Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, 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("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(5.32602181482\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.60496\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.60496 | 1.84199 | 0.920994 | − | 0.389578i | \(-0.127379\pi\) | ||||
0.920994 | + | 0.389578i | \(0.127379\pi\) | |||||||
\(3\) | −1.02046 | −0.589162 | −0.294581 | − | 0.955627i | \(-0.595180\pi\) | ||||
−0.294581 | + | 0.955627i | \(0.595180\pi\) | |||||||
\(4\) | 4.78583 | 2.39292 | ||||||||
\(5\) | 1.68070 | 0.751630 | 0.375815 | − | 0.926695i | \(-0.377363\pi\) | ||||
0.375815 | + | 0.926695i | \(0.377363\pi\) | |||||||
\(6\) | −2.65826 | −1.08523 | ||||||||
\(7\) | 2.80821 | 1.06140 | 0.530701 | − | 0.847559i | \(-0.321929\pi\) | ||||
0.530701 | + | 0.847559i | \(0.321929\pi\) | |||||||
\(8\) | 7.25699 | 2.56573 | ||||||||
\(9\) | −1.95866 | −0.652888 | ||||||||
\(10\) | 4.37815 | 1.38449 | ||||||||
\(11\) | −1.84810 | −0.557225 | −0.278612 | − | 0.960404i | \(-0.589874\pi\) | ||||
−0.278612 | + | 0.960404i | \(0.589874\pi\) | |||||||
\(12\) | −4.88374 | −1.40982 | ||||||||
\(13\) | −0.773187 | −0.214443 | −0.107222 | − | 0.994235i | \(-0.534195\pi\) | ||||
−0.107222 | + | 0.994235i | \(0.534195\pi\) | |||||||
\(14\) | 7.31527 | 1.95509 | ||||||||
\(15\) | −1.71508 | −0.442832 | ||||||||
\(16\) | 9.33253 | 2.33313 | ||||||||
\(17\) | −0.882567 | −0.214054 | −0.107027 | − | 0.994256i | \(-0.534133\pi\) | ||||
−0.107027 | + | 0.994256i | \(0.534133\pi\) | |||||||
\(18\) | −5.10225 | −1.20261 | ||||||||
\(19\) | −3.94266 | −0.904507 | −0.452254 | − | 0.891889i | \(-0.649380\pi\) | ||||
−0.452254 | + | 0.891889i | \(0.649380\pi\) | |||||||
\(20\) | 8.04353 | 1.79859 | ||||||||
\(21\) | −2.86566 | −0.625337 | ||||||||
\(22\) | −4.81425 | −1.02640 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −7.40546 | −1.51163 | ||||||||
\(25\) | −2.17526 | −0.435052 | ||||||||
\(26\) | −2.01412 | −0.395002 | ||||||||
\(27\) | 5.06011 | 0.973819 | ||||||||
\(28\) | 13.4396 | 2.53985 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −4.46772 | −0.815690 | ||||||||
\(31\) | 5.16975 | 0.928514 | 0.464257 | − | 0.885700i | \(-0.346321\pi\) | ||||
0.464257 | + | 0.885700i | \(0.346321\pi\) | |||||||
\(32\) | 9.79691 | 1.73187 | ||||||||
\(33\) | 1.88591 | 0.328295 | ||||||||
\(34\) | −2.29905 | −0.394284 | ||||||||
\(35\) | 4.71974 | 0.797781 | ||||||||
\(36\) | −9.37384 | −1.56231 | ||||||||
\(37\) | 3.00050 | 0.493280 | 0.246640 | − | 0.969107i | \(-0.420674\pi\) | ||||
0.246640 | + | 0.969107i | \(0.420674\pi\) | |||||||
\(38\) | −10.2705 | −1.66609 | ||||||||
\(39\) | 0.789005 | 0.126342 | ||||||||
\(40\) | 12.1968 | 1.92848 | ||||||||
\(41\) | 1.65149 | 0.257920 | 0.128960 | − | 0.991650i | \(-0.458836\pi\) | ||||
0.128960 | + | 0.991650i | \(0.458836\pi\) | |||||||
\(42\) | −7.46493 | −1.15186 | ||||||||
\(43\) | −3.35090 | −0.511007 | −0.255504 | − | 0.966808i | \(-0.582241\pi\) | ||||
−0.255504 | + | 0.966808i | \(0.582241\pi\) | |||||||
\(44\) | −8.84472 | −1.33339 | ||||||||
\(45\) | −3.29192 | −0.490730 | ||||||||
\(46\) | −2.60496 | −0.384081 | ||||||||
\(47\) | −1.98916 | −0.290148 | −0.145074 | − | 0.989421i | \(-0.546342\pi\) | ||||
−0.145074 | + | 0.989421i | \(0.546342\pi\) | |||||||
\(48\) | −9.52346 | −1.37459 | ||||||||
\(49\) | 0.886016 | 0.126574 | ||||||||
\(50\) | −5.66648 | −0.801361 | ||||||||
\(51\) | 0.900622 | 0.126112 | ||||||||
\(52\) | −3.70034 | −0.513145 | ||||||||
\(53\) | 1.44385 | 0.198328 | 0.0991642 | − | 0.995071i | \(-0.468383\pi\) | ||||
0.0991642 | + | 0.995071i | \(0.468383\pi\) | |||||||
\(54\) | 13.1814 | 1.79376 | ||||||||
\(55\) | −3.10610 | −0.418827 | ||||||||
\(56\) | 20.3791 | 2.72327 | ||||||||
\(57\) | 4.02332 | 0.532901 | ||||||||
\(58\) | 2.60496 | 0.342048 | ||||||||
\(59\) | 2.83981 | 0.369711 | 0.184856 | − | 0.982766i | \(-0.440818\pi\) | ||||
0.184856 | + | 0.982766i | \(0.440818\pi\) | |||||||
\(60\) | −8.20809 | −1.05966 | ||||||||
\(61\) | 4.60276 | 0.589323 | 0.294661 | − | 0.955602i | \(-0.404793\pi\) | ||||
0.294661 | + | 0.955602i | \(0.404793\pi\) | |||||||
\(62\) | 13.4670 | 1.71031 | ||||||||
\(63\) | −5.50033 | −0.692977 | ||||||||
\(64\) | 6.85553 | 0.856942 | ||||||||
\(65\) | −1.29949 | −0.161182 | ||||||||
\(66\) | 4.91274 | 0.604716 | ||||||||
\(67\) | −13.2444 | −1.61806 | −0.809032 | − | 0.587764i | \(-0.800008\pi\) | ||||
−0.809032 | + | 0.587764i | \(0.800008\pi\) | |||||||
\(68\) | −4.22382 | −0.512213 | ||||||||
\(69\) | 1.02046 | 0.122849 | ||||||||
\(70\) | 12.2947 | 1.46950 | ||||||||
\(71\) | −14.4949 | −1.72023 | −0.860115 | − | 0.510099i | \(-0.829609\pi\) | ||||
−0.860115 | + | 0.510099i | \(0.829609\pi\) | |||||||
\(72\) | −14.2140 | −1.67514 | ||||||||
\(73\) | −12.2449 | −1.43316 | −0.716579 | − | 0.697506i | \(-0.754293\pi\) | ||||
−0.716579 | + | 0.697506i | \(0.754293\pi\) | |||||||
\(74\) | 7.81620 | 0.908615 | ||||||||
\(75\) | 2.21976 | 0.256316 | ||||||||
\(76\) | −18.8689 | −2.16441 | ||||||||
\(77\) | −5.18986 | −0.591439 | ||||||||
\(78\) | 2.05533 | 0.232720 | ||||||||
\(79\) | −2.29854 | −0.258606 | −0.129303 | − | 0.991605i | \(-0.541274\pi\) | ||||
−0.129303 | + | 0.991605i | \(0.541274\pi\) | |||||||
\(80\) | 15.6851 | 1.75365 | ||||||||
\(81\) | 0.712362 | 0.0791514 | ||||||||
\(82\) | 4.30208 | 0.475085 | ||||||||
\(83\) | 6.46906 | 0.710072 | 0.355036 | − | 0.934853i | \(-0.384469\pi\) | ||||
0.355036 | + | 0.934853i | \(0.384469\pi\) | |||||||
\(84\) | −13.7146 | −1.49638 | ||||||||
\(85\) | −1.48333 | −0.160889 | ||||||||
\(86\) | −8.72897 | −0.941269 | ||||||||
\(87\) | −1.02046 | −0.109405 | ||||||||
\(88\) | −13.4117 | −1.42969 | ||||||||
\(89\) | 16.1242 | 1.70916 | 0.854582 | − | 0.519316i | \(-0.173813\pi\) | ||||
0.854582 | + | 0.519316i | \(0.173813\pi\) | |||||||
\(90\) | −8.57533 | −0.903919 | ||||||||
\(91\) | −2.17127 | −0.227611 | ||||||||
\(92\) | −4.78583 | −0.498958 | ||||||||
\(93\) | −5.27551 | −0.547045 | ||||||||
\(94\) | −5.18168 | −0.534449 | ||||||||
\(95\) | −6.62640 | −0.679855 | ||||||||
\(96\) | −9.99734 | −1.02035 | ||||||||
\(97\) | 11.0455 | 1.12150 | 0.560750 | − | 0.827985i | \(-0.310513\pi\) | ||||
0.560750 | + | 0.827985i | \(0.310513\pi\) | |||||||
\(98\) | 2.30804 | 0.233147 | ||||||||
\(99\) | 3.61982 | 0.363805 | ||||||||
\(100\) | −10.4104 | −1.04104 | ||||||||
\(101\) | −4.27667 | −0.425544 | −0.212772 | − | 0.977102i | \(-0.568249\pi\) | ||||
−0.212772 | + | 0.977102i | \(0.568249\pi\) | |||||||
\(102\) | 2.34609 | 0.232297 | ||||||||
\(103\) | −10.9818 | −1.08207 | −0.541036 | − | 0.840999i | \(-0.681968\pi\) | ||||
−0.541036 | + | 0.840999i | \(0.681968\pi\) | |||||||
\(104\) | −5.61101 | −0.550205 | ||||||||
\(105\) | −4.81630 | −0.470022 | ||||||||
\(106\) | 3.76118 | 0.365318 | ||||||||
\(107\) | −3.61453 | −0.349430 | −0.174715 | − | 0.984619i | \(-0.555900\pi\) | ||||
−0.174715 | + | 0.984619i | \(0.555900\pi\) | |||||||
\(108\) | 24.2168 | 2.33027 | ||||||||
\(109\) | 11.3108 | 1.08338 | 0.541689 | − | 0.840579i | \(-0.317785\pi\) | ||||
0.541689 | + | 0.840579i | \(0.317785\pi\) | |||||||
\(110\) | −8.09128 | −0.771473 | ||||||||
\(111\) | −3.06189 | −0.290622 | ||||||||
\(112\) | 26.2077 | 2.47639 | ||||||||
\(113\) | 8.28187 | 0.779093 | 0.389546 | − | 0.921007i | \(-0.372632\pi\) | ||||
0.389546 | + | 0.921007i | \(0.372632\pi\) | |||||||
\(114\) | 10.4806 | 0.981597 | ||||||||
\(115\) | −1.68070 | −0.156726 | ||||||||
\(116\) | 4.78583 | 0.444353 | ||||||||
\(117\) | 1.51441 | 0.140008 | ||||||||
\(118\) | 7.39759 | 0.681003 | ||||||||
\(119\) | −2.47843 | −0.227197 | ||||||||
\(120\) | −12.4463 | −1.13619 | ||||||||
\(121\) | −7.58451 | −0.689501 | ||||||||
\(122\) | 11.9900 | 1.08553 | ||||||||
\(123\) | −1.68528 | −0.151957 | ||||||||
\(124\) | 24.7416 | 2.22186 | ||||||||
\(125\) | −12.0594 | −1.07863 | ||||||||
\(126\) | −14.3282 | −1.27645 | ||||||||
\(127\) | 14.2573 | 1.26514 | 0.632568 | − | 0.774505i | \(-0.282001\pi\) | ||||
0.632568 | + | 0.774505i | \(0.282001\pi\) | |||||||
\(128\) | −1.73541 | −0.153390 | ||||||||
\(129\) | 3.41945 | 0.301066 | ||||||||
\(130\) | −3.38513 | −0.296895 | ||||||||
\(131\) | 6.25663 | 0.546645 | 0.273322 | − | 0.961923i | \(-0.411877\pi\) | ||||
0.273322 | + | 0.961923i | \(0.411877\pi\) | |||||||
\(132\) | 9.02567 | 0.785584 | ||||||||
\(133\) | −11.0718 | −0.960046 | ||||||||
\(134\) | −34.5013 | −2.98045 | ||||||||
\(135\) | 8.50451 | 0.731951 | ||||||||
\(136\) | −6.40478 | −0.549205 | ||||||||
\(137\) | 9.16909 | 0.783369 | 0.391684 | − | 0.920100i | \(-0.371893\pi\) | ||||
0.391684 | + | 0.920100i | \(0.371893\pi\) | |||||||
\(138\) | 2.65826 | 0.226286 | ||||||||
\(139\) | 4.57593 | 0.388126 | 0.194063 | − | 0.980989i | \(-0.437833\pi\) | ||||
0.194063 | + | 0.980989i | \(0.437833\pi\) | |||||||
\(140\) | 22.5879 | 1.90902 | ||||||||
\(141\) | 2.02985 | 0.170944 | ||||||||
\(142\) | −37.7587 | −3.16864 | ||||||||
\(143\) | 1.42893 | 0.119493 | ||||||||
\(144\) | −18.2793 | −1.52327 | ||||||||
\(145\) | 1.68070 | 0.139574 | ||||||||
\(146\) | −31.8975 | −2.63986 | ||||||||
\(147\) | −0.904143 | −0.0745724 | ||||||||
\(148\) | 14.3599 | 1.18038 | ||||||||
\(149\) | 11.8201 | 0.968344 | 0.484172 | − | 0.874973i | \(-0.339121\pi\) | ||||
0.484172 | + | 0.874973i | \(0.339121\pi\) | |||||||
\(150\) | 5.78240 | 0.472131 | ||||||||
\(151\) | −19.5875 | −1.59401 | −0.797003 | − | 0.603975i | \(-0.793583\pi\) | ||||
−0.797003 | + | 0.603975i | \(0.793583\pi\) | |||||||
\(152\) | −28.6118 | −2.32072 | ||||||||
\(153\) | 1.72865 | 0.139753 | ||||||||
\(154\) | −13.5194 | −1.08942 | ||||||||
\(155\) | 8.68878 | 0.697899 | ||||||||
\(156\) | 3.77605 | 0.302326 | ||||||||
\(157\) | 13.1463 | 1.04919 | 0.524595 | − | 0.851352i | \(-0.324217\pi\) | ||||
0.524595 | + | 0.851352i | \(0.324217\pi\) | |||||||
\(158\) | −5.98761 | −0.476348 | ||||||||
\(159\) | −1.47339 | −0.116848 | ||||||||
\(160\) | 16.4656 | 1.30172 | ||||||||
\(161\) | −2.80821 | −0.221318 | ||||||||
\(162\) | 1.85568 | 0.145796 | ||||||||
\(163\) | −17.5673 | −1.37598 | −0.687988 | − | 0.725722i | \(-0.741506\pi\) | ||||
−0.687988 | + | 0.725722i | \(0.741506\pi\) | |||||||
\(164\) | 7.90377 | 0.617181 | ||||||||
\(165\) | 3.16965 | 0.246757 | ||||||||
\(166\) | 16.8517 | 1.30794 | ||||||||
\(167\) | −2.69139 | −0.208266 | −0.104133 | − | 0.994563i | \(-0.533207\pi\) | ||||
−0.104133 | + | 0.994563i | \(0.533207\pi\) | |||||||
\(168\) | −20.7960 | −1.60445 | ||||||||
\(169\) | −12.4022 | −0.954014 | ||||||||
\(170\) | −3.86401 | −0.296356 | ||||||||
\(171\) | 7.72234 | 0.590542 | ||||||||
\(172\) | −16.0368 | −1.22280 | ||||||||
\(173\) | 4.04664 | 0.307661 | 0.153830 | − | 0.988097i | \(-0.450839\pi\) | ||||
0.153830 | + | 0.988097i | \(0.450839\pi\) | |||||||
\(174\) | −2.65826 | −0.201522 | ||||||||
\(175\) | −6.10858 | −0.461765 | ||||||||
\(176\) | −17.2475 | −1.30008 | ||||||||
\(177\) | −2.89790 | −0.217820 | ||||||||
\(178\) | 42.0030 | 3.14826 | ||||||||
\(179\) | 18.9925 | 1.41956 | 0.709782 | − | 0.704422i | \(-0.248794\pi\) | ||||
0.709782 | + | 0.704422i | \(0.248794\pi\) | |||||||
\(180\) | −15.7546 | −1.17428 | ||||||||
\(181\) | −1.08134 | −0.0803754 | −0.0401877 | − | 0.999192i | \(-0.512796\pi\) | ||||
−0.0401877 | + | 0.999192i | \(0.512796\pi\) | |||||||
\(182\) | −5.65607 | −0.419256 | ||||||||
\(183\) | −4.69692 | −0.347207 | ||||||||
\(184\) | −7.25699 | −0.534992 | ||||||||
\(185\) | 5.04293 | 0.370764 | ||||||||
\(186\) | −13.7425 | −1.00765 | ||||||||
\(187\) | 1.63108 | 0.119276 | ||||||||
\(188\) | −9.51977 | −0.694301 | ||||||||
\(189\) | 14.2098 | 1.03361 | ||||||||
\(190\) | −17.2615 | −1.25228 | ||||||||
\(191\) | −8.42595 | −0.609680 | −0.304840 | − | 0.952404i | \(-0.598603\pi\) | ||||
−0.304840 | + | 0.952404i | \(0.598603\pi\) | |||||||
\(192\) | −6.99579 | −0.504877 | ||||||||
\(193\) | −0.304423 | −0.0219129 | −0.0109564 | − | 0.999940i | \(-0.503488\pi\) | ||||
−0.0109564 | + | 0.999940i | \(0.503488\pi\) | |||||||
\(194\) | 28.7731 | 2.06579 | ||||||||
\(195\) | 1.32608 | 0.0949624 | ||||||||
\(196\) | 4.24033 | 0.302880 | ||||||||
\(197\) | −12.1145 | −0.863119 | −0.431560 | − | 0.902084i | \(-0.642037\pi\) | ||||
−0.431560 | + | 0.902084i | \(0.642037\pi\) | |||||||
\(198\) | 9.42949 | 0.670125 | ||||||||
\(199\) | 13.0890 | 0.927857 | 0.463928 | − | 0.885873i | \(-0.346440\pi\) | ||||
0.463928 | + | 0.885873i | \(0.346440\pi\) | |||||||
\(200\) | −15.7859 | −1.11623 | ||||||||
\(201\) | 13.5154 | 0.953302 | ||||||||
\(202\) | −11.1406 | −0.783847 | ||||||||
\(203\) | 2.80821 | 0.197097 | ||||||||
\(204\) | 4.31023 | 0.301776 | ||||||||
\(205\) | 2.77566 | 0.193860 | ||||||||
\(206\) | −28.6073 | −1.99316 | ||||||||
\(207\) | 1.95866 | 0.136137 | ||||||||
\(208\) | −7.21579 | −0.500325 | ||||||||
\(209\) | 7.28644 | 0.504014 | ||||||||
\(210\) | −12.5463 | −0.865775 | ||||||||
\(211\) | 20.5324 | 1.41351 | 0.706755 | − | 0.707458i | \(-0.250158\pi\) | ||||
0.706755 | + | 0.707458i | \(0.250158\pi\) | |||||||
\(212\) | 6.91004 | 0.474583 | ||||||||
\(213\) | 14.7915 | 1.01349 | ||||||||
\(214\) | −9.41571 | −0.643645 | ||||||||
\(215\) | −5.63184 | −0.384088 | ||||||||
\(216\) | 36.7212 | 2.49856 | ||||||||
\(217\) | 14.5177 | 0.985527 | ||||||||
\(218\) | 29.4642 | 1.99557 | ||||||||
\(219\) | 12.4954 | 0.844362 | ||||||||
\(220\) | −14.8653 | −1.00222 | ||||||||
\(221\) | 0.682389 | 0.0459025 | ||||||||
\(222\) | −7.97611 | −0.535321 | ||||||||
\(223\) | 4.71330 | 0.315626 | 0.157813 | − | 0.987469i | \(-0.449556\pi\) | ||||
0.157813 | + | 0.987469i | \(0.449556\pi\) | |||||||
\(224\) | 27.5117 | 1.83821 | ||||||||
\(225\) | 4.26061 | 0.284041 | ||||||||
\(226\) | 21.5740 | 1.43508 | ||||||||
\(227\) | 15.8873 | 1.05448 | 0.527240 | − | 0.849716i | \(-0.323227\pi\) | ||||
0.527240 | + | 0.849716i | \(0.323227\pi\) | |||||||
\(228\) | 19.2549 | 1.27519 | ||||||||
\(229\) | 24.2731 | 1.60401 | 0.802006 | − | 0.597316i | \(-0.203766\pi\) | ||||
0.802006 | + | 0.597316i | \(0.203766\pi\) | |||||||
\(230\) | −4.37815 | −0.288687 | ||||||||
\(231\) | 5.29603 | 0.348453 | ||||||||
\(232\) | 7.25699 | 0.476445 | ||||||||
\(233\) | 15.0023 | 0.982833 | 0.491416 | − | 0.870925i | \(-0.336479\pi\) | ||||
0.491416 | + | 0.870925i | \(0.336479\pi\) | |||||||
\(234\) | 3.94499 | 0.257892 | ||||||||
\(235\) | −3.34317 | −0.218084 | ||||||||
\(236\) | 13.5908 | 0.884688 | ||||||||
\(237\) | 2.34556 | 0.152361 | ||||||||
\(238\) | −6.45621 | −0.418494 | ||||||||
\(239\) | 3.22723 | 0.208752 | 0.104376 | − | 0.994538i | \(-0.466715\pi\) | ||||
0.104376 | + | 0.994538i | \(0.466715\pi\) | |||||||
\(240\) | −16.0060 | −1.03318 | ||||||||
\(241\) | 18.2846 | 1.17782 | 0.588909 | − | 0.808200i | \(-0.299558\pi\) | ||||
0.588909 | + | 0.808200i | \(0.299558\pi\) | |||||||
\(242\) | −19.7574 | −1.27005 | ||||||||
\(243\) | −15.9073 | −1.02045 | ||||||||
\(244\) | 22.0280 | 1.41020 | ||||||||
\(245\) | 1.48912 | 0.0951366 | ||||||||
\(246\) | −4.39009 | −0.279902 | ||||||||
\(247\) | 3.04841 | 0.193966 | ||||||||
\(248\) | 37.5168 | 2.38232 | ||||||||
\(249\) | −6.60141 | −0.418347 | ||||||||
\(250\) | −31.4144 | −1.98682 | ||||||||
\(251\) | 8.58591 | 0.541938 | 0.270969 | − | 0.962588i | \(-0.412656\pi\) | ||||
0.270969 | + | 0.962588i | \(0.412656\pi\) | |||||||
\(252\) | −26.3237 | −1.65824 | ||||||||
\(253\) | 1.84810 | 0.116189 | ||||||||
\(254\) | 37.1399 | 2.33036 | ||||||||
\(255\) | 1.51367 | 0.0947898 | ||||||||
\(256\) | −18.2317 | −1.13948 | ||||||||
\(257\) | −3.17251 | −0.197896 | −0.0989478 | − | 0.995093i | \(-0.531548\pi\) | ||||
−0.0989478 | + | 0.995093i | \(0.531548\pi\) | |||||||
\(258\) | 8.90755 | 0.554560 | ||||||||
\(259\) | 8.42603 | 0.523568 | ||||||||
\(260\) | −6.21915 | −0.385695 | ||||||||
\(261\) | −1.95866 | −0.121238 | ||||||||
\(262\) | 16.2983 | 1.00691 | ||||||||
\(263\) | 0.895148 | 0.0551972 | 0.0275986 | − | 0.999619i | \(-0.491214\pi\) | ||||
0.0275986 | + | 0.999619i | \(0.491214\pi\) | |||||||
\(264\) | 13.6861 | 0.842319 | ||||||||
\(265\) | 2.42668 | 0.149070 | ||||||||
\(266\) | −28.8416 | −1.76839 | ||||||||
\(267\) | −16.4541 | −1.00697 | ||||||||
\(268\) | −63.3856 | −3.87189 | ||||||||
\(269\) | 16.1610 | 0.985355 | 0.492677 | − | 0.870212i | \(-0.336018\pi\) | ||||
0.492677 | + | 0.870212i | \(0.336018\pi\) | |||||||
\(270\) | 22.1539 | 1.34824 | ||||||||
\(271\) | −7.97606 | −0.484511 | −0.242255 | − | 0.970212i | \(-0.577887\pi\) | ||||
−0.242255 | + | 0.970212i | \(0.577887\pi\) | |||||||
\(272\) | −8.23658 | −0.499416 | ||||||||
\(273\) | 2.21569 | 0.134100 | ||||||||
\(274\) | 23.8852 | 1.44295 | ||||||||
\(275\) | 4.02011 | 0.242422 | ||||||||
\(276\) | 4.88374 | 0.293967 | ||||||||
\(277\) | 3.58237 | 0.215244 | 0.107622 | − | 0.994192i | \(-0.465676\pi\) | ||||
0.107622 | + | 0.994192i | \(0.465676\pi\) | |||||||
\(278\) | 11.9201 | 0.714922 | ||||||||
\(279\) | −10.1258 | −0.606216 | ||||||||
\(280\) | 34.2511 | 2.04689 | ||||||||
\(281\) | 4.75298 | 0.283539 | 0.141770 | − | 0.989900i | \(-0.454721\pi\) | ||||
0.141770 | + | 0.989900i | \(0.454721\pi\) | |||||||
\(282\) | 5.28769 | 0.314877 | ||||||||
\(283\) | −11.3753 | −0.676193 | −0.338096 | − | 0.941111i | \(-0.609783\pi\) | ||||
−0.338096 | + | 0.941111i | \(0.609783\pi\) | |||||||
\(284\) | −69.3703 | −4.11637 | ||||||||
\(285\) | 6.76197 | 0.400544 | ||||||||
\(286\) | 3.72231 | 0.220105 | ||||||||
\(287\) | 4.63773 | 0.273757 | ||||||||
\(288\) | −19.1889 | −1.13071 | ||||||||
\(289\) | −16.2211 | −0.954181 | ||||||||
\(290\) | 4.37815 | 0.257094 | ||||||||
\(291\) | −11.2715 | −0.660745 | ||||||||
\(292\) | −58.6021 | −3.42943 | ||||||||
\(293\) | −13.1847 | −0.770257 | −0.385128 | − | 0.922863i | \(-0.625843\pi\) | ||||
−0.385128 | + | 0.922863i | \(0.625843\pi\) | |||||||
\(294\) | −2.35526 | −0.137361 | ||||||||
\(295\) | 4.77285 | 0.277886 | ||||||||
\(296\) | 21.7746 | 1.26562 | ||||||||
\(297\) | −9.35162 | −0.542636 | ||||||||
\(298\) | 30.7910 | 1.78368 | ||||||||
\(299\) | 0.773187 | 0.0447146 | ||||||||
\(300\) | 10.6234 | 0.613344 | ||||||||
\(301\) | −9.41001 | −0.542384 | ||||||||
\(302\) | −51.0247 | −2.93614 | ||||||||
\(303\) | 4.36416 | 0.250715 | ||||||||
\(304\) | −36.7949 | −2.11033 | ||||||||
\(305\) | 7.73584 | 0.442953 | ||||||||
\(306\) | 4.50308 | 0.257424 | ||||||||
\(307\) | −22.1761 | −1.26566 | −0.632829 | − | 0.774292i | \(-0.718106\pi\) | ||||
−0.632829 | + | 0.774292i | \(0.718106\pi\) | |||||||
\(308\) | −24.8378 | −1.41526 | ||||||||
\(309\) | 11.2065 | 0.637516 | ||||||||
\(310\) | 22.6339 | 1.28552 | ||||||||
\(311\) | −31.3611 | −1.77832 | −0.889161 | − | 0.457594i | \(-0.848711\pi\) | ||||
−0.889161 | + | 0.457594i | \(0.848711\pi\) | |||||||
\(312\) | 5.72580 | 0.324160 | ||||||||
\(313\) | 21.5552 | 1.21837 | 0.609185 | − | 0.793028i | \(-0.291497\pi\) | ||||
0.609185 | + | 0.793028i | \(0.291497\pi\) | |||||||
\(314\) | 34.2457 | 1.93260 | ||||||||
\(315\) | −9.24438 | −0.520862 | ||||||||
\(316\) | −11.0004 | −0.618822 | ||||||||
\(317\) | 25.8705 | 1.45303 | 0.726515 | − | 0.687151i | \(-0.241139\pi\) | ||||
0.726515 | + | 0.687151i | \(0.241139\pi\) | |||||||
\(318\) | −3.83813 | −0.215232 | ||||||||
\(319\) | −1.84810 | −0.103474 | ||||||||
\(320\) | 11.5221 | 0.644103 | ||||||||
\(321\) | 3.68848 | 0.205871 | ||||||||
\(322\) | −7.31527 | −0.407664 | ||||||||
\(323\) | 3.47966 | 0.193613 | ||||||||
\(324\) | 3.40925 | 0.189403 | ||||||||
\(325\) | 1.68188 | 0.0932942 | ||||||||
\(326\) | −45.7621 | −2.53453 | ||||||||
\(327\) | −11.5422 | −0.638285 | ||||||||
\(328\) | 11.9849 | 0.661754 | ||||||||
\(329\) | −5.58596 | −0.307964 | ||||||||
\(330\) | 8.25681 | 0.454523 | ||||||||
\(331\) | 31.0454 | 1.70641 | 0.853205 | − | 0.521576i | \(-0.174656\pi\) | ||||
0.853205 | + | 0.521576i | \(0.174656\pi\) | |||||||
\(332\) | 30.9599 | 1.69914 | ||||||||
\(333\) | −5.87698 | −0.322057 | ||||||||
\(334\) | −7.01098 | −0.383624 | ||||||||
\(335\) | −22.2599 | −1.21619 | ||||||||
\(336\) | −26.7438 | −1.45899 | ||||||||
\(337\) | 21.2178 | 1.15581 | 0.577903 | − | 0.816105i | \(-0.303871\pi\) | ||||
0.577903 | + | 0.816105i | \(0.303871\pi\) | |||||||
\(338\) | −32.3072 | −1.75728 | ||||||||
\(339\) | −8.45130 | −0.459012 | ||||||||
\(340\) | −7.09895 | −0.384995 | ||||||||
\(341\) | −9.55424 | −0.517391 | ||||||||
\(342\) | 20.1164 | 1.08777 | ||||||||
\(343\) | −17.1693 | −0.927056 | ||||||||
\(344\) | −24.3174 | −1.31111 | ||||||||
\(345\) | 1.71508 | 0.0923368 | ||||||||
\(346\) | 10.5414 | 0.566707 | ||||||||
\(347\) | −25.1938 | −1.35248 | −0.676238 | − | 0.736684i | \(-0.736391\pi\) | ||||
−0.676238 | + | 0.736684i | \(0.736391\pi\) | |||||||
\(348\) | −4.88374 | −0.261796 | ||||||||
\(349\) | 27.4503 | 1.46938 | 0.734691 | − | 0.678402i | \(-0.237327\pi\) | ||||
0.734691 | + | 0.678402i | \(0.237327\pi\) | |||||||
\(350\) | −15.9126 | −0.850566 | ||||||||
\(351\) | −3.91241 | −0.208829 | ||||||||
\(352\) | −18.1057 | −0.965038 | ||||||||
\(353\) | 15.5298 | 0.826567 | 0.413283 | − | 0.910602i | \(-0.364382\pi\) | ||||
0.413283 | + | 0.910602i | \(0.364382\pi\) | |||||||
\(354\) | −7.54893 | −0.401221 | ||||||||
\(355\) | −24.3616 | −1.29298 | ||||||||
\(356\) | 77.1679 | 4.08989 | ||||||||
\(357\) | 2.52913 | 0.133856 | ||||||||
\(358\) | 49.4747 | 2.61482 | ||||||||
\(359\) | 8.30533 | 0.438339 | 0.219169 | − | 0.975687i | \(-0.429665\pi\) | ||||
0.219169 | + | 0.975687i | \(0.429665\pi\) | |||||||
\(360\) | −23.8894 | −1.25908 | ||||||||
\(361\) | −3.45547 | −0.181867 | ||||||||
\(362\) | −2.81685 | −0.148050 | ||||||||
\(363\) | 7.73967 | 0.406228 | ||||||||
\(364\) | −10.3913 | −0.544653 | ||||||||
\(365\) | −20.5800 | −1.07720 | ||||||||
\(366\) | −12.2353 | −0.639550 | ||||||||
\(367\) | −13.6556 | −0.712815 | −0.356407 | − | 0.934331i | \(-0.615998\pi\) | ||||
−0.356407 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(368\) | −9.33253 | −0.486492 | ||||||||
\(369\) | −3.23472 | −0.168393 | ||||||||
\(370\) | 13.1367 | 0.682942 | ||||||||
\(371\) | 4.05463 | 0.210506 | ||||||||
\(372\) | −25.2477 | −1.30903 | ||||||||
\(373\) | −33.1536 | −1.71663 | −0.858315 | − | 0.513124i | \(-0.828488\pi\) | ||||
−0.858315 | + | 0.513124i | \(0.828488\pi\) | |||||||
\(374\) | 4.24889 | 0.219705 | ||||||||
\(375\) | 12.3061 | 0.635487 | ||||||||
\(376\) | −14.4353 | −0.744443 | ||||||||
\(377\) | −0.773187 | −0.0398212 | ||||||||
\(378\) | 37.0161 | 1.90390 | ||||||||
\(379\) | −19.4221 | −0.997649 | −0.498824 | − | 0.866703i | \(-0.666235\pi\) | ||||
−0.498824 | + | 0.866703i | \(0.666235\pi\) | |||||||
\(380\) | −31.7129 | −1.62684 | ||||||||
\(381\) | −14.5490 | −0.745369 | ||||||||
\(382\) | −21.9493 | −1.12302 | ||||||||
\(383\) | 10.5047 | 0.536764 | 0.268382 | − | 0.963313i | \(-0.413511\pi\) | ||||
0.268382 | + | 0.963313i | \(0.413511\pi\) | |||||||
\(384\) | 1.77092 | 0.0903716 | ||||||||
\(385\) | −8.72257 | −0.444543 | ||||||||
\(386\) | −0.793011 | −0.0403632 | ||||||||
\(387\) | 6.56329 | 0.333631 | ||||||||
\(388\) | 52.8619 | 2.68365 | ||||||||
\(389\) | −17.3721 | −0.880802 | −0.440401 | − | 0.897801i | \(-0.645164\pi\) | ||||
−0.440401 | + | 0.897801i | \(0.645164\pi\) | |||||||
\(390\) | 3.45438 | 0.174919 | ||||||||
\(391\) | 0.882567 | 0.0446333 | ||||||||
\(392\) | 6.42981 | 0.324755 | ||||||||
\(393\) | −6.38463 | −0.322062 | ||||||||
\(394\) | −31.5577 | −1.58985 | ||||||||
\(395\) | −3.86314 | −0.194376 | ||||||||
\(396\) | 17.3238 | 0.870556 | ||||||||
\(397\) | −12.6473 | −0.634750 | −0.317375 | − | 0.948300i | \(-0.602801\pi\) | ||||
−0.317375 | + | 0.948300i | \(0.602801\pi\) | |||||||
\(398\) | 34.0964 | 1.70910 | ||||||||
\(399\) | 11.2983 | 0.565622 | ||||||||
\(400\) | −20.3007 | −1.01503 | ||||||||
\(401\) | −26.3988 | −1.31829 | −0.659146 | − | 0.752015i | \(-0.729082\pi\) | ||||
−0.659146 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(402\) | 35.2071 | 1.75597 | ||||||||
\(403\) | −3.99718 | −0.199114 | ||||||||
\(404\) | −20.4674 | −1.01829 | ||||||||
\(405\) | 1.19726 | 0.0594925 | ||||||||
\(406\) | 7.31527 | 0.363051 | ||||||||
\(407\) | −5.54525 | −0.274868 | ||||||||
\(408\) | 6.53581 | 0.323571 | ||||||||
\(409\) | 9.29368 | 0.459543 | 0.229771 | − | 0.973245i | \(-0.426202\pi\) | ||||
0.229771 | + | 0.973245i | \(0.426202\pi\) | |||||||
\(410\) | 7.23049 | 0.357088 | ||||||||
\(411\) | −9.35668 | −0.461531 | ||||||||
\(412\) | −52.5572 | −2.58931 | ||||||||
\(413\) | 7.97476 | 0.392412 | ||||||||
\(414\) | 5.10225 | 0.250762 | ||||||||
\(415\) | 10.8725 | 0.533711 | ||||||||
\(416\) | −7.57484 | −0.371387 | ||||||||
\(417\) | −4.66955 | −0.228669 | ||||||||
\(418\) | 18.9809 | 0.928387 | ||||||||
\(419\) | 25.3396 | 1.23792 | 0.618961 | − | 0.785421i | \(-0.287554\pi\) | ||||
0.618961 | + | 0.785421i | \(0.287554\pi\) | |||||||
\(420\) | −23.0500 | −1.12472 | ||||||||
\(421\) | −4.02340 | −0.196089 | −0.0980443 | − | 0.995182i | \(-0.531259\pi\) | ||||
−0.0980443 | + | 0.995182i | \(0.531259\pi\) | |||||||
\(422\) | 53.4862 | 2.60367 | ||||||||
\(423\) | 3.89609 | 0.189434 | ||||||||
\(424\) | 10.4780 | 0.508858 | ||||||||
\(425\) | 1.91981 | 0.0931247 | ||||||||
\(426\) | 38.5312 | 1.86684 | ||||||||
\(427\) | 12.9255 | 0.625508 | ||||||||
\(428\) | −17.2985 | −0.836156 | ||||||||
\(429\) | −1.45816 | −0.0704008 | ||||||||
\(430\) | −14.6707 | −0.707486 | ||||||||
\(431\) | −35.5666 | −1.71318 | −0.856591 | − | 0.515996i | \(-0.827422\pi\) | ||||
−0.856591 | + | 0.515996i | \(0.827422\pi\) | |||||||
\(432\) | 47.2236 | 2.27205 | ||||||||
\(433\) | 30.5767 | 1.46942 | 0.734712 | − | 0.678380i | \(-0.237317\pi\) | ||||
0.734712 | + | 0.678380i | \(0.237317\pi\) | |||||||
\(434\) | 37.8181 | 1.81533 | ||||||||
\(435\) | −1.71508 | −0.0822318 | ||||||||
\(436\) | 54.1316 | 2.59243 | ||||||||
\(437\) | 3.94266 | 0.188603 | ||||||||
\(438\) | 32.5501 | 1.55530 | ||||||||
\(439\) | −31.7051 | −1.51320 | −0.756600 | − | 0.653878i | \(-0.773141\pi\) | ||||
−0.756600 | + | 0.653878i | \(0.773141\pi\) | |||||||
\(440\) | −22.5410 | −1.07460 | ||||||||
\(441\) | −1.73541 | −0.0826385 | ||||||||
\(442\) | 1.77760 | 0.0845517 | ||||||||
\(443\) | 22.0093 | 1.04569 | 0.522846 | − | 0.852427i | \(-0.324870\pi\) | ||||
0.522846 | + | 0.852427i | \(0.324870\pi\) | |||||||
\(444\) | −14.6537 | −0.695433 | ||||||||
\(445\) | 27.0999 | 1.28466 | ||||||||
\(446\) | 12.2780 | 0.581379 | ||||||||
\(447\) | −12.0620 | −0.570511 | ||||||||
\(448\) | 19.2517 | 0.909559 | ||||||||
\(449\) | 2.97968 | 0.140620 | 0.0703098 | − | 0.997525i | \(-0.477601\pi\) | ||||
0.0703098 | + | 0.997525i | \(0.477601\pi\) | |||||||
\(450\) | 11.0987 | 0.523199 | ||||||||
\(451\) | −3.05213 | −0.143719 | ||||||||
\(452\) | 39.6356 | 1.86430 | ||||||||
\(453\) | 19.9882 | 0.939128 | ||||||||
\(454\) | 41.3859 | 1.94234 | ||||||||
\(455\) | −3.64924 | −0.171079 | ||||||||
\(456\) | 29.1972 | 1.36728 | ||||||||
\(457\) | 8.73038 | 0.408390 | 0.204195 | − | 0.978930i | \(-0.434542\pi\) | ||||
0.204195 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(458\) | 63.2305 | 2.95457 | ||||||||
\(459\) | −4.46589 | −0.208450 | ||||||||
\(460\) | −8.04353 | −0.375031 | ||||||||
\(461\) | −12.7674 | −0.594639 | −0.297319 | − | 0.954778i | \(-0.596093\pi\) | ||||
−0.297319 | + | 0.954778i | \(0.596093\pi\) | |||||||
\(462\) | 13.7960 | 0.641847 | ||||||||
\(463\) | 31.1939 | 1.44970 | 0.724851 | − | 0.688906i | \(-0.241909\pi\) | ||||
0.724851 | + | 0.688906i | \(0.241909\pi\) | |||||||
\(464\) | 9.33253 | 0.433252 | ||||||||
\(465\) | −8.86653 | −0.411176 | ||||||||
\(466\) | 39.0804 | 1.81037 | ||||||||
\(467\) | 22.5391 | 1.04299 | 0.521493 | − | 0.853256i | \(-0.325375\pi\) | ||||
0.521493 | + | 0.853256i | \(0.325375\pi\) | |||||||
\(468\) | 7.24773 | 0.335027 | ||||||||
\(469\) | −37.1931 | −1.71742 | ||||||||
\(470\) | −8.70883 | −0.401708 | ||||||||
\(471\) | −13.4153 | −0.618143 | ||||||||
\(472\) | 20.6085 | 0.948581 | ||||||||
\(473\) | 6.19281 | 0.284746 | ||||||||
\(474\) | 6.11010 | 0.280646 | ||||||||
\(475\) | 8.57631 | 0.393508 | ||||||||
\(476\) | −11.8613 | −0.543664 | ||||||||
\(477\) | −2.82802 | −0.129486 | ||||||||
\(478\) | 8.40682 | 0.384519 | ||||||||
\(479\) | −24.5397 | −1.12125 | −0.560623 | − | 0.828071i | \(-0.689438\pi\) | ||||
−0.560623 | + | 0.828071i | \(0.689438\pi\) | |||||||
\(480\) | −16.8025 | −0.766925 | ||||||||
\(481\) | −2.31995 | −0.105781 | ||||||||
\(482\) | 47.6308 | 2.16952 | ||||||||
\(483\) | 2.86566 | 0.130392 | ||||||||
\(484\) | −36.2982 | −1.64992 | ||||||||
\(485\) | 18.5641 | 0.842953 | ||||||||
\(486\) | −41.4378 | −1.87966 | ||||||||
\(487\) | −23.2452 | −1.05334 | −0.526671 | − | 0.850069i | \(-0.676560\pi\) | ||||
−0.526671 | + | 0.850069i | \(0.676560\pi\) | |||||||
\(488\) | 33.4022 | 1.51205 | ||||||||
\(489\) | 17.9267 | 0.810673 | ||||||||
\(490\) | 3.87911 | 0.175240 | ||||||||
\(491\) | −5.76174 | −0.260024 | −0.130012 | − | 0.991512i | \(-0.541502\pi\) | ||||
−0.130012 | + | 0.991512i | \(0.541502\pi\) | |||||||
\(492\) | −8.06547 | −0.363619 | ||||||||
\(493\) | −0.882567 | −0.0397488 | ||||||||
\(494\) | 7.94100 | 0.357282 | ||||||||
\(495\) | 6.08381 | 0.273447 | ||||||||
\(496\) | 48.2468 | 2.16635 | ||||||||
\(497\) | −40.7047 | −1.82586 | ||||||||
\(498\) | −17.1964 | −0.770590 | ||||||||
\(499\) | −30.8637 | −1.38165 | −0.690825 | − | 0.723022i | \(-0.742752\pi\) | ||||
−0.690825 | + | 0.723022i | \(0.742752\pi\) | |||||||
\(500\) | −57.7144 | −2.58107 | ||||||||
\(501\) | 2.74646 | 0.122703 | ||||||||
\(502\) | 22.3660 | 0.998243 | ||||||||
\(503\) | 35.6442 | 1.58930 | 0.794648 | − | 0.607071i | \(-0.207656\pi\) | ||||
0.794648 | + | 0.607071i | \(0.207656\pi\) | |||||||
\(504\) | −39.9159 | −1.77799 | ||||||||
\(505\) | −7.18778 | −0.319852 | ||||||||
\(506\) | 4.81425 | 0.214019 | ||||||||
\(507\) | 12.6559 | 0.562069 | ||||||||
\(508\) | 68.2333 | 3.02736 | ||||||||
\(509\) | −3.06341 | −0.135783 | −0.0678917 | − | 0.997693i | \(-0.521627\pi\) | ||||
−0.0678917 | + | 0.997693i | \(0.521627\pi\) | |||||||
\(510\) | 3.94306 | 0.174602 | ||||||||
\(511\) | −34.3862 | −1.52116 | ||||||||
\(512\) | −44.0222 | −1.94553 | ||||||||
\(513\) | −19.9503 | −0.880826 | ||||||||
\(514\) | −8.26427 | −0.364521 | ||||||||
\(515\) | −18.4571 | −0.813318 | ||||||||
\(516\) | 16.3649 | 0.720426 | ||||||||
\(517\) | 3.67617 | 0.161678 | ||||||||
\(518\) | 21.9495 | 0.964406 | ||||||||
\(519\) | −4.12943 | −0.181262 | ||||||||
\(520\) | −9.43040 | −0.413550 | ||||||||
\(521\) | 30.5468 | 1.33828 | 0.669140 | − | 0.743136i | \(-0.266663\pi\) | ||||
0.669140 | + | 0.743136i | \(0.266663\pi\) | |||||||
\(522\) | −5.10225 | −0.223319 | ||||||||
\(523\) | −25.4624 | −1.11339 | −0.556696 | − | 0.830716i | \(-0.687931\pi\) | ||||
−0.556696 | + | 0.830716i | \(0.687931\pi\) | |||||||
\(524\) | 29.9432 | 1.30807 | ||||||||
\(525\) | 6.23355 | 0.272055 | ||||||||
\(526\) | 2.33183 | 0.101672 | ||||||||
\(527\) | −4.56265 | −0.198752 | ||||||||
\(528\) | 17.6003 | 0.765957 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.32140 | 0.274584 | ||||||||
\(531\) | −5.56223 | −0.241380 | ||||||||
\(532\) | −52.9877 | −2.29731 | ||||||||
\(533\) | −1.27691 | −0.0553093 | ||||||||
\(534\) | −42.8623 | −1.85483 | ||||||||
\(535\) | −6.07492 | −0.262642 | ||||||||
\(536\) | −96.1147 | −4.15152 | ||||||||
\(537\) | −19.3810 | −0.836353 | ||||||||
\(538\) | 42.0989 | 1.81501 | ||||||||
\(539\) | −1.63745 | −0.0705300 | ||||||||
\(540\) | 40.7011 | 1.75150 | ||||||||
\(541\) | 9.43243 | 0.405532 | 0.202766 | − | 0.979227i | \(-0.435007\pi\) | ||||
0.202766 | + | 0.979227i | \(0.435007\pi\) | |||||||
\(542\) | −20.7773 | −0.892463 | ||||||||
\(543\) | 1.10346 | 0.0473541 | ||||||||
\(544\) | −8.64643 | −0.370712 | ||||||||
\(545\) | 19.0100 | 0.814299 | ||||||||
\(546\) | 5.77179 | 0.247010 | ||||||||
\(547\) | 41.5690 | 1.77736 | 0.888681 | − | 0.458527i | \(-0.151623\pi\) | ||||
0.888681 | + | 0.458527i | \(0.151623\pi\) | |||||||
\(548\) | 43.8817 | 1.87454 | ||||||||
\(549\) | −9.01526 | −0.384762 | ||||||||
\(550\) | 10.4722 | 0.446538 | ||||||||
\(551\) | −3.94266 | −0.167963 | ||||||||
\(552\) | 7.40546 | 0.315197 | ||||||||
\(553\) | −6.45477 | −0.274485 | ||||||||
\(554\) | 9.33195 | 0.396477 | ||||||||
\(555\) | −5.14610 | −0.218440 | ||||||||
\(556\) | 21.8997 | 0.928752 | ||||||||
\(557\) | 29.1407 | 1.23473 | 0.617366 | − | 0.786676i | \(-0.288200\pi\) | ||||
0.617366 | + | 0.786676i | \(0.288200\pi\) | |||||||
\(558\) | −26.3774 | −1.11664 | ||||||||
\(559\) | 2.59087 | 0.109582 | ||||||||
\(560\) | 44.0471 | 1.86133 | ||||||||
\(561\) | −1.66444 | −0.0702729 | ||||||||
\(562\) | 12.3813 | 0.522276 | ||||||||
\(563\) | 28.9802 | 1.22137 | 0.610685 | − | 0.791873i | \(-0.290894\pi\) | ||||
0.610685 | + | 0.791873i | \(0.290894\pi\) | |||||||
\(564\) | 9.71453 | 0.409056 | ||||||||
\(565\) | 13.9193 | 0.585590 | ||||||||
\(566\) | −29.6323 | −1.24554 | ||||||||
\(567\) | 2.00046 | 0.0840114 | ||||||||
\(568\) | −105.190 | −4.41365 | ||||||||
\(569\) | −34.2223 | −1.43467 | −0.717337 | − | 0.696726i | \(-0.754639\pi\) | ||||
−0.717337 | + | 0.696726i | \(0.754639\pi\) | |||||||
\(570\) | 17.6147 | 0.737798 | ||||||||
\(571\) | −26.0169 | −1.08877 | −0.544386 | − | 0.838835i | \(-0.683237\pi\) | ||||
−0.544386 | + | 0.838835i | \(0.683237\pi\) | |||||||
\(572\) | 6.83862 | 0.285937 | ||||||||
\(573\) | 8.59833 | 0.359200 | ||||||||
\(574\) | 12.0811 | 0.504256 | ||||||||
\(575\) | 2.17526 | 0.0907147 | ||||||||
\(576\) | −13.4277 | −0.559487 | ||||||||
\(577\) | −28.2981 | −1.17806 | −0.589032 | − | 0.808110i | \(-0.700491\pi\) | ||||
−0.589032 | + | 0.808110i | \(0.700491\pi\) | |||||||
\(578\) | −42.2553 | −1.75759 | ||||||||
\(579\) | 0.310651 | 0.0129102 | ||||||||
\(580\) | 8.04353 | 0.333989 | ||||||||
\(581\) | 18.1665 | 0.753672 | ||||||||
\(582\) | −29.3617 | −1.21708 | ||||||||
\(583\) | −2.66839 | −0.110513 | ||||||||
\(584\) | −88.8612 | −3.67710 | ||||||||
\(585\) | 2.54527 | 0.105234 | ||||||||
\(586\) | −34.3456 | −1.41880 | ||||||||
\(587\) | 17.1615 | 0.708331 | 0.354165 | − | 0.935183i | \(-0.384765\pi\) | ||||
0.354165 | + | 0.935183i | \(0.384765\pi\) | |||||||
\(588\) | −4.32708 | −0.178446 | ||||||||
\(589\) | −20.3825 | −0.839848 | ||||||||
\(590\) | 12.4331 | 0.511863 | ||||||||
\(591\) | 12.3623 | 0.508517 | ||||||||
\(592\) | 28.0023 | 1.15089 | ||||||||
\(593\) | −17.0152 | −0.698731 | −0.349365 | − | 0.936987i | \(-0.613603\pi\) | ||||
−0.349365 | + | 0.936987i | \(0.613603\pi\) | |||||||
\(594\) | −24.3606 | −0.999528 | ||||||||
\(595\) | −4.16548 | −0.170768 | ||||||||
\(596\) | 56.5692 | 2.31717 | ||||||||
\(597\) | −13.3568 | −0.546658 | ||||||||
\(598\) | 2.01412 | 0.0823636 | ||||||||
\(599\) | −6.72206 | −0.274656 | −0.137328 | − | 0.990526i | \(-0.543851\pi\) | ||||
−0.137328 | + | 0.990526i | \(0.543851\pi\) | |||||||
\(600\) | 16.1088 | 0.657639 | ||||||||
\(601\) | −45.1047 | −1.83986 | −0.919930 | − | 0.392082i | \(-0.871755\pi\) | ||||
−0.919930 | + | 0.392082i | \(0.871755\pi\) | |||||||
\(602\) | −24.5127 | −0.999064 | ||||||||
\(603\) | 25.9414 | 1.05642 | ||||||||
\(604\) | −93.7424 | −3.81432 | ||||||||
\(605\) | −12.7472 | −0.518249 | ||||||||
\(606\) | 11.3685 | 0.461813 | ||||||||
\(607\) | −22.7337 | −0.922732 | −0.461366 | − | 0.887210i | \(-0.652640\pi\) | ||||
−0.461366 | + | 0.887210i | \(0.652640\pi\) | |||||||
\(608\) | −38.6258 | −1.56648 | ||||||||
\(609\) | −2.86566 | −0.116122 | ||||||||
\(610\) | 20.1516 | 0.815913 | ||||||||
\(611\) | 1.53799 | 0.0622204 | ||||||||
\(612\) | 8.27304 | 0.334418 | ||||||||
\(613\) | −25.6809 | −1.03724 | −0.518620 | − | 0.855005i | \(-0.673554\pi\) | ||||
−0.518620 | + | 0.855005i | \(0.673554\pi\) | |||||||
\(614\) | −57.7679 | −2.33132 | ||||||||
\(615\) | −2.83244 | −0.114215 | ||||||||
\(616\) | −37.6628 | −1.51748 | ||||||||
\(617\) | 22.8029 | 0.918009 | 0.459004 | − | 0.888434i | \(-0.348206\pi\) | ||||
0.459004 | + | 0.888434i | \(0.348206\pi\) | |||||||
\(618\) | 29.1925 | 1.17430 | ||||||||
\(619\) | 17.3140 | 0.695909 | 0.347955 | − | 0.937511i | \(-0.386876\pi\) | ||||
0.347955 | + | 0.937511i | \(0.386876\pi\) | |||||||
\(620\) | 41.5830 | 1.67001 | ||||||||
\(621\) | −5.06011 | −0.203055 | ||||||||
\(622\) | −81.6944 | −3.27565 | ||||||||
\(623\) | 45.2801 | 1.81411 | ||||||||
\(624\) | 7.36341 | 0.294772 | ||||||||
\(625\) | −9.39192 | −0.375677 | ||||||||
\(626\) | 56.1504 | 2.24422 | ||||||||
\(627\) | −7.43551 | −0.296946 | ||||||||
\(628\) | 62.9161 | 2.51063 | ||||||||
\(629\) | −2.64814 | −0.105588 | ||||||||
\(630\) | −24.0813 | −0.959421 | ||||||||
\(631\) | −4.67782 | −0.186221 | −0.0931105 | − | 0.995656i | \(-0.529681\pi\) | ||||
−0.0931105 | + | 0.995656i | \(0.529681\pi\) | |||||||
\(632\) | −16.6805 | −0.663513 | ||||||||
\(633\) | −20.9525 | −0.832787 | ||||||||
\(634\) | 67.3916 | 2.67646 | ||||||||
\(635\) | 23.9623 | 0.950913 | ||||||||
\(636\) | −7.05140 | −0.279606 | ||||||||
\(637\) | −0.685056 | −0.0271429 | ||||||||
\(638\) | −4.81425 | −0.190598 | ||||||||
\(639\) | 28.3907 | 1.12312 | ||||||||
\(640\) | −2.91670 | −0.115293 | ||||||||
\(641\) | −27.9708 | −1.10478 | −0.552390 | − | 0.833586i | \(-0.686284\pi\) | ||||
−0.552390 | + | 0.833586i | \(0.686284\pi\) | |||||||
\(642\) | 9.60834 | 0.379211 | ||||||||
\(643\) | −29.9724 | −1.18199 | −0.590997 | − | 0.806673i | \(-0.701266\pi\) | ||||
−0.590997 | + | 0.806673i | \(0.701266\pi\) | |||||||
\(644\) | −13.4396 | −0.529594 | ||||||||
\(645\) | 5.74706 | 0.226290 | ||||||||
\(646\) | 9.06438 | 0.356633 | ||||||||
\(647\) | −2.35510 | −0.0925886 | −0.0462943 | − | 0.998928i | \(-0.514741\pi\) | ||||
−0.0462943 | + | 0.998928i | \(0.514741\pi\) | |||||||
\(648\) | 5.16961 | 0.203081 | ||||||||
\(649\) | −5.24826 | −0.206012 | ||||||||
\(650\) | 4.38125 | 0.171847 | ||||||||
\(651\) | −14.8147 | −0.580635 | ||||||||
\(652\) | −84.0741 | −3.29260 | ||||||||
\(653\) | 5.15341 | 0.201668 | 0.100834 | − | 0.994903i | \(-0.467849\pi\) | ||||
0.100834 | + | 0.994903i | \(0.467849\pi\) | |||||||
\(654\) | −30.0670 | −1.17571 | ||||||||
\(655\) | 10.5155 | 0.410875 | ||||||||
\(656\) | 15.4126 | 0.601761 | ||||||||
\(657\) | 23.9837 | 0.935692 | ||||||||
\(658\) | −14.5512 | −0.567266 | ||||||||
\(659\) | 20.5225 | 0.799444 | 0.399722 | − | 0.916636i | \(-0.369107\pi\) | ||||
0.399722 | + | 0.916636i | \(0.369107\pi\) | |||||||
\(660\) | 15.1694 | 0.590468 | ||||||||
\(661\) | −12.3073 | −0.478697 | −0.239348 | − | 0.970934i | \(-0.576934\pi\) | ||||
−0.239348 | + | 0.970934i | \(0.576934\pi\) | |||||||
\(662\) | 80.8721 | 3.14318 | ||||||||
\(663\) | −0.696350 | −0.0270440 | ||||||||
\(664\) | 46.9459 | 1.82186 | ||||||||
\(665\) | −18.6083 | −0.721599 | ||||||||
\(666\) | −15.3093 | −0.593224 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −12.8806 | −0.498364 | ||||||||
\(669\) | −4.80973 | −0.185955 | ||||||||
\(670\) | −57.9861 | −2.24020 | ||||||||
\(671\) | −8.50638 | −0.328385 | ||||||||
\(672\) | −28.0746 | −1.08300 | ||||||||
\(673\) | 6.69894 | 0.258225 | 0.129113 | − | 0.991630i | \(-0.458787\pi\) | ||||
0.129113 | + | 0.991630i | \(0.458787\pi\) | |||||||
\(674\) | 55.2716 | 2.12898 | ||||||||
\(675\) | −11.0071 | −0.423662 | ||||||||
\(676\) | −59.3548 | −2.28288 | ||||||||
\(677\) | 19.1249 | 0.735030 | 0.367515 | − | 0.930018i | \(-0.380209\pi\) | ||||
0.367515 | + | 0.930018i | \(0.380209\pi\) | |||||||
\(678\) | −22.0153 | −0.845494 | ||||||||
\(679\) | 31.0180 | 1.19036 | ||||||||
\(680\) | −10.7645 | −0.412799 | ||||||||
\(681\) | −16.2124 | −0.621259 | ||||||||
\(682\) | −24.8884 | −0.953028 | ||||||||
\(683\) | 7.36478 | 0.281805 | 0.140903 | − | 0.990023i | \(-0.455000\pi\) | ||||
0.140903 | + | 0.990023i | \(0.455000\pi\) | |||||||
\(684\) | 36.9578 | 1.41312 | ||||||||
\(685\) | 15.4105 | 0.588803 | ||||||||
\(686\) | −44.7254 | −1.70763 | ||||||||
\(687\) | −24.7697 | −0.945022 | ||||||||
\(688\) | −31.2724 | −1.19225 | ||||||||
\(689\) | −1.11637 | −0.0425302 | ||||||||
\(690\) | 4.46772 | 0.170083 | ||||||||
\(691\) | −49.1019 | −1.86792 | −0.933961 | − | 0.357374i | \(-0.883672\pi\) | ||||
−0.933961 | + | 0.357374i | \(0.883672\pi\) | |||||||
\(692\) | 19.3666 | 0.736206 | ||||||||
\(693\) | 10.1652 | 0.386144 | ||||||||
\(694\) | −65.6290 | −2.49124 | ||||||||
\(695\) | 7.69075 | 0.291727 | ||||||||
\(696\) | −7.40546 | −0.280703 | ||||||||
\(697\) | −1.45755 | −0.0552088 | ||||||||
\(698\) | 71.5071 | 2.70658 | ||||||||
\(699\) | −15.3092 | −0.579048 | ||||||||
\(700\) | −29.2347 | −1.10497 | ||||||||
\(701\) | 36.2294 | 1.36837 | 0.684183 | − | 0.729310i | \(-0.260159\pi\) | ||||
0.684183 | + | 0.729310i | \(0.260159\pi\) | |||||||
\(702\) | −10.1917 | −0.384660 | ||||||||
\(703\) | −11.8300 | −0.446175 | ||||||||
\(704\) | −12.6697 | −0.477509 | ||||||||
\(705\) | 3.41156 | 0.128487 | ||||||||
\(706\) | 40.4545 | 1.52253 | ||||||||
\(707\) | −12.0098 | −0.451674 | ||||||||
\(708\) | −13.8689 | −0.521225 | ||||||||
\(709\) | −45.7281 | −1.71735 | −0.858677 | − | 0.512518i | \(-0.828713\pi\) | ||||
−0.858677 | + | 0.512518i | \(0.828713\pi\) | |||||||
\(710\) | −63.4609 | −2.38165 | ||||||||
\(711\) | 4.50207 | 0.168841 | ||||||||
\(712\) | 117.013 | 4.38526 | ||||||||
\(713\) | −5.16975 | −0.193609 | ||||||||
\(714\) | 6.58830 | 0.246561 | ||||||||
\(715\) | 2.40160 | 0.0898147 | ||||||||
\(716\) | 90.8947 | 3.39690 | ||||||||
\(717\) | −3.29326 | −0.122989 | ||||||||
\(718\) | 21.6351 | 0.807414 | ||||||||
\(719\) | 33.7657 | 1.25925 | 0.629624 | − | 0.776900i | \(-0.283209\pi\) | ||||
0.629624 | + | 0.776900i | \(0.283209\pi\) | |||||||
\(720\) | −30.7219 | −1.14494 | ||||||||
\(721\) | −30.8392 | −1.14851 | ||||||||
\(722\) | −9.00137 | −0.334996 | ||||||||
\(723\) | −18.6587 | −0.693925 | ||||||||
\(724\) | −5.17512 | −0.192332 | ||||||||
\(725\) | −2.17526 | −0.0807872 | ||||||||
\(726\) | 20.1616 | 0.748266 | ||||||||
\(727\) | −27.4791 | −1.01914 | −0.509571 | − | 0.860429i | \(-0.670196\pi\) | ||||
−0.509571 | + | 0.860429i | \(0.670196\pi\) | |||||||
\(728\) | −15.7569 | −0.583988 | ||||||||
\(729\) | 14.0956 | 0.522060 | ||||||||
\(730\) | −53.6100 | −1.98420 | ||||||||
\(731\) | 2.95739 | 0.109383 | ||||||||
\(732\) | −22.4787 | −0.830836 | ||||||||
\(733\) | −15.6367 | −0.577554 | −0.288777 | − | 0.957396i | \(-0.593249\pi\) | ||||
−0.288777 | + | 0.957396i | \(0.593249\pi\) | |||||||
\(734\) | −35.5723 | −1.31300 | ||||||||
\(735\) | −1.51959 | −0.0560509 | ||||||||
\(736\) | −9.79691 | −0.361119 | ||||||||
\(737\) | 24.4771 | 0.901625 | ||||||||
\(738\) | −8.42633 | −0.310178 | ||||||||
\(739\) | 4.37819 | 0.161054 | 0.0805271 | − | 0.996752i | \(-0.474340\pi\) | ||||
0.0805271 | + | 0.996752i | \(0.474340\pi\) | |||||||
\(740\) | 24.1346 | 0.887207 | ||||||||
\(741\) | −3.11078 | −0.114277 | ||||||||
\(742\) | 10.5622 | 0.387750 | ||||||||
\(743\) | −7.80342 | −0.286280 | −0.143140 | − | 0.989702i | \(-0.545720\pi\) | ||||
−0.143140 | + | 0.989702i | \(0.545720\pi\) | |||||||
\(744\) | −38.2844 | −1.40357 | ||||||||
\(745\) | 19.8661 | 0.727836 | ||||||||
\(746\) | −86.3640 | −3.16201 | ||||||||
\(747\) | −12.6707 | −0.463598 | ||||||||
\(748\) | 7.80606 | 0.285418 | ||||||||
\(749\) | −10.1503 | −0.370885 | ||||||||
\(750\) | 32.0571 | 1.17056 | ||||||||
\(751\) | 36.6586 | 1.33769 | 0.668845 | − | 0.743402i | \(-0.266789\pi\) | ||||
0.668845 | + | 0.743402i | \(0.266789\pi\) | |||||||
\(752\) | −18.5639 | −0.676954 | ||||||||
\(753\) | −8.76157 | −0.319289 | ||||||||
\(754\) | −2.01412 | −0.0733501 | ||||||||
\(755\) | −32.9206 | −1.19810 | ||||||||
\(756\) | 68.0059 | 2.47335 | ||||||||
\(757\) | −15.5724 | −0.565989 | −0.282994 | − | 0.959122i | \(-0.591328\pi\) | ||||
−0.282994 | + | 0.959122i | \(0.591328\pi\) | |||||||
\(758\) | −50.5940 | −1.83766 | ||||||||
\(759\) | −1.88591 | −0.0684543 | ||||||||
\(760\) | −48.0878 | −1.74433 | ||||||||
\(761\) | 27.3332 | 0.990827 | 0.495414 | − | 0.868657i | \(-0.335017\pi\) | ||||
0.495414 | + | 0.868657i | \(0.335017\pi\) | |||||||
\(762\) | −37.8997 | −1.37296 | ||||||||
\(763\) | 31.7630 | 1.14990 | ||||||||
\(764\) | −40.3252 | −1.45891 | ||||||||
\(765\) | 2.90534 | 0.105043 | ||||||||
\(766\) | 27.3643 | 0.988713 | ||||||||
\(767\) | −2.19570 | −0.0792822 | ||||||||
\(768\) | 18.6047 | 0.671341 | ||||||||
\(769\) | 23.2168 | 0.837219 | 0.418610 | − | 0.908166i | \(-0.362518\pi\) | ||||
0.418610 | + | 0.908166i | \(0.362518\pi\) | |||||||
\(770\) | −22.7220 | −0.818843 | ||||||||
\(771\) | 3.23741 | 0.116593 | ||||||||
\(772\) | −1.45692 | −0.0524356 | ||||||||
\(773\) | −7.03205 | −0.252925 | −0.126463 | − | 0.991971i | \(-0.540362\pi\) | ||||
−0.126463 | + | 0.991971i | \(0.540362\pi\) | |||||||
\(774\) | 17.0971 | 0.614543 | ||||||||
\(775\) | −11.2456 | −0.403952 | ||||||||
\(776\) | 80.1570 | 2.87747 | ||||||||
\(777\) | −8.59841 | −0.308466 | ||||||||
\(778\) | −45.2538 | −1.62243 | ||||||||
\(779\) | −6.51127 | −0.233290 | ||||||||
\(780\) | 6.34638 | 0.227237 | ||||||||
\(781\) | 26.7881 | 0.958555 | ||||||||
\(782\) | 2.29905 | 0.0822140 | ||||||||
\(783\) | 5.06011 | 0.180834 | ||||||||
\(784\) | 8.26877 | 0.295313 | ||||||||
\(785\) | 22.0950 | 0.788603 | ||||||||
\(786\) | −16.6317 | −0.593234 | ||||||||
\(787\) | −38.4072 | −1.36907 | −0.684535 | − | 0.728980i | \(-0.739995\pi\) | ||||
−0.684535 | + | 0.728980i | \(0.739995\pi\) | |||||||
\(788\) | −57.9778 | −2.06537 | ||||||||
\(789\) | −0.913461 | −0.0325201 | ||||||||
\(790\) | −10.0633 | −0.358038 | ||||||||
\(791\) | 23.2572 | 0.826931 | ||||||||
\(792\) | 26.2690 | 0.933428 | ||||||||
\(793\) | −3.55879 | −0.126376 | ||||||||
\(794\) | −32.9457 | −1.16920 | ||||||||
\(795\) | −2.47632 | −0.0878261 | ||||||||
\(796\) | 62.6419 | 2.22028 | ||||||||
\(797\) | 29.2736 | 1.03693 | 0.518463 | − | 0.855100i | \(-0.326504\pi\) | ||||
0.518463 | + | 0.855100i | \(0.326504\pi\) | |||||||
\(798\) | 29.4316 | 1.04187 | ||||||||
\(799\) | 1.75556 | 0.0621074 | ||||||||
\(800\) | −21.3108 | −0.753452 | ||||||||
\(801\) | −31.5820 | −1.11589 | ||||||||
\(802\) | −68.7678 | −2.42828 | ||||||||
\(803\) | 22.6299 | 0.798591 | ||||||||
\(804\) | 64.6824 | 2.28117 | ||||||||
\(805\) | −4.71974 | −0.166349 | ||||||||
\(806\) | −10.4125 | −0.366765 | ||||||||
\(807\) | −16.4917 | −0.580534 | ||||||||
\(808\) | −31.0357 | −1.09183 | ||||||||
\(809\) | −53.7604 | −1.89011 | −0.945057 | − | 0.326905i | \(-0.893994\pi\) | ||||
−0.945057 | + | 0.326905i | \(0.893994\pi\) | |||||||
\(810\) | 3.11883 | 0.109584 | ||||||||
\(811\) | −15.2539 | −0.535636 | −0.267818 | − | 0.963470i | \(-0.586303\pi\) | ||||
−0.267818 | + | 0.963470i | \(0.586303\pi\) | |||||||
\(812\) | 13.4396 | 0.471637 | ||||||||
\(813\) | 8.13923 | 0.285455 | ||||||||
\(814\) | −14.4452 | −0.506303 | ||||||||
\(815\) | −29.5253 | −1.03423 | ||||||||
\(816\) | 8.40509 | 0.294237 | ||||||||
\(817\) | 13.2114 | 0.462210 | ||||||||
\(818\) | 24.2097 | 0.846472 | ||||||||
\(819\) | 4.25279 | 0.148604 | ||||||||
\(820\) | 13.2838 | 0.463892 | ||||||||
\(821\) | 32.7377 | 1.14256 | 0.571278 | − | 0.820757i | \(-0.306448\pi\) | ||||
0.571278 | + | 0.820757i | \(0.306448\pi\) | |||||||
\(822\) | −24.3738 | −0.850134 | ||||||||
\(823\) | −34.5678 | −1.20496 | −0.602479 | − | 0.798135i | \(-0.705820\pi\) | ||||
−0.602479 | + | 0.798135i | \(0.705820\pi\) | |||||||
\(824\) | −79.6950 | −2.77631 | ||||||||
\(825\) | −4.10236 | −0.142826 | ||||||||
\(826\) | 20.7740 | 0.722818 | ||||||||
\(827\) | 45.1215 | 1.56903 | 0.784513 | − | 0.620112i | \(-0.212913\pi\) | ||||
0.784513 | + | 0.620112i | \(0.212913\pi\) | |||||||
\(828\) | 9.37384 | 0.325764 | ||||||||
\(829\) | −48.9447 | −1.69992 | −0.849960 | − | 0.526847i | \(-0.823374\pi\) | ||||
−0.849960 | + | 0.526847i | \(0.823374\pi\) | |||||||
\(830\) | 28.3225 | 0.983089 | ||||||||
\(831\) | −3.65566 | −0.126814 | ||||||||
\(832\) | −5.30061 | −0.183766 | ||||||||
\(833\) | −0.781968 | −0.0270936 | ||||||||
\(834\) | −12.1640 | −0.421205 | ||||||||
\(835\) | −4.52341 | −0.156539 | ||||||||
\(836\) | 34.8717 | 1.20606 | ||||||||
\(837\) | 26.1595 | 0.904205 | ||||||||
\(838\) | 66.0088 | 2.28024 | ||||||||
\(839\) | −54.6452 | −1.88656 | −0.943281 | − | 0.331995i | \(-0.892278\pi\) | ||||
−0.943281 | + | 0.331995i | \(0.892278\pi\) | |||||||
\(840\) | −34.9518 | −1.20595 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −10.4808 | −0.361193 | ||||||||
\(843\) | −4.85022 | −0.167051 | ||||||||
\(844\) | 98.2648 | 3.38241 | ||||||||
\(845\) | −20.8443 | −0.717065 | ||||||||
\(846\) | 10.1492 | 0.348936 | ||||||||
\(847\) | −21.2989 | −0.731837 | ||||||||
\(848\) | 13.4748 | 0.462726 | ||||||||
\(849\) | 11.6080 | 0.398387 | ||||||||
\(850\) | 5.00104 | 0.171534 | ||||||||
\(851\) | −3.00050 | −0.102856 | ||||||||
\(852\) | 70.7895 | 2.42521 | ||||||||
\(853\) | −18.9241 | −0.647948 | −0.323974 | − | 0.946066i | \(-0.605019\pi\) | ||||
−0.323974 | + | 0.946066i | \(0.605019\pi\) | |||||||
\(854\) | 33.6704 | 1.15218 | ||||||||
\(855\) | 12.9789 | 0.443869 | ||||||||
\(856\) | −26.2306 | −0.896543 | ||||||||
\(857\) | 14.1409 | 0.483046 | 0.241523 | − | 0.970395i | \(-0.422353\pi\) | ||||
0.241523 | + | 0.970395i | \(0.422353\pi\) | |||||||
\(858\) | −3.79846 | −0.129677 | ||||||||
\(859\) | 55.3730 | 1.88930 | 0.944652 | − | 0.328075i | \(-0.106400\pi\) | ||||
0.944652 | + | 0.328075i | \(0.106400\pi\) | |||||||
\(860\) | −26.9530 | −0.919091 | ||||||||
\(861\) | −4.73261 | −0.161287 | ||||||||
\(862\) | −92.6496 | −3.15566 | ||||||||
\(863\) | −9.62971 | −0.327799 | −0.163900 | − | 0.986477i | \(-0.552407\pi\) | ||||
−0.163900 | + | 0.986477i | \(0.552407\pi\) | |||||||
\(864\) | 49.5735 | 1.68652 | ||||||||
\(865\) | 6.80117 | 0.231247 | ||||||||
\(866\) | 79.6512 | 2.70666 | ||||||||
\(867\) | 16.5529 | 0.562167 | ||||||||
\(868\) | 69.4794 | 2.35828 | ||||||||
\(869\) | 4.24794 | 0.144101 | ||||||||
\(870\) | −4.46772 | −0.151470 | ||||||||
\(871\) | 10.2404 | 0.346983 | ||||||||
\(872\) | 82.0824 | 2.77966 | ||||||||
\(873\) | −21.6344 | −0.732214 | ||||||||
\(874\) | 10.2705 | 0.347404 | ||||||||
\(875\) | −33.8654 | −1.14486 | ||||||||
\(876\) | 59.8010 | 2.02049 | ||||||||
\(877\) | 6.67453 | 0.225383 | 0.112691 | − | 0.993630i | \(-0.464053\pi\) | ||||
0.112691 | + | 0.993630i | \(0.464053\pi\) | |||||||
\(878\) | −82.5905 | −2.78730 | ||||||||
\(879\) | 13.4544 | 0.453806 | ||||||||
\(880\) | −28.9878 | −0.977178 | ||||||||
\(881\) | −56.9064 | −1.91722 | −0.958612 | − | 0.284715i | \(-0.908101\pi\) | ||||
−0.958612 | + | 0.284715i | \(0.908101\pi\) | |||||||
\(882\) | −4.52068 | −0.152219 | ||||||||
\(883\) | 8.65659 | 0.291318 | 0.145659 | − | 0.989335i | \(-0.453470\pi\) | ||||
0.145659 | + | 0.989335i | \(0.453470\pi\) | |||||||
\(884\) | 3.26580 | 0.109841 | ||||||||
\(885\) | −4.87049 | −0.163720 | ||||||||
\(886\) | 57.3334 | 1.92615 | ||||||||
\(887\) | 21.9095 | 0.735648 | 0.367824 | − | 0.929895i | \(-0.380103\pi\) | ||||
0.367824 | + | 0.929895i | \(0.380103\pi\) | |||||||
\(888\) | −22.2201 | −0.745658 | ||||||||
\(889\) | 40.0376 | 1.34282 | ||||||||
\(890\) | 70.5943 | 2.36633 | ||||||||
\(891\) | −1.31652 | −0.0441051 | ||||||||
\(892\) | 22.5571 | 0.755267 | ||||||||
\(893\) | 7.84256 | 0.262441 | ||||||||
\(894\) | −31.4210 | −1.05087 | ||||||||
\(895\) | 31.9205 | 1.06699 | ||||||||
\(896\) | −4.87339 | −0.162809 | ||||||||
\(897\) | −0.789005 | −0.0263441 | ||||||||
\(898\) | 7.76194 | 0.259019 | ||||||||
\(899\) | 5.16975 | 0.172421 | ||||||||
\(900\) | 20.3906 | 0.679685 | ||||||||
\(901\) | −1.27430 | −0.0424530 | ||||||||
\(902\) | −7.95069 | −0.264729 | ||||||||
\(903\) | 9.60252 | 0.319552 | ||||||||
\(904\) | 60.1015 | 1.99895 | ||||||||
\(905\) | −1.81740 | −0.0604126 | ||||||||
\(906\) | 52.0685 | 1.72986 | ||||||||
\(907\) | −50.4844 | −1.67631 | −0.838153 | − | 0.545435i | \(-0.816365\pi\) | ||||
−0.838153 | + | 0.545435i | \(0.816365\pi\) | |||||||
\(908\) | 76.0342 | 2.52328 | ||||||||
\(909\) | 8.37656 | 0.277833 | ||||||||
\(910\) | −9.50614 | −0.315125 | ||||||||
\(911\) | 17.2002 | 0.569867 | 0.284933 | − | 0.958547i | \(-0.408029\pi\) | ||||
0.284933 | + | 0.958547i | \(0.408029\pi\) | |||||||
\(912\) | 37.5477 | 1.24333 | ||||||||
\(913\) | −11.9555 | −0.395670 | ||||||||
\(914\) | 22.7423 | 0.752249 | ||||||||
\(915\) | −7.89410 | −0.260971 | ||||||||
\(916\) | 116.167 | 3.83827 | ||||||||
\(917\) | 17.5699 | 0.580210 | ||||||||
\(918\) | −11.6335 | −0.383962 | ||||||||
\(919\) | −12.9679 | −0.427771 | −0.213886 | − | 0.976859i | \(-0.568612\pi\) | ||||
−0.213886 | + | 0.976859i | \(0.568612\pi\) | |||||||
\(920\) | −12.1968 | −0.402116 | ||||||||
\(921\) | 22.6298 | 0.745677 | ||||||||
\(922\) | −33.2587 | −1.09532 | ||||||||
\(923\) | 11.2073 | 0.368892 | ||||||||
\(924\) | 25.3459 | 0.833820 | ||||||||
\(925\) | −6.52688 | −0.214603 | ||||||||
\(926\) | 81.2588 | 2.67033 | ||||||||
\(927\) | 21.5097 | 0.706472 | ||||||||
\(928\) | 9.79691 | 0.321599 | ||||||||
\(929\) | −47.6705 | −1.56402 | −0.782010 | − | 0.623266i | \(-0.785805\pi\) | ||||
−0.782010 | + | 0.623266i | \(0.785805\pi\) | |||||||
\(930\) | −23.0970 | −0.757380 | ||||||||
\(931\) | −3.49326 | −0.114487 | ||||||||
\(932\) | 71.7985 | 2.35184 | ||||||||
\(933\) | 32.0026 | 1.04772 | ||||||||
\(934\) | 58.7136 | 1.92117 | ||||||||
\(935\) | 2.74134 | 0.0896515 | ||||||||
\(936\) | 10.9901 | 0.359222 | ||||||||
\(937\) | −12.0522 | −0.393727 | −0.196863 | − | 0.980431i | \(-0.563076\pi\) | ||||
−0.196863 | + | 0.980431i | \(0.563076\pi\) | |||||||
\(938\) | −96.8866 | −3.16346 | ||||||||
\(939\) | −21.9962 | −0.717817 | ||||||||
\(940\) | −15.9998 | −0.521857 | ||||||||
\(941\) | 15.0969 | 0.492146 | 0.246073 | − | 0.969251i | \(-0.420860\pi\) | ||||
0.246073 | + | 0.969251i | \(0.420860\pi\) | |||||||
\(942\) | −34.9463 | −1.13861 | ||||||||
\(943\) | −1.65149 | −0.0537800 | ||||||||
\(944\) | 26.5026 | 0.862585 | ||||||||
\(945\) | 23.8824 | 0.776894 | ||||||||
\(946\) | 16.1320 | 0.524498 | ||||||||
\(947\) | 15.8760 | 0.515900 | 0.257950 | − | 0.966158i | \(-0.416953\pi\) | ||||
0.257950 | + | 0.966158i | \(0.416953\pi\) | |||||||
\(948\) | 11.2255 | 0.364586 | ||||||||
\(949\) | 9.46760 | 0.307331 | ||||||||
\(950\) | 22.3410 | 0.724837 | ||||||||
\(951\) | −26.3997 | −0.856069 | ||||||||
\(952\) | −17.9859 | −0.582927 | ||||||||
\(953\) | 24.7437 | 0.801528 | 0.400764 | − | 0.916181i | \(-0.368745\pi\) | ||||
0.400764 | + | 0.916181i | \(0.368745\pi\) | |||||||
\(954\) | −7.36690 | −0.238512 | ||||||||
\(955\) | −14.1615 | −0.458254 | ||||||||
\(956\) | 15.4450 | 0.499527 | ||||||||
\(957\) | 1.88591 | 0.0609629 | ||||||||
\(958\) | −63.9250 | −2.06532 | ||||||||
\(959\) | 25.7487 | 0.831469 | ||||||||
\(960\) | −11.7578 | −0.379481 | ||||||||
\(961\) | −4.27369 | −0.137861 | ||||||||
\(962\) | −6.04339 | −0.194847 | ||||||||
\(963\) | 7.07965 | 0.228138 | ||||||||
\(964\) | 87.5072 | 2.81842 | ||||||||
\(965\) | −0.511643 | −0.0164704 | ||||||||
\(966\) | 7.46493 | 0.240180 | ||||||||
\(967\) | 4.50132 | 0.144753 | 0.0723763 | − | 0.997377i | \(-0.476942\pi\) | ||||
0.0723763 | + | 0.997377i | \(0.476942\pi\) | |||||||
\(968\) | −55.0407 | −1.76908 | ||||||||
\(969\) | −3.55084 | −0.114070 | ||||||||
\(970\) | 48.3588 | 1.55271 | ||||||||
\(971\) | −9.14396 | −0.293444 | −0.146722 | − | 0.989178i | \(-0.546872\pi\) | ||||
−0.146722 | + | 0.989178i | \(0.546872\pi\) | |||||||
\(972\) | −76.1295 | −2.44186 | ||||||||
\(973\) | 12.8502 | 0.411957 | ||||||||
\(974\) | −60.5530 | −1.94024 | ||||||||
\(975\) | −1.71629 | −0.0549654 | ||||||||
\(976\) | 42.9554 | 1.37497 | ||||||||
\(977\) | 26.5953 | 0.850858 | 0.425429 | − | 0.904992i | \(-0.360123\pi\) | ||||
0.425429 | + | 0.904992i | \(0.360123\pi\) | |||||||
\(978\) | 46.6984 | 1.49325 | ||||||||
\(979\) | −29.7993 | −0.952389 | ||||||||
\(980\) | 7.12670 | 0.227654 | ||||||||
\(981\) | −22.1541 | −0.707325 | ||||||||
\(982\) | −15.0091 | −0.478961 | ||||||||
\(983\) | −14.8855 | −0.474773 | −0.237387 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237387 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(984\) | −12.2301 | −0.389880 | ||||||||
\(985\) | −20.3607 | −0.648746 | ||||||||
\(986\) | −2.29905 | −0.0732168 | ||||||||
\(987\) | 5.70024 | 0.181441 | ||||||||
\(988\) | 14.5892 | 0.464144 | ||||||||
\(989\) | 3.35090 | 0.106552 | ||||||||
\(990\) | 15.8481 | 0.503686 | ||||||||
\(991\) | −14.8656 | −0.472222 | −0.236111 | − | 0.971726i | \(-0.575873\pi\) | ||||
−0.236111 | + | 0.971726i | \(0.575873\pi\) | |||||||
\(992\) | 50.6476 | 1.60806 | ||||||||
\(993\) | −31.6805 | −1.00535 | ||||||||
\(994\) | −106.034 | −3.36320 | ||||||||
\(995\) | 21.9987 | 0.697405 | ||||||||
\(996\) | −31.5932 | −1.00107 | ||||||||
\(997\) | −3.64966 | −0.115586 | −0.0577930 | − | 0.998329i | \(-0.518406\pi\) | ||||
−0.0577930 | + | 0.998329i | \(0.518406\pi\) | |||||||
\(998\) | −80.3989 | −2.54498 | ||||||||
\(999\) | 15.1829 | 0.480365 |
(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 | 667.2.a.c.1.13 | ✓ | 13 | |
3.2 | odd | 2 | 6003.2.a.o.1.1 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.c.1.13 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6003.2.a.o.1.1 | 13 | 3.2 | odd | 2 |