Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71076 | −1.91680 | −0.958398 | − | 0.285435i | \(-0.907862\pi\) | ||||
−0.958398 | + | 0.285435i | \(0.907862\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.34821 | 2.67411 | ||||||||
\(5\) | 0.130231 | 0.0582411 | 0.0291205 | − | 0.999576i | \(-0.490729\pi\) | ||||
0.0291205 | + | 0.999576i | \(0.490729\pi\) | |||||||
\(6\) | 2.71076 | 1.10666 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.07620 | −3.20892 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.353025 | −0.111636 | ||||||||
\(11\) | 3.25358 | 0.980991 | 0.490495 | − | 0.871444i | \(-0.336816\pi\) | ||||
0.490495 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(12\) | −5.34821 | −1.54390 | ||||||||
\(13\) | 1.11985 | 0.310591 | 0.155296 | − | 0.987868i | \(-0.450367\pi\) | ||||
0.155296 | + | 0.987868i | \(0.450367\pi\) | |||||||
\(14\) | −2.71076 | −0.724481 | ||||||||
\(15\) | −0.130231 | −0.0336255 | ||||||||
\(16\) | 13.9070 | 3.47674 | ||||||||
\(17\) | 0.0623671 | 0.0151262 | 0.00756312 | − | 0.999971i | \(-0.497593\pi\) | ||||
0.00756312 | + | 0.999971i | \(0.497593\pi\) | |||||||
\(18\) | −2.71076 | −0.638932 | ||||||||
\(19\) | 2.72595 | 0.625375 | 0.312688 | − | 0.949856i | \(-0.398771\pi\) | ||||
0.312688 | + | 0.949856i | \(0.398771\pi\) | |||||||
\(20\) | 0.696503 | 0.155743 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −8.81967 | −1.88036 | ||||||||
\(23\) | 6.67141 | 1.39108 | 0.695542 | − | 0.718485i | \(-0.255164\pi\) | ||||
0.695542 | + | 0.718485i | \(0.255164\pi\) | |||||||
\(24\) | 9.07620 | 1.85267 | ||||||||
\(25\) | −4.98304 | −0.996608 | ||||||||
\(26\) | −3.03565 | −0.595340 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.34821 | 1.01072 | ||||||||
\(29\) | −7.51601 | −1.39569 | −0.697844 | − | 0.716250i | \(-0.745857\pi\) | ||||
−0.697844 | + | 0.716250i | \(0.745857\pi\) | |||||||
\(30\) | 0.353025 | 0.0644532 | ||||||||
\(31\) | 8.48682 | 1.52428 | 0.762139 | − | 0.647414i | \(-0.224149\pi\) | ||||
0.762139 | + | 0.647414i | \(0.224149\pi\) | |||||||
\(32\) | −19.5460 | −3.45528 | ||||||||
\(33\) | −3.25358 | −0.566375 | ||||||||
\(34\) | −0.169062 | −0.0289939 | ||||||||
\(35\) | 0.130231 | 0.0220131 | ||||||||
\(36\) | 5.34821 | 0.891369 | ||||||||
\(37\) | 10.9966 | 1.80783 | 0.903915 | − | 0.427712i | \(-0.140680\pi\) | ||||
0.903915 | + | 0.427712i | \(0.140680\pi\) | |||||||
\(38\) | −7.38938 | −1.19872 | ||||||||
\(39\) | −1.11985 | −0.179320 | ||||||||
\(40\) | −1.18200 | −0.186891 | ||||||||
\(41\) | −6.34625 | −0.991118 | −0.495559 | − | 0.868574i | \(-0.665037\pi\) | ||||
−0.495559 | + | 0.868574i | \(0.665037\pi\) | |||||||
\(42\) | 2.71076 | 0.418279 | ||||||||
\(43\) | 2.41223 | 0.367862 | 0.183931 | − | 0.982939i | \(-0.441118\pi\) | ||||
0.183931 | + | 0.982939i | \(0.441118\pi\) | |||||||
\(44\) | 17.4008 | 2.62327 | ||||||||
\(45\) | 0.130231 | 0.0194137 | ||||||||
\(46\) | −18.0846 | −2.66642 | ||||||||
\(47\) | 7.87767 | 1.14908 | 0.574538 | − | 0.818478i | \(-0.305182\pi\) | ||||
0.574538 | + | 0.818478i | \(0.305182\pi\) | |||||||
\(48\) | −13.9070 | −2.00730 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 13.5078 | 1.91029 | ||||||||
\(51\) | −0.0623671 | −0.00873314 | ||||||||
\(52\) | 5.98922 | 0.830555 | ||||||||
\(53\) | −6.90598 | −0.948609 | −0.474304 | − | 0.880361i | \(-0.657300\pi\) | ||||
−0.474304 | + | 0.880361i | \(0.657300\pi\) | |||||||
\(54\) | 2.71076 | 0.368888 | ||||||||
\(55\) | 0.423717 | 0.0571339 | ||||||||
\(56\) | −9.07620 | −1.21286 | ||||||||
\(57\) | −2.72595 | −0.361060 | ||||||||
\(58\) | 20.3741 | 2.67525 | ||||||||
\(59\) | 9.66024 | 1.25766 | 0.628828 | − | 0.777545i | \(-0.283535\pi\) | ||||
0.628828 | + | 0.777545i | \(0.283535\pi\) | |||||||
\(60\) | −0.696503 | −0.0899182 | ||||||||
\(61\) | −3.59541 | −0.460345 | −0.230172 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230172 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(62\) | −23.0057 | −2.92173 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 25.1706 | 3.14633 | ||||||||
\(65\) | 0.145840 | 0.0180892 | ||||||||
\(66\) | 8.81967 | 1.08563 | ||||||||
\(67\) | 12.8812 | 1.57369 | 0.786845 | − | 0.617151i | \(-0.211713\pi\) | ||||
0.786845 | + | 0.617151i | \(0.211713\pi\) | |||||||
\(68\) | 0.333553 | 0.0404492 | ||||||||
\(69\) | −6.67141 | −0.803143 | ||||||||
\(70\) | −0.353025 | −0.0421945 | ||||||||
\(71\) | −3.03164 | −0.359790 | −0.179895 | − | 0.983686i | \(-0.557576\pi\) | ||||
−0.179895 | + | 0.983686i | \(0.557576\pi\) | |||||||
\(72\) | −9.07620 | −1.06964 | ||||||||
\(73\) | −0.955600 | −0.111844 | −0.0559222 | − | 0.998435i | \(-0.517810\pi\) | ||||
−0.0559222 | + | 0.998435i | \(0.517810\pi\) | |||||||
\(74\) | −29.8091 | −3.46524 | ||||||||
\(75\) | 4.98304 | 0.575392 | ||||||||
\(76\) | 14.5789 | 1.67232 | ||||||||
\(77\) | 3.25358 | 0.370780 | ||||||||
\(78\) | 3.03565 | 0.343720 | ||||||||
\(79\) | −9.46286 | −1.06465 | −0.532327 | − | 0.846539i | \(-0.678682\pi\) | ||||
−0.532327 | + | 0.846539i | \(0.678682\pi\) | |||||||
\(80\) | 1.81112 | 0.202489 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 17.2032 | 1.89977 | ||||||||
\(83\) | 0.768405 | 0.0843434 | 0.0421717 | − | 0.999110i | \(-0.486572\pi\) | ||||
0.0421717 | + | 0.999110i | \(0.486572\pi\) | |||||||
\(84\) | −5.34821 | −0.583538 | ||||||||
\(85\) | 0.00812213 | 0.000880968 0 | ||||||||
\(86\) | −6.53898 | −0.705116 | ||||||||
\(87\) | 7.51601 | 0.805801 | ||||||||
\(88\) | −29.5301 | −3.14792 | ||||||||
\(89\) | 2.54138 | 0.269386 | 0.134693 | − | 0.990887i | \(-0.456995\pi\) | ||||
0.134693 | + | 0.990887i | \(0.456995\pi\) | |||||||
\(90\) | −0.353025 | −0.0372121 | ||||||||
\(91\) | 1.11985 | 0.117393 | ||||||||
\(92\) | 35.6801 | 3.71991 | ||||||||
\(93\) | −8.48682 | −0.880042 | ||||||||
\(94\) | −21.3545 | −2.20254 | ||||||||
\(95\) | 0.355003 | 0.0364225 | ||||||||
\(96\) | 19.5460 | 1.99491 | ||||||||
\(97\) | 2.85023 | 0.289397 | 0.144699 | − | 0.989476i | \(-0.453779\pi\) | ||||
0.144699 | + | 0.989476i | \(0.453779\pi\) | |||||||
\(98\) | −2.71076 | −0.273828 | ||||||||
\(99\) | 3.25358 | 0.326997 | ||||||||
\(100\) | −26.6504 | −2.66504 | ||||||||
\(101\) | −10.0545 | −1.00046 | −0.500231 | − | 0.865892i | \(-0.666752\pi\) | ||||
−0.500231 | + | 0.865892i | \(0.666752\pi\) | |||||||
\(102\) | 0.169062 | 0.0167396 | ||||||||
\(103\) | 9.36566 | 0.922826 | 0.461413 | − | 0.887185i | \(-0.347343\pi\) | ||||
0.461413 | + | 0.887185i | \(0.347343\pi\) | |||||||
\(104\) | −10.1640 | −0.996664 | ||||||||
\(105\) | −0.130231 | −0.0127092 | ||||||||
\(106\) | 18.7204 | 1.81829 | ||||||||
\(107\) | 11.7033 | 1.13140 | 0.565700 | − | 0.824611i | \(-0.308606\pi\) | ||||
0.565700 | + | 0.824611i | \(0.308606\pi\) | |||||||
\(108\) | −5.34821 | −0.514632 | ||||||||
\(109\) | 5.17573 | 0.495745 | 0.247872 | − | 0.968793i | \(-0.420269\pi\) | ||||
0.247872 | + | 0.968793i | \(0.420269\pi\) | |||||||
\(110\) | −1.14859 | −0.109514 | ||||||||
\(111\) | −10.9966 | −1.04375 | ||||||||
\(112\) | 13.9070 | 1.31408 | ||||||||
\(113\) | 8.66917 | 0.815527 | 0.407764 | − | 0.913088i | \(-0.366309\pi\) | ||||
0.407764 | + | 0.913088i | \(0.366309\pi\) | |||||||
\(114\) | 7.38938 | 0.692079 | ||||||||
\(115\) | 0.868824 | 0.0810182 | ||||||||
\(116\) | −40.1972 | −3.73222 | ||||||||
\(117\) | 1.11985 | 0.103530 | ||||||||
\(118\) | −26.1866 | −2.41067 | ||||||||
\(119\) | 0.0623671 | 0.00571718 | ||||||||
\(120\) | 1.18200 | 0.107902 | ||||||||
\(121\) | −0.414226 | −0.0376569 | ||||||||
\(122\) | 9.74628 | 0.882387 | ||||||||
\(123\) | 6.34625 | 0.572222 | ||||||||
\(124\) | 45.3893 | 4.07608 | ||||||||
\(125\) | −1.30010 | −0.116285 | ||||||||
\(126\) | −2.71076 | −0.241494 | ||||||||
\(127\) | −0.493993 | −0.0438348 | −0.0219174 | − | 0.999760i | \(-0.506977\pi\) | ||||
−0.0219174 | + | 0.999760i | \(0.506977\pi\) | |||||||
\(128\) | −29.1395 | −2.57559 | ||||||||
\(129\) | −2.41223 | −0.212385 | ||||||||
\(130\) | −0.395336 | −0.0346733 | ||||||||
\(131\) | −18.9040 | −1.65165 | −0.825824 | − | 0.563927i | \(-0.809290\pi\) | ||||
−0.825824 | + | 0.563927i | \(0.809290\pi\) | |||||||
\(132\) | −17.4008 | −1.51455 | ||||||||
\(133\) | 2.72595 | 0.236370 | ||||||||
\(134\) | −34.9179 | −3.01644 | ||||||||
\(135\) | −0.130231 | −0.0112085 | ||||||||
\(136\) | −0.566056 | −0.0485389 | ||||||||
\(137\) | 13.6960 | 1.17013 | 0.585063 | − | 0.810988i | \(-0.301070\pi\) | ||||
0.585063 | + | 0.810988i | \(0.301070\pi\) | |||||||
\(138\) | 18.0846 | 1.53946 | ||||||||
\(139\) | 2.92684 | 0.248252 | 0.124126 | − | 0.992266i | \(-0.460387\pi\) | ||||
0.124126 | + | 0.992266i | \(0.460387\pi\) | |||||||
\(140\) | 0.696503 | 0.0588653 | ||||||||
\(141\) | −7.87767 | −0.663419 | ||||||||
\(142\) | 8.21806 | 0.689644 | ||||||||
\(143\) | 3.64353 | 0.304687 | ||||||||
\(144\) | 13.9070 | 1.15891 | ||||||||
\(145\) | −0.978817 | −0.0812863 | ||||||||
\(146\) | 2.59040 | 0.214383 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 58.8122 | 4.83433 | ||||||||
\(149\) | −21.5069 | −1.76191 | −0.880957 | − | 0.473197i | \(-0.843100\pi\) | ||||
−0.880957 | + | 0.473197i | \(0.843100\pi\) | |||||||
\(150\) | −13.5078 | −1.10291 | ||||||||
\(151\) | 2.82899 | 0.230220 | 0.115110 | − | 0.993353i | \(-0.463278\pi\) | ||||
0.115110 | + | 0.993353i | \(0.463278\pi\) | |||||||
\(152\) | −24.7412 | −2.00678 | ||||||||
\(153\) | 0.0623671 | 0.00504208 | ||||||||
\(154\) | −8.81967 | −0.710709 | ||||||||
\(155\) | 1.10525 | 0.0887755 | ||||||||
\(156\) | −5.98922 | −0.479521 | ||||||||
\(157\) | 7.59643 | 0.606261 | 0.303130 | − | 0.952949i | \(-0.401968\pi\) | ||||
0.303130 | + | 0.952949i | \(0.401968\pi\) | |||||||
\(158\) | 25.6515 | 2.04073 | ||||||||
\(159\) | 6.90598 | 0.547680 | ||||||||
\(160\) | −2.54550 | −0.201239 | ||||||||
\(161\) | 6.67141 | 0.525780 | ||||||||
\(162\) | −2.71076 | −0.212977 | ||||||||
\(163\) | 5.41853 | 0.424412 | 0.212206 | − | 0.977225i | \(-0.431935\pi\) | ||||
0.212206 | + | 0.977225i | \(0.431935\pi\) | |||||||
\(164\) | −33.9411 | −2.65035 | ||||||||
\(165\) | −0.423717 | −0.0329863 | ||||||||
\(166\) | −2.08296 | −0.161669 | ||||||||
\(167\) | 12.8244 | 0.992382 | 0.496191 | − | 0.868214i | \(-0.334732\pi\) | ||||
0.496191 | + | 0.868214i | \(0.334732\pi\) | |||||||
\(168\) | 9.07620 | 0.700244 | ||||||||
\(169\) | −11.7459 | −0.903533 | ||||||||
\(170\) | −0.0220171 | −0.00168864 | ||||||||
\(171\) | 2.72595 | 0.208458 | ||||||||
\(172\) | 12.9011 | 0.983702 | ||||||||
\(173\) | −3.42175 | −0.260151 | −0.130076 | − | 0.991504i | \(-0.541522\pi\) | ||||
−0.130076 | + | 0.991504i | \(0.541522\pi\) | |||||||
\(174\) | −20.3741 | −1.54456 | ||||||||
\(175\) | −4.98304 | −0.376682 | ||||||||
\(176\) | 45.2474 | 3.41065 | ||||||||
\(177\) | −9.66024 | −0.726108 | ||||||||
\(178\) | −6.88907 | −0.516357 | ||||||||
\(179\) | 11.4708 | 0.857368 | 0.428684 | − | 0.903454i | \(-0.358977\pi\) | ||||
0.428684 | + | 0.903454i | \(0.358977\pi\) | |||||||
\(180\) | 0.696503 | 0.0519143 | ||||||||
\(181\) | −2.92554 | −0.217454 | −0.108727 | − | 0.994072i | \(-0.534677\pi\) | ||||
−0.108727 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(182\) | −3.03565 | −0.225018 | ||||||||
\(183\) | 3.59541 | 0.265780 | ||||||||
\(184\) | −60.5510 | −4.46388 | ||||||||
\(185\) | 1.43210 | 0.105290 | ||||||||
\(186\) | 23.0057 | 1.68686 | ||||||||
\(187\) | 0.202916 | 0.0148387 | ||||||||
\(188\) | 42.1314 | 3.07275 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.962327 | −0.0698145 | ||||||||
\(191\) | −11.3119 | −0.818501 | −0.409250 | − | 0.912422i | \(-0.634210\pi\) | ||||
−0.409250 | + | 0.912422i | \(0.634210\pi\) | |||||||
\(192\) | −25.1706 | −1.81654 | ||||||||
\(193\) | 3.48149 | 0.250603 | 0.125302 | − | 0.992119i | \(-0.460010\pi\) | ||||
0.125302 | + | 0.992119i | \(0.460010\pi\) | |||||||
\(194\) | −7.72629 | −0.554716 | ||||||||
\(195\) | −0.145840 | −0.0104438 | ||||||||
\(196\) | 5.34821 | 0.382015 | ||||||||
\(197\) | 10.9479 | 0.780006 | 0.390003 | − | 0.920814i | \(-0.372474\pi\) | ||||
0.390003 | + | 0.920814i | \(0.372474\pi\) | |||||||
\(198\) | −8.81967 | −0.626786 | ||||||||
\(199\) | 23.1722 | 1.64264 | 0.821318 | − | 0.570471i | \(-0.193239\pi\) | ||||
0.821318 | + | 0.570471i | \(0.193239\pi\) | |||||||
\(200\) | 45.2271 | 3.19804 | ||||||||
\(201\) | −12.8812 | −0.908570 | ||||||||
\(202\) | 27.2554 | 1.91768 | ||||||||
\(203\) | −7.51601 | −0.527520 | ||||||||
\(204\) | −0.333553 | −0.0233534 | ||||||||
\(205\) | −0.826478 | −0.0577237 | ||||||||
\(206\) | −25.3880 | −1.76887 | ||||||||
\(207\) | 6.67141 | 0.463695 | ||||||||
\(208\) | 15.5738 | 1.07985 | ||||||||
\(209\) | 8.86908 | 0.613487 | ||||||||
\(210\) | 0.353025 | 0.0243610 | ||||||||
\(211\) | 20.3087 | 1.39811 | 0.699053 | − | 0.715070i | \(-0.253605\pi\) | ||||
0.699053 | + | 0.715070i | \(0.253605\pi\) | |||||||
\(212\) | −36.9346 | −2.53668 | ||||||||
\(213\) | 3.03164 | 0.207725 | ||||||||
\(214\) | −31.7248 | −2.16866 | ||||||||
\(215\) | 0.314147 | 0.0214247 | ||||||||
\(216\) | 9.07620 | 0.617557 | ||||||||
\(217\) | 8.48682 | 0.576123 | ||||||||
\(218\) | −14.0302 | −0.950242 | ||||||||
\(219\) | 0.955600 | 0.0645734 | ||||||||
\(220\) | 2.26613 | 0.152782 | ||||||||
\(221\) | 0.0698420 | 0.00469808 | ||||||||
\(222\) | 29.8091 | 2.00066 | ||||||||
\(223\) | 27.4714 | 1.83962 | 0.919812 | − | 0.392360i | \(-0.128341\pi\) | ||||
0.919812 | + | 0.392360i | \(0.128341\pi\) | |||||||
\(224\) | −19.5460 | −1.30597 | ||||||||
\(225\) | −4.98304 | −0.332203 | ||||||||
\(226\) | −23.5000 | −1.56320 | ||||||||
\(227\) | −20.5618 | −1.36474 | −0.682369 | − | 0.731008i | \(-0.739050\pi\) | ||||
−0.682369 | + | 0.731008i | \(0.739050\pi\) | |||||||
\(228\) | −14.5789 | −0.965514 | ||||||||
\(229\) | 5.61860 | 0.371288 | 0.185644 | − | 0.982617i | \(-0.440563\pi\) | ||||
0.185644 | + | 0.982617i | \(0.440563\pi\) | |||||||
\(230\) | −2.35517 | −0.155295 | ||||||||
\(231\) | −3.25358 | −0.214070 | ||||||||
\(232\) | 68.2168 | 4.47865 | ||||||||
\(233\) | 7.80020 | 0.511008 | 0.255504 | − | 0.966808i | \(-0.417759\pi\) | ||||
0.255504 | + | 0.966808i | \(0.417759\pi\) | |||||||
\(234\) | −3.03565 | −0.198447 | ||||||||
\(235\) | 1.02592 | 0.0669234 | ||||||||
\(236\) | 51.6650 | 3.36311 | ||||||||
\(237\) | 9.46286 | 0.614679 | ||||||||
\(238\) | −0.169062 | −0.0109587 | ||||||||
\(239\) | 7.89339 | 0.510581 | 0.255290 | − | 0.966864i | \(-0.417829\pi\) | ||||
0.255290 | + | 0.966864i | \(0.417829\pi\) | |||||||
\(240\) | −1.81112 | −0.116907 | ||||||||
\(241\) | −12.0448 | −0.775872 | −0.387936 | − | 0.921686i | \(-0.626812\pi\) | ||||
−0.387936 | + | 0.921686i | \(0.626812\pi\) | |||||||
\(242\) | 1.12287 | 0.0721806 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −19.2290 | −1.23101 | ||||||||
\(245\) | 0.130231 | 0.00832015 | ||||||||
\(246\) | −17.2032 | −1.09683 | ||||||||
\(247\) | 3.05266 | 0.194236 | ||||||||
\(248\) | −77.0281 | −4.89129 | ||||||||
\(249\) | −0.768405 | −0.0486957 | ||||||||
\(250\) | 3.52426 | 0.222894 | ||||||||
\(251\) | −6.39187 | −0.403451 | −0.201726 | − | 0.979442i | \(-0.564655\pi\) | ||||
−0.201726 | + | 0.979442i | \(0.564655\pi\) | |||||||
\(252\) | 5.34821 | 0.336906 | ||||||||
\(253\) | 21.7059 | 1.36464 | ||||||||
\(254\) | 1.33910 | 0.0840224 | ||||||||
\(255\) | −0.00812213 | −0.000508627 0 | ||||||||
\(256\) | 28.6489 | 1.79055 | ||||||||
\(257\) | −26.8685 | −1.67601 | −0.838005 | − | 0.545662i | \(-0.816278\pi\) | ||||
−0.838005 | + | 0.545662i | \(0.816278\pi\) | |||||||
\(258\) | 6.53898 | 0.407099 | ||||||||
\(259\) | 10.9966 | 0.683296 | ||||||||
\(260\) | 0.779981 | 0.0483724 | ||||||||
\(261\) | −7.51601 | −0.465229 | ||||||||
\(262\) | 51.2441 | 3.16587 | ||||||||
\(263\) | −18.2727 | −1.12674 | −0.563372 | − | 0.826204i | \(-0.690496\pi\) | ||||
−0.563372 | + | 0.826204i | \(0.690496\pi\) | |||||||
\(264\) | 29.5301 | 1.81745 | ||||||||
\(265\) | −0.899372 | −0.0552480 | ||||||||
\(266\) | −7.38938 | −0.453072 | ||||||||
\(267\) | −2.54138 | −0.155530 | ||||||||
\(268\) | 68.8915 | 4.20822 | ||||||||
\(269\) | 20.5732 | 1.25437 | 0.627186 | − | 0.778869i | \(-0.284207\pi\) | ||||
0.627186 | + | 0.778869i | \(0.284207\pi\) | |||||||
\(270\) | 0.353025 | 0.0214844 | ||||||||
\(271\) | 1.99413 | 0.121135 | 0.0605674 | − | 0.998164i | \(-0.480709\pi\) | ||||
0.0605674 | + | 0.998164i | \(0.480709\pi\) | |||||||
\(272\) | 0.867337 | 0.0525900 | ||||||||
\(273\) | −1.11985 | −0.0677766 | ||||||||
\(274\) | −37.1265 | −2.24289 | ||||||||
\(275\) | −16.2127 | −0.977663 | ||||||||
\(276\) | −35.6801 | −2.14769 | ||||||||
\(277\) | −22.5582 | −1.35539 | −0.677697 | − | 0.735342i | \(-0.737022\pi\) | ||||
−0.677697 | + | 0.735342i | \(0.737022\pi\) | |||||||
\(278\) | −7.93397 | −0.475848 | ||||||||
\(279\) | 8.48682 | 0.508092 | ||||||||
\(280\) | −1.18200 | −0.0706382 | ||||||||
\(281\) | 1.42401 | 0.0849492 | 0.0424746 | − | 0.999098i | \(-0.486476\pi\) | ||||
0.0424746 | + | 0.999098i | \(0.486476\pi\) | |||||||
\(282\) | 21.3545 | 1.27164 | ||||||||
\(283\) | −5.41435 | −0.321849 | −0.160925 | − | 0.986967i | \(-0.551448\pi\) | ||||
−0.160925 | + | 0.986967i | \(0.551448\pi\) | |||||||
\(284\) | −16.2139 | −0.962117 | ||||||||
\(285\) | −0.355003 | −0.0210285 | ||||||||
\(286\) | −9.87673 | −0.584023 | ||||||||
\(287\) | −6.34625 | −0.374607 | ||||||||
\(288\) | −19.5460 | −1.15176 | ||||||||
\(289\) | −16.9961 | −0.999771 | ||||||||
\(290\) | 2.65334 | 0.155809 | ||||||||
\(291\) | −2.85023 | −0.167084 | ||||||||
\(292\) | −5.11075 | −0.299084 | ||||||||
\(293\) | 12.0874 | 0.706152 | 0.353076 | − | 0.935595i | \(-0.385136\pi\) | ||||
0.353076 | + | 0.935595i | \(0.385136\pi\) | |||||||
\(294\) | 2.71076 | 0.158095 | ||||||||
\(295\) | 1.25806 | 0.0732472 | ||||||||
\(296\) | −99.8074 | −5.80119 | ||||||||
\(297\) | −3.25358 | −0.188792 | ||||||||
\(298\) | 58.3000 | 3.37723 | ||||||||
\(299\) | 7.47099 | 0.432059 | ||||||||
\(300\) | 26.6504 | 1.53866 | ||||||||
\(301\) | 2.41223 | 0.139039 | ||||||||
\(302\) | −7.66870 | −0.441284 | ||||||||
\(303\) | 10.0545 | 0.577617 | ||||||||
\(304\) | 37.9097 | 2.17427 | ||||||||
\(305\) | −0.468233 | −0.0268110 | ||||||||
\(306\) | −0.169062 | −0.00966464 | ||||||||
\(307\) | 3.96360 | 0.226215 | 0.113107 | − | 0.993583i | \(-0.463920\pi\) | ||||
0.113107 | + | 0.993583i | \(0.463920\pi\) | |||||||
\(308\) | 17.4008 | 0.991505 | ||||||||
\(309\) | −9.36566 | −0.532794 | ||||||||
\(310\) | −2.99606 | −0.170165 | ||||||||
\(311\) | −8.25019 | −0.467825 | −0.233913 | − | 0.972258i | \(-0.575153\pi\) | ||||
−0.233913 | + | 0.972258i | \(0.575153\pi\) | |||||||
\(312\) | 10.1640 | 0.575424 | ||||||||
\(313\) | −3.41258 | −0.192890 | −0.0964452 | − | 0.995338i | \(-0.530747\pi\) | ||||
−0.0964452 | + | 0.995338i | \(0.530747\pi\) | |||||||
\(314\) | −20.5921 | −1.16208 | ||||||||
\(315\) | 0.130231 | 0.00733768 | ||||||||
\(316\) | −50.6094 | −2.84700 | ||||||||
\(317\) | −1.19667 | −0.0672116 | −0.0336058 | − | 0.999435i | \(-0.510699\pi\) | ||||
−0.0336058 | + | 0.999435i | \(0.510699\pi\) | |||||||
\(318\) | −18.7204 | −1.04979 | ||||||||
\(319\) | −24.4539 | −1.36916 | ||||||||
\(320\) | 3.27800 | 0.183246 | ||||||||
\(321\) | −11.7033 | −0.653215 | ||||||||
\(322\) | −18.0846 | −1.00781 | ||||||||
\(323\) | 0.170009 | 0.00945957 | ||||||||
\(324\) | 5.34821 | 0.297123 | ||||||||
\(325\) | −5.58027 | −0.309538 | ||||||||
\(326\) | −14.6883 | −0.813511 | ||||||||
\(327\) | −5.17573 | −0.286218 | ||||||||
\(328\) | 57.5998 | 3.18042 | ||||||||
\(329\) | 7.87767 | 0.434310 | ||||||||
\(330\) | 1.14859 | 0.0632280 | ||||||||
\(331\) | 0.820069 | 0.0450751 | 0.0225375 | − | 0.999746i | \(-0.492825\pi\) | ||||
0.0225375 | + | 0.999746i | \(0.492825\pi\) | |||||||
\(332\) | 4.10960 | 0.225543 | ||||||||
\(333\) | 10.9966 | 0.602610 | ||||||||
\(334\) | −34.7638 | −1.90219 | ||||||||
\(335\) | 1.67753 | 0.0916534 | ||||||||
\(336\) | −13.9070 | −0.758687 | ||||||||
\(337\) | −17.0703 | −0.929878 | −0.464939 | − | 0.885343i | \(-0.653924\pi\) | ||||
−0.464939 | + | 0.885343i | \(0.653924\pi\) | |||||||
\(338\) | 31.8404 | 1.73189 | ||||||||
\(339\) | −8.66917 | −0.470845 | ||||||||
\(340\) | 0.0434389 | 0.00235580 | ||||||||
\(341\) | 27.6125 | 1.49530 | ||||||||
\(342\) | −7.38938 | −0.399572 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −21.8939 | −1.18044 | ||||||||
\(345\) | −0.868824 | −0.0467759 | ||||||||
\(346\) | 9.27555 | 0.498657 | ||||||||
\(347\) | −10.3864 | −0.557570 | −0.278785 | − | 0.960354i | \(-0.589932\pi\) | ||||
−0.278785 | + | 0.960354i | \(0.589932\pi\) | |||||||
\(348\) | 40.1972 | 2.15480 | ||||||||
\(349\) | −15.2538 | −0.816516 | −0.408258 | − | 0.912867i | \(-0.633864\pi\) | ||||
−0.408258 | + | 0.912867i | \(0.633864\pi\) | |||||||
\(350\) | 13.5078 | 0.722023 | ||||||||
\(351\) | −1.11985 | −0.0597733 | ||||||||
\(352\) | −63.5946 | −3.38960 | ||||||||
\(353\) | −23.6146 | −1.25688 | −0.628438 | − | 0.777859i | \(-0.716306\pi\) | ||||
−0.628438 | + | 0.777859i | \(0.716306\pi\) | |||||||
\(354\) | 26.1866 | 1.39180 | ||||||||
\(355\) | −0.394814 | −0.0209546 | ||||||||
\(356\) | 13.5918 | 0.720366 | ||||||||
\(357\) | −0.0623671 | −0.00330082 | ||||||||
\(358\) | −31.0946 | −1.64340 | ||||||||
\(359\) | 0.529839 | 0.0279638 | 0.0139819 | − | 0.999902i | \(-0.495549\pi\) | ||||
0.0139819 | + | 0.999902i | \(0.495549\pi\) | |||||||
\(360\) | −1.18200 | −0.0622970 | ||||||||
\(361\) | −11.5692 | −0.608906 | ||||||||
\(362\) | 7.93044 | 0.416814 | ||||||||
\(363\) | 0.414226 | 0.0217412 | ||||||||
\(364\) | 5.98922 | 0.313920 | ||||||||
\(365\) | −0.124449 | −0.00651394 | ||||||||
\(366\) | −9.74628 | −0.509446 | ||||||||
\(367\) | −34.0933 | −1.77966 | −0.889829 | − | 0.456294i | \(-0.849177\pi\) | ||||
−0.889829 | + | 0.456294i | \(0.849177\pi\) | |||||||
\(368\) | 92.7790 | 4.83644 | ||||||||
\(369\) | −6.34625 | −0.330373 | ||||||||
\(370\) | −3.88207 | −0.201819 | ||||||||
\(371\) | −6.90598 | −0.358540 | ||||||||
\(372\) | −45.3893 | −2.35333 | ||||||||
\(373\) | −16.9473 | −0.877497 | −0.438749 | − | 0.898610i | \(-0.644578\pi\) | ||||
−0.438749 | + | 0.898610i | \(0.644578\pi\) | |||||||
\(374\) | −0.550057 | −0.0284428 | ||||||||
\(375\) | 1.30010 | 0.0671369 | ||||||||
\(376\) | −71.4993 | −3.68729 | ||||||||
\(377\) | −8.41683 | −0.433489 | ||||||||
\(378\) | 2.71076 | 0.139426 | ||||||||
\(379\) | 25.2513 | 1.29707 | 0.648537 | − | 0.761183i | \(-0.275381\pi\) | ||||
0.648537 | + | 0.761183i | \(0.275381\pi\) | |||||||
\(380\) | 1.89863 | 0.0973977 | ||||||||
\(381\) | 0.493993 | 0.0253080 | ||||||||
\(382\) | 30.6638 | 1.56890 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 29.1395 | 1.48702 | ||||||||
\(385\) | 0.423717 | 0.0215946 | ||||||||
\(386\) | −9.43749 | −0.480355 | ||||||||
\(387\) | 2.41223 | 0.122621 | ||||||||
\(388\) | 15.2437 | 0.773879 | ||||||||
\(389\) | 9.41733 | 0.477477 | 0.238739 | − | 0.971084i | \(-0.423266\pi\) | ||||
0.238739 | + | 0.971084i | \(0.423266\pi\) | |||||||
\(390\) | 0.395336 | 0.0200186 | ||||||||
\(391\) | 0.416076 | 0.0210419 | ||||||||
\(392\) | −9.07620 | −0.458417 | ||||||||
\(393\) | 18.9040 | 0.953580 | ||||||||
\(394\) | −29.6771 | −1.49511 | ||||||||
\(395\) | −1.23236 | −0.0620066 | ||||||||
\(396\) | 17.4008 | 0.874425 | ||||||||
\(397\) | 20.0566 | 1.00661 | 0.503306 | − | 0.864108i | \(-0.332117\pi\) | ||||
0.503306 | + | 0.864108i | \(0.332117\pi\) | |||||||
\(398\) | −62.8143 | −3.14860 | ||||||||
\(399\) | −2.72595 | −0.136468 | ||||||||
\(400\) | −69.2990 | −3.46495 | ||||||||
\(401\) | −1.89294 | −0.0945290 | −0.0472645 | − | 0.998882i | \(-0.515050\pi\) | ||||
−0.0472645 | + | 0.998882i | \(0.515050\pi\) | |||||||
\(402\) | 34.9179 | 1.74154 | ||||||||
\(403\) | 9.50399 | 0.473427 | ||||||||
\(404\) | −53.7737 | −2.67534 | ||||||||
\(405\) | 0.130231 | 0.00647123 | ||||||||
\(406\) | 20.3741 | 1.01115 | ||||||||
\(407\) | 35.7783 | 1.77346 | ||||||||
\(408\) | 0.566056 | 0.0280240 | ||||||||
\(409\) | −8.73941 | −0.432136 | −0.216068 | − | 0.976378i | \(-0.569323\pi\) | ||||
−0.216068 | + | 0.976378i | \(0.569323\pi\) | |||||||
\(410\) | 2.24038 | 0.110645 | ||||||||
\(411\) | −13.6960 | −0.675572 | ||||||||
\(412\) | 50.0896 | 2.46774 | ||||||||
\(413\) | 9.66024 | 0.475349 | ||||||||
\(414\) | −18.0846 | −0.888808 | ||||||||
\(415\) | 0.100070 | 0.00491225 | ||||||||
\(416\) | −21.8887 | −1.07318 | ||||||||
\(417\) | −2.92684 | −0.143328 | ||||||||
\(418\) | −24.0419 | −1.17593 | ||||||||
\(419\) | −15.8166 | −0.772692 | −0.386346 | − | 0.922354i | \(-0.626263\pi\) | ||||
−0.386346 | + | 0.922354i | \(0.626263\pi\) | |||||||
\(420\) | −0.696503 | −0.0339859 | ||||||||
\(421\) | 0.369195 | 0.0179935 | 0.00899673 | − | 0.999960i | \(-0.497136\pi\) | ||||
0.00899673 | + | 0.999960i | \(0.497136\pi\) | |||||||
\(422\) | −55.0519 | −2.67989 | ||||||||
\(423\) | 7.87767 | 0.383025 | ||||||||
\(424\) | 62.6800 | 3.04401 | ||||||||
\(425\) | −0.310778 | −0.0150749 | ||||||||
\(426\) | −8.21806 | −0.398166 | ||||||||
\(427\) | −3.59541 | −0.173994 | ||||||||
\(428\) | 62.5918 | 3.02549 | ||||||||
\(429\) | −3.64353 | −0.175911 | ||||||||
\(430\) | −0.851577 | −0.0410667 | ||||||||
\(431\) | 35.1026 | 1.69083 | 0.845416 | − | 0.534109i | \(-0.179353\pi\) | ||||
0.845416 | + | 0.534109i | \(0.179353\pi\) | |||||||
\(432\) | −13.9070 | −0.669099 | ||||||||
\(433\) | −13.6961 | −0.658192 | −0.329096 | − | 0.944297i | \(-0.606744\pi\) | ||||
−0.329096 | + | 0.944297i | \(0.606744\pi\) | |||||||
\(434\) | −23.0057 | −1.10431 | ||||||||
\(435\) | 0.978817 | 0.0469307 | ||||||||
\(436\) | 27.6809 | 1.32568 | ||||||||
\(437\) | 18.1859 | 0.869949 | ||||||||
\(438\) | −2.59040 | −0.123774 | ||||||||
\(439\) | −20.7546 | −0.990563 | −0.495281 | − | 0.868733i | \(-0.664935\pi\) | ||||
−0.495281 | + | 0.868733i | \(0.664935\pi\) | |||||||
\(440\) | −3.84574 | −0.183338 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.189325 | −0.00900526 | ||||||||
\(443\) | −20.9446 | −0.995106 | −0.497553 | − | 0.867434i | \(-0.665768\pi\) | ||||
−0.497553 | + | 0.867434i | \(0.665768\pi\) | |||||||
\(444\) | −58.8122 | −2.79110 | ||||||||
\(445\) | 0.330966 | 0.0156893 | ||||||||
\(446\) | −74.4685 | −3.52618 | ||||||||
\(447\) | 21.5069 | 1.01724 | ||||||||
\(448\) | 25.1706 | 1.18920 | ||||||||
\(449\) | 30.2255 | 1.42643 | 0.713214 | − | 0.700946i | \(-0.247239\pi\) | ||||
0.713214 | + | 0.700946i | \(0.247239\pi\) | |||||||
\(450\) | 13.5078 | 0.636765 | ||||||||
\(451\) | −20.6480 | −0.972277 | ||||||||
\(452\) | 46.3646 | 2.18081 | ||||||||
\(453\) | −2.82899 | −0.132917 | ||||||||
\(454\) | 55.7382 | 2.61592 | ||||||||
\(455\) | 0.145840 | 0.00683706 | ||||||||
\(456\) | 24.7412 | 1.15861 | ||||||||
\(457\) | −17.0866 | −0.799277 | −0.399638 | − | 0.916673i | \(-0.630864\pi\) | ||||
−0.399638 | + | 0.916673i | \(0.630864\pi\) | |||||||
\(458\) | −15.2307 | −0.711683 | ||||||||
\(459\) | −0.0623671 | −0.00291105 | ||||||||
\(460\) | 4.64665 | 0.216651 | ||||||||
\(461\) | −29.9374 | −1.39432 | −0.697161 | − | 0.716914i | \(-0.745554\pi\) | ||||
−0.697161 | + | 0.716914i | \(0.745554\pi\) | |||||||
\(462\) | 8.81967 | 0.410328 | ||||||||
\(463\) | 16.4784 | 0.765815 | 0.382907 | − | 0.923787i | \(-0.374923\pi\) | ||||
0.382907 | + | 0.923787i | \(0.374923\pi\) | |||||||
\(464\) | −104.525 | −4.85245 | ||||||||
\(465\) | −1.10525 | −0.0512546 | ||||||||
\(466\) | −21.1445 | −0.979499 | ||||||||
\(467\) | −25.0695 | −1.16008 | −0.580039 | − | 0.814589i | \(-0.696963\pi\) | ||||
−0.580039 | + | 0.814589i | \(0.696963\pi\) | |||||||
\(468\) | 5.98922 | 0.276852 | ||||||||
\(469\) | 12.8812 | 0.594799 | ||||||||
\(470\) | −2.78101 | −0.128278 | ||||||||
\(471\) | −7.59643 | −0.350025 | ||||||||
\(472\) | −87.6782 | −4.03572 | ||||||||
\(473\) | 7.84838 | 0.360869 | ||||||||
\(474\) | −25.6515 | −1.17821 | ||||||||
\(475\) | −13.5835 | −0.623254 | ||||||||
\(476\) | 0.333553 | 0.0152884 | ||||||||
\(477\) | −6.90598 | −0.316203 | ||||||||
\(478\) | −21.3971 | −0.978679 | ||||||||
\(479\) | −37.6782 | −1.72156 | −0.860781 | − | 0.508976i | \(-0.830024\pi\) | ||||
−0.860781 | + | 0.508976i | \(0.830024\pi\) | |||||||
\(480\) | 2.54550 | 0.116186 | ||||||||
\(481\) | 12.3146 | 0.561497 | ||||||||
\(482\) | 32.6505 | 1.48719 | ||||||||
\(483\) | −6.67141 | −0.303559 | ||||||||
\(484\) | −2.21537 | −0.100699 | ||||||||
\(485\) | 0.371189 | 0.0168548 | ||||||||
\(486\) | 2.71076 | 0.122963 | ||||||||
\(487\) | −31.7521 | −1.43882 | −0.719412 | − | 0.694584i | \(-0.755588\pi\) | ||||
−0.719412 | + | 0.694584i | \(0.755588\pi\) | |||||||
\(488\) | 32.6326 | 1.47721 | ||||||||
\(489\) | −5.41853 | −0.245034 | ||||||||
\(490\) | −0.353025 | −0.0159480 | ||||||||
\(491\) | −22.7319 | −1.02588 | −0.512938 | − | 0.858425i | \(-0.671443\pi\) | ||||
−0.512938 | + | 0.858425i | \(0.671443\pi\) | |||||||
\(492\) | 33.9411 | 1.53018 | ||||||||
\(493\) | −0.468752 | −0.0211115 | ||||||||
\(494\) | −8.27503 | −0.372311 | ||||||||
\(495\) | 0.423717 | 0.0190446 | ||||||||
\(496\) | 118.026 | 5.29952 | ||||||||
\(497\) | −3.03164 | −0.135988 | ||||||||
\(498\) | 2.08296 | 0.0933397 | ||||||||
\(499\) | 1.39611 | 0.0624983 | 0.0312492 | − | 0.999512i | \(-0.490051\pi\) | ||||
0.0312492 | + | 0.999512i | \(0.490051\pi\) | |||||||
\(500\) | −6.95322 | −0.310957 | ||||||||
\(501\) | −12.8244 | −0.572952 | ||||||||
\(502\) | 17.3268 | 0.773333 | ||||||||
\(503\) | 26.4249 | 1.17823 | 0.589114 | − | 0.808050i | \(-0.299477\pi\) | ||||
0.589114 | + | 0.808050i | \(0.299477\pi\) | |||||||
\(504\) | −9.07620 | −0.404286 | ||||||||
\(505\) | −1.30941 | −0.0582680 | ||||||||
\(506\) | −58.8396 | −2.61574 | ||||||||
\(507\) | 11.7459 | 0.521655 | ||||||||
\(508\) | −2.64198 | −0.117219 | ||||||||
\(509\) | 34.0757 | 1.51038 | 0.755189 | − | 0.655507i | \(-0.227545\pi\) | ||||
0.755189 | + | 0.655507i | \(0.227545\pi\) | |||||||
\(510\) | 0.0220171 | 0.000974935 0 | ||||||||
\(511\) | −0.955600 | −0.0422732 | ||||||||
\(512\) | −19.3811 | −0.856534 | ||||||||
\(513\) | −2.72595 | −0.120353 | ||||||||
\(514\) | 72.8340 | 3.21257 | ||||||||
\(515\) | 1.21970 | 0.0537464 | ||||||||
\(516\) | −12.9011 | −0.567941 | ||||||||
\(517\) | 25.6306 | 1.12723 | ||||||||
\(518\) | −29.8091 | −1.30974 | ||||||||
\(519\) | 3.42175 | 0.150198 | ||||||||
\(520\) | −1.32367 | −0.0580467 | ||||||||
\(521\) | −17.2741 | −0.756792 | −0.378396 | − | 0.925644i | \(-0.623524\pi\) | ||||
−0.378396 | + | 0.925644i | \(0.623524\pi\) | |||||||
\(522\) | 20.3741 | 0.891750 | ||||||||
\(523\) | 17.7980 | 0.778251 | 0.389126 | − | 0.921185i | \(-0.372777\pi\) | ||||
0.389126 | + | 0.921185i | \(0.372777\pi\) | |||||||
\(524\) | −101.103 | −4.41669 | ||||||||
\(525\) | 4.98304 | 0.217478 | ||||||||
\(526\) | 49.5329 | 2.15974 | ||||||||
\(527\) | 0.529298 | 0.0230566 | ||||||||
\(528\) | −45.2474 | −1.96914 | ||||||||
\(529\) | 21.5076 | 0.935115 | ||||||||
\(530\) | 2.43798 | 0.105899 | ||||||||
\(531\) | 9.66024 | 0.419218 | ||||||||
\(532\) | 14.5789 | 0.632078 | ||||||||
\(533\) | −7.10687 | −0.307833 | ||||||||
\(534\) | 6.88907 | 0.298119 | ||||||||
\(535\) | 1.52413 | 0.0658940 | ||||||||
\(536\) | −116.912 | −5.04985 | ||||||||
\(537\) | −11.4708 | −0.495002 | ||||||||
\(538\) | −55.7691 | −2.40438 | ||||||||
\(539\) | 3.25358 | 0.140142 | ||||||||
\(540\) | −0.696503 | −0.0299727 | ||||||||
\(541\) | −6.78690 | −0.291791 | −0.145896 | − | 0.989300i | \(-0.546606\pi\) | ||||
−0.145896 | + | 0.989300i | \(0.546606\pi\) | |||||||
\(542\) | −5.40561 | −0.232191 | ||||||||
\(543\) | 2.92554 | 0.125547 | ||||||||
\(544\) | −1.21903 | −0.0522654 | ||||||||
\(545\) | 0.674040 | 0.0288727 | ||||||||
\(546\) | 3.03565 | 0.129914 | ||||||||
\(547\) | 19.6562 | 0.840439 | 0.420220 | − | 0.907422i | \(-0.361953\pi\) | ||||
0.420220 | + | 0.907422i | \(0.361953\pi\) | |||||||
\(548\) | 73.2490 | 3.12904 | ||||||||
\(549\) | −3.59541 | −0.153448 | ||||||||
\(550\) | 43.9488 | 1.87398 | ||||||||
\(551\) | −20.4882 | −0.872828 | ||||||||
\(552\) | 60.5510 | 2.57722 | ||||||||
\(553\) | −9.46286 | −0.402402 | ||||||||
\(554\) | 61.1500 | 2.59801 | ||||||||
\(555\) | −1.43210 | −0.0607892 | ||||||||
\(556\) | 15.6534 | 0.663852 | ||||||||
\(557\) | 24.2238 | 1.02640 | 0.513199 | − | 0.858270i | \(-0.328460\pi\) | ||||
0.513199 | + | 0.858270i | \(0.328460\pi\) | |||||||
\(558\) | −23.0057 | −0.973909 | ||||||||
\(559\) | 2.70134 | 0.114255 | ||||||||
\(560\) | 1.81112 | 0.0765337 | ||||||||
\(561\) | −0.202916 | −0.00856713 | ||||||||
\(562\) | −3.86014 | −0.162830 | ||||||||
\(563\) | 16.6008 | 0.699641 | 0.349821 | − | 0.936817i | \(-0.386243\pi\) | ||||
0.349821 | + | 0.936817i | \(0.386243\pi\) | |||||||
\(564\) | −42.1314 | −1.77405 | ||||||||
\(565\) | 1.12899 | 0.0474972 | ||||||||
\(566\) | 14.6770 | 0.616920 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 27.5158 | 1.15454 | ||||||||
\(569\) | 27.7424 | 1.16302 | 0.581511 | − | 0.813539i | \(-0.302462\pi\) | ||||
0.581511 | + | 0.813539i | \(0.302462\pi\) | |||||||
\(570\) | 0.962327 | 0.0403074 | ||||||||
\(571\) | 24.3865 | 1.02054 | 0.510272 | − | 0.860013i | \(-0.329545\pi\) | ||||
0.510272 | + | 0.860013i | \(0.329545\pi\) | |||||||
\(572\) | 19.4864 | 0.814767 | ||||||||
\(573\) | 11.3119 | 0.472562 | ||||||||
\(574\) | 17.2032 | 0.718046 | ||||||||
\(575\) | −33.2439 | −1.38637 | ||||||||
\(576\) | 25.1706 | 1.04878 | ||||||||
\(577\) | −23.9450 | −0.996845 | −0.498423 | − | 0.866934i | \(-0.666087\pi\) | ||||
−0.498423 | + | 0.866934i | \(0.666087\pi\) | |||||||
\(578\) | 46.0724 | 1.91636 | ||||||||
\(579\) | −3.48149 | −0.144686 | ||||||||
\(580\) | −5.23492 | −0.217368 | ||||||||
\(581\) | 0.768405 | 0.0318788 | ||||||||
\(582\) | 7.72629 | 0.320265 | ||||||||
\(583\) | −22.4691 | −0.930577 | ||||||||
\(584\) | 8.67322 | 0.358900 | ||||||||
\(585\) | 0.145840 | 0.00602972 | ||||||||
\(586\) | −32.7659 | −1.35355 | ||||||||
\(587\) | −33.8816 | −1.39844 | −0.699222 | − | 0.714905i | \(-0.746470\pi\) | ||||
−0.699222 | + | 0.714905i | \(0.746470\pi\) | |||||||
\(588\) | −5.34821 | −0.220557 | ||||||||
\(589\) | 23.1346 | 0.953245 | ||||||||
\(590\) | −3.41030 | −0.140400 | ||||||||
\(591\) | −10.9479 | −0.450337 | ||||||||
\(592\) | 152.929 | 6.28536 | ||||||||
\(593\) | 46.5077 | 1.90984 | 0.954921 | − | 0.296860i | \(-0.0959395\pi\) | ||||
0.954921 | + | 0.296860i | \(0.0959395\pi\) | |||||||
\(594\) | 8.81967 | 0.361875 | ||||||||
\(595\) | 0.00812213 | 0.000332975 0 | ||||||||
\(596\) | −115.024 | −4.71155 | ||||||||
\(597\) | −23.1722 | −0.948376 | ||||||||
\(598\) | −20.2521 | −0.828169 | ||||||||
\(599\) | 25.3698 | 1.03658 | 0.518291 | − | 0.855204i | \(-0.326568\pi\) | ||||
0.518291 | + | 0.855204i | \(0.326568\pi\) | |||||||
\(600\) | −45.2271 | −1.84639 | ||||||||
\(601\) | 16.8004 | 0.685303 | 0.342651 | − | 0.939463i | \(-0.388675\pi\) | ||||
0.342651 | + | 0.939463i | \(0.388675\pi\) | |||||||
\(602\) | −6.53898 | −0.266509 | ||||||||
\(603\) | 12.8812 | 0.524563 | ||||||||
\(604\) | 15.1300 | 0.615632 | ||||||||
\(605\) | −0.0539450 | −0.00219318 | ||||||||
\(606\) | −27.2554 | −1.10717 | ||||||||
\(607\) | −31.3882 | −1.27401 | −0.637004 | − | 0.770861i | \(-0.719827\pi\) | ||||
−0.637004 | + | 0.770861i | \(0.719827\pi\) | |||||||
\(608\) | −53.2814 | −2.16085 | ||||||||
\(609\) | 7.51601 | 0.304564 | ||||||||
\(610\) | 1.26927 | 0.0513911 | ||||||||
\(611\) | 8.82183 | 0.356893 | ||||||||
\(612\) | 0.333553 | 0.0134831 | ||||||||
\(613\) | −44.4574 | −1.79562 | −0.897808 | − | 0.440387i | \(-0.854841\pi\) | ||||
−0.897808 | + | 0.440387i | \(0.854841\pi\) | |||||||
\(614\) | −10.7444 | −0.433608 | ||||||||
\(615\) | 0.826478 | 0.0333268 | ||||||||
\(616\) | −29.5301 | −1.18980 | ||||||||
\(617\) | 9.45031 | 0.380455 | 0.190228 | − | 0.981740i | \(-0.439077\pi\) | ||||
0.190228 | + | 0.981740i | \(0.439077\pi\) | |||||||
\(618\) | 25.3880 | 1.02126 | ||||||||
\(619\) | 18.3975 | 0.739457 | 0.369729 | − | 0.929140i | \(-0.379451\pi\) | ||||
0.369729 | + | 0.929140i | \(0.379451\pi\) | |||||||
\(620\) | 5.91109 | 0.237395 | ||||||||
\(621\) | −6.67141 | −0.267714 | ||||||||
\(622\) | 22.3643 | 0.896726 | ||||||||
\(623\) | 2.54138 | 0.101818 | ||||||||
\(624\) | −15.5738 | −0.623449 | ||||||||
\(625\) | 24.7459 | 0.989835 | ||||||||
\(626\) | 9.25068 | 0.369732 | ||||||||
\(627\) | −8.86908 | −0.354197 | ||||||||
\(628\) | 40.6273 | 1.62121 | ||||||||
\(629\) | 0.685826 | 0.0273457 | ||||||||
\(630\) | −0.353025 | −0.0140648 | ||||||||
\(631\) | −17.5690 | −0.699409 | −0.349705 | − | 0.936860i | \(-0.613718\pi\) | ||||
−0.349705 | + | 0.936860i | \(0.613718\pi\) | |||||||
\(632\) | 85.8868 | 3.41639 | ||||||||
\(633\) | −20.3087 | −0.807197 | ||||||||
\(634\) | 3.24388 | 0.128831 | ||||||||
\(635\) | −0.0643332 | −0.00255299 | ||||||||
\(636\) | 36.9346 | 1.46455 | ||||||||
\(637\) | 1.11985 | 0.0443702 | ||||||||
\(638\) | 66.2887 | 2.62439 | ||||||||
\(639\) | −3.03164 | −0.119930 | ||||||||
\(640\) | −3.79486 | −0.150005 | ||||||||
\(641\) | 22.8566 | 0.902782 | 0.451391 | − | 0.892326i | \(-0.350928\pi\) | ||||
0.451391 | + | 0.892326i | \(0.350928\pi\) | |||||||
\(642\) | 31.7248 | 1.25208 | ||||||||
\(643\) | −2.16724 | −0.0854676 | −0.0427338 | − | 0.999086i | \(-0.513607\pi\) | ||||
−0.0427338 | + | 0.999086i | \(0.513607\pi\) | |||||||
\(644\) | 35.6801 | 1.40599 | ||||||||
\(645\) | −0.314147 | −0.0123695 | ||||||||
\(646\) | −0.460854 | −0.0181321 | ||||||||
\(647\) | 35.0366 | 1.37743 | 0.688715 | − | 0.725033i | \(-0.258175\pi\) | ||||
0.688715 | + | 0.725033i | \(0.258175\pi\) | |||||||
\(648\) | −9.07620 | −0.356547 | ||||||||
\(649\) | 31.4303 | 1.23375 | ||||||||
\(650\) | 15.1268 | 0.593321 | ||||||||
\(651\) | −8.48682 | −0.332625 | ||||||||
\(652\) | 28.9795 | 1.13492 | ||||||||
\(653\) | −26.0011 | −1.01750 | −0.508752 | − | 0.860913i | \(-0.669893\pi\) | ||||
−0.508752 | + | 0.860913i | \(0.669893\pi\) | |||||||
\(654\) | 14.0302 | 0.548622 | ||||||||
\(655\) | −2.46188 | −0.0961938 | ||||||||
\(656\) | −88.2571 | −3.44586 | ||||||||
\(657\) | −0.955600 | −0.0372815 | ||||||||
\(658\) | −21.3545 | −0.832483 | ||||||||
\(659\) | 37.3860 | 1.45635 | 0.728175 | − | 0.685391i | \(-0.240369\pi\) | ||||
0.728175 | + | 0.685391i | \(0.240369\pi\) | |||||||
\(660\) | −2.26613 | −0.0882089 | ||||||||
\(661\) | −34.3439 | −1.33582 | −0.667912 | − | 0.744240i | \(-0.732812\pi\) | ||||
−0.667912 | + | 0.744240i | \(0.732812\pi\) | |||||||
\(662\) | −2.22301 | −0.0863998 | ||||||||
\(663\) | −0.0698420 | −0.00271244 | ||||||||
\(664\) | −6.97420 | −0.270651 | ||||||||
\(665\) | 0.355003 | 0.0137664 | ||||||||
\(666\) | −29.8091 | −1.15508 | ||||||||
\(667\) | −50.1423 | −1.94152 | ||||||||
\(668\) | 68.5876 | 2.65373 | ||||||||
\(669\) | −27.4714 | −1.06211 | ||||||||
\(670\) | −4.54739 | −0.175681 | ||||||||
\(671\) | −11.6979 | −0.451594 | ||||||||
\(672\) | 19.5460 | 0.754005 | ||||||||
\(673\) | 35.1605 | 1.35534 | 0.677669 | − | 0.735367i | \(-0.262990\pi\) | ||||
0.677669 | + | 0.735367i | \(0.262990\pi\) | |||||||
\(674\) | 46.2735 | 1.78239 | ||||||||
\(675\) | 4.98304 | 0.191797 | ||||||||
\(676\) | −62.8197 | −2.41614 | ||||||||
\(677\) | 13.2935 | 0.510911 | 0.255456 | − | 0.966821i | \(-0.417775\pi\) | ||||
0.255456 | + | 0.966821i | \(0.417775\pi\) | |||||||
\(678\) | 23.5000 | 0.902513 | ||||||||
\(679\) | 2.85023 | 0.109382 | ||||||||
\(680\) | −0.0737181 | −0.00282696 | ||||||||
\(681\) | 20.5618 | 0.787932 | ||||||||
\(682\) | −74.8509 | −2.86619 | ||||||||
\(683\) | 15.3320 | 0.586661 | 0.293331 | − | 0.956011i | \(-0.405236\pi\) | ||||
0.293331 | + | 0.956011i | \(0.405236\pi\) | |||||||
\(684\) | 14.5789 | 0.557440 | ||||||||
\(685\) | 1.78364 | 0.0681493 | ||||||||
\(686\) | −2.71076 | −0.103497 | ||||||||
\(687\) | −5.61860 | −0.214363 | ||||||||
\(688\) | 33.5468 | 1.27896 | ||||||||
\(689\) | −7.73368 | −0.294630 | ||||||||
\(690\) | 2.35517 | 0.0896598 | ||||||||
\(691\) | −36.1856 | −1.37657 | −0.688283 | − | 0.725443i | \(-0.741635\pi\) | ||||
−0.688283 | + | 0.725443i | \(0.741635\pi\) | |||||||
\(692\) | −18.3003 | −0.695672 | ||||||||
\(693\) | 3.25358 | 0.123593 | ||||||||
\(694\) | 28.1550 | 1.06875 | ||||||||
\(695\) | 0.381166 | 0.0144584 | ||||||||
\(696\) | −68.2168 | −2.58575 | ||||||||
\(697\) | −0.395797 | −0.0149919 | ||||||||
\(698\) | 41.3493 | 1.56509 | ||||||||
\(699\) | −7.80020 | −0.295031 | ||||||||
\(700\) | −26.6504 | −1.00729 | ||||||||
\(701\) | 37.9834 | 1.43461 | 0.717307 | − | 0.696757i | \(-0.245374\pi\) | ||||
0.717307 | + | 0.696757i | \(0.245374\pi\) | |||||||
\(702\) | 3.03565 | 0.114573 | ||||||||
\(703\) | 29.9761 | 1.13057 | ||||||||
\(704\) | 81.8947 | 3.08652 | ||||||||
\(705\) | −1.02592 | −0.0386382 | ||||||||
\(706\) | 64.0134 | 2.40918 | ||||||||
\(707\) | −10.0545 | −0.378139 | ||||||||
\(708\) | −51.6650 | −1.94169 | ||||||||
\(709\) | −6.57688 | −0.247000 | −0.123500 | − | 0.992345i | \(-0.539412\pi\) | ||||
−0.123500 | + | 0.992345i | \(0.539412\pi\) | |||||||
\(710\) | 1.07025 | 0.0401656 | ||||||||
\(711\) | −9.46286 | −0.354885 | ||||||||
\(712\) | −23.0661 | −0.864438 | ||||||||
\(713\) | 56.6190 | 2.12040 | ||||||||
\(714\) | 0.169062 | 0.00632699 | ||||||||
\(715\) | 0.474501 | 0.0177453 | ||||||||
\(716\) | 61.3483 | 2.29269 | ||||||||
\(717\) | −7.89339 | −0.294784 | ||||||||
\(718\) | −1.43626 | −0.0536009 | ||||||||
\(719\) | 6.11475 | 0.228042 | 0.114021 | − | 0.993478i | \(-0.463627\pi\) | ||||
0.114021 | + | 0.993478i | \(0.463627\pi\) | |||||||
\(720\) | 1.81112 | 0.0674964 | ||||||||
\(721\) | 9.36566 | 0.348795 | ||||||||
\(722\) | 31.3614 | 1.16715 | ||||||||
\(723\) | 12.0448 | 0.447950 | ||||||||
\(724\) | −15.6464 | −0.581495 | ||||||||
\(725\) | 37.4526 | 1.39095 | ||||||||
\(726\) | −1.12287 | −0.0416735 | ||||||||
\(727\) | 2.46466 | 0.0914092 | 0.0457046 | − | 0.998955i | \(-0.485447\pi\) | ||||
0.0457046 | + | 0.998955i | \(0.485447\pi\) | |||||||
\(728\) | −10.1640 | −0.376703 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.337350 | 0.0124859 | ||||||||
\(731\) | 0.150444 | 0.00556437 | ||||||||
\(732\) | 19.2290 | 0.710724 | ||||||||
\(733\) | 3.34622 | 0.123595 | 0.0617977 | − | 0.998089i | \(-0.480317\pi\) | ||||
0.0617977 | + | 0.998089i | \(0.480317\pi\) | |||||||
\(734\) | 92.4188 | 3.41124 | ||||||||
\(735\) | −0.130231 | −0.00480364 | ||||||||
\(736\) | −130.400 | −4.80659 | ||||||||
\(737\) | 41.9100 | 1.54378 | ||||||||
\(738\) | 17.2032 | 0.633257 | ||||||||
\(739\) | −24.8920 | −0.915666 | −0.457833 | − | 0.889038i | \(-0.651374\pi\) | ||||
−0.457833 | + | 0.889038i | \(0.651374\pi\) | |||||||
\(740\) | 7.65917 | 0.281557 | ||||||||
\(741\) | −3.05266 | −0.112142 | ||||||||
\(742\) | 18.7204 | 0.687249 | ||||||||
\(743\) | −5.19266 | −0.190500 | −0.0952501 | − | 0.995453i | \(-0.530365\pi\) | ||||
−0.0952501 | + | 0.995453i | \(0.530365\pi\) | |||||||
\(744\) | 77.0281 | 2.82399 | ||||||||
\(745\) | −2.80086 | −0.102616 | ||||||||
\(746\) | 45.9400 | 1.68198 | ||||||||
\(747\) | 0.768405 | 0.0281145 | ||||||||
\(748\) | 1.08524 | 0.0396803 | ||||||||
\(749\) | 11.7033 | 0.427629 | ||||||||
\(750\) | −3.52426 | −0.128688 | ||||||||
\(751\) | 24.9740 | 0.911315 | 0.455658 | − | 0.890155i | \(-0.349404\pi\) | ||||
0.455658 | + | 0.890155i | \(0.349404\pi\) | |||||||
\(752\) | 109.554 | 3.99504 | ||||||||
\(753\) | 6.39187 | 0.232933 | ||||||||
\(754\) | 22.8160 | 0.830909 | ||||||||
\(755\) | 0.368422 | 0.0134082 | ||||||||
\(756\) | −5.34821 | −0.194513 | ||||||||
\(757\) | −26.0322 | −0.946158 | −0.473079 | − | 0.881020i | \(-0.656857\pi\) | ||||
−0.473079 | + | 0.881020i | \(0.656857\pi\) | |||||||
\(758\) | −68.4503 | −2.48623 | ||||||||
\(759\) | −21.7059 | −0.787876 | ||||||||
\(760\) | −3.22208 | −0.116877 | ||||||||
\(761\) | 9.77322 | 0.354279 | 0.177139 | − | 0.984186i | \(-0.443316\pi\) | ||||
0.177139 | + | 0.984186i | \(0.443316\pi\) | |||||||
\(762\) | −1.33910 | −0.0485104 | ||||||||
\(763\) | 5.17573 | 0.187374 | ||||||||
\(764\) | −60.4985 | −2.18876 | ||||||||
\(765\) | 0.00812213 | 0.000293656 0 | ||||||||
\(766\) | 2.71076 | 0.0979437 | ||||||||
\(767\) | 10.8180 | 0.390617 | ||||||||
\(768\) | −28.6489 | −1.03378 | ||||||||
\(769\) | 44.8402 | 1.61698 | 0.808490 | − | 0.588510i | \(-0.200285\pi\) | ||||
0.808490 | + | 0.588510i | \(0.200285\pi\) | |||||||
\(770\) | −1.14859 | −0.0413924 | ||||||||
\(771\) | 26.8685 | 0.967645 | ||||||||
\(772\) | 18.6198 | 0.670140 | ||||||||
\(773\) | −15.1776 | −0.545899 | −0.272950 | − | 0.962028i | \(-0.587999\pi\) | ||||
−0.272950 | + | 0.962028i | \(0.587999\pi\) | |||||||
\(774\) | −6.53898 | −0.235039 | ||||||||
\(775\) | −42.2901 | −1.51911 | ||||||||
\(776\) | −25.8693 | −0.928653 | ||||||||
\(777\) | −10.9966 | −0.394501 | ||||||||
\(778\) | −25.5281 | −0.915227 | ||||||||
\(779\) | −17.2995 | −0.619820 | ||||||||
\(780\) | −0.779981 | −0.0279278 | ||||||||
\(781\) | −9.86370 | −0.352951 | ||||||||
\(782\) | −1.12788 | −0.0403330 | ||||||||
\(783\) | 7.51601 | 0.268600 | ||||||||
\(784\) | 13.9070 | 0.496677 | ||||||||
\(785\) | 0.989290 | 0.0353093 | ||||||||
\(786\) | −51.2441 | −1.82782 | ||||||||
\(787\) | −6.14414 | −0.219015 | −0.109507 | − | 0.993986i | \(-0.534927\pi\) | ||||
−0.109507 | + | 0.993986i | \(0.534927\pi\) | |||||||
\(788\) | 58.5518 | 2.08582 | ||||||||
\(789\) | 18.2727 | 0.650525 | ||||||||
\(790\) | 3.34062 | 0.118854 | ||||||||
\(791\) | 8.66917 | 0.308240 | ||||||||
\(792\) | −29.5301 | −1.04931 | ||||||||
\(793\) | −4.02633 | −0.142979 | ||||||||
\(794\) | −54.3686 | −1.92947 | ||||||||
\(795\) | 0.899372 | 0.0318974 | ||||||||
\(796\) | 123.930 | 4.39258 | ||||||||
\(797\) | −30.1003 | −1.06621 | −0.533104 | − | 0.846050i | \(-0.678975\pi\) | ||||
−0.533104 | + | 0.846050i | \(0.678975\pi\) | |||||||
\(798\) | 7.38938 | 0.261581 | ||||||||
\(799\) | 0.491307 | 0.0173812 | ||||||||
\(800\) | 97.3987 | 3.44356 | ||||||||
\(801\) | 2.54138 | 0.0897952 | ||||||||
\(802\) | 5.13131 | 0.181193 | ||||||||
\(803\) | −3.10912 | −0.109718 | ||||||||
\(804\) | −68.8915 | −2.42961 | ||||||||
\(805\) | 0.868824 | 0.0306220 | ||||||||
\(806\) | −25.7630 | −0.907464 | ||||||||
\(807\) | −20.5732 | −0.724212 | ||||||||
\(808\) | 91.2569 | 3.21041 | ||||||||
\(809\) | 5.38338 | 0.189270 | 0.0946348 | − | 0.995512i | \(-0.469832\pi\) | ||||
0.0946348 | + | 0.995512i | \(0.469832\pi\) | |||||||
\(810\) | −0.353025 | −0.0124040 | ||||||||
\(811\) | 0.721790 | 0.0253455 | 0.0126727 | − | 0.999920i | \(-0.495966\pi\) | ||||
0.0126727 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(812\) | −40.1972 | −1.41065 | ||||||||
\(813\) | −1.99413 | −0.0699373 | ||||||||
\(814\) | −96.9864 | −3.39937 | ||||||||
\(815\) | 0.705660 | 0.0247182 | ||||||||
\(816\) | −0.867337 | −0.0303629 | ||||||||
\(817\) | 6.57561 | 0.230052 | ||||||||
\(818\) | 23.6904 | 0.828317 | ||||||||
\(819\) | 1.11985 | 0.0391308 | ||||||||
\(820\) | −4.42018 | −0.154359 | ||||||||
\(821\) | 28.8889 | 1.00823 | 0.504115 | − | 0.863637i | \(-0.331819\pi\) | ||||
0.504115 | + | 0.863637i | \(0.331819\pi\) | |||||||
\(822\) | 37.1265 | 1.29493 | ||||||||
\(823\) | −6.54311 | −0.228078 | −0.114039 | − | 0.993476i | \(-0.536379\pi\) | ||||
−0.114039 | + | 0.993476i | \(0.536379\pi\) | |||||||
\(824\) | −85.0046 | −2.96128 | ||||||||
\(825\) | 16.2127 | 0.564454 | ||||||||
\(826\) | −26.1866 | −0.911147 | ||||||||
\(827\) | 39.3333 | 1.36775 | 0.683876 | − | 0.729599i | \(-0.260293\pi\) | ||||
0.683876 | + | 0.729599i | \(0.260293\pi\) | |||||||
\(828\) | 35.6801 | 1.23997 | ||||||||
\(829\) | 1.81794 | 0.0631396 | 0.0315698 | − | 0.999502i | \(-0.489949\pi\) | ||||
0.0315698 | + | 0.999502i | \(0.489949\pi\) | |||||||
\(830\) | −0.271266 | −0.00941578 | ||||||||
\(831\) | 22.5582 | 0.782537 | ||||||||
\(832\) | 28.1874 | 0.977223 | ||||||||
\(833\) | 0.0623671 | 0.00216089 | ||||||||
\(834\) | 7.93397 | 0.274731 | ||||||||
\(835\) | 1.67013 | 0.0577974 | ||||||||
\(836\) | 47.4338 | 1.64053 | ||||||||
\(837\) | −8.48682 | −0.293347 | ||||||||
\(838\) | 42.8750 | 1.48109 | ||||||||
\(839\) | 38.7823 | 1.33891 | 0.669457 | − | 0.742851i | \(-0.266527\pi\) | ||||
0.669457 | + | 0.742851i | \(0.266527\pi\) | |||||||
\(840\) | 1.18200 | 0.0407830 | ||||||||
\(841\) | 27.4904 | 0.947944 | ||||||||
\(842\) | −1.00080 | −0.0344898 | ||||||||
\(843\) | −1.42401 | −0.0490454 | ||||||||
\(844\) | 108.615 | 3.73869 | ||||||||
\(845\) | −1.52968 | −0.0526227 | ||||||||
\(846\) | −21.3545 | −0.734181 | ||||||||
\(847\) | −0.414226 | −0.0142330 | ||||||||
\(848\) | −96.0412 | −3.29807 | ||||||||
\(849\) | 5.41435 | 0.185820 | ||||||||
\(850\) | 0.842443 | 0.0288956 | ||||||||
\(851\) | 73.3628 | 2.51484 | ||||||||
\(852\) | 16.2139 | 0.555479 | ||||||||
\(853\) | 33.2662 | 1.13901 | 0.569506 | − | 0.821987i | \(-0.307135\pi\) | ||||
0.569506 | + | 0.821987i | \(0.307135\pi\) | |||||||
\(854\) | 9.74628 | 0.333511 | ||||||||
\(855\) | 0.355003 | 0.0121408 | ||||||||
\(856\) | −106.222 | −3.63058 | ||||||||
\(857\) | 2.22266 | 0.0759245 | 0.0379622 | − | 0.999279i | \(-0.487913\pi\) | ||||
0.0379622 | + | 0.999279i | \(0.487913\pi\) | |||||||
\(858\) | 9.87673 | 0.337186 | ||||||||
\(859\) | 47.6152 | 1.62461 | 0.812305 | − | 0.583233i | \(-0.198212\pi\) | ||||
0.812305 | + | 0.583233i | \(0.198212\pi\) | |||||||
\(860\) | 1.68013 | 0.0572918 | ||||||||
\(861\) | 6.34625 | 0.216280 | ||||||||
\(862\) | −95.1546 | −3.24098 | ||||||||
\(863\) | −2.91403 | −0.0991948 | −0.0495974 | − | 0.998769i | \(-0.515794\pi\) | ||||
−0.0495974 | + | 0.998769i | \(0.515794\pi\) | |||||||
\(864\) | 19.5460 | 0.664970 | ||||||||
\(865\) | −0.445618 | −0.0151515 | ||||||||
\(866\) | 37.1268 | 1.26162 | ||||||||
\(867\) | 16.9961 | 0.577218 | ||||||||
\(868\) | 45.3893 | 1.54061 | ||||||||
\(869\) | −30.7882 | −1.04442 | ||||||||
\(870\) | −2.65334 | −0.0899566 | ||||||||
\(871\) | 14.4251 | 0.488775 | ||||||||
\(872\) | −46.9760 | −1.59081 | ||||||||
\(873\) | 2.85023 | 0.0964658 | ||||||||
\(874\) | −49.2976 | −1.66752 | ||||||||
\(875\) | −1.30010 | −0.0439514 | ||||||||
\(876\) | 5.11075 | 0.172676 | ||||||||
\(877\) | 7.83945 | 0.264720 | 0.132360 | − | 0.991202i | \(-0.457745\pi\) | ||||
0.132360 | + | 0.991202i | \(0.457745\pi\) | |||||||
\(878\) | 56.2607 | 1.89871 | ||||||||
\(879\) | −12.0874 | −0.407697 | ||||||||
\(880\) | 5.89261 | 0.198640 | ||||||||
\(881\) | −38.3717 | −1.29278 | −0.646389 | − | 0.763008i | \(-0.723721\pi\) | ||||
−0.646389 | + | 0.763008i | \(0.723721\pi\) | |||||||
\(882\) | −2.71076 | −0.0912760 | ||||||||
\(883\) | 17.7826 | 0.598431 | 0.299216 | − | 0.954186i | \(-0.403275\pi\) | ||||
0.299216 | + | 0.954186i | \(0.403275\pi\) | |||||||
\(884\) | 0.373530 | 0.0125632 | ||||||||
\(885\) | −1.25806 | −0.0422893 | ||||||||
\(886\) | 56.7756 | 1.90741 | ||||||||
\(887\) | 1.22071 | 0.0409875 | 0.0204938 | − | 0.999790i | \(-0.493476\pi\) | ||||
0.0204938 | + | 0.999790i | \(0.493476\pi\) | |||||||
\(888\) | 99.8074 | 3.34932 | ||||||||
\(889\) | −0.493993 | −0.0165680 | ||||||||
\(890\) | −0.897170 | −0.0300732 | ||||||||
\(891\) | 3.25358 | 0.108999 | ||||||||
\(892\) | 146.923 | 4.91935 | ||||||||
\(893\) | 21.4741 | 0.718603 | ||||||||
\(894\) | −58.3000 | −1.94984 | ||||||||
\(895\) | 1.49385 | 0.0499340 | ||||||||
\(896\) | −29.1395 | −0.973482 | ||||||||
\(897\) | −7.47099 | −0.249449 | ||||||||
\(898\) | −81.9340 | −2.73417 | ||||||||
\(899\) | −63.7870 | −2.12741 | ||||||||
\(900\) | −26.6504 | −0.888345 | ||||||||
\(901\) | −0.430706 | −0.0143489 | ||||||||
\(902\) | 55.9718 | 1.86366 | ||||||||
\(903\) | −2.41223 | −0.0802740 | ||||||||
\(904\) | −78.6831 | −2.61696 | ||||||||
\(905\) | −0.380996 | −0.0126647 | ||||||||
\(906\) | 7.66870 | 0.254776 | ||||||||
\(907\) | −22.1739 | −0.736274 | −0.368137 | − | 0.929772i | \(-0.620004\pi\) | ||||
−0.368137 | + | 0.929772i | \(0.620004\pi\) | |||||||
\(908\) | −109.969 | −3.64945 | ||||||||
\(909\) | −10.0545 | −0.333487 | ||||||||
\(910\) | −0.395336 | −0.0131053 | ||||||||
\(911\) | −13.8113 | −0.457588 | −0.228794 | − | 0.973475i | \(-0.573478\pi\) | ||||
−0.228794 | + | 0.973475i | \(0.573478\pi\) | |||||||
\(912\) | −37.9097 | −1.25531 | ||||||||
\(913\) | 2.50007 | 0.0827401 | ||||||||
\(914\) | 46.3176 | 1.53205 | ||||||||
\(915\) | 0.468233 | 0.0154793 | ||||||||
\(916\) | 30.0495 | 0.992863 | ||||||||
\(917\) | −18.9040 | −0.624265 | ||||||||
\(918\) | 0.169062 | 0.00557988 | ||||||||
\(919\) | −54.5506 | −1.79946 | −0.899730 | − | 0.436448i | \(-0.856236\pi\) | ||||
−0.899730 | + | 0.436448i | \(0.856236\pi\) | |||||||
\(920\) | −7.88562 | −0.259981 | ||||||||
\(921\) | −3.96360 | −0.130605 | ||||||||
\(922\) | 81.1530 | 2.67263 | ||||||||
\(923\) | −3.39500 | −0.111748 | ||||||||
\(924\) | −17.4008 | −0.572445 | ||||||||
\(925\) | −54.7965 | −1.80170 | ||||||||
\(926\) | −44.6689 | −1.46791 | ||||||||
\(927\) | 9.36566 | 0.307609 | ||||||||
\(928\) | 146.908 | 4.82250 | ||||||||
\(929\) | 22.3940 | 0.734724 | 0.367362 | − | 0.930078i | \(-0.380261\pi\) | ||||
0.367362 | + | 0.930078i | \(0.380261\pi\) | |||||||
\(930\) | 2.99606 | 0.0982446 | ||||||||
\(931\) | 2.72595 | 0.0893393 | ||||||||
\(932\) | 41.7172 | 1.36649 | ||||||||
\(933\) | 8.25019 | 0.270099 | ||||||||
\(934\) | 67.9574 | 2.22363 | ||||||||
\(935\) | 0.0264260 | 0.000864222 0 | ||||||||
\(936\) | −10.1640 | −0.332221 | ||||||||
\(937\) | −16.2670 | −0.531419 | −0.265710 | − | 0.964053i | \(-0.585606\pi\) | ||||
−0.265710 | + | 0.964053i | \(0.585606\pi\) | |||||||
\(938\) | −34.9179 | −1.14011 | ||||||||
\(939\) | 3.41258 | 0.111365 | ||||||||
\(940\) | 5.48682 | 0.178960 | ||||||||
\(941\) | 42.6848 | 1.39149 | 0.695743 | − | 0.718291i | \(-0.255075\pi\) | ||||
0.695743 | + | 0.718291i | \(0.255075\pi\) | |||||||
\(942\) | 20.5921 | 0.670926 | ||||||||
\(943\) | −42.3384 | −1.37873 | ||||||||
\(944\) | 134.345 | 4.37254 | ||||||||
\(945\) | −0.130231 | −0.00423641 | ||||||||
\(946\) | −21.2751 | −0.691712 | ||||||||
\(947\) | −2.02208 | −0.0657088 | −0.0328544 | − | 0.999460i | \(-0.510460\pi\) | ||||
−0.0328544 | + | 0.999460i | \(0.510460\pi\) | |||||||
\(948\) | 50.6094 | 1.64372 | ||||||||
\(949\) | −1.07013 | −0.0347379 | ||||||||
\(950\) | 36.8216 | 1.19465 | ||||||||
\(951\) | 1.19667 | 0.0388047 | ||||||||
\(952\) | −0.566056 | −0.0183460 | ||||||||
\(953\) | 44.7699 | 1.45024 | 0.725119 | − | 0.688624i | \(-0.241785\pi\) | ||||
0.725119 | + | 0.688624i | \(0.241785\pi\) | |||||||
\(954\) | 18.7204 | 0.606097 | ||||||||
\(955\) | −1.47316 | −0.0476703 | ||||||||
\(956\) | 42.2155 | 1.36535 | ||||||||
\(957\) | 24.4539 | 0.790483 | ||||||||
\(958\) | 102.137 | 3.29988 | ||||||||
\(959\) | 13.6960 | 0.442266 | ||||||||
\(960\) | −3.27800 | −0.105797 | ||||||||
\(961\) | 41.0260 | 1.32342 | ||||||||
\(962\) | −33.3819 | −1.07627 | ||||||||
\(963\) | 11.7033 | 0.377134 | ||||||||
\(964\) | −64.4180 | −2.07476 | ||||||||
\(965\) | 0.453398 | 0.0145954 | ||||||||
\(966\) | 18.0846 | 0.581862 | ||||||||
\(967\) | 22.2040 | 0.714032 | 0.357016 | − | 0.934098i | \(-0.383794\pi\) | ||||
0.357016 | + | 0.934098i | \(0.383794\pi\) | |||||||
\(968\) | 3.75960 | 0.120838 | ||||||||
\(969\) | −0.170009 | −0.00546149 | ||||||||
\(970\) | −1.00620 | −0.0323072 | ||||||||
\(971\) | 16.5395 | 0.530778 | 0.265389 | − | 0.964141i | \(-0.414500\pi\) | ||||
0.265389 | + | 0.964141i | \(0.414500\pi\) | |||||||
\(972\) | −5.34821 | −0.171544 | ||||||||
\(973\) | 2.92684 | 0.0938303 | ||||||||
\(974\) | 86.0722 | 2.75793 | ||||||||
\(975\) | 5.58027 | 0.178712 | ||||||||
\(976\) | −50.0012 | −1.60050 | ||||||||
\(977\) | 39.3154 | 1.25781 | 0.628906 | − | 0.777482i | \(-0.283503\pi\) | ||||
0.628906 | + | 0.777482i | \(0.283503\pi\) | |||||||
\(978\) | 14.6883 | 0.469681 | ||||||||
\(979\) | 8.26858 | 0.264265 | ||||||||
\(980\) | 0.696503 | 0.0222490 | ||||||||
\(981\) | 5.17573 | 0.165248 | ||||||||
\(982\) | 61.6207 | 1.96640 | ||||||||
\(983\) | 3.20276 | 0.102152 | 0.0510761 | − | 0.998695i | \(-0.483735\pi\) | ||||
0.0510761 | + | 0.998695i | \(0.483735\pi\) | |||||||
\(984\) | −57.5998 | −1.83622 | ||||||||
\(985\) | 1.42576 | 0.0454284 | ||||||||
\(986\) | 1.27067 | 0.0404665 | ||||||||
\(987\) | −7.87767 | −0.250749 | ||||||||
\(988\) | 16.3263 | 0.519408 | ||||||||
\(989\) | 16.0930 | 0.511727 | ||||||||
\(990\) | −1.14859 | −0.0365047 | ||||||||
\(991\) | 19.0357 | 0.604689 | 0.302344 | − | 0.953199i | \(-0.402231\pi\) | ||||
0.302344 | + | 0.953199i | \(0.402231\pi\) | |||||||
\(992\) | −165.884 | −5.26681 | ||||||||
\(993\) | −0.820069 | −0.0260241 | ||||||||
\(994\) | 8.21806 | 0.260661 | ||||||||
\(995\) | 3.01774 | 0.0956689 | ||||||||
\(996\) | −4.10960 | −0.130218 | ||||||||
\(997\) | 55.0507 | 1.74347 | 0.871736 | − | 0.489976i | \(-0.162994\pi\) | ||||
0.871736 | + | 0.489976i | \(0.162994\pi\) | |||||||
\(998\) | −3.78451 | −0.119797 | ||||||||
\(999\) | −10.9966 | −0.347917 |
(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 | 8043.2.a.t.1.2 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.2 | ✓ | 52 | 1.1 | even | 1 | trivial |