Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, 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("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32611 | −1.64481 | −0.822405 | − | 0.568903i | \(-0.807368\pi\) | ||||
−0.822405 | + | 0.568903i | \(0.807368\pi\) | |||||||
\(3\) | 2.50152 | 1.44426 | 0.722128 | − | 0.691760i | \(-0.243164\pi\) | ||||
0.722128 | + | 0.691760i | \(0.243164\pi\) | |||||||
\(4\) | 3.41079 | 1.70540 | ||||||||
\(5\) | 0.271197 | 0.121283 | 0.0606415 | − | 0.998160i | \(-0.480685\pi\) | ||||
0.0606415 | + | 0.998160i | \(0.480685\pi\) | |||||||
\(6\) | −5.81882 | −2.37552 | ||||||||
\(7\) | 2.22103 | 0.839472 | 0.419736 | − | 0.907646i | \(-0.362123\pi\) | ||||
0.419736 | + | 0.907646i | \(0.362123\pi\) | |||||||
\(8\) | −3.28166 | −1.16024 | ||||||||
\(9\) | 3.25762 | 1.08587 | ||||||||
\(10\) | −0.630834 | −0.199487 | ||||||||
\(11\) | 4.90915 | 1.48016 | 0.740082 | − | 0.672516i | \(-0.234786\pi\) | ||||
0.740082 | + | 0.672516i | \(0.234786\pi\) | |||||||
\(12\) | 8.53218 | 2.46303 | ||||||||
\(13\) | 4.75288 | 1.31821 | 0.659105 | − | 0.752051i | \(-0.270935\pi\) | ||||
0.659105 | + | 0.752051i | \(0.270935\pi\) | |||||||
\(14\) | −5.16637 | −1.38077 | ||||||||
\(15\) | 0.678405 | 0.175164 | ||||||||
\(16\) | 0.811925 | 0.202981 | ||||||||
\(17\) | −3.39026 | −0.822259 | −0.411130 | − | 0.911577i | \(-0.634866\pi\) | ||||
−0.411130 | + | 0.911577i | \(0.634866\pi\) | |||||||
\(18\) | −7.57760 | −1.78606 | ||||||||
\(19\) | −0.868020 | −0.199137 | −0.0995687 | − | 0.995031i | \(-0.531746\pi\) | ||||
−0.0995687 | + | 0.995031i | \(0.531746\pi\) | |||||||
\(20\) | 0.924996 | 0.206835 | ||||||||
\(21\) | 5.55597 | 1.21241 | ||||||||
\(22\) | −11.4192 | −2.43459 | ||||||||
\(23\) | −7.92420 | −1.65231 | −0.826155 | − | 0.563443i | \(-0.809476\pi\) | ||||
−0.826155 | + | 0.563443i | \(0.809476\pi\) | |||||||
\(24\) | −8.20916 | −1.67569 | ||||||||
\(25\) | −4.92645 | −0.985290 | ||||||||
\(26\) | −11.0557 | −2.16820 | ||||||||
\(27\) | 0.644453 | 0.124025 | ||||||||
\(28\) | 7.57549 | 1.43163 | ||||||||
\(29\) | 6.56045 | 1.21825 | 0.609123 | − | 0.793076i | \(-0.291522\pi\) | ||||
0.609123 | + | 0.793076i | \(0.291522\pi\) | |||||||
\(30\) | −1.57805 | −0.288111 | ||||||||
\(31\) | −0.772720 | −0.138785 | −0.0693923 | − | 0.997589i | \(-0.522106\pi\) | ||||
−0.0693923 | + | 0.997589i | \(0.522106\pi\) | |||||||
\(32\) | 4.67470 | 0.826377 | ||||||||
\(33\) | 12.2804 | 2.13774 | ||||||||
\(34\) | 7.88612 | 1.35246 | ||||||||
\(35\) | 0.602337 | 0.101814 | ||||||||
\(36\) | 11.1111 | 1.85185 | ||||||||
\(37\) | −3.69055 | −0.606723 | −0.303362 | − | 0.952876i | \(-0.598109\pi\) | ||||
−0.303362 | + | 0.952876i | \(0.598109\pi\) | |||||||
\(38\) | 2.01911 | 0.327543 | ||||||||
\(39\) | 11.8894 | 1.90383 | ||||||||
\(40\) | −0.889977 | −0.140718 | ||||||||
\(41\) | 9.67528 | 1.51102 | 0.755512 | − | 0.655134i | \(-0.227388\pi\) | ||||
0.755512 | + | 0.655134i | \(0.227388\pi\) | |||||||
\(42\) | −12.9238 | −1.99419 | ||||||||
\(43\) | −4.85912 | −0.741009 | −0.370504 | − | 0.928831i | \(-0.620815\pi\) | ||||
−0.370504 | + | 0.928831i | \(0.620815\pi\) | |||||||
\(44\) | 16.7441 | 2.52427 | ||||||||
\(45\) | 0.883457 | 0.131698 | ||||||||
\(46\) | 18.4326 | 2.71773 | ||||||||
\(47\) | 13.0957 | 1.91021 | 0.955104 | − | 0.296269i | \(-0.0957425\pi\) | ||||
0.955104 | + | 0.296269i | \(0.0957425\pi\) | |||||||
\(48\) | 2.03105 | 0.293157 | ||||||||
\(49\) | −2.06701 | −0.295287 | ||||||||
\(50\) | 11.4595 | 1.62061 | ||||||||
\(51\) | −8.48082 | −1.18755 | ||||||||
\(52\) | 16.2111 | 2.24807 | ||||||||
\(53\) | 12.3523 | 1.69672 | 0.848361 | − | 0.529419i | \(-0.177590\pi\) | ||||
0.848361 | + | 0.529419i | \(0.177590\pi\) | |||||||
\(54\) | −1.49907 | −0.203997 | ||||||||
\(55\) | 1.33135 | 0.179519 | ||||||||
\(56\) | −7.28868 | −0.973991 | ||||||||
\(57\) | −2.17137 | −0.287605 | ||||||||
\(58\) | −15.2603 | −2.00378 | ||||||||
\(59\) | 6.25615 | 0.814481 | 0.407241 | − | 0.913321i | \(-0.366491\pi\) | ||||
0.407241 | + | 0.913321i | \(0.366491\pi\) | |||||||
\(60\) | 2.31390 | 0.298723 | ||||||||
\(61\) | 9.50978 | 1.21760 | 0.608801 | − | 0.793323i | \(-0.291651\pi\) | ||||
0.608801 | + | 0.793323i | \(0.291651\pi\) | |||||||
\(62\) | 1.79743 | 0.228274 | ||||||||
\(63\) | 7.23529 | 0.911561 | ||||||||
\(64\) | −12.4977 | −1.56221 | ||||||||
\(65\) | 1.28896 | 0.159876 | ||||||||
\(66\) | −28.5655 | −3.51617 | ||||||||
\(67\) | 10.5996 | 1.29494 | 0.647471 | − | 0.762090i | \(-0.275827\pi\) | ||||
0.647471 | + | 0.762090i | \(0.275827\pi\) | |||||||
\(68\) | −11.5635 | −1.40228 | ||||||||
\(69\) | −19.8226 | −2.38636 | ||||||||
\(70\) | −1.40110 | −0.167464 | ||||||||
\(71\) | −10.1120 | −1.20007 | −0.600036 | − | 0.799973i | \(-0.704847\pi\) | ||||
−0.600036 | + | 0.799973i | \(0.704847\pi\) | |||||||
\(72\) | −10.6904 | −1.25988 | ||||||||
\(73\) | 13.3187 | 1.55884 | 0.779418 | − | 0.626504i | \(-0.215515\pi\) | ||||
0.779418 | + | 0.626504i | \(0.215515\pi\) | |||||||
\(74\) | 8.58464 | 0.997944 | ||||||||
\(75\) | −12.3236 | −1.42301 | ||||||||
\(76\) | −2.96064 | −0.339608 | ||||||||
\(77\) | 10.9034 | 1.24256 | ||||||||
\(78\) | −27.6561 | −3.13144 | ||||||||
\(79\) | −10.5815 | −1.19052 | −0.595258 | − | 0.803534i | \(-0.702950\pi\) | ||||
−0.595258 | + | 0.803534i | \(0.702950\pi\) | |||||||
\(80\) | 0.220192 | 0.0246182 | ||||||||
\(81\) | −8.16076 | −0.906751 | ||||||||
\(82\) | −22.5058 | −2.48535 | ||||||||
\(83\) | 1.26181 | 0.138502 | 0.0692509 | − | 0.997599i | \(-0.477939\pi\) | ||||
0.0692509 | + | 0.997599i | \(0.477939\pi\) | |||||||
\(84\) | 18.9503 | 2.06764 | ||||||||
\(85\) | −0.919428 | −0.0997260 | ||||||||
\(86\) | 11.3028 | 1.21882 | ||||||||
\(87\) | 16.4111 | 1.75946 | ||||||||
\(88\) | −16.1102 | −1.71735 | ||||||||
\(89\) | 0.0481094 | 0.00509958 | 0.00254979 | − | 0.999997i | \(-0.499188\pi\) | ||||
0.00254979 | + | 0.999997i | \(0.499188\pi\) | |||||||
\(90\) | −2.05502 | −0.216618 | ||||||||
\(91\) | 10.5563 | 1.10660 | ||||||||
\(92\) | −27.0278 | −2.81784 | ||||||||
\(93\) | −1.93298 | −0.200440 | ||||||||
\(94\) | −30.4621 | −3.14193 | ||||||||
\(95\) | −0.235404 | −0.0241520 | ||||||||
\(96\) | 11.6939 | 1.19350 | ||||||||
\(97\) | −4.91163 | −0.498700 | −0.249350 | − | 0.968413i | \(-0.580217\pi\) | ||||
−0.249350 | + | 0.968413i | \(0.580217\pi\) | |||||||
\(98\) | 4.80810 | 0.485691 | ||||||||
\(99\) | 15.9922 | 1.60727 | ||||||||
\(100\) | −16.8031 | −1.68031 | ||||||||
\(101\) | −0.0247299 | −0.00246071 | −0.00123036 | − | 0.999999i | \(-0.500392\pi\) | ||||
−0.00123036 | + | 0.999999i | \(0.500392\pi\) | |||||||
\(102\) | 19.7273 | 1.95330 | ||||||||
\(103\) | −10.5795 | −1.04243 | −0.521213 | − | 0.853427i | \(-0.674520\pi\) | ||||
−0.521213 | + | 0.853427i | \(0.674520\pi\) | |||||||
\(104\) | −15.5973 | −1.52944 | ||||||||
\(105\) | 1.50676 | 0.147045 | ||||||||
\(106\) | −28.7329 | −2.79078 | ||||||||
\(107\) | −10.0790 | −0.974370 | −0.487185 | − | 0.873299i | \(-0.661976\pi\) | ||||
−0.487185 | + | 0.873299i | \(0.661976\pi\) | |||||||
\(108\) | 2.19810 | 0.211512 | ||||||||
\(109\) | −3.04268 | −0.291435 | −0.145718 | − | 0.989326i | \(-0.546549\pi\) | ||||
−0.145718 | + | 0.989326i | \(0.546549\pi\) | |||||||
\(110\) | −3.09686 | −0.295274 | ||||||||
\(111\) | −9.23201 | −0.876263 | ||||||||
\(112\) | 1.80331 | 0.170397 | ||||||||
\(113\) | 20.1706 | 1.89749 | 0.948743 | − | 0.316047i | \(-0.102356\pi\) | ||||
0.948743 | + | 0.316047i | \(0.102356\pi\) | |||||||
\(114\) | 5.05085 | 0.473056 | ||||||||
\(115\) | −2.14902 | −0.200397 | ||||||||
\(116\) | 22.3763 | 2.07759 | ||||||||
\(117\) | 15.4831 | 1.43141 | ||||||||
\(118\) | −14.5525 | −1.33967 | ||||||||
\(119\) | −7.52988 | −0.690263 | ||||||||
\(120\) | −2.22630 | −0.203232 | ||||||||
\(121\) | 13.0998 | 1.19089 | ||||||||
\(122\) | −22.1208 | −2.00272 | ||||||||
\(123\) | 24.2029 | 2.18231 | ||||||||
\(124\) | −2.63559 | −0.236683 | ||||||||
\(125\) | −2.69202 | −0.240782 | ||||||||
\(126\) | −16.8301 | −1.49934 | ||||||||
\(127\) | 5.48670 | 0.486866 | 0.243433 | − | 0.969918i | \(-0.421726\pi\) | ||||
0.243433 | + | 0.969918i | \(0.421726\pi\) | |||||||
\(128\) | 19.7217 | 1.74317 | ||||||||
\(129\) | −12.1552 | −1.07021 | ||||||||
\(130\) | −2.99828 | −0.262966 | ||||||||
\(131\) | 6.37401 | 0.556900 | 0.278450 | − | 0.960451i | \(-0.410179\pi\) | ||||
0.278450 | + | 0.960451i | \(0.410179\pi\) | |||||||
\(132\) | 41.8858 | 3.64569 | ||||||||
\(133\) | −1.92790 | −0.167170 | ||||||||
\(134\) | −24.6557 | −2.12993 | ||||||||
\(135\) | 0.174774 | 0.0150421 | ||||||||
\(136\) | 11.1257 | 0.954020 | ||||||||
\(137\) | 14.3030 | 1.22199 | 0.610994 | − | 0.791635i | \(-0.290770\pi\) | ||||
0.610994 | + | 0.791635i | \(0.290770\pi\) | |||||||
\(138\) | 46.1095 | 3.92510 | ||||||||
\(139\) | −0.576912 | −0.0489331 | −0.0244665 | − | 0.999701i | \(-0.507789\pi\) | ||||
−0.0244665 | + | 0.999701i | \(0.507789\pi\) | |||||||
\(140\) | 2.05445 | 0.173633 | ||||||||
\(141\) | 32.7593 | 2.75883 | ||||||||
\(142\) | 23.5216 | 1.97389 | ||||||||
\(143\) | 23.3326 | 1.95117 | ||||||||
\(144\) | 2.64495 | 0.220412 | ||||||||
\(145\) | 1.77917 | 0.147752 | ||||||||
\(146\) | −30.9808 | −2.56399 | ||||||||
\(147\) | −5.17068 | −0.426470 | ||||||||
\(148\) | −12.5877 | −1.03470 | ||||||||
\(149\) | −15.9403 | −1.30588 | −0.652940 | − | 0.757410i | \(-0.726464\pi\) | ||||
−0.652940 | + | 0.757410i | \(0.726464\pi\) | |||||||
\(150\) | 28.6662 | 2.34058 | ||||||||
\(151\) | −7.37360 | −0.600055 | −0.300028 | − | 0.953931i | \(-0.596996\pi\) | ||||
−0.300028 | + | 0.953931i | \(0.596996\pi\) | |||||||
\(152\) | 2.84855 | 0.231048 | ||||||||
\(153\) | −11.0442 | −0.892870 | ||||||||
\(154\) | −25.3625 | −2.04377 | ||||||||
\(155\) | −0.209559 | −0.0168322 | ||||||||
\(156\) | 40.5524 | 3.24679 | ||||||||
\(157\) | −8.69718 | −0.694111 | −0.347055 | − | 0.937845i | \(-0.612818\pi\) | ||||
−0.347055 | + | 0.937845i | \(0.612818\pi\) | |||||||
\(158\) | 24.6138 | 1.95817 | ||||||||
\(159\) | 30.8996 | 2.45050 | ||||||||
\(160\) | 1.26776 | 0.100225 | ||||||||
\(161\) | −17.5999 | −1.38707 | ||||||||
\(162\) | 18.9828 | 1.49143 | ||||||||
\(163\) | −15.8668 | −1.24278 | −0.621391 | − | 0.783500i | \(-0.713432\pi\) | ||||
−0.621391 | + | 0.783500i | \(0.713432\pi\) | |||||||
\(164\) | 33.0004 | 2.57690 | ||||||||
\(165\) | 3.33040 | 0.259271 | ||||||||
\(166\) | −2.93511 | −0.227809 | ||||||||
\(167\) | −0.228934 | −0.0177155 | −0.00885773 | − | 0.999961i | \(-0.502820\pi\) | ||||
−0.00885773 | + | 0.999961i | \(0.502820\pi\) | |||||||
\(168\) | −18.2328 | −1.40669 | ||||||||
\(169\) | 9.58982 | 0.737679 | ||||||||
\(170\) | 2.13869 | 0.164030 | ||||||||
\(171\) | −2.82768 | −0.216238 | ||||||||
\(172\) | −16.5734 | −1.26371 | ||||||||
\(173\) | 1.11355 | 0.0846620 | 0.0423310 | − | 0.999104i | \(-0.486522\pi\) | ||||
0.0423310 | + | 0.999104i | \(0.486522\pi\) | |||||||
\(174\) | −38.1741 | −2.89397 | ||||||||
\(175\) | −10.9418 | −0.827123 | ||||||||
\(176\) | 3.98587 | 0.300446 | ||||||||
\(177\) | 15.6499 | 1.17632 | ||||||||
\(178\) | −0.111908 | −0.00838784 | ||||||||
\(179\) | −3.83925 | −0.286959 | −0.143480 | − | 0.989653i | \(-0.545829\pi\) | ||||
−0.143480 | + | 0.989653i | \(0.545829\pi\) | |||||||
\(180\) | 3.01329 | 0.224597 | ||||||||
\(181\) | 8.09138 | 0.601428 | 0.300714 | − | 0.953714i | \(-0.402775\pi\) | ||||
0.300714 | + | 0.953714i | \(0.402775\pi\) | |||||||
\(182\) | −24.5551 | −1.82015 | ||||||||
\(183\) | 23.7890 | 1.75853 | ||||||||
\(184\) | 26.0046 | 1.91708 | ||||||||
\(185\) | −1.00087 | −0.0735851 | ||||||||
\(186\) | 4.49632 | 0.329686 | ||||||||
\(187\) | −16.6433 | −1.21708 | ||||||||
\(188\) | 44.6668 | 3.25766 | ||||||||
\(189\) | 1.43135 | 0.104116 | ||||||||
\(190\) | 0.547576 | 0.0397254 | ||||||||
\(191\) | −13.0090 | −0.941296 | −0.470648 | − | 0.882321i | \(-0.655980\pi\) | ||||
−0.470648 | + | 0.882321i | \(0.655980\pi\) | |||||||
\(192\) | −31.2633 | −2.25624 | ||||||||
\(193\) | 5.25224 | 0.378065 | 0.189032 | − | 0.981971i | \(-0.439465\pi\) | ||||
0.189032 | + | 0.981971i | \(0.439465\pi\) | |||||||
\(194\) | 11.4250 | 0.820266 | ||||||||
\(195\) | 3.22438 | 0.230902 | ||||||||
\(196\) | −7.05015 | −0.503582 | ||||||||
\(197\) | 24.1401 | 1.71991 | 0.859955 | − | 0.510370i | \(-0.170492\pi\) | ||||
0.859955 | + | 0.510370i | \(0.170492\pi\) | |||||||
\(198\) | −37.1996 | −2.64366 | ||||||||
\(199\) | −20.4144 | −1.44714 | −0.723569 | − | 0.690253i | \(-0.757499\pi\) | ||||
−0.723569 | + | 0.690253i | \(0.757499\pi\) | |||||||
\(200\) | 16.1670 | 1.14318 | ||||||||
\(201\) | 26.5150 | 1.87023 | ||||||||
\(202\) | 0.0575244 | 0.00404741 | ||||||||
\(203\) | 14.5710 | 1.02268 | ||||||||
\(204\) | −28.9263 | −2.02525 | ||||||||
\(205\) | 2.62390 | 0.183261 | ||||||||
\(206\) | 24.6090 | 1.71459 | ||||||||
\(207\) | −25.8141 | −1.79420 | ||||||||
\(208\) | 3.85898 | 0.267572 | ||||||||
\(209\) | −4.26124 | −0.294756 | ||||||||
\(210\) | −3.50489 | −0.241861 | ||||||||
\(211\) | 9.24353 | 0.636351 | 0.318175 | − | 0.948032i | \(-0.396930\pi\) | ||||
0.318175 | + | 0.948032i | \(0.396930\pi\) | |||||||
\(212\) | 42.1312 | 2.89358 | ||||||||
\(213\) | −25.2954 | −1.73321 | ||||||||
\(214\) | 23.4448 | 1.60265 | ||||||||
\(215\) | −1.31778 | −0.0898717 | ||||||||
\(216\) | −2.11488 | −0.143899 | ||||||||
\(217\) | −1.71624 | −0.116506 | ||||||||
\(218\) | 7.07760 | 0.479356 | ||||||||
\(219\) | 33.3171 | 2.25136 | ||||||||
\(220\) | 4.54095 | 0.306151 | ||||||||
\(221\) | −16.1135 | −1.08391 | ||||||||
\(222\) | 21.4747 | 1.44129 | ||||||||
\(223\) | 11.2975 | 0.756537 | 0.378269 | − | 0.925696i | \(-0.376520\pi\) | ||||
0.378269 | + | 0.925696i | \(0.376520\pi\) | |||||||
\(224\) | 10.3827 | 0.693720 | ||||||||
\(225\) | −16.0485 | −1.06990 | ||||||||
\(226\) | −46.9190 | −3.12100 | ||||||||
\(227\) | 2.02413 | 0.134346 | 0.0671732 | − | 0.997741i | \(-0.478602\pi\) | ||||
0.0671732 | + | 0.997741i | \(0.478602\pi\) | |||||||
\(228\) | −7.40610 | −0.490481 | ||||||||
\(229\) | 11.9549 | 0.789999 | 0.395000 | − | 0.918681i | \(-0.370745\pi\) | ||||
0.395000 | + | 0.918681i | \(0.370745\pi\) | |||||||
\(230\) | 4.99886 | 0.329615 | ||||||||
\(231\) | 27.2751 | 1.79457 | ||||||||
\(232\) | −21.5292 | −1.41346 | ||||||||
\(233\) | −28.1718 | −1.84560 | −0.922799 | − | 0.385282i | \(-0.874104\pi\) | ||||
−0.922799 | + | 0.385282i | \(0.874104\pi\) | |||||||
\(234\) | −36.0154 | −2.35440 | ||||||||
\(235\) | 3.55152 | 0.231676 | ||||||||
\(236\) | 21.3384 | 1.38901 | ||||||||
\(237\) | −26.4700 | −1.71941 | ||||||||
\(238\) | 17.5153 | 1.13535 | ||||||||
\(239\) | −4.49543 | −0.290785 | −0.145393 | − | 0.989374i | \(-0.546444\pi\) | ||||
−0.145393 | + | 0.989374i | \(0.546444\pi\) | |||||||
\(240\) | 0.550815 | 0.0355549 | ||||||||
\(241\) | 15.3477 | 0.988631 | 0.494315 | − | 0.869283i | \(-0.335419\pi\) | ||||
0.494315 | + | 0.869283i | \(0.335419\pi\) | |||||||
\(242\) | −30.4715 | −1.95878 | ||||||||
\(243\) | −22.3477 | −1.43361 | ||||||||
\(244\) | 32.4359 | 2.07650 | ||||||||
\(245\) | −0.560567 | −0.0358133 | ||||||||
\(246\) | −56.2987 | −3.58948 | ||||||||
\(247\) | −4.12559 | −0.262505 | ||||||||
\(248\) | 2.53581 | 0.161024 | ||||||||
\(249\) | 3.15645 | 0.200032 | ||||||||
\(250\) | 6.26194 | 0.396040 | ||||||||
\(251\) | 14.2360 | 0.898570 | 0.449285 | − | 0.893388i | \(-0.351679\pi\) | ||||
0.449285 | + | 0.893388i | \(0.351679\pi\) | |||||||
\(252\) | 24.6781 | 1.55457 | ||||||||
\(253\) | −38.9011 | −2.44569 | ||||||||
\(254\) | −12.7627 | −0.800801 | ||||||||
\(255\) | −2.29997 | −0.144030 | ||||||||
\(256\) | −20.8794 | −1.30496 | ||||||||
\(257\) | −19.4820 | −1.21525 | −0.607627 | − | 0.794223i | \(-0.707878\pi\) | ||||
−0.607627 | + | 0.794223i | \(0.707878\pi\) | |||||||
\(258\) | 28.2744 | 1.76028 | ||||||||
\(259\) | −8.19684 | −0.509327 | ||||||||
\(260\) | 4.39639 | 0.272653 | ||||||||
\(261\) | 21.3715 | 1.32286 | ||||||||
\(262\) | −14.8267 | −0.915994 | ||||||||
\(263\) | −13.5147 | −0.833353 | −0.416676 | − | 0.909055i | \(-0.636805\pi\) | ||||
−0.416676 | + | 0.909055i | \(0.636805\pi\) | |||||||
\(264\) | −40.3000 | −2.48029 | ||||||||
\(265\) | 3.34991 | 0.205783 | ||||||||
\(266\) | 4.48451 | 0.274963 | ||||||||
\(267\) | 0.120347 | 0.00736510 | ||||||||
\(268\) | 36.1529 | 2.20839 | ||||||||
\(269\) | 20.2994 | 1.23767 | 0.618837 | − | 0.785519i | \(-0.287604\pi\) | ||||
0.618837 | + | 0.785519i | \(0.287604\pi\) | |||||||
\(270\) | −0.406543 | −0.0247414 | ||||||||
\(271\) | −2.42275 | −0.147171 | −0.0735857 | − | 0.997289i | \(-0.523444\pi\) | ||||
−0.0735857 | + | 0.997289i | \(0.523444\pi\) | |||||||
\(272\) | −2.75264 | −0.166903 | ||||||||
\(273\) | 26.4068 | 1.59821 | ||||||||
\(274\) | −33.2704 | −2.00994 | ||||||||
\(275\) | −24.1847 | −1.45839 | ||||||||
\(276\) | −67.6107 | −4.06969 | ||||||||
\(277\) | 8.18806 | 0.491973 | 0.245986 | − | 0.969273i | \(-0.420888\pi\) | ||||
0.245986 | + | 0.969273i | \(0.420888\pi\) | |||||||
\(278\) | 1.34196 | 0.0804855 | ||||||||
\(279\) | −2.51723 | −0.150703 | ||||||||
\(280\) | −1.97667 | −0.118128 | ||||||||
\(281\) | 20.4467 | 1.21975 | 0.609875 | − | 0.792498i | \(-0.291220\pi\) | ||||
0.609875 | + | 0.792498i | \(0.291220\pi\) | |||||||
\(282\) | −76.2018 | −4.53775 | ||||||||
\(283\) | −22.1221 | −1.31503 | −0.657513 | − | 0.753444i | \(-0.728391\pi\) | ||||
−0.657513 | + | 0.753444i | \(0.728391\pi\) | |||||||
\(284\) | −34.4899 | −2.04660 | ||||||||
\(285\) | −0.588869 | −0.0348816 | ||||||||
\(286\) | −54.2742 | −3.20930 | ||||||||
\(287\) | 21.4891 | 1.26846 | ||||||||
\(288\) | 15.2284 | 0.897342 | ||||||||
\(289\) | −5.50613 | −0.323890 | ||||||||
\(290\) | −4.13856 | −0.243024 | ||||||||
\(291\) | −12.2866 | −0.720250 | ||||||||
\(292\) | 45.4273 | 2.65843 | ||||||||
\(293\) | −22.8363 | −1.33411 | −0.667054 | − | 0.745009i | \(-0.732445\pi\) | ||||
−0.667054 | + | 0.745009i | \(0.732445\pi\) | |||||||
\(294\) | 12.0276 | 0.701462 | ||||||||
\(295\) | 1.69665 | 0.0987827 | ||||||||
\(296\) | 12.1111 | 0.703946 | ||||||||
\(297\) | 3.16372 | 0.183577 | ||||||||
\(298\) | 37.0789 | 2.14792 | ||||||||
\(299\) | −37.6627 | −2.17809 | ||||||||
\(300\) | −42.0334 | −2.42680 | ||||||||
\(301\) | −10.7923 | −0.622056 | ||||||||
\(302\) | 17.1518 | 0.986976 | ||||||||
\(303\) | −0.0618624 | −0.00355390 | ||||||||
\(304\) | −0.704767 | −0.0404212 | ||||||||
\(305\) | 2.57902 | 0.147674 | ||||||||
\(306\) | 25.6900 | 1.46860 | ||||||||
\(307\) | 12.3684 | 0.705901 | 0.352951 | − | 0.935642i | \(-0.385178\pi\) | ||||
0.352951 | + | 0.935642i | \(0.385178\pi\) | |||||||
\(308\) | 37.1892 | 2.11905 | ||||||||
\(309\) | −26.4648 | −1.50553 | ||||||||
\(310\) | 0.487458 | 0.0276857 | ||||||||
\(311\) | −11.1417 | −0.631788 | −0.315894 | − | 0.948794i | \(-0.602304\pi\) | ||||
−0.315894 | + | 0.948794i | \(0.602304\pi\) | |||||||
\(312\) | −39.0171 | −2.20891 | ||||||||
\(313\) | −5.13903 | −0.290475 | −0.145238 | − | 0.989397i | \(-0.546395\pi\) | ||||
−0.145238 | + | 0.989397i | \(0.546395\pi\) | |||||||
\(314\) | 20.2306 | 1.14168 | ||||||||
\(315\) | 1.96219 | 0.110557 | ||||||||
\(316\) | −36.0915 | −2.03030 | ||||||||
\(317\) | 15.8677 | 0.891217 | 0.445609 | − | 0.895228i | \(-0.352987\pi\) | ||||
0.445609 | + | 0.895228i | \(0.352987\pi\) | |||||||
\(318\) | −71.8760 | −4.03060 | ||||||||
\(319\) | 32.2062 | 1.80320 | ||||||||
\(320\) | −3.38934 | −0.189470 | ||||||||
\(321\) | −25.2128 | −1.40724 | ||||||||
\(322\) | 40.9394 | 2.28146 | ||||||||
\(323\) | 2.94281 | 0.163743 | ||||||||
\(324\) | −27.8347 | −1.54637 | ||||||||
\(325\) | −23.4148 | −1.29882 | ||||||||
\(326\) | 36.9079 | 2.04414 | ||||||||
\(327\) | −7.61133 | −0.420907 | ||||||||
\(328\) | −31.7510 | −1.75316 | ||||||||
\(329\) | 29.0861 | 1.60357 | ||||||||
\(330\) | −7.74687 | −0.426451 | ||||||||
\(331\) | 35.3509 | 1.94306 | 0.971530 | − | 0.236918i | \(-0.0761374\pi\) | ||||
0.971530 | + | 0.236918i | \(0.0761374\pi\) | |||||||
\(332\) | 4.30378 | 0.236200 | ||||||||
\(333\) | −12.0224 | −0.658825 | ||||||||
\(334\) | 0.532526 | 0.0291386 | ||||||||
\(335\) | 2.87457 | 0.157054 | ||||||||
\(336\) | 4.51103 | 0.246097 | ||||||||
\(337\) | 0.272100 | 0.0148222 | 0.00741111 | − | 0.999973i | \(-0.497641\pi\) | ||||
0.00741111 | + | 0.999973i | \(0.497641\pi\) | |||||||
\(338\) | −22.3070 | −1.21334 | ||||||||
\(339\) | 50.4572 | 2.74046 | ||||||||
\(340\) | −3.13598 | −0.170072 | ||||||||
\(341\) | −3.79340 | −0.205424 | ||||||||
\(342\) | 6.57750 | 0.355671 | ||||||||
\(343\) | −20.1381 | −1.08736 | ||||||||
\(344\) | 15.9460 | 0.859750 | ||||||||
\(345\) | −5.37582 | −0.289424 | ||||||||
\(346\) | −2.59025 | −0.139253 | ||||||||
\(347\) | −21.4339 | −1.15063 | −0.575316 | − | 0.817931i | \(-0.695121\pi\) | ||||
−0.575316 | + | 0.817931i | \(0.695121\pi\) | |||||||
\(348\) | 55.9750 | 3.00057 | ||||||||
\(349\) | 15.8190 | 0.846771 | 0.423386 | − | 0.905950i | \(-0.360842\pi\) | ||||
0.423386 | + | 0.905950i | \(0.360842\pi\) | |||||||
\(350\) | 25.4519 | 1.36046 | ||||||||
\(351\) | 3.06300 | 0.163491 | ||||||||
\(352\) | 22.9488 | 1.22317 | ||||||||
\(353\) | 6.05735 | 0.322400 | 0.161200 | − | 0.986922i | \(-0.448464\pi\) | ||||
0.161200 | + | 0.986922i | \(0.448464\pi\) | |||||||
\(354\) | −36.4034 | −1.93482 | ||||||||
\(355\) | −2.74234 | −0.145548 | ||||||||
\(356\) | 0.164091 | 0.00869681 | ||||||||
\(357\) | −18.8362 | −0.996917 | ||||||||
\(358\) | 8.93052 | 0.471993 | ||||||||
\(359\) | −10.3774 | −0.547697 | −0.273848 | − | 0.961773i | \(-0.588297\pi\) | ||||
−0.273848 | + | 0.961773i | \(0.588297\pi\) | |||||||
\(360\) | −2.89921 | −0.152802 | ||||||||
\(361\) | −18.2465 | −0.960344 | ||||||||
\(362\) | −18.8215 | −0.989234 | ||||||||
\(363\) | 32.7694 | 1.71995 | ||||||||
\(364\) | 36.0053 | 1.88719 | ||||||||
\(365\) | 3.61199 | 0.189060 | ||||||||
\(366\) | −55.3357 | −2.89245 | ||||||||
\(367\) | 30.7027 | 1.60267 | 0.801335 | − | 0.598216i | \(-0.204124\pi\) | ||||
0.801335 | + | 0.598216i | \(0.204124\pi\) | |||||||
\(368\) | −6.43386 | −0.335388 | ||||||||
\(369\) | 31.5184 | 1.64078 | ||||||||
\(370\) | 2.32813 | 0.121034 | ||||||||
\(371\) | 27.4349 | 1.42435 | ||||||||
\(372\) | −6.59299 | −0.341830 | ||||||||
\(373\) | −29.1844 | −1.51111 | −0.755557 | − | 0.655083i | \(-0.772634\pi\) | ||||
−0.755557 | + | 0.655083i | \(0.772634\pi\) | |||||||
\(374\) | 38.7142 | 2.00186 | ||||||||
\(375\) | −6.73416 | −0.347751 | ||||||||
\(376\) | −42.9758 | −2.21631 | ||||||||
\(377\) | 31.1810 | 1.60590 | ||||||||
\(378\) | −3.32948 | −0.171250 | ||||||||
\(379\) | −22.3543 | −1.14827 | −0.574133 | − | 0.818762i | \(-0.694661\pi\) | ||||
−0.574133 | + | 0.818762i | \(0.694661\pi\) | |||||||
\(380\) | −0.802915 | −0.0411887 | ||||||||
\(381\) | 13.7251 | 0.703158 | ||||||||
\(382\) | 30.2603 | 1.54825 | ||||||||
\(383\) | 35.6178 | 1.81998 | 0.909991 | − | 0.414627i | \(-0.136088\pi\) | ||||
0.909991 | + | 0.414627i | \(0.136088\pi\) | |||||||
\(384\) | 49.3343 | 2.51758 | ||||||||
\(385\) | 2.95696 | 0.150701 | ||||||||
\(386\) | −12.2173 | −0.621844 | ||||||||
\(387\) | −15.8292 | −0.804642 | ||||||||
\(388\) | −16.7525 | −0.850481 | ||||||||
\(389\) | −0.784297 | −0.0397654 | −0.0198827 | − | 0.999802i | \(-0.506329\pi\) | ||||
−0.0198827 | + | 0.999802i | \(0.506329\pi\) | |||||||
\(390\) | −7.50026 | −0.379790 | ||||||||
\(391\) | 26.8651 | 1.35863 | ||||||||
\(392\) | 6.78323 | 0.342605 | ||||||||
\(393\) | 15.9447 | 0.804306 | ||||||||
\(394\) | −56.1525 | −2.82892 | ||||||||
\(395\) | −2.86968 | −0.144389 | ||||||||
\(396\) | 54.5460 | 2.74104 | ||||||||
\(397\) | −21.4992 | −1.07902 | −0.539508 | − | 0.841981i | \(-0.681390\pi\) | ||||
−0.539508 | + | 0.841981i | \(0.681390\pi\) | |||||||
\(398\) | 47.4861 | 2.38026 | ||||||||
\(399\) | −4.82269 | −0.241436 | ||||||||
\(400\) | −3.99991 | −0.199996 | ||||||||
\(401\) | −27.2862 | −1.36261 | −0.681303 | − | 0.732002i | \(-0.738586\pi\) | ||||
−0.681303 | + | 0.732002i | \(0.738586\pi\) | |||||||
\(402\) | −61.6770 | −3.07617 | ||||||||
\(403\) | −3.67264 | −0.182947 | ||||||||
\(404\) | −0.0843485 | −0.00419649 | ||||||||
\(405\) | −2.21317 | −0.109973 | ||||||||
\(406\) | −33.8937 | −1.68212 | ||||||||
\(407\) | −18.1175 | −0.898050 | ||||||||
\(408\) | 27.8312 | 1.37785 | ||||||||
\(409\) | −17.6447 | −0.872473 | −0.436237 | − | 0.899832i | \(-0.643689\pi\) | ||||
−0.436237 | + | 0.899832i | \(0.643689\pi\) | |||||||
\(410\) | −6.10349 | −0.301430 | ||||||||
\(411\) | 35.7793 | 1.76486 | ||||||||
\(412\) | −36.0844 | −1.77775 | ||||||||
\(413\) | 13.8951 | 0.683734 | ||||||||
\(414\) | 60.0464 | 2.95112 | ||||||||
\(415\) | 0.342199 | 0.0167979 | ||||||||
\(416\) | 22.2182 | 1.08934 | ||||||||
\(417\) | −1.44316 | −0.0706719 | ||||||||
\(418\) | 9.91212 | 0.484818 | ||||||||
\(419\) | 12.5452 | 0.612876 | 0.306438 | − | 0.951891i | \(-0.400863\pi\) | ||||
0.306438 | + | 0.951891i | \(0.400863\pi\) | |||||||
\(420\) | 5.13925 | 0.250770 | ||||||||
\(421\) | 40.4126 | 1.96959 | 0.984794 | − | 0.173725i | \(-0.0555803\pi\) | ||||
0.984794 | + | 0.173725i | \(0.0555803\pi\) | |||||||
\(422\) | −21.5015 | −1.04668 | ||||||||
\(423\) | 42.6610 | 2.07425 | ||||||||
\(424\) | −40.5361 | −1.96861 | ||||||||
\(425\) | 16.7020 | 0.810164 | ||||||||
\(426\) | 58.8399 | 2.85080 | ||||||||
\(427\) | 21.1215 | 1.02214 | ||||||||
\(428\) | −34.3773 | −1.66169 | ||||||||
\(429\) | 58.3670 | 2.81799 | ||||||||
\(430\) | 3.06530 | 0.147822 | ||||||||
\(431\) | 28.2987 | 1.36310 | 0.681551 | − | 0.731771i | \(-0.261306\pi\) | ||||
0.681551 | + | 0.731771i | \(0.261306\pi\) | |||||||
\(432\) | 0.523248 | 0.0251748 | ||||||||
\(433\) | 14.1155 | 0.678346 | 0.339173 | − | 0.940724i | \(-0.389853\pi\) | ||||
0.339173 | + | 0.940724i | \(0.389853\pi\) | |||||||
\(434\) | 3.99216 | 0.191630 | ||||||||
\(435\) | 4.45065 | 0.213392 | ||||||||
\(436\) | −10.3779 | −0.497013 | ||||||||
\(437\) | 6.87836 | 0.329037 | ||||||||
\(438\) | −77.4992 | −3.70305 | ||||||||
\(439\) | −34.1947 | −1.63202 | −0.816012 | − | 0.578035i | \(-0.803820\pi\) | ||||
−0.816012 | + | 0.578035i | \(0.803820\pi\) | |||||||
\(440\) | −4.36903 | −0.208285 | ||||||||
\(441\) | −6.73354 | −0.320645 | ||||||||
\(442\) | 37.4818 | 1.78283 | ||||||||
\(443\) | −29.5320 | −1.40311 | −0.701553 | − | 0.712617i | \(-0.747510\pi\) | ||||
−0.701553 | + | 0.712617i | \(0.747510\pi\) | |||||||
\(444\) | −31.4885 | −1.49438 | ||||||||
\(445\) | 0.0130471 | 0.000618492 0 | ||||||||
\(446\) | −26.2793 | −1.24436 | ||||||||
\(447\) | −39.8750 | −1.88602 | ||||||||
\(448\) | −27.7578 | −1.31143 | ||||||||
\(449\) | −7.90501 | −0.373060 | −0.186530 | − | 0.982449i | \(-0.559724\pi\) | ||||
−0.186530 | + | 0.982449i | \(0.559724\pi\) | |||||||
\(450\) | 37.3307 | 1.75978 | ||||||||
\(451\) | 47.4974 | 2.23657 | ||||||||
\(452\) | 68.7976 | 3.23597 | ||||||||
\(453\) | −18.4452 | −0.866633 | ||||||||
\(454\) | −4.70836 | −0.220974 | ||||||||
\(455\) | 2.86283 | 0.134212 | ||||||||
\(456\) | 7.12571 | 0.333692 | ||||||||
\(457\) | 9.83855 | 0.460228 | 0.230114 | − | 0.973164i | \(-0.426090\pi\) | ||||
0.230114 | + | 0.973164i | \(0.426090\pi\) | |||||||
\(458\) | −27.8083 | −1.29940 | ||||||||
\(459\) | −2.18486 | −0.101981 | ||||||||
\(460\) | −7.32986 | −0.341756 | ||||||||
\(461\) | −29.8511 | −1.39030 | −0.695152 | − | 0.718862i | \(-0.744663\pi\) | ||||
−0.695152 | + | 0.718862i | \(0.744663\pi\) | |||||||
\(462\) | −63.4449 | −2.95172 | ||||||||
\(463\) | −38.9046 | −1.80805 | −0.904025 | − | 0.427480i | \(-0.859402\pi\) | ||||
−0.904025 | + | 0.427480i | \(0.859402\pi\) | |||||||
\(464\) | 5.32660 | 0.247281 | ||||||||
\(465\) | −0.524217 | −0.0243100 | ||||||||
\(466\) | 65.5308 | 3.03566 | ||||||||
\(467\) | 10.3800 | 0.480330 | 0.240165 | − | 0.970732i | \(-0.422798\pi\) | ||||
0.240165 | + | 0.970732i | \(0.422798\pi\) | |||||||
\(468\) | 52.8096 | 2.44112 | ||||||||
\(469\) | 23.5420 | 1.08707 | ||||||||
\(470\) | −8.26123 | −0.381062 | ||||||||
\(471\) | −21.7562 | −1.00247 | ||||||||
\(472\) | −20.5306 | −0.944996 | ||||||||
\(473\) | −23.8541 | −1.09681 | ||||||||
\(474\) | 61.5721 | 2.82810 | ||||||||
\(475\) | 4.27626 | 0.196208 | ||||||||
\(476\) | −25.6829 | −1.17717 | ||||||||
\(477\) | 40.2392 | 1.84243 | ||||||||
\(478\) | 10.4569 | 0.478286 | ||||||||
\(479\) | 11.3549 | 0.518817 | 0.259408 | − | 0.965768i | \(-0.416472\pi\) | ||||
0.259408 | + | 0.965768i | \(0.416472\pi\) | |||||||
\(480\) | 3.17134 | 0.144751 | ||||||||
\(481\) | −17.5407 | −0.799789 | ||||||||
\(482\) | −35.7004 | −1.62611 | ||||||||
\(483\) | −44.0266 | −2.00328 | ||||||||
\(484\) | 44.6806 | 2.03094 | ||||||||
\(485\) | −1.33202 | −0.0604838 | ||||||||
\(486\) | 51.9832 | 2.35801 | ||||||||
\(487\) | 10.6873 | 0.484287 | 0.242143 | − | 0.970240i | \(-0.422150\pi\) | ||||
0.242143 | + | 0.970240i | \(0.422150\pi\) | |||||||
\(488\) | −31.2079 | −1.41272 | ||||||||
\(489\) | −39.6912 | −1.79490 | ||||||||
\(490\) | 1.30394 | 0.0589060 | ||||||||
\(491\) | 16.0231 | 0.723112 | 0.361556 | − | 0.932350i | \(-0.382246\pi\) | ||||
0.361556 | + | 0.932350i | \(0.382246\pi\) | |||||||
\(492\) | 82.5512 | 3.72170 | ||||||||
\(493\) | −22.2416 | −1.00171 | ||||||||
\(494\) | 9.59658 | 0.431770 | ||||||||
\(495\) | 4.33703 | 0.194935 | ||||||||
\(496\) | −0.627391 | −0.0281707 | ||||||||
\(497\) | −22.4591 | −1.00743 | ||||||||
\(498\) | −7.34226 | −0.329014 | ||||||||
\(499\) | −14.3257 | −0.641306 | −0.320653 | − | 0.947197i | \(-0.603902\pi\) | ||||
−0.320653 | + | 0.947197i | \(0.603902\pi\) | |||||||
\(500\) | −9.18193 | −0.410629 | ||||||||
\(501\) | −0.572685 | −0.0255857 | ||||||||
\(502\) | −33.1146 | −1.47798 | ||||||||
\(503\) | 31.9707 | 1.42550 | 0.712751 | − | 0.701417i | \(-0.247449\pi\) | ||||
0.712751 | + | 0.701417i | \(0.247449\pi\) | |||||||
\(504\) | −23.7438 | −1.05763 | ||||||||
\(505\) | −0.00670666 | −0.000298443 0 | ||||||||
\(506\) | 90.4883 | 4.02270 | ||||||||
\(507\) | 23.9892 | 1.06540 | ||||||||
\(508\) | 18.7140 | 0.830299 | ||||||||
\(509\) | −0.711031 | −0.0315159 | −0.0157579 | − | 0.999876i | \(-0.505016\pi\) | ||||
−0.0157579 | + | 0.999876i | \(0.505016\pi\) | |||||||
\(510\) | 5.34999 | 0.236902 | ||||||||
\(511\) | 29.5813 | 1.30860 | ||||||||
\(512\) | 9.12444 | 0.403247 | ||||||||
\(513\) | −0.559398 | −0.0246980 | ||||||||
\(514\) | 45.3173 | 1.99886 | ||||||||
\(515\) | −2.86912 | −0.126428 | ||||||||
\(516\) | −41.4589 | −1.82513 | ||||||||
\(517\) | 64.2889 | 2.82742 | ||||||||
\(518\) | 19.0668 | 0.837745 | ||||||||
\(519\) | 2.78558 | 0.122274 | ||||||||
\(520\) | −4.22995 | −0.185495 | ||||||||
\(521\) | −28.8712 | −1.26487 | −0.632435 | − | 0.774613i | \(-0.717945\pi\) | ||||
−0.632435 | + | 0.774613i | \(0.717945\pi\) | |||||||
\(522\) | −49.7124 | −2.17585 | ||||||||
\(523\) | −27.9348 | −1.22150 | −0.610751 | − | 0.791823i | \(-0.709132\pi\) | ||||
−0.610751 | + | 0.791823i | \(0.709132\pi\) | |||||||
\(524\) | 21.7404 | 0.949735 | ||||||||
\(525\) | −27.3712 | −1.19458 | ||||||||
\(526\) | 31.4367 | 1.37071 | ||||||||
\(527\) | 2.61972 | 0.114117 | ||||||||
\(528\) | 9.97074 | 0.433921 | ||||||||
\(529\) | 39.7930 | 1.73013 | ||||||||
\(530\) | −7.79226 | −0.338474 | ||||||||
\(531\) | 20.3802 | 0.884425 | ||||||||
\(532\) | −6.57567 | −0.285091 | ||||||||
\(533\) | 45.9854 | 1.99185 | ||||||||
\(534\) | −0.279940 | −0.0121142 | ||||||||
\(535\) | −2.73338 | −0.118174 | ||||||||
\(536\) | −34.7842 | −1.50245 | ||||||||
\(537\) | −9.60398 | −0.414442 | ||||||||
\(538\) | −47.2186 | −2.03574 | ||||||||
\(539\) | −10.1473 | −0.437074 | ||||||||
\(540\) | 0.596117 | 0.0256528 | ||||||||
\(541\) | −23.0677 | −0.991757 | −0.495879 | − | 0.868392i | \(-0.665154\pi\) | ||||
−0.495879 | + | 0.868392i | \(0.665154\pi\) | |||||||
\(542\) | 5.63558 | 0.242069 | ||||||||
\(543\) | 20.2408 | 0.868615 | ||||||||
\(544\) | −15.8484 | −0.679496 | ||||||||
\(545\) | −0.825164 | −0.0353461 | ||||||||
\(546\) | −61.4252 | −2.62876 | ||||||||
\(547\) | 10.4165 | 0.445377 | 0.222688 | − | 0.974890i | \(-0.428517\pi\) | ||||
0.222688 | + | 0.974890i | \(0.428517\pi\) | |||||||
\(548\) | 48.7846 | 2.08397 | ||||||||
\(549\) | 30.9793 | 1.32216 | ||||||||
\(550\) | 56.2563 | 2.39878 | ||||||||
\(551\) | −5.69460 | −0.242598 | ||||||||
\(552\) | 65.0510 | 2.76876 | ||||||||
\(553\) | −23.5020 | −0.999405 | ||||||||
\(554\) | −19.0463 | −0.809201 | ||||||||
\(555\) | −2.50369 | −0.106276 | ||||||||
\(556\) | −1.96773 | −0.0834503 | ||||||||
\(557\) | −17.6256 | −0.746819 | −0.373410 | − | 0.927667i | \(-0.621811\pi\) | ||||
−0.373410 | + | 0.927667i | \(0.621811\pi\) | |||||||
\(558\) | 5.85536 | 0.247877 | ||||||||
\(559\) | −23.0948 | −0.976805 | ||||||||
\(560\) | 0.489053 | 0.0206663 | ||||||||
\(561\) | −41.6336 | −1.75777 | ||||||||
\(562\) | −47.5614 | −2.00626 | ||||||||
\(563\) | 15.4735 | 0.652128 | 0.326064 | − | 0.945348i | \(-0.394277\pi\) | ||||
0.326064 | + | 0.945348i | \(0.394277\pi\) | |||||||
\(564\) | 111.735 | 4.70490 | ||||||||
\(565\) | 5.47019 | 0.230133 | ||||||||
\(566\) | 51.4586 | 2.16297 | ||||||||
\(567\) | −18.1253 | −0.761192 | ||||||||
\(568\) | 33.1841 | 1.39238 | ||||||||
\(569\) | −19.2204 | −0.805763 | −0.402881 | − | 0.915252i | \(-0.631991\pi\) | ||||
−0.402881 | + | 0.915252i | \(0.631991\pi\) | |||||||
\(570\) | 1.36978 | 0.0573736 | ||||||||
\(571\) | −5.21232 | −0.218129 | −0.109064 | − | 0.994035i | \(-0.534785\pi\) | ||||
−0.109064 | + | 0.994035i | \(0.534785\pi\) | |||||||
\(572\) | 79.5826 | 3.32752 | ||||||||
\(573\) | −32.5423 | −1.35947 | ||||||||
\(574\) | −49.9861 | −2.08638 | ||||||||
\(575\) | 39.0382 | 1.62801 | ||||||||
\(576\) | −40.7129 | −1.69637 | ||||||||
\(577\) | −38.7555 | −1.61341 | −0.806707 | − | 0.590952i | \(-0.798752\pi\) | ||||
−0.806707 | + | 0.590952i | \(0.798752\pi\) | |||||||
\(578\) | 12.8079 | 0.532737 | ||||||||
\(579\) | 13.1386 | 0.546022 | ||||||||
\(580\) | 6.06839 | 0.251976 | ||||||||
\(581\) | 2.80252 | 0.116268 | ||||||||
\(582\) | 28.5799 | 1.18467 | ||||||||
\(583\) | 60.6394 | 2.51143 | ||||||||
\(584\) | −43.7075 | −1.80863 | ||||||||
\(585\) | 4.19896 | 0.173606 | ||||||||
\(586\) | 53.1197 | 2.19435 | ||||||||
\(587\) | 3.06646 | 0.126566 | 0.0632832 | − | 0.997996i | \(-0.479843\pi\) | ||||
0.0632832 | + | 0.997996i | \(0.479843\pi\) | |||||||
\(588\) | −17.6361 | −0.727301 | ||||||||
\(589\) | 0.670736 | 0.0276372 | ||||||||
\(590\) | −3.94659 | −0.162479 | ||||||||
\(591\) | 60.3870 | 2.48399 | ||||||||
\(592\) | −2.99645 | −0.123153 | ||||||||
\(593\) | −6.84348 | −0.281028 | −0.140514 | − | 0.990079i | \(-0.544876\pi\) | ||||
−0.140514 | + | 0.990079i | \(0.544876\pi\) | |||||||
\(594\) | −7.35916 | −0.301950 | ||||||||
\(595\) | −2.04208 | −0.0837171 | ||||||||
\(596\) | −54.3690 | −2.22704 | ||||||||
\(597\) | −51.0671 | −2.09004 | ||||||||
\(598\) | 87.6077 | 3.58255 | ||||||||
\(599\) | −37.0353 | −1.51322 | −0.756610 | − | 0.653866i | \(-0.773146\pi\) | ||||
−0.756610 | + | 0.653866i | \(0.773146\pi\) | |||||||
\(600\) | 40.4420 | 1.65104 | ||||||||
\(601\) | 38.9440 | 1.58856 | 0.794280 | − | 0.607552i | \(-0.207848\pi\) | ||||
0.794280 | + | 0.607552i | \(0.207848\pi\) | |||||||
\(602\) | 25.1040 | 1.02316 | ||||||||
\(603\) | 34.5294 | 1.40614 | ||||||||
\(604\) | −25.1498 | −1.02333 | ||||||||
\(605\) | 3.55262 | 0.144434 | ||||||||
\(606\) | 0.143899 | 0.00584549 | ||||||||
\(607\) | 1.58674 | 0.0644040 | 0.0322020 | − | 0.999481i | \(-0.489748\pi\) | ||||
0.0322020 | + | 0.999481i | \(0.489748\pi\) | |||||||
\(608\) | −4.05773 | −0.164563 | ||||||||
\(609\) | 36.4497 | 1.47701 | ||||||||
\(610\) | −5.99909 | −0.242896 | ||||||||
\(611\) | 62.2424 | 2.51806 | ||||||||
\(612\) | −37.6695 | −1.52270 | ||||||||
\(613\) | −3.52832 | −0.142507 | −0.0712537 | − | 0.997458i | \(-0.522700\pi\) | ||||
−0.0712537 | + | 0.997458i | \(0.522700\pi\) | |||||||
\(614\) | −28.7703 | −1.16107 | ||||||||
\(615\) | 6.56376 | 0.264676 | ||||||||
\(616\) | −35.7812 | −1.44167 | ||||||||
\(617\) | 35.4685 | 1.42791 | 0.713955 | − | 0.700192i | \(-0.246902\pi\) | ||||
0.713955 | + | 0.700192i | \(0.246902\pi\) | |||||||
\(618\) | 61.5600 | 2.47631 | ||||||||
\(619\) | 39.6901 | 1.59528 | 0.797640 | − | 0.603133i | \(-0.206081\pi\) | ||||
0.797640 | + | 0.603133i | \(0.206081\pi\) | |||||||
\(620\) | −0.714763 | −0.0287056 | ||||||||
\(621\) | −5.10677 | −0.204928 | ||||||||
\(622\) | 25.9169 | 1.03917 | ||||||||
\(623\) | 0.106852 | 0.00428095 | ||||||||
\(624\) | 9.65333 | 0.386443 | ||||||||
\(625\) | 23.9022 | 0.956088 | ||||||||
\(626\) | 11.9540 | 0.477776 | ||||||||
\(627\) | −10.6596 | −0.425703 | ||||||||
\(628\) | −29.6643 | −1.18373 | ||||||||
\(629\) | 12.5119 | 0.498884 | ||||||||
\(630\) | −4.56427 | −0.181845 | ||||||||
\(631\) | 12.0235 | 0.478646 | 0.239323 | − | 0.970940i | \(-0.423074\pi\) | ||||
0.239323 | + | 0.970940i | \(0.423074\pi\) | |||||||
\(632\) | 34.7251 | 1.38129 | ||||||||
\(633\) | 23.1229 | 0.919053 | ||||||||
\(634\) | −36.9100 | −1.46588 | ||||||||
\(635\) | 1.48797 | 0.0590485 | ||||||||
\(636\) | 105.392 | 4.17907 | ||||||||
\(637\) | −9.82424 | −0.389251 | ||||||||
\(638\) | −74.9153 | −2.96593 | ||||||||
\(639\) | −32.9411 | −1.30313 | ||||||||
\(640\) | 5.34846 | 0.211416 | ||||||||
\(641\) | −19.0504 | −0.752445 | −0.376223 | − | 0.926529i | \(-0.622777\pi\) | ||||
−0.376223 | + | 0.926529i | \(0.622777\pi\) | |||||||
\(642\) | 58.6477 | 2.31464 | ||||||||
\(643\) | −30.9846 | −1.22191 | −0.610956 | − | 0.791665i | \(-0.709215\pi\) | ||||
−0.610956 | + | 0.791665i | \(0.709215\pi\) | |||||||
\(644\) | −60.0297 | −2.36550 | ||||||||
\(645\) | −3.29645 | −0.129798 | ||||||||
\(646\) | −6.84531 | −0.269325 | ||||||||
\(647\) | 19.0168 | 0.747627 | 0.373814 | − | 0.927504i | \(-0.378050\pi\) | ||||
0.373814 | + | 0.927504i | \(0.378050\pi\) | |||||||
\(648\) | 26.7809 | 1.05205 | ||||||||
\(649\) | 30.7124 | 1.20557 | ||||||||
\(650\) | 54.4655 | 2.13631 | ||||||||
\(651\) | −4.29321 | −0.168264 | ||||||||
\(652\) | −54.1183 | −2.11944 | ||||||||
\(653\) | 28.3896 | 1.11097 | 0.555486 | − | 0.831526i | \(-0.312532\pi\) | ||||
0.555486 | + | 0.831526i | \(0.312532\pi\) | |||||||
\(654\) | 17.7048 | 0.692312 | ||||||||
\(655\) | 1.72861 | 0.0675424 | ||||||||
\(656\) | 7.85560 | 0.306710 | ||||||||
\(657\) | 43.3873 | 1.69270 | ||||||||
\(658\) | −67.6574 | −2.63756 | ||||||||
\(659\) | −34.2699 | −1.33497 | −0.667483 | − | 0.744625i | \(-0.732628\pi\) | ||||
−0.667483 | + | 0.744625i | \(0.732628\pi\) | |||||||
\(660\) | 11.3593 | 0.442160 | ||||||||
\(661\) | 3.09710 | 0.120463 | 0.0602316 | − | 0.998184i | \(-0.480816\pi\) | ||||
0.0602316 | + | 0.998184i | \(0.480816\pi\) | |||||||
\(662\) | −82.2300 | −3.19596 | ||||||||
\(663\) | −40.3083 | −1.56544 | ||||||||
\(664\) | −4.14084 | −0.160696 | ||||||||
\(665\) | −0.522841 | −0.0202749 | ||||||||
\(666\) | 27.9655 | 1.08364 | ||||||||
\(667\) | −51.9863 | −2.01292 | ||||||||
\(668\) | −0.780847 | −0.0302119 | ||||||||
\(669\) | 28.2610 | 1.09263 | ||||||||
\(670\) | −6.68656 | −0.258324 | ||||||||
\(671\) | 46.6850 | 1.80225 | ||||||||
\(672\) | 25.9725 | 1.00191 | ||||||||
\(673\) | 26.6957 | 1.02904 | 0.514522 | − | 0.857477i | \(-0.327969\pi\) | ||||
0.514522 | + | 0.857477i | \(0.327969\pi\) | |||||||
\(674\) | −0.632935 | −0.0243797 | ||||||||
\(675\) | −3.17487 | −0.122201 | ||||||||
\(676\) | 32.7089 | 1.25803 | ||||||||
\(677\) | 2.19321 | 0.0842917 | 0.0421459 | − | 0.999111i | \(-0.486581\pi\) | ||||
0.0421459 | + | 0.999111i | \(0.486581\pi\) | |||||||
\(678\) | −117.369 | −4.50753 | ||||||||
\(679\) | −10.9089 | −0.418645 | ||||||||
\(680\) | 3.01725 | 0.115706 | ||||||||
\(681\) | 5.06342 | 0.194031 | ||||||||
\(682\) | 8.82387 | 0.337883 | ||||||||
\(683\) | 20.0502 | 0.767200 | 0.383600 | − | 0.923499i | \(-0.374684\pi\) | ||||
0.383600 | + | 0.923499i | \(0.374684\pi\) | |||||||
\(684\) | −9.64464 | −0.368772 | ||||||||
\(685\) | 3.87893 | 0.148206 | ||||||||
\(686\) | 46.8435 | 1.78849 | ||||||||
\(687\) | 29.9054 | 1.14096 | ||||||||
\(688\) | −3.94524 | −0.150411 | ||||||||
\(689\) | 58.7090 | 2.23664 | ||||||||
\(690\) | 12.5048 | 0.476048 | ||||||||
\(691\) | 16.5811 | 0.630774 | 0.315387 | − | 0.948963i | \(-0.397866\pi\) | ||||
0.315387 | + | 0.948963i | \(0.397866\pi\) | |||||||
\(692\) | 3.79811 | 0.144382 | ||||||||
\(693\) | 35.5191 | 1.34926 | ||||||||
\(694\) | 49.8576 | 1.89257 | ||||||||
\(695\) | −0.156457 | −0.00593474 | ||||||||
\(696\) | −53.8558 | −2.04140 | ||||||||
\(697\) | −32.8017 | −1.24245 | ||||||||
\(698\) | −36.7967 | −1.39278 | ||||||||
\(699\) | −70.4725 | −2.66552 | ||||||||
\(700\) | −37.3203 | −1.41057 | ||||||||
\(701\) | −30.3337 | −1.14569 | −0.572844 | − | 0.819664i | \(-0.694160\pi\) | ||||
−0.572844 | + | 0.819664i | \(0.694160\pi\) | |||||||
\(702\) | −7.12489 | −0.268912 | ||||||||
\(703\) | 3.20347 | 0.120821 | ||||||||
\(704\) | −61.3532 | −2.31233 | ||||||||
\(705\) | 8.88422 | 0.334599 | ||||||||
\(706\) | −14.0901 | −0.530287 | ||||||||
\(707\) | −0.0549259 | −0.00206570 | ||||||||
\(708\) | 53.3786 | 2.00609 | ||||||||
\(709\) | −48.3777 | −1.81686 | −0.908431 | − | 0.418035i | \(-0.862719\pi\) | ||||
−0.908431 | + | 0.418035i | \(0.862719\pi\) | |||||||
\(710\) | 6.37899 | 0.239399 | ||||||||
\(711\) | −34.4707 | −1.29275 | ||||||||
\(712\) | −0.157879 | −0.00591675 | ||||||||
\(713\) | 6.12319 | 0.229315 | ||||||||
\(714\) | 43.8151 | 1.63974 | ||||||||
\(715\) | 6.32772 | 0.236643 | ||||||||
\(716\) | −13.0949 | −0.489379 | ||||||||
\(717\) | −11.2454 | −0.419968 | ||||||||
\(718\) | 24.1389 | 0.900856 | ||||||||
\(719\) | −24.6084 | −0.917738 | −0.458869 | − | 0.888504i | \(-0.651745\pi\) | ||||
−0.458869 | + | 0.888504i | \(0.651745\pi\) | |||||||
\(720\) | 0.717302 | 0.0267322 | ||||||||
\(721\) | −23.4973 | −0.875087 | ||||||||
\(722\) | 42.4435 | 1.57958 | ||||||||
\(723\) | 38.3926 | 1.42784 | ||||||||
\(724\) | 27.5980 | 1.02567 | ||||||||
\(725\) | −32.3197 | −1.20033 | ||||||||
\(726\) | −76.2252 | −2.82898 | ||||||||
\(727\) | −11.0507 | −0.409847 | −0.204924 | − | 0.978778i | \(-0.565695\pi\) | ||||
−0.204924 | + | 0.978778i | \(0.565695\pi\) | |||||||
\(728\) | −34.6422 | −1.28393 | ||||||||
\(729\) | −31.4210 | −1.16374 | ||||||||
\(730\) | −8.40189 | −0.310968 | ||||||||
\(731\) | 16.4737 | 0.609301 | ||||||||
\(732\) | 81.1392 | 2.99899 | ||||||||
\(733\) | −11.4154 | −0.421639 | −0.210819 | − | 0.977525i | \(-0.567613\pi\) | ||||
−0.210819 | + | 0.977525i | \(0.567613\pi\) | |||||||
\(734\) | −71.4180 | −2.63609 | ||||||||
\(735\) | −1.40227 | −0.0517236 | ||||||||
\(736\) | −37.0432 | −1.36543 | ||||||||
\(737\) | 52.0348 | 1.91673 | ||||||||
\(738\) | −73.3154 | −2.69878 | ||||||||
\(739\) | −42.8950 | −1.57792 | −0.788959 | − | 0.614446i | \(-0.789379\pi\) | ||||
−0.788959 | + | 0.614446i | \(0.789379\pi\) | |||||||
\(740\) | −3.41375 | −0.125492 | ||||||||
\(741\) | −10.3203 | −0.379124 | ||||||||
\(742\) | −63.8167 | −2.34278 | ||||||||
\(743\) | −21.8038 | −0.799905 | −0.399953 | − | 0.916536i | \(-0.630973\pi\) | ||||
−0.399953 | + | 0.916536i | \(0.630973\pi\) | |||||||
\(744\) | 6.34338 | 0.232560 | ||||||||
\(745\) | −4.32296 | −0.158381 | ||||||||
\(746\) | 67.8863 | 2.48549 | ||||||||
\(747\) | 4.11051 | 0.150396 | ||||||||
\(748\) | −56.7669 | −2.07560 | ||||||||
\(749\) | −22.3857 | −0.817956 | ||||||||
\(750\) | 15.6644 | 0.571983 | ||||||||
\(751\) | −6.10080 | −0.222621 | −0.111311 | − | 0.993786i | \(-0.535505\pi\) | ||||
−0.111311 | + | 0.993786i | \(0.535505\pi\) | |||||||
\(752\) | 10.6328 | 0.387737 | ||||||||
\(753\) | 35.6118 | 1.29777 | ||||||||
\(754\) | −72.5305 | −2.64140 | ||||||||
\(755\) | −1.99970 | −0.0727764 | ||||||||
\(756\) | 4.88204 | 0.177558 | ||||||||
\(757\) | −34.2410 | −1.24451 | −0.622255 | − | 0.782815i | \(-0.713783\pi\) | ||||
−0.622255 | + | 0.782815i | \(0.713783\pi\) | |||||||
\(758\) | 51.9987 | 1.88868 | ||||||||
\(759\) | −97.3120 | −3.53220 | ||||||||
\(760\) | 0.772517 | 0.0280221 | ||||||||
\(761\) | −18.5644 | −0.672957 | −0.336479 | − | 0.941691i | \(-0.609236\pi\) | ||||
−0.336479 | + | 0.941691i | \(0.609236\pi\) | |||||||
\(762\) | −31.9261 | −1.15656 | ||||||||
\(763\) | −6.75788 | −0.244652 | ||||||||
\(764\) | −44.3709 | −1.60528 | ||||||||
\(765\) | −2.99515 | −0.108290 | ||||||||
\(766\) | −82.8509 | −2.99352 | ||||||||
\(767\) | 29.7347 | 1.07366 | ||||||||
\(768\) | −52.2303 | −1.88470 | ||||||||
\(769\) | 24.7904 | 0.893966 | 0.446983 | − | 0.894542i | \(-0.352498\pi\) | ||||
0.446983 | + | 0.894542i | \(0.352498\pi\) | |||||||
\(770\) | −6.87823 | −0.247874 | ||||||||
\(771\) | −48.7347 | −1.75514 | ||||||||
\(772\) | 17.9143 | 0.644750 | ||||||||
\(773\) | −38.7959 | −1.39539 | −0.697696 | − | 0.716394i | \(-0.745791\pi\) | ||||
−0.697696 | + | 0.716394i | \(0.745791\pi\) | |||||||
\(774\) | 36.8204 | 1.32348 | ||||||||
\(775\) | 3.80677 | 0.136743 | ||||||||
\(776\) | 16.1183 | 0.578613 | ||||||||
\(777\) | −20.5046 | −0.735598 | ||||||||
\(778\) | 1.82436 | 0.0654065 | ||||||||
\(779\) | −8.39833 | −0.300901 | ||||||||
\(780\) | 10.9977 | 0.393780 | ||||||||
\(781\) | −49.6413 | −1.77631 | ||||||||
\(782\) | −62.4912 | −2.23468 | ||||||||
\(783\) | 4.22790 | 0.151093 | ||||||||
\(784\) | −1.67826 | −0.0599378 | ||||||||
\(785\) | −2.35865 | −0.0841838 | ||||||||
\(786\) | −37.0892 | −1.32293 | ||||||||
\(787\) | 0.957677 | 0.0341375 | 0.0170687 | − | 0.999854i | \(-0.494567\pi\) | ||||
0.0170687 | + | 0.999854i | \(0.494567\pi\) | |||||||
\(788\) | 82.3368 | 2.93313 | ||||||||
\(789\) | −33.8074 | −1.20357 | ||||||||
\(790\) | 6.67520 | 0.237493 | ||||||||
\(791\) | 44.7995 | 1.59289 | ||||||||
\(792\) | −52.4809 | −1.86483 | ||||||||
\(793\) | 45.1988 | 1.60506 | ||||||||
\(794\) | 50.0096 | 1.77477 | ||||||||
\(795\) | 8.37988 | 0.297204 | ||||||||
\(796\) | −69.6292 | −2.46794 | ||||||||
\(797\) | 46.0174 | 1.63002 | 0.815009 | − | 0.579448i | \(-0.196732\pi\) | ||||
0.815009 | + | 0.579448i | \(0.196732\pi\) | |||||||
\(798\) | 11.2181 | 0.397117 | ||||||||
\(799\) | −44.3980 | −1.57069 | ||||||||
\(800\) | −23.0297 | −0.814222 | ||||||||
\(801\) | 0.156722 | 0.00553751 | ||||||||
\(802\) | 63.4706 | 2.24123 | ||||||||
\(803\) | 65.3835 | 2.30733 | ||||||||
\(804\) | 90.4374 | 3.18948 | ||||||||
\(805\) | −4.77304 | −0.168228 | ||||||||
\(806\) | 8.54297 | 0.300913 | ||||||||
\(807\) | 50.7794 | 1.78752 | ||||||||
\(808\) | 0.0811551 | 0.00285503 | ||||||||
\(809\) | −24.4160 | −0.858420 | −0.429210 | − | 0.903205i | \(-0.641208\pi\) | ||||
−0.429210 | + | 0.903205i | \(0.641208\pi\) | |||||||
\(810\) | 5.14808 | 0.180885 | ||||||||
\(811\) | −34.1686 | −1.19982 | −0.599911 | − | 0.800066i | \(-0.704798\pi\) | ||||
−0.599911 | + | 0.800066i | \(0.704798\pi\) | |||||||
\(812\) | 49.6986 | 1.74408 | ||||||||
\(813\) | −6.06056 | −0.212553 | ||||||||
\(814\) | 42.1433 | 1.47712 | ||||||||
\(815\) | −4.30302 | −0.150728 | ||||||||
\(816\) | −6.88579 | −0.241051 | ||||||||
\(817\) | 4.21781 | 0.147562 | ||||||||
\(818\) | 41.0435 | 1.43505 | ||||||||
\(819\) | 34.3884 | 1.20163 | ||||||||
\(820\) | 8.94960 | 0.312534 | ||||||||
\(821\) | −25.3672 | −0.885320 | −0.442660 | − | 0.896690i | \(-0.645965\pi\) | ||||
−0.442660 | + | 0.896690i | \(0.645965\pi\) | |||||||
\(822\) | −83.2266 | −2.90286 | ||||||||
\(823\) | 37.5985 | 1.31060 | 0.655301 | − | 0.755368i | \(-0.272542\pi\) | ||||
0.655301 | + | 0.755368i | \(0.272542\pi\) | |||||||
\(824\) | 34.7182 | 1.20947 | ||||||||
\(825\) | −60.4986 | −2.10629 | ||||||||
\(826\) | −32.3216 | −1.12461 | ||||||||
\(827\) | −12.1826 | −0.423629 | −0.211815 | − | 0.977310i | \(-0.567937\pi\) | ||||
−0.211815 | + | 0.977310i | \(0.567937\pi\) | |||||||
\(828\) | −88.0464 | −3.05983 | ||||||||
\(829\) | −28.0127 | −0.972923 | −0.486461 | − | 0.873702i | \(-0.661713\pi\) | ||||
−0.486461 | + | 0.873702i | \(0.661713\pi\) | |||||||
\(830\) | −0.795993 | −0.0276293 | ||||||||
\(831\) | 20.4826 | 0.710534 | ||||||||
\(832\) | −59.4001 | −2.05933 | ||||||||
\(833\) | 7.00771 | 0.242803 | ||||||||
\(834\) | 3.35695 | 0.116242 | ||||||||
\(835\) | −0.0620862 | −0.00214858 | ||||||||
\(836\) | −14.5342 | −0.502676 | ||||||||
\(837\) | −0.497982 | −0.0172128 | ||||||||
\(838\) | −29.1816 | −1.00806 | ||||||||
\(839\) | 10.1670 | 0.351002 | 0.175501 | − | 0.984479i | \(-0.443845\pi\) | ||||
0.175501 | + | 0.984479i | \(0.443845\pi\) | |||||||
\(840\) | −4.94468 | −0.170608 | ||||||||
\(841\) | 14.0395 | 0.484121 | ||||||||
\(842\) | −94.0042 | −3.23960 | ||||||||
\(843\) | 51.1480 | 1.76163 | ||||||||
\(844\) | 31.5278 | 1.08523 | ||||||||
\(845\) | 2.60073 | 0.0894678 | ||||||||
\(846\) | −99.2342 | −3.41174 | ||||||||
\(847\) | 29.0950 | 0.999717 | ||||||||
\(848\) | 10.0292 | 0.344403 | ||||||||
\(849\) | −55.3391 | −1.89923 | ||||||||
\(850\) | −38.8506 | −1.33257 | ||||||||
\(851\) | 29.2447 | 1.00249 | ||||||||
\(852\) | −86.2773 | −2.95581 | ||||||||
\(853\) | 7.02855 | 0.240653 | 0.120326 | − | 0.992734i | \(-0.461606\pi\) | ||||
0.120326 | + | 0.992734i | \(0.461606\pi\) | |||||||
\(854\) | −49.1311 | −1.68123 | ||||||||
\(855\) | −0.766858 | −0.0262260 | ||||||||
\(856\) | 33.0758 | 1.13051 | ||||||||
\(857\) | 17.7230 | 0.605407 | 0.302703 | − | 0.953085i | \(-0.402111\pi\) | ||||
0.302703 | + | 0.953085i | \(0.402111\pi\) | |||||||
\(858\) | −135.768 | −4.63505 | ||||||||
\(859\) | −29.5077 | −1.00679 | −0.503395 | − | 0.864057i | \(-0.667916\pi\) | ||||
−0.503395 | + | 0.864057i | \(0.667916\pi\) | |||||||
\(860\) | −4.49467 | −0.153267 | ||||||||
\(861\) | 53.7555 | 1.83198 | ||||||||
\(862\) | −65.8260 | −2.24204 | ||||||||
\(863\) | 53.6261 | 1.82545 | 0.912727 | − | 0.408571i | \(-0.133973\pi\) | ||||
0.912727 | + | 0.408571i | \(0.133973\pi\) | |||||||
\(864\) | 3.01262 | 0.102491 | ||||||||
\(865\) | 0.301993 | 0.0102681 | ||||||||
\(866\) | −32.8341 | −1.11575 | ||||||||
\(867\) | −13.7737 | −0.467780 | ||||||||
\(868\) | −5.85373 | −0.198688 | ||||||||
\(869\) | −51.9464 | −1.76216 | ||||||||
\(870\) | −10.3527 | −0.350989 | ||||||||
\(871\) | 50.3784 | 1.70701 | ||||||||
\(872\) | 9.98503 | 0.338136 | ||||||||
\(873\) | −16.0002 | −0.541526 | ||||||||
\(874\) | −15.9998 | −0.541202 | ||||||||
\(875\) | −5.97907 | −0.202130 | ||||||||
\(876\) | 113.638 | 3.83946 | ||||||||
\(877\) | −39.7822 | −1.34335 | −0.671674 | − | 0.740847i | \(-0.734425\pi\) | ||||
−0.671674 | + | 0.740847i | \(0.734425\pi\) | |||||||
\(878\) | 79.5407 | 2.68437 | ||||||||
\(879\) | −57.1255 | −1.92679 | ||||||||
\(880\) | 1.08095 | 0.0364390 | ||||||||
\(881\) | 41.0685 | 1.38363 | 0.691816 | − | 0.722074i | \(-0.256811\pi\) | ||||
0.691816 | + | 0.722074i | \(0.256811\pi\) | |||||||
\(882\) | 15.6630 | 0.527400 | ||||||||
\(883\) | −14.0568 | −0.473048 | −0.236524 | − | 0.971626i | \(-0.576008\pi\) | ||||
−0.236524 | + | 0.971626i | \(0.576008\pi\) | |||||||
\(884\) | −54.9598 | −1.84850 | ||||||||
\(885\) | 4.24421 | 0.142667 | ||||||||
\(886\) | 68.6947 | 2.30784 | ||||||||
\(887\) | 53.7433 | 1.80452 | 0.902261 | − | 0.431190i | \(-0.141906\pi\) | ||||
0.902261 | + | 0.431190i | \(0.141906\pi\) | |||||||
\(888\) | 30.2963 | 1.01668 | ||||||||
\(889\) | 12.1861 | 0.408710 | ||||||||
\(890\) | −0.0303490 | −0.00101730 | ||||||||
\(891\) | −40.0624 | −1.34214 | ||||||||
\(892\) | 38.5335 | 1.29020 | ||||||||
\(893\) | −11.3674 | −0.380394 | ||||||||
\(894\) | 92.7537 | 3.10215 | ||||||||
\(895\) | −1.04119 | −0.0348032 | ||||||||
\(896\) | 43.8025 | 1.46334 | ||||||||
\(897\) | −94.2142 | −3.14572 | ||||||||
\(898\) | 18.3879 | 0.613613 | ||||||||
\(899\) | −5.06939 | −0.169074 | ||||||||
\(900\) | −54.7382 | −1.82461 | ||||||||
\(901\) | −41.8776 | −1.39514 | ||||||||
\(902\) | −110.484 | −3.67872 | ||||||||
\(903\) | −26.9971 | −0.898408 | ||||||||
\(904\) | −66.1930 | −2.20155 | ||||||||
\(905\) | 2.19436 | 0.0729429 | ||||||||
\(906\) | 42.9057 | 1.42545 | ||||||||
\(907\) | −44.3918 | −1.47401 | −0.737003 | − | 0.675889i | \(-0.763760\pi\) | ||||
−0.737003 | + | 0.675889i | \(0.763760\pi\) | |||||||
\(908\) | 6.90390 | 0.229114 | ||||||||
\(909\) | −0.0805606 | −0.00267203 | ||||||||
\(910\) | −6.65927 | −0.220753 | ||||||||
\(911\) | 28.4411 | 0.942297 | 0.471149 | − | 0.882054i | \(-0.343840\pi\) | ||||
0.471149 | + | 0.882054i | \(0.343840\pi\) | |||||||
\(912\) | −1.76299 | −0.0583785 | ||||||||
\(913\) | 6.19442 | 0.205005 | ||||||||
\(914\) | −22.8856 | −0.756987 | ||||||||
\(915\) | 6.45149 | 0.213280 | ||||||||
\(916\) | 40.7755 | 1.34726 | ||||||||
\(917\) | 14.1569 | 0.467502 | ||||||||
\(918\) | 5.08224 | 0.167739 | ||||||||
\(919\) | 2.36681 | 0.0780738 | 0.0390369 | − | 0.999238i | \(-0.487571\pi\) | ||||
0.0390369 | + | 0.999238i | \(0.487571\pi\) | |||||||
\(920\) | 7.05235 | 0.232509 | ||||||||
\(921\) | 30.9398 | 1.01950 | ||||||||
\(922\) | 69.4370 | 2.28679 | ||||||||
\(923\) | −48.0610 | −1.58195 | ||||||||
\(924\) | 93.0297 | 3.06045 | ||||||||
\(925\) | 18.1813 | 0.597798 | ||||||||
\(926\) | 90.4964 | 2.97390 | ||||||||
\(927\) | −34.4639 | −1.13194 | ||||||||
\(928\) | 30.6681 | 1.00673 | ||||||||
\(929\) | −10.9903 | −0.360580 | −0.180290 | − | 0.983613i | \(-0.557704\pi\) | ||||
−0.180290 | + | 0.983613i | \(0.557704\pi\) | |||||||
\(930\) | 1.21939 | 0.0399853 | ||||||||
\(931\) | 1.79421 | 0.0588027 | ||||||||
\(932\) | −96.0883 | −3.14748 | ||||||||
\(933\) | −27.8713 | −0.912464 | ||||||||
\(934\) | −24.1451 | −0.790051 | ||||||||
\(935\) | −4.51361 | −0.147611 | ||||||||
\(936\) | −50.8102 | −1.66078 | ||||||||
\(937\) | 13.6099 | 0.444617 | 0.222308 | − | 0.974976i | \(-0.428641\pi\) | ||||
0.222308 | + | 0.974976i | \(0.428641\pi\) | |||||||
\(938\) | −54.7612 | −1.78802 | ||||||||
\(939\) | −12.8554 | −0.419521 | ||||||||
\(940\) | 12.1135 | 0.395099 | ||||||||
\(941\) | 36.7911 | 1.19935 | 0.599677 | − | 0.800242i | \(-0.295296\pi\) | ||||
0.599677 | + | 0.800242i | \(0.295296\pi\) | |||||||
\(942\) | 50.6074 | 1.64888 | ||||||||
\(943\) | −76.6688 | −2.49668 | ||||||||
\(944\) | 5.07953 | 0.165325 | ||||||||
\(945\) | 0.388178 | 0.0126274 | ||||||||
\(946\) | 55.4874 | 1.80405 | ||||||||
\(947\) | −18.9667 | −0.616334 | −0.308167 | − | 0.951332i | \(-0.599716\pi\) | ||||
−0.308167 | + | 0.951332i | \(0.599716\pi\) | |||||||
\(948\) | −90.2837 | −2.93228 | ||||||||
\(949\) | 63.3021 | 2.05487 | ||||||||
\(950\) | −9.94705 | −0.322725 | ||||||||
\(951\) | 39.6934 | 1.28715 | ||||||||
\(952\) | 24.7105 | 0.800873 | ||||||||
\(953\) | 37.2818 | 1.20768 | 0.603838 | − | 0.797107i | \(-0.293637\pi\) | ||||
0.603838 | + | 0.797107i | \(0.293637\pi\) | |||||||
\(954\) | −93.6009 | −3.03044 | ||||||||
\(955\) | −3.52799 | −0.114163 | ||||||||
\(956\) | −15.3330 | −0.495904 | ||||||||
\(957\) | 80.5647 | 2.60429 | ||||||||
\(958\) | −26.4127 | −0.853354 | ||||||||
\(959\) | 31.7674 | 1.02582 | ||||||||
\(960\) | −8.47852 | −0.273643 | ||||||||
\(961\) | −30.4029 | −0.980739 | ||||||||
\(962\) | 40.8017 | 1.31550 | ||||||||
\(963\) | −32.8335 | −1.05804 | ||||||||
\(964\) | 52.3478 | 1.68601 | ||||||||
\(965\) | 1.42439 | 0.0458528 | ||||||||
\(966\) | 102.411 | 3.29501 | ||||||||
\(967\) | −13.5739 | −0.436508 | −0.218254 | − | 0.975892i | \(-0.570036\pi\) | ||||
−0.218254 | + | 0.975892i | \(0.570036\pi\) | |||||||
\(968\) | −42.9890 | −1.38172 | ||||||||
\(969\) | 7.36152 | 0.236486 | ||||||||
\(970\) | 3.09842 | 0.0994843 | ||||||||
\(971\) | −22.7808 | −0.731072 | −0.365536 | − | 0.930797i | \(-0.619114\pi\) | ||||
−0.365536 | + | 0.930797i | \(0.619114\pi\) | |||||||
\(972\) | −76.2234 | −2.44487 | ||||||||
\(973\) | −1.28134 | −0.0410779 | ||||||||
\(974\) | −24.8598 | −0.796559 | ||||||||
\(975\) | −58.5727 | −1.87583 | ||||||||
\(976\) | 7.72123 | 0.247151 | ||||||||
\(977\) | −33.0961 | −1.05884 | −0.529420 | − | 0.848360i | \(-0.677590\pi\) | ||||
−0.529420 | + | 0.848360i | \(0.677590\pi\) | |||||||
\(978\) | 92.3261 | 2.95226 | ||||||||
\(979\) | 0.236176 | 0.00754822 | ||||||||
\(980\) | −1.91198 | −0.0610759 | ||||||||
\(981\) | −9.91189 | −0.316462 | ||||||||
\(982\) | −37.2715 | −1.18938 | ||||||||
\(983\) | 32.3224 | 1.03092 | 0.515462 | − | 0.856913i | \(-0.327620\pi\) | ||||
0.515462 | + | 0.856913i | \(0.327620\pi\) | |||||||
\(984\) | −79.4259 | −2.53201 | ||||||||
\(985\) | 6.54671 | 0.208596 | ||||||||
\(986\) | 51.7365 | 1.64763 | ||||||||
\(987\) | 72.7595 | 2.31596 | ||||||||
\(988\) | −14.0715 | −0.447675 | ||||||||
\(989\) | 38.5046 | 1.22438 | ||||||||
\(990\) | −10.0884 | −0.320631 | ||||||||
\(991\) | 2.33683 | 0.0742318 | 0.0371159 | − | 0.999311i | \(-0.488183\pi\) | ||||
0.0371159 | + | 0.999311i | \(0.488183\pi\) | |||||||
\(992\) | −3.61223 | −0.114688 | ||||||||
\(993\) | 88.4310 | 2.80627 | ||||||||
\(994\) | 52.2423 | 1.65702 | ||||||||
\(995\) | −5.53632 | −0.175513 | ||||||||
\(996\) | 10.7660 | 0.341134 | ||||||||
\(997\) | 13.3112 | 0.421568 | 0.210784 | − | 0.977533i | \(-0.432398\pi\) | ||||
0.210784 | + | 0.977533i | \(0.432398\pi\) | |||||||
\(998\) | 33.3232 | 1.05483 | ||||||||
\(999\) | −2.37839 | −0.0752489 |
(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 | 4003.2.a.c.1.20 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.c.1.20 | ✓ | 179 | 1.1 | even | 1 | trivial |