Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.46 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00349 | 1.73407 | 0.867034 | − | 0.498249i | \(-0.166024\pi\) | ||||
0.867034 | + | 0.498249i | \(0.166024\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.90143 | 1.74477 | 0.872385 | − | 0.488819i | \(-0.162572\pi\) | ||||
0.872385 | + | 0.488819i | \(0.162572\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.05459 | −1.53249 | −0.766245 | − | 0.642548i | \(-0.777877\pi\) | ||||
−0.766245 | + | 0.642548i | \(0.777877\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.02097 | 2.00699 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.15784 | −0.349103 | −0.174551 | − | 0.984648i | \(-0.555848\pi\) | ||||
−0.174551 | + | 0.984648i | \(0.555848\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.06308 | 0.849547 | 0.424773 | − | 0.905300i | \(-0.360354\pi\) | ||||
0.424773 | + | 0.905300i | \(0.360354\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.7179 | 3.02555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.39254 | 0.580276 | 0.290138 | − | 0.956985i | \(-0.406299\pi\) | ||||
0.290138 | + | 0.956985i | \(0.406299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.08326 | −1.16618 | −0.583090 | − | 0.812407i | \(-0.698157\pi\) | ||||
−0.583090 | + | 0.812407i | \(0.698157\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.1779 | −2.65744 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.68251 | 1.18489 | 0.592443 | − | 0.805613i | \(-0.298164\pi\) | ||||
0.592443 | + | 0.805613i | \(0.298164\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.2211 | 2.04422 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.07346 | 1.74619 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.19683 | −1.15072 | −0.575361 | − | 0.817900i | \(-0.695138\pi\) | ||||
−0.575361 | + | 0.817900i | \(0.695138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.20190 | 0.215867 | 0.107933 | − | 0.994158i | \(-0.465577\pi\) | ||||
0.107933 | + | 0.994158i | \(0.465577\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.47758 | −0.605368 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.8187 | −2.67384 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.702594 | −0.115506 | −0.0577529 | − | 0.998331i | \(-0.518394\pi\) | ||||
−0.0577529 | + | 0.998331i | \(0.518394\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.19995 | 1.47317 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.20524 | 0.500575 | 0.250287 | − | 0.968172i | \(-0.419475\pi\) | ||||
0.250287 | + | 0.968172i | \(0.419475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.852294 | 0.129974 | 0.0649868 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649868 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 23.4904 | 3.50174 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.40596 | 1.37200 | 0.686000 | − | 0.727601i | \(-0.259365\pi\) | ||||
0.686000 | + | 0.727601i | \(0.259365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.43969 | 1.34853 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.18597 | 1.00624 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.44430 | 0.335750 | 0.167875 | − | 0.985808i | \(-0.446309\pi\) | ||||
0.167875 | + | 0.985808i | \(0.446309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.51724 | −0.609105 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.2676 | −2.02224 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.28158 | 1.07817 | 0.539085 | − | 0.842251i | \(-0.318770\pi\) | ||||
0.539085 | + | 0.842251i | \(0.318770\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0969 | 1.29278 | 0.646389 | − | 0.763008i | \(-0.276278\pi\) | ||||
0.646389 | + | 0.763008i | \(0.276278\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −24.4126 | −3.07569 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.9504 | 1.48226 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.8704 | 1.69454 | 0.847271 | − | 0.531161i | \(-0.178244\pi\) | ||||
0.847271 | + | 0.531161i | \(0.178244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.0674 | 2.05467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0237590 | −0.00281967 | −0.00140984 | − | 0.999999i | \(-0.500449\pi\) | ||||
−0.00140984 | + | 0.999999i | \(0.500449\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.97219 | 0.230828 | 0.115414 | − | 0.993317i | \(-0.463181\pi\) | ||||
0.115414 | + | 0.993317i | \(0.463181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 30.6991 | 3.54482 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.69458 | 0.534997 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3522 | −1.27722 | −0.638610 | − | 0.769531i | \(-0.720490\pi\) | ||||
−0.638610 | + | 0.769531i | \(0.720490\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.18918 | 1.02102 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.2999 | −1.56962 | −0.784808 | − | 0.619740i | \(-0.787238\pi\) | ||||
−0.784808 | + | 0.619740i | \(0.787238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.33431 | 1.01245 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.6121 | −1.99543 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.64695 | −1.02257 | −0.511287 | − | 0.859410i | \(-0.670831\pi\) | ||||
−0.511287 | + | 0.859410i | \(0.670831\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4195 | −1.30192 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.60989 | 0.374328 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.8320 | −2.03472 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.93677 | −0.501253 | −0.250626 | − | 0.968084i | \(-0.580637\pi\) | ||||
−0.250626 | + | 0.968084i | \(0.580637\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.97134 | −0.700646 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.7732 | 1.86800 | 0.933999 | − | 0.357275i | \(-0.116294\pi\) | ||||
0.933999 | + | 0.357275i | \(0.116294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.107261 | −0.0105688 | −0.00528439 | − | 0.999986i | \(-0.501682\pi\) | ||||
−0.00528439 | + | 0.999986i | \(0.501682\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −47.5113 | −4.63663 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.8588 | −1.62980 | −0.814899 | − | 0.579603i | \(-0.803208\pi\) | ||||
−0.814899 | + | 0.579603i | \(0.803208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.81198 | −0.652470 | −0.326235 | − | 0.945289i | \(-0.605780\pi\) | ||||
−0.326235 | + | 0.945289i | \(0.605780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.11024 | −0.200295 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.8033 | 1.39257 | 0.696287 | − | 0.717763i | \(-0.254834\pi\) | ||||
0.696287 | + | 0.717763i | \(0.254834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.1699 | 2.06735 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.4427 | 1.70503 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.70076 | −0.889267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.65940 | −0.878127 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.62692 | 0.868030 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.3698 | 1.82193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.70889 | −0.506582 | −0.253291 | − | 0.967390i | \(-0.581513\pi\) | ||||
−0.253291 | + | 0.967390i | \(0.581513\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.55986 | 0.225383 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.52028 | 0.220198 | 0.110099 | − | 0.993921i | \(-0.464883\pi\) | ||||
0.110099 | + | 0.993921i | \(0.464883\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.6105 | 1.78716 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 35.3994 | 3.04670 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.5337 | 1.58344 | 0.791720 | − | 0.610884i | \(-0.209186\pi\) | ||||
0.791720 | + | 0.610884i | \(0.209186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.88645 | −0.160006 | −0.0800032 | − | 0.996795i | \(-0.525493\pi\) | ||||
−0.0800032 | + | 0.996795i | \(0.525493\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 28.2507 | 2.37914 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.54657 | −0.296579 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.1765 | −2.00775 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 28.3521 | 2.33844 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5348 | 1.19074 | 0.595369 | − | 0.803452i | \(-0.297006\pi\) | ||||
0.595369 | + | 0.803452i | \(0.297006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.11314 | 0.416102 | 0.208051 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208051 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.4054 | 1.16461 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.68911 | 0.376638 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.6197 | −1.56582 | −0.782911 | − | 0.622134i | \(-0.786266\pi\) | ||||
−0.782911 | + | 0.622134i | \(0.786266\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.34143 | 0.582213 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.0402 | −1.81583 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5788 | −1.22023 | −0.610113 | − | 0.792314i | \(-0.708876\pi\) | ||||
−0.610113 | + | 0.792314i | \(0.708876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.5675 | −1.05623 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.61496 | −0.744028 | −0.372014 | − | 0.928227i | \(-0.621333\pi\) | ||||
−0.372014 | + | 0.928227i | \(0.621333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.61752 | −0.278271 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30.6062 | −2.34051 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.8050 | −1.20163 | −0.600815 | − | 0.799388i | \(-0.705157\pi\) | ||||
−0.600815 | + | 0.799388i | \(0.705157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −41.4424 | −3.13275 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.8737 | 1.86962 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.66479 | −0.647637 | −0.323818 | − | 0.946119i | \(-0.604967\pi\) | ||||
−0.323818 | + | 0.946119i | \(0.604967\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5265 | 1.15407 | 0.577036 | − | 0.816719i | \(-0.304209\pi\) | ||||
0.577036 | + | 0.816719i | \(0.304209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.3260 | 2.24177 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.74112 | −0.201531 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.77019 | −0.202576 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −36.7892 | −2.67602 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8356 | −0.856397 | −0.428198 | − | 0.903685i | \(-0.640852\pi\) | ||||
−0.428198 | + | 0.903685i | \(0.640852\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.3978 | −0.820433 | −0.410216 | − | 0.911988i | \(-0.634547\pi\) | ||||
−0.410216 | + | 0.911988i | \(0.634547\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 35.8929 | 2.57035 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5156 | 0.962948 | 0.481474 | − | 0.876460i | \(-0.340102\pi\) | ||||
0.481474 | + | 0.876460i | \(0.340102\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0080 | −1.20567 | −0.602834 | − | 0.797867i | \(-0.705962\pi\) | ||||
−0.602834 | + | 0.797867i | \(0.705962\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.6597 | 2.93845 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.1256 | 1.76347 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5050 | 0.873388 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 34.2142 | 2.37805 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.88563 | 0.407117 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.71123 | 0.668549 | 0.334274 | − | 0.942476i | \(-0.391509\pi\) | ||||
0.334274 | + | 0.942476i | \(0.391509\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0713600 | −0.00488951 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.32516 | 0.226774 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.87319 | −0.330814 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.92347 | 0.400271 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.32855 | 0.492971 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.4988 | 1.37270 | 0.686352 | − | 0.727269i | \(-0.259211\pi\) | ||||
0.686352 | + | 0.727269i | \(0.259211\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 61.5411 | 4.10274 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.250591 | 0.0166323 | 0.00831614 | − | 0.999965i | \(-0.497353\pi\) | ||||
0.00831614 | + | 0.999965i | \(0.497353\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.1239 | −1.46199 | −0.730994 | − | 0.682384i | \(-0.760943\pi\) | ||||
−0.730994 | + | 0.682384i | \(0.760943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.1001 | 0.927721 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.70985 | −0.439577 | −0.219788 | − | 0.975548i | \(-0.570537\pi\) | ||||
−0.219788 | + | 0.975548i | \(0.570537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.6967 | 2.39383 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −34.0962 | −2.21479 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.8665 | −0.702895 | −0.351447 | − | 0.936208i | \(-0.614310\pi\) | ||||
−0.351447 | + | 0.936208i | \(0.614310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.17637 | −0.0757767 | −0.0378884 | − | 0.999282i | \(-0.512063\pi\) | ||||
−0.0378884 | + | 0.999282i | \(0.512063\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.379235 | 0.0243279 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 36.8283 | 2.35287 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.5705 | −0.990725 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −42.9496 | −2.72182 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.9124 | −1.25686 | −0.628431 | − | 0.777865i | \(-0.716302\pi\) | ||||
−0.628431 | + | 0.777865i | \(0.716302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.57946 | −0.413647 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 28.0355 | 1.75565 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.7530 | −0.920264 | −0.460132 | − | 0.887850i | \(-0.652198\pi\) | ||||
−0.460132 | + | 0.887850i | \(0.652198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.84873 | 0.177011 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −37.3109 | −2.30949 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.8677 | 1.47174 | 0.735872 | − | 0.677120i | \(-0.236772\pi\) | ||||
0.735872 | + | 0.677120i | \(0.236772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.53625 | 0.585807 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.9745 | −1.77321 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.84139 | 0.539069 | 0.269535 | − | 0.962991i | \(-0.413130\pi\) | ||||
0.269535 | + | 0.962991i | \(0.413130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.77312 | 0.472184 | 0.236092 | − | 0.971731i | \(-0.424133\pi\) | ||||
0.236092 | + | 0.971731i | \(0.424133\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −37.3020 | −2.25762 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.8345 | −0.713645 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1444 | −0.970026 | −0.485013 | − | 0.874507i | \(-0.661185\pi\) | ||||
−0.485013 | + | 0.874507i | \(0.661185\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.23658 | 0.433243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.4431 | 1.93539 | 0.967697 | − | 0.252117i | \(-0.0811268\pi\) | ||||
0.967697 | + | 0.252117i | \(0.0811268\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.4402 | −1.27449 | −0.637245 | − | 0.770661i | \(-0.719926\pi\) | ||||
−0.637245 | + | 0.770661i | \(0.719926\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −59.5652 | −3.52834 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.9959 | −0.767126 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.2758 | −0.663280 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8275 | −0.869206 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.2796 | 0.834225 | 0.417113 | − | 0.908855i | \(-0.363042\pi\) | ||||
0.417113 | + | 0.908855i | \(0.363042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.3100 | 1.88116 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.5057 | −0.609600 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.4060 | 1.00662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.45570 | −0.199183 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 56.3850 | 3.23924 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.3924 | 2.25560 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.01951 | 0.457698 | 0.228849 | − | 0.973462i | \(-0.426504\pi\) | ||||
0.228849 | + | 0.973462i | \(0.426504\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.322159 | −0.0183270 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.7129 | 1.34464 | 0.672318 | − | 0.740263i | \(-0.265299\pi\) | ||||
0.672318 | + | 0.740263i | \(0.265299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.6785 | −1.56448 | −0.782242 | − | 0.622975i | \(-0.785924\pi\) | ||||
−0.782242 | + | 0.622975i | \(0.785924\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −95.2438 | −5.36638 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.0060 | −1.17981 | −0.589907 | − | 0.807471i | \(-0.700836\pi\) | ||||
−0.589907 | + | 0.807471i | \(0.700836\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.17496 | 0.401721 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −50.6352 | −2.82618 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.1619 | −0.676707 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.3081 | 1.73666 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.4597 | −1.13143 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −38.1373 | −2.10258 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.87277 | −0.322796 | −0.161398 | − | 0.986889i | \(-0.551600\pi\) | ||||
−0.161398 | + | 0.986889i | \(0.551600\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.23030 | −0.231819 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 54.1144 | 2.95659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.0951 | −1.36702 | −0.683508 | − | 0.729943i | \(-0.739547\pi\) | ||||
−0.683508 | + | 0.729943i | \(0.739547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 44.4615 | 2.41482 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.39161 | −0.0753598 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.89195 | −0.534115 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 66.5871 | 3.58493 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.6888 | −1.54010 | −0.770048 | − | 0.637986i | \(-0.779768\pi\) | ||||
−0.770048 | + | 0.637986i | \(0.779768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.227950 | −0.0122019 | −0.00610093 | − | 0.999981i | \(-0.501942\pi\) | ||||
−0.00610093 | + | 0.999981i | \(0.501942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.7928 | 1.48347 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.91068 | 0.208144 | 0.104072 | − | 0.994570i | \(-0.466813\pi\) | ||||
0.104072 | + | 0.994570i | \(0.466813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0926939 | −0.00491968 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.1362 | −1.54205 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.2834 | 1.01774 | 0.508870 | − | 0.860843i | \(-0.330063\pi\) | ||||
0.508870 | + | 0.860843i | \(0.330063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.83958 | 0.359978 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.0119 | −1.52273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.69437 | 0.402742 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.9097 | −1.45687 | −0.728437 | − | 0.685113i | \(-0.759753\pi\) | ||||
−0.728437 | + | 0.685113i | \(0.759753\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.2987 | 1.00465 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.91062 | −0.514534 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.58737 | −0.237525 | −0.118762 | − | 0.992923i | \(-0.537893\pi\) | ||||
−0.118762 | + | 0.992923i | \(0.537893\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 61.1806 | 3.15935 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.9814 | −0.977592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.24248 | −0.115189 | −0.0575943 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575943 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1466 | −0.878447 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.1039 | −1.74263 | −0.871315 | − | 0.490724i | \(-0.836732\pi\) | ||||
−0.871315 | + | 0.490724i | \(0.836732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.3156 | 0.933447 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.13164 | 0.260856 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.2078 | 1.17668 | 0.588342 | − | 0.808612i | \(-0.299781\pi\) | ||||
0.588342 | + | 0.808612i | \(0.299781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5956 | 0.687561 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.56965 | 0.381838 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −44.2897 | −2.22846 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2947 | 0.918182 | 0.459091 | − | 0.888389i | \(-0.348175\pi\) | ||||
0.459091 | + | 0.888389i | \(0.348175\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 61.9036 | 3.09906 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.1942 | −1.00845 | −0.504224 | − | 0.863573i | \(-0.668222\pi\) | ||||
−0.504224 | + | 0.863573i | \(0.668222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.68151 | 0.183389 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35.8509 | 1.78144 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.813494 | 0.0403234 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.90809 | −0.341583 | −0.170791 | − | 0.985307i | \(-0.554632\pi\) | ||||
−0.170791 | + | 0.985307i | \(0.554632\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 55.6658 | 2.74579 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.5784 | −1.65229 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −55.7899 | −2.73862 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.66594 | −0.277462 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.8613 | 1.60538 | 0.802689 | − | 0.596397i | \(-0.203402\pi\) | ||||
0.802689 | + | 0.596397i | \(0.203402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.32397 | 0.162000 | 0.0810002 | − | 0.996714i | \(-0.474189\pi\) | ||||
0.0810002 | + | 0.996714i | \(0.474189\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 56.6330 | 2.75359 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.4544 | 1.18621 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.9389 | −1.98117 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.6521 | −0.514288 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.563527 | −0.0271442 | −0.0135721 | − | 0.999908i | \(-0.504320\pi\) | ||||
−0.0135721 | + | 0.999908i | \(0.504320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.6983 | −1.66749 | −0.833746 | − | 0.552148i | \(-0.813808\pi\) | ||||
−0.833746 | + | 0.552148i | \(0.813808\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −72.6138 | −3.48157 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.8857 | −1.38179 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.95916 | −0.427597 | −0.213799 | − | 0.976878i | \(-0.568584\pi\) | ||||
−0.213799 | + | 0.976878i | \(0.568584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 56.8361 | 2.70648 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.2674 | −1.77063 | −0.885314 | − | 0.464993i | \(-0.846057\pi\) | ||||
−0.885314 | + | 0.464993i | \(0.846057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.6369 | −1.78416 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 43.6552 | 2.06482 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.1091 | 1.09058 | 0.545292 | − | 0.838246i | \(-0.316419\pi\) | ||||
0.545292 | + | 0.838246i | \(0.316419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.71117 | −0.174752 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.3573 | 0.721549 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −48.4539 | −2.27156 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.86020 | −0.227350 | −0.113675 | − | 0.993518i | \(-0.536262\pi\) | ||||
−0.113675 | + | 0.993518i | \(0.536262\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.7086 | 1.01327 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9215 | 0.881261 | 0.440630 | − | 0.897689i | \(-0.354755\pi\) | ||||
0.440630 | + | 0.897689i | \(0.354755\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.98053 | −0.0920429 | −0.0460215 | − | 0.998940i | \(-0.514654\pi\) | ||||
−0.0460215 | + | 0.998940i | \(0.514654\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.0837 | 0.653116 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.206755 | 0.00956749 | 0.00478375 | − | 0.999989i | \(-0.498477\pi\) | ||||
0.00478375 | + | 0.999989i | \(0.498477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −56.2389 | −2.59687 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −58.9276 | −2.71524 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.986823 | −0.0453742 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −51.9567 | −2.38393 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.7170 | 0.673847 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.8039 | 0.539333 | 0.269667 | − | 0.962954i | \(-0.413086\pi\) | ||||
0.269667 | + | 0.962954i | \(0.413086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.15210 | −0.0981275 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −69.2012 | −3.14876 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.2604 | −0.874571 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.1579 | −0.550925 | −0.275462 | − | 0.961312i | \(-0.588831\pi\) | ||||
−0.275462 | + | 0.961312i | \(0.588831\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.7909 | −2.11596 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6769 | 0.662357 | 0.331179 | − | 0.943568i | \(-0.392554\pi\) | ||||
0.331179 | + | 0.943568i | \(0.392554\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.8262 | −0.667736 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.1982 | −1.22247 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0963330 | 0.00432112 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.63326 | 0.117881 | 0.0589403 | − | 0.998262i | \(-0.481228\pi\) | ||||
0.0589403 | + | 0.998262i | \(0.481228\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.8785 | −1.29019 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.48187 | 0.244425 | 0.122212 | − | 0.992504i | \(-0.461001\pi\) | ||||
0.122212 | + | 0.992504i | \(0.461001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 73.2421 | 3.25923 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.8652 | −0.482540 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.8677 | −0.481703 | −0.240852 | − | 0.970562i | \(-0.577427\pi\) | ||||
−0.240852 | + | 0.970562i | \(0.577427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.99644 | −0.353742 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.1228 | −2.03637 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.418472 | −0.0184401 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8906 | −0.478969 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −47.4702 | −2.08371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.7378 | −0.996161 | −0.498081 | − | 0.867131i | \(-0.665962\pi\) | ||||
−0.498081 | + | 0.867131i | \(0.665962\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.29385 | −0.187757 | −0.0938784 | − | 0.995584i | \(-0.529927\pi\) | ||||
−0.0938784 | + | 0.995584i | \(0.529927\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −124.472 | −5.43241 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.87558 | 0.125262 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.29093 | 0.403953 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 49.8632 | 2.16388 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.81793 | 0.425262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −65.7732 | −2.84362 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.0246 | −1.12305 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.9297 | −0.470775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.58128 | 0.153971 | 0.0769855 | − | 0.997032i | \(-0.475470\pi\) | ||||
0.0769855 | + | 0.997032i | \(0.475470\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.6336 | 2.00124 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.5764 | −1.13841 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6549 | 0.797624 | 0.398812 | − | 0.917033i | \(-0.369423\pi\) | ||||
0.398812 | + | 0.917033i | \(0.369423\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 60.7933 | 2.59459 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.5001 | 1.34195 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.0284 | 1.95733 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.23293 | −0.349468 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.6996 | 0.665213 | 0.332607 | − | 0.943066i | \(-0.392072\pi\) | ||||
0.332607 | + | 0.943066i | \(0.392072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.61065 | 0.110419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.32024 | −0.351281 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.0469 | 1.26633 | 0.633163 | − | 0.774018i | \(-0.281756\pi\) | ||||
0.633163 | + | 0.774018i | \(0.281756\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 57.7538 | 2.42972 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −37.2583 | −1.56470 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.4359 | 1.77900 | 0.889502 | − | 0.456931i | \(-0.151051\pi\) | ||||
0.889502 | + | 0.456931i | \(0.151051\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.0387 | −1.80111 | −0.900557 | − | 0.434738i | \(-0.856841\pi\) | ||||
−0.900557 | + | 0.434738i | \(0.856841\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.5482 | −1.48505 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 58.0816 | 2.42217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.4394 | 0.476226 | 0.238113 | − | 0.971237i | \(-0.423471\pi\) | ||||
0.238113 | + | 0.971237i | \(0.423471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.2333 | −1.42269 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 57.9801 | 2.40542 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.83011 | −0.117211 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 71.9530 | 2.97489 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.6737 | −1.72006 | −0.860029 | − | 0.510245i | \(-0.829555\pi\) | ||||
−0.860029 | + | 0.510245i | \(0.829555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.10955 | −0.251740 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.5941 | 1.66982 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.1597 | 1.07425 | 0.537126 | − | 0.843502i | \(-0.319510\pi\) | ||||
0.537126 | + | 0.843502i | \(0.319510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37.8468 | −1.55157 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −51.0835 | −2.09071 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.5297 | −1.08397 | −0.541987 | − | 0.840387i | \(-0.682328\pi\) | ||||
−0.541987 | + | 0.840387i | \(0.682328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.94788 | −0.283410 | −0.141705 | − | 0.989909i | \(-0.545258\pi\) | ||||
−0.141705 | + | 0.989909i | \(0.545258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 83.5134 | 3.40093 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.6854 | −1.53213 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.63243 | 0.350380 | 0.175190 | − | 0.984535i | \(-0.443946\pi\) | ||||
0.175190 | + | 0.984535i | \(0.443946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 75.4645 | 3.05798 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.8112 | 1.16558 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.9695 | −1.45279 | −0.726396 | − | 0.687276i | \(-0.758806\pi\) | ||||
−0.726396 | + | 0.687276i | \(0.758806\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 37.5587 | 1.51451 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0267 | −1.20883 | −0.604415 | − | 0.796670i | \(-0.706593\pi\) | ||||
−0.604415 | + | 0.796670i | \(0.706593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4891 | 0.743139 | 0.371569 | − | 0.928405i | \(-0.378820\pi\) | ||||
0.371569 | + | 0.928405i | \(0.378820\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 51.5601 | 2.06903 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.1144 | 1.56709 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.3657 | 1.13463 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.6774 | 0.705969 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.68098 | −0.0670252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.17204 | −0.205896 | −0.102948 | − | 0.994687i | \(-0.532827\pi\) | ||||
−0.102948 | + | 0.994687i | \(0.532827\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.1676 | 1.15931 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.2728 | −0.883869 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.9146 | 1.14564 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.143052 | −0.00565906 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.9314 | −0.668750 | −0.334375 | − | 0.942440i | \(-0.608525\pi\) | ||||
−0.334375 | + | 0.942440i | \(0.608525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.4872 | 1.79384 | 0.896920 | − | 0.442193i | \(-0.145799\pi\) | ||||
0.896920 | + | 0.442193i | \(0.145799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.98710 | 0.393242 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.7207 | 1.32570 | 0.662848 | − | 0.748754i | \(-0.269348\pi\) | ||||
0.662848 | + | 0.748754i | \(0.269348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.58878 | −0.376393 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.6366 | −0.573654 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.3457 | 1.65711 | 0.828557 | − | 0.559904i | \(-0.189162\pi\) | ||||
0.828557 | + | 0.559904i | \(0.189162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.83270 | 0.384195 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.8745 | 0.463269 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.8143 | −1.94049 | −0.970244 | − | 0.242129i | \(-0.922154\pi\) | ||||
−0.970244 | + | 0.242129i | \(0.922154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5547 | 0.566114 | 0.283057 | − | 0.959103i | \(-0.408651\pi\) | ||||
0.283057 | + | 0.959103i | \(0.408651\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.0112 | 0.854846 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 80.4105 | 3.11819 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.2135 | −1.36347 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 61.5681 | 2.38036 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.6907 | −0.451313 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.8922 | −0.959523 | −0.479761 | − | 0.877399i | \(-0.659277\pi\) | ||||
−0.479761 | + | 0.877399i | \(0.659277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 92.7410 | 3.56960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.3177 | 1.16520 | 0.582601 | − | 0.812758i | \(-0.302035\pi\) | ||||
0.582601 | + | 0.812758i | \(0.302035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0166 | 0.768165 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.752647 | 0.0288415 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0088 | 0.765616 | 0.382808 | − | 0.923828i | \(-0.374957\pi\) | ||||
0.382808 | + | 0.923828i | \(0.374957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 72.3078 | 2.76274 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −66.4490 | −2.53519 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.48709 | 0.285235 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.5242 | 1.42749 | 0.713744 | − | 0.700406i | \(-0.246998\pi\) | ||||
0.713744 | + | 0.700406i | \(0.246998\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.2659 | 1.07373 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.35984 | −0.279175 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.66867 | 0.290471 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.1530 | −0.762256 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.8949 | −1.09134 | −0.545672 | − | 0.837999i | \(-0.683726\pi\) | ||||
−0.545672 | + | 0.837999i | \(0.683726\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.57147 | 0.134701 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 110.218 | 4.15106 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −76.1174 | −2.86269 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.28959 | 0.161099 | 0.0805495 | − | 0.996751i | \(-0.474332\pi\) | ||||
0.0805495 | + | 0.996751i | \(0.474332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −68.3511 | −2.56337 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.82979 | 0.255777 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.8367 | −0.517463 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −32.6374 | −1.21887 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0572 | −1.04636 | −0.523179 | − | 0.852223i | \(-0.675254\pi\) | ||||
−0.523179 | + | 0.852223i | \(0.675254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.434901 | 0.0161965 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.53322 | −0.131402 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −63.3385 | −2.35233 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.5405 | −1.54065 | −0.770327 | − | 0.637649i | \(-0.779907\pi\) | ||||
−0.770327 | + | 0.637649i | \(0.779907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.4285 | −0.978833 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.03915 | 0.0754206 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.3178 | 1.89547 | 0.947733 | − | 0.319065i | \(-0.103369\pi\) | ||||
0.947733 | + | 0.319065i | \(0.103369\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 110.613 | 4.08004 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0598 | −0.591570 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.61636 | 0.243387 | 0.121693 | − | 0.992568i | \(-0.461168\pi\) | ||||
0.121693 | + | 0.992568i | \(0.461168\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46.7658 | −1.71798 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.8632 | 1.71924 | 0.859622 | − | 0.510930i | \(-0.170699\pi\) | ||||
0.859622 | + | 0.510930i | \(0.170699\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 56.7065 | 2.07757 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −86.0991 | −3.15020 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 68.3554 | 2.49765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −59.8069 | −2.17948 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.9486 | 0.726002 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.4260 | 0.851432 | 0.425716 | − | 0.904857i | \(-0.360022\pi\) | ||||
0.425716 | + | 0.904857i | \(0.360022\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.7614 | −0.717292 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.8260 | −0.936191 | −0.468096 | − | 0.883678i | \(-0.655060\pi\) | ||||
−0.468096 | + | 0.883678i | \(0.655060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.6198 | 0.999904 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56.2016 | 2.03197 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.3672 | 0.915956 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.5921 | −1.10318 | −0.551590 | − | 0.834116i | \(-0.685979\pi\) | ||||
−0.551590 | + | 0.834116i | \(0.685979\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.3104 | −1.59580 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6287 | −0.921799 | −0.460900 | − | 0.887452i | \(-0.652473\pi\) | ||||
−0.460900 | + | 0.887452i | \(0.652473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.2847 | 0.441280 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.55614 | 0.306950 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.2931 | −0.583761 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0275092 | 0.000984357 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −56.2267 | −2.00938 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −76.5447 | −2.73200 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.9337 | 0.425392 | 0.212696 | − | 0.977118i | \(-0.431776\pi\) | ||||
0.212696 | + | 0.977118i | \(0.431776\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 71.6864 | 2.55210 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.0212 | −2.13411 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.9277 | 1.09828 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.6420 | 1.01583 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.0053 | −0.460670 | −0.230335 | − | 0.973111i | \(-0.573982\pi\) | ||||
−0.230335 | + | 0.973111i | \(0.573982\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5041 | 0.796139 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −58.0840 | −2.05230 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.28349 | −0.0805827 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −89.8898 | −3.16820 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.5551 | 0.934782 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.5912 | 1.07553 | 0.537765 | − | 0.843095i | \(-0.319269\pi\) | ||||
0.537765 | + | 0.843095i | \(0.319269\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.49311 | −0.333348 | −0.166674 | − | 0.986012i | \(-0.553303\pi\) | ||||
−0.166674 | + | 0.986012i | \(0.553303\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.3465 | 0.818798 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −60.7796 | −2.12902 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.33244 | −0.151573 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −74.7777 | −2.61295 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.9272 | 1.60287 | 0.801435 | − | 0.598081i | \(-0.204070\pi\) | ||||
0.801435 | + | 0.598081i | \(0.204070\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.7332 | −0.443852 | −0.221926 | − | 0.975064i | \(-0.571234\pi\) | ||||
−0.221926 | + | 0.975064i | \(0.571234\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35.5447 | −1.23751 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.63891 | 0.0569906 | 0.0284953 | − | 0.999594i | \(-0.490928\pi\) | ||||
0.0284953 | + | 0.999594i | \(0.490928\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.733575 | 0.0254781 | 0.0127391 | − | 0.999919i | \(-0.495945\pi\) | ||||
0.0127391 | + | 0.999919i | \(0.495945\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.4897 | −1.68209 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.5848 | 0.782518 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.5120 | −1.29816 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.9054 | 0.376944 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.17085 | −0.143994 | −0.0719968 | − | 0.997405i | \(-0.522937\pi\) | ||||
−0.0719968 | + | 0.997405i | \(0.522937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.40069 | 0.324162 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 97.4427 | 3.35610 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.1135 | −0.485518 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.1649 | 1.34572 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −64.3956 | −2.21005 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.99250 | −0.136861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.0380 | −1.02848 | −0.514240 | − | 0.857646i | \(-0.671926\pi\) | ||||
−0.514240 | + | 0.857646i | \(0.671926\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −119.408 | −4.08366 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.5241 | −1.31596 | −0.657979 | − | 0.753036i | \(-0.728588\pi\) | ||||
−0.657979 | + | 0.753036i | \(0.728588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.3399 | 1.61522 | 0.807608 | − | 0.589720i | \(-0.200762\pi\) | ||||
0.807608 | + | 0.589720i | \(0.200762\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.0332 | −1.33025 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.2960 | −0.486642 | −0.243321 | − | 0.969946i | \(-0.578237\pi\) | ||||
−0.243321 | + | 0.969946i | \(0.578237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.6620 | −2.09657 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.8667 | −1.15017 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.1441 | 0.445881 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.4863 | 1.43959 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.7241 | −1.00601 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −82.5912 | −2.79209 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.720461 | −0.0243282 | −0.0121641 | − | 0.999926i | \(-0.503872\pi\) | ||||
−0.0121641 | + | 0.999926i | \(0.503872\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.8888 | 1.44660 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7151 | 1.50649 | 0.753245 | − | 0.657740i | \(-0.228487\pi\) | ||||
0.753245 | + | 0.657740i | \(0.228487\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.3774 | −0.988629 | −0.494314 | − | 0.869283i | \(-0.664581\pi\) | ||||
−0.494314 | + | 0.869283i | \(0.664581\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 97.0428 | 3.26206 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.2596 | 0.848133 | 0.424067 | − | 0.905631i | \(-0.360602\pi\) | ||||
0.424067 | + | 0.905631i | \(0.360602\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.1472 | 0.776332 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.6396 | −0.356441 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −47.8130 | −1.60000 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.8050 | −1.12998 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 52.2788 | 1.74554 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.44794 | −0.248403 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.84808 | 0.194828 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.3792 | −0.345397 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 60.5753 | 2.01359 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3854 | 0.411252 | 0.205626 | − | 0.978631i | \(-0.434077\pi\) | ||||
0.205626 | + | 0.978631i | \(0.434077\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 113.033 | 3.74906 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0835 | 0.400345 | 0.200173 | − | 0.979761i | \(-0.435850\pi\) | ||||
0.200173 | + | 0.979761i | \(0.435850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.5570 | 0.547957 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 118.315 | 3.91137 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2187 | −0.337452 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0939 | −0.860758 | −0.430379 | − | 0.902648i | \(-0.641620\pi\) | ||||
−0.430379 | + | 0.902648i | \(0.641620\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.0866 | 0.793679 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0727758 | −0.00239544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.18130 | −0.236120 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.645817 | −0.0212114 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.5428 | 0.411517 | 0.205759 | − | 0.978603i | \(-0.434034\pi\) | ||||
0.205759 | + | 0.978603i | \(0.434034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −47.9845 | −1.57263 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 71.2215 | 2.33169 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.8077 | −0.353449 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.8980 | 0.486697 | 0.243348 | − | 0.969939i | \(-0.421754\pi\) | ||||
0.243348 | + | 0.969939i | \(0.421754\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −83.1323 | −2.71292 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.1199 | 0.851485 | 0.425743 | − | 0.904844i | \(-0.360013\pi\) | ||||
0.425743 | + | 0.904844i | \(0.360013\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.2138 | 0.593124 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −143.530 | −4.66904 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.9973 | −1.26724 | −0.633620 | − | 0.773644i | \(-0.718432\pi\) | ||||
−0.633620 | + | 0.773644i | \(0.718432\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.04100 | 0.196099 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −63.0914 | −2.04588 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.9205 | 0.515715 | 0.257858 | − | 0.966183i | \(-0.416983\pi\) | ||||
0.257858 | + | 0.966183i | \(0.416983\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.1758 | −1.49422 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.5499 | 0.696611 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −75.1465 | −2.42661 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5554 | −0.953402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −101.506 | −3.27099 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.4677 | −1.43147 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4744 | 1.17294 | 0.586470 | − | 0.809971i | \(-0.300517\pi\) | ||||
0.586470 | + | 0.809971i | \(0.300517\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.5282 | −1.17346 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.2365 | 0.617328 | 0.308664 | − | 0.951171i | \(-0.400118\pi\) | ||||
0.308664 | + | 0.951171i | \(0.400118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.64877 | 0.245208 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 94.0338 | 3.01149 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.59668 | −0.0830751 | −0.0415375 | − | 0.999137i | \(-0.513226\pi\) | ||||
−0.0415375 | + | 0.999137i | \(0.513226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1697 | 0.356984 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41.0148 | −1.30950 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.7358 | 0.469998 | 0.234999 | − | 0.971996i | \(-0.424491\pi\) | ||||
0.234999 | + | 0.971996i | \(0.424491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.7302 | 1.68012 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −114.545 | −3.64601 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.84317 | 0.154004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.8704 | 1.17123 | 0.585614 | − | 0.810590i | \(-0.300854\pi\) | ||||
0.585614 | + | 0.810590i | \(0.300854\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.6388 | −0.559751 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −66.3556 | −2.10361 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.1457 | −0.764703 | −0.382352 | − | 0.924017i | \(-0.624886\pi\) | ||||
−0.382352 | + | 0.924017i | \(0.624886\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.37496 | −0.201695 |
(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 | 6008.2.a.e.1.46 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.46 | ✓ | 50 | 1.1 | even | 1 | trivial |