Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 88x^{8} - 197x^{6} + 172x^{4} - 36x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.499987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.499987 | 0.353544 | 0.176772 | − | 0.984252i | \(-0.443434\pi\) | ||||
0.176772 | + | 0.984252i | \(0.443434\pi\) | |||||||
\(3\) | −0.849601 | −0.490518 | −0.245259 | − | 0.969458i | \(-0.578873\pi\) | ||||
−0.245259 | + | 0.969458i | \(0.578873\pi\) | |||||||
\(4\) | −1.75001 | −0.875007 | ||||||||
\(5\) | 1.04248 | 0.466209 | 0.233105 | − | 0.972452i | \(-0.425112\pi\) | ||||
0.233105 | + | 0.972452i | \(0.425112\pi\) | |||||||
\(6\) | −0.424789 | −0.173420 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.87496 | −0.662897 | ||||||||
\(9\) | −2.27818 | −0.759392 | ||||||||
\(10\) | 0.521224 | 0.164825 | ||||||||
\(11\) | 3.96730 | 1.19619 | 0.598094 | − | 0.801426i | \(-0.295925\pi\) | ||||
0.598094 | + | 0.801426i | \(0.295925\pi\) | |||||||
\(12\) | 1.48681 | 0.429206 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.885688 | −0.228684 | ||||||||
\(16\) | 2.56257 | 0.640643 | ||||||||
\(17\) | 0.142035 | 0.0344486 | 0.0172243 | − | 0.999852i | \(-0.494517\pi\) | ||||
0.0172243 | + | 0.999852i | \(0.494517\pi\) | |||||||
\(18\) | −1.13906 | −0.268479 | ||||||||
\(19\) | −5.50977 | −1.26403 | −0.632014 | − | 0.774957i | \(-0.717771\pi\) | ||||
−0.632014 | + | 0.774957i | \(0.717771\pi\) | |||||||
\(20\) | −1.82435 | −0.407936 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.98360 | 0.422905 | ||||||||
\(23\) | 4.39098 | 0.915582 | 0.457791 | − | 0.889060i | \(-0.348641\pi\) | ||||
0.457791 | + | 0.889060i | \(0.348641\pi\) | |||||||
\(24\) | 1.59297 | 0.325163 | ||||||||
\(25\) | −3.91325 | −0.782649 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.48435 | 0.863013 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.39759 | −1.55939 | −0.779697 | − | 0.626157i | \(-0.784627\pi\) | ||||
−0.779697 | + | 0.626157i | \(0.784627\pi\) | |||||||
\(30\) | −0.442832 | −0.0808498 | ||||||||
\(31\) | 2.84652 | 0.511251 | 0.255625 | − | 0.966776i | \(-0.417719\pi\) | ||||
0.255625 | + | 0.966776i | \(0.417719\pi\) | |||||||
\(32\) | 5.03117 | 0.889393 | ||||||||
\(33\) | −3.37063 | −0.586751 | ||||||||
\(34\) | 0.0710158 | 0.0121791 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.98684 | 0.664473 | ||||||||
\(37\) | 0.843187 | 0.138619 | 0.0693095 | − | 0.997595i | \(-0.477920\pi\) | ||||
0.0693095 | + | 0.997595i | \(0.477920\pi\) | |||||||
\(38\) | −2.75481 | −0.446889 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.95460 | −0.309049 | ||||||||
\(41\) | 12.0974 | 1.88929 | 0.944647 | − | 0.328089i | \(-0.106405\pi\) | ||||
0.944647 | + | 0.328089i | \(0.106405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.82323 | 0.735536 | 0.367768 | − | 0.929918i | \(-0.380122\pi\) | ||||
0.367768 | + | 0.929918i | \(0.380122\pi\) | |||||||
\(44\) | −6.94284 | −1.04667 | ||||||||
\(45\) | −2.37494 | −0.354036 | ||||||||
\(46\) | 2.19543 | 0.323699 | ||||||||
\(47\) | −4.55648 | −0.664630 | −0.332315 | − | 0.943168i | \(-0.607830\pi\) | ||||
−0.332315 | + | 0.943168i | \(0.607830\pi\) | |||||||
\(48\) | −2.17717 | −0.314247 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.95657 | −0.276701 | ||||||||
\(51\) | −0.120673 | −0.0168977 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.279600 | −0.0384060 | −0.0192030 | − | 0.999816i | \(-0.506113\pi\) | ||||
−0.0192030 | + | 0.999816i | \(0.506113\pi\) | |||||||
\(54\) | 2.24211 | 0.305113 | ||||||||
\(55\) | 4.13582 | 0.557673 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.68111 | 0.620028 | ||||||||
\(58\) | −4.19868 | −0.551314 | ||||||||
\(59\) | −10.7815 | −1.40363 | −0.701815 | − | 0.712359i | \(-0.747627\pi\) | ||||
−0.701815 | + | 0.712359i | \(0.747627\pi\) | |||||||
\(60\) | 1.54997 | 0.200100 | ||||||||
\(61\) | 5.86354 | 0.750749 | 0.375374 | − | 0.926873i | \(-0.377514\pi\) | ||||
0.375374 | + | 0.926873i | \(0.377514\pi\) | |||||||
\(62\) | 1.42322 | 0.180750 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.60963 | −0.326204 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.68527 | −0.207442 | ||||||||
\(67\) | −5.14447 | −0.628497 | −0.314248 | − | 0.949341i | \(-0.601753\pi\) | ||||
−0.314248 | + | 0.949341i | \(0.601753\pi\) | |||||||
\(68\) | −0.248564 | −0.0301428 | ||||||||
\(69\) | −3.73058 | −0.449109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.69880 | −0.438967 | −0.219484 | − | 0.975616i | \(-0.570437\pi\) | ||||
−0.219484 | + | 0.975616i | \(0.570437\pi\) | |||||||
\(72\) | 4.27148 | 0.503399 | ||||||||
\(73\) | −6.61281 | −0.773970 | −0.386985 | − | 0.922086i | \(-0.626484\pi\) | ||||
−0.386985 | + | 0.922086i | \(0.626484\pi\) | |||||||
\(74\) | 0.421582 | 0.0490079 | ||||||||
\(75\) | 3.32470 | 0.383903 | ||||||||
\(76\) | 9.64216 | 1.10603 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9227 | 1.34141 | 0.670705 | − | 0.741725i | \(-0.265992\pi\) | ||||
0.670705 | + | 0.741725i | \(0.265992\pi\) | |||||||
\(80\) | 2.67142 | 0.298674 | ||||||||
\(81\) | 3.02462 | 0.336069 | ||||||||
\(82\) | 6.04853 | 0.667948 | ||||||||
\(83\) | 2.87321 | 0.315376 | 0.157688 | − | 0.987489i | \(-0.449596\pi\) | ||||
0.157688 | + | 0.987489i | \(0.449596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.148068 | 0.0160603 | ||||||||
\(86\) | 2.41155 | 0.260044 | ||||||||
\(87\) | 7.13461 | 0.764910 | ||||||||
\(88\) | −7.43852 | −0.792949 | ||||||||
\(89\) | 1.74765 | 0.185250 | 0.0926252 | − | 0.995701i | \(-0.470474\pi\) | ||||
0.0926252 | + | 0.995701i | \(0.470474\pi\) | |||||||
\(90\) | −1.18744 | −0.125167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.68427 | −0.801141 | ||||||||
\(93\) | −2.41841 | −0.250777 | ||||||||
\(94\) | −2.27818 | −0.234976 | ||||||||
\(95\) | −5.74379 | −0.589301 | ||||||||
\(96\) | −4.27449 | −0.436263 | ||||||||
\(97\) | −2.70291 | −0.274438 | −0.137219 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137219 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.03822 | −0.908376 | ||||||||
\(100\) | 6.84823 | 0.684823 | ||||||||
\(101\) | −11.4722 | −1.14153 | −0.570765 | − | 0.821114i | \(-0.693353\pi\) | ||||
−0.570765 | + | 0.821114i | \(0.693353\pi\) | |||||||
\(102\) | −0.0603351 | −0.00597407 | ||||||||
\(103\) | −4.16950 | −0.410834 | −0.205417 | − | 0.978675i | \(-0.565855\pi\) | ||||
−0.205417 | + | 0.978675i | \(0.565855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.139796 | −0.0135782 | ||||||||
\(107\) | 8.48742 | 0.820510 | 0.410255 | − | 0.911971i | \(-0.365440\pi\) | ||||
0.410255 | + | 0.911971i | \(0.365440\pi\) | |||||||
\(108\) | −7.84767 | −0.755142 | ||||||||
\(109\) | −6.43036 | −0.615917 | −0.307958 | − | 0.951400i | \(-0.599646\pi\) | ||||
−0.307958 | + | 0.951400i | \(0.599646\pi\) | |||||||
\(110\) | 2.06785 | 0.197162 | ||||||||
\(111\) | −0.716373 | −0.0679951 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9633 | 1.03134 | 0.515670 | − | 0.856788i | \(-0.327543\pi\) | ||||
0.515670 | + | 0.856788i | \(0.327543\pi\) | |||||||
\(114\) | 2.34049 | 0.219207 | ||||||||
\(115\) | 4.57749 | 0.426853 | ||||||||
\(116\) | 14.6959 | 1.36448 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.39060 | −0.496245 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.66063 | 0.151594 | ||||||||
\(121\) | 4.73951 | 0.430864 | ||||||||
\(122\) | 2.93169 | 0.265423 | ||||||||
\(123\) | −10.2780 | −0.926732 | ||||||||
\(124\) | −4.98145 | −0.447348 | ||||||||
\(125\) | −9.29184 | −0.831087 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00787 | −0.178170 | −0.0890849 | − | 0.996024i | \(-0.528394\pi\) | ||||
−0.0890849 | + | 0.996024i | \(0.528394\pi\) | |||||||
\(128\) | −11.3671 | −1.00472 | ||||||||
\(129\) | −4.09782 | −0.360793 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4502 | 1.08778 | 0.543890 | − | 0.839156i | \(-0.316951\pi\) | ||||
0.543890 | + | 0.839156i | \(0.316951\pi\) | |||||||
\(132\) | 5.89864 | 0.513411 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.57217 | −0.222201 | ||||||||
\(135\) | 4.67482 | 0.402344 | ||||||||
\(136\) | −0.266310 | −0.0228359 | ||||||||
\(137\) | 5.24518 | 0.448126 | 0.224063 | − | 0.974575i | \(-0.428068\pi\) | ||||
0.224063 | + | 0.974575i | \(0.428068\pi\) | |||||||
\(138\) | −1.86524 | −0.158780 | ||||||||
\(139\) | 20.7385 | 1.75902 | 0.879510 | − | 0.475881i | \(-0.157871\pi\) | ||||
0.879510 | + | 0.475881i | \(0.157871\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.87119 | 0.326013 | ||||||||
\(142\) | −1.84935 | −0.155194 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.83800 | −0.486500 | ||||||||
\(145\) | −8.75428 | −0.727004 | ||||||||
\(146\) | −3.30631 | −0.273633 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.47559 | −0.121293 | ||||||||
\(149\) | −0.0113760 | −0.000931956 0 | −0.000465978 | − | 1.00000i | \(-0.500148\pi\) | ||||
−0.000465978 | 1.00000i | \(0.500148\pi\) | ||||||||
\(150\) | 1.66231 | 0.135727 | ||||||||
\(151\) | −18.9054 | −1.53850 | −0.769251 | − | 0.638947i | \(-0.779370\pi\) | ||||
−0.769251 | + | 0.638947i | \(0.779370\pi\) | |||||||
\(152\) | 10.3306 | 0.837920 | ||||||||
\(153\) | −0.323582 | −0.0261600 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.96743 | 0.238350 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.7937 | −1.57971 | −0.789856 | − | 0.613292i | \(-0.789845\pi\) | ||||
−0.789856 | + | 0.613292i | \(0.789845\pi\) | |||||||
\(158\) | 5.96119 | 0.474247 | ||||||||
\(159\) | 0.237549 | 0.0188388 | ||||||||
\(160\) | 5.24486 | 0.414643 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.51227 | 0.118815 | ||||||||
\(163\) | 8.93255 | 0.699651 | 0.349825 | − | 0.936815i | \(-0.386241\pi\) | ||||
0.349825 | + | 0.936815i | \(0.386241\pi\) | |||||||
\(164\) | −21.1706 | −1.65314 | ||||||||
\(165\) | −3.51380 | −0.273549 | ||||||||
\(166\) | 1.43657 | 0.111499 | ||||||||
\(167\) | −6.13469 | −0.474716 | −0.237358 | − | 0.971422i | \(-0.576281\pi\) | ||||
−0.237358 | + | 0.971422i | \(0.576281\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.0740322 | 0.00567801 | ||||||||
\(171\) | 12.5522 | 0.959893 | ||||||||
\(172\) | −8.44072 | −0.643599 | ||||||||
\(173\) | −24.2628 | −1.84466 | −0.922332 | − | 0.386399i | \(-0.873719\pi\) | ||||
−0.922332 | + | 0.386399i | \(0.873719\pi\) | |||||||
\(174\) | 3.56721 | 0.270429 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.1665 | 0.766330 | ||||||||
\(177\) | 9.15997 | 0.688506 | ||||||||
\(178\) | 0.873801 | 0.0654942 | ||||||||
\(179\) | −4.13675 | −0.309195 | −0.154598 | − | 0.987978i | \(-0.549408\pi\) | ||||
−0.154598 | + | 0.987978i | \(0.549408\pi\) | |||||||
\(180\) | 4.15618 | 0.309784 | ||||||||
\(181\) | −7.86568 | −0.584651 | −0.292326 | − | 0.956319i | \(-0.594429\pi\) | ||||
−0.292326 | + | 0.956319i | \(0.594429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.98167 | −0.368256 | ||||||||
\(184\) | −8.23289 | −0.606937 | ||||||||
\(185\) | 0.879001 | 0.0646254 | ||||||||
\(186\) | −1.20917 | −0.0886608 | ||||||||
\(187\) | 0.563498 | 0.0412070 | ||||||||
\(188\) | 7.97389 | 0.581556 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.87182 | −0.208344 | ||||||||
\(191\) | −6.47866 | −0.468780 | −0.234390 | − | 0.972143i | \(-0.575309\pi\) | ||||
−0.234390 | + | 0.972143i | \(0.575309\pi\) | |||||||
\(192\) | 2.21715 | 0.160009 | ||||||||
\(193\) | −4.82928 | −0.347619 | −0.173810 | − | 0.984779i | \(-0.555608\pi\) | ||||
−0.173810 | + | 0.984779i | \(0.555608\pi\) | |||||||
\(194\) | −1.35142 | −0.0970261 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.8362 | 1.84075 | 0.920377 | − | 0.391032i | \(-0.127882\pi\) | ||||
0.920377 | + | 0.391032i | \(0.127882\pi\) | |||||||
\(198\) | −4.51899 | −0.321151 | ||||||||
\(199\) | −17.1146 | −1.21322 | −0.606612 | − | 0.794998i | \(-0.707472\pi\) | ||||
−0.606612 | + | 0.794998i | \(0.707472\pi\) | |||||||
\(200\) | 7.33717 | 0.518816 | ||||||||
\(201\) | 4.37075 | 0.308289 | ||||||||
\(202\) | −5.73596 | −0.403581 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.211180 | 0.0147856 | ||||||||
\(205\) | 12.6112 | 0.880806 | ||||||||
\(206\) | −2.08470 | −0.145248 | ||||||||
\(207\) | −10.0034 | −0.695286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.8589 | −1.51201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2911 | 1.25921 | 0.629607 | − | 0.776914i | \(-0.283216\pi\) | ||||
0.629607 | + | 0.776914i | \(0.283216\pi\) | |||||||
\(212\) | 0.489304 | 0.0336055 | ||||||||
\(213\) | 3.14251 | 0.215321 | ||||||||
\(214\) | 4.24360 | 0.290086 | ||||||||
\(215\) | 5.02810 | 0.342913 | ||||||||
\(216\) | −8.40796 | −0.572089 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.21509 | −0.217754 | ||||||||
\(219\) | 5.61825 | 0.379646 | ||||||||
\(220\) | −7.23773 | −0.487968 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.358177 | −0.0240392 | ||||||||
\(223\) | −11.5087 | −0.770679 | −0.385340 | − | 0.922775i | \(-0.625916\pi\) | ||||
−0.385340 | + | 0.922775i | \(0.625916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.91507 | 0.594338 | ||||||||
\(226\) | 5.48150 | 0.364624 | ||||||||
\(227\) | 17.9045 | 1.18836 | 0.594181 | − | 0.804332i | \(-0.297476\pi\) | ||||
0.594181 | + | 0.804332i | \(0.297476\pi\) | |||||||
\(228\) | −8.19200 | −0.542528 | ||||||||
\(229\) | −3.86350 | −0.255307 | −0.127654 | − | 0.991819i | \(-0.540745\pi\) | ||||
−0.127654 | + | 0.991819i | \(0.540745\pi\) | |||||||
\(230\) | 2.28868 | 0.150911 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.7451 | 1.03372 | ||||||||
\(233\) | 25.0642 | 1.64201 | 0.821004 | − | 0.570922i | \(-0.193414\pi\) | ||||
0.821004 | + | 0.570922i | \(0.193414\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.75001 | −0.309857 | ||||||||
\(236\) | 18.8678 | 1.22819 | ||||||||
\(237\) | −10.1295 | −0.657985 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.80462 | −0.504839 | −0.252419 | − | 0.967618i | \(-0.581226\pi\) | ||||
−0.252419 | + | 0.967618i | \(0.581226\pi\) | |||||||
\(240\) | −2.26964 | −0.146505 | ||||||||
\(241\) | −21.7653 | −1.40202 | −0.701012 | − | 0.713150i | \(-0.747268\pi\) | ||||
−0.701012 | + | 0.713150i | \(0.747268\pi\) | |||||||
\(242\) | 2.36969 | 0.152329 | ||||||||
\(243\) | −16.0228 | −1.02786 | ||||||||
\(244\) | −10.2613 | −0.656910 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.13884 | −0.327640 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.33711 | −0.338907 | ||||||||
\(249\) | −2.44109 | −0.154698 | ||||||||
\(250\) | −4.64579 | −0.293826 | ||||||||
\(251\) | −7.67980 | −0.484745 | −0.242372 | − | 0.970183i | \(-0.577926\pi\) | ||||
−0.242372 | + | 0.970183i | \(0.577926\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.4203 | 1.09521 | ||||||||
\(254\) | −1.00391 | −0.0629909 | ||||||||
\(255\) | −0.125799 | −0.00787784 | ||||||||
\(256\) | −0.464141 | −0.0290088 | ||||||||
\(257\) | −13.6237 | −0.849826 | −0.424913 | − | 0.905234i | \(-0.639695\pi\) | ||||
−0.424913 | + | 0.905234i | \(0.639695\pi\) | |||||||
\(258\) | −2.04886 | −0.127556 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.1312 | 1.18419 | ||||||||
\(262\) | 6.22494 | 0.384578 | ||||||||
\(263\) | −11.7232 | −0.722880 | −0.361440 | − | 0.932395i | \(-0.617715\pi\) | ||||
−0.361440 | + | 0.932395i | \(0.617715\pi\) | |||||||
\(264\) | 6.31978 | 0.388956 | ||||||||
\(265\) | −0.291476 | −0.0179052 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.48481 | −0.0908686 | ||||||||
\(268\) | 9.00289 | 0.549939 | ||||||||
\(269\) | −9.19876 | −0.560858 | −0.280429 | − | 0.959875i | \(-0.590477\pi\) | ||||
−0.280429 | + | 0.959875i | \(0.590477\pi\) | |||||||
\(270\) | 2.33735 | 0.142246 | ||||||||
\(271\) | 2.56369 | 0.155733 | 0.0778665 | − | 0.996964i | \(-0.475189\pi\) | ||||
0.0778665 | + | 0.996964i | \(0.475189\pi\) | |||||||
\(272\) | 0.363976 | 0.0220693 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.62252 | 0.158432 | ||||||||
\(275\) | −15.5250 | −0.936195 | ||||||||
\(276\) | 6.52857 | 0.392974 | ||||||||
\(277\) | −0.933882 | −0.0561115 | −0.0280558 | − | 0.999606i | \(-0.508932\pi\) | ||||
−0.0280558 | + | 0.999606i | \(0.508932\pi\) | |||||||
\(278\) | 10.3690 | 0.621891 | ||||||||
\(279\) | −6.48488 | −0.388240 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.45288 | 0.384947 | 0.192473 | − | 0.981302i | \(-0.438349\pi\) | ||||
0.192473 | + | 0.981302i | \(0.438349\pi\) | |||||||
\(282\) | 1.93554 | 0.115260 | ||||||||
\(283\) | −22.1746 | −1.31814 | −0.659071 | − | 0.752081i | \(-0.729050\pi\) | ||||
−0.659071 | + | 0.752081i | \(0.729050\pi\) | |||||||
\(284\) | 6.47296 | 0.384099 | ||||||||
\(285\) | 4.87994 | 0.289062 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −11.4619 | −0.675398 | ||||||||
\(289\) | −16.9798 | −0.998813 | ||||||||
\(290\) | −4.37702 | −0.257028 | ||||||||
\(291\) | 2.29639 | 0.134617 | ||||||||
\(292\) | 11.5725 | 0.677229 | ||||||||
\(293\) | −24.2026 | −1.41393 | −0.706964 | − | 0.707249i | \(-0.749936\pi\) | ||||
−0.706964 | + | 0.707249i | \(0.749936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2394 | −0.654385 | ||||||||
\(296\) | −1.58094 | −0.0918902 | ||||||||
\(297\) | 17.7908 | 1.03233 | ||||||||
\(298\) | −0.00568784 | −0.000329487 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.81827 | −0.335918 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.45246 | −0.543928 | ||||||||
\(303\) | 9.74683 | 0.559940 | ||||||||
\(304\) | −14.1192 | −0.809791 | ||||||||
\(305\) | 6.11259 | 0.350006 | ||||||||
\(306\) | −0.161787 | −0.00924872 | ||||||||
\(307\) | −24.2924 | −1.38644 | −0.693220 | − | 0.720726i | \(-0.743809\pi\) | ||||
−0.693220 | + | 0.720726i | \(0.743809\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.54242 | 0.201521 | ||||||||
\(310\) | 1.48367 | 0.0842671 | ||||||||
\(311\) | −3.98711 | −0.226088 | −0.113044 | − | 0.993590i | \(-0.536060\pi\) | ||||
−0.113044 | + | 0.993590i | \(0.536060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.4754 | −1.60953 | −0.804763 | − | 0.593597i | \(-0.797707\pi\) | ||||
−0.804763 | + | 0.593597i | \(0.797707\pi\) | |||||||
\(314\) | −9.89661 | −0.558498 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.8649 | −1.17374 | ||||||||
\(317\) | −16.8161 | −0.944487 | −0.472244 | − | 0.881468i | \(-0.656556\pi\) | ||||
−0.472244 | + | 0.881468i | \(0.656556\pi\) | |||||||
\(318\) | 0.118771 | 0.00666036 | ||||||||
\(319\) | −33.3158 | −1.86533 | ||||||||
\(320\) | −2.72048 | −0.152079 | ||||||||
\(321\) | −7.21093 | −0.402475 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.782582 | −0.0435440 | ||||||||
\(324\) | −5.29313 | −0.294063 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.46615 | 0.247357 | ||||||||
\(327\) | 5.46324 | 0.302118 | ||||||||
\(328\) | −22.6821 | −1.25241 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.75685 | −0.0967115 | ||||||||
\(331\) | −6.20917 | −0.341287 | −0.170644 | − | 0.985333i | \(-0.554585\pi\) | ||||
−0.170644 | + | 0.985333i | \(0.554585\pi\) | |||||||
\(332\) | −5.02816 | −0.275956 | ||||||||
\(333\) | −1.92093 | −0.105266 | ||||||||
\(334\) | −3.06726 | −0.167833 | ||||||||
\(335\) | −5.36298 | −0.293011 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.69650 | −0.419255 | −0.209628 | − | 0.977781i | \(-0.567225\pi\) | ||||
−0.209628 | + | 0.977781i | \(0.567225\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.31442 | −0.505890 | ||||||||
\(340\) | −0.259122 | −0.0140528 | ||||||||
\(341\) | 11.2930 | 0.611552 | ||||||||
\(342\) | 6.27594 | 0.339364 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.04335 | −0.487585 | ||||||||
\(345\) | −3.88904 | −0.209379 | ||||||||
\(346\) | −12.1311 | −0.652170 | ||||||||
\(347\) | 30.4094 | 1.63246 | 0.816231 | − | 0.577725i | \(-0.196059\pi\) | ||||
0.816231 | + | 0.577725i | \(0.196059\pi\) | |||||||
\(348\) | −12.4857 | −0.669302 | ||||||||
\(349\) | 16.1581 | 0.864924 | 0.432462 | − | 0.901652i | \(-0.357645\pi\) | ||||
0.432462 | + | 0.901652i | \(0.357645\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.9602 | 1.06388 | ||||||||
\(353\) | 11.8424 | 0.630306 | 0.315153 | − | 0.949041i | \(-0.397944\pi\) | ||||
0.315153 | + | 0.949041i | \(0.397944\pi\) | |||||||
\(354\) | 4.57986 | 0.243417 | ||||||||
\(355\) | −3.85591 | −0.204651 | ||||||||
\(356\) | −3.05841 | −0.162095 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.06832 | −0.109314 | ||||||||
\(359\) | 31.3653 | 1.65540 | 0.827698 | − | 0.561174i | \(-0.189650\pi\) | ||||
0.827698 | + | 0.561174i | \(0.189650\pi\) | |||||||
\(360\) | 4.45292 | 0.234689 | ||||||||
\(361\) | 11.3575 | 0.597765 | ||||||||
\(362\) | −3.93273 | −0.206700 | ||||||||
\(363\) | −4.02669 | −0.211346 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.89369 | −0.360832 | ||||||||
\(366\) | −2.49077 | −0.130195 | ||||||||
\(367\) | −24.0774 | −1.25683 | −0.628415 | − | 0.777878i | \(-0.716296\pi\) | ||||
−0.628415 | + | 0.777878i | \(0.716296\pi\) | |||||||
\(368\) | 11.2522 | 0.586562 | ||||||||
\(369\) | −27.5600 | −1.43472 | ||||||||
\(370\) | 0.439489 | 0.0228479 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.23225 | 0.219432 | ||||||||
\(373\) | −18.3922 | −0.952314 | −0.476157 | − | 0.879360i | \(-0.657971\pi\) | ||||
−0.476157 | + | 0.879360i | \(0.657971\pi\) | |||||||
\(374\) | 0.281741 | 0.0145685 | ||||||||
\(375\) | 7.89436 | 0.407663 | ||||||||
\(376\) | 8.54320 | 0.440582 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.13740 | 0.417990 | 0.208995 | − | 0.977917i | \(-0.432981\pi\) | ||||
0.208995 | + | 0.977917i | \(0.432981\pi\) | |||||||
\(380\) | 10.0517 | 0.515642 | ||||||||
\(381\) | 1.70589 | 0.0873955 | ||||||||
\(382\) | −3.23925 | −0.165734 | ||||||||
\(383\) | −22.3711 | −1.14311 | −0.571555 | − | 0.820564i | \(-0.693660\pi\) | ||||
−0.571555 | + | 0.820564i | \(0.693660\pi\) | |||||||
\(384\) | 9.65752 | 0.492833 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.41458 | −0.122899 | ||||||||
\(387\) | −10.9882 | −0.558560 | ||||||||
\(388\) | 4.73012 | 0.240136 | ||||||||
\(389\) | −21.3946 | −1.08475 | −0.542374 | − | 0.840137i | \(-0.682475\pi\) | ||||
−0.542374 | + | 0.840137i | \(0.682475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.623674 | 0.0315406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.5777 | −0.533576 | ||||||||
\(394\) | 12.9178 | 0.650788 | ||||||||
\(395\) | 12.4291 | 0.625377 | ||||||||
\(396\) | 15.8170 | 0.794835 | ||||||||
\(397\) | −1.19673 | −0.0600622 | −0.0300311 | − | 0.999549i | \(-0.509561\pi\) | ||||
−0.0300311 | + | 0.999549i | \(0.509561\pi\) | |||||||
\(398\) | −8.55708 | −0.428928 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.0280 | −0.501399 | ||||||||
\(401\) | −36.2749 | −1.81148 | −0.905741 | − | 0.423831i | \(-0.860685\pi\) | ||||
−0.905741 | + | 0.423831i | \(0.860685\pi\) | |||||||
\(402\) | 2.18532 | 0.108994 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 20.0766 | 0.998846 | ||||||||
\(405\) | 3.15309 | 0.156679 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.34518 | 0.165814 | ||||||||
\(408\) | 0.226257 | 0.0112014 | ||||||||
\(409\) | −14.6723 | −0.725500 | −0.362750 | − | 0.931887i | \(-0.618162\pi\) | ||||
−0.362750 | + | 0.931887i | \(0.618162\pi\) | |||||||
\(410\) | 6.30544 | 0.311404 | ||||||||
\(411\) | −4.45631 | −0.219814 | ||||||||
\(412\) | 7.29669 | 0.359482 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.00158 | −0.245814 | ||||||||
\(415\) | 2.99525 | 0.147031 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.6195 | −0.862830 | ||||||||
\(418\) | −10.9292 | −0.534563 | ||||||||
\(419\) | 5.93348 | 0.289870 | 0.144935 | − | 0.989441i | \(-0.453703\pi\) | ||||
0.144935 | + | 0.989441i | \(0.453703\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.63174 | 0.128263 | 0.0641317 | − | 0.997941i | \(-0.479572\pi\) | ||||
0.0641317 | + | 0.997941i | \(0.479572\pi\) | |||||||
\(422\) | 9.14532 | 0.445187 | ||||||||
\(423\) | 10.3805 | 0.504715 | ||||||||
\(424\) | 0.524238 | 0.0254593 | ||||||||
\(425\) | −0.555819 | −0.0269612 | ||||||||
\(426\) | 1.57121 | 0.0761255 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.8531 | −0.717952 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.51398 | 0.121235 | ||||||||
\(431\) | 18.8377 | 0.907378 | 0.453689 | − | 0.891160i | \(-0.350108\pi\) | ||||
0.453689 | + | 0.891160i | \(0.350108\pi\) | |||||||
\(432\) | 11.4915 | 0.552884 | ||||||||
\(433\) | −19.1355 | −0.919591 | −0.459796 | − | 0.888025i | \(-0.652077\pi\) | ||||
−0.459796 | + | 0.888025i | \(0.652077\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.43765 | 0.356608 | ||||||||
\(436\) | 11.2532 | 0.538931 | ||||||||
\(437\) | −24.1933 | −1.15732 | ||||||||
\(438\) | 2.80905 | 0.134222 | ||||||||
\(439\) | 1.26511 | 0.0603803 | 0.0301901 | − | 0.999544i | \(-0.490389\pi\) | ||||
0.0301901 | + | 0.999544i | \(0.490389\pi\) | |||||||
\(440\) | −7.75448 | −0.369680 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.9392 | −0.994853 | −0.497426 | − | 0.867506i | \(-0.665722\pi\) | ||||
−0.497426 | + | 0.867506i | \(0.665722\pi\) | |||||||
\(444\) | 1.25366 | 0.0594961 | ||||||||
\(445\) | 1.82188 | 0.0863654 | ||||||||
\(446\) | −5.75419 | −0.272469 | ||||||||
\(447\) | 0.00966505 | 0.000457141 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.8632 | −0.843018 | −0.421509 | − | 0.906824i | \(-0.638499\pi\) | ||||
−0.421509 | + | 0.906824i | \(0.638499\pi\) | |||||||
\(450\) | 4.45741 | 0.210125 | ||||||||
\(451\) | 47.9940 | 2.25995 | ||||||||
\(452\) | −19.1859 | −0.902429 | ||||||||
\(453\) | 16.0621 | 0.754662 | ||||||||
\(454\) | 8.95199 | 0.420138 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.77687 | −0.411015 | ||||||||
\(457\) | −6.56597 | −0.307143 | −0.153571 | − | 0.988138i | \(-0.549078\pi\) | ||||
−0.153571 | + | 0.988138i | \(0.549078\pi\) | |||||||
\(458\) | −1.93170 | −0.0902624 | ||||||||
\(459\) | 0.636936 | 0.0297296 | ||||||||
\(460\) | −8.01066 | −0.373499 | ||||||||
\(461\) | 5.11364 | 0.238166 | 0.119083 | − | 0.992884i | \(-0.462005\pi\) | ||||
0.119083 | + | 0.992884i | \(0.462005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.3239 | −1.54869 | −0.774347 | − | 0.632761i | \(-0.781921\pi\) | ||||
−0.774347 | + | 0.632761i | \(0.781921\pi\) | |||||||
\(464\) | −21.5194 | −0.999015 | ||||||||
\(465\) | −2.52113 | −0.116915 | ||||||||
\(466\) | 12.5317 | 0.580522 | ||||||||
\(467\) | 12.9494 | 0.599229 | 0.299614 | − | 0.954060i | \(-0.403142\pi\) | ||||
0.299614 | + | 0.954060i | \(0.403142\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.37494 | −0.109548 | ||||||||
\(471\) | 16.8168 | 0.774877 | ||||||||
\(472\) | 20.2148 | 0.930463 | ||||||||
\(473\) | 19.1352 | 0.879838 | ||||||||
\(474\) | −5.06464 | −0.232627 | ||||||||
\(475\) | 21.5611 | 0.989290 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.636979 | 0.0291652 | ||||||||
\(478\) | −3.90221 | −0.178483 | ||||||||
\(479\) | 27.0119 | 1.23421 | 0.617104 | − | 0.786882i | \(-0.288306\pi\) | ||||
0.617104 | + | 0.786882i | \(0.288306\pi\) | |||||||
\(480\) | −4.45605 | −0.203390 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.8823 | −0.495677 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.29420 | −0.377009 | ||||||||
\(485\) | −2.81771 | −0.127946 | ||||||||
\(486\) | −8.01117 | −0.363394 | ||||||||
\(487\) | −32.0838 | −1.45386 | −0.726928 | − | 0.686713i | \(-0.759053\pi\) | ||||
−0.726928 | + | 0.686713i | \(0.759053\pi\) | |||||||
\(488\) | −10.9939 | −0.497669 | ||||||||
\(489\) | −7.58910 | −0.343191 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6040 | −1.29088 | −0.645440 | − | 0.763811i | \(-0.723326\pi\) | ||||
−0.645440 | + | 0.763811i | \(0.723326\pi\) | |||||||
\(492\) | 17.9866 | 0.810897 | ||||||||
\(493\) | −1.19276 | −0.0537190 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.42212 | −0.423493 | ||||||||
\(496\) | 7.29442 | 0.327529 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.22051 | −0.0546924 | ||||||||
\(499\) | 1.79816 | 0.0804969 | 0.0402484 | − | 0.999190i | \(-0.487185\pi\) | ||||
0.0402484 | + | 0.999190i | \(0.487185\pi\) | |||||||
\(500\) | 16.2608 | 0.727207 | ||||||||
\(501\) | 5.21204 | 0.232857 | ||||||||
\(502\) | −3.83980 | −0.171379 | ||||||||
\(503\) | −29.0772 | −1.29649 | −0.648245 | − | 0.761432i | \(-0.724497\pi\) | ||||
−0.648245 | + | 0.761432i | \(0.724497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.9595 | −0.532191 | ||||||||
\(506\) | 8.70994 | 0.387204 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.51380 | 0.155900 | ||||||||
\(509\) | −23.1913 | −1.02794 | −0.513969 | − | 0.857809i | \(-0.671825\pi\) | ||||
−0.513969 | + | 0.857809i | \(0.671825\pi\) | |||||||
\(510\) | −0.0628979 | −0.00278516 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.5022 | 0.994464 | ||||||||
\(513\) | −24.7077 | −1.09087 | ||||||||
\(514\) | −6.81169 | −0.300451 | ||||||||
\(515\) | −4.34660 | −0.191534 | ||||||||
\(516\) | 7.17125 | 0.315696 | ||||||||
\(517\) | −18.0769 | −0.795022 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.6137 | 0.904840 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.2510 | −1.45675 | −0.728376 | − | 0.685178i | \(-0.759725\pi\) | ||||
−0.728376 | + | 0.685178i | \(0.759725\pi\) | |||||||
\(522\) | 9.56535 | 0.418664 | ||||||||
\(523\) | −38.7121 | −1.69276 | −0.846380 | − | 0.532579i | \(-0.821223\pi\) | ||||
−0.846380 | + | 0.532579i | \(0.821223\pi\) | |||||||
\(524\) | −21.7881 | −0.951816 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.86142 | −0.255570 | ||||||||
\(527\) | 0.404307 | 0.0176119 | ||||||||
\(528\) | −8.63748 | −0.375898 | ||||||||
\(529\) | −3.71931 | −0.161709 | ||||||||
\(530\) | −0.145734 | −0.00633029 | ||||||||
\(531\) | 24.5622 | 1.06591 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.742383 | −0.0321260 | ||||||||
\(535\) | 8.84793 | 0.382529 | ||||||||
\(536\) | 9.64566 | 0.416629 | ||||||||
\(537\) | 3.51459 | 0.151666 | ||||||||
\(538\) | −4.59926 | −0.198288 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.18100 | −0.352054 | ||||||||
\(541\) | 22.6675 | 0.974551 | 0.487275 | − | 0.873248i | \(-0.337991\pi\) | ||||
0.487275 | + | 0.873248i | \(0.337991\pi\) | |||||||
\(542\) | 1.28181 | 0.0550585 | ||||||||
\(543\) | 6.68269 | 0.286782 | ||||||||
\(544\) | 0.714603 | 0.0306384 | ||||||||
\(545\) | −6.70349 | −0.287146 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.21134 | −0.393848 | −0.196924 | − | 0.980419i | \(-0.563095\pi\) | ||||
−0.196924 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(548\) | −9.17913 | −0.392113 | ||||||||
\(549\) | −13.3582 | −0.570113 | ||||||||
\(550\) | −7.76231 | −0.330986 | ||||||||
\(551\) | 46.2688 | 1.97112 | ||||||||
\(552\) | 6.99468 | 0.297713 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.466928 | −0.0198379 | ||||||||
\(555\) | −0.746801 | −0.0316999 | ||||||||
\(556\) | −36.2927 | −1.53915 | ||||||||
\(557\) | −11.3281 | −0.479986 | −0.239993 | − | 0.970775i | \(-0.577145\pi\) | ||||
−0.239993 | + | 0.970775i | \(0.577145\pi\) | |||||||
\(558\) | −3.24236 | −0.137260 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.478748 | −0.0202128 | ||||||||
\(562\) | 3.22636 | 0.136096 | ||||||||
\(563\) | −32.6386 | −1.37555 | −0.687777 | − | 0.725922i | \(-0.741414\pi\) | ||||
−0.687777 | + | 0.725922i | \(0.741414\pi\) | |||||||
\(564\) | −6.77463 | −0.285264 | ||||||||
\(565\) | 11.4290 | 0.480820 | ||||||||
\(566\) | −11.0870 | −0.466021 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.93510 | 0.290990 | ||||||||
\(569\) | 35.0091 | 1.46766 | 0.733829 | − | 0.679335i | \(-0.237731\pi\) | ||||
0.733829 | + | 0.679335i | \(0.237731\pi\) | |||||||
\(570\) | 2.43990 | 0.102196 | ||||||||
\(571\) | 26.2546 | 1.09872 | 0.549360 | − | 0.835586i | \(-0.314872\pi\) | ||||
0.549360 | + | 0.835586i | \(0.314872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.50428 | 0.229945 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.1830 | −0.716580 | ||||||||
\(576\) | 5.94520 | 0.247717 | ||||||||
\(577\) | 24.5727 | 1.02297 | 0.511487 | − | 0.859291i | \(-0.329095\pi\) | ||||
0.511487 | + | 0.859291i | \(0.329095\pi\) | |||||||
\(578\) | −8.48969 | −0.353124 | ||||||||
\(579\) | 4.10296 | 0.170513 | ||||||||
\(580\) | 15.3201 | 0.636133 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.14817 | 0.0475930 | ||||||||
\(583\) | −1.10926 | −0.0459408 | ||||||||
\(584\) | 12.3987 | 0.513063 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.1010 | −0.499886 | ||||||||
\(587\) | 20.5279 | 0.847279 | 0.423639 | − | 0.905831i | \(-0.360752\pi\) | ||||
0.423639 | + | 0.905831i | \(0.360752\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6837 | −0.646235 | ||||||||
\(590\) | −5.61957 | −0.231354 | ||||||||
\(591\) | −21.9505 | −0.902923 | ||||||||
\(592\) | 2.16073 | 0.0888054 | ||||||||
\(593\) | 38.2835 | 1.57211 | 0.786057 | − | 0.618154i | \(-0.212119\pi\) | ||||
0.786057 | + | 0.618154i | \(0.212119\pi\) | |||||||
\(594\) | 8.89515 | 0.364972 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0199081 | 0.000815468 0 | ||||||||
\(597\) | 14.5406 | 0.595107 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0713 | 0.574939 | 0.287470 | − | 0.957790i | \(-0.407186\pi\) | ||||
0.287470 | + | 0.957790i | \(0.407186\pi\) | |||||||
\(600\) | −6.23367 | −0.254488 | ||||||||
\(601\) | 20.2342 | 0.825369 | 0.412685 | − | 0.910874i | \(-0.364591\pi\) | ||||
0.412685 | + | 0.910874i | \(0.364591\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7200 | 0.477276 | ||||||||
\(604\) | 33.0847 | 1.34620 | ||||||||
\(605\) | 4.94082 | 0.200873 | ||||||||
\(606\) | 4.87328 | 0.197964 | ||||||||
\(607\) | −6.55127 | −0.265908 | −0.132954 | − | 0.991122i | \(-0.542446\pi\) | ||||
−0.132954 | + | 0.991122i | \(0.542446\pi\) | |||||||
\(608\) | −27.7205 | −1.12422 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.05621 | 0.123742 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.566272 | 0.0228902 | ||||||||
\(613\) | 33.3244 | 1.34596 | 0.672980 | − | 0.739660i | \(-0.265014\pi\) | ||||
0.672980 | + | 0.739660i | \(0.265014\pi\) | |||||||
\(614\) | −12.1459 | −0.490168 | ||||||||
\(615\) | −10.7145 | −0.432051 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.76038 | 0.272162 | 0.136081 | − | 0.990698i | \(-0.456549\pi\) | ||||
0.136081 | + | 0.990698i | \(0.456549\pi\) | |||||||
\(618\) | 1.77116 | 0.0712466 | ||||||||
\(619\) | −17.6186 | −0.708152 | −0.354076 | − | 0.935217i | \(-0.615205\pi\) | ||||
−0.354076 | + | 0.935217i | \(0.615205\pi\) | |||||||
\(620\) | −5.19304 | −0.208558 | ||||||||
\(621\) | 19.6907 | 0.790159 | ||||||||
\(622\) | −1.99350 | −0.0799321 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.87972 | 0.395189 | ||||||||
\(626\) | −14.2373 | −0.569038 | ||||||||
\(627\) | 18.5714 | 0.741669 | ||||||||
\(628\) | 34.6393 | 1.38226 | ||||||||
\(629\) | 0.119762 | 0.00477524 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.7519 | −0.627074 | −0.313537 | − | 0.949576i | \(-0.601514\pi\) | ||||
−0.313537 | + | 0.949576i | \(0.601514\pi\) | |||||||
\(632\) | −22.3546 | −0.889216 | ||||||||
\(633\) | −15.5402 | −0.617667 | ||||||||
\(634\) | −8.40783 | −0.333918 | ||||||||
\(635\) | −2.09316 | −0.0830644 | ||||||||
\(636\) | −0.415713 | −0.0164841 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.6575 | −0.659475 | ||||||||
\(639\) | 8.42653 | 0.333348 | ||||||||
\(640\) | −11.8499 | −0.468410 | ||||||||
\(641\) | −20.9405 | −0.827099 | −0.413550 | − | 0.910482i | \(-0.635711\pi\) | ||||
−0.413550 | + | 0.910482i | \(0.635711\pi\) | |||||||
\(642\) | −3.60537 | −0.142293 | ||||||||
\(643\) | 18.9315 | 0.746586 | 0.373293 | − | 0.927713i | \(-0.378229\pi\) | ||||
0.373293 | + | 0.927713i | \(0.378229\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.27188 | −0.168205 | ||||||||
\(646\) | −0.391280 | −0.0153947 | ||||||||
\(647\) | 37.6768 | 1.48123 | 0.740614 | − | 0.671930i | \(-0.234535\pi\) | ||||
0.740614 | + | 0.671930i | \(0.234535\pi\) | |||||||
\(648\) | −5.67104 | −0.222779 | ||||||||
\(649\) | −42.7735 | −1.67901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.6321 | −0.612199 | ||||||||
\(653\) | 29.0326 | 1.13613 | 0.568066 | − | 0.822983i | \(-0.307692\pi\) | ||||
0.568066 | + | 0.822983i | \(0.307692\pi\) | |||||||
\(654\) | 2.73155 | 0.106812 | ||||||||
\(655\) | 12.9790 | 0.507133 | ||||||||
\(656\) | 31.0004 | 1.21036 | ||||||||
\(657\) | 15.0651 | 0.587747 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.41830 | −0.0552493 | −0.0276247 | − | 0.999618i | \(-0.508794\pi\) | ||||
−0.0276247 | + | 0.999618i | \(0.508794\pi\) | |||||||
\(660\) | 6.14919 | 0.239357 | ||||||||
\(661\) | −4.59298 | −0.178646 | −0.0893231 | − | 0.996003i | \(-0.528470\pi\) | ||||
−0.0893231 | + | 0.996003i | \(0.528470\pi\) | |||||||
\(662\) | −3.10450 | −0.120660 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.38715 | −0.209062 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.960439 | −0.0372162 | ||||||||
\(667\) | −36.8736 | −1.42775 | ||||||||
\(668\) | 10.7358 | 0.415380 | ||||||||
\(669\) | 9.77780 | 0.378032 | ||||||||
\(670\) | −2.68142 | −0.103592 | ||||||||
\(671\) | 23.2624 | 0.898036 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.20223 | −0.161984 | −0.0809920 | − | 0.996715i | \(-0.525809\pi\) | ||||
−0.0809920 | + | 0.996715i | \(0.525809\pi\) | |||||||
\(674\) | −3.84815 | −0.148225 | ||||||||
\(675\) | −17.5484 | −0.675436 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.08708 | −0.310812 | −0.155406 | − | 0.987851i | \(-0.549669\pi\) | ||||
−0.155406 | + | 0.987851i | \(0.549669\pi\) | |||||||
\(678\) | −4.65709 | −0.178854 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.277622 | −0.0106463 | ||||||||
\(681\) | −15.2117 | −0.582912 | ||||||||
\(682\) | 5.64636 | 0.216210 | ||||||||
\(683\) | 24.6865 | 0.944604 | 0.472302 | − | 0.881437i | \(-0.343423\pi\) | ||||
0.472302 | + | 0.881437i | \(0.343423\pi\) | |||||||
\(684\) | −21.9666 | −0.839912 | ||||||||
\(685\) | 5.46797 | 0.208920 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.28244 | 0.125233 | ||||||||
\(688\) | 12.3599 | 0.471216 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.94447 | −0.0740246 | ||||||||
\(691\) | 11.2567 | 0.428225 | 0.214113 | − | 0.976809i | \(-0.431314\pi\) | ||||
0.214113 | + | 0.976809i | \(0.431314\pi\) | |||||||
\(692\) | 42.4602 | 1.61409 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.2043 | 0.577147 | ||||||||
\(695\) | 21.6194 | 0.820071 | ||||||||
\(696\) | −13.3771 | −0.507057 | ||||||||
\(697\) | 1.71826 | 0.0650836 | ||||||||
\(698\) | 8.07884 | 0.305789 | ||||||||
\(699\) | −21.2946 | −0.805434 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.2305 | −0.839635 | −0.419818 | − | 0.907608i | \(-0.637906\pi\) | ||||
−0.419818 | + | 0.907608i | \(0.637906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.64576 | −0.175218 | ||||||||
\(704\) | −10.3532 | −0.390201 | ||||||||
\(705\) | 4.03562 | 0.151990 | ||||||||
\(706\) | 5.92103 | 0.222841 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −16.0301 | −0.602447 | ||||||||
\(709\) | 23.7741 | 0.892854 | 0.446427 | − | 0.894820i | \(-0.352696\pi\) | ||||
0.446427 | + | 0.894820i | \(0.352696\pi\) | |||||||
\(710\) | −1.92790 | −0.0723530 | ||||||||
\(711\) | −27.1620 | −1.01866 | ||||||||
\(712\) | −3.27677 | −0.122802 | ||||||||
\(713\) | 12.4990 | 0.468092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.23937 | 0.270548 | ||||||||
\(717\) | 6.63082 | 0.247632 | ||||||||
\(718\) | 15.6822 | 0.585255 | ||||||||
\(719\) | −20.7808 | −0.774992 | −0.387496 | − | 0.921871i | \(-0.626660\pi\) | ||||
−0.387496 | + | 0.921871i | \(0.626660\pi\) | |||||||
\(720\) | −6.08597 | −0.226811 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.67861 | 0.211336 | ||||||||
\(723\) | 18.4918 | 0.687717 | ||||||||
\(724\) | 13.7650 | 0.511574 | ||||||||
\(725\) | 32.8618 | 1.22046 | ||||||||
\(726\) | −2.01329 | −0.0747203 | ||||||||
\(727\) | −26.7719 | −0.992915 | −0.496457 | − | 0.868061i | \(-0.665366\pi\) | ||||
−0.496457 | + | 0.868061i | \(0.665366\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.53910 | 0.168115 | ||||||||
\(730\) | −3.44675 | −0.127570 | ||||||||
\(731\) | 0.685069 | 0.0253382 | ||||||||
\(732\) | 8.71799 | 0.322226 | ||||||||
\(733\) | −5.25647 | −0.194152 | −0.0970761 | − | 0.995277i | \(-0.530949\pi\) | ||||
−0.0970761 | + | 0.995277i | \(0.530949\pi\) | |||||||
\(734\) | −12.0384 | −0.444345 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.0917 | 0.814312 | ||||||||
\(737\) | −20.4097 | −0.751800 | ||||||||
\(738\) | −13.7796 | −0.507235 | ||||||||
\(739\) | −7.15001 | −0.263017 | −0.131509 | − | 0.991315i | \(-0.541982\pi\) | ||||
−0.131509 | + | 0.991315i | \(0.541982\pi\) | |||||||
\(740\) | −1.53826 | −0.0565477 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.713641 | 0.0261810 | 0.0130905 | − | 0.999914i | \(-0.495833\pi\) | ||||
0.0130905 | + | 0.999914i | \(0.495833\pi\) | |||||||
\(744\) | 4.53441 | 0.166240 | ||||||||
\(745\) | −0.0118592 | −0.000434486 0 | ||||||||
\(746\) | −9.19587 | −0.336685 | ||||||||
\(747\) | −6.54569 | −0.239494 | ||||||||
\(748\) | −0.986128 | −0.0360564 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.94707 | 0.144127 | ||||||||
\(751\) | −25.7013 | −0.937854 | −0.468927 | − | 0.883237i | \(-0.655359\pi\) | ||||
−0.468927 | + | 0.883237i | \(0.655359\pi\) | |||||||
\(752\) | −11.6763 | −0.425791 | ||||||||
\(753\) | 6.52477 | 0.237776 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.7084 | −0.717263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3885 | 0.595650 | 0.297825 | − | 0.954621i | \(-0.403739\pi\) | ||||
0.297825 | + | 0.954621i | \(0.403739\pi\) | |||||||
\(758\) | 4.06859 | 0.147778 | ||||||||
\(759\) | −14.8004 | −0.537219 | ||||||||
\(760\) | 10.7694 | 0.390646 | ||||||||
\(761\) | −8.31998 | −0.301599 | −0.150800 | − | 0.988564i | \(-0.548185\pi\) | ||||
−0.150800 | + | 0.988564i | \(0.548185\pi\) | |||||||
\(762\) | 0.852923 | 0.0308981 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11.3378 | 0.410185 | ||||||||
\(765\) | −0.337326 | −0.0121960 | ||||||||
\(766\) | −11.1853 | −0.404140 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.394335 | 0.0142293 | ||||||||
\(769\) | 25.5588 | 0.921675 | 0.460838 | − | 0.887485i | \(-0.347549\pi\) | ||||
0.460838 | + | 0.887485i | \(0.347549\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.5748 | 0.416855 | ||||||||
\(772\) | 8.45131 | 0.304169 | ||||||||
\(773\) | 8.40077 | 0.302155 | 0.151077 | − | 0.988522i | \(-0.451726\pi\) | ||||
0.151077 | + | 0.988522i | \(0.451726\pi\) | |||||||
\(774\) | −5.49394 | −0.197476 | ||||||||
\(775\) | −11.1391 | −0.400130 | ||||||||
\(776\) | 5.06783 | 0.181925 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.6970 | −0.383506 | ||||||||
\(779\) | −66.6537 | −2.38812 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.6743 | −0.525087 | ||||||||
\(782\) | 0.311829 | 0.0111510 | ||||||||
\(783\) | −37.6577 | −1.34578 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.6345 | −0.736476 | ||||||||
\(786\) | −5.28872 | −0.188642 | ||||||||
\(787\) | 35.0644 | 1.24991 | 0.624956 | − | 0.780660i | \(-0.285117\pi\) | ||||
0.624956 | + | 0.780660i | \(0.285117\pi\) | |||||||
\(788\) | −45.2137 | −1.61067 | ||||||||
\(789\) | 9.96001 | 0.354586 | ||||||||
\(790\) | 6.21440 | 0.221098 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16.9463 | 0.602160 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.598349 | −0.0212346 | ||||||||
\(795\) | 0.247639 | 0.00878284 | ||||||||
\(796\) | 29.9508 | 1.06158 | ||||||||
\(797\) | 24.5752 | 0.870500 | 0.435250 | − | 0.900310i | \(-0.356660\pi\) | ||||
0.435250 | + | 0.900310i | \(0.356660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.647181 | −0.0228956 | ||||||||
\(800\) | −19.6882 | −0.696083 | ||||||||
\(801\) | −3.98145 | −0.140678 | ||||||||
\(802\) | −18.1370 | −0.640439 | ||||||||
\(803\) | −26.2350 | −0.925814 | ||||||||
\(804\) | −7.64887 | −0.269755 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.81528 | 0.275111 | ||||||||
\(808\) | 21.5099 | 0.756717 | ||||||||
\(809\) | −31.8012 | −1.11807 | −0.559035 | − | 0.829144i | \(-0.688828\pi\) | ||||
−0.559035 | + | 0.829144i | \(0.688828\pi\) | |||||||
\(810\) | 1.57651 | 0.0553927 | ||||||||
\(811\) | 10.3633 | 0.363905 | 0.181953 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181953 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.17811 | −0.0763898 | ||||||||
\(814\) | 1.67254 | 0.0586226 | ||||||||
\(815\) | 9.31196 | 0.326184 | ||||||||
\(816\) | −0.309235 | −0.0108254 | ||||||||
\(817\) | −26.5749 | −0.929737 | ||||||||
\(818\) | −7.33597 | −0.256496 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.0698 | −0.770711 | ||||||||
\(821\) | 4.05592 | 0.141552 | 0.0707762 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707762 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(822\) | −2.22810 | −0.0777138 | ||||||||
\(823\) | 8.71697 | 0.303854 | 0.151927 | − | 0.988392i | \(-0.451452\pi\) | ||||
0.151927 | + | 0.988392i | \(0.451452\pi\) | |||||||
\(824\) | 7.81764 | 0.272340 | ||||||||
\(825\) | 13.1901 | 0.459220 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.5788 | −0.819915 | −0.409957 | − | 0.912105i | \(-0.634456\pi\) | ||||
−0.409957 | + | 0.912105i | \(0.634456\pi\) | |||||||
\(828\) | 17.5061 | 0.608380 | ||||||||
\(829\) | 29.0406 | 1.00862 | 0.504311 | − | 0.863522i | \(-0.331747\pi\) | ||||
0.504311 | + | 0.863522i | \(0.331747\pi\) | |||||||
\(830\) | 1.49759 | 0.0519820 | ||||||||
\(831\) | 0.793427 | 0.0275237 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.80951 | −0.305048 | ||||||||
\(835\) | −6.39526 | −0.221317 | ||||||||
\(836\) | 38.2534 | 1.32302 | ||||||||
\(837\) | 12.7648 | 0.441216 | ||||||||
\(838\) | 2.96666 | 0.102482 | ||||||||
\(839\) | −11.5574 | −0.399007 | −0.199503 | − | 0.979897i | \(-0.563933\pi\) | ||||
−0.199503 | + | 0.979897i | \(0.563933\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.5196 | 1.43171 | ||||||||
\(842\) | 1.31584 | 0.0453467 | ||||||||
\(843\) | −5.48238 | −0.188823 | ||||||||
\(844\) | −32.0097 | −1.10182 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.19009 | 0.178439 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.716496 | −0.0246046 | ||||||||
\(849\) | 18.8395 | 0.646572 | ||||||||
\(850\) | −0.277902 | −0.00953197 | ||||||||
\(851\) | 3.70241 | 0.126917 | ||||||||
\(852\) | −5.49943 | −0.188408 | ||||||||
\(853\) | 1.51845 | 0.0519906 | 0.0259953 | − | 0.999662i | \(-0.491725\pi\) | ||||
0.0259953 | + | 0.999662i | \(0.491725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.0854 | 0.447511 | ||||||||
\(856\) | −15.9136 | −0.543914 | ||||||||
\(857\) | 6.00119 | 0.204997 | 0.102498 | − | 0.994733i | \(-0.467316\pi\) | ||||
0.102498 | + | 0.994733i | \(0.467316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.67604 | −0.0571858 | −0.0285929 | − | 0.999591i | \(-0.509103\pi\) | ||||
−0.0285929 | + | 0.999591i | \(0.509103\pi\) | |||||||
\(860\) | −8.79924 | −0.300051 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.41858 | 0.320798 | ||||||||
\(863\) | 42.0504 | 1.43141 | 0.715706 | − | 0.698401i | \(-0.246105\pi\) | ||||
0.715706 | + | 0.698401i | \(0.246105\pi\) | |||||||
\(864\) | 22.5615 | 0.767558 | ||||||||
\(865\) | −25.2933 | −0.859999 | ||||||||
\(866\) | −9.56747 | −0.325116 | ||||||||
\(867\) | 14.4261 | 0.489936 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.3010 | 1.60458 | ||||||||
\(870\) | 3.71873 | 0.126077 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.0566 | 0.408290 | ||||||||
\(873\) | 6.15770 | 0.208407 | ||||||||
\(874\) | −12.0963 | −0.409164 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.83201 | −0.332193 | ||||||||
\(877\) | −30.8630 | −1.04217 | −0.521084 | − | 0.853505i | \(-0.674472\pi\) | ||||
−0.521084 | + | 0.853505i | \(0.674472\pi\) | |||||||
\(878\) | 0.632537 | 0.0213471 | ||||||||
\(879\) | 20.5625 | 0.693557 | ||||||||
\(880\) | 10.5983 | 0.357270 | ||||||||
\(881\) | 55.7338 | 1.87772 | 0.938860 | − | 0.344298i | \(-0.111883\pi\) | ||||
0.938860 | + | 0.344298i | \(0.111883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.92007 | 0.0982681 | 0.0491341 | − | 0.998792i | \(-0.484354\pi\) | ||||
0.0491341 | + | 0.998792i | \(0.484354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.54904 | 0.320988 | ||||||||
\(886\) | −10.4693 | −0.351724 | ||||||||
\(887\) | −1.87909 | −0.0630937 | −0.0315468 | − | 0.999502i | \(-0.510043\pi\) | ||||
−0.0315468 | + | 0.999502i | \(0.510043\pi\) | |||||||
\(888\) | 1.34317 | 0.0450737 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.910916 | 0.0305340 | ||||||||
\(891\) | 11.9996 | 0.402002 | ||||||||
\(892\) | 20.1404 | 0.674349 | ||||||||
\(893\) | 25.1051 | 0.840111 | ||||||||
\(894\) | 0.00483239 | 0.000161619 0 | ||||||||
\(895\) | −4.31246 | −0.144150 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.93138 | −0.298044 | ||||||||
\(899\) | −23.9039 | −0.797241 | ||||||||
\(900\) | −15.6015 | −0.520050 | ||||||||
\(901\) | −0.0397131 | −0.00132304 | ||||||||
\(902\) | 23.9964 | 0.798991 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.5557 | −0.683672 | ||||||||
\(905\) | −8.19978 | −0.272570 | ||||||||
\(906\) | 8.03082 | 0.266806 | ||||||||
\(907\) | −35.6164 | −1.18262 | −0.591311 | − | 0.806444i | \(-0.701389\pi\) | ||||
−0.591311 | + | 0.806444i | \(0.701389\pi\) | |||||||
\(908\) | −31.3331 | −1.03982 | ||||||||
\(909\) | 26.1358 | 0.866869 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.2844 | 1.46721 | 0.733604 | − | 0.679577i | \(-0.237837\pi\) | ||||
0.733604 | + | 0.679577i | \(0.237837\pi\) | |||||||
\(912\) | 11.9957 | 0.397217 | ||||||||
\(913\) | 11.3989 | 0.377249 | ||||||||
\(914\) | −3.28290 | −0.108589 | ||||||||
\(915\) | −5.19327 | −0.171684 | ||||||||
\(916\) | 6.76118 | 0.223396 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.318459 | 0.0105107 | ||||||||
\(919\) | 26.1128 | 0.861382 | 0.430691 | − | 0.902499i | \(-0.358270\pi\) | ||||
0.430691 | + | 0.902499i | \(0.358270\pi\) | |||||||
\(920\) | −8.58259 | −0.282959 | ||||||||
\(921\) | 20.6389 | 0.680074 | ||||||||
\(922\) | 2.55675 | 0.0842021 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.29960 | −0.108490 | ||||||||
\(926\) | −16.6615 | −0.547531 | ||||||||
\(927\) | 9.49887 | 0.311984 | ||||||||
\(928\) | −42.2497 | −1.38691 | ||||||||
\(929\) | −10.0231 | −0.328849 | −0.164424 | − | 0.986390i | \(-0.552577\pi\) | ||||
−0.164424 | + | 0.986390i | \(0.552577\pi\) | |||||||
\(930\) | −1.26053 | −0.0413345 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −43.8626 | −1.43677 | ||||||||
\(933\) | 3.38745 | 0.110900 | ||||||||
\(934\) | 6.47455 | 0.211854 | ||||||||
\(935\) | 0.587432 | 0.0192111 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.916838 | 0.0299518 | 0.0149759 | − | 0.999888i | \(-0.495233\pi\) | ||||
0.0149759 | + | 0.999888i | \(0.495233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.1928 | 0.789501 | ||||||||
\(940\) | 8.31259 | 0.271127 | ||||||||
\(941\) | −17.0896 | −0.557107 | −0.278553 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278553 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(942\) | 8.40817 | 0.273953 | ||||||||
\(943\) | 53.1193 | 1.72980 | ||||||||
\(944\) | −27.6284 | −0.899227 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.56735 | 0.311062 | ||||||||
\(947\) | −21.7555 | −0.706957 | −0.353479 | − | 0.935443i | \(-0.615001\pi\) | ||||
−0.353479 | + | 0.935443i | \(0.615001\pi\) | |||||||
\(948\) | 17.7268 | 0.575741 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 10.7802 | 0.349757 | ||||||||
\(951\) | 14.2870 | 0.463288 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.8081 | −0.576862 | −0.288431 | − | 0.957501i | \(-0.593134\pi\) | ||||
−0.288431 | + | 0.957501i | \(0.593134\pi\) | |||||||
\(954\) | 0.318481 | 0.0103112 | ||||||||
\(955\) | −6.75385 | −0.218549 | ||||||||
\(956\) | 13.6582 | 0.441737 | ||||||||
\(957\) | 28.3052 | 0.914976 | ||||||||
\(958\) | 13.5056 | 0.436347 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.31132 | 0.0745975 | ||||||||
\(961\) | −22.8973 | −0.738623 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.3359 | −0.623089 | ||||||||
\(964\) | 38.0895 | 1.22678 | ||||||||
\(965\) | −5.03441 | −0.162063 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.3813 | −1.13779 | −0.568893 | − | 0.822412i | \(-0.692628\pi\) | ||||
−0.568893 | + | 0.822412i | \(0.692628\pi\) | |||||||
\(968\) | −8.88637 | −0.285619 | ||||||||
\(969\) | 0.664883 | 0.0213591 | ||||||||
\(970\) | −1.40882 | −0.0452344 | ||||||||
\(971\) | −49.7067 | −1.59516 | −0.797582 | − | 0.603211i | \(-0.793888\pi\) | ||||
−0.797582 | + | 0.603211i | \(0.793888\pi\) | |||||||
\(972\) | 28.0401 | 0.899385 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −16.0415 | −0.514002 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.0257 | 0.480962 | ||||||||
\(977\) | −61.2801 | −1.96052 | −0.980262 | − | 0.197702i | \(-0.936652\pi\) | ||||
−0.980262 | + | 0.197702i | \(0.936652\pi\) | |||||||
\(978\) | −3.79445 | −0.121333 | ||||||||
\(979\) | 6.93346 | 0.221594 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.6495 | 0.467723 | ||||||||
\(982\) | −14.3016 | −0.456383 | ||||||||
\(983\) | 6.98962 | 0.222934 | 0.111467 | − | 0.993768i | \(-0.464445\pi\) | ||||
0.111467 | + | 0.993768i | \(0.464445\pi\) | |||||||
\(984\) | 19.2707 | 0.614328 | ||||||||
\(985\) | 26.9336 | 0.858176 | ||||||||
\(986\) | −0.596362 | −0.0189920 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.1787 | 0.673443 | ||||||||
\(990\) | −4.71094 | −0.149723 | ||||||||
\(991\) | −32.7341 | −1.03983 | −0.519917 | − | 0.854217i | \(-0.674037\pi\) | ||||
−0.519917 | + | 0.854217i | \(0.674037\pi\) | |||||||
\(992\) | 14.3213 | 0.454703 | ||||||||
\(993\) | 5.27532 | 0.167407 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.8416 | −0.565616 | ||||||||
\(996\) | 4.27193 | 0.135361 | ||||||||
\(997\) | −57.7897 | −1.83022 | −0.915109 | − | 0.403207i | \(-0.867896\pi\) | ||||
−0.915109 | + | 0.403207i | \(0.867896\pi\) | |||||||
\(998\) | 0.899058 | 0.0284592 | ||||||||
\(999\) | 3.78114 | 0.119630 |
(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 | 8281.2.a.co.1.8 | 12 | ||
7.3 | odd | 6 | 1183.2.e.j.170.5 | 24 | |||
7.5 | odd | 6 | 1183.2.e.j.508.5 | 24 | |||
7.6 | odd | 2 | 8281.2.a.cp.1.8 | 12 | |||
13.6 | odd | 12 | 637.2.q.i.491.3 | 12 | |||
13.11 | odd | 12 | 637.2.q.i.589.3 | 12 | |||
13.12 | even | 2 | inner | 8281.2.a.co.1.5 | 12 | ||
91.6 | even | 12 | 637.2.q.g.491.3 | 12 | |||
91.11 | odd | 12 | 637.2.u.g.30.4 | 12 | |||
91.12 | odd | 6 | 1183.2.e.j.508.8 | 24 | |||
91.19 | even | 12 | 91.2.u.b.88.4 | yes | 12 | ||
91.24 | even | 12 | 91.2.u.b.30.4 | yes | 12 | ||
91.32 | odd | 12 | 637.2.k.i.569.3 | 12 | |||
91.37 | odd | 12 | 637.2.k.i.459.4 | 12 | |||
91.38 | odd | 6 | 1183.2.e.j.170.8 | 24 | |||
91.45 | even | 12 | 91.2.k.b.23.3 | yes | 12 | ||
91.58 | odd | 12 | 637.2.u.g.361.4 | 12 | |||
91.76 | even | 12 | 637.2.q.g.589.3 | 12 | |||
91.89 | even | 12 | 91.2.k.b.4.4 | ✓ | 12 | ||
91.90 | odd | 2 | 8281.2.a.cp.1.5 | 12 | |||
273.89 | odd | 12 | 819.2.bm.f.550.3 | 12 | |||
273.110 | odd | 12 | 819.2.do.e.361.3 | 12 | |||
273.206 | odd | 12 | 819.2.do.e.667.3 | 12 | |||
273.227 | odd | 12 | 819.2.bm.f.478.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.4 | ✓ | 12 | 91.89 | even | 12 | ||
91.2.k.b.23.3 | yes | 12 | 91.45 | even | 12 | ||
91.2.u.b.30.4 | yes | 12 | 91.24 | even | 12 | ||
91.2.u.b.88.4 | yes | 12 | 91.19 | even | 12 | ||
637.2.k.i.459.4 | 12 | 91.37 | odd | 12 | |||
637.2.k.i.569.3 | 12 | 91.32 | odd | 12 | |||
637.2.q.g.491.3 | 12 | 91.6 | even | 12 | |||
637.2.q.g.589.3 | 12 | 91.76 | even | 12 | |||
637.2.q.i.491.3 | 12 | 13.6 | odd | 12 | |||
637.2.q.i.589.3 | 12 | 13.11 | odd | 12 | |||
637.2.u.g.30.4 | 12 | 91.11 | odd | 12 | |||
637.2.u.g.361.4 | 12 | 91.58 | odd | 12 | |||
819.2.bm.f.478.4 | 12 | 273.227 | odd | 12 | |||
819.2.bm.f.550.3 | 12 | 273.89 | odd | 12 | |||
819.2.do.e.361.3 | 12 | 273.110 | odd | 12 | |||
819.2.do.e.667.3 | 12 | 273.206 | odd | 12 | |||
1183.2.e.j.170.5 | 24 | 7.3 | odd | 6 | |||
1183.2.e.j.170.8 | 24 | 91.38 | odd | 6 | |||
1183.2.e.j.508.5 | 24 | 7.5 | odd | 6 | |||
1183.2.e.j.508.8 | 24 | 91.12 | odd | 6 | |||
8281.2.a.co.1.5 | 12 | 13.12 | even | 2 | inner | ||
8281.2.a.co.1.8 | 12 | 1.1 | even | 1 | trivial | ||
8281.2.a.cp.1.5 | 12 | 91.90 | odd | 2 | |||
8281.2.a.cp.1.8 | 12 | 7.6 | odd | 2 |