Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60586 | −1.84262 | −0.921312 | − | 0.388823i | \(-0.872882\pi\) | ||||
−0.921312 | + | 0.388823i | \(0.872882\pi\) | |||||||
\(3\) | −2.49081 | −1.43807 | −0.719034 | − | 0.694974i | \(-0.755416\pi\) | ||||
−0.719034 | + | 0.694974i | \(0.755416\pi\) | |||||||
\(4\) | 4.79053 | 2.39527 | ||||||||
\(5\) | −1.82309 | −0.815311 | −0.407655 | − | 0.913136i | \(-0.633653\pi\) | ||||
−0.407655 | + | 0.913136i | \(0.633653\pi\) | |||||||
\(6\) | 6.49071 | 2.64982 | ||||||||
\(7\) | 1.00898 | 0.381359 | 0.190679 | − | 0.981652i | \(-0.438931\pi\) | ||||
0.190679 | + | 0.981652i | \(0.438931\pi\) | |||||||
\(8\) | −7.27175 | −2.57095 | ||||||||
\(9\) | 3.20413 | 1.06804 | ||||||||
\(10\) | 4.75073 | 1.50231 | ||||||||
\(11\) | 0.511549 | 0.154238 | 0.0771189 | − | 0.997022i | \(-0.475428\pi\) | ||||
0.0771189 | + | 0.997022i | \(0.475428\pi\) | |||||||
\(12\) | −11.9323 | −3.44456 | ||||||||
\(13\) | −1.90222 | −0.527581 | −0.263790 | − | 0.964580i | \(-0.584973\pi\) | ||||
−0.263790 | + | 0.964580i | \(0.584973\pi\) | |||||||
\(14\) | −2.62927 | −0.702701 | ||||||||
\(15\) | 4.54097 | 1.17247 | ||||||||
\(16\) | 9.36813 | 2.34203 | ||||||||
\(17\) | 2.82608 | 0.685426 | 0.342713 | − | 0.939440i | \(-0.388654\pi\) | ||||
0.342713 | + | 0.939440i | \(0.388654\pi\) | |||||||
\(18\) | −8.34952 | −1.96800 | ||||||||
\(19\) | −6.99053 | −1.60374 | −0.801869 | − | 0.597500i | \(-0.796161\pi\) | ||||
−0.801869 | + | 0.597500i | \(0.796161\pi\) | |||||||
\(20\) | −8.73357 | −1.95289 | ||||||||
\(21\) | −2.51318 | −0.548420 | ||||||||
\(22\) | −1.33303 | −0.284203 | ||||||||
\(23\) | 0.587350 | 0.122471 | 0.0612355 | − | 0.998123i | \(-0.480496\pi\) | ||||
0.0612355 | + | 0.998123i | \(0.480496\pi\) | |||||||
\(24\) | 18.1125 | 3.69721 | ||||||||
\(25\) | −1.67634 | −0.335269 | ||||||||
\(26\) | 4.95693 | 0.972133 | ||||||||
\(27\) | −0.508441 | −0.0978495 | ||||||||
\(28\) | 4.83355 | 0.913455 | ||||||||
\(29\) | −2.47910 | −0.460357 | −0.230178 | − | 0.973148i | \(-0.573931\pi\) | ||||
−0.230178 | + | 0.973148i | \(0.573931\pi\) | |||||||
\(30\) | −11.8331 | −2.16043 | ||||||||
\(31\) | −6.46857 | −1.16179 | −0.580894 | − | 0.813979i | \(-0.697297\pi\) | ||||
−0.580894 | + | 0.813979i | \(0.697297\pi\) | |||||||
\(32\) | −9.86858 | −1.74454 | ||||||||
\(33\) | −1.27417 | −0.221805 | ||||||||
\(34\) | −7.36439 | −1.26298 | ||||||||
\(35\) | −1.83946 | −0.310926 | ||||||||
\(36\) | 15.3495 | 2.55825 | ||||||||
\(37\) | −4.94263 | −0.812564 | −0.406282 | − | 0.913748i | \(-0.633175\pi\) | ||||
−0.406282 | + | 0.913748i | \(0.633175\pi\) | |||||||
\(38\) | 18.2164 | 2.95509 | ||||||||
\(39\) | 4.73806 | 0.758697 | ||||||||
\(40\) | 13.2570 | 2.09612 | ||||||||
\(41\) | 6.23684 | 0.974031 | 0.487015 | − | 0.873393i | \(-0.338086\pi\) | ||||
0.487015 | + | 0.873393i | \(0.338086\pi\) | |||||||
\(42\) | 6.54900 | 1.01053 | ||||||||
\(43\) | 6.10118 | 0.930422 | 0.465211 | − | 0.885200i | \(-0.345978\pi\) | ||||
0.465211 | + | 0.885200i | \(0.345978\pi\) | |||||||
\(44\) | 2.45059 | 0.369441 | ||||||||
\(45\) | −5.84141 | −0.870786 | ||||||||
\(46\) | −1.53056 | −0.225668 | ||||||||
\(47\) | −7.83478 | −1.14282 | −0.571410 | − | 0.820665i | \(-0.693603\pi\) | ||||
−0.571410 | + | 0.820665i | \(0.693603\pi\) | |||||||
\(48\) | −23.3342 | −3.36800 | ||||||||
\(49\) | −5.98196 | −0.854566 | ||||||||
\(50\) | 4.36833 | 0.617774 | ||||||||
\(51\) | −7.03923 | −0.985690 | ||||||||
\(52\) | −9.11264 | −1.26370 | ||||||||
\(53\) | 8.97211 | 1.23241 | 0.616207 | − | 0.787584i | \(-0.288668\pi\) | ||||
0.616207 | + | 0.787584i | \(0.288668\pi\) | |||||||
\(54\) | 1.32493 | 0.180300 | ||||||||
\(55\) | −0.932600 | −0.125752 | ||||||||
\(56\) | −7.33705 | −0.980454 | ||||||||
\(57\) | 17.4121 | 2.30629 | ||||||||
\(58\) | 6.46019 | 0.848265 | ||||||||
\(59\) | 8.10985 | 1.05581 | 0.527906 | − | 0.849303i | \(-0.322977\pi\) | ||||
0.527906 | + | 0.849303i | \(0.322977\pi\) | |||||||
\(60\) | 21.7536 | 2.80838 | ||||||||
\(61\) | −7.44405 | −0.953113 | −0.476556 | − | 0.879144i | \(-0.658115\pi\) | ||||
−0.476556 | + | 0.879144i | \(0.658115\pi\) | |||||||
\(62\) | 16.8562 | 2.14074 | ||||||||
\(63\) | 3.23290 | 0.407307 | ||||||||
\(64\) | 6.97993 | 0.872492 | ||||||||
\(65\) | 3.46792 | 0.430142 | ||||||||
\(66\) | 3.32032 | 0.408703 | ||||||||
\(67\) | 3.14046 | 0.383668 | 0.191834 | − | 0.981427i | \(-0.438557\pi\) | ||||
0.191834 | + | 0.981427i | \(0.438557\pi\) | |||||||
\(68\) | 13.5384 | 1.64178 | ||||||||
\(69\) | −1.46298 | −0.176122 | ||||||||
\(70\) | 4.79339 | 0.572919 | ||||||||
\(71\) | −9.63889 | −1.14393 | −0.571963 | − | 0.820279i | \(-0.693818\pi\) | ||||
−0.571963 | + | 0.820279i | \(0.693818\pi\) | |||||||
\(72\) | −23.2996 | −2.74588 | ||||||||
\(73\) | −1.31652 | −0.154087 | −0.0770435 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770435 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(74\) | 12.8798 | 1.49725 | ||||||||
\(75\) | 4.17545 | 0.482140 | ||||||||
\(76\) | −33.4884 | −3.84138 | ||||||||
\(77\) | 0.516143 | 0.0588199 | ||||||||
\(78\) | −12.3468 | −1.39799 | ||||||||
\(79\) | −3.25687 | −0.366426 | −0.183213 | − | 0.983073i | \(-0.558650\pi\) | ||||
−0.183213 | + | 0.983073i | \(0.558650\pi\) | |||||||
\(80\) | −17.0789 | −1.90948 | ||||||||
\(81\) | −8.34595 | −0.927328 | ||||||||
\(82\) | −16.2524 | −1.79477 | ||||||||
\(83\) | 11.2454 | 1.23434 | 0.617171 | − | 0.786829i | \(-0.288279\pi\) | ||||
0.617171 | + | 0.786829i | \(0.288279\pi\) | |||||||
\(84\) | −12.0394 | −1.31361 | ||||||||
\(85\) | −5.15220 | −0.558835 | ||||||||
\(86\) | −15.8989 | −1.71442 | ||||||||
\(87\) | 6.17496 | 0.662025 | ||||||||
\(88\) | −3.71986 | −0.396538 | ||||||||
\(89\) | −4.85320 | −0.514438 | −0.257219 | − | 0.966353i | \(-0.582806\pi\) | ||||
−0.257219 | + | 0.966353i | \(0.582806\pi\) | |||||||
\(90\) | 15.2219 | 1.60453 | ||||||||
\(91\) | −1.91930 | −0.201197 | ||||||||
\(92\) | 2.81372 | 0.293351 | ||||||||
\(93\) | 16.1120 | 1.67073 | ||||||||
\(94\) | 20.4164 | 2.10579 | ||||||||
\(95\) | 12.7444 | 1.30754 | ||||||||
\(96\) | 24.5807 | 2.50876 | ||||||||
\(97\) | 9.47521 | 0.962062 | 0.481031 | − | 0.876704i | \(-0.340262\pi\) | ||||
0.481031 | + | 0.876704i | \(0.340262\pi\) | |||||||
\(98\) | 15.5882 | 1.57464 | ||||||||
\(99\) | 1.63907 | 0.164733 | ||||||||
\(100\) | −8.03058 | −0.803058 | ||||||||
\(101\) | −0.234664 | −0.0233499 | −0.0116750 | − | 0.999932i | \(-0.503716\pi\) | ||||
−0.0116750 | + | 0.999932i | \(0.503716\pi\) | |||||||
\(102\) | 18.3433 | 1.81626 | ||||||||
\(103\) | −13.9259 | −1.37216 | −0.686082 | − | 0.727524i | \(-0.740671\pi\) | ||||
−0.686082 | + | 0.727524i | \(0.740671\pi\) | |||||||
\(104\) | 13.8325 | 1.35638 | ||||||||
\(105\) | 4.58175 | 0.447133 | ||||||||
\(106\) | −23.3801 | −2.27088 | ||||||||
\(107\) | 4.84502 | 0.468386 | 0.234193 | − | 0.972190i | \(-0.424755\pi\) | ||||
0.234193 | + | 0.972190i | \(0.424755\pi\) | |||||||
\(108\) | −2.43570 | −0.234376 | ||||||||
\(109\) | 2.65863 | 0.254651 | 0.127325 | − | 0.991861i | \(-0.459361\pi\) | ||||
0.127325 | + | 0.991861i | \(0.459361\pi\) | |||||||
\(110\) | 2.43023 | 0.231713 | ||||||||
\(111\) | 12.3111 | 1.16852 | ||||||||
\(112\) | 9.45225 | 0.893154 | ||||||||
\(113\) | −8.68881 | −0.817375 | −0.408687 | − | 0.912674i | \(-0.634013\pi\) | ||||
−0.408687 | + | 0.912674i | \(0.634013\pi\) | |||||||
\(114\) | −45.3735 | −4.24962 | ||||||||
\(115\) | −1.07079 | −0.0998519 | ||||||||
\(116\) | −11.8762 | −1.10268 | ||||||||
\(117\) | −6.09495 | −0.563478 | ||||||||
\(118\) | −21.1332 | −1.94547 | ||||||||
\(119\) | 2.85146 | 0.261393 | ||||||||
\(120\) | −33.0208 | −3.01437 | ||||||||
\(121\) | −10.7383 | −0.976211 | ||||||||
\(122\) | 19.3982 | 1.75623 | ||||||||
\(123\) | −15.5348 | −1.40072 | ||||||||
\(124\) | −30.9879 | −2.78279 | ||||||||
\(125\) | 12.1716 | 1.08866 | ||||||||
\(126\) | −8.42450 | −0.750514 | ||||||||
\(127\) | 20.3895 | 1.80928 | 0.904640 | − | 0.426177i | \(-0.140140\pi\) | ||||
0.904640 | + | 0.426177i | \(0.140140\pi\) | |||||||
\(128\) | 1.54840 | 0.136861 | ||||||||
\(129\) | −15.1969 | −1.33801 | ||||||||
\(130\) | −9.03692 | −0.792590 | ||||||||
\(131\) | 7.87096 | 0.687689 | 0.343845 | − | 0.939027i | \(-0.388271\pi\) | ||||
0.343845 | + | 0.939027i | \(0.388271\pi\) | |||||||
\(132\) | −6.10396 | −0.531281 | ||||||||
\(133\) | −7.05331 | −0.611599 | ||||||||
\(134\) | −8.18360 | −0.706956 | ||||||||
\(135\) | 0.926934 | 0.0797778 | ||||||||
\(136\) | −20.5506 | −1.76220 | ||||||||
\(137\) | −10.1279 | −0.865287 | −0.432644 | − | 0.901565i | \(-0.642419\pi\) | ||||
−0.432644 | + | 0.901565i | \(0.642419\pi\) | |||||||
\(138\) | 3.81232 | 0.324526 | ||||||||
\(139\) | −1.08895 | −0.0923635 | −0.0461818 | − | 0.998933i | \(-0.514705\pi\) | ||||
−0.0461818 | + | 0.998933i | \(0.514705\pi\) | |||||||
\(140\) | −8.81200 | −0.744750 | ||||||||
\(141\) | 19.5149 | 1.64345 | ||||||||
\(142\) | 25.1177 | 2.10783 | ||||||||
\(143\) | −0.973079 | −0.0813729 | ||||||||
\(144\) | 30.0167 | 2.50139 | ||||||||
\(145\) | 4.51962 | 0.375334 | ||||||||
\(146\) | 3.43067 | 0.283925 | ||||||||
\(147\) | 14.8999 | 1.22892 | ||||||||
\(148\) | −23.6778 | −1.94631 | ||||||||
\(149\) | −5.14799 | −0.421740 | −0.210870 | − | 0.977514i | \(-0.567630\pi\) | ||||
−0.210870 | + | 0.977514i | \(0.567630\pi\) | |||||||
\(150\) | −10.8807 | −0.888402 | ||||||||
\(151\) | −15.3967 | −1.25296 | −0.626482 | − | 0.779436i | \(-0.715506\pi\) | ||||
−0.626482 | + | 0.779436i | \(0.715506\pi\) | |||||||
\(152\) | 50.8334 | 4.12313 | ||||||||
\(153\) | 9.05513 | 0.732064 | ||||||||
\(154\) | −1.34500 | −0.108383 | ||||||||
\(155\) | 11.7928 | 0.947219 | ||||||||
\(156\) | 22.6978 | 1.81728 | ||||||||
\(157\) | −5.04819 | −0.402889 | −0.201445 | − | 0.979500i | \(-0.564564\pi\) | ||||
−0.201445 | + | 0.979500i | \(0.564564\pi\) | |||||||
\(158\) | 8.48696 | 0.675186 | ||||||||
\(159\) | −22.3478 | −1.77230 | ||||||||
\(160\) | 17.9913 | 1.42234 | ||||||||
\(161\) | 0.592625 | 0.0467054 | ||||||||
\(162\) | 21.7484 | 1.70872 | ||||||||
\(163\) | −6.10587 | −0.478248 | −0.239124 | − | 0.970989i | \(-0.576860\pi\) | ||||
−0.239124 | + | 0.970989i | \(0.576860\pi\) | |||||||
\(164\) | 29.8778 | 2.33306 | ||||||||
\(165\) | 2.32293 | 0.180840 | ||||||||
\(166\) | −29.3040 | −2.27443 | ||||||||
\(167\) | 5.15193 | 0.398668 | 0.199334 | − | 0.979932i | \(-0.436122\pi\) | ||||
0.199334 | + | 0.979932i | \(0.436122\pi\) | |||||||
\(168\) | 18.2752 | 1.40996 | ||||||||
\(169\) | −9.38156 | −0.721659 | ||||||||
\(170\) | 13.4259 | 1.02972 | ||||||||
\(171\) | −22.3985 | −1.71286 | ||||||||
\(172\) | 29.2279 | 2.22861 | ||||||||
\(173\) | 0.917417 | 0.0697499 | 0.0348750 | − | 0.999392i | \(-0.488897\pi\) | ||||
0.0348750 | + | 0.999392i | \(0.488897\pi\) | |||||||
\(174\) | −16.0911 | −1.21986 | ||||||||
\(175\) | −1.69140 | −0.127858 | ||||||||
\(176\) | 4.79226 | 0.361230 | ||||||||
\(177\) | −20.2001 | −1.51833 | ||||||||
\(178\) | 12.6468 | 0.947917 | ||||||||
\(179\) | −21.3926 | −1.59896 | −0.799481 | − | 0.600692i | \(-0.794892\pi\) | ||||
−0.799481 | + | 0.600692i | \(0.794892\pi\) | |||||||
\(180\) | −27.9835 | −2.08576 | ||||||||
\(181\) | −8.36271 | −0.621596 | −0.310798 | − | 0.950476i | \(-0.600596\pi\) | ||||
−0.310798 | + | 0.950476i | \(0.600596\pi\) | |||||||
\(182\) | 5.00144 | 0.370731 | ||||||||
\(183\) | 18.5417 | 1.37064 | ||||||||
\(184\) | −4.27106 | −0.314867 | ||||||||
\(185\) | 9.01086 | 0.662492 | ||||||||
\(186\) | −41.9856 | −3.07853 | ||||||||
\(187\) | 1.44568 | 0.105719 | ||||||||
\(188\) | −37.5328 | −2.73736 | ||||||||
\(189\) | −0.513007 | −0.0373158 | ||||||||
\(190\) | −33.2101 | −2.40931 | ||||||||
\(191\) | −18.2098 | −1.31762 | −0.658809 | − | 0.752310i | \(-0.728940\pi\) | ||||
−0.658809 | + | 0.752310i | \(0.728940\pi\) | |||||||
\(192\) | −17.3857 | −1.25470 | ||||||||
\(193\) | −9.56005 | −0.688147 | −0.344074 | − | 0.938943i | \(-0.611807\pi\) | ||||
−0.344074 | + | 0.938943i | \(0.611807\pi\) | |||||||
\(194\) | −24.6911 | −1.77272 | ||||||||
\(195\) | −8.63792 | −0.618574 | ||||||||
\(196\) | −28.6568 | −2.04691 | ||||||||
\(197\) | −26.9883 | −1.92284 | −0.961418 | − | 0.275091i | \(-0.911292\pi\) | ||||
−0.961418 | + | 0.275091i | \(0.911292\pi\) | |||||||
\(198\) | −4.27119 | −0.303540 | ||||||||
\(199\) | −9.79020 | −0.694009 | −0.347004 | − | 0.937863i | \(-0.612801\pi\) | ||||
−0.347004 | + | 0.937863i | \(0.612801\pi\) | |||||||
\(200\) | 12.1899 | 0.861960 | ||||||||
\(201\) | −7.82227 | −0.551741 | ||||||||
\(202\) | 0.611503 | 0.0430252 | ||||||||
\(203\) | −2.50136 | −0.175561 | ||||||||
\(204\) | −33.7217 | −2.36099 | ||||||||
\(205\) | −11.3703 | −0.794137 | ||||||||
\(206\) | 36.2891 | 2.52838 | ||||||||
\(207\) | 1.88194 | 0.130804 | ||||||||
\(208\) | −17.8202 | −1.23561 | ||||||||
\(209\) | −3.57600 | −0.247357 | ||||||||
\(210\) | −11.9394 | −0.823897 | ||||||||
\(211\) | 12.0283 | 0.828062 | 0.414031 | − | 0.910263i | \(-0.364121\pi\) | ||||
0.414031 | + | 0.910263i | \(0.364121\pi\) | |||||||
\(212\) | 42.9812 | 2.95196 | ||||||||
\(213\) | 24.0086 | 1.64504 | ||||||||
\(214\) | −12.6255 | −0.863059 | ||||||||
\(215\) | −11.1230 | −0.758583 | ||||||||
\(216\) | 3.69726 | 0.251566 | ||||||||
\(217\) | −6.52665 | −0.443058 | ||||||||
\(218\) | −6.92803 | −0.469226 | ||||||||
\(219\) | 3.27920 | 0.221588 | ||||||||
\(220\) | −4.46765 | −0.301209 | ||||||||
\(221\) | −5.37583 | −0.361617 | ||||||||
\(222\) | −32.0812 | −2.15315 | ||||||||
\(223\) | 0.646705 | 0.0433065 | 0.0216533 | − | 0.999766i | \(-0.493107\pi\) | ||||
0.0216533 | + | 0.999766i | \(0.493107\pi\) | |||||||
\(224\) | −9.95720 | −0.665294 | ||||||||
\(225\) | −5.37122 | −0.358081 | ||||||||
\(226\) | 22.6419 | 1.50611 | ||||||||
\(227\) | −6.67837 | −0.443259 | −0.221629 | − | 0.975131i | \(-0.571138\pi\) | ||||
−0.221629 | + | 0.975131i | \(0.571138\pi\) | |||||||
\(228\) | 83.4131 | 5.52417 | ||||||||
\(229\) | 15.9744 | 1.05562 | 0.527810 | − | 0.849362i | \(-0.323013\pi\) | ||||
0.527810 | + | 0.849362i | \(0.323013\pi\) | |||||||
\(230\) | 2.79034 | 0.183990 | ||||||||
\(231\) | −1.28561 | −0.0845871 | ||||||||
\(232\) | 18.0274 | 1.18355 | ||||||||
\(233\) | 2.38839 | 0.156468 | 0.0782342 | − | 0.996935i | \(-0.475072\pi\) | ||||
0.0782342 | + | 0.996935i | \(0.475072\pi\) | |||||||
\(234\) | 15.8826 | 1.03828 | ||||||||
\(235\) | 14.2835 | 0.931754 | ||||||||
\(236\) | 38.8505 | 2.52895 | ||||||||
\(237\) | 8.11224 | 0.526947 | ||||||||
\(238\) | −7.43052 | −0.481649 | ||||||||
\(239\) | −13.7632 | −0.890269 | −0.445134 | − | 0.895464i | \(-0.646844\pi\) | ||||
−0.445134 | + | 0.895464i | \(0.646844\pi\) | |||||||
\(240\) | 42.5404 | 2.74597 | ||||||||
\(241\) | 23.5847 | 1.51922 | 0.759612 | − | 0.650377i | \(-0.225389\pi\) | ||||
0.759612 | + | 0.650377i | \(0.225389\pi\) | |||||||
\(242\) | 27.9826 | 1.79879 | ||||||||
\(243\) | 22.3135 | 1.43141 | ||||||||
\(244\) | −35.6610 | −2.28296 | ||||||||
\(245\) | 10.9056 | 0.696736 | ||||||||
\(246\) | 40.4815 | 2.58101 | ||||||||
\(247\) | 13.2975 | 0.846101 | ||||||||
\(248\) | 47.0378 | 2.98690 | ||||||||
\(249\) | −28.0101 | −1.77507 | ||||||||
\(250\) | −31.7175 | −2.00599 | ||||||||
\(251\) | 2.30491 | 0.145484 | 0.0727422 | − | 0.997351i | \(-0.476825\pi\) | ||||
0.0727422 | + | 0.997351i | \(0.476825\pi\) | |||||||
\(252\) | 15.4873 | 0.975609 | ||||||||
\(253\) | 0.300459 | 0.0188897 | ||||||||
\(254\) | −53.1324 | −3.33382 | ||||||||
\(255\) | 12.8332 | 0.803643 | ||||||||
\(256\) | −17.9948 | −1.12467 | ||||||||
\(257\) | −20.6002 | −1.28501 | −0.642503 | − | 0.766283i | \(-0.722104\pi\) | ||||
−0.642503 | + | 0.766283i | \(0.722104\pi\) | |||||||
\(258\) | 39.6010 | 2.46545 | ||||||||
\(259\) | −4.98702 | −0.309878 | ||||||||
\(260\) | 16.6132 | 1.03030 | ||||||||
\(261\) | −7.94334 | −0.491681 | ||||||||
\(262\) | −20.5107 | −1.26715 | ||||||||
\(263\) | −17.3874 | −1.07216 | −0.536078 | − | 0.844169i | \(-0.680095\pi\) | ||||
−0.536078 | + | 0.844169i | \(0.680095\pi\) | |||||||
\(264\) | 9.26545 | 0.570249 | ||||||||
\(265\) | −16.3570 | −1.00480 | ||||||||
\(266\) | 18.3800 | 1.12695 | ||||||||
\(267\) | 12.0884 | 0.739798 | ||||||||
\(268\) | 15.0445 | 0.918986 | ||||||||
\(269\) | −9.39296 | −0.572699 | −0.286350 | − | 0.958125i | \(-0.592442\pi\) | ||||
−0.286350 | + | 0.958125i | \(0.592442\pi\) | |||||||
\(270\) | −2.41546 | −0.147000 | ||||||||
\(271\) | −2.74135 | −0.166525 | −0.0832627 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832627 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(272\) | 26.4751 | 1.60529 | ||||||||
\(273\) | 4.78061 | 0.289336 | ||||||||
\(274\) | 26.3920 | 1.59440 | ||||||||
\(275\) | −0.857532 | −0.0517111 | ||||||||
\(276\) | −7.00844 | −0.421858 | ||||||||
\(277\) | −27.9439 | −1.67898 | −0.839492 | − | 0.543372i | \(-0.817147\pi\) | ||||
−0.839492 | + | 0.543372i | \(0.817147\pi\) | |||||||
\(278\) | 2.83766 | 0.170191 | ||||||||
\(279\) | −20.7261 | −1.24084 | ||||||||
\(280\) | 13.3761 | 0.799375 | ||||||||
\(281\) | 31.7298 | 1.89284 | 0.946420 | − | 0.322938i | \(-0.104671\pi\) | ||||
0.946420 | + | 0.322938i | \(0.104671\pi\) | |||||||
\(282\) | −50.8533 | −3.02827 | ||||||||
\(283\) | 4.56782 | 0.271529 | 0.135764 | − | 0.990741i | \(-0.456651\pi\) | ||||
0.135764 | + | 0.990741i | \(0.456651\pi\) | |||||||
\(284\) | −46.1754 | −2.74001 | ||||||||
\(285\) | −31.7438 | −1.88034 | ||||||||
\(286\) | 2.53571 | 0.149940 | ||||||||
\(287\) | 6.29285 | 0.371455 | ||||||||
\(288\) | −31.6202 | −1.86324 | ||||||||
\(289\) | −9.01325 | −0.530191 | ||||||||
\(290\) | −11.7775 | −0.691599 | ||||||||
\(291\) | −23.6009 | −1.38351 | ||||||||
\(292\) | −6.30683 | −0.369079 | ||||||||
\(293\) | 9.06200 | 0.529408 | 0.264704 | − | 0.964330i | \(-0.414726\pi\) | ||||
0.264704 | + | 0.964330i | \(0.414726\pi\) | |||||||
\(294\) | −38.8272 | −2.26445 | ||||||||
\(295\) | −14.7850 | −0.860815 | ||||||||
\(296\) | 35.9416 | 2.08906 | ||||||||
\(297\) | −0.260093 | −0.0150921 | ||||||||
\(298\) | 13.4150 | 0.777109 | ||||||||
\(299\) | −1.11727 | −0.0646133 | ||||||||
\(300\) | 20.0026 | 1.15485 | ||||||||
\(301\) | 6.15597 | 0.354824 | ||||||||
\(302\) | 40.1217 | 2.30874 | ||||||||
\(303\) | 0.584503 | 0.0335788 | ||||||||
\(304\) | −65.4882 | −3.75601 | ||||||||
\(305\) | 13.5712 | 0.777083 | ||||||||
\(306\) | −23.5964 | −1.34892 | ||||||||
\(307\) | 12.5727 | 0.717562 | 0.358781 | − | 0.933422i | \(-0.383193\pi\) | ||||
0.358781 | + | 0.933422i | \(0.383193\pi\) | |||||||
\(308\) | 2.47260 | 0.140889 | ||||||||
\(309\) | 34.6869 | 1.97327 | ||||||||
\(310\) | −30.7304 | −1.74537 | ||||||||
\(311\) | 7.52906 | 0.426934 | 0.213467 | − | 0.976950i | \(-0.431524\pi\) | ||||
0.213467 | + | 0.976950i | \(0.431524\pi\) | |||||||
\(312\) | −34.4540 | −1.95057 | ||||||||
\(313\) | −31.8445 | −1.79996 | −0.899979 | − | 0.435933i | \(-0.856418\pi\) | ||||
−0.899979 | + | 0.435933i | \(0.856418\pi\) | |||||||
\(314\) | 13.1549 | 0.742374 | ||||||||
\(315\) | −5.89387 | −0.332082 | ||||||||
\(316\) | −15.6021 | −0.877689 | ||||||||
\(317\) | 0.582959 | 0.0327423 | 0.0163711 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163711 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(318\) | 58.2354 | 3.26568 | ||||||||
\(319\) | −1.26818 | −0.0710045 | ||||||||
\(320\) | −12.7250 | −0.711352 | ||||||||
\(321\) | −12.0680 | −0.673571 | ||||||||
\(322\) | −1.54430 | −0.0860604 | ||||||||
\(323\) | −19.7558 | −1.09924 | ||||||||
\(324\) | −39.9815 | −2.22120 | ||||||||
\(325\) | 3.18877 | 0.176881 | ||||||||
\(326\) | 15.9111 | 0.881232 | ||||||||
\(327\) | −6.62214 | −0.366205 | ||||||||
\(328\) | −45.3527 | −2.50418 | ||||||||
\(329\) | −7.90514 | −0.435824 | ||||||||
\(330\) | −6.05324 | −0.333220 | ||||||||
\(331\) | −1.13949 | −0.0626320 | −0.0313160 | − | 0.999510i | \(-0.509970\pi\) | ||||
−0.0313160 | + | 0.999510i | \(0.509970\pi\) | |||||||
\(332\) | 53.8714 | 2.95658 | ||||||||
\(333\) | −15.8368 | −0.867852 | ||||||||
\(334\) | −13.4252 | −0.734596 | ||||||||
\(335\) | −5.72533 | −0.312808 | ||||||||
\(336\) | −23.5438 | −1.28442 | ||||||||
\(337\) | −0.152131 | −0.00828712 | −0.00414356 | − | 0.999991i | \(-0.501319\pi\) | ||||
−0.00414356 | + | 0.999991i | \(0.501319\pi\) | |||||||
\(338\) | 24.4471 | 1.32975 | ||||||||
\(339\) | 21.6422 | 1.17544 | ||||||||
\(340\) | −24.6818 | −1.33856 | ||||||||
\(341\) | −3.30899 | −0.179192 | ||||||||
\(342\) | 58.3676 | 3.15616 | ||||||||
\(343\) | −13.0985 | −0.707255 | ||||||||
\(344\) | −44.3663 | −2.39207 | ||||||||
\(345\) | 2.66714 | 0.143594 | ||||||||
\(346\) | −2.39066 | −0.128523 | ||||||||
\(347\) | 0.120036 | 0.00644387 | 0.00322194 | − | 0.999995i | \(-0.498974\pi\) | ||||
0.00322194 | + | 0.999995i | \(0.498974\pi\) | |||||||
\(348\) | 29.5813 | 1.58573 | ||||||||
\(349\) | 13.1587 | 0.704368 | 0.352184 | − | 0.935931i | \(-0.385439\pi\) | ||||
0.352184 | + | 0.935931i | \(0.385439\pi\) | |||||||
\(350\) | 4.40755 | 0.235594 | ||||||||
\(351\) | 0.967166 | 0.0516235 | ||||||||
\(352\) | −5.04827 | −0.269073 | ||||||||
\(353\) | 34.2251 | 1.82162 | 0.910808 | − | 0.412830i | \(-0.135459\pi\) | ||||
0.910808 | + | 0.412830i | \(0.135459\pi\) | |||||||
\(354\) | 52.6387 | 2.79772 | ||||||||
\(355\) | 17.5726 | 0.932655 | ||||||||
\(356\) | −23.2494 | −1.23222 | ||||||||
\(357\) | −7.10244 | −0.375901 | ||||||||
\(358\) | 55.7463 | 2.94629 | ||||||||
\(359\) | −12.1287 | −0.640126 | −0.320063 | − | 0.947396i | \(-0.603704\pi\) | ||||
−0.320063 | + | 0.947396i | \(0.603704\pi\) | |||||||
\(360\) | 42.4773 | 2.23875 | ||||||||
\(361\) | 29.8675 | 1.57198 | ||||||||
\(362\) | 21.7921 | 1.14537 | ||||||||
\(363\) | 26.7471 | 1.40386 | ||||||||
\(364\) | −9.19447 | −0.481921 | ||||||||
\(365\) | 2.40013 | 0.125629 | ||||||||
\(366\) | −48.3172 | −2.52558 | ||||||||
\(367\) | −17.8610 | −0.932334 | −0.466167 | − | 0.884697i | \(-0.654365\pi\) | ||||
−0.466167 | + | 0.884697i | \(0.654365\pi\) | |||||||
\(368\) | 5.50237 | 0.286831 | ||||||||
\(369\) | 19.9836 | 1.04031 | ||||||||
\(370\) | −23.4811 | −1.22072 | ||||||||
\(371\) | 9.05268 | 0.469992 | ||||||||
\(372\) | 77.1848 | 4.00185 | ||||||||
\(373\) | −11.5526 | −0.598168 | −0.299084 | − | 0.954227i | \(-0.596681\pi\) | ||||
−0.299084 | + | 0.954227i | \(0.596681\pi\) | |||||||
\(374\) | −3.76725 | −0.194800 | ||||||||
\(375\) | −30.3171 | −1.56557 | ||||||||
\(376\) | 56.9726 | 2.93814 | ||||||||
\(377\) | 4.71579 | 0.242875 | ||||||||
\(378\) | 1.33683 | 0.0687589 | ||||||||
\(379\) | 11.2799 | 0.579412 | 0.289706 | − | 0.957116i | \(-0.406442\pi\) | ||||
0.289706 | + | 0.957116i | \(0.406442\pi\) | |||||||
\(380\) | 61.0523 | 3.13192 | ||||||||
\(381\) | −50.7865 | −2.60187 | ||||||||
\(382\) | 47.4524 | 2.42788 | ||||||||
\(383\) | 35.8703 | 1.83289 | 0.916444 | − | 0.400162i | \(-0.131046\pi\) | ||||
0.916444 | + | 0.400162i | \(0.131046\pi\) | |||||||
\(384\) | −3.85677 | −0.196815 | ||||||||
\(385\) | −0.940975 | −0.0479565 | ||||||||
\(386\) | 24.9122 | 1.26800 | ||||||||
\(387\) | 19.5490 | 0.993730 | ||||||||
\(388\) | 45.3913 | 2.30439 | ||||||||
\(389\) | −0.603763 | −0.0306120 | −0.0153060 | − | 0.999883i | \(-0.504872\pi\) | ||||
−0.0153060 | + | 0.999883i | \(0.504872\pi\) | |||||||
\(390\) | 22.5092 | 1.13980 | ||||||||
\(391\) | 1.65990 | 0.0839448 | ||||||||
\(392\) | 43.4993 | 2.19705 | ||||||||
\(393\) | −19.6051 | −0.988944 | ||||||||
\(394\) | 70.3278 | 3.54307 | ||||||||
\(395\) | 5.93757 | 0.298751 | ||||||||
\(396\) | 7.85201 | 0.394578 | ||||||||
\(397\) | 14.8741 | 0.746509 | 0.373255 | − | 0.927729i | \(-0.378242\pi\) | ||||
0.373255 | + | 0.927729i | \(0.378242\pi\) | |||||||
\(398\) | 25.5119 | 1.27880 | ||||||||
\(399\) | 17.5684 | 0.879522 | ||||||||
\(400\) | −15.7042 | −0.785210 | ||||||||
\(401\) | −4.22916 | −0.211194 | −0.105597 | − | 0.994409i | \(-0.533675\pi\) | ||||
−0.105597 | + | 0.994409i | \(0.533675\pi\) | |||||||
\(402\) | 20.3838 | 1.01665 | ||||||||
\(403\) | 12.3046 | 0.612937 | ||||||||
\(404\) | −1.12417 | −0.0559293 | ||||||||
\(405\) | 15.2154 | 0.756060 | ||||||||
\(406\) | 6.51821 | 0.323493 | ||||||||
\(407\) | −2.52840 | −0.125328 | ||||||||
\(408\) | 51.1875 | 2.53416 | ||||||||
\(409\) | 29.6035 | 1.46380 | 0.731900 | − | 0.681412i | \(-0.238634\pi\) | ||||
0.731900 | + | 0.681412i | \(0.238634\pi\) | |||||||
\(410\) | 29.6295 | 1.46330 | ||||||||
\(411\) | 25.2267 | 1.24434 | ||||||||
\(412\) | −66.7127 | −3.28670 | ||||||||
\(413\) | 8.18268 | 0.402643 | ||||||||
\(414\) | −4.90409 | −0.241023 | ||||||||
\(415\) | −20.5014 | −1.00637 | ||||||||
\(416\) | 18.7722 | 0.920383 | ||||||||
\(417\) | 2.71237 | 0.132825 | ||||||||
\(418\) | 9.31857 | 0.455786 | ||||||||
\(419\) | −13.5660 | −0.662744 | −0.331372 | − | 0.943500i | \(-0.607512\pi\) | ||||
−0.331372 | + | 0.943500i | \(0.607512\pi\) | |||||||
\(420\) | 21.9490 | 1.07100 | ||||||||
\(421\) | 28.3994 | 1.38410 | 0.692051 | − | 0.721848i | \(-0.256707\pi\) | ||||
0.692051 | + | 0.721848i | \(0.256707\pi\) | |||||||
\(422\) | −31.3441 | −1.52581 | ||||||||
\(423\) | −25.1036 | −1.22058 | ||||||||
\(424\) | −65.2429 | −3.16848 | ||||||||
\(425\) | −4.73749 | −0.229802 | ||||||||
\(426\) | −62.5633 | −3.03120 | ||||||||
\(427\) | −7.51090 | −0.363478 | ||||||||
\(428\) | 23.2102 | 1.12191 | ||||||||
\(429\) | 2.42375 | 0.117020 | ||||||||
\(430\) | 28.9851 | 1.39778 | ||||||||
\(431\) | 5.22646 | 0.251750 | 0.125875 | − | 0.992046i | \(-0.459826\pi\) | ||||
0.125875 | + | 0.992046i | \(0.459826\pi\) | |||||||
\(432\) | −4.76314 | −0.229167 | ||||||||
\(433\) | −16.5974 | −0.797621 | −0.398810 | − | 0.917033i | \(-0.630577\pi\) | ||||
−0.398810 | + | 0.917033i | \(0.630577\pi\) | |||||||
\(434\) | 17.0076 | 0.816390 | ||||||||
\(435\) | −11.2575 | −0.539756 | ||||||||
\(436\) | 12.7363 | 0.609956 | ||||||||
\(437\) | −4.10589 | −0.196411 | ||||||||
\(438\) | −8.54515 | −0.408303 | ||||||||
\(439\) | −19.2735 | −0.919873 | −0.459937 | − | 0.887952i | \(-0.652128\pi\) | ||||
−0.459937 | + | 0.887952i | \(0.652128\pi\) | |||||||
\(440\) | 6.78163 | 0.323302 | ||||||||
\(441\) | −19.1670 | −0.912712 | ||||||||
\(442\) | 14.0087 | 0.666325 | ||||||||
\(443\) | 21.4715 | 1.02014 | 0.510070 | − | 0.860133i | \(-0.329619\pi\) | ||||
0.510070 | + | 0.860133i | \(0.329619\pi\) | |||||||
\(444\) | 58.9769 | 2.79892 | ||||||||
\(445\) | 8.84782 | 0.419427 | ||||||||
\(446\) | −1.68522 | −0.0797977 | ||||||||
\(447\) | 12.8227 | 0.606491 | ||||||||
\(448\) | 7.04261 | 0.332732 | ||||||||
\(449\) | 31.4800 | 1.48564 | 0.742818 | − | 0.669494i | \(-0.233489\pi\) | ||||
0.742818 | + | 0.669494i | \(0.233489\pi\) | |||||||
\(450\) | 13.9967 | 0.659809 | ||||||||
\(451\) | 3.19045 | 0.150232 | ||||||||
\(452\) | −41.6240 | −1.95783 | ||||||||
\(453\) | 38.3502 | 1.80185 | ||||||||
\(454\) | 17.4029 | 0.816760 | ||||||||
\(455\) | 3.49906 | 0.164038 | ||||||||
\(456\) | −126.616 | −5.92935 | ||||||||
\(457\) | 5.20215 | 0.243347 | 0.121673 | − | 0.992570i | \(-0.461174\pi\) | ||||
0.121673 | + | 0.992570i | \(0.461174\pi\) | |||||||
\(458\) | −41.6272 | −1.94511 | ||||||||
\(459\) | −1.43690 | −0.0670686 | ||||||||
\(460\) | −5.12966 | −0.239172 | ||||||||
\(461\) | −1.77185 | −0.0825232 | −0.0412616 | − | 0.999148i | \(-0.513138\pi\) | ||||
−0.0412616 | + | 0.999148i | \(0.513138\pi\) | |||||||
\(462\) | 3.35013 | 0.155862 | ||||||||
\(463\) | −24.0150 | −1.11607 | −0.558035 | − | 0.829817i | \(-0.688445\pi\) | ||||
−0.558035 | + | 0.829817i | \(0.688445\pi\) | |||||||
\(464\) | −23.2245 | −1.07817 | ||||||||
\(465\) | −29.3735 | −1.36217 | ||||||||
\(466\) | −6.22381 | −0.288312 | ||||||||
\(467\) | 24.9213 | 1.15322 | 0.576610 | − | 0.817019i | \(-0.304375\pi\) | ||||
0.576610 | + | 0.817019i | \(0.304375\pi\) | |||||||
\(468\) | −29.1981 | −1.34968 | ||||||||
\(469\) | 3.16866 | 0.146315 | ||||||||
\(470\) | −37.2209 | −1.71687 | ||||||||
\(471\) | 12.5741 | 0.579383 | ||||||||
\(472\) | −58.9728 | −2.71444 | ||||||||
\(473\) | 3.12106 | 0.143506 | ||||||||
\(474\) | −21.1394 | −0.970965 | ||||||||
\(475\) | 11.7185 | 0.537683 | ||||||||
\(476\) | 13.6600 | 0.626106 | ||||||||
\(477\) | 28.7478 | 1.31627 | ||||||||
\(478\) | 35.8651 | 1.64043 | ||||||||
\(479\) | 5.10932 | 0.233451 | 0.116725 | − | 0.993164i | \(-0.462760\pi\) | ||||
0.116725 | + | 0.993164i | \(0.462760\pi\) | |||||||
\(480\) | −44.8129 | −2.04542 | ||||||||
\(481\) | 9.40197 | 0.428693 | ||||||||
\(482\) | −61.4585 | −2.79936 | ||||||||
\(483\) | −1.47611 | −0.0671655 | ||||||||
\(484\) | −51.4422 | −2.33828 | ||||||||
\(485\) | −17.2742 | −0.784379 | ||||||||
\(486\) | −58.1459 | −2.63755 | ||||||||
\(487\) | −12.6127 | −0.571537 | −0.285768 | − | 0.958299i | \(-0.592249\pi\) | ||||
−0.285768 | + | 0.958299i | \(0.592249\pi\) | |||||||
\(488\) | 54.1313 | 2.45041 | ||||||||
\(489\) | 15.2085 | 0.687754 | ||||||||
\(490\) | −28.4186 | −1.28382 | ||||||||
\(491\) | −24.3935 | −1.10087 | −0.550433 | − | 0.834880i | \(-0.685537\pi\) | ||||
−0.550433 | + | 0.834880i | \(0.685537\pi\) | |||||||
\(492\) | −74.4198 | −3.35510 | ||||||||
\(493\) | −7.00614 | −0.315540 | ||||||||
\(494\) | −34.6515 | −1.55905 | ||||||||
\(495\) | −2.98817 | −0.134308 | ||||||||
\(496\) | −60.5984 | −2.72095 | ||||||||
\(497\) | −9.72545 | −0.436246 | ||||||||
\(498\) | 72.9906 | 3.27079 | ||||||||
\(499\) | 3.22212 | 0.144242 | 0.0721210 | − | 0.997396i | \(-0.477023\pi\) | ||||
0.0721210 | + | 0.997396i | \(0.477023\pi\) | |||||||
\(500\) | 58.3083 | 2.60763 | ||||||||
\(501\) | −12.8325 | −0.573312 | ||||||||
\(502\) | −6.00628 | −0.268073 | ||||||||
\(503\) | 5.29761 | 0.236209 | 0.118104 | − | 0.993001i | \(-0.462318\pi\) | ||||
0.118104 | + | 0.993001i | \(0.462318\pi\) | |||||||
\(504\) | −23.5088 | −1.04717 | ||||||||
\(505\) | 0.427814 | 0.0190375 | ||||||||
\(506\) | −0.782954 | −0.0348066 | ||||||||
\(507\) | 23.3677 | 1.03779 | ||||||||
\(508\) | 97.6768 | 4.33371 | ||||||||
\(509\) | 3.76173 | 0.166736 | 0.0833679 | − | 0.996519i | \(-0.473432\pi\) | ||||
0.0833679 | + | 0.996519i | \(0.473432\pi\) | |||||||
\(510\) | −33.4415 | −1.48081 | ||||||||
\(511\) | −1.32834 | −0.0587624 | ||||||||
\(512\) | 43.7952 | 1.93549 | ||||||||
\(513\) | 3.55427 | 0.156925 | ||||||||
\(514\) | 53.6814 | 2.36779 | ||||||||
\(515\) | 25.3882 | 1.11874 | ||||||||
\(516\) | −72.8011 | −3.20489 | ||||||||
\(517\) | −4.00788 | −0.176266 | ||||||||
\(518\) | 12.9955 | 0.570989 | ||||||||
\(519\) | −2.28511 | −0.100305 | ||||||||
\(520\) | −25.2178 | −1.10587 | ||||||||
\(521\) | 32.2817 | 1.41429 | 0.707144 | − | 0.707070i | \(-0.249983\pi\) | ||||
0.707144 | + | 0.707070i | \(0.249983\pi\) | |||||||
\(522\) | 20.6993 | 0.905983 | ||||||||
\(523\) | 24.6596 | 1.07829 | 0.539144 | − | 0.842213i | \(-0.318748\pi\) | ||||
0.539144 | + | 0.842213i | \(0.318748\pi\) | |||||||
\(524\) | 37.7061 | 1.64720 | ||||||||
\(525\) | 4.21295 | 0.183868 | ||||||||
\(526\) | 45.3093 | 1.97558 | ||||||||
\(527\) | −18.2807 | −0.796320 | ||||||||
\(528\) | −11.9366 | −0.519474 | ||||||||
\(529\) | −22.6550 | −0.985001 | ||||||||
\(530\) | 42.6240 | 1.85147 | ||||||||
\(531\) | 25.9850 | 1.12765 | ||||||||
\(532\) | −33.7891 | −1.46494 | ||||||||
\(533\) | −11.8638 | −0.513880 | ||||||||
\(534\) | −31.5007 | −1.36317 | ||||||||
\(535\) | −8.83290 | −0.381880 | ||||||||
\(536\) | −22.8366 | −0.986391 | ||||||||
\(537\) | 53.2850 | 2.29942 | ||||||||
\(538\) | 24.4768 | 1.05527 | ||||||||
\(539\) | −3.06007 | −0.131806 | ||||||||
\(540\) | 4.44051 | 0.191089 | ||||||||
\(541\) | 6.42711 | 0.276323 | 0.138162 | − | 0.990410i | \(-0.455881\pi\) | ||||
0.138162 | + | 0.990410i | \(0.455881\pi\) | |||||||
\(542\) | 7.14359 | 0.306844 | ||||||||
\(543\) | 20.8299 | 0.893897 | ||||||||
\(544\) | −27.8894 | −1.19575 | ||||||||
\(545\) | −4.84692 | −0.207619 | ||||||||
\(546\) | −12.4576 | −0.533137 | ||||||||
\(547\) | 30.3950 | 1.29960 | 0.649798 | − | 0.760107i | \(-0.274854\pi\) | ||||
0.649798 | + | 0.760107i | \(0.274854\pi\) | |||||||
\(548\) | −48.5181 | −2.07259 | ||||||||
\(549\) | −23.8517 | −1.01796 | ||||||||
\(550\) | 2.23461 | 0.0952842 | ||||||||
\(551\) | 17.3302 | 0.738292 | ||||||||
\(552\) | 10.6384 | 0.452800 | ||||||||
\(553\) | −3.28612 | −0.139740 | ||||||||
\(554\) | 72.8179 | 3.09374 | ||||||||
\(555\) | −22.4443 | −0.952709 | ||||||||
\(556\) | −5.21665 | −0.221235 | ||||||||
\(557\) | −46.0868 | −1.95276 | −0.976381 | − | 0.216058i | \(-0.930680\pi\) | ||||
−0.976381 | + | 0.216058i | \(0.930680\pi\) | |||||||
\(558\) | 54.0094 | 2.28640 | ||||||||
\(559\) | −11.6058 | −0.490873 | ||||||||
\(560\) | −17.2323 | −0.728198 | ||||||||
\(561\) | −3.60091 | −0.152031 | ||||||||
\(562\) | −82.6835 | −3.48779 | ||||||||
\(563\) | 14.9732 | 0.631044 | 0.315522 | − | 0.948918i | \(-0.397820\pi\) | ||||
0.315522 | + | 0.948918i | \(0.397820\pi\) | |||||||
\(564\) | 93.4870 | 3.93651 | ||||||||
\(565\) | 15.8405 | 0.666414 | ||||||||
\(566\) | −11.9031 | −0.500326 | ||||||||
\(567\) | −8.42090 | −0.353644 | ||||||||
\(568\) | 70.0916 | 2.94098 | ||||||||
\(569\) | 0.144784 | 0.00606967 | 0.00303483 | − | 0.999995i | \(-0.499034\pi\) | ||||
0.00303483 | + | 0.999995i | \(0.499034\pi\) | |||||||
\(570\) | 82.7200 | 3.46476 | ||||||||
\(571\) | 16.7381 | 0.700469 | 0.350234 | − | 0.936662i | \(-0.386102\pi\) | ||||
0.350234 | + | 0.936662i | \(0.386102\pi\) | |||||||
\(572\) | −4.66156 | −0.194910 | ||||||||
\(573\) | 45.3572 | 1.89483 | ||||||||
\(574\) | −16.3983 | −0.684452 | ||||||||
\(575\) | −0.984601 | −0.0410607 | ||||||||
\(576\) | 22.3646 | 0.931858 | ||||||||
\(577\) | 18.2490 | 0.759717 | 0.379858 | − | 0.925045i | \(-0.375973\pi\) | ||||
0.379858 | + | 0.925045i | \(0.375973\pi\) | |||||||
\(578\) | 23.4873 | 0.976944 | ||||||||
\(579\) | 23.8122 | 0.989603 | ||||||||
\(580\) | 21.6514 | 0.899024 | ||||||||
\(581\) | 11.3464 | 0.470727 | ||||||||
\(582\) | 61.5008 | 2.54929 | ||||||||
\(583\) | 4.58968 | 0.190085 | ||||||||
\(584\) | 9.57340 | 0.396150 | ||||||||
\(585\) | 11.1116 | 0.459410 | ||||||||
\(586\) | −23.6144 | −0.975500 | ||||||||
\(587\) | 23.0261 | 0.950390 | 0.475195 | − | 0.879881i | \(-0.342378\pi\) | ||||
0.475195 | + | 0.879881i | \(0.342378\pi\) | |||||||
\(588\) | 71.3785 | 2.94360 | ||||||||
\(589\) | 45.2187 | 1.86320 | ||||||||
\(590\) | 38.5277 | 1.58616 | ||||||||
\(591\) | 67.2227 | 2.76517 | ||||||||
\(592\) | −46.3032 | −1.90305 | ||||||||
\(593\) | −2.49751 | −0.102560 | −0.0512801 | − | 0.998684i | \(-0.516330\pi\) | ||||
−0.0512801 | + | 0.998684i | \(0.516330\pi\) | |||||||
\(594\) | 0.677766 | 0.0278091 | ||||||||
\(595\) | −5.19847 | −0.213117 | ||||||||
\(596\) | −24.6616 | −1.01018 | ||||||||
\(597\) | 24.3855 | 0.998033 | ||||||||
\(598\) | 2.91145 | 0.119058 | ||||||||
\(599\) | −25.7810 | −1.05338 | −0.526692 | − | 0.850056i | \(-0.676568\pi\) | ||||
−0.526692 | + | 0.850056i | \(0.676568\pi\) | |||||||
\(600\) | −30.3628 | −1.23956 | ||||||||
\(601\) | −1.21827 | −0.0496943 | −0.0248471 | − | 0.999691i | \(-0.507910\pi\) | ||||
−0.0248471 | + | 0.999691i | \(0.507910\pi\) | |||||||
\(602\) | −16.0416 | −0.653808 | ||||||||
\(603\) | 10.0624 | 0.409773 | ||||||||
\(604\) | −73.7583 | −3.00118 | ||||||||
\(605\) | 19.5769 | 0.795915 | ||||||||
\(606\) | −1.52314 | −0.0618732 | ||||||||
\(607\) | 17.0989 | 0.694023 | 0.347011 | − | 0.937861i | \(-0.387197\pi\) | ||||
0.347011 | + | 0.937861i | \(0.387197\pi\) | |||||||
\(608\) | 68.9866 | 2.79778 | ||||||||
\(609\) | 6.23041 | 0.252469 | ||||||||
\(610\) | −35.3646 | −1.43187 | ||||||||
\(611\) | 14.9035 | 0.602930 | ||||||||
\(612\) | 43.3789 | 1.75349 | ||||||||
\(613\) | 5.42080 | 0.218944 | 0.109472 | − | 0.993990i | \(-0.465084\pi\) | ||||
0.109472 | + | 0.993990i | \(0.465084\pi\) | |||||||
\(614\) | −32.7628 | −1.32220 | ||||||||
\(615\) | 28.3213 | 1.14202 | ||||||||
\(616\) | −3.75326 | −0.151223 | ||||||||
\(617\) | −30.3190 | −1.22060 | −0.610298 | − | 0.792172i | \(-0.708950\pi\) | ||||
−0.610298 | + | 0.792172i | \(0.708950\pi\) | |||||||
\(618\) | −90.3893 | −3.63599 | ||||||||
\(619\) | 33.8769 | 1.36163 | 0.680814 | − | 0.732457i | \(-0.261626\pi\) | ||||
0.680814 | + | 0.732457i | \(0.261626\pi\) | |||||||
\(620\) | 56.4937 | 2.26884 | ||||||||
\(621\) | −0.298633 | −0.0119837 | ||||||||
\(622\) | −19.6197 | −0.786679 | ||||||||
\(623\) | −4.89678 | −0.196186 | ||||||||
\(624\) | 44.3868 | 1.77689 | ||||||||
\(625\) | −13.8082 | −0.552326 | ||||||||
\(626\) | 82.9825 | 3.31665 | ||||||||
\(627\) | 8.90713 | 0.355717 | ||||||||
\(628\) | −24.1835 | −0.965027 | ||||||||
\(629\) | −13.9683 | −0.556952 | ||||||||
\(630\) | 15.3586 | 0.611902 | ||||||||
\(631\) | 12.6245 | 0.502574 | 0.251287 | − | 0.967913i | \(-0.419146\pi\) | ||||
0.251287 | + | 0.967913i | \(0.419146\pi\) | |||||||
\(632\) | 23.6831 | 0.942065 | ||||||||
\(633\) | −29.9602 | −1.19081 | ||||||||
\(634\) | −1.51911 | −0.0603317 | ||||||||
\(635\) | −37.1720 | −1.47512 | ||||||||
\(636\) | −107.058 | −4.24512 | ||||||||
\(637\) | 11.3790 | 0.450852 | ||||||||
\(638\) | 3.30471 | 0.130835 | ||||||||
\(639\) | −30.8842 | −1.22176 | ||||||||
\(640\) | −2.82287 | −0.111584 | ||||||||
\(641\) | −19.9617 | −0.788441 | −0.394220 | − | 0.919016i | \(-0.628985\pi\) | ||||
−0.394220 | + | 0.919016i | \(0.628985\pi\) | |||||||
\(642\) | 31.4476 | 1.24114 | ||||||||
\(643\) | 33.2942 | 1.31299 | 0.656497 | − | 0.754328i | \(-0.272037\pi\) | ||||
0.656497 | + | 0.754328i | \(0.272037\pi\) | |||||||
\(644\) | 2.83899 | 0.111872 | ||||||||
\(645\) | 27.7053 | 1.09089 | ||||||||
\(646\) | 51.4810 | 2.02549 | ||||||||
\(647\) | 20.2749 | 0.797089 | 0.398544 | − | 0.917149i | \(-0.369516\pi\) | ||||
0.398544 | + | 0.917149i | \(0.369516\pi\) | |||||||
\(648\) | 60.6897 | 2.38411 | ||||||||
\(649\) | 4.14859 | 0.162846 | ||||||||
\(650\) | −8.30951 | −0.325926 | ||||||||
\(651\) | 16.2566 | 0.637148 | ||||||||
\(652\) | −29.2503 | −1.14553 | ||||||||
\(653\) | −9.38264 | −0.367171 | −0.183585 | − | 0.983004i | \(-0.558770\pi\) | ||||
−0.183585 | + | 0.983004i | \(0.558770\pi\) | |||||||
\(654\) | 17.2564 | 0.674779 | ||||||||
\(655\) | −14.3495 | −0.560680 | ||||||||
\(656\) | 58.4275 | 2.28121 | ||||||||
\(657\) | −4.21830 | −0.164571 | ||||||||
\(658\) | 20.5997 | 0.803061 | ||||||||
\(659\) | 20.3747 | 0.793684 | 0.396842 | − | 0.917887i | \(-0.370106\pi\) | ||||
0.396842 | + | 0.917887i | \(0.370106\pi\) | |||||||
\(660\) | 11.1281 | 0.433159 | ||||||||
\(661\) | −26.1158 | −1.01579 | −0.507893 | − | 0.861420i | \(-0.669576\pi\) | ||||
−0.507893 | + | 0.861420i | \(0.669576\pi\) | |||||||
\(662\) | 2.96936 | 0.115407 | ||||||||
\(663\) | 13.3902 | 0.520031 | ||||||||
\(664\) | −81.7736 | −3.17343 | ||||||||
\(665\) | 12.8588 | 0.498643 | ||||||||
\(666\) | 41.2686 | 1.59913 | ||||||||
\(667\) | −1.45610 | −0.0563803 | ||||||||
\(668\) | 24.6805 | 0.954916 | ||||||||
\(669\) | −1.61082 | −0.0622778 | ||||||||
\(670\) | 14.9194 | 0.576388 | ||||||||
\(671\) | −3.80800 | −0.147006 | ||||||||
\(672\) | 24.8015 | 0.956738 | ||||||||
\(673\) | −11.0833 | −0.427229 | −0.213614 | − | 0.976918i | \(-0.568524\pi\) | ||||
−0.213614 | + | 0.976918i | \(0.568524\pi\) | |||||||
\(674\) | 0.396433 | 0.0152700 | ||||||||
\(675\) | 0.852322 | 0.0328059 | ||||||||
\(676\) | −44.9427 | −1.72856 | ||||||||
\(677\) | 30.0550 | 1.15511 | 0.577554 | − | 0.816353i | \(-0.304007\pi\) | ||||
0.577554 | + | 0.816353i | \(0.304007\pi\) | |||||||
\(678\) | −56.3966 | −2.16590 | ||||||||
\(679\) | 9.56030 | 0.366891 | ||||||||
\(680\) | 37.4655 | 1.43674 | ||||||||
\(681\) | 16.6345 | 0.637437 | ||||||||
\(682\) | 8.62278 | 0.330183 | ||||||||
\(683\) | 12.2145 | 0.467375 | 0.233688 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233688 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(684\) | −107.301 | −4.10275 | ||||||||
\(685\) | 18.4641 | 0.705478 | ||||||||
\(686\) | 34.1330 | 1.30320 | ||||||||
\(687\) | −39.7893 | −1.51806 | ||||||||
\(688\) | 57.1567 | 2.17908 | ||||||||
\(689\) | −17.0669 | −0.650198 | ||||||||
\(690\) | −6.95020 | −0.264590 | ||||||||
\(691\) | 34.3195 | 1.30558 | 0.652788 | − | 0.757541i | \(-0.273599\pi\) | ||||
0.652788 | + | 0.757541i | \(0.273599\pi\) | |||||||
\(692\) | 4.39491 | 0.167070 | ||||||||
\(693\) | 1.65379 | 0.0628222 | ||||||||
\(694\) | −0.312798 | −0.0118736 | ||||||||
\(695\) | 1.98525 | 0.0753050 | ||||||||
\(696\) | −44.9027 | −1.70203 | ||||||||
\(697\) | 17.6258 | 0.667626 | ||||||||
\(698\) | −34.2897 | −1.29789 | ||||||||
\(699\) | −5.94901 | −0.225012 | ||||||||
\(700\) | −8.10269 | −0.306253 | ||||||||
\(701\) | 18.2364 | 0.688778 | 0.344389 | − | 0.938827i | \(-0.388086\pi\) | ||||
0.344389 | + | 0.938827i | \(0.388086\pi\) | |||||||
\(702\) | −2.52031 | −0.0951228 | ||||||||
\(703\) | 34.5516 | 1.30314 | ||||||||
\(704\) | 3.57058 | 0.134571 | ||||||||
\(705\) | −35.5775 | −1.33993 | ||||||||
\(706\) | −89.1859 | −3.35656 | ||||||||
\(707\) | −0.236771 | −0.00890470 | ||||||||
\(708\) | −96.7692 | −3.63681 | ||||||||
\(709\) | 11.0432 | 0.414737 | 0.207369 | − | 0.978263i | \(-0.433510\pi\) | ||||
0.207369 | + | 0.978263i | \(0.433510\pi\) | |||||||
\(710\) | −45.7917 | −1.71853 | ||||||||
\(711\) | −10.4354 | −0.391359 | ||||||||
\(712\) | 35.2913 | 1.32260 | ||||||||
\(713\) | −3.79931 | −0.142285 | ||||||||
\(714\) | 18.5080 | 0.692645 | ||||||||
\(715\) | 1.77401 | 0.0663442 | ||||||||
\(716\) | −102.482 | −3.82994 | ||||||||
\(717\) | 34.2815 | 1.28027 | ||||||||
\(718\) | 31.6056 | 1.17951 | ||||||||
\(719\) | −20.7963 | −0.775573 | −0.387786 | − | 0.921749i | \(-0.626760\pi\) | ||||
−0.387786 | + | 0.921749i | \(0.626760\pi\) | |||||||
\(720\) | −54.7231 | −2.03941 | ||||||||
\(721\) | −14.0510 | −0.523287 | ||||||||
\(722\) | −77.8307 | −2.89656 | ||||||||
\(723\) | −58.7449 | −2.18475 | ||||||||
\(724\) | −40.0618 | −1.48889 | ||||||||
\(725\) | 4.15582 | 0.154343 | ||||||||
\(726\) | −69.6993 | −2.58678 | ||||||||
\(727\) | 34.2227 | 1.26925 | 0.634626 | − | 0.772820i | \(-0.281154\pi\) | ||||
0.634626 | + | 0.772820i | \(0.281154\pi\) | |||||||
\(728\) | 13.9567 | 0.517269 | ||||||||
\(729\) | −30.5408 | −1.13114 | ||||||||
\(730\) | −6.25443 | −0.231487 | ||||||||
\(731\) | 17.2425 | 0.637735 | ||||||||
\(732\) | 88.8246 | 3.28305 | ||||||||
\(733\) | 19.0539 | 0.703770 | 0.351885 | − | 0.936043i | \(-0.385541\pi\) | ||||
0.351885 | + | 0.936043i | \(0.385541\pi\) | |||||||
\(734\) | 46.5432 | 1.71794 | ||||||||
\(735\) | −27.1639 | −1.00195 | ||||||||
\(736\) | −5.79631 | −0.213655 | ||||||||
\(737\) | 1.60650 | 0.0591761 | ||||||||
\(738\) | −52.0746 | −1.91689 | ||||||||
\(739\) | −19.3324 | −0.711154 | −0.355577 | − | 0.934647i | \(-0.615716\pi\) | ||||
−0.355577 | + | 0.934647i | \(0.615716\pi\) | |||||||
\(740\) | 43.1668 | 1.58684 | ||||||||
\(741\) | −33.1216 | −1.21675 | ||||||||
\(742\) | −23.5901 | −0.866018 | ||||||||
\(743\) | −3.84534 | −0.141072 | −0.0705360 | − | 0.997509i | \(-0.522471\pi\) | ||||
−0.0705360 | + | 0.997509i | \(0.522471\pi\) | |||||||
\(744\) | −117.162 | −4.29537 | ||||||||
\(745\) | 9.38525 | 0.343849 | ||||||||
\(746\) | 30.1044 | 1.10220 | ||||||||
\(747\) | 36.0317 | 1.31833 | ||||||||
\(748\) | 6.92558 | 0.253224 | ||||||||
\(749\) | 4.88853 | 0.178623 | ||||||||
\(750\) | 79.0022 | 2.88475 | ||||||||
\(751\) | 30.3013 | 1.10571 | 0.552856 | − | 0.833277i | \(-0.313538\pi\) | ||||
0.552856 | + | 0.833277i | \(0.313538\pi\) | |||||||
\(752\) | −73.3973 | −2.67652 | ||||||||
\(753\) | −5.74108 | −0.209217 | ||||||||
\(754\) | −12.2887 | −0.447528 | ||||||||
\(755\) | 28.0695 | 1.02156 | ||||||||
\(756\) | −2.45758 | −0.0893812 | ||||||||
\(757\) | 4.48076 | 0.162856 | 0.0814280 | − | 0.996679i | \(-0.474052\pi\) | ||||
0.0814280 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(758\) | −29.3940 | −1.06764 | ||||||||
\(759\) | −0.748385 | −0.0271646 | ||||||||
\(760\) | −92.6738 | −3.36163 | ||||||||
\(761\) | 12.5828 | 0.456126 | 0.228063 | − | 0.973646i | \(-0.426761\pi\) | ||||
0.228063 | + | 0.973646i | \(0.426761\pi\) | |||||||
\(762\) | 132.343 | 4.79427 | ||||||||
\(763\) | 2.68251 | 0.0971132 | ||||||||
\(764\) | −87.2348 | −3.15605 | ||||||||
\(765\) | −16.5083 | −0.596859 | ||||||||
\(766\) | −93.4733 | −3.37733 | ||||||||
\(767\) | −15.4267 | −0.557026 | ||||||||
\(768\) | 44.8216 | 1.61736 | ||||||||
\(769\) | 6.77960 | 0.244478 | 0.122239 | − | 0.992501i | \(-0.460992\pi\) | ||||
0.122239 | + | 0.992501i | \(0.460992\pi\) | |||||||
\(770\) | 2.45205 | 0.0883659 | ||||||||
\(771\) | 51.3112 | 1.84793 | ||||||||
\(772\) | −45.7977 | −1.64830 | ||||||||
\(773\) | −29.6637 | −1.06693 | −0.533465 | − | 0.845822i | \(-0.679110\pi\) | ||||
−0.533465 | + | 0.845822i | \(0.679110\pi\) | |||||||
\(774\) | −50.9420 | −1.83107 | ||||||||
\(775\) | 10.8435 | 0.389511 | ||||||||
\(776\) | −68.9013 | −2.47341 | ||||||||
\(777\) | 12.4217 | 0.445626 | ||||||||
\(778\) | 1.57332 | 0.0564064 | ||||||||
\(779\) | −43.5988 | −1.56209 | ||||||||
\(780\) | −41.3802 | −1.48165 | ||||||||
\(781\) | −4.93077 | −0.176437 | ||||||||
\(782\) | −4.32548 | −0.154679 | ||||||||
\(783\) | 1.26048 | 0.0450457 | ||||||||
\(784\) | −56.0398 | −2.00142 | ||||||||
\(785\) | 9.20330 | 0.328480 | ||||||||
\(786\) | 51.0881 | 1.82225 | ||||||||
\(787\) | 12.6089 | 0.449458 | 0.224729 | − | 0.974421i | \(-0.427850\pi\) | ||||
0.224729 | + | 0.974421i | \(0.427850\pi\) | |||||||
\(788\) | −129.288 | −4.60570 | ||||||||
\(789\) | 43.3088 | 1.54183 | ||||||||
\(790\) | −15.4725 | −0.550487 | ||||||||
\(791\) | −8.76684 | −0.311713 | ||||||||
\(792\) | −11.9189 | −0.423519 | ||||||||
\(793\) | 14.1602 | 0.502844 | ||||||||
\(794\) | −38.7599 | −1.37554 | ||||||||
\(795\) | 40.7421 | 1.44497 | ||||||||
\(796\) | −46.9003 | −1.66234 | ||||||||
\(797\) | −11.4369 | −0.405115 | −0.202558 | − | 0.979270i | \(-0.564925\pi\) | ||||
−0.202558 | + | 0.979270i | \(0.564925\pi\) | |||||||
\(798\) | −45.7810 | −1.62063 | ||||||||
\(799\) | −22.1418 | −0.783319 | ||||||||
\(800\) | 16.5431 | 0.584888 | ||||||||
\(801\) | −15.5503 | −0.549442 | ||||||||
\(802\) | 11.0206 | 0.389151 | ||||||||
\(803\) | −0.673465 | −0.0237661 | ||||||||
\(804\) | −37.4728 | −1.32157 | ||||||||
\(805\) | −1.08041 | −0.0380794 | ||||||||
\(806\) | −32.0642 | −1.12941 | ||||||||
\(807\) | 23.3961 | 0.823581 | ||||||||
\(808\) | 1.70642 | 0.0600316 | ||||||||
\(809\) | 12.1518 | 0.427235 | 0.213617 | − | 0.976917i | \(-0.431475\pi\) | ||||
0.213617 | + | 0.976917i | \(0.431475\pi\) | |||||||
\(810\) | −39.6493 | −1.39314 | ||||||||
\(811\) | −51.7254 | −1.81632 | −0.908162 | − | 0.418618i | \(-0.862515\pi\) | ||||
−0.908162 | + | 0.418618i | \(0.862515\pi\) | |||||||
\(812\) | −11.9828 | −0.420515 | ||||||||
\(813\) | 6.82818 | 0.239475 | ||||||||
\(814\) | 6.58867 | 0.230933 | ||||||||
\(815\) | 11.1315 | 0.389921 | ||||||||
\(816\) | −65.9444 | −2.30852 | ||||||||
\(817\) | −42.6505 | −1.49215 | ||||||||
\(818\) | −77.1428 | −2.69724 | ||||||||
\(819\) | −6.14968 | −0.214887 | ||||||||
\(820\) | −54.4699 | −1.90217 | ||||||||
\(821\) | −18.1746 | −0.634296 | −0.317148 | − | 0.948376i | \(-0.602725\pi\) | ||||
−0.317148 | + | 0.948376i | \(0.602725\pi\) | |||||||
\(822\) | −65.7374 | −2.29286 | ||||||||
\(823\) | 38.8847 | 1.35544 | 0.677718 | − | 0.735322i | \(-0.262969\pi\) | ||||
0.677718 | + | 0.735322i | \(0.262969\pi\) | |||||||
\(824\) | 101.266 | 3.52777 | ||||||||
\(825\) | 2.13595 | 0.0743642 | ||||||||
\(826\) | −21.3230 | −0.741920 | ||||||||
\(827\) | 51.0148 | 1.77396 | 0.886980 | − | 0.461808i | \(-0.152799\pi\) | ||||
0.886980 | + | 0.461808i | \(0.152799\pi\) | |||||||
\(828\) | 9.01551 | 0.313311 | ||||||||
\(829\) | −16.7616 | −0.582154 | −0.291077 | − | 0.956700i | \(-0.594014\pi\) | ||||
−0.291077 | + | 0.956700i | \(0.594014\pi\) | |||||||
\(830\) | 53.4238 | 1.85437 | ||||||||
\(831\) | 69.6028 | 2.41449 | ||||||||
\(832\) | −13.2774 | −0.460310 | ||||||||
\(833\) | −16.9055 | −0.585741 | ||||||||
\(834\) | −7.06806 | −0.244747 | ||||||||
\(835\) | −9.39242 | −0.325038 | ||||||||
\(836\) | −17.1309 | −0.592486 | ||||||||
\(837\) | 3.28888 | 0.113680 | ||||||||
\(838\) | 35.3512 | 1.22119 | ||||||||
\(839\) | 36.1741 | 1.24887 | 0.624434 | − | 0.781078i | \(-0.285330\pi\) | ||||
0.624434 | + | 0.781078i | \(0.285330\pi\) | |||||||
\(840\) | −33.3173 | −1.14956 | ||||||||
\(841\) | −22.8541 | −0.788072 | ||||||||
\(842\) | −74.0050 | −2.55038 | ||||||||
\(843\) | −79.0328 | −2.72203 | ||||||||
\(844\) | 57.6219 | 1.98343 | ||||||||
\(845\) | 17.1034 | 0.588376 | ||||||||
\(846\) | 65.4167 | 2.24907 | ||||||||
\(847\) | −10.8347 | −0.372286 | ||||||||
\(848\) | 84.0519 | 2.88635 | ||||||||
\(849\) | −11.3776 | −0.390477 | ||||||||
\(850\) | 12.3453 | 0.423439 | ||||||||
\(851\) | −2.90306 | −0.0995155 | ||||||||
\(852\) | 115.014 | 3.94032 | ||||||||
\(853\) | −13.6631 | −0.467817 | −0.233909 | − | 0.972259i | \(-0.575152\pi\) | ||||
−0.233909 | + | 0.972259i | \(0.575152\pi\) | |||||||
\(854\) | 19.5724 | 0.669753 | ||||||||
\(855\) | 40.8346 | 1.39651 | ||||||||
\(856\) | −35.2318 | −1.20420 | ||||||||
\(857\) | −56.4956 | −1.92985 | −0.964927 | − | 0.262517i | \(-0.915447\pi\) | ||||
−0.964927 | + | 0.262517i | \(0.915447\pi\) | |||||||
\(858\) | −6.31597 | −0.215624 | ||||||||
\(859\) | −51.2510 | −1.74866 | −0.874331 | − | 0.485330i | \(-0.838699\pi\) | ||||
−0.874331 | + | 0.485330i | \(0.838699\pi\) | |||||||
\(860\) | −53.2851 | −1.81701 | ||||||||
\(861\) | −15.6743 | −0.534178 | ||||||||
\(862\) | −13.6194 | −0.463880 | ||||||||
\(863\) | 31.5105 | 1.07263 | 0.536315 | − | 0.844018i | \(-0.319816\pi\) | ||||
0.536315 | + | 0.844018i | \(0.319816\pi\) | |||||||
\(864\) | 5.01759 | 0.170702 | ||||||||
\(865\) | −1.67253 | −0.0568678 | ||||||||
\(866\) | 43.2506 | 1.46972 | ||||||||
\(867\) | 22.4503 | 0.762452 | ||||||||
\(868\) | −31.2661 | −1.06124 | ||||||||
\(869\) | −1.66605 | −0.0565168 | ||||||||
\(870\) | 29.3355 | 0.994567 | ||||||||
\(871\) | −5.97383 | −0.202416 | ||||||||
\(872\) | −19.3329 | −0.654694 | ||||||||
\(873\) | 30.3598 | 1.02752 | ||||||||
\(874\) | 10.6994 | 0.361912 | ||||||||
\(875\) | 12.2809 | 0.415169 | ||||||||
\(876\) | 15.7091 | 0.530762 | ||||||||
\(877\) | −37.4596 | −1.26492 | −0.632461 | − | 0.774592i | \(-0.717955\pi\) | ||||
−0.632461 | + | 0.774592i | \(0.717955\pi\) | |||||||
\(878\) | 50.2241 | 1.69498 | ||||||||
\(879\) | −22.5717 | −0.761325 | ||||||||
\(880\) | −8.73672 | −0.294515 | ||||||||
\(881\) | 10.6576 | 0.359063 | 0.179532 | − | 0.983752i | \(-0.442542\pi\) | ||||
0.179532 | + | 0.983752i | \(0.442542\pi\) | |||||||
\(882\) | 49.9465 | 1.68179 | ||||||||
\(883\) | 18.6573 | 0.627868 | 0.313934 | − | 0.949445i | \(-0.398353\pi\) | ||||
0.313934 | + | 0.949445i | \(0.398353\pi\) | |||||||
\(884\) | −25.7531 | −0.866170 | ||||||||
\(885\) | 36.8266 | 1.23791 | ||||||||
\(886\) | −55.9518 | −1.87974 | ||||||||
\(887\) | −54.8453 | −1.84152 | −0.920762 | − | 0.390125i | \(-0.872432\pi\) | ||||
−0.920762 | + | 0.390125i | \(0.872432\pi\) | |||||||
\(888\) | −89.5236 | −3.00421 | ||||||||
\(889\) | 20.5726 | 0.689984 | ||||||||
\(890\) | −23.0562 | −0.772847 | ||||||||
\(891\) | −4.26936 | −0.143029 | ||||||||
\(892\) | 3.09806 | 0.103731 | ||||||||
\(893\) | 54.7693 | 1.83278 | ||||||||
\(894\) | −33.4141 | −1.11754 | ||||||||
\(895\) | 39.0007 | 1.30365 | ||||||||
\(896\) | 1.56231 | 0.0521930 | ||||||||
\(897\) | 2.78290 | 0.0929184 | ||||||||
\(898\) | −82.0327 | −2.73747 | ||||||||
\(899\) | 16.0362 | 0.534837 | ||||||||
\(900\) | −25.7310 | −0.857700 | ||||||||
\(901\) | 25.3559 | 0.844729 | ||||||||
\(902\) | −8.31388 | −0.276822 | ||||||||
\(903\) | −15.3334 | −0.510262 | ||||||||
\(904\) | 63.1829 | 2.10143 | ||||||||
\(905\) | 15.2460 | 0.506793 | ||||||||
\(906\) | −99.9355 | −3.32013 | ||||||||
\(907\) | 5.91976 | 0.196562 | 0.0982812 | − | 0.995159i | \(-0.468666\pi\) | ||||
0.0982812 | + | 0.995159i | \(0.468666\pi\) | |||||||
\(908\) | −31.9929 | −1.06172 | ||||||||
\(909\) | −0.751893 | −0.0249387 | ||||||||
\(910\) | −9.11807 | −0.302261 | ||||||||
\(911\) | 18.5577 | 0.614844 | 0.307422 | − | 0.951573i | \(-0.400534\pi\) | ||||
0.307422 | + | 0.951573i | \(0.400534\pi\) | |||||||
\(912\) | 163.119 | 5.40140 | ||||||||
\(913\) | 5.75257 | 0.190382 | ||||||||
\(914\) | −13.5561 | −0.448396 | ||||||||
\(915\) | −33.8032 | −1.11750 | ||||||||
\(916\) | 76.5261 | 2.52849 | ||||||||
\(917\) | 7.94164 | 0.262256 | ||||||||
\(918\) | 3.74436 | 0.123582 | ||||||||
\(919\) | −15.6685 | −0.516856 | −0.258428 | − | 0.966031i | \(-0.583205\pi\) | ||||
−0.258428 | + | 0.966031i | \(0.583205\pi\) | |||||||
\(920\) | 7.78653 | 0.256714 | ||||||||
\(921\) | −31.3162 | −1.03190 | ||||||||
\(922\) | 4.61720 | 0.152059 | ||||||||
\(923\) | 18.3353 | 0.603513 | ||||||||
\(924\) | −6.15877 | −0.202609 | ||||||||
\(925\) | 8.28555 | 0.272427 | ||||||||
\(926\) | 62.5798 | 2.05650 | ||||||||
\(927\) | −44.6205 | −1.46553 | ||||||||
\(928\) | 24.4652 | 0.803109 | ||||||||
\(929\) | −17.9017 | −0.587337 | −0.293669 | − | 0.955907i | \(-0.594876\pi\) | ||||
−0.293669 | + | 0.955907i | \(0.594876\pi\) | |||||||
\(930\) | 76.5435 | 2.50996 | ||||||||
\(931\) | 41.8171 | 1.37050 | ||||||||
\(932\) | 11.4416 | 0.374783 | ||||||||
\(933\) | −18.7535 | −0.613960 | ||||||||
\(934\) | −64.9415 | −2.12495 | ||||||||
\(935\) | −2.63561 | −0.0861935 | ||||||||
\(936\) | 44.3210 | 1.44868 | ||||||||
\(937\) | 13.3190 | 0.435114 | 0.217557 | − | 0.976048i | \(-0.430191\pi\) | ||||
0.217557 | + | 0.976048i | \(0.430191\pi\) | |||||||
\(938\) | −8.25709 | −0.269604 | ||||||||
\(939\) | 79.3186 | 2.58846 | ||||||||
\(940\) | 68.4256 | 2.23180 | ||||||||
\(941\) | 24.9670 | 0.813901 | 0.406950 | − | 0.913450i | \(-0.366592\pi\) | ||||
0.406950 | + | 0.913450i | \(0.366592\pi\) | |||||||
\(942\) | −32.7663 | −1.06758 | ||||||||
\(943\) | 3.66321 | 0.119290 | ||||||||
\(944\) | 75.9741 | 2.47275 | ||||||||
\(945\) | 0.935258 | 0.0304239 | ||||||||
\(946\) | −8.13305 | −0.264428 | ||||||||
\(947\) | 55.4434 | 1.80167 | 0.900835 | − | 0.434162i | \(-0.142955\pi\) | ||||
0.900835 | + | 0.434162i | \(0.142955\pi\) | |||||||
\(948\) | 38.8619 | 1.26218 | ||||||||
\(949\) | 2.50431 | 0.0812933 | ||||||||
\(950\) | −30.5369 | −0.990748 | ||||||||
\(951\) | −1.45204 | −0.0470856 | ||||||||
\(952\) | −20.7351 | −0.672029 | ||||||||
\(953\) | −14.5306 | −0.470692 | −0.235346 | − | 0.971912i | \(-0.575622\pi\) | ||||
−0.235346 | + | 0.971912i | \(0.575622\pi\) | |||||||
\(954\) | −74.9128 | −2.42539 | ||||||||
\(955\) | 33.1982 | 1.07427 | ||||||||
\(956\) | −65.9331 | −2.13243 | ||||||||
\(957\) | 3.15879 | 0.102109 | ||||||||
\(958\) | −13.3142 | −0.430162 | ||||||||
\(959\) | −10.2189 | −0.329985 | ||||||||
\(960\) | 31.6957 | 1.02297 | ||||||||
\(961\) | 10.8423 | 0.349753 | ||||||||
\(962\) | −24.5003 | −0.789920 | ||||||||
\(963\) | 15.5241 | 0.500256 | ||||||||
\(964\) | 112.983 | 3.63894 | ||||||||
\(965\) | 17.4288 | 0.561054 | ||||||||
\(966\) | 3.84655 | 0.123761 | ||||||||
\(967\) | −8.27100 | −0.265977 | −0.132989 | − | 0.991118i | \(-0.542457\pi\) | ||||
−0.132989 | + | 0.991118i | \(0.542457\pi\) | |||||||
\(968\) | 78.0863 | 2.50979 | ||||||||
\(969\) | 49.2080 | 1.58079 | ||||||||
\(970\) | 45.0141 | 1.44532 | ||||||||
\(971\) | −47.7019 | −1.53083 | −0.765414 | − | 0.643538i | \(-0.777466\pi\) | ||||
−0.765414 | + | 0.643538i | \(0.777466\pi\) | |||||||
\(972\) | 106.893 | 3.42861 | ||||||||
\(973\) | −1.09873 | −0.0352236 | ||||||||
\(974\) | 32.8670 | 1.05313 | ||||||||
\(975\) | −7.94262 | −0.254368 | ||||||||
\(976\) | −69.7368 | −2.23222 | ||||||||
\(977\) | −14.1422 | −0.452448 | −0.226224 | − | 0.974075i | \(-0.572638\pi\) | ||||
−0.226224 | + | 0.974075i | \(0.572638\pi\) | |||||||
\(978\) | −39.6314 | −1.26727 | ||||||||
\(979\) | −2.48265 | −0.0793459 | ||||||||
\(980\) | 52.2439 | 1.66887 | ||||||||
\(981\) | 8.51859 | 0.271978 | ||||||||
\(982\) | 63.5663 | 2.02848 | ||||||||
\(983\) | −14.6631 | −0.467681 | −0.233841 | − | 0.972275i | \(-0.575129\pi\) | ||||
−0.233841 | + | 0.972275i | \(0.575129\pi\) | |||||||
\(984\) | 112.965 | 3.60119 | ||||||||
\(985\) | 49.2021 | 1.56771 | ||||||||
\(986\) | 18.2570 | 0.581423 | ||||||||
\(987\) | 19.6902 | 0.626746 | ||||||||
\(988\) | 63.7022 | 2.02664 | ||||||||
\(989\) | 3.58353 | 0.113950 | ||||||||
\(990\) | 7.78677 | 0.247480 | ||||||||
\(991\) | −14.1814 | −0.450487 | −0.225244 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225244 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(992\) | 63.8356 | 2.02678 | ||||||||
\(993\) | 2.83825 | 0.0900691 | ||||||||
\(994\) | 25.3432 | 0.803838 | ||||||||
\(995\) | 17.8484 | 0.565833 | ||||||||
\(996\) | −134.183 | −4.25176 | ||||||||
\(997\) | −2.72541 | −0.0863145 | −0.0431573 | − | 0.999068i | \(-0.513742\pi\) | ||||
−0.0431573 | + | 0.999068i | \(0.513742\pi\) | |||||||
\(998\) | −8.39642 | −0.265784 | ||||||||
\(999\) | 2.51304 | 0.0795090 |
(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 | 5077.2.a.c.1.8 | ✓ | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.c.1.8 | ✓ | 216 | 1.1 | even | 1 | trivial |