | \(0.508508\pi\) | |||||||
\(558\) | 18.4049 | 0.779142 | ||||||||
\(559\) | 8.22080 | 0.347703 | ||||||||
\(560\) | 0.181430 | 0.00766683 | ||||||||
\(561\) | −1.22603 | −0.0517630 | ||||||||
\(562\) | 10.4542 | 0.440984 | ||||||||
\(563\) | −3.61481 | −0.152346 | −0.0761731 | − | 0.997095i | \(-0.524270\pi\) | ||||
−0.0761731 | + | 0.997095i | \(0.524270\pi\) | |||||||
\(564\) | −0.193848 | −0.00816249 | ||||||||
\(565\) | −2.25921 | −0.0950457 | ||||||||
\(566\) | 4.85289 | 0.203982 | ||||||||
\(567\) | 8.55816 | 0.359409 | ||||||||
\(568\) | −3.51206 | −0.147363 | ||||||||
\(569\) | 32.5639 | 1.36515 | 0.682574 | − | 0.730816i | \(-0.260860\pi\) | ||||
0.682574 | + | 0.730816i | \(0.260860\pi\) | |||||||
\(570\) | −0.00728859 | −0.000305286 0 | ||||||||
\(571\) | −8.32894 | −0.348555 | −0.174278 | − | 0.984697i | \(-0.555759\pi\) | ||||
−0.174278 | + | 0.984697i | \(0.555759\pi\) | |||||||
\(572\) | 1.29301 | 0.0540635 | ||||||||
\(573\) | −2.11106 | −0.0881908 | ||||||||
\(574\) | −9.18400 | −0.383333 | ||||||||
\(575\) | 45.0697 | 1.87954 | ||||||||
\(576\) | −2.95064 | −0.122943 | ||||||||
\(577\) | 35.0961 | 1.46107 | 0.730535 | − | 0.682876i | \(-0.239271\pi\) | ||||
0.730535 | + | 0.682876i | \(0.239271\pi\) | |||||||
\(578\) | 6.35310 | 0.264254 | ||||||||
\(579\) | −3.31492 | −0.137764 | ||||||||
\(580\) | 0.411563 | 0.0170892 | ||||||||
\(581\) | 12.5383 | 0.520174 | ||||||||
\(582\) | 2.58812 | 0.107281 | ||||||||
\(583\) | −7.52284 | −0.311564 | ||||||||
\(584\) | 0.619658 | 0.0256416 | ||||||||
\(585\) | 0.409303 | 0.0169226 | ||||||||
\(586\) | 16.7739 | 0.692922 | ||||||||
\(587\) | 35.6815 | 1.47273 | 0.736367 | − | 0.676583i | \(-0.236540\pi\) | ||||
0.736367 | + | 0.676583i | \(0.236540\pi\) | |||||||
\(588\) | −0.222181 | −0.00916259 | ||||||||
\(589\) | −1.12783 | −0.0464716 | ||||||||
\(590\) | −1.53095 | −0.0630280 | ||||||||
\(591\) | −2.23040 | −0.0917463 | ||||||||
\(592\) | −6.61975 | −0.272070 | ||||||||
\(593\) | −37.6621 | −1.54660 | −0.773299 | − | 0.634042i | \(-0.781395\pi\) | ||||
−0.773299 | + | 0.634042i | \(0.781395\pi\) | |||||||
\(594\) | 2.23590 | 0.0917402 | ||||||||
\(595\) | −0.591999 | −0.0242696 | ||||||||
\(596\) | 8.65495 | 0.354521 | ||||||||
\(597\) | −2.80692 | −0.114879 | ||||||||
\(598\) | −6.93750 | −0.283695 | ||||||||
\(599\) | 18.4917 | 0.755551 | 0.377776 | − | 0.925897i | \(-0.376689\pi\) | ||||
0.377776 | + | 0.925897i | \(0.376689\pi\) | |||||||
\(600\) | −1.10359 | −0.0450540 | ||||||||
\(601\) | 24.1633 | 0.985640 | 0.492820 | − | 0.870131i | \(-0.335966\pi\) | ||||
0.492820 | + | 0.870131i | \(0.335966\pi\) | |||||||
\(602\) | 10.7521 | 0.438224 | ||||||||
\(603\) | 18.6156 | 0.758088 | ||||||||
\(604\) | 0.864486 | 0.0351755 | ||||||||
\(605\) | −1.47684 | −0.0600422 | ||||||||
\(606\) | 1.69037 | 0.0686664 | ||||||||
\(607\) | −5.29316 | −0.214843 | −0.107421 | − | 0.994214i | \(-0.534259\pi\) | ||||
−0.107421 | + | 0.994214i | \(0.534259\pi\) | |||||||
\(608\) | 0.180812 | 0.00733289 | ||||||||
\(609\) | −0.504003 | −0.0204232 | ||||||||
\(610\) | 0.262875 | 0.0106435 | ||||||||
\(611\) | −0.667075 | −0.0269870 | ||||||||
\(612\) | 9.62780 | 0.389181 | ||||||||
\(613\) | 26.4744 | 1.06929 | 0.534646 | − | 0.845076i | \(-0.320445\pi\) | ||||
0.534646 | + | 0.845076i | \(0.320445\pi\) | |||||||
\(614\) | −2.02016 | −0.0815269 | ||||||||
\(615\) | −0.370211 | −0.0149283 | ||||||||
\(616\) | 1.69115 | 0.0681384 | ||||||||
\(617\) | −14.3109 | −0.576136 | −0.288068 | − | 0.957610i | \(-0.593013\pi\) | ||||
−0.288068 | + | 0.957610i | \(0.593013\pi\) | |||||||
\(618\) | −0.510315 | −0.0205279 | ||||||||
\(619\) | 43.7445 | 1.75824 | 0.879120 | − | 0.476600i | \(-0.158131\pi\) | ||||
0.879120 | + | 0.476600i | \(0.158131\pi\) | |||||||
\(620\) | 1.13169 | 0.0454498 | ||||||||
\(621\) | −11.9965 | −0.481402 | ||||||||
\(622\) | −22.6040 | −0.906338 | ||||||||
\(623\) | −0.954562 | −0.0382437 | ||||||||
\(624\) | 0.169874 | 0.00680040 | ||||||||
\(625\) | 24.5073 | 0.980293 | ||||||||
\(626\) | −27.6395 | −1.10470 | ||||||||
\(627\) | −0.0679386 | −0.00271321 | ||||||||
\(628\) | −10.4682 | −0.417727 | ||||||||
\(629\) | 21.6000 | 0.861247 | ||||||||
\(630\) | 0.535335 | 0.0213282 | ||||||||
\(631\) | 26.5405 | 1.05656 | 0.528280 | − | 0.849070i | \(-0.322837\pi\) | ||||
0.528280 | + | 0.849070i | \(0.322837\pi\) | |||||||
\(632\) | −8.64934 | −0.344052 | ||||||||
\(633\) | −2.24231 | −0.0891239 | ||||||||
\(634\) | −2.82069 | −0.112024 | ||||||||
\(635\) | −1.37728 | −0.0546557 | ||||||||
\(636\) | −0.988340 | −0.0391902 | ||||||||
\(637\) | −0.764574 | −0.0302935 | ||||||||
\(638\) | 3.83627 | 0.151879 | ||||||||
\(639\) | −10.3628 | −0.409946 | ||||||||
\(640\) | −0.181430 | −0.00717166 | ||||||||
\(641\) | 3.66224 | 0.144650 | 0.0723249 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723249 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(642\) | 0.691518 | 0.0272920 | ||||||||
\(643\) | 49.6520 | 1.95808 | 0.979041 | − | 0.203662i | \(-0.0652842\pi\) | ||||
0.979041 | + | 0.203662i | \(0.0652842\pi\) | |||||||
\(644\) | −9.07368 | −0.357553 | ||||||||
\(645\) | 0.433422 | 0.0170660 | ||||||||
\(646\) | −0.589982 | −0.0232125 | ||||||||
\(647\) | 9.81980 | 0.386056 | 0.193028 | − | 0.981193i | \(-0.438169\pi\) | ||||
0.193028 | + | 0.981193i | \(0.438169\pi\) | |||||||
\(648\) | −8.55816 | −0.336196 | ||||||||
\(649\) | −14.2703 | −0.560158 | ||||||||
\(650\) | −3.79770 | −0.148958 | ||||||||
\(651\) | −1.38588 | −0.0543168 | ||||||||
\(652\) | −21.5570 | −0.844237 | ||||||||
\(653\) | −9.80228 | −0.383593 | −0.191796 | − | 0.981435i | \(-0.561431\pi\) | ||||
−0.191796 | + | 0.981435i | \(0.561431\pi\) | |||||||
\(654\) | 1.67104 | 0.0653427 | ||||||||
\(655\) | 2.64106 | 0.103195 | ||||||||
\(656\) | 9.18400 | 0.358575 | ||||||||
\(657\) | 1.82839 | 0.0713321 | ||||||||
\(658\) | −0.872479 | −0.0340128 | ||||||||
\(659\) | −0.605696 | −0.0235946 | −0.0117973 | − | 0.999930i | \(-0.503755\pi\) | ||||
−0.0117973 | + | 0.999930i | \(0.503755\pi\) | |||||||
\(660\) | 0.0681710 | 0.00265355 | ||||||||
\(661\) | −23.2628 | −0.904817 | −0.452409 | − | 0.891811i | \(-0.649435\pi\) | ||||
−0.452409 | + | 0.891811i | \(0.649435\pi\) | |||||||
\(662\) | −2.57504 | −0.100082 | ||||||||
\(663\) | −0.554292 | −0.0215269 | ||||||||
\(664\) | −12.5383 | −0.486579 | ||||||||
\(665\) | −0.0328047 | −0.00127211 | ||||||||
\(666\) | −19.5325 | −0.756868 | ||||||||
\(667\) | −20.5830 | −0.796978 | ||||||||
\(668\) | 11.1046 | 0.429651 | ||||||||
\(669\) | 5.00381 | 0.193459 | ||||||||
\(670\) | 1.14465 | 0.0442216 | ||||||||
\(671\) | 2.45031 | 0.0945933 | ||||||||
\(672\) | 0.222181 | 0.00857082 | ||||||||
\(673\) | −26.8544 | −1.03516 | −0.517581 | − | 0.855634i | \(-0.673167\pi\) | ||||
−0.517581 | + | 0.855634i | \(0.673167\pi\) | |||||||
\(674\) | −25.6528 | −0.988111 | ||||||||
\(675\) | −6.56707 | −0.252767 | ||||||||
\(676\) | −12.4154 | −0.477516 | ||||||||
\(677\) | 41.6367 | 1.60023 | 0.800113 | − | 0.599849i | \(-0.204773\pi\) | ||||
0.800113 | + | 0.599849i | \(0.204773\pi\) | |||||||
\(678\) | −2.76665 | −0.106252 | ||||||||
\(679\) | 11.6487 | 0.447035 | ||||||||
\(680\) | 0.591999 | 0.0227021 | ||||||||
\(681\) | 4.12365 | 0.158019 | ||||||||
\(682\) | 10.5487 | 0.403932 | ||||||||
\(683\) | 39.0735 | 1.49511 | 0.747553 | − | 0.664202i | \(-0.231228\pi\) | ||||
0.747553 | + | 0.664202i | \(0.231228\pi\) | |||||||
\(684\) | 0.533510 | 0.0203993 | ||||||||
\(685\) | 3.19581 | 0.122106 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 3.24073 | 0.123641 | ||||||||
\(688\) | −10.7521 | −0.409921 | ||||||||
\(689\) | −3.40109 | −0.129571 | ||||||||
\(690\) | −0.365763 | −0.0139244 | ||||||||
\(691\) | 9.88876 | 0.376186 | 0.188093 | − | 0.982151i | \(-0.439769\pi\) | ||||
0.188093 | + | 0.982151i | \(0.439769\pi\) | |||||||
\(692\) | 15.8285 | 0.601709 | ||||||||
\(693\) | 4.98997 | 0.189553 | ||||||||
\(694\) | −7.27047 | −0.275983 | ||||||||
\(695\) | 2.35263 | 0.0892403 | ||||||||
\(696\) | 0.504003 | 0.0191042 | ||||||||
\(697\) | −29.9670 | −1.13508 | ||||||||
\(698\) | 2.62662 | 0.0994190 | ||||||||
\(699\) | −2.79852 | −0.105850 | ||||||||
\(700\) | −4.96708 | −0.187738 | ||||||||
\(701\) | −45.2366 | −1.70856 | −0.854281 | − | 0.519812i | \(-0.826002\pi\) | ||||
−0.854281 | + | 0.519812i | \(0.826002\pi\) | |||||||
\(702\) | 1.01086 | 0.0381524 | ||||||||
\(703\) | 1.19693 | 0.0451430 | ||||||||
\(704\) | −1.69115 | −0.0637377 | ||||||||
\(705\) | −0.0351700 | −0.00132458 | ||||||||
\(706\) | −3.01229 | −0.113369 | ||||||||
\(707\) | 7.60806 | 0.286130 | ||||||||
\(708\) | −1.87481 | −0.0704596 | ||||||||
\(709\) | −41.0990 | −1.54351 | −0.771753 | − | 0.635923i | \(-0.780620\pi\) | ||||
−0.771753 | + | 0.635923i | \(0.780620\pi\) | |||||||
\(710\) | −0.637194 | −0.0239134 | ||||||||
\(711\) | −25.5210 | −0.957114 | ||||||||
\(712\) | 0.954562 | 0.0357737 | ||||||||
\(713\) | −56.5980 | −2.11961 | ||||||||
\(714\) | −0.724968 | −0.0271312 | ||||||||
\(715\) | 0.234591 | 0.00877322 | ||||||||
\(716\) | −15.6984 | −0.586678 | ||||||||
\(717\) | −1.87221 | −0.0699190 | ||||||||
\(718\) | 22.6329 | 0.844653 | ||||||||
\(719\) | −8.88811 | −0.331470 | −0.165735 | − | 0.986170i | \(-0.553000\pi\) | ||||
−0.165735 | + | 0.986170i | \(0.553000\pi\) | |||||||
\(720\) | −0.535335 | −0.0199507 | ||||||||
\(721\) | −2.29684 | −0.0855389 | ||||||||
\(722\) | 18.9673 | 0.705890 | ||||||||
\(723\) | 3.02635 | 0.112551 | ||||||||
\(724\) | 2.21669 | 0.0823827 | ||||||||
\(725\) | −11.2675 | −0.418464 | ||||||||
\(726\) | −1.80856 | −0.0671218 | ||||||||
\(727\) | −49.4887 | −1.83543 | −0.917717 | − | 0.397235i | \(-0.869970\pi\) | ||||
−0.917717 | + | 0.397235i | \(0.869970\pi\) | |||||||
\(728\) | 0.764574 | 0.0283370 | ||||||||
\(729\) | −24.3708 | −0.902620 | ||||||||
\(730\) | 0.112425 | 0.00416103 | ||||||||
\(731\) | 35.0837 | 1.29762 | ||||||||
\(732\) | 0.321919 | 0.0118985 | ||||||||
\(733\) | 11.3903 | 0.420709 | 0.210354 | − | 0.977625i | \(-0.432538\pi\) | ||||
0.210354 | + | 0.977625i | \(0.432538\pi\) | |||||||
\(734\) | 21.7500 | 0.802806 | ||||||||
\(735\) | −0.0403104 | −0.00148687 | ||||||||
\(736\) | 9.07368 | 0.334460 | ||||||||
\(737\) | 10.6695 | 0.393017 | ||||||||
\(738\) | 27.0986 | 0.997515 | ||||||||
\(739\) | −42.6236 | −1.56793 | −0.783966 | − | 0.620803i | \(-0.786807\pi\) | ||||
−0.783966 | + | 0.620803i | \(0.786807\pi\) | |||||||
\(740\) | −1.20102 | −0.0441505 | ||||||||
\(741\) | −0.0307152 | −0.00112835 | ||||||||
\(742\) | −4.44835 | −0.163304 | ||||||||
\(743\) | −32.8497 | −1.20514 | −0.602570 | − | 0.798066i | \(-0.705857\pi\) | ||||
−0.602570 | + | 0.798066i | \(0.705857\pi\) | |||||||
\(744\) | 1.38588 | 0.0508088 | ||||||||
\(745\) | 1.57027 | 0.0575302 | ||||||||
\(746\) | 19.4177 | 0.710934 | ||||||||
\(747\) | −36.9958 | −1.35361 | ||||||||
\(748\) | 5.51816 | 0.201764 | ||||||||
\(749\) | 3.11241 | 0.113725 | ||||||||
\(750\) | −0.401777 | −0.0146708 | ||||||||
\(751\) | −21.8231 | −0.796336 | −0.398168 | − | 0.917313i | \(-0.630354\pi\) | ||||
−0.398168 | + | 0.917313i | \(0.630354\pi\) | |||||||
\(752\) | 0.872479 | 0.0318160 | ||||||||
\(753\) | −3.61618 | −0.131781 | ||||||||
\(754\) | 1.73439 | 0.0631626 | ||||||||
\(755\) | 0.156844 | 0.00570814 | ||||||||
\(756\) | 1.32212 | 0.0480850 | ||||||||
\(757\) | 41.5711 | 1.51093 | 0.755464 | − | 0.655190i | \(-0.227412\pi\) | ||||
0.755464 | + | 0.655190i | \(0.227412\pi\) | |||||||
\(758\) | 7.48114 | 0.271727 | ||||||||
\(759\) | −3.40936 | −0.123752 | ||||||||
\(760\) | 0.0328047 | 0.00118995 | ||||||||
\(761\) | 12.4935 | 0.452890 | 0.226445 | − | 0.974024i | \(-0.427290\pi\) | ||||
0.226445 | + | 0.974024i | \(0.427290\pi\) | |||||||
\(762\) | −1.68663 | −0.0611001 | ||||||||
\(763\) | 7.52106 | 0.272281 | ||||||||
\(764\) | 9.50153 | 0.343753 | ||||||||
\(765\) | 1.74677 | 0.0631548 | ||||||||
\(766\) | 20.9325 | 0.756322 | ||||||||
\(767\) | −6.45163 | −0.232955 | ||||||||
\(768\) | −0.222181 | −0.00801727 | ||||||||
\(769\) | −27.3982 | −0.988005 | −0.494002 | − | 0.869461i | \(-0.664467\pi\) | ||||
−0.494002 | + | 0.869461i | \(0.664467\pi\) | |||||||
\(770\) | 0.306826 | 0.0110572 | ||||||||
\(771\) | 0.152675 | 0.00549846 | ||||||||
\(772\) | 14.9199 | 0.536980 | ||||||||
\(773\) | 50.8343 | 1.82838 | 0.914192 | − | 0.405282i | \(-0.132827\pi\) | ||||
0.914192 | + | 0.405282i | \(0.132827\pi\) | |||||||
\(774\) | −31.7256 | −1.14035 | ||||||||
\(775\) | −30.9827 | −1.11293 | ||||||||
\(776\) | −11.6487 | −0.418163 | ||||||||
\(777\) | 1.47078 | 0.0527641 | ||||||||
\(778\) | −21.6585 | −0.776496 | ||||||||
\(779\) | −1.66058 | −0.0594963 | ||||||||
\(780\) | 0.0308203 | 0.00110354 | ||||||||
\(781\) | −5.93942 | −0.212529 | ||||||||
\(782\) | −29.6070 | −1.05875 | ||||||||
\(783\) | 2.99914 | 0.107180 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −1.89925 | −0.0677872 | ||||||||
\(786\) | 3.23427 | 0.115363 | ||||||||
\(787\) | 0.493542 | 0.0175929 | 0.00879644 | − | 0.999961i | \(-0.497200\pi\) | ||||
0.00879644 | + | 0.999961i | \(0.497200\pi\) | |||||||
\(788\) | 10.0386 | 0.357612 | ||||||||
\(789\) | 1.62520 | 0.0578588 | ||||||||
\(790\) | −1.56925 | −0.0558315 | ||||||||
\(791\) | −12.4522 | −0.442750 | ||||||||
\(792\) | −4.98997 | −0.177311 | ||||||||
\(793\) | 1.10779 | 0.0393389 | ||||||||
\(794\) | 7.88730 | 0.279910 | ||||||||
\(795\) | −0.179315 | −0.00635964 | ||||||||
\(796\) | 12.6335 | 0.447781 | ||||||||
\(797\) | −36.3198 | −1.28651 | −0.643256 | − | 0.765651i | \(-0.722417\pi\) | ||||
−0.643256 | + | 0.765651i | \(0.722417\pi\) | |||||||
\(798\) | −0.0401730 | −0.00142211 | ||||||||
\(799\) | −2.84686 | −0.100715 | ||||||||
\(800\) | 4.96708 | 0.175613 | ||||||||
\(801\) | 2.81656 | 0.0995184 | ||||||||
\(802\) | −4.85539 | −0.171450 | ||||||||
\(803\) | 1.04794 | 0.0369809 | ||||||||
\(804\) | 1.40175 | 0.0494358 | ||||||||
\(805\) | −1.64624 | −0.0580223 | ||||||||
\(806\) | 4.76911 | 0.167985 | ||||||||
\(807\) | −0.225186 | −0.00792694 | ||||||||
\(808\) | −7.60806 | −0.267650 | ||||||||
\(809\) | 49.1509 | 1.72805 | 0.864027 | − | 0.503446i | \(-0.167935\pi\) | ||||
0.864027 | + | 0.503446i | \(0.167935\pi\) | |||||||
\(810\) | −1.55271 | −0.0545566 | ||||||||
\(811\) | 33.7687 | 1.18578 | 0.592890 | − | 0.805284i | \(-0.297987\pi\) | ||||
0.592890 | + | 0.805284i | \(0.297987\pi\) | |||||||
\(812\) | 2.26843 | 0.0796064 | ||||||||
\(813\) | 2.51805 | 0.0883119 | ||||||||
\(814\) | −11.1950 | −0.392385 | ||||||||
\(815\) | −3.91109 | −0.137000 | ||||||||
\(816\) | 0.724968 | 0.0253789 | ||||||||
\(817\) | 1.94411 | 0.0680159 | ||||||||
\(818\) | −8.40627 | −0.293918 | ||||||||
\(819\) | 2.25598 | 0.0788303 | ||||||||
\(820\) | 1.66626 | 0.0581882 | ||||||||
\(821\) | 13.9867 | 0.488141 | 0.244070 | − | 0.969758i | \(-0.421517\pi\) | ||||
0.244070 | + | 0.969758i | \(0.421517\pi\) | |||||||
\(822\) | 3.91362 | 0.136503 | ||||||||
\(823\) | 5.27876 | 0.184006 | 0.0920029 | − | 0.995759i | \(-0.470673\pi\) | ||||
0.0920029 | + | 0.995759i | \(0.470673\pi\) | |||||||
\(824\) | 2.29684 | 0.0800144 | ||||||||
\(825\) | −1.86634 | −0.0649777 | ||||||||
\(826\) | −8.43820 | −0.293603 | ||||||||
\(827\) | −29.9732 | −1.04227 | −0.521135 | − | 0.853474i | \(-0.674491\pi\) | ||||
−0.521135 | + | 0.853474i | \(0.674491\pi\) | |||||||
\(828\) | 26.7731 | 0.930430 | ||||||||
\(829\) | 23.1779 | 0.805001 | 0.402501 | − | 0.915420i | \(-0.368141\pi\) | ||||
0.402501 | + | 0.915420i | \(0.368141\pi\) | |||||||
\(830\) | −2.27482 | −0.0789601 | ||||||||
\(831\) | −2.24960 | −0.0780379 | ||||||||
\(832\) | −0.764574 | −0.0265068 | ||||||||
\(833\) | −3.26296 | −0.113055 | ||||||||
\(834\) | 2.88105 | 0.0997626 | ||||||||
\(835\) | 2.01472 | 0.0697221 | ||||||||
\(836\) | 0.305780 | 0.0105756 | ||||||||
\(837\) | 8.24686 | 0.285053 | ||||||||
\(838\) | −28.7383 | −0.992749 | ||||||||
\(839\) | 31.7932 | 1.09762 | 0.548811 | − | 0.835946i | \(-0.315081\pi\) | ||||
0.548811 | + | 0.835946i | \(0.315081\pi\) | |||||||
\(840\) | 0.0403104 | 0.00139084 | ||||||||
\(841\) | −23.8542 | −0.822559 | ||||||||
\(842\) | −13.7606 | −0.474223 | ||||||||
\(843\) | 2.32272 | 0.0799989 | ||||||||
\(844\) | 10.0923 | 0.347390 | ||||||||
\(845\) | −2.25253 | −0.0774895 | ||||||||
\(846\) | 2.57437 | 0.0885086 | ||||||||
\(847\) | −8.14001 | −0.279694 | ||||||||
\(848\) | 4.44835 | 0.152757 | ||||||||
\(849\) | 1.07822 | 0.0370045 | ||||||||
\(850\) | −16.2074 | −0.555909 | ||||||||
\(851\) | 60.0655 | 2.05902 | ||||||||
\(852\) | −0.780313 | −0.0267331 | ||||||||
\(853\) | −23.9796 | −0.821045 | −0.410523 | − | 0.911850i | \(-0.634654\pi\) | ||||
−0.410523 | + | 0.911850i | \(0.634654\pi\) | |||||||
\(854\) | 1.44890 | 0.0495804 | ||||||||
\(855\) | 0.0967948 | 0.00331031 | ||||||||
\(856\) | −3.11241 | −0.106380 | ||||||||
\(857\) | −32.3002 | −1.10335 | −0.551676 | − | 0.834058i | \(-0.686012\pi\) | ||||
−0.551676 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(858\) | 0.287283 | 0.00980767 | ||||||||
\(859\) | −13.4031 | −0.457309 | −0.228655 | − | 0.973508i | \(-0.573433\pi\) | ||||
−0.228655 | + | 0.973508i | \(0.573433\pi\) | |||||||
\(860\) | −1.95076 | −0.0665204 | ||||||||
\(861\) | −2.04051 | −0.0695405 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | 35.8740 | 1.22116 | 0.610582 | − | 0.791953i | \(-0.290936\pi\) | ||||
0.610582 | + | 0.791953i | \(0.290936\pi\) | |||||||
\(864\) | −1.32212 | −0.0449794 | ||||||||
\(865\) | 2.87177 | 0.0976431 | ||||||||
\(866\) | −26.5821 | −0.903295 | ||||||||
\(867\) | 1.41154 | 0.0479384 | ||||||||
\(868\) | 6.23761 | 0.211718 | ||||||||
\(869\) | −14.6273 | −0.496199 | ||||||||
\(870\) | 0.0914414 | 0.00310015 | ||||||||
\(871\) | 4.82372 | 0.163446 | ||||||||
\(872\) | −7.52106 | −0.254695 | ||||||||
\(873\) | −34.3710 | −1.16328 | ||||||||
\(874\) | −1.64063 | −0.0554951 | ||||||||
\(875\) | −1.80833 | −0.0611327 | ||||||||
\(876\) | 0.137676 | 0.00465165 | ||||||||
\(877\) | −33.2518 | −1.12283 | −0.561416 | − | 0.827533i | \(-0.689743\pi\) | ||||
−0.561416 | + | 0.827533i | \(0.689743\pi\) | |||||||
\(878\) | −29.1398 | −0.983420 | ||||||||
\(879\) | 3.72683 | 0.125703 | ||||||||
\(880\) | −0.306826 | −0.0103431 | ||||||||
\(881\) | −54.7340 | −1.84404 | −0.922018 | − | 0.387146i | \(-0.873461\pi\) | ||||
−0.922018 | + | 0.387146i | \(0.873461\pi\) | |||||||
\(882\) | 2.95064 | 0.0993531 | ||||||||
\(883\) | −32.4511 | −1.09207 | −0.546033 | − | 0.837763i | \(-0.683863\pi\) | ||||
−0.546033 | + | 0.837763i | \(0.683863\pi\) | |||||||
\(884\) | 2.49477 | 0.0839083 | ||||||||
\(885\) | −0.340147 | −0.0114339 | ||||||||
\(886\) | 3.97756 | 0.133629 | ||||||||
\(887\) | 30.6836 | 1.03026 | 0.515128 | − | 0.857113i | \(-0.327744\pi\) | ||||
0.515128 | + | 0.857113i | \(0.327744\pi\) | |||||||
\(888\) | −1.47078 | −0.0493563 | ||||||||
\(889\) | −7.59123 | −0.254602 | ||||||||
\(890\) | 0.173186 | 0.00580522 | ||||||||
\(891\) | −14.4731 | −0.484869 | ||||||||
\(892\) | −22.5213 | −0.754070 | ||||||||
\(893\) | −0.157755 | −0.00527906 | ||||||||
\(894\) | 1.92297 | 0.0643136 | ||||||||
\(895\) | −2.84817 | −0.0952039 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −1.54138 | −0.0514652 | ||||||||
\(898\) | 37.6928 | 1.25782 | ||||||||
\(899\) | 14.1496 | 0.471915 | ||||||||
\(900\) | 14.6561 | 0.488535 | ||||||||
\(901\) | −14.5148 | −0.483558 | ||||||||
\(902\) | 15.5315 | 0.517144 | ||||||||
\(903\) | 2.38892 | 0.0794982 | ||||||||
\(904\) | 12.4522 | 0.414155 | ||||||||
\(905\) | 0.402175 | 0.0133688 | ||||||||
\(906\) | 0.192073 | 0.00638118 | ||||||||
\(907\) | 44.6104 | 1.48126 | 0.740632 | − | 0.671910i | \(-0.234526\pi\) | ||||
0.740632 | + | 0.671910i | \(0.234526\pi\) | |||||||
\(908\) | −18.5599 | −0.615930 | ||||||||
\(909\) | −22.4486 | −0.744573 | ||||||||
\(910\) | 0.138717 | 0.00459842 | ||||||||
\(911\) | −28.3826 | −0.940358 | −0.470179 | − | 0.882571i | \(-0.655811\pi\) | ||||
−0.470179 | + | 0.882571i | \(0.655811\pi\) | |||||||
\(912\) | 0.0401730 | 0.00133026 | ||||||||
\(913\) | −21.2041 | −0.701753 | ||||||||
\(914\) | 15.5137 | 0.513148 | ||||||||
\(915\) | 0.0584058 | 0.00193084 | ||||||||
\(916\) | −14.5860 | −0.481934 | ||||||||
\(917\) | 14.5569 | 0.480711 | ||||||||
\(918\) | 4.31402 | 0.142384 | ||||||||
\(919\) | 0.869292 | 0.0286753 | 0.0143376 | − | 0.999897i | \(-0.495436\pi\) | ||||
0.0143376 | + | 0.999897i | \(0.495436\pi\) | |||||||
\(920\) | 1.64624 | 0.0542749 | ||||||||
\(921\) | −0.448841 | −0.0147898 | ||||||||
\(922\) | 8.71695 | 0.287078 | ||||||||
\(923\) | −2.68523 | −0.0883854 | ||||||||
\(924\) | 0.375742 | 0.0123610 | ||||||||
\(925\) | 32.8808 | 1.08112 | ||||||||
\(926\) | −2.18324 | −0.0717458 | ||||||||
\(927\) | 6.77715 | 0.222591 | ||||||||
\(928\) | −2.26843 | −0.0744650 | ||||||||
\(929\) | −21.3795 | −0.701438 | −0.350719 | − | 0.936481i | \(-0.614063\pi\) | ||||
−0.350719 | + | 0.936481i | \(0.614063\pi\) | |||||||
\(930\) | 0.251440 | 0.00824505 | ||||||||
\(931\) | −0.180812 | −0.00592587 | ||||||||
\(932\) | 12.5957 | 0.412586 | ||||||||
\(933\) | −5.02218 | −0.164419 | ||||||||
\(934\) | −10.4903 | −0.343253 | ||||||||
\(935\) | 1.00116 | 0.0327415 | ||||||||
\(936\) | −2.25598 | −0.0737390 | ||||||||
\(937\) | 50.2248 | 1.64077 | 0.820386 | − | 0.571810i | \(-0.193759\pi\) | ||||
0.820386 | + | 0.571810i | \(0.193759\pi\) | |||||||
\(938\) | 6.30903 | 0.205997 | ||||||||
\(939\) | −6.14098 | −0.200403 | ||||||||
\(940\) | 0.158294 | 0.00516298 | ||||||||
\(941\) | 43.8993 | 1.43108 | 0.715539 | − | 0.698573i | \(-0.246181\pi\) | ||||
0.715539 | + | 0.698573i | \(0.246181\pi\) | |||||||
\(942\) | −2.32584 | −0.0757800 | ||||||||
\(943\) | −83.3327 | −2.71368 | ||||||||
\(944\) | 8.43820 | 0.274640 | ||||||||
\(945\) | 0.239872 | 0.00780305 | ||||||||
\(946\) | −18.1835 | −0.591196 | ||||||||
\(947\) | 50.4144 | 1.63825 | 0.819124 | − | 0.573617i | \(-0.194460\pi\) | ||||
0.819124 | + | 0.573617i | \(0.194460\pi\) | |||||||
\(948\) | −1.92172 | −0.0624145 | ||||||||
\(949\) | 0.473775 | 0.0153794 | ||||||||
\(950\) | −0.898108 | −0.0291385 | ||||||||
\(951\) | −0.626704 | −0.0203223 | ||||||||
\(952\) | 3.26296 | 0.105753 | ||||||||
\(953\) | −13.2352 | −0.428729 | −0.214364 | − | 0.976754i | \(-0.568768\pi\) | ||||
−0.214364 | + | 0.976754i | \(0.568768\pi\) | |||||||
\(954\) | 13.1255 | 0.424953 | ||||||||
\(955\) | 1.72387 | 0.0557830 | ||||||||
\(956\) | 8.42651 | 0.272533 | ||||||||
\(957\) | 0.852346 | 0.0275524 | ||||||||
\(958\) | 15.1276 | 0.488752 | ||||||||
\(959\) | 17.6146 | 0.568804 | ||||||||
\(960\) | −0.0403104 | −0.00130101 | ||||||||
\(961\) | 7.90773 | 0.255088 | ||||||||
\(962\) | −5.06129 | −0.163183 | ||||||||
\(963\) | −9.18358 | −0.295937 | ||||||||
\(964\) | −13.6211 | −0.438705 | ||||||||
\(965\) | 2.70693 | 0.0871390 | ||||||||
\(966\) | −2.01600 | −0.0648637 | ||||||||
\(967\) | 23.2874 | 0.748871 | 0.374435 | − | 0.927253i | \(-0.377837\pi\) | ||||
0.374435 | + | 0.927253i | \(0.377837\pi\) | |||||||
\(968\) | 8.14001 | 0.261630 | ||||||||
\(969\) | −0.131083 | −0.00421098 | ||||||||
\(970\) | −2.11342 | −0.0678579 | ||||||||
\(971\) | −25.5910 | −0.821253 | −0.410627 | − | 0.911804i | \(-0.634690\pi\) | ||||
−0.410627 | + | 0.911804i | \(0.634690\pi\) | |||||||
\(972\) | −5.86782 | −0.188210 | ||||||||
\(973\) | 12.9671 | 0.415707 | ||||||||
\(974\) | −38.1697 | −1.22303 | ||||||||
\(975\) | −0.843778 | −0.0270225 | ||||||||
\(976\) | −1.44890 | −0.0463782 | ||||||||
\(977\) | −12.0856 | −0.386653 | −0.193326 | − | 0.981134i | \(-0.561928\pi\) | ||||
−0.193326 | + | 0.981134i | \(0.561928\pi\) | |||||||
\(978\) | −4.78956 | −0.153153 | ||||||||
\(979\) | 1.61431 | 0.0515935 | ||||||||
\(980\) | 0.181430 | 0.00579558 | ||||||||
\(981\) | −22.1919 | −0.708533 | ||||||||
\(982\) | −23.6915 | −0.756027 | ||||||||
\(983\) | −19.7032 | −0.628434 | −0.314217 | − | 0.949351i | \(-0.601742\pi\) | ||||
−0.314217 | + | 0.949351i | \(0.601742\pi\) | |||||||
\(984\) | 2.04051 | 0.0650491 | ||||||||
\(985\) | 1.82131 | 0.0580319 | ||||||||
\(986\) | 7.40180 | 0.235721 | ||||||||
\(987\) | −0.193848 | −0.00617026 | ||||||||
\(988\) | 0.138244 | 0.00439813 | ||||||||
\(989\) | 97.5613 | 3.10227 | ||||||||
\(990\) | −0.905332 | −0.0287733 | ||||||||
\(991\) | −23.2132 | −0.737390 | −0.368695 | − | 0.929550i | \(-0.620195\pi\) | ||||
−0.368695 | + | 0.929550i | \(0.620195\pi\) | |||||||
\(992\) | −6.23761 | −0.198044 | ||||||||
\(993\) | −0.572125 | −0.0181558 | ||||||||
\(994\) | −3.51206 | −0.111396 | ||||||||
\(995\) | 2.29209 | 0.0726642 | ||||||||
\(996\) | −2.78576 | −0.0882703 | ||||||||
\(997\) | 11.1354 | 0.352662 | 0.176331 | − | 0.984331i | \(-0.443577\pi\) | ||||
0.176331 | + | 0.984331i | \(0.443577\pi\) | |||||||
\(998\) | 4.81388 | 0.152381 | ||||||||
\(999\) | −8.75210 | −0.276904 |
(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 | 6034.2.a.p.1.14 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.p.1.14 | ✓ | 27 | 1.1 | even | 1 | trivial |