Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(74\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85483 | −1.31157 | −0.655783 | − | 0.754950i | \(-0.727661\pi\) | ||||
−0.655783 | + | 0.754950i | \(0.727661\pi\) | |||||||
\(3\) | 0.655235 | 0.378300 | 0.189150 | − | 0.981948i | \(-0.439427\pi\) | ||||
0.189150 | + | 0.981948i | \(0.439427\pi\) | |||||||
\(4\) | 1.44041 | 0.720204 | ||||||||
\(5\) | 4.10800 | 1.83715 | 0.918576 | − | 0.395243i | \(-0.129340\pi\) | ||||
0.918576 | + | 0.395243i | \(0.129340\pi\) | |||||||
\(6\) | −1.21535 | −0.496165 | ||||||||
\(7\) | −1.24342 | −0.469970 | −0.234985 | − | 0.971999i | \(-0.575504\pi\) | ||||
−0.234985 | + | 0.971999i | \(0.575504\pi\) | |||||||
\(8\) | 1.03795 | 0.366971 | ||||||||
\(9\) | −2.57067 | −0.856889 | ||||||||
\(10\) | −7.61965 | −2.40955 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.943805 | 0.272453 | ||||||||
\(13\) | 2.04423 | 0.566968 | 0.283484 | − | 0.958977i | \(-0.408510\pi\) | ||||
0.283484 | + | 0.958977i | \(0.408510\pi\) | |||||||
\(14\) | 2.30634 | 0.616396 | ||||||||
\(15\) | 2.69170 | 0.694995 | ||||||||
\(16\) | −4.80604 | −1.20151 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 4.76816 | 1.12387 | ||||||||
\(19\) | 5.72719 | 1.31391 | 0.656954 | − | 0.753930i | \(-0.271844\pi\) | ||||
0.656954 | + | 0.753930i | \(0.271844\pi\) | |||||||
\(20\) | 5.91719 | 1.32312 | ||||||||
\(21\) | −0.814734 | −0.177790 | ||||||||
\(22\) | 1.85483 | 0.395452 | ||||||||
\(23\) | −5.52036 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(24\) | 0.680101 | 0.138825 | ||||||||
\(25\) | 11.8757 | 2.37513 | ||||||||
\(26\) | −3.79171 | −0.743615 | ||||||||
\(27\) | −3.65009 | −0.702461 | ||||||||
\(28\) | −1.79104 | −0.338474 | ||||||||
\(29\) | −8.74117 | −1.62319 | −0.811597 | − | 0.584217i | \(-0.801402\pi\) | ||||
−0.811597 | + | 0.584217i | \(0.801402\pi\) | |||||||
\(30\) | −4.99266 | −0.911531 | ||||||||
\(31\) | 2.93216 | 0.526631 | 0.263316 | − | 0.964710i | \(-0.415184\pi\) | ||||
0.263316 | + | 0.964710i | \(0.415184\pi\) | |||||||
\(32\) | 6.83850 | 1.20889 | ||||||||
\(33\) | −0.655235 | −0.114062 | ||||||||
\(34\) | 1.85483 | 0.318101 | ||||||||
\(35\) | −5.10798 | −0.863407 | ||||||||
\(36\) | −3.70281 | −0.617135 | ||||||||
\(37\) | 1.56239 | 0.256855 | 0.128427 | − | 0.991719i | \(-0.459007\pi\) | ||||
0.128427 | + | 0.991719i | \(0.459007\pi\) | |||||||
\(38\) | −10.6230 | −1.72328 | ||||||||
\(39\) | 1.33945 | 0.214484 | ||||||||
\(40\) | 4.26390 | 0.674182 | ||||||||
\(41\) | −6.25556 | −0.976954 | −0.488477 | − | 0.872577i | \(-0.662447\pi\) | ||||
−0.488477 | + | 0.872577i | \(0.662447\pi\) | |||||||
\(42\) | 1.51120 | 0.233183 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −1.44041 | −0.217150 | ||||||||
\(45\) | −10.5603 | −1.57424 | ||||||||
\(46\) | 10.2393 | 1.50971 | ||||||||
\(47\) | −7.49069 | −1.09263 | −0.546314 | − | 0.837580i | \(-0.683970\pi\) | ||||
−0.546314 | + | 0.837580i | \(0.683970\pi\) | |||||||
\(48\) | −3.14909 | −0.454531 | ||||||||
\(49\) | −5.45390 | −0.779128 | ||||||||
\(50\) | −22.0274 | −3.11514 | ||||||||
\(51\) | −0.655235 | −0.0917512 | ||||||||
\(52\) | 2.94453 | 0.408332 | ||||||||
\(53\) | 1.86093 | 0.255618 | 0.127809 | − | 0.991799i | \(-0.459206\pi\) | ||||
0.127809 | + | 0.991799i | \(0.459206\pi\) | |||||||
\(54\) | 6.77032 | 0.921324 | ||||||||
\(55\) | −4.10800 | −0.553922 | ||||||||
\(56\) | −1.29061 | −0.172465 | ||||||||
\(57\) | 3.75266 | 0.497052 | ||||||||
\(58\) | 16.2134 | 2.12893 | ||||||||
\(59\) | −8.57050 | −1.11578 | −0.557892 | − | 0.829914i | \(-0.688390\pi\) | ||||
−0.557892 | + | 0.829914i | \(0.688390\pi\) | |||||||
\(60\) | 3.87715 | 0.500538 | ||||||||
\(61\) | 6.86031 | 0.878373 | 0.439187 | − | 0.898396i | \(-0.355267\pi\) | ||||
0.439187 | + | 0.898396i | \(0.355267\pi\) | |||||||
\(62\) | −5.43867 | −0.690712 | ||||||||
\(63\) | 3.19643 | 0.402712 | ||||||||
\(64\) | −3.07221 | −0.384026 | ||||||||
\(65\) | 8.39770 | 1.04161 | ||||||||
\(66\) | 1.21535 | 0.149599 | ||||||||
\(67\) | 11.6268 | 1.42044 | 0.710221 | − | 0.703979i | \(-0.248595\pi\) | ||||
0.710221 | + | 0.703979i | \(0.248595\pi\) | |||||||
\(68\) | −1.44041 | −0.174675 | ||||||||
\(69\) | −3.61713 | −0.435451 | ||||||||
\(70\) | 9.47446 | 1.13241 | ||||||||
\(71\) | −7.96033 | −0.944717 | −0.472358 | − | 0.881407i | \(-0.656597\pi\) | ||||
−0.472358 | + | 0.881407i | \(0.656597\pi\) | |||||||
\(72\) | −2.66823 | −0.314453 | ||||||||
\(73\) | −12.0888 | −1.41488 | −0.707441 | − | 0.706772i | \(-0.750151\pi\) | ||||
−0.707441 | + | 0.706772i | \(0.750151\pi\) | |||||||
\(74\) | −2.89797 | −0.336882 | ||||||||
\(75\) | 7.78134 | 0.898512 | ||||||||
\(76\) | 8.24949 | 0.946282 | ||||||||
\(77\) | 1.24342 | 0.141701 | ||||||||
\(78\) | −2.48446 | −0.281310 | ||||||||
\(79\) | 6.30339 | 0.709187 | 0.354594 | − | 0.935021i | \(-0.384619\pi\) | ||||
0.354594 | + | 0.935021i | \(0.384619\pi\) | |||||||
\(80\) | −19.7432 | −2.20736 | ||||||||
\(81\) | 5.32033 | 0.591148 | ||||||||
\(82\) | 11.6030 | 1.28134 | ||||||||
\(83\) | −7.80352 | −0.856547 | −0.428274 | − | 0.903649i | \(-0.640878\pi\) | ||||
−0.428274 | + | 0.903649i | \(0.640878\pi\) | |||||||
\(84\) | −1.17355 | −0.128045 | ||||||||
\(85\) | −4.10800 | −0.445575 | ||||||||
\(86\) | 1.85483 | 0.200012 | ||||||||
\(87\) | −5.72752 | −0.614054 | ||||||||
\(88\) | −1.03795 | −0.110646 | ||||||||
\(89\) | 2.05894 | 0.218248 | 0.109124 | − | 0.994028i | \(-0.465196\pi\) | ||||
0.109124 | + | 0.994028i | \(0.465196\pi\) | |||||||
\(90\) | 19.5876 | 2.06471 | ||||||||
\(91\) | −2.54184 | −0.266458 | ||||||||
\(92\) | −7.95156 | −0.829008 | ||||||||
\(93\) | 1.92125 | 0.199225 | ||||||||
\(94\) | 13.8940 | 1.43305 | ||||||||
\(95\) | 23.5273 | 2.41385 | ||||||||
\(96\) | 4.48083 | 0.457322 | ||||||||
\(97\) | −6.35396 | −0.645147 | −0.322573 | − | 0.946544i | \(-0.604548\pi\) | ||||
−0.322573 | + | 0.946544i | \(0.604548\pi\) | |||||||
\(98\) | 10.1161 | 1.02188 | ||||||||
\(99\) | 2.57067 | 0.258362 | ||||||||
\(100\) | 17.1058 | 1.71058 | ||||||||
\(101\) | 8.07955 | 0.803945 | 0.401973 | − | 0.915652i | \(-0.368325\pi\) | ||||
0.401973 | + | 0.915652i | \(0.368325\pi\) | |||||||
\(102\) | 1.21535 | 0.120338 | ||||||||
\(103\) | −3.52162 | −0.346995 | −0.173498 | − | 0.984834i | \(-0.555507\pi\) | ||||
−0.173498 | + | 0.984834i | \(0.555507\pi\) | |||||||
\(104\) | 2.12181 | 0.208061 | ||||||||
\(105\) | −3.34693 | −0.326627 | ||||||||
\(106\) | −3.45171 | −0.335260 | ||||||||
\(107\) | −9.71384 | −0.939072 | −0.469536 | − | 0.882913i | \(-0.655579\pi\) | ||||
−0.469536 | + | 0.882913i | \(0.655579\pi\) | |||||||
\(108\) | −5.25762 | −0.505915 | ||||||||
\(109\) | 3.86982 | 0.370661 | 0.185331 | − | 0.982676i | \(-0.440664\pi\) | ||||
0.185331 | + | 0.982676i | \(0.440664\pi\) | |||||||
\(110\) | 7.61965 | 0.726505 | ||||||||
\(111\) | 1.02373 | 0.0971682 | ||||||||
\(112\) | 5.97595 | 0.564674 | ||||||||
\(113\) | 16.2691 | 1.53047 | 0.765233 | − | 0.643754i | \(-0.222624\pi\) | ||||
0.765233 | + | 0.643754i | \(0.222624\pi\) | |||||||
\(114\) | −6.96055 | −0.651916 | ||||||||
\(115\) | −22.6776 | −2.11470 | ||||||||
\(116\) | −12.5908 | −1.16903 | ||||||||
\(117\) | −5.25504 | −0.485828 | ||||||||
\(118\) | 15.8968 | 1.46342 | ||||||||
\(119\) | 1.24342 | 0.113984 | ||||||||
\(120\) | 2.79386 | 0.255043 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −12.7247 | −1.15204 | ||||||||
\(123\) | −4.09886 | −0.369582 | ||||||||
\(124\) | 4.22351 | 0.379282 | ||||||||
\(125\) | 28.2452 | 2.52632 | ||||||||
\(126\) | −5.92884 | −0.528183 | ||||||||
\(127\) | −10.7446 | −0.953426 | −0.476713 | − | 0.879059i | \(-0.658172\pi\) | ||||
−0.476713 | + | 0.879059i | \(0.658172\pi\) | |||||||
\(128\) | −7.97858 | −0.705213 | ||||||||
\(129\) | −0.655235 | −0.0576902 | ||||||||
\(130\) | −15.5763 | −1.36613 | ||||||||
\(131\) | −14.5595 | −1.27207 | −0.636034 | − | 0.771661i | \(-0.719426\pi\) | ||||
−0.636034 | + | 0.771661i | \(0.719426\pi\) | |||||||
\(132\) | −0.943805 | −0.0821477 | ||||||||
\(133\) | −7.12133 | −0.617498 | ||||||||
\(134\) | −21.5658 | −1.86300 | ||||||||
\(135\) | −14.9946 | −1.29053 | ||||||||
\(136\) | −1.03795 | −0.0890035 | ||||||||
\(137\) | −2.59301 | −0.221536 | −0.110768 | − | 0.993846i | \(-0.535331\pi\) | ||||
−0.110768 | + | 0.993846i | \(0.535331\pi\) | |||||||
\(138\) | 6.70917 | 0.571123 | ||||||||
\(139\) | −20.0709 | −1.70239 | −0.851194 | − | 0.524851i | \(-0.824121\pi\) | ||||
−0.851194 | + | 0.524851i | \(0.824121\pi\) | |||||||
\(140\) | −7.35758 | −0.621829 | ||||||||
\(141\) | −4.90816 | −0.413341 | ||||||||
\(142\) | 14.7651 | 1.23906 | ||||||||
\(143\) | −2.04423 | −0.170947 | ||||||||
\(144\) | 12.3547 | 1.02956 | ||||||||
\(145\) | −35.9087 | −2.98206 | ||||||||
\(146\) | 22.4226 | 1.85571 | ||||||||
\(147\) | −3.57358 | −0.294744 | ||||||||
\(148\) | 2.25048 | 0.184988 | ||||||||
\(149\) | −11.8744 | −0.972790 | −0.486395 | − | 0.873739i | \(-0.661688\pi\) | ||||
−0.486395 | + | 0.873739i | \(0.661688\pi\) | |||||||
\(150\) | −14.4331 | −1.17846 | ||||||||
\(151\) | −2.43319 | −0.198010 | −0.0990051 | − | 0.995087i | \(-0.531566\pi\) | ||||
−0.0990051 | + | 0.995087i | \(0.531566\pi\) | |||||||
\(152\) | 5.94455 | 0.482166 | ||||||||
\(153\) | 2.57067 | 0.207826 | ||||||||
\(154\) | −2.30634 | −0.185850 | ||||||||
\(155\) | 12.0453 | 0.967502 | ||||||||
\(156\) | 1.92936 | 0.154472 | ||||||||
\(157\) | 3.77020 | 0.300895 | 0.150447 | − | 0.988618i | \(-0.451929\pi\) | ||||
0.150447 | + | 0.988618i | \(0.451929\pi\) | |||||||
\(158\) | −11.6917 | −0.930145 | ||||||||
\(159\) | 1.21934 | 0.0967003 | ||||||||
\(160\) | 28.0926 | 2.22091 | ||||||||
\(161\) | 6.86414 | 0.540970 | ||||||||
\(162\) | −9.86833 | −0.775329 | ||||||||
\(163\) | 21.8095 | 1.70825 | 0.854127 | − | 0.520065i | \(-0.174092\pi\) | ||||
0.854127 | + | 0.520065i | \(0.174092\pi\) | |||||||
\(164\) | −9.01056 | −0.703606 | ||||||||
\(165\) | −2.69170 | −0.209549 | ||||||||
\(166\) | 14.4742 | 1.12342 | ||||||||
\(167\) | 1.35784 | 0.105073 | 0.0525363 | − | 0.998619i | \(-0.483269\pi\) | ||||
0.0525363 | + | 0.998619i | \(0.483269\pi\) | |||||||
\(168\) | −0.845654 | −0.0652436 | ||||||||
\(169\) | −8.82112 | −0.678548 | ||||||||
\(170\) | 7.61965 | 0.584401 | ||||||||
\(171\) | −14.7227 | −1.12587 | ||||||||
\(172\) | −1.44041 | −0.109830 | ||||||||
\(173\) | −22.7356 | −1.72856 | −0.864279 | − | 0.503013i | \(-0.832225\pi\) | ||||
−0.864279 | + | 0.503013i | \(0.832225\pi\) | |||||||
\(174\) | 10.6236 | 0.805372 | ||||||||
\(175\) | −14.7665 | −1.11624 | ||||||||
\(176\) | 4.80604 | 0.362269 | ||||||||
\(177\) | −5.61569 | −0.422101 | ||||||||
\(178\) | −3.81900 | −0.286246 | ||||||||
\(179\) | 5.44221 | 0.406770 | 0.203385 | − | 0.979099i | \(-0.434806\pi\) | ||||
0.203385 | + | 0.979099i | \(0.434806\pi\) | |||||||
\(180\) | −15.2111 | −1.13377 | ||||||||
\(181\) | 0.553468 | 0.0411389 | 0.0205695 | − | 0.999788i | \(-0.493452\pi\) | ||||
0.0205695 | + | 0.999788i | \(0.493452\pi\) | |||||||
\(182\) | 4.71470 | 0.349477 | ||||||||
\(183\) | 4.49512 | 0.332288 | ||||||||
\(184\) | −5.72986 | −0.422411 | ||||||||
\(185\) | 6.41829 | 0.471882 | ||||||||
\(186\) | −3.56360 | −0.261296 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −10.7896 | −0.786915 | ||||||||
\(189\) | 4.53861 | 0.330136 | ||||||||
\(190\) | −43.6392 | −3.16592 | ||||||||
\(191\) | 0.792894 | 0.0573718 | 0.0286859 | − | 0.999588i | \(-0.490868\pi\) | ||||
0.0286859 | + | 0.999588i | \(0.490868\pi\) | |||||||
\(192\) | −2.01302 | −0.145277 | ||||||||
\(193\) | 3.29520 | 0.237194 | 0.118597 | − | 0.992942i | \(-0.462160\pi\) | ||||
0.118597 | + | 0.992942i | \(0.462160\pi\) | |||||||
\(194\) | 11.7855 | 0.846152 | ||||||||
\(195\) | 5.50246 | 0.394039 | ||||||||
\(196\) | −7.85584 | −0.561131 | ||||||||
\(197\) | 2.62816 | 0.187248 | 0.0936242 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936242 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(198\) | −4.76816 | −0.338858 | ||||||||
\(199\) | 16.9415 | 1.20095 | 0.600475 | − | 0.799643i | \(-0.294978\pi\) | ||||
0.600475 | + | 0.799643i | \(0.294978\pi\) | |||||||
\(200\) | 12.3263 | 0.871604 | ||||||||
\(201\) | 7.61830 | 0.537353 | ||||||||
\(202\) | −14.9862 | −1.05443 | ||||||||
\(203\) | 10.8690 | 0.762853 | ||||||||
\(204\) | −0.943805 | −0.0660796 | ||||||||
\(205\) | −25.6978 | −1.79481 | ||||||||
\(206\) | 6.53201 | 0.455107 | ||||||||
\(207\) | 14.1910 | 0.986343 | ||||||||
\(208\) | −9.82466 | −0.681217 | ||||||||
\(209\) | −5.72719 | −0.396158 | ||||||||
\(210\) | 6.20799 | 0.428392 | ||||||||
\(211\) | −9.12966 | −0.628512 | −0.314256 | − | 0.949338i | \(-0.601755\pi\) | ||||
−0.314256 | + | 0.949338i | \(0.601755\pi\) | |||||||
\(212\) | 2.68049 | 0.184097 | ||||||||
\(213\) | −5.21588 | −0.357386 | ||||||||
\(214\) | 18.0176 | 1.23165 | ||||||||
\(215\) | −4.10800 | −0.280163 | ||||||||
\(216\) | −3.78862 | −0.257783 | ||||||||
\(217\) | −3.64592 | −0.247501 | ||||||||
\(218\) | −7.17787 | −0.486147 | ||||||||
\(219\) | −7.92098 | −0.535250 | ||||||||
\(220\) | −5.91719 | −0.398937 | ||||||||
\(221\) | −2.04423 | −0.137510 | ||||||||
\(222\) | −1.89885 | −0.127442 | ||||||||
\(223\) | −28.5249 | −1.91017 | −0.955084 | − | 0.296334i | \(-0.904236\pi\) | ||||
−0.955084 | + | 0.296334i | \(0.904236\pi\) | |||||||
\(224\) | −8.50316 | −0.568141 | ||||||||
\(225\) | −30.5284 | −2.03522 | ||||||||
\(226\) | −30.1764 | −2.00731 | ||||||||
\(227\) | 3.68379 | 0.244502 | 0.122251 | − | 0.992499i | \(-0.460989\pi\) | ||||
0.122251 | + | 0.992499i | \(0.460989\pi\) | |||||||
\(228\) | 5.40536 | 0.357978 | ||||||||
\(229\) | 9.32019 | 0.615896 | 0.307948 | − | 0.951403i | \(-0.400358\pi\) | ||||
0.307948 | + | 0.951403i | \(0.400358\pi\) | |||||||
\(230\) | 42.0632 | 2.77357 | ||||||||
\(231\) | 0.814734 | 0.0536056 | ||||||||
\(232\) | −9.07290 | −0.595665 | ||||||||
\(233\) | −21.4356 | −1.40429 | −0.702146 | − | 0.712033i | \(-0.747775\pi\) | ||||
−0.702146 | + | 0.712033i | \(0.747775\pi\) | |||||||
\(234\) | 9.74722 | 0.637196 | ||||||||
\(235\) | −30.7717 | −2.00733 | ||||||||
\(236\) | −12.3450 | −0.803592 | ||||||||
\(237\) | 4.13020 | 0.268285 | ||||||||
\(238\) | −2.30634 | −0.149498 | ||||||||
\(239\) | −25.6556 | −1.65952 | −0.829760 | − | 0.558121i | \(-0.811523\pi\) | ||||
−0.829760 | + | 0.558121i | \(0.811523\pi\) | |||||||
\(240\) | −12.9364 | −0.835043 | ||||||||
\(241\) | −12.0090 | −0.773568 | −0.386784 | − | 0.922170i | \(-0.626414\pi\) | ||||
−0.386784 | + | 0.922170i | \(0.626414\pi\) | |||||||
\(242\) | −1.85483 | −0.119233 | ||||||||
\(243\) | 14.4364 | 0.926092 | ||||||||
\(244\) | 9.88165 | 0.632608 | ||||||||
\(245\) | −22.4046 | −1.43138 | ||||||||
\(246\) | 7.60270 | 0.484731 | ||||||||
\(247\) | 11.7077 | 0.744943 | ||||||||
\(248\) | 3.04344 | 0.193258 | ||||||||
\(249\) | −5.11314 | −0.324032 | ||||||||
\(250\) | −52.3901 | −3.31344 | ||||||||
\(251\) | 2.62589 | 0.165744 | 0.0828722 | − | 0.996560i | \(-0.473591\pi\) | ||||
0.0828722 | + | 0.996560i | \(0.473591\pi\) | |||||||
\(252\) | 4.60416 | 0.290035 | ||||||||
\(253\) | 5.52036 | 0.347062 | ||||||||
\(254\) | 19.9294 | 1.25048 | ||||||||
\(255\) | −2.69170 | −0.168561 | ||||||||
\(256\) | 20.9433 | 1.30896 | ||||||||
\(257\) | −13.6681 | −0.852594 | −0.426297 | − | 0.904583i | \(-0.640182\pi\) | ||||
−0.426297 | + | 0.904583i | \(0.640182\pi\) | |||||||
\(258\) | 1.21535 | 0.0756645 | ||||||||
\(259\) | −1.94271 | −0.120714 | ||||||||
\(260\) | 12.0961 | 0.750169 | ||||||||
\(261\) | 22.4706 | 1.39090 | ||||||||
\(262\) | 27.0054 | 1.66840 | ||||||||
\(263\) | −5.68662 | −0.350652 | −0.175326 | − | 0.984510i | \(-0.556098\pi\) | ||||
−0.175326 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(264\) | −0.680101 | −0.0418574 | ||||||||
\(265\) | 7.64468 | 0.469609 | ||||||||
\(266\) | 13.2089 | 0.809888 | ||||||||
\(267\) | 1.34909 | 0.0825630 | ||||||||
\(268\) | 16.7474 | 1.02301 | ||||||||
\(269\) | 25.8214 | 1.57436 | 0.787179 | − | 0.616724i | \(-0.211541\pi\) | ||||
0.787179 | + | 0.616724i | \(0.211541\pi\) | |||||||
\(270\) | 27.8125 | 1.69261 | ||||||||
\(271\) | −4.37192 | −0.265575 | −0.132787 | − | 0.991145i | \(-0.542393\pi\) | ||||
−0.132787 | + | 0.991145i | \(0.542393\pi\) | |||||||
\(272\) | 4.80604 | 0.291409 | ||||||||
\(273\) | −1.66550 | −0.100801 | ||||||||
\(274\) | 4.80961 | 0.290559 | ||||||||
\(275\) | −11.8757 | −0.716129 | ||||||||
\(276\) | −5.21014 | −0.313614 | ||||||||
\(277\) | −15.4016 | −0.925390 | −0.462695 | − | 0.886518i | \(-0.653117\pi\) | ||||
−0.462695 | + | 0.886518i | \(0.653117\pi\) | |||||||
\(278\) | 37.2281 | 2.23279 | ||||||||
\(279\) | −7.53761 | −0.451265 | ||||||||
\(280\) | −5.30183 | −0.316845 | ||||||||
\(281\) | −24.2974 | −1.44946 | −0.724730 | − | 0.689033i | \(-0.758036\pi\) | ||||
−0.724730 | + | 0.689033i | \(0.758036\pi\) | |||||||
\(282\) | 9.10382 | 0.542124 | ||||||||
\(283\) | −12.5168 | −0.744046 | −0.372023 | − | 0.928224i | \(-0.621336\pi\) | ||||
−0.372023 | + | 0.928224i | \(0.621336\pi\) | |||||||
\(284\) | −11.4661 | −0.680389 | ||||||||
\(285\) | 15.4159 | 0.913160 | ||||||||
\(286\) | 3.79171 | 0.224208 | ||||||||
\(287\) | 7.77831 | 0.459139 | ||||||||
\(288\) | −17.5795 | −1.03588 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 66.6047 | 3.91116 | ||||||||
\(291\) | −4.16333 | −0.244059 | ||||||||
\(292\) | −17.4127 | −1.01900 | ||||||||
\(293\) | 28.7021 | 1.67680 | 0.838398 | − | 0.545058i | \(-0.183492\pi\) | ||||
0.838398 | + | 0.545058i | \(0.183492\pi\) | |||||||
\(294\) | 6.62840 | 0.386576 | ||||||||
\(295\) | −35.2076 | −2.04986 | ||||||||
\(296\) | 1.62168 | 0.0942583 | ||||||||
\(297\) | 3.65009 | 0.211800 | ||||||||
\(298\) | 22.0251 | 1.27588 | ||||||||
\(299\) | −11.2849 | −0.652621 | ||||||||
\(300\) | 11.2083 | 0.647112 | ||||||||
\(301\) | 1.24342 | 0.0716697 | ||||||||
\(302\) | 4.51316 | 0.259703 | ||||||||
\(303\) | 5.29400 | 0.304132 | ||||||||
\(304\) | −27.5251 | −1.57867 | ||||||||
\(305\) | 28.1822 | 1.61371 | ||||||||
\(306\) | −4.76816 | −0.272578 | ||||||||
\(307\) | −0.184798 | −0.0105470 | −0.00527350 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527350 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(308\) | 1.79104 | 0.102054 | ||||||||
\(309\) | −2.30749 | −0.131268 | ||||||||
\(310\) | −22.3420 | −1.26894 | ||||||||
\(311\) | 14.8388 | 0.841430 | 0.420715 | − | 0.907193i | \(-0.361779\pi\) | ||||
0.420715 | + | 0.907193i | \(0.361779\pi\) | |||||||
\(312\) | 1.39028 | 0.0787093 | ||||||||
\(313\) | 14.3331 | 0.810154 | 0.405077 | − | 0.914283i | \(-0.367245\pi\) | ||||
0.405077 | + | 0.914283i | \(0.367245\pi\) | |||||||
\(314\) | −6.99310 | −0.394643 | ||||||||
\(315\) | 13.1309 | 0.739844 | ||||||||
\(316\) | 9.07946 | 0.510759 | ||||||||
\(317\) | 2.98640 | 0.167733 | 0.0838666 | − | 0.996477i | \(-0.473273\pi\) | ||||
0.0838666 | + | 0.996477i | \(0.473273\pi\) | |||||||
\(318\) | −2.26168 | −0.126829 | ||||||||
\(319\) | 8.74117 | 0.489412 | ||||||||
\(320\) | −12.6206 | −0.705514 | ||||||||
\(321\) | −6.36485 | −0.355251 | ||||||||
\(322\) | −12.7318 | −0.709518 | ||||||||
\(323\) | −5.72719 | −0.318670 | ||||||||
\(324\) | 7.66345 | 0.425747 | ||||||||
\(325\) | 24.2766 | 1.34662 | ||||||||
\(326\) | −40.4530 | −2.24049 | ||||||||
\(327\) | 2.53564 | 0.140221 | ||||||||
\(328\) | −6.49296 | −0.358514 | ||||||||
\(329\) | 9.31410 | 0.513503 | ||||||||
\(330\) | 4.99266 | 0.274837 | ||||||||
\(331\) | 27.5579 | 1.51472 | 0.757359 | − | 0.652999i | \(-0.226490\pi\) | ||||
0.757359 | + | 0.652999i | \(0.226490\pi\) | |||||||
\(332\) | −11.2402 | −0.616889 | ||||||||
\(333\) | −4.01638 | −0.220096 | ||||||||
\(334\) | −2.51856 | −0.137809 | ||||||||
\(335\) | 47.7630 | 2.60957 | ||||||||
\(336\) | 3.91565 | 0.213616 | ||||||||
\(337\) | −0.282699 | −0.0153996 | −0.00769979 | − | 0.999970i | \(-0.502451\pi\) | ||||
−0.00769979 | + | 0.999970i | \(0.502451\pi\) | |||||||
\(338\) | 16.3617 | 0.889960 | ||||||||
\(339\) | 10.6601 | 0.578975 | ||||||||
\(340\) | −5.91719 | −0.320905 | ||||||||
\(341\) | −2.93216 | −0.158785 | ||||||||
\(342\) | 27.3082 | 1.47666 | ||||||||
\(343\) | 15.4855 | 0.836137 | ||||||||
\(344\) | −1.03795 | −0.0559626 | ||||||||
\(345\) | −14.8592 | −0.799990 | ||||||||
\(346\) | 42.1708 | 2.26712 | ||||||||
\(347\) | −5.85346 | −0.314230 | −0.157115 | − | 0.987580i | \(-0.550219\pi\) | ||||
−0.157115 | + | 0.987580i | \(0.550219\pi\) | |||||||
\(348\) | −8.24996 | −0.442244 | ||||||||
\(349\) | 12.6721 | 0.678321 | 0.339160 | − | 0.940729i | \(-0.389857\pi\) | ||||
0.339160 | + | 0.940729i | \(0.389857\pi\) | |||||||
\(350\) | 27.3893 | 1.46402 | ||||||||
\(351\) | −7.46164 | −0.398273 | ||||||||
\(352\) | −6.83850 | −0.364494 | ||||||||
\(353\) | 2.31261 | 0.123088 | 0.0615438 | − | 0.998104i | \(-0.480398\pi\) | ||||
0.0615438 | + | 0.998104i | \(0.480398\pi\) | |||||||
\(354\) | 10.4162 | 0.553613 | ||||||||
\(355\) | −32.7010 | −1.73559 | ||||||||
\(356\) | 2.96572 | 0.157183 | ||||||||
\(357\) | 0.814734 | 0.0431203 | ||||||||
\(358\) | −10.0944 | −0.533505 | ||||||||
\(359\) | 8.35980 | 0.441214 | 0.220607 | − | 0.975363i | \(-0.429196\pi\) | ||||
0.220607 | + | 0.975363i | \(0.429196\pi\) | |||||||
\(360\) | −10.9611 | −0.577699 | ||||||||
\(361\) | 13.8008 | 0.726356 | ||||||||
\(362\) | −1.02659 | −0.0539564 | ||||||||
\(363\) | 0.655235 | 0.0343909 | ||||||||
\(364\) | −3.66129 | −0.191904 | ||||||||
\(365\) | −49.6606 | −2.59936 | ||||||||
\(366\) | −8.33769 | −0.435818 | ||||||||
\(367\) | −29.1041 | −1.51922 | −0.759611 | − | 0.650377i | \(-0.774611\pi\) | ||||
−0.759611 | + | 0.650377i | \(0.774611\pi\) | |||||||
\(368\) | 26.5311 | 1.38303 | ||||||||
\(369\) | 16.0810 | 0.837142 | ||||||||
\(370\) | −11.9049 | −0.618904 | ||||||||
\(371\) | −2.31392 | −0.120133 | ||||||||
\(372\) | 2.76739 | 0.143482 | ||||||||
\(373\) | −2.83225 | −0.146648 | −0.0733242 | − | 0.997308i | \(-0.523361\pi\) | ||||
−0.0733242 | + | 0.997308i | \(0.523361\pi\) | |||||||
\(374\) | −1.85483 | −0.0959112 | ||||||||
\(375\) | 18.5072 | 0.955708 | ||||||||
\(376\) | −7.77496 | −0.400963 | ||||||||
\(377\) | −17.8690 | −0.920298 | ||||||||
\(378\) | −8.41837 | −0.432994 | ||||||||
\(379\) | 17.6568 | 0.906969 | 0.453484 | − | 0.891264i | \(-0.350181\pi\) | ||||
0.453484 | + | 0.891264i | \(0.350181\pi\) | |||||||
\(380\) | 33.8889 | 1.73846 | ||||||||
\(381\) | −7.04022 | −0.360681 | ||||||||
\(382\) | −1.47069 | −0.0752469 | ||||||||
\(383\) | 22.0366 | 1.12602 | 0.563010 | − | 0.826450i | \(-0.309643\pi\) | ||||
0.563010 | + | 0.826450i | \(0.309643\pi\) | |||||||
\(384\) | −5.22784 | −0.266782 | ||||||||
\(385\) | 5.10798 | 0.260327 | ||||||||
\(386\) | −6.11205 | −0.311095 | ||||||||
\(387\) | 2.57067 | 0.130674 | ||||||||
\(388\) | −9.15229 | −0.464637 | ||||||||
\(389\) | 6.60282 | 0.334777 | 0.167388 | − | 0.985891i | \(-0.446467\pi\) | ||||
0.167388 | + | 0.985891i | \(0.446467\pi\) | |||||||
\(390\) | −10.2062 | −0.516809 | ||||||||
\(391\) | 5.52036 | 0.279176 | ||||||||
\(392\) | −5.66088 | −0.285917 | ||||||||
\(393\) | −9.53988 | −0.481223 | ||||||||
\(394\) | −4.87479 | −0.245588 | ||||||||
\(395\) | 25.8943 | 1.30289 | ||||||||
\(396\) | 3.70281 | 0.186073 | ||||||||
\(397\) | 2.00210 | 0.100482 | 0.0502412 | − | 0.998737i | \(-0.484001\pi\) | ||||
0.0502412 | + | 0.998737i | \(0.484001\pi\) | |||||||
\(398\) | −31.4237 | −1.57513 | ||||||||
\(399\) | −4.66614 | −0.233599 | ||||||||
\(400\) | −57.0749 | −2.85374 | ||||||||
\(401\) | −9.69953 | −0.484371 | −0.242186 | − | 0.970230i | \(-0.577864\pi\) | ||||
−0.242186 | + | 0.970230i | \(0.577864\pi\) | |||||||
\(402\) | −14.1307 | −0.704774 | ||||||||
\(403\) | 5.99401 | 0.298583 | ||||||||
\(404\) | 11.6378 | 0.579004 | ||||||||
\(405\) | 21.8559 | 1.08603 | ||||||||
\(406\) | −20.1601 | −1.00053 | ||||||||
\(407\) | −1.56239 | −0.0774447 | ||||||||
\(408\) | −0.680101 | −0.0336700 | ||||||||
\(409\) | 27.9924 | 1.38413 | 0.692067 | − | 0.721833i | \(-0.256700\pi\) | ||||
0.692067 | + | 0.721833i | \(0.256700\pi\) | |||||||
\(410\) | 47.6652 | 2.35402 | ||||||||
\(411\) | −1.69903 | −0.0838071 | ||||||||
\(412\) | −5.07256 | −0.249907 | ||||||||
\(413\) | 10.6568 | 0.524385 | ||||||||
\(414\) | −26.3219 | −1.29365 | ||||||||
\(415\) | −32.0568 | −1.57361 | ||||||||
\(416\) | 13.9795 | 0.685400 | ||||||||
\(417\) | −13.1511 | −0.644013 | ||||||||
\(418\) | 10.6230 | 0.519588 | ||||||||
\(419\) | 5.97522 | 0.291908 | 0.145954 | − | 0.989291i | \(-0.453375\pi\) | ||||
0.145954 | + | 0.989291i | \(0.453375\pi\) | |||||||
\(420\) | −4.82094 | −0.235238 | ||||||||
\(421\) | −35.5002 | −1.73017 | −0.865087 | − | 0.501622i | \(-0.832737\pi\) | ||||
−0.865087 | + | 0.501622i | \(0.832737\pi\) | |||||||
\(422\) | 16.9340 | 0.824334 | ||||||||
\(423\) | 19.2561 | 0.936262 | ||||||||
\(424\) | 1.93155 | 0.0938044 | ||||||||
\(425\) | −11.8757 | −0.576054 | ||||||||
\(426\) | 9.67459 | 0.468736 | ||||||||
\(427\) | −8.53028 | −0.412809 | ||||||||
\(428\) | −13.9919 | −0.676324 | ||||||||
\(429\) | −1.33945 | −0.0646693 | ||||||||
\(430\) | 7.61965 | 0.367452 | ||||||||
\(431\) | 3.16422 | 0.152415 | 0.0762074 | − | 0.997092i | \(-0.475719\pi\) | ||||
0.0762074 | + | 0.997092i | \(0.475719\pi\) | |||||||
\(432\) | 17.5425 | 0.844014 | ||||||||
\(433\) | 34.2592 | 1.64639 | 0.823196 | − | 0.567758i | \(-0.192189\pi\) | ||||
0.823196 | + | 0.567758i | \(0.192189\pi\) | |||||||
\(434\) | 6.76257 | 0.324614 | ||||||||
\(435\) | −23.5286 | −1.12811 | ||||||||
\(436\) | 5.57412 | 0.266952 | ||||||||
\(437\) | −31.6162 | −1.51241 | ||||||||
\(438\) | 14.6921 | 0.702016 | ||||||||
\(439\) | −10.9894 | −0.524497 | −0.262249 | − | 0.965000i | \(-0.584464\pi\) | ||||
−0.262249 | + | 0.965000i | \(0.584464\pi\) | |||||||
\(440\) | −4.26390 | −0.203273 | ||||||||
\(441\) | 14.0202 | 0.667627 | ||||||||
\(442\) | 3.79171 | 0.180353 | ||||||||
\(443\) | −25.4110 | −1.20731 | −0.603657 | − | 0.797245i | \(-0.706290\pi\) | ||||
−0.603657 | + | 0.797245i | \(0.706290\pi\) | |||||||
\(444\) | 1.47459 | 0.0699809 | ||||||||
\(445\) | 8.45814 | 0.400954 | ||||||||
\(446\) | 52.9090 | 2.50531 | ||||||||
\(447\) | −7.78053 | −0.368007 | ||||||||
\(448\) | 3.82005 | 0.180481 | ||||||||
\(449\) | 16.7522 | 0.790584 | 0.395292 | − | 0.918556i | \(-0.370643\pi\) | ||||
0.395292 | + | 0.918556i | \(0.370643\pi\) | |||||||
\(450\) | 56.6250 | 2.66933 | ||||||||
\(451\) | 6.25556 | 0.294563 | ||||||||
\(452\) | 23.4341 | 1.10225 | ||||||||
\(453\) | −1.59431 | −0.0749072 | ||||||||
\(454\) | −6.83282 | −0.320680 | ||||||||
\(455\) | −10.4419 | −0.489524 | ||||||||
\(456\) | 3.89507 | 0.182404 | ||||||||
\(457\) | 0.243385 | 0.0113851 | 0.00569254 | − | 0.999984i | \(-0.498188\pi\) | ||||
0.00569254 | + | 0.999984i | \(0.498188\pi\) | |||||||
\(458\) | −17.2874 | −0.807788 | ||||||||
\(459\) | 3.65009 | 0.170372 | ||||||||
\(460\) | −32.6650 | −1.52301 | ||||||||
\(461\) | 29.2917 | 1.36425 | 0.682125 | − | 0.731236i | \(-0.261056\pi\) | ||||
0.682125 | + | 0.731236i | \(0.261056\pi\) | |||||||
\(462\) | −1.51120 | −0.0703072 | ||||||||
\(463\) | −18.0454 | −0.838641 | −0.419321 | − | 0.907838i | \(-0.637732\pi\) | ||||
−0.419321 | + | 0.907838i | \(0.637732\pi\) | |||||||
\(464\) | 42.0104 | 1.95028 | ||||||||
\(465\) | 7.89250 | 0.366006 | ||||||||
\(466\) | 39.7595 | 1.84182 | ||||||||
\(467\) | 17.1839 | 0.795176 | 0.397588 | − | 0.917564i | \(-0.369847\pi\) | ||||
0.397588 | + | 0.917564i | \(0.369847\pi\) | |||||||
\(468\) | −7.56939 | −0.349895 | ||||||||
\(469\) | −14.4571 | −0.667565 | ||||||||
\(470\) | 57.0764 | 2.63274 | ||||||||
\(471\) | 2.47037 | 0.113829 | ||||||||
\(472\) | −8.89575 | −0.409460 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −7.66084 | −0.351874 | ||||||||
\(475\) | 68.0142 | 3.12070 | ||||||||
\(476\) | 1.79104 | 0.0820920 | ||||||||
\(477\) | −4.78382 | −0.219036 | ||||||||
\(478\) | 47.5868 | 2.17657 | ||||||||
\(479\) | −22.8204 | −1.04269 | −0.521345 | − | 0.853346i | \(-0.674570\pi\) | ||||
−0.521345 | + | 0.853346i | \(0.674570\pi\) | |||||||
\(480\) | 18.4072 | 0.840171 | ||||||||
\(481\) | 3.19388 | 0.145628 | ||||||||
\(482\) | 22.2747 | 1.01458 | ||||||||
\(483\) | 4.49762 | 0.204649 | ||||||||
\(484\) | 1.44041 | 0.0654731 | ||||||||
\(485\) | −26.1021 | −1.18523 | ||||||||
\(486\) | −26.7770 | −1.21463 | ||||||||
\(487\) | −39.4780 | −1.78892 | −0.894459 | − | 0.447149i | \(-0.852439\pi\) | ||||
−0.894459 | + | 0.447149i | \(0.852439\pi\) | |||||||
\(488\) | 7.12067 | 0.322337 | ||||||||
\(489\) | 14.2904 | 0.646232 | ||||||||
\(490\) | 41.5568 | 1.87735 | ||||||||
\(491\) | −15.8012 | −0.713099 | −0.356549 | − | 0.934277i | \(-0.616047\pi\) | ||||
−0.356549 | + | 0.934277i | \(0.616047\pi\) | |||||||
\(492\) | −5.90403 | −0.266174 | ||||||||
\(493\) | 8.74117 | 0.393682 | ||||||||
\(494\) | −21.7158 | −0.977042 | ||||||||
\(495\) | 10.5603 | 0.474650 | ||||||||
\(496\) | −14.0921 | −0.632753 | ||||||||
\(497\) | 9.89806 | 0.443989 | ||||||||
\(498\) | 9.48402 | 0.424989 | ||||||||
\(499\) | 18.2453 | 0.816772 | 0.408386 | − | 0.912809i | \(-0.366092\pi\) | ||||
0.408386 | + | 0.912809i | \(0.366092\pi\) | |||||||
\(500\) | 40.6846 | 1.81947 | ||||||||
\(501\) | 0.889701 | 0.0397489 | ||||||||
\(502\) | −4.87058 | −0.217385 | ||||||||
\(503\) | 29.5953 | 1.31959 | 0.659795 | − | 0.751446i | \(-0.270643\pi\) | ||||
0.659795 | + | 0.751446i | \(0.270643\pi\) | |||||||
\(504\) | 3.31774 | 0.147784 | ||||||||
\(505\) | 33.1908 | 1.47697 | ||||||||
\(506\) | −10.2393 | −0.455194 | ||||||||
\(507\) | −5.77991 | −0.256695 | ||||||||
\(508\) | −15.4766 | −0.686661 | ||||||||
\(509\) | −34.0495 | −1.50922 | −0.754608 | − | 0.656176i | \(-0.772173\pi\) | ||||
−0.754608 | + | 0.656176i | \(0.772173\pi\) | |||||||
\(510\) | 4.99266 | 0.221079 | ||||||||
\(511\) | 15.0315 | 0.664952 | ||||||||
\(512\) | −22.8893 | −1.01157 | ||||||||
\(513\) | −20.9048 | −0.922970 | ||||||||
\(514\) | 25.3521 | 1.11823 | ||||||||
\(515\) | −14.4668 | −0.637483 | ||||||||
\(516\) | −0.943805 | −0.0415487 | ||||||||
\(517\) | 7.49069 | 0.329440 | ||||||||
\(518\) | 3.60340 | 0.158324 | ||||||||
\(519\) | −14.8972 | −0.653913 | ||||||||
\(520\) | 8.71640 | 0.382239 | ||||||||
\(521\) | −3.89218 | −0.170520 | −0.0852599 | − | 0.996359i | \(-0.527172\pi\) | ||||
−0.0852599 | + | 0.996359i | \(0.527172\pi\) | |||||||
\(522\) | −41.6793 | −1.82425 | ||||||||
\(523\) | 37.8610 | 1.65555 | 0.827774 | − | 0.561062i | \(-0.189607\pi\) | ||||
0.827774 | + | 0.561062i | \(0.189607\pi\) | |||||||
\(524\) | −20.9716 | −0.916148 | ||||||||
\(525\) | −9.67550 | −0.422274 | ||||||||
\(526\) | 10.5477 | 0.459903 | ||||||||
\(527\) | −2.93216 | −0.127727 | ||||||||
\(528\) | 3.14909 | 0.137046 | ||||||||
\(529\) | 7.47433 | 0.324971 | ||||||||
\(530\) | −14.1796 | −0.615923 | ||||||||
\(531\) | 22.0319 | 0.956103 | ||||||||
\(532\) | −10.2576 | −0.444724 | ||||||||
\(533\) | −12.7878 | −0.553901 | ||||||||
\(534\) | −2.50234 | −0.108287 | ||||||||
\(535\) | −39.9044 | −1.72522 | ||||||||
\(536\) | 12.0681 | 0.521261 | ||||||||
\(537\) | 3.56593 | 0.153881 | ||||||||
\(538\) | −47.8944 | −2.06487 | ||||||||
\(539\) | 5.45390 | 0.234916 | ||||||||
\(540\) | −21.5983 | −0.929443 | ||||||||
\(541\) | −34.0047 | −1.46198 | −0.730988 | − | 0.682390i | \(-0.760941\pi\) | ||||
−0.730988 | + | 0.682390i | \(0.760941\pi\) | |||||||
\(542\) | 8.10917 | 0.348319 | ||||||||
\(543\) | 0.362651 | 0.0155629 | ||||||||
\(544\) | −6.83850 | −0.293198 | ||||||||
\(545\) | 15.8972 | 0.680962 | ||||||||
\(546\) | 3.08923 | 0.132207 | ||||||||
\(547\) | −13.2042 | −0.564570 | −0.282285 | − | 0.959331i | \(-0.591092\pi\) | ||||
−0.282285 | + | 0.959331i | \(0.591092\pi\) | |||||||
\(548\) | −3.73500 | −0.159551 | ||||||||
\(549\) | −17.6356 | −0.752668 | ||||||||
\(550\) | 22.0274 | 0.939250 | ||||||||
\(551\) | −50.0624 | −2.13273 | ||||||||
\(552\) | −3.75440 | −0.159798 | ||||||||
\(553\) | −7.83779 | −0.333297 | ||||||||
\(554\) | 28.5673 | 1.21371 | ||||||||
\(555\) | 4.20548 | 0.178513 | ||||||||
\(556\) | −28.9102 | −1.22607 | ||||||||
\(557\) | −10.2731 | −0.435284 | −0.217642 | − | 0.976029i | \(-0.569836\pi\) | ||||
−0.217642 | + | 0.976029i | \(0.569836\pi\) | |||||||
\(558\) | 13.9810 | 0.591863 | ||||||||
\(559\) | −2.04423 | −0.0864617 | ||||||||
\(560\) | 24.5492 | 1.03739 | ||||||||
\(561\) | 0.655235 | 0.0276640 | ||||||||
\(562\) | 45.0676 | 1.90106 | ||||||||
\(563\) | −18.8701 | −0.795280 | −0.397640 | − | 0.917542i | \(-0.630171\pi\) | ||||
−0.397640 | + | 0.917542i | \(0.630171\pi\) | |||||||
\(564\) | −7.06975 | −0.297690 | ||||||||
\(565\) | 66.8333 | 2.81170 | ||||||||
\(566\) | 23.2165 | 0.975864 | ||||||||
\(567\) | −6.61543 | −0.277822 | ||||||||
\(568\) | −8.26243 | −0.346684 | ||||||||
\(569\) | 21.0006 | 0.880391 | 0.440195 | − | 0.897902i | \(-0.354909\pi\) | ||||
0.440195 | + | 0.897902i | \(0.354909\pi\) | |||||||
\(570\) | −28.5939 | −1.19767 | ||||||||
\(571\) | −10.4340 | −0.436649 | −0.218324 | − | 0.975876i | \(-0.570059\pi\) | ||||
−0.218324 | + | 0.975876i | \(0.570059\pi\) | |||||||
\(572\) | −2.94453 | −0.123117 | ||||||||
\(573\) | 0.519532 | 0.0217038 | ||||||||
\(574\) | −14.4275 | −0.602191 | ||||||||
\(575\) | −65.5578 | −2.73395 | ||||||||
\(576\) | 7.89762 | 0.329068 | ||||||||
\(577\) | −32.8945 | −1.36941 | −0.684707 | − | 0.728818i | \(-0.740070\pi\) | ||||
−0.684707 | + | 0.728818i | \(0.740070\pi\) | |||||||
\(578\) | −1.85483 | −0.0771509 | ||||||||
\(579\) | 2.15913 | 0.0897304 | ||||||||
\(580\) | −51.7232 | −2.14769 | ||||||||
\(581\) | 9.70308 | 0.402552 | ||||||||
\(582\) | 7.72229 | 0.320099 | ||||||||
\(583\) | −1.86093 | −0.0770717 | ||||||||
\(584\) | −12.5475 | −0.519221 | ||||||||
\(585\) | −21.5877 | −0.892541 | ||||||||
\(586\) | −53.2377 | −2.19923 | ||||||||
\(587\) | 2.85287 | 0.117751 | 0.0588753 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588753 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(588\) | −5.14742 | −0.212276 | ||||||||
\(589\) | 16.7931 | 0.691946 | ||||||||
\(590\) | 65.3042 | 2.68853 | ||||||||
\(591\) | 1.72206 | 0.0708360 | ||||||||
\(592\) | −7.50890 | −0.308614 | ||||||||
\(593\) | 9.04829 | 0.371569 | 0.185784 | − | 0.982591i | \(-0.440517\pi\) | ||||
0.185784 | + | 0.982591i | \(0.440517\pi\) | |||||||
\(594\) | −6.77032 | −0.277790 | ||||||||
\(595\) | 5.10798 | 0.209407 | ||||||||
\(596\) | −17.1040 | −0.700607 | ||||||||
\(597\) | 11.1007 | 0.454320 | ||||||||
\(598\) | 20.9316 | 0.855956 | ||||||||
\(599\) | −4.43690 | −0.181287 | −0.0906434 | − | 0.995883i | \(-0.528892\pi\) | ||||
−0.0906434 | + | 0.995883i | \(0.528892\pi\) | |||||||
\(600\) | 8.07665 | 0.329728 | ||||||||
\(601\) | 5.40516 | 0.220481 | 0.110240 | − | 0.993905i | \(-0.464838\pi\) | ||||
0.110240 | + | 0.993905i | \(0.464838\pi\) | |||||||
\(602\) | −2.30634 | −0.0939996 | ||||||||
\(603\) | −29.8887 | −1.21716 | ||||||||
\(604\) | −3.50478 | −0.142608 | ||||||||
\(605\) | 4.10800 | 0.167014 | ||||||||
\(606\) | −9.81949 | −0.398890 | ||||||||
\(607\) | 30.9503 | 1.25623 | 0.628117 | − | 0.778119i | \(-0.283826\pi\) | ||||
0.628117 | + | 0.778119i | \(0.283826\pi\) | |||||||
\(608\) | 39.1654 | 1.58837 | ||||||||
\(609\) | 7.12173 | 0.288587 | ||||||||
\(610\) | −52.2732 | −2.11648 | ||||||||
\(611\) | −15.3127 | −0.619485 | ||||||||
\(612\) | 3.70281 | 0.149677 | ||||||||
\(613\) | 41.1320 | 1.66130 | 0.830652 | − | 0.556792i | \(-0.187968\pi\) | ||||
0.830652 | + | 0.556792i | \(0.187968\pi\) | |||||||
\(614\) | 0.342770 | 0.0138331 | ||||||||
\(615\) | −16.8381 | −0.678978 | ||||||||
\(616\) | 1.29061 | 0.0520003 | ||||||||
\(617\) | 9.43884 | 0.379993 | 0.189997 | − | 0.981785i | \(-0.439152\pi\) | ||||
0.189997 | + | 0.981785i | \(0.439152\pi\) | |||||||
\(618\) | 4.28000 | 0.172167 | ||||||||
\(619\) | −18.4197 | −0.740349 | −0.370175 | − | 0.928962i | \(-0.620702\pi\) | ||||
−0.370175 | + | 0.928962i | \(0.620702\pi\) | |||||||
\(620\) | 17.3502 | 0.696799 | ||||||||
\(621\) | 20.1498 | 0.808585 | ||||||||
\(622\) | −27.5235 | −1.10359 | ||||||||
\(623\) | −2.56014 | −0.102570 | ||||||||
\(624\) | −6.43746 | −0.257704 | ||||||||
\(625\) | 56.6528 | 2.26611 | ||||||||
\(626\) | −26.5855 | −1.06257 | ||||||||
\(627\) | −3.75266 | −0.149867 | ||||||||
\(628\) | 5.43063 | 0.216706 | ||||||||
\(629\) | −1.56239 | −0.0622965 | ||||||||
\(630\) | −24.3557 | −0.970353 | ||||||||
\(631\) | 4.51522 | 0.179748 | 0.0898739 | − | 0.995953i | \(-0.471354\pi\) | ||||
0.0898739 | + | 0.995953i | \(0.471354\pi\) | |||||||
\(632\) | 6.54261 | 0.260251 | ||||||||
\(633\) | −5.98207 | −0.237766 | ||||||||
\(634\) | −5.53928 | −0.219993 | ||||||||
\(635\) | −44.1387 | −1.75159 | ||||||||
\(636\) | 1.75635 | 0.0696439 | ||||||||
\(637\) | −11.1490 | −0.441740 | ||||||||
\(638\) | −16.2134 | −0.641895 | ||||||||
\(639\) | 20.4633 | 0.809518 | ||||||||
\(640\) | −32.7760 | −1.29558 | ||||||||
\(641\) | −41.7113 | −1.64750 | −0.823748 | − | 0.566956i | \(-0.808121\pi\) | ||||
−0.823748 | + | 0.566956i | \(0.808121\pi\) | |||||||
\(642\) | 11.8057 | 0.465935 | ||||||||
\(643\) | −33.9006 | −1.33691 | −0.668454 | − | 0.743753i | \(-0.733044\pi\) | ||||
−0.668454 | + | 0.743753i | \(0.733044\pi\) | |||||||
\(644\) | 9.88716 | 0.389609 | ||||||||
\(645\) | −2.69170 | −0.105986 | ||||||||
\(646\) | 10.6230 | 0.417956 | ||||||||
\(647\) | −36.7380 | −1.44432 | −0.722161 | − | 0.691725i | \(-0.756851\pi\) | ||||
−0.722161 | + | 0.691725i | \(0.756851\pi\) | |||||||
\(648\) | 5.52224 | 0.216934 | ||||||||
\(649\) | 8.57050 | 0.336421 | ||||||||
\(650\) | −45.0290 | −1.76618 | ||||||||
\(651\) | −2.38893 | −0.0936296 | ||||||||
\(652\) | 31.4146 | 1.23029 | ||||||||
\(653\) | −41.3608 | −1.61857 | −0.809287 | − | 0.587413i | \(-0.800146\pi\) | ||||
−0.809287 | + | 0.587413i | \(0.800146\pi\) | |||||||
\(654\) | −4.70319 | −0.183909 | ||||||||
\(655\) | −59.8103 | −2.33698 | ||||||||
\(656\) | 30.0645 | 1.17382 | ||||||||
\(657\) | 31.0762 | 1.21240 | ||||||||
\(658\) | −17.2761 | −0.673492 | ||||||||
\(659\) | 24.9762 | 0.972936 | 0.486468 | − | 0.873698i | \(-0.338285\pi\) | ||||
0.486468 | + | 0.873698i | \(0.338285\pi\) | |||||||
\(660\) | −3.87715 | −0.150918 | ||||||||
\(661\) | 8.75996 | 0.340723 | 0.170361 | − | 0.985382i | \(-0.445506\pi\) | ||||
0.170361 | + | 0.985382i | \(0.445506\pi\) | |||||||
\(662\) | −51.1153 | −1.98665 | ||||||||
\(663\) | −1.33945 | −0.0520200 | ||||||||
\(664\) | −8.09967 | −0.314328 | ||||||||
\(665\) | −29.2544 | −1.13444 | ||||||||
\(666\) | 7.44972 | 0.288671 | ||||||||
\(667\) | 48.2544 | 1.86842 | ||||||||
\(668\) | 1.95584 | 0.0756736 | ||||||||
\(669\) | −18.6905 | −0.722617 | ||||||||
\(670\) | −88.5923 | −3.42262 | ||||||||
\(671\) | −6.86031 | −0.264839 | ||||||||
\(672\) | −5.57156 | −0.214928 | ||||||||
\(673\) | 13.3231 | 0.513570 | 0.256785 | − | 0.966469i | \(-0.417337\pi\) | ||||
0.256785 | + | 0.966469i | \(0.417337\pi\) | |||||||
\(674\) | 0.524359 | 0.0201976 | ||||||||
\(675\) | −43.3473 | −1.66844 | ||||||||
\(676\) | −12.7060 | −0.488693 | ||||||||
\(677\) | 4.86560 | 0.187000 | 0.0935001 | − | 0.995619i | \(-0.470194\pi\) | ||||
0.0935001 | + | 0.995619i | \(0.470194\pi\) | |||||||
\(678\) | −19.7726 | −0.759364 | ||||||||
\(679\) | 7.90066 | 0.303200 | ||||||||
\(680\) | −4.26390 | −0.163513 | ||||||||
\(681\) | 2.41375 | 0.0924951 | ||||||||
\(682\) | 5.43867 | 0.208257 | ||||||||
\(683\) | 15.1521 | 0.579780 | 0.289890 | − | 0.957060i | \(-0.406381\pi\) | ||||
0.289890 | + | 0.957060i | \(0.406381\pi\) | |||||||
\(684\) | −21.2067 | −0.810859 | ||||||||
\(685\) | −10.6521 | −0.406996 | ||||||||
\(686\) | −28.7230 | −1.09665 | ||||||||
\(687\) | 6.10692 | 0.232993 | ||||||||
\(688\) | 4.80604 | 0.183229 | ||||||||
\(689\) | 3.80416 | 0.144927 | ||||||||
\(690\) | 27.5613 | 1.04924 | ||||||||
\(691\) | 0.533417 | 0.0202921 | 0.0101461 | − | 0.999949i | \(-0.496770\pi\) | ||||
0.0101461 | + | 0.999949i | \(0.496770\pi\) | |||||||
\(692\) | −32.7486 | −1.24491 | ||||||||
\(693\) | −3.19643 | −0.121422 | ||||||||
\(694\) | 10.8572 | 0.412134 | ||||||||
\(695\) | −82.4511 | −3.12755 | ||||||||
\(696\) | −5.94488 | −0.225340 | ||||||||
\(697\) | 6.25556 | 0.236946 | ||||||||
\(698\) | −23.5046 | −0.889662 | ||||||||
\(699\) | −14.0454 | −0.531244 | ||||||||
\(700\) | −21.2697 | −0.803920 | ||||||||
\(701\) | −15.2661 | −0.576594 | −0.288297 | − | 0.957541i | \(-0.593089\pi\) | ||||
−0.288297 | + | 0.957541i | \(0.593089\pi\) | |||||||
\(702\) | 13.8401 | 0.522361 | ||||||||
\(703\) | 8.94810 | 0.337484 | ||||||||
\(704\) | 3.07221 | 0.115788 | ||||||||
\(705\) | −20.1627 | −0.759371 | ||||||||
\(706\) | −4.28950 | −0.161437 | ||||||||
\(707\) | −10.0463 | −0.377830 | ||||||||
\(708\) | −8.08888 | −0.303999 | ||||||||
\(709\) | 23.1022 | 0.867621 | 0.433811 | − | 0.901004i | \(-0.357169\pi\) | ||||
0.433811 | + | 0.901004i | \(0.357169\pi\) | |||||||
\(710\) | 60.6549 | 2.27634 | ||||||||
\(711\) | −16.2039 | −0.607695 | ||||||||
\(712\) | 2.13708 | 0.0800905 | ||||||||
\(713\) | −16.1866 | −0.606192 | ||||||||
\(714\) | −1.51120 | −0.0565551 | ||||||||
\(715\) | −8.39770 | −0.314056 | ||||||||
\(716\) | 7.83900 | 0.292957 | ||||||||
\(717\) | −16.8104 | −0.627796 | ||||||||
\(718\) | −15.5060 | −0.578680 | ||||||||
\(719\) | −16.1498 | −0.602285 | −0.301143 | − | 0.953579i | \(-0.597368\pi\) | ||||
−0.301143 | + | 0.953579i | \(0.597368\pi\) | |||||||
\(720\) | 50.7532 | 1.89146 | ||||||||
\(721\) | 4.37886 | 0.163077 | ||||||||
\(722\) | −25.5981 | −0.952663 | ||||||||
\(723\) | −7.86872 | −0.292641 | ||||||||
\(724\) | 0.797219 | 0.0296284 | ||||||||
\(725\) | −103.807 | −3.85530 | ||||||||
\(726\) | −1.21535 | −0.0451059 | ||||||||
\(727\) | 8.82634 | 0.327351 | 0.163675 | − | 0.986514i | \(-0.447665\pi\) | ||||
0.163675 | + | 0.986514i | \(0.447665\pi\) | |||||||
\(728\) | −2.63831 | −0.0977823 | ||||||||
\(729\) | −6.50180 | −0.240807 | ||||||||
\(730\) | 92.1122 | 3.40923 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 6.47480 | 0.239315 | ||||||||
\(733\) | 48.1676 | 1.77911 | 0.889555 | − | 0.456829i | \(-0.151015\pi\) | ||||
0.889555 | + | 0.456829i | \(0.151015\pi\) | |||||||
\(734\) | 53.9833 | 1.99256 | ||||||||
\(735\) | −14.6803 | −0.541490 | ||||||||
\(736\) | −37.7510 | −1.39152 | ||||||||
\(737\) | −11.6268 | −0.428279 | ||||||||
\(738\) | −29.8275 | −1.09797 | ||||||||
\(739\) | 30.3296 | 1.11569 | 0.557846 | − | 0.829944i | \(-0.311628\pi\) | ||||
0.557846 | + | 0.829944i | \(0.311628\pi\) | |||||||
\(740\) | 9.24495 | 0.339851 | ||||||||
\(741\) | 7.67130 | 0.281812 | ||||||||
\(742\) | 4.29194 | 0.157562 | ||||||||
\(743\) | 4.69039 | 0.172074 | 0.0860368 | − | 0.996292i | \(-0.472580\pi\) | ||||
0.0860368 | + | 0.996292i | \(0.472580\pi\) | |||||||
\(744\) | 1.99417 | 0.0731097 | ||||||||
\(745\) | −48.7801 | −1.78716 | ||||||||
\(746\) | 5.25336 | 0.192339 | ||||||||
\(747\) | 20.0602 | 0.733966 | ||||||||
\(748\) | 1.44041 | 0.0526665 | ||||||||
\(749\) | 12.0784 | 0.441336 | ||||||||
\(750\) | −34.3278 | −1.25347 | ||||||||
\(751\) | −41.7424 | −1.52320 | −0.761601 | − | 0.648046i | \(-0.775587\pi\) | ||||
−0.761601 | + | 0.648046i | \(0.775587\pi\) | |||||||
\(752\) | 36.0005 | 1.31280 | ||||||||
\(753\) | 1.72057 | 0.0627011 | ||||||||
\(754\) | 33.1440 | 1.20703 | ||||||||
\(755\) | −9.99554 | −0.363775 | ||||||||
\(756\) | 6.53745 | 0.237765 | ||||||||
\(757\) | 40.7576 | 1.48136 | 0.740680 | − | 0.671858i | \(-0.234503\pi\) | ||||
0.740680 | + | 0.671858i | \(0.234503\pi\) | |||||||
\(758\) | −32.7504 | −1.18955 | ||||||||
\(759\) | 3.61713 | 0.131293 | ||||||||
\(760\) | 24.4202 | 0.885813 | ||||||||
\(761\) | −24.3814 | −0.883824 | −0.441912 | − | 0.897059i | \(-0.645700\pi\) | ||||
−0.441912 | + | 0.897059i | \(0.645700\pi\) | |||||||
\(762\) | 13.0584 | 0.473057 | ||||||||
\(763\) | −4.81182 | −0.174200 | ||||||||
\(764\) | 1.14209 | 0.0413194 | ||||||||
\(765\) | 10.5603 | 0.381808 | ||||||||
\(766\) | −40.8743 | −1.47685 | ||||||||
\(767\) | −17.5201 | −0.632613 | ||||||||
\(768\) | 13.7228 | 0.495179 | ||||||||
\(769\) | −17.8909 | −0.645162 | −0.322581 | − | 0.946542i | \(-0.604551\pi\) | ||||
−0.322581 | + | 0.946542i | \(0.604551\pi\) | |||||||
\(770\) | −9.47446 | −0.341436 | ||||||||
\(771\) | −8.95583 | −0.322536 | ||||||||
\(772\) | 4.74643 | 0.170828 | ||||||||
\(773\) | 37.3850 | 1.34464 | 0.672322 | − | 0.740259i | \(-0.265297\pi\) | ||||
0.672322 | + | 0.740259i | \(0.265297\pi\) | |||||||
\(774\) | −4.76816 | −0.171388 | ||||||||
\(775\) | 34.8213 | 1.25082 | ||||||||
\(776\) | −6.59510 | −0.236750 | ||||||||
\(777\) | −1.27293 | −0.0456661 | ||||||||
\(778\) | −12.2471 | −0.439081 | ||||||||
\(779\) | −35.8268 | −1.28363 | ||||||||
\(780\) | 7.92579 | 0.283789 | ||||||||
\(781\) | 7.96033 | 0.284843 | ||||||||
\(782\) | −10.2393 | −0.366158 | ||||||||
\(783\) | 31.9061 | 1.14023 | ||||||||
\(784\) | 26.2117 | 0.936131 | ||||||||
\(785\) | 15.4880 | 0.552790 | ||||||||
\(786\) | 17.6949 | 0.631156 | ||||||||
\(787\) | −42.9548 | −1.53117 | −0.765586 | − | 0.643333i | \(-0.777551\pi\) | ||||
−0.765586 | + | 0.643333i | \(0.777551\pi\) | |||||||
\(788\) | 3.78562 | 0.134857 | ||||||||
\(789\) | −3.72607 | −0.132652 | ||||||||
\(790\) | −48.0297 | −1.70882 | ||||||||
\(791\) | −20.2294 | −0.719273 | ||||||||
\(792\) | 2.66823 | 0.0948113 | ||||||||
\(793\) | 14.0241 | 0.498009 | ||||||||
\(794\) | −3.71355 | −0.131789 | ||||||||
\(795\) | 5.00906 | 0.177653 | ||||||||
\(796\) | 24.4027 | 0.864929 | ||||||||
\(797\) | −38.1922 | −1.35284 | −0.676418 | − | 0.736518i | \(-0.736469\pi\) | ||||
−0.676418 | + | 0.736518i | \(0.736469\pi\) | |||||||
\(798\) | 8.65492 | 0.306381 | ||||||||
\(799\) | 7.49069 | 0.265001 | ||||||||
\(800\) | 81.2117 | 2.87127 | ||||||||
\(801\) | −5.29286 | −0.187014 | ||||||||
\(802\) | 17.9910 | 0.635285 | ||||||||
\(803\) | 12.0888 | 0.426603 | ||||||||
\(804\) | 10.9735 | 0.387004 | ||||||||
\(805\) | 28.1979 | 0.993845 | ||||||||
\(806\) | −11.1179 | −0.391611 | ||||||||
\(807\) | 16.9191 | 0.595580 | ||||||||
\(808\) | 8.38617 | 0.295025 | ||||||||
\(809\) | −22.2887 | −0.783629 | −0.391814 | − | 0.920044i | \(-0.628152\pi\) | ||||
−0.391814 | + | 0.920044i | \(0.628152\pi\) | |||||||
\(810\) | −40.5391 | −1.42440 | ||||||||
\(811\) | 11.7272 | 0.411799 | 0.205899 | − | 0.978573i | \(-0.433988\pi\) | ||||
0.205899 | + | 0.978573i | \(0.433988\pi\) | |||||||
\(812\) | 15.6558 | 0.549409 | ||||||||
\(813\) | −2.86463 | −0.100467 | ||||||||
\(814\) | 2.89797 | 0.101574 | ||||||||
\(815\) | 89.5935 | 3.13832 | ||||||||
\(816\) | 3.14909 | 0.110240 | ||||||||
\(817\) | −5.72719 | −0.200369 | ||||||||
\(818\) | −51.9212 | −1.81538 | ||||||||
\(819\) | 6.53424 | 0.228325 | ||||||||
\(820\) | −37.0154 | −1.29263 | ||||||||
\(821\) | −45.5258 | −1.58886 | −0.794430 | − | 0.607355i | \(-0.792230\pi\) | ||||
−0.794430 | + | 0.607355i | \(0.792230\pi\) | |||||||
\(822\) | 3.15142 | 0.109918 | ||||||||
\(823\) | −48.1450 | −1.67823 | −0.839115 | − | 0.543955i | \(-0.816926\pi\) | ||||
−0.839115 | + | 0.543955i | \(0.816926\pi\) | |||||||
\(824\) | −3.65527 | −0.127337 | ||||||||
\(825\) | −7.78134 | −0.270911 | ||||||||
\(826\) | −19.7665 | −0.687765 | ||||||||
\(827\) | −16.2434 | −0.564838 | −0.282419 | − | 0.959291i | \(-0.591137\pi\) | ||||
−0.282419 | + | 0.959291i | \(0.591137\pi\) | |||||||
\(828\) | 20.4408 | 0.710368 | ||||||||
\(829\) | 19.7099 | 0.684552 | 0.342276 | − | 0.939599i | \(-0.388802\pi\) | ||||
0.342276 | + | 0.939599i | \(0.388802\pi\) | |||||||
\(830\) | 59.4601 | 2.06389 | ||||||||
\(831\) | −10.0916 | −0.350075 | ||||||||
\(832\) | −6.28030 | −0.217730 | ||||||||
\(833\) | 5.45390 | 0.188966 | ||||||||
\(834\) | 24.3932 | 0.844666 | ||||||||
\(835\) | 5.57799 | 0.193034 | ||||||||
\(836\) | −8.24949 | −0.285315 | ||||||||
\(837\) | −10.7027 | −0.369938 | ||||||||
\(838\) | −11.0830 | −0.382857 | ||||||||
\(839\) | −21.7476 | −0.750811 | −0.375406 | − | 0.926861i | \(-0.622497\pi\) | ||||
−0.375406 | + | 0.926861i | \(0.622497\pi\) | |||||||
\(840\) | −3.47395 | −0.119863 | ||||||||
\(841\) | 47.4080 | 1.63476 | ||||||||
\(842\) | 65.8470 | 2.26924 | ||||||||
\(843\) | −15.9205 | −0.548331 | ||||||||
\(844\) | −13.1504 | −0.452656 | ||||||||
\(845\) | −36.2372 | −1.24660 | ||||||||
\(846\) | −35.7168 | −1.22797 | ||||||||
\(847\) | −1.24342 | −0.0427245 | ||||||||
\(848\) | −8.94369 | −0.307128 | ||||||||
\(849\) | −8.20143 | −0.281472 | ||||||||
\(850\) | 22.0274 | 0.755532 | ||||||||
\(851\) | −8.62494 | −0.295659 | ||||||||
\(852\) | −7.51300 | −0.257391 | ||||||||
\(853\) | 2.31018 | 0.0790989 | 0.0395494 | − | 0.999218i | \(-0.487408\pi\) | ||||
0.0395494 | + | 0.999218i | \(0.487408\pi\) | |||||||
\(854\) | 15.8222 | 0.541426 | ||||||||
\(855\) | −60.4809 | −2.06840 | ||||||||
\(856\) | −10.0825 | −0.344612 | ||||||||
\(857\) | 30.6874 | 1.04826 | 0.524131 | − | 0.851638i | \(-0.324390\pi\) | ||||
0.524131 | + | 0.851638i | \(0.324390\pi\) | |||||||
\(858\) | 2.48446 | 0.0848180 | ||||||||
\(859\) | −25.5723 | −0.872516 | −0.436258 | − | 0.899822i | \(-0.643697\pi\) | ||||
−0.436258 | + | 0.899822i | \(0.643697\pi\) | |||||||
\(860\) | −5.91719 | −0.201775 | ||||||||
\(861\) | 5.09662 | 0.173692 | ||||||||
\(862\) | −5.86909 | −0.199902 | ||||||||
\(863\) | 36.6473 | 1.24749 | 0.623745 | − | 0.781628i | \(-0.285610\pi\) | ||||
0.623745 | + | 0.781628i | \(0.285610\pi\) | |||||||
\(864\) | −24.9612 | −0.849197 | ||||||||
\(865\) | −93.3979 | −3.17562 | ||||||||
\(866\) | −63.5451 | −2.15935 | ||||||||
\(867\) | 0.655235 | 0.0222529 | ||||||||
\(868\) | −5.25161 | −0.178251 | ||||||||
\(869\) | −6.30339 | −0.213828 | ||||||||
\(870\) | 43.6417 | 1.47959 | ||||||||
\(871\) | 23.7679 | 0.805344 | ||||||||
\(872\) | 4.01668 | 0.136022 | ||||||||
\(873\) | 16.3339 | 0.552819 | ||||||||
\(874\) | 58.6427 | 1.98362 | ||||||||
\(875\) | −35.1207 | −1.18730 | ||||||||
\(876\) | −11.4094 | −0.385489 | ||||||||
\(877\) | −39.7705 | −1.34296 | −0.671478 | − | 0.741025i | \(-0.734340\pi\) | ||||
−0.671478 | + | 0.741025i | \(0.734340\pi\) | |||||||
\(878\) | 20.3836 | 0.687912 | ||||||||
\(879\) | 18.8066 | 0.634332 | ||||||||
\(880\) | 19.7432 | 0.665543 | ||||||||
\(881\) | −34.4179 | −1.15957 | −0.579783 | − | 0.814771i | \(-0.696863\pi\) | ||||
−0.579783 | + | 0.814771i | \(0.696863\pi\) | |||||||
\(882\) | −26.0051 | −0.875636 | ||||||||
\(883\) | −40.8671 | −1.37529 | −0.687643 | − | 0.726049i | \(-0.741355\pi\) | ||||
−0.687643 | + | 0.726049i | \(0.741355\pi\) | |||||||
\(884\) | −2.94453 | −0.0990351 | ||||||||
\(885\) | −23.0692 | −0.775464 | ||||||||
\(886\) | 47.1332 | 1.58347 | ||||||||
\(887\) | −5.93180 | −0.199170 | −0.0995852 | − | 0.995029i | \(-0.531752\pi\) | ||||
−0.0995852 | + | 0.995029i | \(0.531752\pi\) | |||||||
\(888\) | 1.06258 | 0.0356579 | ||||||||
\(889\) | 13.3601 | 0.448082 | ||||||||
\(890\) | −15.6884 | −0.525877 | ||||||||
\(891\) | −5.32033 | −0.178238 | ||||||||
\(892\) | −41.0875 | −1.37571 | ||||||||
\(893\) | −42.9006 | −1.43561 | ||||||||
\(894\) | 14.4316 | 0.482665 | ||||||||
\(895\) | 22.3566 | 0.747299 | ||||||||
\(896\) | 9.92075 | 0.331429 | ||||||||
\(897\) | −7.39425 | −0.246887 | ||||||||
\(898\) | −31.0725 | −1.03690 | ||||||||
\(899\) | −25.6305 | −0.854825 | ||||||||
\(900\) | −43.9733 | −1.46578 | ||||||||
\(901\) | −1.86093 | −0.0619965 | ||||||||
\(902\) | −11.6030 | −0.386338 | ||||||||
\(903\) | 0.814734 | 0.0271127 | ||||||||
\(904\) | 16.8865 | 0.561637 | ||||||||
\(905\) | 2.27364 | 0.0755785 | ||||||||
\(906\) | 2.95718 | 0.0982457 | ||||||||
\(907\) | −15.7301 | −0.522311 | −0.261155 | − | 0.965297i | \(-0.584103\pi\) | ||||
−0.261155 | + | 0.965297i | \(0.584103\pi\) | |||||||
\(908\) | 5.30616 | 0.176091 | ||||||||
\(909\) | −20.7698 | −0.688892 | ||||||||
\(910\) | 19.3680 | 0.642042 | ||||||||
\(911\) | 54.9890 | 1.82187 | 0.910934 | − | 0.412552i | \(-0.135363\pi\) | ||||
0.910934 | + | 0.412552i | \(0.135363\pi\) | |||||||
\(912\) | −18.0354 | −0.597213 | ||||||||
\(913\) | 7.80352 | 0.258259 | ||||||||
\(914\) | −0.451439 | −0.0149323 | ||||||||
\(915\) | 18.4659 | 0.610465 | ||||||||
\(916\) | 13.4249 | 0.443570 | ||||||||
\(917\) | 18.1036 | 0.597834 | ||||||||
\(918\) | −6.77032 | −0.223454 | ||||||||
\(919\) | −11.4712 | −0.378399 | −0.189199 | − | 0.981939i | \(-0.560589\pi\) | ||||
−0.189199 | + | 0.981939i | \(0.560589\pi\) | |||||||
\(920\) | −23.5382 | −0.776033 | ||||||||
\(921\) | −0.121086 | −0.00398993 | ||||||||
\(922\) | −54.3312 | −1.78930 | ||||||||
\(923\) | −16.2727 | −0.535624 | ||||||||
\(924\) | 1.17355 | 0.0386069 | ||||||||
\(925\) | 18.5544 | 0.610064 | ||||||||
\(926\) | 33.4712 | 1.09993 | ||||||||
\(927\) | 9.05291 | 0.297337 | ||||||||
\(928\) | −59.7765 | −1.96226 | ||||||||
\(929\) | 49.9260 | 1.63802 | 0.819009 | − | 0.573781i | \(-0.194524\pi\) | ||||
0.819009 | + | 0.573781i | \(0.194524\pi\) | |||||||
\(930\) | −14.6393 | −0.480041 | ||||||||
\(931\) | −31.2355 | −1.02370 | ||||||||
\(932\) | −30.8760 | −1.01138 | ||||||||
\(933\) | 9.72288 | 0.318313 | ||||||||
\(934\) | −31.8733 | −1.04293 | ||||||||
\(935\) | 4.10800 | 0.134346 | ||||||||
\(936\) | −5.45447 | −0.178285 | ||||||||
\(937\) | −26.9071 | −0.879018 | −0.439509 | − | 0.898238i | \(-0.644848\pi\) | ||||
−0.439509 | + | 0.898238i | \(0.644848\pi\) | |||||||
\(938\) | 26.8154 | 0.875555 | ||||||||
\(939\) | 9.39154 | 0.306481 | ||||||||
\(940\) | −44.3238 | −1.44568 | ||||||||
\(941\) | −21.3862 | −0.697169 | −0.348585 | − | 0.937277i | \(-0.613338\pi\) | ||||
−0.348585 | + | 0.937277i | \(0.613338\pi\) | |||||||
\(942\) | −4.58212 | −0.149294 | ||||||||
\(943\) | 34.5329 | 1.12455 | ||||||||
\(944\) | 41.1902 | 1.34063 | ||||||||
\(945\) | 18.6446 | 0.606510 | ||||||||
\(946\) | −1.85483 | −0.0603058 | ||||||||
\(947\) | −2.58087 | −0.0838670 | −0.0419335 | − | 0.999120i | \(-0.513352\pi\) | ||||
−0.0419335 | + | 0.999120i | \(0.513352\pi\) | |||||||
\(948\) | 5.94917 | 0.193220 | ||||||||
\(949\) | −24.7122 | −0.802193 | ||||||||
\(950\) | −126.155 | −4.09301 | ||||||||
\(951\) | 1.95680 | 0.0634534 | ||||||||
\(952\) | 1.29061 | 0.0418290 | ||||||||
\(953\) | −23.1739 | −0.750677 | −0.375338 | − | 0.926888i | \(-0.622473\pi\) | ||||
−0.375338 | + | 0.926888i | \(0.622473\pi\) | |||||||
\(954\) | 8.87320 | 0.287280 | ||||||||
\(955\) | 3.25721 | 0.105401 | ||||||||
\(956\) | −36.9545 | −1.19519 | ||||||||
\(957\) | 5.72752 | 0.185144 | ||||||||
\(958\) | 42.3280 | 1.36756 | ||||||||
\(959\) | 3.22421 | 0.104115 | ||||||||
\(960\) | −8.26947 | −0.266896 | ||||||||
\(961\) | −22.4024 | −0.722659 | ||||||||
\(962\) | −5.92412 | −0.191001 | ||||||||
\(963\) | 24.9711 | 0.804681 | ||||||||
\(964\) | −17.2979 | −0.557127 | ||||||||
\(965\) | 13.5367 | 0.435761 | ||||||||
\(966\) | −8.34234 | −0.268410 | ||||||||
\(967\) | 33.9606 | 1.09210 | 0.546050 | − | 0.837752i | \(-0.316131\pi\) | ||||
0.546050 | + | 0.837752i | \(0.316131\pi\) | |||||||
\(968\) | 1.03795 | 0.0333610 | ||||||||
\(969\) | −3.75266 | −0.120553 | ||||||||
\(970\) | 48.4150 | 1.55451 | ||||||||
\(971\) | −10.4918 | −0.336698 | −0.168349 | − | 0.985727i | \(-0.553844\pi\) | ||||
−0.168349 | + | 0.985727i | \(0.553844\pi\) | |||||||
\(972\) | 20.7942 | 0.666975 | ||||||||
\(973\) | 24.9566 | 0.800071 | ||||||||
\(974\) | 73.2251 | 2.34628 | ||||||||
\(975\) | 15.9069 | 0.509427 | ||||||||
\(976\) | −32.9709 | −1.05537 | ||||||||
\(977\) | 24.1691 | 0.773238 | 0.386619 | − | 0.922240i | \(-0.373643\pi\) | ||||
0.386619 | + | 0.922240i | \(0.373643\pi\) | |||||||
\(978\) | −26.5062 | −0.847576 | ||||||||
\(979\) | −2.05894 | −0.0658041 | ||||||||
\(980\) | −32.2718 | −1.03088 | ||||||||
\(981\) | −9.94802 | −0.317616 | ||||||||
\(982\) | 29.3086 | 0.935275 | ||||||||
\(983\) | −36.9801 | −1.17948 | −0.589740 | − | 0.807593i | \(-0.700770\pi\) | ||||
−0.589740 | + | 0.807593i | \(0.700770\pi\) | |||||||
\(984\) | −4.25442 | −0.135626 | ||||||||
\(985\) | 10.7965 | 0.344004 | ||||||||
\(986\) | −16.2134 | −0.516340 | ||||||||
\(987\) | 6.10292 | 0.194258 | ||||||||
\(988\) | 16.8639 | 0.536511 | ||||||||
\(989\) | 5.52036 | 0.175537 | ||||||||
\(990\) | −19.5876 | −0.622535 | ||||||||
\(991\) | −29.4127 | −0.934325 | −0.467162 | − | 0.884172i | \(-0.654724\pi\) | ||||
−0.467162 | + | 0.884172i | \(0.654724\pi\) | |||||||
\(992\) | 20.0516 | 0.636639 | ||||||||
\(993\) | 18.0569 | 0.573017 | ||||||||
\(994\) | −18.3592 | −0.582320 | ||||||||
\(995\) | 69.5956 | 2.20633 | ||||||||
\(996\) | −7.36500 | −0.233369 | ||||||||
\(997\) | 11.5880 | 0.366997 | 0.183499 | − | 0.983020i | \(-0.441258\pi\) | ||||
0.183499 | + | 0.983020i | \(0.441258\pi\) | |||||||
\(998\) | −33.8420 | −1.07125 | ||||||||
\(999\) | −5.70286 | −0.180431 |
(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 | 8041.2.a.h.1.17 | ✓ | 74 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.h.1.17 | ✓ | 74 | 1.1 | even | 1 | trivial |