Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −0.249551 | −0.144078 | −0.0720391 | − | 0.997402i | \(-0.522951\pi\) | ||||
−0.0720391 | + | 0.997402i | \(0.522951\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.41933 | −1.52917 | −0.764585 | − | 0.644523i | \(-0.777056\pi\) | ||||
−0.764585 | + | 0.644523i | \(0.777056\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.14640 | 1.18923 | 0.594614 | − | 0.804011i | \(-0.297305\pi\) | ||||
0.594614 | + | 0.804011i | \(0.297305\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.93772 | −0.979241 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.41666 | 1.33167 | 0.665836 | − | 0.746098i | \(-0.268075\pi\) | ||||
0.665836 | + | 0.746098i | \(0.268075\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.12764 | 1.42215 | 0.711076 | − | 0.703115i | \(-0.248208\pi\) | ||||
0.711076 | + | 0.703115i | \(0.248208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.853296 | 0.220320 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.01726 | 1.45940 | 0.729700 | − | 0.683767i | \(-0.239660\pi\) | ||||
0.729700 | + | 0.683767i | \(0.239660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.70136 | 1.30798 | 0.653991 | − | 0.756502i | \(-0.273093\pi\) | ||||
0.653991 | + | 0.756502i | \(0.273093\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.785187 | −0.171342 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.81100 | −0.794648 | −0.397324 | − | 0.917678i | \(-0.630061\pi\) | ||||
−0.397324 | + | 0.917678i | \(0.630061\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.69180 | 1.33836 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.48176 | 0.285166 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.63013 | −0.302707 | −0.151353 | − | 0.988480i | \(-0.548363\pi\) | ||||
−0.151353 | + | 0.988480i | \(0.548363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.23433 | −0.580904 | −0.290452 | − | 0.956890i | \(-0.593806\pi\) | ||||
−0.290452 | + | 0.956890i | \(0.593806\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.10218 | −0.191865 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.7586 | −1.81853 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.58346 | 0.753516 | 0.376758 | − | 0.926312i | \(-0.377039\pi\) | ||||
0.376758 | + | 0.926312i | \(0.377039\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.27961 | −0.204901 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.55052 | 1.33537 | 0.667684 | − | 0.744445i | \(-0.267286\pi\) | ||||
0.667684 | + | 0.744445i | \(0.267286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.40991 | 1.13000 | 0.565000 | − | 0.825091i | \(-0.308876\pi\) | ||||
0.565000 | + | 0.825091i | \(0.308876\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.0450 | 1.49743 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.286091 | −0.0417307 | −0.0208653 | − | 0.999782i | \(-0.506642\pi\) | ||||
−0.0208653 | + | 0.999782i | \(0.506642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.89984 | 0.414263 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50161 | −0.210268 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.90591 | −0.399158 | −0.199579 | − | 0.979882i | \(-0.563957\pi\) | ||||
−0.199579 | + | 0.979882i | \(0.563957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.1020 | −2.03635 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.42278 | −0.188452 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.10726 | −0.664909 | −0.332455 | − | 0.943119i | \(-0.607877\pi\) | ||||
−0.332455 | + | 0.943119i | \(0.607877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.08325 | 0.138696 | 0.0693480 | − | 0.997593i | \(-0.477908\pi\) | ||||
0.0693480 | + | 0.997593i | \(0.477908\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.24326 | −1.16454 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.5331 | −2.17471 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.78698 | −0.340484 | −0.170242 | − | 0.985402i | \(-0.554455\pi\) | ||||
−0.170242 | + | 0.985402i | \(0.554455\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.951037 | 0.114491 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.27819 | 0.151693 | 0.0758467 | − | 0.997119i | \(-0.475834\pi\) | ||||
0.0758467 | + | 0.997119i | \(0.475834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0666 | 1.41229 | 0.706144 | − | 0.708068i | \(-0.250433\pi\) | ||||
0.706144 | + | 0.708068i | \(0.250433\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.66994 | −0.192829 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.8966 | 1.58366 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0744 | 1.58349 | 0.791747 | − | 0.610849i | \(-0.209172\pi\) | ||||
0.791747 | + | 0.610849i | \(0.209172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.44340 | 0.938155 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.3504 | −1.13610 | −0.568051 | − | 0.822994i | \(-0.692302\pi\) | ||||
−0.568051 | + | 0.822994i | \(0.692302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.5750 | −2.23167 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.406799 | 0.0436135 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.69526 | −0.179697 | −0.0898487 | − | 0.995955i | \(-0.528638\pi\) | ||||
−0.0898487 | + | 0.995955i | \(0.528638\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.1336 | 1.69126 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.807131 | 0.0836956 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.4948 | −2.00013 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.26933 | −0.230415 | −0.115208 | − | 0.993341i | \(-0.536753\pi\) | ||||
−0.115208 | + | 0.993341i | \(0.536753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.9749 | −1.30403 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.603233 | −0.0600240 | −0.0300120 | − | 0.999550i | \(-0.509555\pi\) | ||||
−0.0300120 | + | 0.999550i | \(0.509555\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.07973 | −0.796119 | −0.398060 | − | 0.917360i | \(-0.630316\pi\) | ||||
−0.398060 | + | 0.917360i | \(0.630316\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.68481 | 0.262011 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.27015 | −0.316137 | −0.158069 | − | 0.987428i | \(-0.550527\pi\) | ||||
−0.158069 | + | 0.987428i | \(0.550527\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0790 | −1.15696 | −0.578479 | − | 0.815698i | \(-0.696353\pi\) | ||||
−0.578479 | + | 0.815698i | \(0.696353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.14381 | −0.108565 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.19405 | −0.770832 | −0.385416 | − | 0.922743i | \(-0.625942\pi\) | ||||
−0.385416 | + | 0.922743i | \(0.625942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.0310 | 1.21515 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.0636 | −1.39263 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.9327 | 1.73556 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.50687 | 0.773352 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.13379 | −0.192397 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.78482 | −0.517410 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.27060 | −0.201483 | −0.100742 | − | 0.994913i | \(-0.532122\pi\) | ||||
−0.100742 | + | 0.994913i | \(0.532122\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.84915 | −0.162809 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9078 | −1.47724 | −0.738619 | − | 0.674123i | \(-0.764522\pi\) | ||||
−0.738619 | + | 0.674123i | \(0.764522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.9388 | 1.55549 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.06664 | −0.436067 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.3040 | 1.56381 | 0.781907 | − | 0.623395i | \(-0.214247\pi\) | ||||
0.781907 | + | 0.623395i | \(0.214247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.33049 | 0.621764 | 0.310882 | − | 0.950449i | \(-0.399376\pi\) | ||||
0.310882 | + | 0.950449i | \(0.399376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0713943 | 0.00601248 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.6470 | 1.89384 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.57394 | 0.462890 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.723658 | −0.0596863 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.1496 | −1.89649 | −0.948243 | − | 0.317545i | \(-0.897142\pi\) | ||||
−0.948243 | + | 0.317545i | \(0.897142\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9903 | −1.38265 | −0.691326 | − | 0.722543i | \(-0.742973\pi\) | ||||
−0.691326 | + | 0.722543i | \(0.742973\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.6771 | −1.42911 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.0592 | 0.888300 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.29534 | −0.741849 | −0.370924 | − | 0.928663i | \(-0.620959\pi\) | ||||
−0.370924 | + | 0.928663i | \(0.620959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.725173 | 0.0575100 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.9909 | −0.945017 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.5792 | −1.53356 | −0.766782 | − | 0.641908i | \(-0.778143\pi\) | ||||
−0.766782 | + | 0.641908i | \(0.778143\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.76872 | 0.293394 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.52102 | 0.349847 | 0.174924 | − | 0.984582i | \(-0.444032\pi\) | ||||
0.174924 | + | 0.984582i | \(0.444032\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.2927 | 1.02252 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.7490 | −1.28083 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.04673 | −0.383696 | −0.191848 | − | 0.981425i | \(-0.561448\pi\) | ||||
−0.191848 | + | 0.981425i | \(0.561448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.0551 | 1.59162 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.27452 | 0.0957989 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.0396 | 1.04937 | 0.524683 | − | 0.851297i | \(-0.324184\pi\) | ||||
0.524683 | + | 0.851297i | \(0.324184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5186 | 0.930503 | 0.465251 | − | 0.885179i | \(-0.345964\pi\) | ||||
0.465251 | + | 0.885179i | \(0.345964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.270326 | −0.0199831 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.6723 | −1.15225 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.5762 | 1.94344 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.66222 | 0.339127 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6964 | −0.991039 | −0.495520 | − | 0.868597i | \(-0.665022\pi\) | ||||
−0.495520 | + | 0.868597i | \(0.665022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0423 | 1.51465 | 0.757327 | − | 0.653036i | \(-0.226505\pi\) | ||||
0.757327 | + | 0.653036i | \(0.226505\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.37540 | 0.313329 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.22257 | 0.514587 | 0.257293 | − | 0.966333i | \(-0.417169\pi\) | ||||
0.257293 | + | 0.966333i | \(0.417169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.30012 | −0.304828 | −0.152414 | − | 0.988317i | \(-0.548705\pi\) | ||||
−0.152414 | + | 0.988317i | \(0.548705\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.695494 | 0.0490563 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.12903 | −0.359987 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.2370 | −2.04200 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.1957 | 0.778152 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.1810 | 1.74180 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.14730 | −0.354354 | −0.177177 | − | 0.984179i | \(-0.556697\pi\) | ||||
−0.177177 | + | 0.984179i | \(0.556697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.318974 | −0.0218557 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.3369 | −1.72796 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1765 | −0.690827 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.01123 | −0.203480 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.8544 | 2.07549 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7155 | 1.25328 | 0.626642 | − | 0.779308i | \(-0.284429\pi\) | ||||
0.626642 | + | 0.779308i | \(0.284429\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.6587 | −1.31058 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.39574 | 0.0926385 | 0.0463193 | − | 0.998927i | \(-0.485251\pi\) | ||||
0.0463193 | + | 0.998927i | \(0.485251\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.5174 | 1.48799 | 0.743997 | − | 0.668183i | \(-0.232928\pi\) | ||||
0.743997 | + | 0.668183i | \(0.232928\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.46790 | −0.228171 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.40361 | −0.222978 | −0.111489 | − | 0.993766i | \(-0.535562\pi\) | ||||
−0.111489 | + | 0.993766i | \(0.535562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.978239 | 0.0638133 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.51228 | −0.228147 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.6423 | 1.52929 | 0.764647 | − | 0.644449i | \(-0.222913\pi\) | ||||
0.764647 | + | 0.644449i | \(0.222913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3500 | −0.924368 | −0.462184 | − | 0.886784i | \(-0.652934\pi\) | ||||
−0.462184 | + | 0.886784i | \(0.652934\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.55235 | −0.420333 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.91551 | −0.633479 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.2346 | 1.86015 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.58295 | 0.163688 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.21285 | −0.265913 | −0.132956 | − | 0.991122i | \(-0.542447\pi\) | ||||
−0.132956 | + | 0.991122i | \(0.542447\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8319 | −1.05821 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.13451 | 0.321535 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.39309 | 0.523546 | 0.261773 | − | 0.965129i | \(-0.415693\pi\) | ||||
0.261773 | + | 0.965129i | \(0.415693\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.4214 | 0.896102 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.78886 | 0.296423 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.71809 | 0.352592 | 0.176296 | − | 0.984337i | \(-0.443588\pi\) | ||||
0.176296 | + | 0.984337i | \(0.443588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.93627 | 0.610380 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.423054 | 0.0258905 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.0279 | 1.52598 | 0.762990 | − | 0.646410i | \(-0.223731\pi\) | ||||
0.762990 | + | 0.646410i | \(0.223731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.2035 | 0.680565 | 0.340282 | − | 0.940323i | \(-0.389477\pi\) | ||||
0.340282 | + | 0.940323i | \(0.389477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.02616 | −0.243674 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 29.5554 | 1.78226 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.67194 | 0.100457 | 0.0502286 | − | 0.998738i | \(-0.484005\pi\) | ||||
0.0502286 | + | 0.998738i | \(0.484005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.50158 | 0.568845 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.69457 | 0.578330 | 0.289165 | − | 0.957279i | \(-0.406622\pi\) | ||||
0.289165 | + | 0.957279i | \(0.406622\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0644 | 0.954928 | 0.477464 | − | 0.878651i | \(-0.341556\pi\) | ||||
0.477464 | + | 0.878651i | \(0.341556\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.86495 | 0.288175 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.9034 | 1.58806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.2075 | 1.12985 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.566313 | 0.0331979 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3639 | −0.897567 | −0.448783 | − | 0.893641i | \(-0.648143\pi\) | ||||
−0.448783 | + | 0.893641i | \(0.648143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.4634 | 1.01676 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.54445 | 0.379747 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.5414 | −1.13011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3146 | 1.34383 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.150537 | 0.00864815 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.70399 | −0.212090 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.9676 | 1.82449 | 0.912245 | − | 0.409645i | \(-0.134348\pi\) | ||||
0.912245 | + | 0.409645i | \(0.134348\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.01630 | 0.114703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.3149 | 1.20866 | 0.604328 | − | 0.796736i | \(-0.293442\pi\) | ||||
0.604328 | + | 0.796736i | \(0.293442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.08215 | 0.0611667 | 0.0305833 | − | 0.999532i | \(-0.490264\pi\) | ||||
0.0305833 | + | 0.999532i | \(0.490264\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 31.6057 | 1.78078 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.38550 | −0.358645 | −0.179323 | − | 0.983790i | \(-0.557391\pi\) | ||||
−0.179323 | + | 0.983790i | \(0.557391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.19971 | −0.403106 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.816068 | 0.0455485 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.3066 | 1.90887 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.3132 | 1.90335 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.01432 | 0.166692 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.900157 | −0.0496273 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.58779 | 0.197203 | 0.0986014 | − | 0.995127i | \(-0.468563\pi\) | ||||
0.0986014 | + | 0.995127i | \(0.468563\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.4649 | −0.737874 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.52960 | 0.520658 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4395 | 0.677624 | 0.338812 | − | 0.940854i | \(-0.389975\pi\) | ||||
0.338812 | + | 0.940854i | \(0.389975\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.04483 | 0.111060 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.2850 | −0.773573 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.9007 | −0.696575 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.25191 | −0.175077 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.1358 | −1.93987 | −0.969936 | − | 0.243359i | \(-0.921751\pi\) | ||||
−0.969936 | + | 0.243359i | \(0.921751\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.3208 | 1.35539 | 0.677695 | − | 0.735343i | \(-0.262979\pi\) | ||||
0.677695 | + | 0.735343i | \(0.262979\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.59796 | 0.405549 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.7478 | 1.58332 | 0.791659 | − | 0.610963i | \(-0.209218\pi\) | ||||
0.791659 | + | 0.610963i | \(0.209218\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.37056 | −0.231965 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.72468 | −0.250056 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1156 | −0.586658 | −0.293329 | − | 0.956011i | \(-0.594763\pi\) | ||||
−0.293329 | + | 0.956011i | \(0.594763\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5055 | 0.710818 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.12290 | −0.111423 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −41.2596 | −2.15963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.09458 | 0.318135 | 0.159067 | − | 0.987268i | \(-0.449151\pi\) | ||||
0.159067 | + | 0.987268i | \(0.449151\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.1191 | −1.30765 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.14317 | −0.474690 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.6135 | −1.22266 | −0.611331 | − | 0.791375i | \(-0.709365\pi\) | ||||
−0.611331 | + | 0.791375i | \(0.709365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.44361 | 0.0745475 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.35870 | −0.430495 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.4236 | −1.76822 | −0.884110 | − | 0.467278i | \(-0.845235\pi\) | ||||
−0.884110 | + | 0.467278i | \(0.845235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.566630 | 0.0290293 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.4911 | −0.638267 | −0.319133 | − | 0.947710i | \(-0.603392\pi\) | ||||
−0.319133 | + | 0.947710i | \(0.603392\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −47.5170 | −2.42169 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.7683 | −1.10654 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.3367 | 1.13252 | 0.566258 | − | 0.824228i | \(-0.308391\pi\) | ||||
0.566258 | + | 0.824228i | \(0.308391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.9318 | −1.15971 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.21935 | 0.212838 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −48.1250 | −2.42143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.4105 | 1.77720 | 0.888601 | − | 0.458681i | \(-0.151678\pi\) | ||||
0.888601 | + | 0.458681i | \(0.151678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.47664 | −0.224112 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2302 | 1.80925 | 0.904625 | − | 0.426208i | \(-0.140151\pi\) | ||||
0.904625 | + | 0.426208i | \(0.140151\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.5845 | −0.826133 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −28.8707 | −1.43460 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.2436 | 1.00344 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.31877 | 0.213549 | 0.106775 | − | 0.994283i | \(-0.465948\pi\) | ||||
0.106775 | + | 0.994283i | \(0.465948\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.56777 | −0.225312 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.0695 | −0.790729 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.3913 | 1.73729 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.82933 | −0.0895827 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.0794 | −1.76259 | −0.881296 | − | 0.472564i | \(-0.843329\pi\) | ||||
−0.881296 | + | 0.472564i | \(0.843329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.25150 | −0.353417 | −0.176708 | − | 0.984263i | \(-0.556545\pi\) | ||||
−0.176708 | + | 0.984263i | \(0.556545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.840456 | 0.0408644 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 40.2663 | 1.95320 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.40834 | 0.164941 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.65159 | −0.272861 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.2094 | 0.539939 | 0.269970 | − | 0.962869i | \(-0.412986\pi\) | ||||
0.269970 | + | 0.962869i | \(0.412986\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.51226 | 0.361016 | 0.180508 | − | 0.983574i | \(-0.442226\pi\) | ||||
0.180508 | + | 0.983574i | \(0.442226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.39098 | −0.0666924 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.7279 | −1.03939 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.55983 | −0.122174 | −0.0610870 | − | 0.998132i | \(-0.519457\pi\) | ||||
−0.0610870 | + | 0.998132i | \(0.519457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.51894 | −0.405664 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.773786 | −0.0367637 | −0.0183819 | − | 0.999831i | \(-0.505851\pi\) | ||||
−0.0183819 | + | 0.999831i | \(0.505851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.79665 | 0.274788 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.77699 | 0.273242 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.3342 | 1.24279 | 0.621395 | − | 0.783497i | \(-0.286566\pi\) | ||||
0.621395 | + | 0.783497i | \(0.286566\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.7647 | 1.77827 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.23995 | 0.199210 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −55.1661 | −2.58623 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.22931 | −0.197839 | −0.0989193 | − | 0.995095i | \(-0.531539\pi\) | ||||
−0.0989193 | + | 0.995095i | \(0.531539\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.91616 | 0.416171 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.2410 | 0.849568 | 0.424784 | − | 0.905295i | \(-0.360350\pi\) | ||||
0.424784 | + | 0.905295i | \(0.360350\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.8683 | −1.24868 | −0.624339 | − | 0.781154i | \(-0.714632\pi\) | ||||
−0.624339 | + | 0.781154i | \(0.714632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.75984 | −0.127985 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.0159 | 1.57407 | 0.787034 | − | 0.616910i | \(-0.211616\pi\) | ||||
0.787034 | + | 0.616910i | \(0.211616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.76896 | −0.404913 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.31966 | 0.106884 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.7271 | 1.50479 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.1524 | 1.75055 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.53677 | 0.390872 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.9326 | 0.682286 | 0.341143 | − | 0.940011i | \(-0.389186\pi\) | ||||
0.341143 | + | 0.940011i | \(0.389186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.5023 | 1.07161 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.99235 | 0.136156 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.75958 | 0.352344 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.9187 | −1.03854 | −0.519272 | − | 0.854609i | \(-0.673797\pi\) | ||||
−0.519272 | + | 0.854609i | \(0.673797\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.88601 | 0.220953 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.62408 | 0.389199 | 0.194600 | − | 0.980883i | \(-0.437659\pi\) | ||||
0.194600 | + | 0.980883i | \(0.437659\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.80890 | −0.441771 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 44.3655 | 1.99408 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.02171 | 0.180398 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.70698 | −0.300245 | −0.150123 | − | 0.988667i | \(-0.547967\pi\) | ||||
−0.150123 | + | 0.988667i | \(0.547967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.12822 | −0.0504053 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.06265 | 0.0917868 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.31721 | −0.147322 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.2859 | −1.60834 | −0.804172 | − | 0.594396i | \(-0.797391\pi\) | ||||
−0.804172 | + | 0.594396i | \(0.797391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.9664 | 1.67953 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.44808 | 0.372992 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.6272 | 1.21740 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.26357 | −0.0555716 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.25942 | 0.0552822 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.9946 | −0.613113 | −0.306556 | − | 0.951853i | \(-0.599177\pi\) | ||||
−0.306556 | + | 0.951853i | \(0.599177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.9203 | −0.652418 | −0.326209 | − | 0.945298i | \(-0.605771\pi\) | ||||
−0.326209 | + | 0.945298i | \(0.605771\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.25432 | −0.229317 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.4618 | −0.847771 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.47631 | −0.368535 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.0037 | 0.651107 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.8440 | 1.89910 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.1817 | 0.483427 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50359 | −0.151191 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.8076 | 0.551663 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.25747 | −0.269030 | −0.134515 | − | 0.990912i | \(-0.542948\pi\) | ||||
−0.134515 | + | 0.990912i | \(0.542948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.12404 | −0.134065 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.3020 | 1.76918 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.52078 | −0.107781 | −0.0538903 | − | 0.998547i | \(-0.517162\pi\) | ||||
−0.0538903 | + | 0.998547i | \(0.517162\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.18229 | −0.135817 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.29394 | −0.395935 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.2837 | 1.88313 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.91105 | 0.166015 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.5318 | −1.84450 | −0.922251 | − | 0.386592i | \(-0.873652\pi\) | ||||
−0.922251 | + | 0.386592i | \(0.873652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.9954 | 1.60703 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.63211 | −0.280008 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.9369 | −1.38812 | −0.694062 | − | 0.719915i | \(-0.744181\pi\) | ||||
−0.694062 | + | 0.719915i | \(0.744181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.0181 | 1.17873 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.5663 | 1.11568 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.6741 | 1.28593 | 0.642963 | − | 0.765897i | \(-0.277705\pi\) | ||||
0.642963 | + | 0.765897i | \(0.277705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7285 | 0.574518 | 0.287259 | − | 0.957853i | \(-0.407256\pi\) | ||||
0.287259 | + | 0.957853i | \(0.407256\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.41796 | 0.142787 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.5024 | −1.06352 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.27924 | 0.178147 | 0.0890735 | − | 0.996025i | \(-0.471609\pi\) | ||||
0.0890735 | + | 0.996025i | \(0.471609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.25111 | −0.218229 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.5664 | −1.35108 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.8344 | −0.531548 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 51.5074 | 2.12957 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.5066 | −1.13532 | −0.567660 | − | 0.823263i | \(-0.692151\pi\) | ||||
−0.567660 | + | 0.823263i | \(0.692151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.4401 | −0.759812 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.80240 | −0.0741407 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.7697 | −0.483322 | −0.241661 | − | 0.970361i | \(-0.577692\pi\) | ||||
−0.241661 | + | 0.970361i | \(0.577692\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −64.7372 | −2.65397 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.07310 | 0.0439190 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.1565 | 0.741853 | 0.370926 | − | 0.928662i | \(-0.379040\pi\) | ||||
0.370926 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6836 | 0.476584 | 0.238292 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238292 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.18739 | 0.333416 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −29.0878 | −1.18259 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.86359 | 0.400351 | 0.200175 | − | 0.979760i | \(-0.435849\pi\) | ||||
0.200175 | + | 0.979760i | \(0.435849\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.27995 | 0.0518664 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.46697 | −0.0593473 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.5408 | −0.587298 | −0.293649 | − | 0.955913i | \(-0.594870\pi\) | ||||
−0.293649 | + | 0.955913i | \(0.594870\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.29613 | 0.294208 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.1178 | 0.769655 | 0.384828 | − | 0.922988i | \(-0.374261\pi\) | ||||
0.384828 | + | 0.922988i | \(0.374261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.05831 | 0.163117 | 0.0815586 | − | 0.996669i | \(-0.474010\pi\) | ||||
0.0815586 | + | 0.996669i | \(0.474010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.64700 | −0.226606 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.33397 | −0.213701 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.6788 | −0.547152 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.28393 | −0.250956 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.5799 | 1.09968 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.4761 | 0.894760 | 0.447380 | − | 0.894344i | \(-0.352357\pi\) | ||||
0.447380 | + | 0.894344i | \(0.352357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.28451 | 0.0510548 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.76392 | 0.308102 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.8694 | 0.589145 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.75498 | −0.148545 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.8624 | 0.468536 | 0.234268 | − | 0.972172i | \(-0.424731\pi\) | ||||
0.234268 | + | 0.972172i | \(0.424731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.5003 | −1.16338 | −0.581689 | − | 0.813412i | \(-0.697608\pi\) | ||||
−0.581689 | + | 0.813412i | \(0.697608\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.32285 | 0.248962 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.3929 | −0.526531 | −0.263265 | − | 0.964723i | \(-0.584800\pi\) | ||||
−0.263265 | + | 0.964723i | \(0.584800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.5570 | −0.885441 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.53956 | 0.0995331 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.8275 | −0.775911 | −0.387955 | − | 0.921678i | \(-0.626819\pi\) | ||||
−0.387955 | + | 0.921678i | \(0.626819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.8132 | 2.25895 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.4483 | −1.38297 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.34099 | 0.0522376 | 0.0261188 | − | 0.999659i | \(-0.491685\pi\) | ||||
0.0261188 | + | 0.999659i | \(0.491685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.0535 | 1.40232 | 0.701160 | − | 0.713004i | \(-0.252666\pi\) | ||||
0.701160 | + | 0.713004i | \(0.252666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.69973 | −0.299033 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −61.3386 | −2.37861 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.21241 | 0.240545 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.67047 | −0.180571 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.78435 | 0.184698 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.6803 | −0.797167 | −0.398583 | − | 0.917132i | \(-0.630498\pi\) | ||||
−0.398583 | + | 0.917132i | \(0.630498\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.91567 | 0.381654 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.7381 | −1.64256 | −0.821280 | − | 0.570526i | \(-0.806740\pi\) | ||||
−0.821280 | + | 0.570526i | \(0.806740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.14022 | −0.274017 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.348308 | −0.0133472 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.23750 | 0.162143 | 0.0810716 | − | 0.996708i | \(-0.474166\pi\) | ||||
0.0810716 | + | 0.996708i | \(0.474166\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −62.5873 | −2.39134 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.61924 | −0.214387 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.9005 | −0.567663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.29484 | −0.201425 | −0.100713 | − | 0.994916i | \(-0.532112\pi\) | ||||
−0.100713 | + | 0.994916i | \(0.532112\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −40.8243 | −1.55079 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.0653 | −0.950783 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 51.4507 | 1.94884 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.849375 | 0.0321263 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9675 | −0.754163 | −0.377082 | − | 0.926180i | \(-0.623072\pi\) | ||||
−0.377082 | + | 0.926180i | \(0.623072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.1320 | 0.985586 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.244120 | −0.00919410 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.89801 | −0.0713822 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.83463 | −0.144012 | −0.0720062 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720062 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.3467 | −1.55062 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.3260 | 0.461614 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −77.4377 | −2.89600 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.89996 | −0.220338 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.93826 | 0.258753 | 0.129377 | − | 0.991596i | \(-0.458702\pi\) | ||||
0.129377 | + | 0.991596i | \(0.458702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.4221 | −0.946767 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.58107 | 0.133181 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.9085 | −0.405131 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.7607 | −1.73426 | −0.867129 | − | 0.498084i | \(-0.834037\pi\) | ||||
−0.867129 | + | 0.498084i | \(0.834037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.6950 | −0.877594 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.5874 | 1.64912 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.50440 | −0.314117 | −0.157059 | − | 0.987589i | \(-0.550201\pi\) | ||||
−0.157059 | + | 0.987589i | \(0.550201\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.47442 | 0.0912705 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.3091 | −0.453413 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9848 | 0.735153 | 0.367577 | − | 0.929993i | \(-0.380188\pi\) | ||||
0.367577 | + | 0.929993i | \(0.380188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.29551 | −0.268007 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.20328 | −0.0441442 | −0.0220721 | − | 0.999756i | \(-0.507026\pi\) | ||||
−0.0220721 | + | 0.999756i | \(0.507026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 79.1559 | 2.90005 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.4066 | 1.11252 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.2892 | −0.375959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.4312 | −0.745546 | −0.372773 | − | 0.927923i | \(-0.621593\pi\) | ||||
−0.372773 | + | 0.927923i | \(0.621593\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.05132 | 0.0383122 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 58.0955 | 2.11431 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.1282 | 1.09503 | 0.547514 | − | 0.836796i | \(-0.315574\pi\) | ||||
0.547514 | + | 0.836796i | \(0.315574\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.20041 | 0.152465 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.50437 | −0.0907832 | −0.0453916 | − | 0.998969i | \(-0.514454\pi\) | ||||
−0.0453916 | + | 0.998969i | \(0.514454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.0053 | −1.37589 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 60.4437 | 2.18535 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.1882 | −0.945602 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.8242 | 1.14761 | 0.573805 | − | 0.818992i | \(-0.305467\pi\) | ||||
0.573805 | + | 0.818992i | \(0.305467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.09450 | −0.0754317 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.8710 | −1.14632 | −0.573160 | − | 0.819443i | \(-0.694283\pi\) | ||||
−0.573160 | + | 0.819443i | \(0.694283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.6435 | −0.777458 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.59887 | −0.129109 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48.7496 | 1.74664 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.64534 | 0.202006 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.41546 | −0.0863216 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 31.7838 | 1.13441 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.79776 | 0.242314 | 0.121157 | − | 0.992633i | \(-0.461340\pi\) | ||||
0.121157 | + | 0.992633i | \(0.461340\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.42695 | −0.0508009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.7818 | −0.916694 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.55452 | 0.197247 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.47960 | −0.0879425 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.34934 | −0.295749 | −0.147874 | − | 0.989006i | \(-0.547243\pi\) | ||||
−0.147874 | + | 0.989006i | \(0.547243\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.72148 | −0.0609018 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.98021 | 0.175967 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 53.2940 | 1.88071 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.0009 | 1.44509 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.24574 | −0.219861 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.99656 | 0.210828 | 0.105414 | − | 0.994428i | \(-0.466383\pi\) | ||||
0.105414 | + | 0.994428i | \(0.466383\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.49461 | 0.157827 | 0.0789135 | − | 0.996881i | \(-0.474855\pi\) | ||||
0.0789135 | + | 0.996881i | \(0.474855\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.79584 | −0.0980546 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.9478 | 2.34508 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.2466 | 1.47802 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −47.3961 | −1.65615 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.8301 | −0.447775 | −0.223887 | − | 0.974615i | \(-0.571875\pi\) | ||||
−0.223887 | + | 0.974615i | \(0.571875\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.0580 | −1.11747 | −0.558736 | − | 0.829346i | \(-0.688713\pi\) | ||||
−0.558736 | + | 0.829346i | \(0.688713\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.37557 | −0.256785 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.8056 | −0.480067 | −0.240033 | − | 0.970765i | \(-0.577158\pi\) | ||||
−0.240033 | + | 0.970765i | \(0.577158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.6122 | 0.959012 | 0.479506 | − | 0.877539i | \(-0.340816\pi\) | ||||
0.479506 | + | 0.877539i | \(0.340816\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.417234 | −0.0144737 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.4491 | 0.604576 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.4588 | −0.534975 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.79252 | −0.165654 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.2002 | −1.80215 | −0.901075 | − | 0.433664i | \(-0.857221\pi\) | ||||
−0.901075 | + | 0.433664i | \(0.857221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3427 | −0.908369 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.41929 | −0.0833247 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45.4521 | −1.56360 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.7660 | 0.919692 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.00888 | −0.137584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.4675 | −0.598780 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.1534 | −1.20363 | −0.601815 | − | 0.798635i | \(-0.705556\pi\) | ||||
−0.601815 | + | 0.798635i | \(0.705556\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 57.2704 | 1.95861 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.5507 | 1.00943 | 0.504717 | − | 0.863285i | \(-0.331597\pi\) | ||||
0.504717 | + | 0.863285i | \(0.331597\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.5173 | 1.62127 | 0.810634 | − | 0.585553i | \(-0.199122\pi\) | ||||
0.810634 | + | 0.585553i | \(0.199122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.71376 | −0.228804 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.3256 | 1.13442 | 0.567208 | − | 0.823575i | \(-0.308024\pi\) | ||||
0.567208 | + | 0.823575i | \(0.308024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.2564 | 0.586736 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.79324 | −0.162787 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.1618 | 2.10869 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.2906 | −0.484220 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.66666 | 0.225632 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.2014 | −0.615318 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.4900 | −0.455526 | −0.227763 | − | 0.973717i | \(-0.573141\pi\) | ||||
−0.227763 | + | 0.973717i | \(0.573141\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.83407 | 0.129320 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.4577 | 0.756619 | 0.378309 | − | 0.925679i | \(-0.376506\pi\) | ||||
0.378309 | + | 0.925679i | \(0.376506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.1656 | −0.914194 | −0.457097 | − | 0.889417i | \(-0.651111\pi\) | ||||
−0.457097 | + | 0.889417i | \(0.651111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.35801 | −0.146493 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.0317 | −1.47844 | −0.739219 | − | 0.673465i | \(-0.764805\pi\) | ||||
−0.739219 | + | 0.673465i | \(0.764805\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.14422 | −0.239609 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.2916 | 1.24932 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.63111 | −0.0545830 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −48.0059 | −1.60466 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.87658 | 0.162824 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.27237 | 0.175844 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.4856 | −0.582531 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.81817 | −0.193616 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −42.8053 | −1.42290 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.3798 | 1.34079 | 0.670395 | − | 0.742005i | \(-0.266125\pi\) | ||||
0.670395 | + | 0.742005i | \(0.266125\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.77213 | 0.0587779 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5817 | −0.946953 | −0.473477 | − | 0.880806i | \(-0.657001\pi\) | ||||
−0.473477 | + | 0.880806i | \(0.657001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.7141 | −1.51292 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.924334 | 0.0305575 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −53.1986 | −1.75677 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.6365 | 0.581773 | 0.290886 | − | 0.956758i | \(-0.406050\pi\) | ||||
0.290886 | + | 0.956758i | \(0.406050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.97755 | −0.262869 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.55411 | 0.215731 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.6716 | 1.00848 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.7360 | 0.779593 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.6827 | 0.416104 | 0.208052 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208052 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.5331 | 0.541849 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.31914 | −0.174141 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −90.8727 | −2.97186 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.9762 | −1.50198 | −0.750988 | − | 0.660315i | \(-0.770423\pi\) | ||||
−0.750988 | + | 0.660315i | \(0.770423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.270051 | −0.00881279 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6920 | −0.381147 | −0.190573 | − | 0.981673i | \(-0.561035\pi\) | ||||
−0.190573 | + | 0.981673i | \(0.561035\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.5860 | −1.06115 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.9417 | −0.518583 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.5772 | 0.896138 | 0.448069 | − | 0.893999i | \(-0.352112\pi\) | ||||
0.448069 | + | 0.893999i | \(0.352112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.8732 | 2.00849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.59351 | 0.0516730 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.5211 | 1.24782 | 0.623910 | − | 0.781496i | \(-0.285543\pi\) | ||||
0.623910 | + | 0.781496i | \(0.285543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.8326 | 1.51547 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.79669 | 0.0580789 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 57.5917 | 1.85973 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5391 | −0.662551 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.60679 | 0.309575 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −71.9504 | −2.31616 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.89304 | −0.125192 | −0.0625958 | − | 0.998039i | \(-0.519938\pi\) | ||||
−0.0625958 | + | 0.998039i | \(0.519938\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.56124 | −0.275027 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.7208 | 0.953786 | 0.476893 | − | 0.878961i | \(-0.341763\pi\) | ||||
0.476893 | + | 0.878961i | \(0.341763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.0647 | 0.739419 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.56288 | −0.274232 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.60092 | 0.211182 | 0.105591 | − | 0.994410i | \(-0.466327\pi\) | ||||
0.105591 | + | 0.994410i | \(0.466327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.48739 | −0.239298 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.4847 | 1.13294 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.2962 | −0.647350 | −0.323675 | − | 0.946168i | \(-0.604918\pi\) | ||||
−0.323675 | + | 0.946168i | \(0.604918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.6963 | −0.786890 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.224635 | 0.00715021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.2391 | −0.897953 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.9316 | −0.506083 | −0.253041 | − | 0.967455i | \(-0.581431\pi\) | ||||
−0.253041 | + | 0.967455i | \(0.581431\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.895336 | −0.0284126 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.7035 | 0.466133 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.3449 | 0.992702 | 0.496351 | − | 0.868122i | \(-0.334673\pi\) | ||||
0.496351 | + | 0.868122i | \(0.334673\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.79160 | 0.214877 |
(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 | 8048.2.a.u.1.13 | 26 | ||
4.3 | odd | 2 | 503.2.a.f.1.1 | ✓ | 26 | ||
12.11 | even | 2 | 4527.2.a.o.1.26 | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.f.1.1 | ✓ | 26 | 4.3 | odd | 2 | ||
4527.2.a.o.1.26 | 26 | 12.11 | even | 2 | |||
8048.2.a.u.1.13 | 26 | 1.1 | even | 1 | trivial |