Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, 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("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.2661761.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 6x^{4} + 3x^{3} + 9x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.34697\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.782747 | 0.553486 | 0.276743 | − | 0.960944i | \(-0.410745\pi\) | ||||
0.276743 | + | 0.960944i | \(0.410745\pi\) | |||||||
\(3\) | 1.34697 | 0.777672 | 0.388836 | − | 0.921307i | \(-0.372877\pi\) | ||||
0.388836 | + | 0.921307i | \(0.372877\pi\) | |||||||
\(4\) | −1.38731 | −0.693653 | ||||||||
\(5\) | −0.742408 | −0.332015 | −0.166008 | − | 0.986124i | \(-0.553088\pi\) | ||||
−0.166008 | + | 0.986124i | \(0.553088\pi\) | |||||||
\(6\) | 1.05434 | 0.430431 | ||||||||
\(7\) | −2.34697 | −0.887070 | −0.443535 | − | 0.896257i | \(-0.646276\pi\) | ||||
−0.443535 | + | 0.896257i | \(0.646276\pi\) | |||||||
\(8\) | −2.65140 | −0.937413 | ||||||||
\(9\) | −1.18568 | −0.395226 | ||||||||
\(10\) | −0.581118 | −0.183766 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.86866 | −0.539435 | ||||||||
\(13\) | −2.09467 | −0.580958 | −0.290479 | − | 0.956881i | \(-0.593815\pi\) | ||||
−0.290479 | + | 0.956881i | \(0.593815\pi\) | |||||||
\(14\) | −1.83708 | −0.490981 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0.699234 | 0.174808 | ||||||||
\(17\) | −4.14567 | −1.00547 | −0.502736 | − | 0.864440i | \(-0.667673\pi\) | ||||
−0.502736 | + | 0.864440i | \(0.667673\pi\) | |||||||
\(18\) | −0.928086 | −0.218752 | ||||||||
\(19\) | 3.60293 | 0.826569 | 0.413285 | − | 0.910602i | \(-0.364381\pi\) | ||||
0.413285 | + | 0.910602i | \(0.364381\pi\) | |||||||
\(20\) | 1.02995 | 0.230303 | ||||||||
\(21\) | −3.16129 | −0.689850 | ||||||||
\(22\) | −0.782747 | −0.166882 | ||||||||
\(23\) | −0.776241 | −0.161857 | −0.0809287 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809287 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(24\) | −3.57136 | −0.729000 | ||||||||
\(25\) | −4.44883 | −0.889766 | ||||||||
\(26\) | −1.63960 | −0.321552 | ||||||||
\(27\) | −5.63797 | −1.08503 | ||||||||
\(28\) | 3.25596 | 0.615319 | ||||||||
\(29\) | 2.99837 | 0.556784 | 0.278392 | − | 0.960468i | \(-0.410199\pi\) | ||||
0.278392 | + | 0.960468i | \(0.410199\pi\) | |||||||
\(30\) | −0.782747 | −0.142909 | ||||||||
\(31\) | −5.41725 | −0.972968 | −0.486484 | − | 0.873690i | \(-0.661721\pi\) | ||||
−0.486484 | + | 0.873690i | \(0.661721\pi\) | |||||||
\(32\) | 5.85013 | 1.03417 | ||||||||
\(33\) | −1.34697 | −0.234477 | ||||||||
\(34\) | −3.24501 | −0.556514 | ||||||||
\(35\) | 1.74241 | 0.294521 | ||||||||
\(36\) | 1.64490 | 0.274150 | ||||||||
\(37\) | 8.69435 | 1.42934 | 0.714671 | − | 0.699460i | \(-0.246576\pi\) | ||||
0.714671 | + | 0.699460i | \(0.246576\pi\) | |||||||
\(38\) | 2.82019 | 0.457494 | ||||||||
\(39\) | −2.82146 | −0.451795 | ||||||||
\(40\) | 1.96842 | 0.311235 | ||||||||
\(41\) | 7.27899 | 1.13679 | 0.568393 | − | 0.822757i | \(-0.307565\pi\) | ||||
0.568393 | + | 0.822757i | \(0.307565\pi\) | |||||||
\(42\) | −2.47449 | −0.381822 | ||||||||
\(43\) | −10.4140 | −1.58812 | −0.794060 | − | 0.607839i | \(-0.792036\pi\) | ||||
−0.794060 | + | 0.607839i | \(0.792036\pi\) | |||||||
\(44\) | 1.38731 | 0.209144 | ||||||||
\(45\) | 0.880257 | 0.131221 | ||||||||
\(46\) | −0.607600 | −0.0895858 | ||||||||
\(47\) | 9.01495 | 1.31497 | 0.657483 | − | 0.753469i | \(-0.271621\pi\) | ||||
0.657483 | + | 0.753469i | \(0.271621\pi\) | |||||||
\(48\) | 0.941846 | 0.135944 | ||||||||
\(49\) | −1.49174 | −0.213106 | ||||||||
\(50\) | −3.48231 | −0.492473 | ||||||||
\(51\) | −5.58408 | −0.781928 | ||||||||
\(52\) | 2.90596 | 0.402984 | ||||||||
\(53\) | −8.90673 | −1.22343 | −0.611716 | − | 0.791077i | \(-0.709521\pi\) | ||||
−0.611716 | + | 0.791077i | \(0.709521\pi\) | |||||||
\(54\) | −4.41311 | −0.600548 | ||||||||
\(55\) | 0.742408 | 0.100106 | ||||||||
\(56\) | 6.22276 | 0.831552 | ||||||||
\(57\) | 4.85303 | 0.642800 | ||||||||
\(58\) | 2.34697 | 0.308172 | ||||||||
\(59\) | −7.30217 | −0.950661 | −0.475331 | − | 0.879807i | \(-0.657672\pi\) | ||||
−0.475331 | + | 0.879807i | \(0.657672\pi\) | |||||||
\(60\) | 1.38731 | 0.179101 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −4.24034 | −0.538524 | ||||||||
\(63\) | 2.78275 | 0.350593 | ||||||||
\(64\) | 3.18071 | 0.397588 | ||||||||
\(65\) | 1.55510 | 0.192887 | ||||||||
\(66\) | −1.05434 | −0.129780 | ||||||||
\(67\) | 12.2026 | 1.49079 | 0.745393 | − | 0.666625i | \(-0.232262\pi\) | ||||
0.745393 | + | 0.666625i | \(0.232262\pi\) | |||||||
\(68\) | 5.75131 | 0.697449 | ||||||||
\(69\) | −1.04557 | −0.125872 | ||||||||
\(70\) | 1.36387 | 0.163013 | ||||||||
\(71\) | −14.2107 | −1.68651 | −0.843253 | − | 0.537518i | \(-0.819362\pi\) | ||||
−0.843253 | + | 0.537518i | \(0.819362\pi\) | |||||||
\(72\) | 3.14371 | 0.370490 | ||||||||
\(73\) | 11.6807 | 1.36712 | 0.683560 | − | 0.729894i | \(-0.260431\pi\) | ||||
0.683560 | + | 0.729894i | \(0.260431\pi\) | |||||||
\(74\) | 6.80548 | 0.791121 | ||||||||
\(75\) | −5.99243 | −0.691946 | ||||||||
\(76\) | −4.99837 | −0.573353 | ||||||||
\(77\) | 2.34697 | 0.267462 | ||||||||
\(78\) | −2.20849 | −0.250062 | ||||||||
\(79\) | 8.08687 | 0.909844 | 0.454922 | − | 0.890531i | \(-0.349667\pi\) | ||||
0.454922 | + | 0.890531i | \(0.349667\pi\) | |||||||
\(80\) | −0.519117 | −0.0580390 | ||||||||
\(81\) | −4.03714 | −0.448571 | ||||||||
\(82\) | 5.69761 | 0.629195 | ||||||||
\(83\) | −0.786515 | −0.0863312 | −0.0431656 | − | 0.999068i | \(-0.513744\pi\) | ||||
−0.0431656 | + | 0.999068i | \(0.513744\pi\) | |||||||
\(84\) | 4.38568 | 0.478517 | ||||||||
\(85\) | 3.07778 | 0.333832 | ||||||||
\(86\) | −8.15153 | −0.879002 | ||||||||
\(87\) | 4.03871 | 0.432995 | ||||||||
\(88\) | 2.65140 | 0.282641 | ||||||||
\(89\) | −4.13148 | −0.437936 | −0.218968 | − | 0.975732i | \(-0.570269\pi\) | ||||
−0.218968 | + | 0.975732i | \(0.570269\pi\) | |||||||
\(90\) | 0.689019 | 0.0726289 | ||||||||
\(91\) | 4.91613 | 0.515351 | ||||||||
\(92\) | 1.07688 | 0.112273 | ||||||||
\(93\) | −7.29687 | −0.756650 | ||||||||
\(94\) | 7.05643 | 0.727815 | ||||||||
\(95\) | −2.67485 | −0.274433 | ||||||||
\(96\) | 7.87994 | 0.804243 | ||||||||
\(97\) | −10.2966 | −1.04546 | −0.522729 | − | 0.852499i | \(-0.675086\pi\) | ||||
−0.522729 | + | 0.852499i | \(0.675086\pi\) | |||||||
\(98\) | −1.16766 | −0.117951 | ||||||||
\(99\) | 1.18568 | 0.119165 | ||||||||
\(100\) | 6.17189 | 0.617189 | ||||||||
\(101\) | −4.05895 | −0.403881 | −0.201940 | − | 0.979398i | \(-0.564725\pi\) | ||||
−0.201940 | + | 0.979398i | \(0.564725\pi\) | |||||||
\(102\) | −4.37092 | −0.432786 | ||||||||
\(103\) | −5.66377 | −0.558068 | −0.279034 | − | 0.960281i | \(-0.590014\pi\) | ||||
−0.279034 | + | 0.960281i | \(0.590014\pi\) | |||||||
\(104\) | 5.55383 | 0.544598 | ||||||||
\(105\) | 2.34697 | 0.229041 | ||||||||
\(106\) | −6.97171 | −0.677153 | ||||||||
\(107\) | 2.69077 | 0.260127 | 0.130063 | − | 0.991506i | \(-0.458482\pi\) | ||||
0.130063 | + | 0.991506i | \(0.458482\pi\) | |||||||
\(108\) | 7.82160 | 0.752634 | ||||||||
\(109\) | −15.6641 | −1.50035 | −0.750174 | − | 0.661240i | \(-0.770031\pi\) | ||||
−0.750174 | + | 0.661240i | \(0.770031\pi\) | |||||||
\(110\) | 0.581118 | 0.0554074 | ||||||||
\(111\) | 11.7110 | 1.11156 | ||||||||
\(112\) | −1.64108 | −0.155067 | ||||||||
\(113\) | −1.78319 | −0.167748 | −0.0838742 | − | 0.996476i | \(-0.526729\pi\) | ||||
−0.0838742 | + | 0.996476i | \(0.526729\pi\) | |||||||
\(114\) | 3.79870 | 0.355781 | ||||||||
\(115\) | 0.576288 | 0.0537391 | ||||||||
\(116\) | −4.15966 | −0.386215 | ||||||||
\(117\) | 2.48361 | 0.229610 | ||||||||
\(118\) | −5.71575 | −0.526177 | ||||||||
\(119\) | 9.72975 | 0.891924 | ||||||||
\(120\) | 2.65140 | 0.242039 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.782747 | −0.0708666 | ||||||||
\(123\) | 9.80456 | 0.884048 | ||||||||
\(124\) | 7.51539 | 0.674902 | ||||||||
\(125\) | 7.01489 | 0.627431 | ||||||||
\(126\) | 2.17819 | 0.194048 | ||||||||
\(127\) | −2.31761 | −0.205655 | −0.102827 | − | 0.994699i | \(-0.532789\pi\) | ||||
−0.102827 | + | 0.994699i | \(0.532789\pi\) | |||||||
\(128\) | −9.21058 | −0.814108 | ||||||||
\(129\) | −14.0273 | −1.23504 | ||||||||
\(130\) | 1.21725 | 0.106760 | ||||||||
\(131\) | −0.614737 | −0.0537098 | −0.0268549 | − | 0.999639i | \(-0.508549\pi\) | ||||
−0.0268549 | + | 0.999639i | \(0.508549\pi\) | |||||||
\(132\) | 1.86866 | 0.162646 | ||||||||
\(133\) | −8.45597 | −0.733225 | ||||||||
\(134\) | 9.55156 | 0.825129 | ||||||||
\(135\) | 4.18568 | 0.360246 | ||||||||
\(136\) | 10.9918 | 0.942543 | ||||||||
\(137\) | 16.8439 | 1.43907 | 0.719535 | − | 0.694456i | \(-0.244355\pi\) | ||||
0.719535 | + | 0.694456i | \(0.244355\pi\) | |||||||
\(138\) | −0.818418 | −0.0696684 | ||||||||
\(139\) | −10.1653 | −0.862211 | −0.431106 | − | 0.902301i | \(-0.641876\pi\) | ||||
−0.431106 | + | 0.902301i | \(0.641876\pi\) | |||||||
\(140\) | −2.41725 | −0.204295 | ||||||||
\(141\) | 12.1429 | 1.02261 | ||||||||
\(142\) | −11.1234 | −0.933457 | ||||||||
\(143\) | 2.09467 | 0.175165 | ||||||||
\(144\) | −0.829066 | −0.0690888 | ||||||||
\(145\) | −2.22602 | −0.184861 | ||||||||
\(146\) | 9.14302 | 0.756682 | ||||||||
\(147\) | −2.00933 | −0.165727 | ||||||||
\(148\) | −12.0617 | −0.991468 | ||||||||
\(149\) | −9.13134 | −0.748068 | −0.374034 | − | 0.927415i | \(-0.622026\pi\) | ||||
−0.374034 | + | 0.927415i | \(0.622026\pi\) | |||||||
\(150\) | −4.69056 | −0.382983 | ||||||||
\(151\) | 19.9281 | 1.62172 | 0.810862 | − | 0.585238i | \(-0.198999\pi\) | ||||
0.810862 | + | 0.585238i | \(0.198999\pi\) | |||||||
\(152\) | −9.55283 | −0.774837 | ||||||||
\(153\) | 4.91542 | 0.397388 | ||||||||
\(154\) | 1.83708 | 0.148036 | ||||||||
\(155\) | 4.02181 | 0.323040 | ||||||||
\(156\) | 3.91423 | 0.313389 | ||||||||
\(157\) | 4.89609 | 0.390750 | 0.195375 | − | 0.980729i | \(-0.437408\pi\) | ||||
0.195375 | + | 0.980729i | \(0.437408\pi\) | |||||||
\(158\) | 6.32997 | 0.503586 | ||||||||
\(159\) | −11.9971 | −0.951430 | ||||||||
\(160\) | −4.34319 | −0.343359 | ||||||||
\(161\) | 1.82181 | 0.143579 | ||||||||
\(162\) | −3.16006 | −0.248278 | ||||||||
\(163\) | −15.2596 | −1.19522 | −0.597610 | − | 0.801787i | \(-0.703883\pi\) | ||||
−0.597610 | + | 0.801787i | \(0.703883\pi\) | |||||||
\(164\) | −10.0982 | −0.788536 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | −0.615642 | −0.0477831 | ||||||||
\(167\) | 8.81814 | 0.682368 | 0.341184 | − | 0.939996i | \(-0.389172\pi\) | ||||
0.341184 | + | 0.939996i | \(0.389172\pi\) | |||||||
\(168\) | 8.38186 | 0.646675 | ||||||||
\(169\) | −8.61234 | −0.662488 | ||||||||
\(170\) | 2.40912 | 0.184771 | ||||||||
\(171\) | −4.27192 | −0.326682 | ||||||||
\(172\) | 14.4474 | 1.10160 | ||||||||
\(173\) | −7.21491 | −0.548540 | −0.274270 | − | 0.961653i | \(-0.588436\pi\) | ||||
−0.274270 | + | 0.961653i | \(0.588436\pi\) | |||||||
\(174\) | 3.16129 | 0.239657 | ||||||||
\(175\) | 10.4413 | 0.789285 | ||||||||
\(176\) | −0.699234 | −0.0527067 | ||||||||
\(177\) | −9.83578 | −0.739303 | ||||||||
\(178\) | −3.23391 | −0.242392 | ||||||||
\(179\) | −1.51078 | −0.112921 | −0.0564604 | − | 0.998405i | \(-0.517981\pi\) | ||||
−0.0564604 | + | 0.998405i | \(0.517981\pi\) | |||||||
\(180\) | −1.22119 | −0.0910218 | ||||||||
\(181\) | −22.7664 | −1.69221 | −0.846106 | − | 0.533014i | \(-0.821059\pi\) | ||||
−0.846106 | + | 0.533014i | \(0.821059\pi\) | |||||||
\(182\) | 3.84809 | 0.285239 | ||||||||
\(183\) | −1.34697 | −0.0995707 | ||||||||
\(184\) | 2.05813 | 0.151727 | ||||||||
\(185\) | −6.45476 | −0.474563 | ||||||||
\(186\) | −5.71160 | −0.418795 | ||||||||
\(187\) | 4.14567 | 0.303161 | ||||||||
\(188\) | −12.5065 | −0.912131 | ||||||||
\(189\) | 13.2321 | 0.962497 | ||||||||
\(190\) | −2.09373 | −0.151895 | ||||||||
\(191\) | 18.2867 | 1.32318 | 0.661591 | − | 0.749865i | \(-0.269882\pi\) | ||||
0.661591 | + | 0.749865i | \(0.269882\pi\) | |||||||
\(192\) | 4.28431 | 0.309193 | ||||||||
\(193\) | −15.9280 | −1.14652 | −0.573262 | − | 0.819372i | \(-0.694322\pi\) | ||||
−0.573262 | + | 0.819372i | \(0.694322\pi\) | |||||||
\(194\) | −8.05961 | −0.578646 | ||||||||
\(195\) | 2.09467 | 0.150003 | ||||||||
\(196\) | 2.06950 | 0.147822 | ||||||||
\(197\) | 25.0595 | 1.78542 | 0.892708 | − | 0.450635i | \(-0.148802\pi\) | ||||
0.892708 | + | 0.450635i | \(0.148802\pi\) | |||||||
\(198\) | 0.928086 | 0.0659562 | ||||||||
\(199\) | −14.1429 | −1.00257 | −0.501283 | − | 0.865283i | \(-0.667139\pi\) | ||||
−0.501283 | + | 0.865283i | \(0.667139\pi\) | |||||||
\(200\) | 11.7956 | 0.834078 | ||||||||
\(201\) | 16.4365 | 1.15934 | ||||||||
\(202\) | −3.17713 | −0.223542 | ||||||||
\(203\) | −7.03708 | −0.493907 | ||||||||
\(204\) | 7.74683 | 0.542387 | ||||||||
\(205\) | −5.40398 | −0.377430 | ||||||||
\(206\) | −4.43330 | −0.308883 | ||||||||
\(207\) | 0.920371 | 0.0639702 | ||||||||
\(208\) | −1.46467 | −0.101556 | ||||||||
\(209\) | −3.60293 | −0.249220 | ||||||||
\(210\) | 1.83708 | 0.126771 | ||||||||
\(211\) | 1.14274 | 0.0786697 | 0.0393348 | − | 0.999226i | \(-0.487476\pi\) | ||||
0.0393348 | + | 0.999226i | \(0.487476\pi\) | |||||||
\(212\) | 12.3564 | 0.848638 | ||||||||
\(213\) | −19.1414 | −1.31155 | ||||||||
\(214\) | 2.10619 | 0.143976 | ||||||||
\(215\) | 7.73144 | 0.527280 | ||||||||
\(216\) | 14.9485 | 1.01712 | ||||||||
\(217\) | 12.7141 | 0.863091 | ||||||||
\(218\) | −12.2610 | −0.830422 | ||||||||
\(219\) | 15.7335 | 1.06317 | ||||||||
\(220\) | −1.02995 | −0.0694391 | ||||||||
\(221\) | 8.68382 | 0.584137 | ||||||||
\(222\) | 9.16676 | 0.615233 | ||||||||
\(223\) | 21.1618 | 1.41710 | 0.708549 | − | 0.705661i | \(-0.249350\pi\) | ||||
0.708549 | + | 0.705661i | \(0.249350\pi\) | |||||||
\(224\) | −13.7301 | −0.917379 | ||||||||
\(225\) | 5.27488 | 0.351659 | ||||||||
\(226\) | −1.39579 | −0.0928463 | ||||||||
\(227\) | −16.4976 | −1.09499 | −0.547493 | − | 0.836810i | \(-0.684418\pi\) | ||||
−0.547493 | + | 0.836810i | \(0.684418\pi\) | |||||||
\(228\) | −6.73265 | −0.445880 | ||||||||
\(229\) | −8.65820 | −0.572150 | −0.286075 | − | 0.958207i | \(-0.592351\pi\) | ||||
−0.286075 | + | 0.958207i | \(0.592351\pi\) | |||||||
\(230\) | 0.451088 | 0.0297438 | ||||||||
\(231\) | 3.16129 | 0.207998 | ||||||||
\(232\) | −7.94990 | −0.521937 | ||||||||
\(233\) | 6.62984 | 0.434335 | 0.217168 | − | 0.976134i | \(-0.430318\pi\) | ||||
0.217168 | + | 0.976134i | \(0.430318\pi\) | |||||||
\(234\) | 1.94404 | 0.127086 | ||||||||
\(235\) | −6.69278 | −0.436589 | ||||||||
\(236\) | 10.1303 | 0.659429 | ||||||||
\(237\) | 10.8928 | 0.707560 | ||||||||
\(238\) | 7.61593 | 0.493668 | ||||||||
\(239\) | −19.6278 | −1.26962 | −0.634810 | − | 0.772669i | \(-0.718921\pi\) | ||||
−0.634810 | + | 0.772669i | \(0.718921\pi\) | |||||||
\(240\) | −0.699234 | −0.0451354 | ||||||||
\(241\) | −2.16872 | −0.139699 | −0.0698497 | − | 0.997558i | \(-0.522252\pi\) | ||||
−0.0698497 | + | 0.997558i | \(0.522252\pi\) | |||||||
\(242\) | 0.782747 | 0.0503169 | ||||||||
\(243\) | 11.4760 | 0.736187 | ||||||||
\(244\) | 1.38731 | 0.0888132 | ||||||||
\(245\) | 1.10748 | 0.0707544 | ||||||||
\(246\) | 7.67449 | 0.489308 | ||||||||
\(247\) | −7.54697 | −0.480202 | ||||||||
\(248\) | 14.3633 | 0.912073 | ||||||||
\(249\) | −1.05941 | −0.0671374 | ||||||||
\(250\) | 5.49088 | 0.347274 | ||||||||
\(251\) | 4.59988 | 0.290342 | 0.145171 | − | 0.989407i | \(-0.453627\pi\) | ||||
0.145171 | + | 0.989407i | \(0.453627\pi\) | |||||||
\(252\) | −3.86052 | −0.243190 | ||||||||
\(253\) | 0.776241 | 0.0488018 | ||||||||
\(254\) | −1.81410 | −0.113827 | ||||||||
\(255\) | 4.14567 | 0.259612 | ||||||||
\(256\) | −13.5710 | −0.848185 | ||||||||
\(257\) | −28.6344 | −1.78617 | −0.893084 | − | 0.449891i | \(-0.851463\pi\) | ||||
−0.893084 | + | 0.449891i | \(0.851463\pi\) | |||||||
\(258\) | −10.9798 | −0.683575 | ||||||||
\(259\) | −20.4054 | −1.26793 | ||||||||
\(260\) | −2.15741 | −0.133797 | ||||||||
\(261\) | −3.55510 | −0.220055 | ||||||||
\(262\) | −0.481184 | −0.0297276 | ||||||||
\(263\) | 25.2920 | 1.55957 | 0.779785 | − | 0.626047i | \(-0.215328\pi\) | ||||
0.779785 | + | 0.626047i | \(0.215328\pi\) | |||||||
\(264\) | 3.57136 | 0.219802 | ||||||||
\(265\) | 6.61243 | 0.406198 | ||||||||
\(266\) | −6.61888 | −0.405830 | ||||||||
\(267\) | −5.56497 | −0.340571 | ||||||||
\(268\) | −16.9288 | −1.03409 | ||||||||
\(269\) | 27.0396 | 1.64864 | 0.824318 | − | 0.566127i | \(-0.191559\pi\) | ||||
0.824318 | + | 0.566127i | \(0.191559\pi\) | |||||||
\(270\) | 3.27633 | 0.199391 | ||||||||
\(271\) | 14.8280 | 0.900735 | 0.450367 | − | 0.892843i | \(-0.351293\pi\) | ||||
0.450367 | + | 0.892843i | \(0.351293\pi\) | |||||||
\(272\) | −2.89879 | −0.175765 | ||||||||
\(273\) | 6.62187 | 0.400774 | ||||||||
\(274\) | 13.1845 | 0.796505 | ||||||||
\(275\) | 4.44883 | 0.268275 | ||||||||
\(276\) | 1.45053 | 0.0873116 | ||||||||
\(277\) | 16.3212 | 0.980648 | 0.490324 | − | 0.871540i | \(-0.336878\pi\) | ||||
0.490324 | + | 0.871540i | \(0.336878\pi\) | |||||||
\(278\) | −7.95688 | −0.477222 | ||||||||
\(279\) | 6.42312 | 0.384542 | ||||||||
\(280\) | −4.61983 | −0.276088 | ||||||||
\(281\) | 5.15314 | 0.307411 | 0.153705 | − | 0.988117i | \(-0.450879\pi\) | ||||
0.153705 | + | 0.988117i | \(0.450879\pi\) | |||||||
\(282\) | 9.50478 | 0.566002 | ||||||||
\(283\) | −13.8984 | −0.826173 | −0.413087 | − | 0.910692i | \(-0.635549\pi\) | ||||
−0.413087 | + | 0.910692i | \(0.635549\pi\) | |||||||
\(284\) | 19.7147 | 1.16985 | ||||||||
\(285\) | −3.60293 | −0.213419 | ||||||||
\(286\) | 1.63960 | 0.0969516 | ||||||||
\(287\) | −17.0835 | −1.00841 | ||||||||
\(288\) | −6.93637 | −0.408730 | ||||||||
\(289\) | 0.186552 | 0.0109737 | ||||||||
\(290\) | −1.74241 | −0.102318 | ||||||||
\(291\) | −13.8691 | −0.813024 | ||||||||
\(292\) | −16.2047 | −0.948308 | ||||||||
\(293\) | 20.8020 | 1.21527 | 0.607633 | − | 0.794218i | \(-0.292119\pi\) | ||||
0.607633 | + | 0.794218i | \(0.292119\pi\) | |||||||
\(294\) | −1.57280 | −0.0917273 | ||||||||
\(295\) | 5.42119 | 0.315634 | ||||||||
\(296\) | −23.0522 | −1.33988 | ||||||||
\(297\) | 5.63797 | 0.327148 | ||||||||
\(298\) | −7.14753 | −0.414045 | ||||||||
\(299\) | 1.62597 | 0.0940324 | ||||||||
\(300\) | 8.31334 | 0.479971 | ||||||||
\(301\) | 24.4413 | 1.40877 | ||||||||
\(302\) | 15.5986 | 0.897601 | ||||||||
\(303\) | −5.46728 | −0.314087 | ||||||||
\(304\) | 2.51929 | 0.144491 | ||||||||
\(305\) | 0.742408 | 0.0425102 | ||||||||
\(306\) | 3.84753 | 0.219949 | ||||||||
\(307\) | −24.7144 | −1.41053 | −0.705263 | − | 0.708945i | \(-0.749171\pi\) | ||||
−0.705263 | + | 0.708945i | \(0.749171\pi\) | |||||||
\(308\) | −3.25596 | −0.185526 | ||||||||
\(309\) | −7.62892 | −0.433994 | ||||||||
\(310\) | 3.14806 | 0.178798 | ||||||||
\(311\) | −32.5170 | −1.84387 | −0.921935 | − | 0.387344i | \(-0.873393\pi\) | ||||
−0.921935 | + | 0.387344i | \(0.873393\pi\) | |||||||
\(312\) | 7.48083 | 0.423519 | ||||||||
\(313\) | −24.8070 | −1.40217 | −0.701086 | − | 0.713077i | \(-0.747301\pi\) | ||||
−0.701086 | + | 0.713077i | \(0.747301\pi\) | |||||||
\(314\) | 3.83240 | 0.216275 | ||||||||
\(315\) | −2.06593 | −0.116402 | ||||||||
\(316\) | −11.2190 | −0.631116 | ||||||||
\(317\) | −11.9411 | −0.670680 | −0.335340 | − | 0.942097i | \(-0.608851\pi\) | ||||
−0.335340 | + | 0.942097i | \(0.608851\pi\) | |||||||
\(318\) | −9.39068 | −0.526603 | ||||||||
\(319\) | −2.99837 | −0.167877 | ||||||||
\(320\) | −2.36138 | −0.132005 | ||||||||
\(321\) | 3.62438 | 0.202293 | ||||||||
\(322\) | 1.42602 | 0.0794689 | ||||||||
\(323\) | −14.9366 | −0.831092 | ||||||||
\(324\) | 5.60075 | 0.311153 | ||||||||
\(325\) | 9.31885 | 0.516917 | ||||||||
\(326\) | −11.9444 | −0.661538 | ||||||||
\(327\) | −21.0990 | −1.16678 | ||||||||
\(328\) | −19.2995 | −1.06564 | ||||||||
\(329\) | −21.1578 | −1.16647 | ||||||||
\(330\) | 0.782747 | 0.0430888 | ||||||||
\(331\) | −27.7681 | −1.52627 | −0.763137 | − | 0.646236i | \(-0.776342\pi\) | ||||
−0.763137 | + | 0.646236i | \(0.776342\pi\) | |||||||
\(332\) | 1.09114 | 0.0598839 | ||||||||
\(333\) | −10.3087 | −0.564913 | ||||||||
\(334\) | 6.90238 | 0.377681 | ||||||||
\(335\) | −9.05932 | −0.494963 | ||||||||
\(336\) | −2.21048 | −0.120592 | ||||||||
\(337\) | −21.9254 | −1.19435 | −0.597177 | − | 0.802109i | \(-0.703711\pi\) | ||||
−0.597177 | + | 0.802109i | \(0.703711\pi\) | |||||||
\(338\) | −6.74128 | −0.366678 | ||||||||
\(339\) | −2.40190 | −0.130453 | ||||||||
\(340\) | −4.26982 | −0.231564 | ||||||||
\(341\) | 5.41725 | 0.293361 | ||||||||
\(342\) | −3.34383 | −0.180814 | ||||||||
\(343\) | 19.9298 | 1.07611 | ||||||||
\(344\) | 27.6117 | 1.48872 | ||||||||
\(345\) | 0.776241 | 0.0417914 | ||||||||
\(346\) | −5.64745 | −0.303609 | ||||||||
\(347\) | 15.0235 | 0.806503 | 0.403251 | − | 0.915089i | \(-0.367880\pi\) | ||||
0.403251 | + | 0.915089i | \(0.367880\pi\) | |||||||
\(348\) | −5.60293 | −0.300349 | ||||||||
\(349\) | 8.84347 | 0.473380 | 0.236690 | − | 0.971585i | \(-0.423937\pi\) | ||||
0.236690 | + | 0.971585i | \(0.423937\pi\) | |||||||
\(350\) | 8.17287 | 0.436858 | ||||||||
\(351\) | 11.8097 | 0.630356 | ||||||||
\(352\) | −5.85013 | −0.311813 | ||||||||
\(353\) | −15.4240 | −0.820939 | −0.410469 | − | 0.911874i | \(-0.634635\pi\) | ||||
−0.410469 | + | 0.911874i | \(0.634635\pi\) | |||||||
\(354\) | −7.69893 | −0.409194 | ||||||||
\(355\) | 10.5502 | 0.559945 | ||||||||
\(356\) | 5.73163 | 0.303776 | ||||||||
\(357\) | 13.1057 | 0.693625 | ||||||||
\(358\) | −1.18256 | −0.0625001 | ||||||||
\(359\) | 15.0616 | 0.794921 | 0.397461 | − | 0.917619i | \(-0.369892\pi\) | ||||
0.397461 | + | 0.917619i | \(0.369892\pi\) | |||||||
\(360\) | −2.33392 | −0.123008 | ||||||||
\(361\) | −6.01888 | −0.316783 | ||||||||
\(362\) | −17.8203 | −0.936616 | ||||||||
\(363\) | 1.34697 | 0.0706975 | ||||||||
\(364\) | −6.82019 | −0.357475 | ||||||||
\(365\) | −8.67184 | −0.453905 | ||||||||
\(366\) | −1.05434 | −0.0551110 | ||||||||
\(367\) | −10.4821 | −0.547160 | −0.273580 | − | 0.961849i | \(-0.588208\pi\) | ||||
−0.273580 | + | 0.961849i | \(0.588208\pi\) | |||||||
\(368\) | −0.542774 | −0.0282940 | ||||||||
\(369\) | −8.63053 | −0.449288 | ||||||||
\(370\) | −5.05244 | −0.262664 | ||||||||
\(371\) | 20.9038 | 1.08527 | ||||||||
\(372\) | 10.1230 | 0.524853 | ||||||||
\(373\) | −34.6725 | −1.79527 | −0.897637 | − | 0.440735i | \(-0.854718\pi\) | ||||
−0.897637 | + | 0.440735i | \(0.854718\pi\) | |||||||
\(374\) | 3.24501 | 0.167795 | ||||||||
\(375\) | 9.44883 | 0.487935 | ||||||||
\(376\) | −23.9023 | −1.23267 | ||||||||
\(377\) | −6.28061 | −0.323468 | ||||||||
\(378\) | 10.3574 | 0.532728 | ||||||||
\(379\) | −8.67507 | −0.445609 | −0.222804 | − | 0.974863i | \(-0.571521\pi\) | ||||
−0.222804 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(380\) | 3.71083 | 0.190362 | ||||||||
\(381\) | −3.12175 | −0.159932 | ||||||||
\(382\) | 14.3139 | 0.732362 | ||||||||
\(383\) | −22.9990 | −1.17519 | −0.587596 | − | 0.809154i | \(-0.699926\pi\) | ||||
−0.587596 | + | 0.809154i | \(0.699926\pi\) | |||||||
\(384\) | −12.4064 | −0.633109 | ||||||||
\(385\) | −1.74241 | −0.0888013 | ||||||||
\(386\) | −12.4676 | −0.634584 | ||||||||
\(387\) | 12.3476 | 0.627666 | ||||||||
\(388\) | 14.2845 | 0.725185 | ||||||||
\(389\) | −4.71837 | −0.239231 | −0.119615 | − | 0.992820i | \(-0.538166\pi\) | ||||
−0.119615 | + | 0.992820i | \(0.538166\pi\) | |||||||
\(390\) | 1.63960 | 0.0830244 | ||||||||
\(391\) | 3.21804 | 0.162743 | ||||||||
\(392\) | 3.95521 | 0.199768 | ||||||||
\(393\) | −0.828031 | −0.0417686 | ||||||||
\(394\) | 19.6153 | 0.988203 | ||||||||
\(395\) | −6.00376 | −0.302082 | ||||||||
\(396\) | −1.64490 | −0.0826593 | ||||||||
\(397\) | −15.8309 | −0.794532 | −0.397266 | − | 0.917704i | \(-0.630041\pi\) | ||||
−0.397266 | + | 0.917704i | \(0.630041\pi\) | |||||||
\(398\) | −11.0704 | −0.554907 | ||||||||
\(399\) | −11.3899 | −0.570209 | ||||||||
\(400\) | −3.11077 | −0.155539 | ||||||||
\(401\) | −4.05194 | −0.202344 | −0.101172 | − | 0.994869i | \(-0.532259\pi\) | ||||
−0.101172 | + | 0.994869i | \(0.532259\pi\) | |||||||
\(402\) | 12.8656 | 0.641680 | ||||||||
\(403\) | 11.3474 | 0.565253 | ||||||||
\(404\) | 5.63101 | 0.280153 | ||||||||
\(405\) | 2.99720 | 0.148932 | ||||||||
\(406\) | −5.50826 | −0.273370 | ||||||||
\(407\) | −8.69435 | −0.430963 | ||||||||
\(408\) | 14.8057 | 0.732989 | ||||||||
\(409\) | −23.6231 | −1.16809 | −0.584044 | − | 0.811722i | \(-0.698530\pi\) | ||||
−0.584044 | + | 0.811722i | \(0.698530\pi\) | |||||||
\(410\) | −4.22995 | −0.208902 | ||||||||
\(411\) | 22.6882 | 1.11912 | ||||||||
\(412\) | 7.85739 | 0.387106 | ||||||||
\(413\) | 17.1379 | 0.843303 | ||||||||
\(414\) | 0.720418 | 0.0354066 | ||||||||
\(415\) | 0.583915 | 0.0286633 | ||||||||
\(416\) | −12.2541 | −0.600808 | ||||||||
\(417\) | −13.6924 | −0.670518 | ||||||||
\(418\) | −2.82019 | −0.137940 | ||||||||
\(419\) | 11.2846 | 0.551289 | 0.275644 | − | 0.961260i | \(-0.411109\pi\) | ||||
0.275644 | + | 0.961260i | \(0.411109\pi\) | |||||||
\(420\) | −3.25596 | −0.158875 | ||||||||
\(421\) | −6.66693 | −0.324926 | −0.162463 | − | 0.986715i | \(-0.551944\pi\) | ||||
−0.162463 | + | 0.986715i | \(0.551944\pi\) | |||||||
\(422\) | 0.894479 | 0.0435425 | ||||||||
\(423\) | −10.6888 | −0.519709 | ||||||||
\(424\) | 23.6153 | 1.14686 | ||||||||
\(425\) | 18.4434 | 0.894635 | ||||||||
\(426\) | −14.9829 | −0.725923 | ||||||||
\(427\) | 2.34697 | 0.113578 | ||||||||
\(428\) | −3.73293 | −0.180438 | ||||||||
\(429\) | 2.82146 | 0.136221 | ||||||||
\(430\) | 6.05176 | 0.291842 | ||||||||
\(431\) | 36.0050 | 1.73430 | 0.867149 | − | 0.498049i | \(-0.165950\pi\) | ||||
0.867149 | + | 0.498049i | \(0.165950\pi\) | |||||||
\(432\) | −3.94226 | −0.189672 | ||||||||
\(433\) | 28.1159 | 1.35116 | 0.675581 | − | 0.737286i | \(-0.263893\pi\) | ||||
0.675581 | + | 0.737286i | \(0.263893\pi\) | |||||||
\(434\) | 9.95194 | 0.477709 | ||||||||
\(435\) | −2.99837 | −0.143761 | ||||||||
\(436\) | 21.7309 | 1.04072 | ||||||||
\(437\) | −2.79674 | −0.133786 | ||||||||
\(438\) | 12.3154 | 0.588451 | ||||||||
\(439\) | 15.1618 | 0.723631 | 0.361816 | − | 0.932250i | \(-0.382157\pi\) | ||||
0.361816 | + | 0.932250i | \(0.382157\pi\) | |||||||
\(440\) | −1.96842 | −0.0938410 | ||||||||
\(441\) | 1.76872 | 0.0842250 | ||||||||
\(442\) | 6.79724 | 0.323312 | ||||||||
\(443\) | 5.44752 | 0.258820 | 0.129410 | − | 0.991591i | \(-0.458692\pi\) | ||||
0.129410 | + | 0.991591i | \(0.458692\pi\) | |||||||
\(444\) | −16.2468 | −0.771038 | ||||||||
\(445\) | 3.06725 | 0.145401 | ||||||||
\(446\) | 16.5643 | 0.784344 | ||||||||
\(447\) | −12.2996 | −0.581752 | ||||||||
\(448\) | −7.46502 | −0.352689 | ||||||||
\(449\) | −38.0951 | −1.79782 | −0.898910 | − | 0.438133i | \(-0.855640\pi\) | ||||
−0.898910 | + | 0.438133i | \(0.855640\pi\) | |||||||
\(450\) | 4.12890 | 0.194638 | ||||||||
\(451\) | −7.27899 | −0.342754 | ||||||||
\(452\) | 2.47383 | 0.116359 | ||||||||
\(453\) | 26.8425 | 1.26117 | ||||||||
\(454\) | −12.9135 | −0.606059 | ||||||||
\(455\) | −3.64978 | −0.171104 | ||||||||
\(456\) | −12.8674 | −0.602569 | ||||||||
\(457\) | −27.3024 | −1.27715 | −0.638576 | − | 0.769559i | \(-0.720476\pi\) | ||||
−0.638576 | + | 0.769559i | \(0.720476\pi\) | |||||||
\(458\) | −6.77718 | −0.316677 | ||||||||
\(459\) | 23.3732 | 1.09097 | ||||||||
\(460\) | −0.799488 | −0.0372763 | ||||||||
\(461\) | −20.5148 | −0.955470 | −0.477735 | − | 0.878504i | \(-0.658542\pi\) | ||||
−0.477735 | + | 0.878504i | \(0.658542\pi\) | |||||||
\(462\) | 2.47449 | 0.115124 | ||||||||
\(463\) | −27.1915 | −1.26370 | −0.631848 | − | 0.775092i | \(-0.717703\pi\) | ||||
−0.631848 | + | 0.775092i | \(0.717703\pi\) | |||||||
\(464\) | 2.09656 | 0.0973305 | ||||||||
\(465\) | 5.41725 | 0.251219 | ||||||||
\(466\) | 5.18949 | 0.240398 | ||||||||
\(467\) | 27.6045 | 1.27739 | 0.638693 | − | 0.769462i | \(-0.279476\pi\) | ||||
0.638693 | + | 0.769462i | \(0.279476\pi\) | |||||||
\(468\) | −3.44553 | −0.159270 | ||||||||
\(469\) | −28.6391 | −1.32243 | ||||||||
\(470\) | −5.23875 | −0.241646 | ||||||||
\(471\) | 6.59487 | 0.303876 | ||||||||
\(472\) | 19.3610 | 0.891162 | ||||||||
\(473\) | 10.4140 | 0.478836 | ||||||||
\(474\) | 8.52627 | 0.391625 | ||||||||
\(475\) | −16.0288 | −0.735453 | ||||||||
\(476\) | −13.4981 | −0.618686 | ||||||||
\(477\) | 10.5605 | 0.483532 | ||||||||
\(478\) | −15.3636 | −0.702716 | ||||||||
\(479\) | 30.7998 | 1.40728 | 0.703638 | − | 0.710558i | \(-0.251557\pi\) | ||||
0.703638 | + | 0.710558i | \(0.251557\pi\) | |||||||
\(480\) | −5.85013 | −0.267021 | ||||||||
\(481\) | −18.2118 | −0.830388 | ||||||||
\(482\) | −1.69756 | −0.0773217 | ||||||||
\(483\) | 2.45392 | 0.111657 | ||||||||
\(484\) | −1.38731 | −0.0630594 | ||||||||
\(485\) | 7.64426 | 0.347108 | ||||||||
\(486\) | 8.98283 | 0.407469 | ||||||||
\(487\) | 33.2214 | 1.50541 | 0.752703 | − | 0.658360i | \(-0.228750\pi\) | ||||
0.752703 | + | 0.658360i | \(0.228750\pi\) | |||||||
\(488\) | 2.65140 | 0.120023 | ||||||||
\(489\) | −20.5541 | −0.929490 | ||||||||
\(490\) | 0.866878 | 0.0391616 | ||||||||
\(491\) | 21.6482 | 0.976969 | 0.488485 | − | 0.872572i | \(-0.337550\pi\) | ||||
0.488485 | + | 0.872572i | \(0.337550\pi\) | |||||||
\(492\) | −13.6019 | −0.613223 | ||||||||
\(493\) | −12.4303 | −0.559830 | ||||||||
\(494\) | −5.90737 | −0.265785 | ||||||||
\(495\) | −0.880257 | −0.0395646 | ||||||||
\(496\) | −3.78793 | −0.170083 | ||||||||
\(497\) | 33.3522 | 1.49605 | ||||||||
\(498\) | −0.829250 | −0.0371596 | ||||||||
\(499\) | 8.29598 | 0.371379 | 0.185690 | − | 0.982608i | \(-0.440548\pi\) | ||||
0.185690 | + | 0.982608i | \(0.440548\pi\) | |||||||
\(500\) | −9.73180 | −0.435219 | ||||||||
\(501\) | 11.8778 | 0.530659 | ||||||||
\(502\) | 3.60055 | 0.160700 | ||||||||
\(503\) | 22.0223 | 0.981926 | 0.490963 | − | 0.871180i | \(-0.336645\pi\) | ||||
0.490963 | + | 0.871180i | \(0.336645\pi\) | |||||||
\(504\) | −7.37819 | −0.328651 | ||||||||
\(505\) | 3.01340 | 0.134094 | ||||||||
\(506\) | 0.607600 | 0.0270111 | ||||||||
\(507\) | −11.6005 | −0.515198 | ||||||||
\(508\) | 3.21524 | 0.142653 | ||||||||
\(509\) | 29.7192 | 1.31728 | 0.658640 | − | 0.752458i | \(-0.271132\pi\) | ||||
0.658640 | + | 0.752458i | \(0.271132\pi\) | |||||||
\(510\) | 3.24501 | 0.143691 | ||||||||
\(511\) | −27.4142 | −1.21273 | ||||||||
\(512\) | 7.79852 | 0.344649 | ||||||||
\(513\) | −20.3132 | −0.896851 | ||||||||
\(514\) | −22.4135 | −0.988618 | ||||||||
\(515\) | 4.20483 | 0.185287 | ||||||||
\(516\) | 19.4602 | 0.856688 | ||||||||
\(517\) | −9.01495 | −0.396477 | ||||||||
\(518\) | −15.9722 | −0.701780 | ||||||||
\(519\) | −9.71826 | −0.426584 | ||||||||
\(520\) | −4.12321 | −0.180815 | ||||||||
\(521\) | −5.09711 | −0.223308 | −0.111654 | − | 0.993747i | \(-0.535615\pi\) | ||||
−0.111654 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(522\) | −2.78275 | −0.121798 | ||||||||
\(523\) | 29.5947 | 1.29408 | 0.647042 | − | 0.762454i | \(-0.276006\pi\) | ||||
0.647042 | + | 0.762454i | \(0.276006\pi\) | |||||||
\(524\) | 0.852829 | 0.0372560 | ||||||||
\(525\) | 14.0640 | 0.613805 | ||||||||
\(526\) | 19.7972 | 0.863200 | ||||||||
\(527\) | 22.4581 | 0.978292 | ||||||||
\(528\) | −0.941846 | −0.0409886 | ||||||||
\(529\) | −22.3975 | −0.973802 | ||||||||
\(530\) | 5.17586 | 0.224825 | ||||||||
\(531\) | 8.65801 | 0.375726 | ||||||||
\(532\) | 11.7310 | 0.508604 | ||||||||
\(533\) | −15.2471 | −0.660426 | ||||||||
\(534\) | −4.35597 | −0.188501 | ||||||||
\(535\) | −1.99765 | −0.0863660 | ||||||||
\(536\) | −32.3541 | −1.39748 | ||||||||
\(537\) | −2.03497 | −0.0878154 | ||||||||
\(538\) | 21.1652 | 0.912497 | ||||||||
\(539\) | 1.49174 | 0.0642539 | ||||||||
\(540\) | −5.80682 | −0.249886 | ||||||||
\(541\) | −14.3729 | −0.617939 | −0.308969 | − | 0.951072i | \(-0.599984\pi\) | ||||
−0.308969 | + | 0.951072i | \(0.599984\pi\) | |||||||
\(542\) | 11.6065 | 0.498544 | ||||||||
\(543\) | −30.6656 | −1.31599 | ||||||||
\(544\) | −24.2527 | −1.03983 | ||||||||
\(545\) | 11.6292 | 0.498138 | ||||||||
\(546\) | 5.18325 | 0.221823 | ||||||||
\(547\) | 8.45243 | 0.361400 | 0.180700 | − | 0.983538i | \(-0.442164\pi\) | ||||
0.180700 | + | 0.983538i | \(0.442164\pi\) | |||||||
\(548\) | −23.3676 | −0.998215 | ||||||||
\(549\) | 1.18568 | 0.0506035 | ||||||||
\(550\) | 3.48231 | 0.148486 | ||||||||
\(551\) | 10.8029 | 0.460220 | ||||||||
\(552\) | 2.77223 | 0.117994 | ||||||||
\(553\) | −18.9796 | −0.807096 | ||||||||
\(554\) | 12.7754 | 0.542775 | ||||||||
\(555\) | −8.69435 | −0.369055 | ||||||||
\(556\) | 14.1024 | 0.598076 | ||||||||
\(557\) | 21.8207 | 0.924572 | 0.462286 | − | 0.886731i | \(-0.347029\pi\) | ||||
0.462286 | + | 0.886731i | \(0.347029\pi\) | |||||||
\(558\) | 5.02768 | 0.212839 | ||||||||
\(559\) | 21.8139 | 0.922631 | ||||||||
\(560\) | 1.21835 | 0.0514847 | ||||||||
\(561\) | 5.58408 | 0.235760 | ||||||||
\(562\) | 4.03361 | 0.170148 | ||||||||
\(563\) | 6.93536 | 0.292291 | 0.146145 | − | 0.989263i | \(-0.453313\pi\) | ||||
0.146145 | + | 0.989263i | \(0.453313\pi\) | |||||||
\(564\) | −16.8459 | −0.709339 | ||||||||
\(565\) | 1.32385 | 0.0556950 | ||||||||
\(566\) | −10.8789 | −0.457275 | ||||||||
\(567\) | 9.47503 | 0.397914 | ||||||||
\(568\) | 37.6784 | 1.58095 | ||||||||
\(569\) | −13.8735 | −0.581608 | −0.290804 | − | 0.956783i | \(-0.593923\pi\) | ||||
−0.290804 | + | 0.956783i | \(0.593923\pi\) | |||||||
\(570\) | −2.82019 | −0.118125 | ||||||||
\(571\) | 0.346433 | 0.0144978 | 0.00724888 | − | 0.999974i | \(-0.497693\pi\) | ||||
0.00724888 | + | 0.999974i | \(0.497693\pi\) | |||||||
\(572\) | −2.90596 | −0.121504 | ||||||||
\(573\) | 24.6316 | 1.02900 | ||||||||
\(574\) | −13.3721 | −0.558141 | ||||||||
\(575\) | 3.45336 | 0.144015 | ||||||||
\(576\) | −3.77129 | −0.157137 | ||||||||
\(577\) | 16.0839 | 0.669583 | 0.334791 | − | 0.942292i | \(-0.391334\pi\) | ||||
0.334791 | + | 0.942292i | \(0.391334\pi\) | |||||||
\(578\) | 0.146023 | 0.00607377 | ||||||||
\(579\) | −21.4545 | −0.891619 | ||||||||
\(580\) | 3.08817 | 0.128229 | ||||||||
\(581\) | 1.84593 | 0.0765819 | ||||||||
\(582\) | −10.8560 | −0.449997 | ||||||||
\(583\) | 8.90673 | 0.368879 | ||||||||
\(584\) | −30.9702 | −1.28156 | ||||||||
\(585\) | −1.84385 | −0.0762339 | ||||||||
\(586\) | 16.2827 | 0.672633 | ||||||||
\(587\) | 5.60753 | 0.231448 | 0.115724 | − | 0.993281i | \(-0.463081\pi\) | ||||
0.115724 | + | 0.993281i | \(0.463081\pi\) | |||||||
\(588\) | 2.78755 | 0.114957 | ||||||||
\(589\) | −19.5180 | −0.804225 | ||||||||
\(590\) | 4.24342 | 0.174699 | ||||||||
\(591\) | 33.7544 | 1.38847 | ||||||||
\(592\) | 6.07939 | 0.249861 | ||||||||
\(593\) | 1.21408 | 0.0498565 | 0.0249282 | − | 0.999689i | \(-0.492064\pi\) | ||||
0.0249282 | + | 0.999689i | \(0.492064\pi\) | |||||||
\(594\) | 4.41311 | 0.181072 | ||||||||
\(595\) | −7.22344 | −0.296132 | ||||||||
\(596\) | 12.6680 | 0.518900 | ||||||||
\(597\) | −19.0501 | −0.779668 | ||||||||
\(598\) | 1.27272 | 0.0520456 | ||||||||
\(599\) | 26.6122 | 1.08735 | 0.543673 | − | 0.839297i | \(-0.317033\pi\) | ||||
0.543673 | + | 0.839297i | \(0.317033\pi\) | |||||||
\(600\) | 15.8884 | 0.648640 | ||||||||
\(601\) | 30.0085 | 1.22407 | 0.612036 | − | 0.790830i | \(-0.290351\pi\) | ||||
0.612036 | + | 0.790830i | \(0.290351\pi\) | |||||||
\(602\) | 19.1314 | 0.779737 | ||||||||
\(603\) | −14.4684 | −0.589197 | ||||||||
\(604\) | −27.6463 | −1.12491 | ||||||||
\(605\) | −0.742408 | −0.0301832 | ||||||||
\(606\) | −4.27949 | −0.173843 | ||||||||
\(607\) | −13.2646 | −0.538395 | −0.269197 | − | 0.963085i | \(-0.586758\pi\) | ||||
−0.269197 | + | 0.963085i | \(0.586758\pi\) | |||||||
\(608\) | 21.0776 | 0.854811 | ||||||||
\(609\) | −9.47873 | −0.384097 | ||||||||
\(610\) | 0.581118 | 0.0235288 | ||||||||
\(611\) | −18.8834 | −0.763940 | ||||||||
\(612\) | −6.81920 | −0.275650 | ||||||||
\(613\) | 18.3360 | 0.740585 | 0.370292 | − | 0.928915i | \(-0.379257\pi\) | ||||
0.370292 | + | 0.928915i | \(0.379257\pi\) | |||||||
\(614\) | −19.3452 | −0.780707 | ||||||||
\(615\) | −7.27899 | −0.293517 | ||||||||
\(616\) | −6.22276 | −0.250722 | ||||||||
\(617\) | −18.8802 | −0.760089 | −0.380045 | − | 0.924968i | \(-0.624091\pi\) | ||||
−0.380045 | + | 0.924968i | \(0.624091\pi\) | |||||||
\(618\) | −5.97152 | −0.240210 | ||||||||
\(619\) | 12.8874 | 0.517987 | 0.258993 | − | 0.965879i | \(-0.416609\pi\) | ||||
0.258993 | + | 0.965879i | \(0.416609\pi\) | |||||||
\(620\) | −5.57949 | −0.224078 | ||||||||
\(621\) | 4.37643 | 0.175620 | ||||||||
\(622\) | −25.4526 | −1.02056 | ||||||||
\(623\) | 9.69646 | 0.388480 | ||||||||
\(624\) | −1.97286 | −0.0789776 | ||||||||
\(625\) | 17.0362 | 0.681450 | ||||||||
\(626\) | −19.4176 | −0.776082 | ||||||||
\(627\) | −4.85303 | −0.193812 | ||||||||
\(628\) | −6.79237 | −0.271045 | ||||||||
\(629\) | −36.0439 | −1.43716 | ||||||||
\(630\) | −1.61710 | −0.0644270 | ||||||||
\(631\) | −27.7977 | −1.10661 | −0.553304 | − | 0.832980i | \(-0.686633\pi\) | ||||
−0.553304 | + | 0.832980i | \(0.686633\pi\) | |||||||
\(632\) | −21.4416 | −0.852900 | ||||||||
\(633\) | 1.53924 | 0.0611792 | ||||||||
\(634\) | −9.34688 | −0.371212 | ||||||||
\(635\) | 1.72061 | 0.0682805 | ||||||||
\(636\) | 16.6436 | 0.659963 | ||||||||
\(637\) | 3.12471 | 0.123806 | ||||||||
\(638\) | −2.34697 | −0.0929173 | ||||||||
\(639\) | 16.8494 | 0.666550 | ||||||||
\(640\) | 6.83801 | 0.270296 | ||||||||
\(641\) | 17.3218 | 0.684172 | 0.342086 | − | 0.939669i | \(-0.388867\pi\) | ||||
0.342086 | + | 0.939669i | \(0.388867\pi\) | |||||||
\(642\) | 2.83698 | 0.111967 | ||||||||
\(643\) | 31.5859 | 1.24563 | 0.622813 | − | 0.782371i | \(-0.285990\pi\) | ||||
0.622813 | + | 0.782371i | \(0.285990\pi\) | |||||||
\(644\) | −2.52741 | −0.0995940 | ||||||||
\(645\) | 10.4140 | 0.410051 | ||||||||
\(646\) | −11.6915 | −0.459998 | ||||||||
\(647\) | 24.2187 | 0.952137 | 0.476069 | − | 0.879408i | \(-0.342061\pi\) | ||||
0.476069 | + | 0.879408i | \(0.342061\pi\) | |||||||
\(648\) | 10.7041 | 0.420496 | ||||||||
\(649\) | 7.30217 | 0.286635 | ||||||||
\(650\) | 7.29430 | 0.286106 | ||||||||
\(651\) | 17.1255 | 0.671202 | ||||||||
\(652\) | 21.1697 | 0.829069 | ||||||||
\(653\) | −18.8038 | −0.735849 | −0.367924 | − | 0.929856i | \(-0.619931\pi\) | ||||
−0.367924 | + | 0.929856i | \(0.619931\pi\) | |||||||
\(654\) | −16.5152 | −0.645796 | ||||||||
\(655\) | 0.456386 | 0.0178325 | ||||||||
\(656\) | 5.08971 | 0.198720 | ||||||||
\(657\) | −13.8495 | −0.540321 | ||||||||
\(658\) | −16.5612 | −0.645623 | ||||||||
\(659\) | 11.7243 | 0.456715 | 0.228358 | − | 0.973577i | \(-0.426664\pi\) | ||||
0.228358 | + | 0.973577i | \(0.426664\pi\) | |||||||
\(660\) | −1.38731 | −0.0540008 | ||||||||
\(661\) | 16.5459 | 0.643560 | 0.321780 | − | 0.946815i | \(-0.395719\pi\) | ||||
0.321780 | + | 0.946815i | \(0.395719\pi\) | |||||||
\(662\) | −21.7354 | −0.844771 | ||||||||
\(663\) | 11.6968 | 0.454267 | ||||||||
\(664\) | 2.08537 | 0.0809280 | ||||||||
\(665\) | 6.27778 | 0.243442 | ||||||||
\(666\) | −8.06910 | −0.312671 | ||||||||
\(667\) | −2.32746 | −0.0901196 | ||||||||
\(668\) | −12.2335 | −0.473327 | ||||||||
\(669\) | 28.5043 | 1.10204 | ||||||||
\(670\) | −7.09116 | −0.273955 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −18.4940 | −0.713420 | ||||||||
\(673\) | 49.7277 | 1.91686 | 0.958431 | − | 0.285326i | \(-0.0921019\pi\) | ||||
0.958431 | + | 0.285326i | \(0.0921019\pi\) | |||||||
\(674\) | −17.1621 | −0.661058 | ||||||||
\(675\) | 25.0824 | 0.965421 | ||||||||
\(676\) | 11.9480 | 0.459537 | ||||||||
\(677\) | 27.4558 | 1.05521 | 0.527606 | − | 0.849489i | \(-0.323090\pi\) | ||||
0.527606 | + | 0.849489i | \(0.323090\pi\) | |||||||
\(678\) | −1.88008 | −0.0722040 | ||||||||
\(679\) | 24.1657 | 0.927395 | ||||||||
\(680\) | −8.16043 | −0.312938 | ||||||||
\(681\) | −22.2218 | −0.851540 | ||||||||
\(682\) | 4.24034 | 0.162371 | ||||||||
\(683\) | −23.2171 | −0.888379 | −0.444189 | − | 0.895933i | \(-0.646508\pi\) | ||||
−0.444189 | + | 0.895933i | \(0.646508\pi\) | |||||||
\(684\) | 5.92646 | 0.226604 | ||||||||
\(685\) | −12.5050 | −0.477793 | ||||||||
\(686\) | 15.6000 | 0.595612 | ||||||||
\(687\) | −11.6623 | −0.444945 | ||||||||
\(688\) | −7.28182 | −0.277617 | ||||||||
\(689\) | 18.6567 | 0.710763 | ||||||||
\(690\) | 0.607600 | 0.0231310 | ||||||||
\(691\) | −1.30752 | −0.0497405 | −0.0248702 | − | 0.999691i | \(-0.507917\pi\) | ||||
−0.0248702 | + | 0.999691i | \(0.507917\pi\) | |||||||
\(692\) | 10.0093 | 0.380496 | ||||||||
\(693\) | −2.78275 | −0.105708 | ||||||||
\(694\) | 11.7596 | 0.446388 | ||||||||
\(695\) | 7.54682 | 0.286267 | ||||||||
\(696\) | −10.7083 | −0.405896 | ||||||||
\(697\) | −30.1763 | −1.14301 | ||||||||
\(698\) | 6.92220 | 0.262009 | ||||||||
\(699\) | 8.93018 | 0.337771 | ||||||||
\(700\) | −14.4852 | −0.547490 | ||||||||
\(701\) | 24.2219 | 0.914848 | 0.457424 | − | 0.889249i | \(-0.348772\pi\) | ||||
0.457424 | + | 0.889249i | \(0.348772\pi\) | |||||||
\(702\) | 9.24402 | 0.348893 | ||||||||
\(703\) | 31.3252 | 1.18145 | ||||||||
\(704\) | −3.18071 | −0.119877 | ||||||||
\(705\) | −9.01495 | −0.339523 | ||||||||
\(706\) | −12.0731 | −0.454378 | ||||||||
\(707\) | 9.52623 | 0.358271 | ||||||||
\(708\) | 13.6452 | 0.512820 | ||||||||
\(709\) | −6.36928 | −0.239203 | −0.119602 | − | 0.992822i | \(-0.538162\pi\) | ||||
−0.119602 | + | 0.992822i | \(0.538162\pi\) | |||||||
\(710\) | 8.25812 | 0.309922 | ||||||||
\(711\) | −9.58842 | −0.359594 | ||||||||
\(712\) | 10.9542 | 0.410527 | ||||||||
\(713\) | 4.20509 | 0.157482 | ||||||||
\(714\) | 10.2584 | 0.383912 | ||||||||
\(715\) | −1.55510 | −0.0581576 | ||||||||
\(716\) | 2.09591 | 0.0783279 | ||||||||
\(717\) | −26.4381 | −0.987347 | ||||||||
\(718\) | 11.7894 | 0.439978 | ||||||||
\(719\) | 40.1944 | 1.49900 | 0.749499 | − | 0.662006i | \(-0.230295\pi\) | ||||
0.749499 | + | 0.662006i | \(0.230295\pi\) | |||||||
\(720\) | 0.615505 | 0.0229385 | ||||||||
\(721\) | 13.2927 | 0.495046 | ||||||||
\(722\) | −4.71126 | −0.175335 | ||||||||
\(723\) | −2.92120 | −0.108640 | ||||||||
\(724\) | 31.5840 | 1.17381 | ||||||||
\(725\) | −13.3393 | −0.495407 | ||||||||
\(726\) | 1.05434 | 0.0391301 | ||||||||
\(727\) | 28.5809 | 1.06001 | 0.530003 | − | 0.847996i | \(-0.322191\pi\) | ||||
0.530003 | + | 0.847996i | \(0.322191\pi\) | |||||||
\(728\) | −13.0347 | −0.483097 | ||||||||
\(729\) | 27.5692 | 1.02108 | ||||||||
\(730\) | −6.78786 | −0.251230 | ||||||||
\(731\) | 43.1730 | 1.59681 | ||||||||
\(732\) | 1.86866 | 0.0690676 | ||||||||
\(733\) | −23.6903 | −0.875023 | −0.437511 | − | 0.899213i | \(-0.644140\pi\) | ||||
−0.437511 | + | 0.899213i | \(0.644140\pi\) | |||||||
\(734\) | −8.20481 | −0.302845 | ||||||||
\(735\) | 1.49174 | 0.0550237 | ||||||||
\(736\) | −4.54111 | −0.167388 | ||||||||
\(737\) | −12.2026 | −0.449489 | ||||||||
\(738\) | −6.75552 | −0.248674 | ||||||||
\(739\) | −26.2807 | −0.966751 | −0.483375 | − | 0.875413i | \(-0.660589\pi\) | ||||
−0.483375 | + | 0.875413i | \(0.660589\pi\) | |||||||
\(740\) | 8.95473 | 0.329182 | ||||||||
\(741\) | −10.1655 | −0.373440 | ||||||||
\(742\) | 16.3624 | 0.600682 | ||||||||
\(743\) | −44.7849 | −1.64300 | −0.821500 | − | 0.570209i | \(-0.806862\pi\) | ||||
−0.821500 | + | 0.570209i | \(0.806862\pi\) | |||||||
\(744\) | 19.3470 | 0.709294 | ||||||||
\(745\) | 6.77918 | 0.248370 | ||||||||
\(746\) | −27.1398 | −0.993659 | ||||||||
\(747\) | 0.932553 | 0.0341203 | ||||||||
\(748\) | −5.75131 | −0.210289 | ||||||||
\(749\) | −6.31516 | −0.230751 | ||||||||
\(750\) | 7.39605 | 0.270065 | ||||||||
\(751\) | 8.52302 | 0.311009 | 0.155505 | − | 0.987835i | \(-0.450300\pi\) | ||||
0.155505 | + | 0.987835i | \(0.450300\pi\) | |||||||
\(752\) | 6.30356 | 0.229867 | ||||||||
\(753\) | 6.19590 | 0.225791 | ||||||||
\(754\) | −4.91613 | −0.179035 | ||||||||
\(755\) | −14.7948 | −0.538437 | ||||||||
\(756\) | −18.3570 | −0.667639 | ||||||||
\(757\) | −21.1129 | −0.767362 | −0.383681 | − | 0.923466i | \(-0.625344\pi\) | ||||
−0.383681 | + | 0.923466i | \(0.625344\pi\) | |||||||
\(758\) | −6.79039 | −0.246638 | ||||||||
\(759\) | 1.04557 | 0.0379518 | ||||||||
\(760\) | 7.09210 | 0.257258 | ||||||||
\(761\) | 45.7062 | 1.65685 | 0.828424 | − | 0.560101i | \(-0.189238\pi\) | ||||
0.828424 | + | 0.560101i | \(0.189238\pi\) | |||||||
\(762\) | −2.44354 | −0.0885201 | ||||||||
\(763\) | 36.7631 | 1.33092 | ||||||||
\(764\) | −25.3693 | −0.917829 | ||||||||
\(765\) | −3.64925 | −0.131939 | ||||||||
\(766\) | −18.0024 | −0.650453 | ||||||||
\(767\) | 15.2957 | 0.552294 | ||||||||
\(768\) | −18.2797 | −0.659610 | ||||||||
\(769\) | −25.3430 | −0.913892 | −0.456946 | − | 0.889494i | \(-0.651057\pi\) | ||||
−0.456946 | + | 0.889494i | \(0.651057\pi\) | |||||||
\(770\) | −1.36387 | −0.0491503 | ||||||||
\(771\) | −38.5697 | −1.38905 | ||||||||
\(772\) | 22.0970 | 0.795290 | ||||||||
\(773\) | −22.8642 | −0.822367 | −0.411183 | − | 0.911553i | \(-0.634884\pi\) | ||||
−0.411183 | + | 0.911553i | \(0.634884\pi\) | |||||||
\(774\) | 9.66509 | 0.347404 | ||||||||
\(775\) | 24.1004 | 0.865714 | ||||||||
\(776\) | 27.3004 | 0.980026 | ||||||||
\(777\) | −27.4854 | −0.986032 | ||||||||
\(778\) | −3.69329 | −0.132411 | ||||||||
\(779\) | 26.2257 | 0.939633 | ||||||||
\(780\) | −2.90596 | −0.104050 | ||||||||
\(781\) | 14.2107 | 0.508500 | ||||||||
\(782\) | 2.51891 | 0.0900760 | ||||||||
\(783\) | −16.9047 | −0.604126 | ||||||||
\(784\) | −1.04308 | −0.0372527 | ||||||||
\(785\) | −3.63489 | −0.129735 | ||||||||
\(786\) | −0.648139 | −0.0231183 | ||||||||
\(787\) | 15.6127 | 0.556531 | 0.278266 | − | 0.960504i | \(-0.410240\pi\) | ||||
0.278266 | + | 0.960504i | \(0.410240\pi\) | |||||||
\(788\) | −34.7652 | −1.23846 | ||||||||
\(789\) | 34.0675 | 1.21283 | ||||||||
\(790\) | −4.69942 | −0.167198 | ||||||||
\(791\) | 4.18509 | 0.148805 | ||||||||
\(792\) | −3.14371 | −0.111707 | ||||||||
\(793\) | 2.09467 | 0.0743841 | ||||||||
\(794\) | −12.3916 | −0.439762 | ||||||||
\(795\) | 8.90673 | 0.315889 | ||||||||
\(796\) | 19.6206 | 0.695434 | ||||||||
\(797\) | −4.30125 | −0.152358 | −0.0761790 | − | 0.997094i | \(-0.524272\pi\) | ||||
−0.0761790 | + | 0.997094i | \(0.524272\pi\) | |||||||
\(798\) | −8.91542 | −0.315603 | ||||||||
\(799\) | −37.3730 | −1.32216 | ||||||||
\(800\) | −26.0262 | −0.920167 | ||||||||
\(801\) | 4.89861 | 0.173084 | ||||||||
\(802\) | −3.17164 | −0.111995 | ||||||||
\(803\) | −11.6807 | −0.412202 | ||||||||
\(804\) | −22.8025 | −0.804182 | ||||||||
\(805\) | −1.35253 | −0.0476704 | ||||||||
\(806\) | 8.88213 | 0.312860 | ||||||||
\(807\) | 36.4215 | 1.28210 | ||||||||
\(808\) | 10.7619 | 0.378603 | ||||||||
\(809\) | −23.8068 | −0.837003 | −0.418502 | − | 0.908216i | \(-0.637445\pi\) | ||||
−0.418502 | + | 0.908216i | \(0.637445\pi\) | |||||||
\(810\) | 2.34605 | 0.0824319 | ||||||||
\(811\) | −21.2381 | −0.745769 | −0.372885 | − | 0.927878i | \(-0.621631\pi\) | ||||
−0.372885 | + | 0.927878i | \(0.621631\pi\) | |||||||
\(812\) | 9.76260 | 0.342600 | ||||||||
\(813\) | 19.9728 | 0.700476 | ||||||||
\(814\) | −6.80548 | −0.238532 | ||||||||
\(815\) | 11.3288 | 0.396831 | ||||||||
\(816\) | −3.90458 | −0.136688 | ||||||||
\(817\) | −37.5209 | −1.31269 | ||||||||
\(818\) | −18.4909 | −0.646520 | ||||||||
\(819\) | −5.82895 | −0.203680 | ||||||||
\(820\) | 7.49698 | 0.261806 | ||||||||
\(821\) | −12.0309 | −0.419882 | −0.209941 | − | 0.977714i | \(-0.567327\pi\) | ||||
−0.209941 | + | 0.977714i | \(0.567327\pi\) | |||||||
\(822\) | 17.7591 | 0.619420 | ||||||||
\(823\) | 45.3529 | 1.58090 | 0.790452 | − | 0.612525i | \(-0.209846\pi\) | ||||
0.790452 | + | 0.612525i | \(0.209846\pi\) | |||||||
\(824\) | 15.0170 | 0.523141 | ||||||||
\(825\) | 5.99243 | 0.208630 | ||||||||
\(826\) | 13.4147 | 0.466756 | ||||||||
\(827\) | 12.2112 | 0.424627 | 0.212313 | − | 0.977202i | \(-0.431900\pi\) | ||||
0.212313 | + | 0.977202i | \(0.431900\pi\) | |||||||
\(828\) | −1.27684 | −0.0443732 | ||||||||
\(829\) | −2.05546 | −0.0713892 | −0.0356946 | − | 0.999363i | \(-0.511364\pi\) | ||||
−0.0356946 | + | 0.999363i | \(0.511364\pi\) | |||||||
\(830\) | 0.457058 | 0.0158647 | ||||||||
\(831\) | 21.9842 | 0.762623 | ||||||||
\(832\) | −6.66255 | −0.230982 | ||||||||
\(833\) | 6.18426 | 0.214272 | ||||||||
\(834\) | −10.7177 | −0.371122 | ||||||||
\(835\) | −6.54666 | −0.226557 | ||||||||
\(836\) | 4.99837 | 0.172872 | ||||||||
\(837\) | 30.5423 | 1.05570 | ||||||||
\(838\) | 8.83299 | 0.305130 | ||||||||
\(839\) | −21.5294 | −0.743278 | −0.371639 | − | 0.928377i | \(-0.621204\pi\) | ||||
−0.371639 | + | 0.928377i | \(0.621204\pi\) | |||||||
\(840\) | −6.22276 | −0.214706 | ||||||||
\(841\) | −20.0098 | −0.689992 | ||||||||
\(842\) | −5.21852 | −0.179842 | ||||||||
\(843\) | 6.94112 | 0.239065 | ||||||||
\(844\) | −1.58534 | −0.0545695 | ||||||||
\(845\) | 6.39387 | 0.219956 | ||||||||
\(846\) | −8.36665 | −0.287651 | ||||||||
\(847\) | −2.34697 | −0.0806428 | ||||||||
\(848\) | −6.22789 | −0.213866 | ||||||||
\(849\) | −18.7207 | −0.642492 | ||||||||
\(850\) | 14.4365 | 0.495168 | ||||||||
\(851\) | −6.74891 | −0.231350 | ||||||||
\(852\) | 26.5550 | 0.909760 | ||||||||
\(853\) | 14.9370 | 0.511432 | 0.255716 | − | 0.966752i | \(-0.417689\pi\) | ||||
0.255716 | + | 0.966752i | \(0.417689\pi\) | |||||||
\(854\) | 1.83708 | 0.0628637 | ||||||||
\(855\) | 3.17151 | 0.108463 | ||||||||
\(856\) | −7.13433 | −0.243846 | ||||||||
\(857\) | 38.4497 | 1.31342 | 0.656708 | − | 0.754145i | \(-0.271948\pi\) | ||||
0.656708 | + | 0.754145i | \(0.271948\pi\) | |||||||
\(858\) | 2.20849 | 0.0753966 | ||||||||
\(859\) | −8.13613 | −0.277601 | −0.138801 | − | 0.990320i | \(-0.544325\pi\) | ||||
−0.138801 | + | 0.990320i | \(0.544325\pi\) | |||||||
\(860\) | −10.7259 | −0.365749 | ||||||||
\(861\) | −23.0110 | −0.784212 | ||||||||
\(862\) | 28.1828 | 0.959910 | ||||||||
\(863\) | −15.3403 | −0.522191 | −0.261096 | − | 0.965313i | \(-0.584084\pi\) | ||||
−0.261096 | + | 0.965313i | \(0.584084\pi\) | |||||||
\(864\) | −32.9829 | −1.12210 | ||||||||
\(865\) | 5.35641 | 0.182123 | ||||||||
\(866\) | 22.0076 | 0.747849 | ||||||||
\(867\) | 0.251280 | 0.00853392 | ||||||||
\(868\) | −17.6384 | −0.598686 | ||||||||
\(869\) | −8.08687 | −0.274328 | ||||||||
\(870\) | −2.34697 | −0.0795697 | ||||||||
\(871\) | −25.5605 | −0.866084 | ||||||||
\(872\) | 41.5319 | 1.40645 | ||||||||
\(873\) | 12.2084 | 0.413192 | ||||||||
\(874\) | −2.18914 | −0.0740489 | ||||||||
\(875\) | −16.4637 | −0.556575 | ||||||||
\(876\) | −21.8272 | −0.737473 | ||||||||
\(877\) | 13.3372 | 0.450366 | 0.225183 | − | 0.974316i | \(-0.427702\pi\) | ||||
0.225183 | + | 0.974316i | \(0.427702\pi\) | |||||||
\(878\) | 11.8678 | 0.400520 | ||||||||
\(879\) | 28.0196 | 0.945079 | ||||||||
\(880\) | 0.519117 | 0.0174994 | ||||||||
\(881\) | −16.8053 | −0.566186 | −0.283093 | − | 0.959092i | \(-0.591361\pi\) | ||||
−0.283093 | + | 0.959092i | \(0.591361\pi\) | |||||||
\(882\) | 1.38446 | 0.0466173 | ||||||||
\(883\) | −9.84775 | −0.331403 | −0.165702 | − | 0.986176i | \(-0.552989\pi\) | ||||
−0.165702 | + | 0.986176i | \(0.552989\pi\) | |||||||
\(884\) | −12.0471 | −0.405189 | ||||||||
\(885\) | 7.30217 | 0.245460 | ||||||||
\(886\) | 4.26403 | 0.143253 | ||||||||
\(887\) | −1.36447 | −0.0458145 | −0.0229072 | − | 0.999738i | \(-0.507292\pi\) | ||||
−0.0229072 | + | 0.999738i | \(0.507292\pi\) | |||||||
\(888\) | −31.0506 | −1.04199 | ||||||||
\(889\) | 5.43936 | 0.182430 | ||||||||
\(890\) | 2.40088 | 0.0804776 | ||||||||
\(891\) | 4.03714 | 0.135249 | ||||||||
\(892\) | −29.3579 | −0.982976 | ||||||||
\(893\) | 32.4803 | 1.08691 | ||||||||
\(894\) | −9.62749 | −0.321992 | ||||||||
\(895\) | 1.12161 | 0.0374914 | ||||||||
\(896\) | 21.6169 | 0.722171 | ||||||||
\(897\) | 2.19013 | 0.0731264 | ||||||||
\(898\) | −29.8189 | −0.995068 | ||||||||
\(899\) | −16.2429 | −0.541733 | ||||||||
\(900\) | −7.31787 | −0.243929 | ||||||||
\(901\) | 36.9243 | 1.23013 | ||||||||
\(902\) | −5.69761 | −0.189710 | ||||||||
\(903\) | 32.9217 | 1.09556 | ||||||||
\(904\) | 4.72796 | 0.157249 | ||||||||
\(905\) | 16.9020 | 0.561840 | ||||||||
\(906\) | 21.0109 | 0.698039 | ||||||||
\(907\) | −8.95204 | −0.297248 | −0.148624 | − | 0.988894i | \(-0.547484\pi\) | ||||
−0.148624 | + | 0.988894i | \(0.547484\pi\) | |||||||
\(908\) | 22.8873 | 0.759541 | ||||||||
\(909\) | 4.81261 | 0.159624 | ||||||||
\(910\) | −2.85685 | −0.0947038 | ||||||||
\(911\) | −15.5635 | −0.515641 | −0.257820 | − | 0.966193i | \(-0.583004\pi\) | ||||
−0.257820 | + | 0.966193i | \(0.583004\pi\) | |||||||
\(912\) | 3.39341 | 0.112367 | ||||||||
\(913\) | 0.786515 | 0.0260298 | ||||||||
\(914\) | −21.3709 | −0.706885 | ||||||||
\(915\) | 1.00000 | 0.0330590 | ||||||||
\(916\) | 12.0116 | 0.396874 | ||||||||
\(917\) | 1.44277 | 0.0476444 | ||||||||
\(918\) | 18.2953 | 0.603834 | ||||||||
\(919\) | −8.14172 | −0.268571 | −0.134285 | − | 0.990943i | \(-0.542874\pi\) | ||||
−0.134285 | + | 0.990943i | \(0.542874\pi\) | |||||||
\(920\) | −1.52797 | −0.0503757 | ||||||||
\(921\) | −33.2895 | −1.09693 | ||||||||
\(922\) | −16.0579 | −0.528839 | ||||||||
\(923\) | 29.7669 | 0.979789 | ||||||||
\(924\) | −4.38568 | −0.144278 | ||||||||
\(925\) | −38.6797 | −1.27178 | ||||||||
\(926\) | −21.2841 | −0.699438 | ||||||||
\(927\) | 6.71541 | 0.220563 | ||||||||
\(928\) | 17.5409 | 0.575808 | ||||||||
\(929\) | 32.0097 | 1.05020 | 0.525102 | − | 0.851039i | \(-0.324027\pi\) | ||||
0.525102 | + | 0.851039i | \(0.324027\pi\) | |||||||
\(930\) | 4.24034 | 0.139046 | ||||||||
\(931\) | −5.37465 | −0.176147 | ||||||||
\(932\) | −9.19762 | −0.301278 | ||||||||
\(933\) | −43.7994 | −1.43393 | ||||||||
\(934\) | 21.6074 | 0.707015 | ||||||||
\(935\) | −3.07778 | −0.100654 | ||||||||
\(936\) | −6.58505 | −0.215239 | ||||||||
\(937\) | −24.4613 | −0.799114 | −0.399557 | − | 0.916708i | \(-0.630836\pi\) | ||||
−0.399557 | + | 0.916708i | \(0.630836\pi\) | |||||||
\(938\) | −22.4172 | −0.731948 | ||||||||
\(939\) | −33.4142 | −1.09043 | ||||||||
\(940\) | 9.28493 | 0.302841 | ||||||||
\(941\) | −34.8804 | −1.13707 | −0.568534 | − | 0.822660i | \(-0.692489\pi\) | ||||
−0.568534 | + | 0.822660i | \(0.692489\pi\) | |||||||
\(942\) | 5.16212 | 0.168191 | ||||||||
\(943\) | −5.65025 | −0.183997 | ||||||||
\(944\) | −5.10592 | −0.166184 | ||||||||
\(945\) | −9.82365 | −0.319563 | ||||||||
\(946\) | 8.15153 | 0.265029 | ||||||||
\(947\) | −11.9348 | −0.387830 | −0.193915 | − | 0.981018i | \(-0.562119\pi\) | ||||
−0.193915 | + | 0.981018i | \(0.562119\pi\) | |||||||
\(948\) | −15.1116 | −0.490802 | ||||||||
\(949\) | −24.4672 | −0.794240 | ||||||||
\(950\) | −12.5465 | −0.407063 | ||||||||
\(951\) | −16.0843 | −0.521569 | ||||||||
\(952\) | −25.7975 | −0.836102 | ||||||||
\(953\) | −16.3997 | −0.531238 | −0.265619 | − | 0.964078i | \(-0.585576\pi\) | ||||
−0.265619 | + | 0.964078i | \(0.585576\pi\) | |||||||
\(954\) | 8.26621 | 0.267628 | ||||||||
\(955\) | −13.5762 | −0.439316 | ||||||||
\(956\) | 27.2298 | 0.880676 | ||||||||
\(957\) | −4.03871 | −0.130553 | ||||||||
\(958\) | 24.1084 | 0.778908 | ||||||||
\(959\) | −39.5320 | −1.27656 | ||||||||
\(960\) | −3.18071 | −0.102657 | ||||||||
\(961\) | −1.65335 | −0.0533339 | ||||||||
\(962\) | −14.2553 | −0.459608 | ||||||||
\(963\) | −3.19039 | −0.102809 | ||||||||
\(964\) | 3.00868 | 0.0969030 | ||||||||
\(965\) | 11.8251 | 0.380663 | ||||||||
\(966\) | 1.92080 | 0.0618008 | ||||||||
\(967\) | 52.4183 | 1.68566 | 0.842830 | − | 0.538180i | \(-0.180888\pi\) | ||||
0.842830 | + | 0.538180i | \(0.180888\pi\) | |||||||
\(968\) | −2.65140 | −0.0852194 | ||||||||
\(969\) | −20.1191 | −0.646317 | ||||||||
\(970\) | 5.98352 | 0.192119 | ||||||||
\(971\) | −39.7148 | −1.27451 | −0.637254 | − | 0.770654i | \(-0.719930\pi\) | ||||
−0.637254 | + | 0.770654i | \(0.719930\pi\) | |||||||
\(972\) | −15.9208 | −0.510659 | ||||||||
\(973\) | 23.8577 | 0.764842 | ||||||||
\(974\) | 26.0040 | 0.833221 | ||||||||
\(975\) | 12.5522 | 0.401992 | ||||||||
\(976\) | −0.699234 | −0.0223819 | ||||||||
\(977\) | −1.51718 | −0.0485390 | −0.0242695 | − | 0.999705i | \(-0.507726\pi\) | ||||
−0.0242695 | + | 0.999705i | \(0.507726\pi\) | |||||||
\(978\) | −16.0887 | −0.514460 | ||||||||
\(979\) | 4.13148 | 0.132043 | ||||||||
\(980\) | −1.53642 | −0.0490790 | ||||||||
\(981\) | 18.5726 | 0.592977 | ||||||||
\(982\) | 16.9451 | 0.540739 | ||||||||
\(983\) | −22.4709 | −0.716709 | −0.358355 | − | 0.933586i | \(-0.616662\pi\) | ||||
−0.358355 | + | 0.933586i | \(0.616662\pi\) | |||||||
\(984\) | −25.9959 | −0.828718 | ||||||||
\(985\) | −18.6044 | −0.592785 | ||||||||
\(986\) | −9.72975 | −0.309858 | ||||||||
\(987\) | −28.4989 | −0.907130 | ||||||||
\(988\) | 10.4700 | 0.333094 | ||||||||
\(989\) | 8.08377 | 0.257049 | ||||||||
\(990\) | −0.689019 | −0.0218984 | ||||||||
\(991\) | 45.2946 | 1.43883 | 0.719415 | − | 0.694581i | \(-0.244410\pi\) | ||||
0.719415 | + | 0.694581i | \(0.244410\pi\) | |||||||
\(992\) | −31.6917 | −1.00621 | ||||||||
\(993\) | −37.4028 | −1.18694 | ||||||||
\(994\) | 26.1063 | 0.828042 | ||||||||
\(995\) | 10.4998 | 0.332867 | ||||||||
\(996\) | 1.46973 | 0.0465701 | ||||||||
\(997\) | −1.80367 | −0.0571228 | −0.0285614 | − | 0.999592i | \(-0.509093\pi\) | ||||
−0.0285614 | + | 0.999592i | \(0.509093\pi\) | |||||||
\(998\) | 6.49366 | 0.205553 | ||||||||
\(999\) | −49.0185 | −1.55088 |
(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 | 671.2.a.b.1.4 | ✓ | 6 | |
3.2 | odd | 2 | 6039.2.a.b.1.3 | 6 | |||
11.10 | odd | 2 | 7381.2.a.h.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.b.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6039.2.a.b.1.3 | 6 | 3.2 | odd | 2 | |||
7381.2.a.h.1.3 | 6 | 11.10 | odd | 2 |