Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(1,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.713538\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.77733 | 1.60349 | 0.801745 | − | 0.597666i | \(-0.203905\pi\) | ||||
0.801745 | + | 0.597666i | \(0.203905\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.77733 | 1.13384 | ||||||||
\(7\) | −4.69527 | −1.77464 | −0.887322 | − | 0.461151i | \(-0.847437\pi\) | ||||
−0.887322 | + | 0.461151i | \(0.847437\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.71354 | 1.57118 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.40880 | 1.93233 | 0.966163 | − | 0.257931i | \(-0.0830406\pi\) | ||||
0.966163 | + | 0.257931i | \(0.0830406\pi\) | |||||||
\(12\) | 2.77733 | 0.801745 | ||||||||
\(13\) | 1.06379 | 0.295042 | 0.147521 | − | 0.989059i | \(-0.452871\pi\) | ||||
0.147521 | + | 0.989059i | \(0.452871\pi\) | |||||||
\(14\) | −4.69527 | −1.25486 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.91794 | 0.465169 | 0.232584 | − | 0.972576i | \(-0.425282\pi\) | ||||
0.232584 | + | 0.972576i | \(0.425282\pi\) | |||||||
\(18\) | 4.71354 | 1.11099 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −13.0403 | −2.84562 | ||||||||
\(22\) | 6.40880 | 1.36636 | ||||||||
\(23\) | 1.79560 | 0.374408 | 0.187204 | − | 0.982321i | \(-0.440057\pi\) | ||||
0.187204 | + | 0.982321i | \(0.440057\pi\) | |||||||
\(24\) | 2.77733 | 0.566919 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.06379 | 0.208626 | ||||||||
\(27\) | 4.75905 | 0.915880 | ||||||||
\(28\) | −4.69527 | −0.887322 | ||||||||
\(29\) | 2.93621 | 0.545241 | 0.272620 | − | 0.962122i | \(-0.412110\pi\) | ||||
0.272620 | + | 0.962122i | \(0.412110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.55465 | −0.997645 | −0.498822 | − | 0.866704i | \(-0.666234\pi\) | ||||
−0.498822 | + | 0.866704i | \(0.666234\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 17.7993 | 3.09847 | ||||||||
\(34\) | 1.91794 | 0.328924 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.71354 | 0.785590 | ||||||||
\(37\) | −11.4088 | −1.87560 | −0.937798 | − | 0.347182i | \(-0.887139\pi\) | ||||
−0.937798 | + | 0.347182i | \(0.887139\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.95449 | 0.473096 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.14585 | −0.178951 | −0.0894757 | − | 0.995989i | \(-0.528519\pi\) | ||||
−0.0894757 | + | 0.995989i | \(0.528519\pi\) | |||||||
\(42\) | −13.0403 | −2.01216 | ||||||||
\(43\) | −3.55465 | −0.542079 | −0.271040 | − | 0.962568i | \(-0.587367\pi\) | ||||
−0.271040 | + | 0.962568i | \(0.587367\pi\) | |||||||
\(44\) | 6.40880 | 0.966163 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.79560 | 0.264747 | ||||||||
\(47\) | 10.8359 | 1.58058 | 0.790288 | − | 0.612736i | \(-0.209931\pi\) | ||||
0.790288 | + | 0.612736i | \(0.209931\pi\) | |||||||
\(48\) | 2.77733 | 0.400872 | ||||||||
\(49\) | 15.0455 | 2.14936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.32674 | 0.745893 | ||||||||
\(52\) | 1.06379 | 0.147521 | ||||||||
\(53\) | −8.69527 | −1.19439 | −0.597193 | − | 0.802097i | \(-0.703717\pi\) | ||||
−0.597193 | + | 0.802097i | \(0.703717\pi\) | |||||||
\(54\) | 4.75905 | 0.647625 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.69527 | −0.627431 | ||||||||
\(57\) | −2.77733 | −0.367866 | ||||||||
\(58\) | 2.93621 | 0.385544 | ||||||||
\(59\) | −5.63148 | −0.733156 | −0.366578 | − | 0.930387i | \(-0.619471\pi\) | ||||
−0.366578 | + | 0.930387i | \(0.619471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.39053 | −0.434113 | −0.217056 | − | 0.976159i | \(-0.569646\pi\) | ||||
−0.217056 | + | 0.976159i | \(0.569646\pi\) | |||||||
\(62\) | −5.55465 | −0.705441 | ||||||||
\(63\) | −22.1313 | −2.78828 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 17.7993 | 2.19095 | ||||||||
\(67\) | −8.82284 | −1.07788 | −0.538941 | − | 0.842344i | \(-0.681175\pi\) | ||||
−0.538941 | + | 0.842344i | \(0.681175\pi\) | |||||||
\(68\) | 1.91794 | 0.232584 | ||||||||
\(69\) | 4.98696 | 0.600360 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.42708 | −0.169363 | −0.0846814 | − | 0.996408i | \(-0.526987\pi\) | ||||
−0.0846814 | + | 0.996408i | \(0.526987\pi\) | |||||||
\(72\) | 4.71354 | 0.555496 | ||||||||
\(73\) | −12.6132 | −1.47626 | −0.738132 | − | 0.674656i | \(-0.764292\pi\) | ||||
−0.738132 | + | 0.674656i | \(0.764292\pi\) | |||||||
\(74\) | −11.4088 | −1.32625 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −30.0910 | −3.42919 | ||||||||
\(78\) | 2.95449 | 0.334530 | ||||||||
\(79\) | −1.96345 | −0.220906 | −0.110453 | − | 0.993881i | \(-0.535230\pi\) | ||||
−0.110453 | + | 0.993881i | \(0.535230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.923174 | −0.102575 | ||||||||
\(82\) | −1.14585 | −0.126538 | ||||||||
\(83\) | 16.2447 | 1.78309 | 0.891543 | − | 0.452937i | \(-0.149624\pi\) | ||||
0.891543 | + | 0.452937i | \(0.149624\pi\) | |||||||
\(84\) | −13.0403 | −1.42281 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.55465 | −0.383308 | ||||||||
\(87\) | 8.15482 | 0.874288 | ||||||||
\(88\) | 6.40880 | 0.683181 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.99477 | −0.523594 | ||||||||
\(92\) | 1.79560 | 0.187204 | ||||||||
\(93\) | −15.4271 | −1.59971 | ||||||||
\(94\) | 10.8359 | 1.11764 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.77733 | 0.283460 | ||||||||
\(97\) | −14.9452 | −1.51745 | −0.758727 | − | 0.651409i | \(-0.774178\pi\) | ||||
−0.758727 | + | 0.651409i | \(0.774178\pi\) | |||||||
\(98\) | 15.0455 | 1.51983 | ||||||||
\(99\) | 30.2081 | 3.03603 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5364 | 1.04841 | 0.524204 | − | 0.851592i | \(-0.324363\pi\) | ||||
0.524204 | + | 0.851592i | \(0.324363\pi\) | |||||||
\(102\) | 5.32674 | 0.527426 | ||||||||
\(103\) | −16.9817 | −1.67326 | −0.836630 | − | 0.547769i | \(-0.815477\pi\) | ||||
−0.836630 | + | 0.547769i | \(0.815477\pi\) | |||||||
\(104\) | 1.06379 | 0.104313 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.69527 | −0.844559 | ||||||||
\(107\) | −1.79036 | −0.173081 | −0.0865405 | − | 0.996248i | \(-0.527581\pi\) | ||||
−0.0865405 | + | 0.996248i | \(0.527581\pi\) | |||||||
\(108\) | 4.75905 | 0.457940 | ||||||||
\(109\) | 2.41404 | 0.231223 | 0.115611 | − | 0.993295i | \(-0.463117\pi\) | ||||
0.115611 | + | 0.993295i | \(0.463117\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −31.6860 | −3.00750 | ||||||||
\(112\) | −4.69527 | −0.443661 | ||||||||
\(113\) | 7.14585 | 0.672225 | 0.336112 | − | 0.941822i | \(-0.390888\pi\) | ||||
0.336112 | + | 0.941822i | \(0.390888\pi\) | |||||||
\(114\) | −2.77733 | −0.260120 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.93621 | 0.272620 | ||||||||
\(117\) | 5.01420 | 0.463563 | ||||||||
\(118\) | −5.63148 | −0.518420 | ||||||||
\(119\) | −9.00523 | −0.825508 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.0728 | 2.73389 | ||||||||
\(122\) | −3.39053 | −0.306964 | ||||||||
\(123\) | −3.18239 | −0.286947 | ||||||||
\(124\) | −5.55465 | −0.498822 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −22.1313 | −1.97161 | ||||||||
\(127\) | 9.26295 | 0.821954 | 0.410977 | − | 0.911646i | \(-0.365188\pi\) | ||||
0.410977 | + | 0.911646i | \(0.365188\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.87242 | −0.869219 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5181 | 1.00634 | 0.503171 | − | 0.864187i | \(-0.332167\pi\) | ||||
0.503171 | + | 0.864187i | \(0.332167\pi\) | |||||||
\(132\) | 17.7993 | 1.54923 | ||||||||
\(133\) | 4.69527 | 0.407131 | ||||||||
\(134\) | −8.82284 | −0.762177 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.91794 | 0.164462 | ||||||||
\(137\) | 15.1041 | 1.29043 | 0.645214 | − | 0.764002i | \(-0.276768\pi\) | ||||
0.645214 | + | 0.764002i | \(0.276768\pi\) | |||||||
\(138\) | 4.98696 | 0.424518 | ||||||||
\(139\) | −0.700500 | −0.0594156 | −0.0297078 | − | 0.999559i | \(-0.509458\pi\) | ||||
−0.0297078 | + | 0.999559i | \(0.509458\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30.0948 | 2.53444 | ||||||||
\(142\) | −1.42708 | −0.119758 | ||||||||
\(143\) | 6.81761 | 0.570117 | ||||||||
\(144\) | 4.71354 | 0.392795 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.6132 | −1.04388 | ||||||||
\(147\) | 41.7863 | 3.44648 | ||||||||
\(148\) | −11.4088 | −0.937798 | ||||||||
\(149\) | 12.9452 | 1.06051 | 0.530255 | − | 0.847838i | \(-0.322096\pi\) | ||||
0.530255 | + | 0.847838i | \(0.322096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.70830 | 0.464535 | 0.232268 | − | 0.972652i | \(-0.425385\pi\) | ||||
0.232268 | + | 0.972652i | \(0.425385\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 9.04028 | 0.730863 | ||||||||
\(154\) | −30.0910 | −2.42480 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.95449 | 0.236548 | ||||||||
\(157\) | 9.26295 | 0.739264 | 0.369632 | − | 0.929178i | \(-0.379484\pi\) | ||||
0.369632 | + | 0.929178i | \(0.379484\pi\) | |||||||
\(158\) | −1.96345 | −0.156204 | ||||||||
\(159\) | −24.1496 | −1.91519 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.43081 | −0.664441 | ||||||||
\(162\) | −0.923174 | −0.0725314 | ||||||||
\(163\) | 4.28123 | 0.335332 | 0.167666 | − | 0.985844i | \(-0.446377\pi\) | ||||
0.167666 | + | 0.985844i | \(0.446377\pi\) | |||||||
\(164\) | −1.14585 | −0.0894757 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.2447 | 1.26083 | ||||||||
\(167\) | −15.2264 | −1.17825 | −0.589127 | − | 0.808040i | \(-0.700528\pi\) | ||||
−0.589127 | + | 0.808040i | \(0.700528\pi\) | |||||||
\(168\) | −13.0403 | −1.00608 | ||||||||
\(169\) | −11.8684 | −0.912950 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.71354 | −0.360453 | ||||||||
\(172\) | −3.55465 | −0.271040 | ||||||||
\(173\) | −12.2630 | −0.932335 | −0.466168 | − | 0.884696i | \(-0.654366\pi\) | ||||
−0.466168 | + | 0.884696i | \(0.654366\pi\) | |||||||
\(174\) | 8.15482 | 0.618215 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.40880 | 0.483082 | ||||||||
\(177\) | −15.6404 | −1.17561 | ||||||||
\(178\) | −10.0000 | −0.749532 | ||||||||
\(179\) | −1.57292 | −0.117566 | −0.0587829 | − | 0.998271i | \(-0.518722\pi\) | ||||
−0.0587829 | + | 0.998271i | \(0.518722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4088 | 0.848010 | 0.424005 | − | 0.905660i | \(-0.360624\pi\) | ||||
0.424005 | + | 0.905660i | \(0.360624\pi\) | |||||||
\(182\) | −4.99477 | −0.370237 | ||||||||
\(183\) | −9.41661 | −0.696096 | ||||||||
\(184\) | 1.79560 | 0.132373 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.4271 | −1.13117 | ||||||||
\(187\) | 12.2917 | 0.898858 | ||||||||
\(188\) | 10.8359 | 0.790288 | ||||||||
\(189\) | −22.3450 | −1.62536 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.35805 | −0.460053 | −0.230026 | − | 0.973184i | \(-0.573881\pi\) | ||||
−0.230026 | + | 0.973184i | \(0.573881\pi\) | |||||||
\(192\) | 2.77733 | 0.200436 | ||||||||
\(193\) | 14.4998 | 1.04372 | 0.521860 | − | 0.853031i | \(-0.325238\pi\) | ||||
0.521860 | + | 0.853031i | \(0.325238\pi\) | |||||||
\(194\) | −14.9452 | −1.07300 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.0455 | 1.07468 | ||||||||
\(197\) | −5.14585 | −0.366627 | −0.183313 | − | 0.983055i | \(-0.558682\pi\) | ||||
−0.183313 | + | 0.983055i | \(0.558682\pi\) | |||||||
\(198\) | 30.2081 | 2.14680 | ||||||||
\(199\) | 3.87766 | 0.274880 | 0.137440 | − | 0.990510i | \(-0.456113\pi\) | ||||
0.137440 | + | 0.990510i | \(0.456113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.5039 | −1.72837 | ||||||||
\(202\) | 10.5364 | 0.741337 | ||||||||
\(203\) | −13.7863 | −0.967608 | ||||||||
\(204\) | 5.32674 | 0.372947 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.9817 | −1.18317 | ||||||||
\(207\) | 8.46362 | 0.588262 | ||||||||
\(208\) | 1.06379 | 0.0737604 | ||||||||
\(209\) | −6.40880 | −0.443306 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1496 | 1.18063 | 0.590313 | − | 0.807174i | \(-0.299004\pi\) | ||||
0.590313 | + | 0.807174i | \(0.299004\pi\) | |||||||
\(212\) | −8.69527 | −0.597193 | ||||||||
\(213\) | −3.96345 | −0.271571 | ||||||||
\(214\) | −1.79036 | −0.122387 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.75905 | 0.323813 | ||||||||
\(217\) | 26.0806 | 1.77046 | ||||||||
\(218\) | 2.41404 | 0.163499 | ||||||||
\(219\) | −35.0310 | −2.36717 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.04028 | 0.137244 | ||||||||
\(222\) | −31.6860 | −2.12662 | ||||||||
\(223\) | 7.84635 | 0.525430 | 0.262715 | − | 0.964873i | \(-0.415382\pi\) | ||||
0.262715 | + | 0.964873i | \(0.415382\pi\) | |||||||
\(224\) | −4.69527 | −0.313716 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.14585 | 0.475335 | ||||||||
\(227\) | 6.28646 | 0.417247 | 0.208624 | − | 0.977996i | \(-0.433102\pi\) | ||||
0.208624 | + | 0.977996i | \(0.433102\pi\) | |||||||
\(228\) | −2.77733 | −0.183933 | ||||||||
\(229\) | −3.14585 | −0.207884 | −0.103942 | − | 0.994583i | \(-0.533146\pi\) | ||||
−0.103942 | + | 0.994583i | \(0.533146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −83.5726 | −5.49867 | ||||||||
\(232\) | 2.93621 | 0.192772 | ||||||||
\(233\) | 0.182394 | 0.0119490 | 0.00597451 | − | 0.999982i | \(-0.498098\pi\) | ||||
0.00597451 | + | 0.999982i | \(0.498098\pi\) | |||||||
\(234\) | 5.01420 | 0.327789 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.63148 | −0.366578 | ||||||||
\(237\) | −5.45315 | −0.354220 | ||||||||
\(238\) | −9.00523 | −0.583723 | ||||||||
\(239\) | −11.5039 | −0.744126 | −0.372063 | − | 0.928208i | \(-0.621349\pi\) | ||||
−0.372063 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.445349 | −0.0286874 | −0.0143437 | − | 0.999897i | \(-0.504566\pi\) | ||||
−0.0143437 | + | 0.999897i | \(0.504566\pi\) | |||||||
\(242\) | 30.0728 | 1.93315 | ||||||||
\(243\) | −16.8411 | −1.08036 | ||||||||
\(244\) | −3.39053 | −0.217056 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.18239 | −0.202902 | ||||||||
\(247\) | −1.06379 | −0.0676872 | ||||||||
\(248\) | −5.55465 | −0.352721 | ||||||||
\(249\) | 45.1168 | 2.85916 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.2630 | 0.837150 | 0.418575 | − | 0.908182i | \(-0.362530\pi\) | ||||
0.418575 | + | 0.908182i | \(0.362530\pi\) | |||||||
\(252\) | −22.1313 | −1.39414 | ||||||||
\(253\) | 11.5076 | 0.723479 | ||||||||
\(254\) | 9.26295 | 0.581209 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.4816 | −1.46474 | −0.732370 | − | 0.680907i | \(-0.761586\pi\) | ||||
−0.732370 | + | 0.680907i | \(0.761586\pi\) | |||||||
\(258\) | −9.87242 | −0.614630 | ||||||||
\(259\) | 53.5674 | 3.32851 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.8399 | 0.856671 | ||||||||
\(262\) | 11.5181 | 0.711591 | ||||||||
\(263\) | 27.9269 | 1.72205 | 0.861023 | − | 0.508565i | \(-0.169824\pi\) | ||||
0.861023 | + | 0.508565i | \(0.169824\pi\) | |||||||
\(264\) | 17.7993 | 1.09547 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.69527 | 0.287885 | ||||||||
\(267\) | −27.7733 | −1.69970 | ||||||||
\(268\) | −8.82284 | −0.538941 | ||||||||
\(269\) | 16.4816 | 1.00490 | 0.502449 | − | 0.864607i | \(-0.332432\pi\) | ||||
0.502449 | + | 0.864607i | \(0.332432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.46736 | −0.0891356 | −0.0445678 | − | 0.999006i | \(-0.514191\pi\) | ||||
−0.0445678 | + | 0.999006i | \(0.514191\pi\) | |||||||
\(272\) | 1.91794 | 0.116292 | ||||||||
\(273\) | −13.8721 | −0.839577 | ||||||||
\(274\) | 15.1041 | 0.912470 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.98696 | 0.300180 | ||||||||
\(277\) | 15.8359 | 0.951486 | 0.475743 | − | 0.879584i | \(-0.342179\pi\) | ||||
0.475743 | + | 0.879584i | \(0.342179\pi\) | |||||||
\(278\) | −0.700500 | −0.0420132 | ||||||||
\(279\) | −26.1821 | −1.56748 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.25515 | −0.373151 | −0.186576 | − | 0.982441i | \(-0.559739\pi\) | ||||
−0.186576 | + | 0.982441i | \(0.559739\pi\) | |||||||
\(282\) | 30.0948 | 1.79212 | ||||||||
\(283\) | −16.7005 | −0.992742 | −0.496371 | − | 0.868111i | \(-0.665334\pi\) | ||||
−0.496371 | + | 0.868111i | \(0.665334\pi\) | |||||||
\(284\) | −1.42708 | −0.0846814 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.81761 | 0.403134 | ||||||||
\(287\) | 5.38006 | 0.317575 | ||||||||
\(288\) | 4.71354 | 0.277748 | ||||||||
\(289\) | −13.3215 | −0.783618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −41.5076 | −2.43322 | ||||||||
\(292\) | −12.6132 | −0.738132 | ||||||||
\(293\) | 0.644516 | 0.0376530 | 0.0188265 | − | 0.999823i | \(-0.494007\pi\) | ||||
0.0188265 | + | 0.999823i | \(0.494007\pi\) | |||||||
\(294\) | 41.7863 | 2.43703 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.4088 | −0.663123 | ||||||||
\(297\) | 30.4998 | 1.76978 | ||||||||
\(298\) | 12.9452 | 0.749894 | ||||||||
\(299\) | 1.91014 | 0.110466 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6900 | 0.961997 | ||||||||
\(302\) | 5.70830 | 0.328476 | ||||||||
\(303\) | 29.2630 | 1.68111 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.04028 | 0.516798 | ||||||||
\(307\) | 26.6457 | 1.52075 | 0.760375 | − | 0.649485i | \(-0.225015\pi\) | ||||
0.760375 | + | 0.649485i | \(0.225015\pi\) | |||||||
\(308\) | −30.0910 | −1.71460 | ||||||||
\(309\) | −47.1638 | −2.68305 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5494 | 0.654907 | 0.327454 | − | 0.944867i | \(-0.393809\pi\) | ||||
0.327454 | + | 0.944867i | \(0.393809\pi\) | |||||||
\(312\) | 2.95449 | 0.167265 | ||||||||
\(313\) | −23.0638 | −1.30364 | −0.651821 | − | 0.758373i | \(-0.725995\pi\) | ||||
−0.651821 | + | 0.758373i | \(0.725995\pi\) | |||||||
\(314\) | 9.26295 | 0.522739 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.96345 | −0.110453 | ||||||||
\(317\) | −13.9232 | −0.782003 | −0.391002 | − | 0.920390i | \(-0.627871\pi\) | ||||
−0.391002 | + | 0.920390i | \(0.627871\pi\) | |||||||
\(318\) | −24.1496 | −1.35424 | ||||||||
\(319\) | 18.8176 | 1.05358 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.97242 | −0.277534 | ||||||||
\(322\) | −8.43081 | −0.469831 | ||||||||
\(323\) | −1.91794 | −0.106717 | ||||||||
\(324\) | −0.923174 | −0.0512874 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.28123 | 0.237115 | ||||||||
\(327\) | 6.70457 | 0.370763 | ||||||||
\(328\) | −1.14585 | −0.0632689 | ||||||||
\(329\) | −50.8773 | −2.80496 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.735546 | −0.0404292 | −0.0202146 | − | 0.999796i | \(-0.506435\pi\) | ||||
−0.0202146 | + | 0.999796i | \(0.506435\pi\) | |||||||
\(332\) | 16.2447 | 0.891543 | ||||||||
\(333\) | −53.7758 | −2.94690 | ||||||||
\(334\) | −15.2264 | −0.833152 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13.0403 | −0.711406 | ||||||||
\(337\) | −2.28123 | −0.124266 | −0.0621332 | − | 0.998068i | \(-0.519790\pi\) | ||||
−0.0621332 | + | 0.998068i | \(0.519790\pi\) | |||||||
\(338\) | −11.8684 | −0.645553 | ||||||||
\(339\) | 19.8463 | 1.07791 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.5987 | −1.92778 | ||||||||
\(342\) | −4.71354 | −0.254879 | ||||||||
\(343\) | −37.7758 | −2.03970 | ||||||||
\(344\) | −3.55465 | −0.191654 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.2630 | −0.659261 | ||||||||
\(347\) | −2.56246 | −0.137560 | −0.0687799 | − | 0.997632i | \(-0.521911\pi\) | ||||
−0.0687799 | + | 0.997632i | \(0.521911\pi\) | |||||||
\(348\) | 8.15482 | 0.437144 | ||||||||
\(349\) | −5.67176 | −0.303602 | −0.151801 | − | 0.988411i | \(-0.548507\pi\) | ||||
−0.151801 | + | 0.988411i | \(0.548507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.06262 | 0.270223 | ||||||||
\(352\) | 6.40880 | 0.341590 | ||||||||
\(353\) | −23.6665 | −1.25964 | −0.629821 | − | 0.776740i | \(-0.716872\pi\) | ||||
−0.629821 | + | 0.776740i | \(0.716872\pi\) | |||||||
\(354\) | −15.6404 | −0.831280 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | −25.0105 | −1.32369 | ||||||||
\(358\) | −1.57292 | −0.0831316 | ||||||||
\(359\) | 31.9724 | 1.68744 | 0.843720 | − | 0.536784i | \(-0.180361\pi\) | ||||
0.843720 | + | 0.536784i | \(0.180361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 11.4088 | 0.599633 | ||||||||
\(363\) | 83.5218 | 4.38376 | ||||||||
\(364\) | −4.99477 | −0.261797 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.41661 | −0.492214 | ||||||||
\(367\) | 1.14585 | 0.0598128 | 0.0299064 | − | 0.999553i | \(-0.490479\pi\) | ||||
0.0299064 | + | 0.999553i | \(0.490479\pi\) | |||||||
\(368\) | 1.79560 | 0.0936020 | ||||||||
\(369\) | −5.40100 | −0.281165 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.8266 | 2.11961 | ||||||||
\(372\) | −15.4271 | −0.799857 | ||||||||
\(373\) | 32.8579 | 1.70132 | 0.850658 | − | 0.525719i | \(-0.176204\pi\) | ||||
0.850658 | + | 0.525719i | \(0.176204\pi\) | |||||||
\(374\) | 12.2917 | 0.635588 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.8359 | 0.558818 | ||||||||
\(377\) | 3.12351 | 0.160869 | ||||||||
\(378\) | −22.3450 | −1.14930 | ||||||||
\(379\) | −18.2865 | −0.939312 | −0.469656 | − | 0.882849i | \(-0.655622\pi\) | ||||
−0.469656 | + | 0.882849i | \(0.655622\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.7262 | 1.31800 | ||||||||
\(382\) | −6.35805 | −0.325306 | ||||||||
\(383\) | 20.8542 | 1.06560 | 0.532799 | − | 0.846242i | \(-0.321140\pi\) | ||||
0.532799 | + | 0.846242i | \(0.321140\pi\) | |||||||
\(384\) | 2.77733 | 0.141730 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.4998 | 0.738022 | ||||||||
\(387\) | −16.7550 | −0.851704 | ||||||||
\(388\) | −14.9452 | −0.758727 | ||||||||
\(389\) | −24.9086 | −1.26292 | −0.631459 | − | 0.775409i | \(-0.717544\pi\) | ||||
−0.631459 | + | 0.775409i | \(0.717544\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.44385 | 0.174163 | ||||||||
\(392\) | 15.0455 | 0.759913 | ||||||||
\(393\) | 31.9895 | 1.61366 | ||||||||
\(394\) | −5.14585 | −0.259244 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 30.2081 | 1.51802 | ||||||||
\(397\) | −24.7445 | −1.24189 | −0.620946 | − | 0.783853i | \(-0.713251\pi\) | ||||
−0.620946 | + | 0.783853i | \(0.713251\pi\) | |||||||
\(398\) | 3.87766 | 0.194369 | ||||||||
\(399\) | 13.0403 | 0.652831 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.6457 | 0.781308 | 0.390654 | − | 0.920538i | \(-0.372249\pi\) | ||||
0.390654 | + | 0.920538i | \(0.372249\pi\) | |||||||
\(402\) | −24.5039 | −1.22214 | ||||||||
\(403\) | −5.90897 | −0.294347 | ||||||||
\(404\) | 10.5364 | 0.524204 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.7863 | −0.684202 | ||||||||
\(407\) | −73.1168 | −3.62426 | ||||||||
\(408\) | 5.32674 | 0.263713 | ||||||||
\(409\) | 30.5804 | 1.51210 | 0.756052 | − | 0.654512i | \(-0.227126\pi\) | ||||
0.756052 | + | 0.654512i | \(0.227126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.9489 | 2.06919 | ||||||||
\(412\) | −16.9817 | −0.836630 | ||||||||
\(413\) | 26.4413 | 1.30109 | ||||||||
\(414\) | 8.46362 | 0.415964 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.06379 | 0.0521565 | ||||||||
\(417\) | −1.94552 | −0.0952723 | ||||||||
\(418\) | −6.40880 | −0.313465 | ||||||||
\(419\) | 1.96345 | 0.0959210 | 0.0479605 | − | 0.998849i | \(-0.484728\pi\) | ||||
0.0479605 | + | 0.998849i | \(0.484728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.5949 | −1.24742 | −0.623710 | − | 0.781656i | \(-0.714376\pi\) | ||||
−0.623710 | + | 0.781656i | \(0.714376\pi\) | |||||||
\(422\) | 17.1496 | 0.834829 | ||||||||
\(423\) | 51.0753 | 2.48337 | ||||||||
\(424\) | −8.69527 | −0.422279 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.96345 | −0.192030 | ||||||||
\(427\) | 15.9194 | 0.770396 | ||||||||
\(428\) | −1.79036 | −0.0865405 | ||||||||
\(429\) | 18.9347 | 0.914177 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3540 | −0.739575 | −0.369788 | − | 0.929116i | \(-0.620570\pi\) | ||||
−0.369788 | + | 0.929116i | \(0.620570\pi\) | |||||||
\(432\) | 4.75905 | 0.228970 | ||||||||
\(433\) | 16.6640 | 0.800819 | 0.400409 | − | 0.916336i | \(-0.368868\pi\) | ||||
0.400409 | + | 0.916336i | \(0.368868\pi\) | |||||||
\(434\) | 26.0806 | 1.25191 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.41404 | 0.115611 | ||||||||
\(437\) | −1.79560 | −0.0858951 | ||||||||
\(438\) | −35.0310 | −1.67384 | ||||||||
\(439\) | −19.5987 | −0.935393 | −0.467697 | − | 0.883889i | \(-0.654916\pi\) | ||||
−0.467697 | + | 0.883889i | \(0.654916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 70.9176 | 3.37703 | ||||||||
\(442\) | 2.04028 | 0.0970462 | ||||||||
\(443\) | 13.0183 | 0.618517 | 0.309258 | − | 0.950978i | \(-0.399919\pi\) | ||||
0.309258 | + | 0.950978i | \(0.399919\pi\) | |||||||
\(444\) | −31.6860 | −1.50375 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.84635 | 0.371535 | ||||||||
\(447\) | 35.9530 | 1.70052 | ||||||||
\(448\) | −4.69527 | −0.221830 | ||||||||
\(449\) | 6.77359 | 0.319666 | 0.159833 | − | 0.987144i | \(-0.448905\pi\) | ||||
0.159833 | + | 0.987144i | \(0.448905\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.34352 | −0.345793 | ||||||||
\(452\) | 7.14585 | 0.336112 | ||||||||
\(453\) | 15.8538 | 0.744877 | ||||||||
\(454\) | 6.28646 | 0.295038 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.77733 | −0.130060 | ||||||||
\(457\) | −27.3189 | −1.27793 | −0.638963 | − | 0.769237i | \(-0.720636\pi\) | ||||
−0.638963 | + | 0.769237i | \(0.720636\pi\) | |||||||
\(458\) | −3.14585 | −0.146996 | ||||||||
\(459\) | 9.12758 | 0.426039 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.7993 | −1.29474 | −0.647372 | − | 0.762174i | \(-0.724132\pi\) | ||||
−0.647372 | + | 0.762174i | \(0.724132\pi\) | |||||||
\(462\) | −83.5726 | −3.88815 | ||||||||
\(463\) | 38.2369 | 1.77702 | 0.888509 | − | 0.458859i | \(-0.151742\pi\) | ||||
0.888509 | + | 0.458859i | \(0.151742\pi\) | |||||||
\(464\) | 2.93621 | 0.136310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.182394 | 0.00844923 | ||||||||
\(467\) | 23.4711 | 1.08611 | 0.543056 | − | 0.839696i | \(-0.317267\pi\) | ||||
0.543056 | + | 0.839696i | \(0.317267\pi\) | |||||||
\(468\) | 5.01420 | 0.231782 | ||||||||
\(469\) | 41.4256 | 1.91286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.7262 | 1.18540 | ||||||||
\(472\) | −5.63148 | −0.259210 | ||||||||
\(473\) | −22.7811 | −1.04747 | ||||||||
\(474\) | −5.45315 | −0.250472 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.00523 | −0.412754 | ||||||||
\(477\) | −40.9855 | −1.87660 | ||||||||
\(478\) | −11.5039 | −0.526176 | ||||||||
\(479\) | −19.6900 | −0.899660 | −0.449830 | − | 0.893114i | \(-0.648516\pi\) | ||||
−0.449830 | + | 0.893114i | \(0.648516\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.1365 | −0.553379 | ||||||||
\(482\) | −0.445349 | −0.0202851 | ||||||||
\(483\) | −23.4151 | −1.06542 | ||||||||
\(484\) | 30.0728 | 1.36694 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −16.8411 | −0.763928 | ||||||||
\(487\) | 16.3357 | 0.740242 | 0.370121 | − | 0.928984i | \(-0.379316\pi\) | ||||
0.370121 | + | 0.928984i | \(0.379316\pi\) | |||||||
\(488\) | −3.39053 | −0.153482 | ||||||||
\(489\) | 11.8904 | 0.537701 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.1093 | 1.22343 | 0.611713 | − | 0.791080i | \(-0.290481\pi\) | ||||
0.611713 | + | 0.791080i | \(0.290481\pi\) | |||||||
\(492\) | −3.18239 | −0.143473 | ||||||||
\(493\) | 5.63148 | 0.253629 | ||||||||
\(494\) | −1.06379 | −0.0478621 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.55465 | −0.249411 | ||||||||
\(497\) | 6.70050 | 0.300558 | ||||||||
\(498\) | 45.1168 | 2.02173 | ||||||||
\(499\) | −4.69003 | −0.209955 | −0.104977 | − | 0.994475i | \(-0.533477\pi\) | ||||
−0.104977 | + | 0.994475i | \(0.533477\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.2887 | −1.88932 | ||||||||
\(502\) | 13.2630 | 0.591955 | ||||||||
\(503\) | 5.19136 | 0.231471 | 0.115736 | − | 0.993280i | \(-0.463077\pi\) | ||||
0.115736 | + | 0.993280i | \(0.463077\pi\) | |||||||
\(504\) | −22.1313 | −0.985807 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.5076 | 0.511577 | ||||||||
\(507\) | −32.9623 | −1.46391 | ||||||||
\(508\) | 9.26295 | 0.410977 | ||||||||
\(509\) | −4.51811 | −0.200262 | −0.100131 | − | 0.994974i | \(-0.531926\pi\) | ||||
−0.100131 | + | 0.994974i | \(0.531926\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.2223 | 2.61984 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.75905 | −0.210117 | ||||||||
\(514\) | −23.4816 | −1.03573 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.87242 | −0.434609 | ||||||||
\(517\) | 69.4450 | 3.05419 | ||||||||
\(518\) | 53.5674 | 2.35361 | ||||||||
\(519\) | −34.0582 | −1.49499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.4453 | 0.632862 | 0.316431 | − | 0.948615i | \(-0.397515\pi\) | ||||
0.316431 | + | 0.948615i | \(0.397515\pi\) | |||||||
\(522\) | 13.8399 | 0.605758 | ||||||||
\(523\) | −18.2134 | −0.796415 | −0.398208 | − | 0.917295i | \(-0.630368\pi\) | ||||
−0.398208 | + | 0.917295i | \(0.630368\pi\) | |||||||
\(524\) | 11.5181 | 0.503171 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.9269 | 1.21767 | ||||||||
\(527\) | −10.6535 | −0.464073 | ||||||||
\(528\) | 17.7993 | 0.774617 | ||||||||
\(529\) | −19.7758 | −0.859819 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.5442 | −1.15192 | ||||||||
\(532\) | 4.69527 | 0.203566 | ||||||||
\(533\) | −1.21894 | −0.0527981 | ||||||||
\(534\) | −27.7733 | −1.20187 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.82284 | −0.381089 | ||||||||
\(537\) | −4.36852 | −0.188516 | ||||||||
\(538\) | 16.4816 | 0.710571 | ||||||||
\(539\) | 96.4237 | 4.15326 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.3905 | 1.60754 | 0.803772 | − | 0.594937i | \(-0.202823\pi\) | ||||
0.803772 | + | 0.594937i | \(0.202823\pi\) | |||||||
\(542\) | −1.46736 | −0.0630284 | ||||||||
\(543\) | 31.6860 | 1.35977 | ||||||||
\(544\) | 1.91794 | 0.0822310 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.8721 | −0.593671 | ||||||||
\(547\) | 29.5621 | 1.26399 | 0.631993 | − | 0.774974i | \(-0.282237\pi\) | ||||
0.631993 | + | 0.774974i | \(0.282237\pi\) | |||||||
\(548\) | 15.1041 | 0.645214 | ||||||||
\(549\) | −15.9814 | −0.682069 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.93621 | −0.125087 | ||||||||
\(552\) | 4.98696 | 0.212259 | ||||||||
\(553\) | 9.21894 | 0.392029 | ||||||||
\(554\) | 15.8359 | 0.672802 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.700500 | −0.0297078 | ||||||||
\(557\) | 14.3723 | 0.608972 | 0.304486 | − | 0.952517i | \(-0.401515\pi\) | ||||
0.304486 | + | 0.952517i | \(0.401515\pi\) | |||||||
\(558\) | −26.1821 | −1.10837 | ||||||||
\(559\) | −3.78139 | −0.159936 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.1380 | 1.44131 | ||||||||
\(562\) | −6.25515 | −0.263858 | ||||||||
\(563\) | −6.39053 | −0.269329 | −0.134664 | − | 0.990891i | \(-0.542996\pi\) | ||||
−0.134664 | + | 0.990891i | \(0.542996\pi\) | |||||||
\(564\) | 30.0948 | 1.26722 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.7005 | −0.701974 | ||||||||
\(567\) | 4.33455 | 0.182034 | ||||||||
\(568\) | −1.42708 | −0.0598788 | ||||||||
\(569\) | −44.9086 | −1.88267 | −0.941334 | − | 0.337476i | \(-0.890427\pi\) | ||||
−0.941334 | + | 0.337476i | \(0.890427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.4193 | 0.519730 | 0.259865 | − | 0.965645i | \(-0.416322\pi\) | ||||
0.259865 | + | 0.965645i | \(0.416322\pi\) | |||||||
\(572\) | 6.81761 | 0.285058 | ||||||||
\(573\) | −17.6584 | −0.737690 | ||||||||
\(574\) | 5.38006 | 0.224559 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.71354 | 0.196397 | ||||||||
\(577\) | −4.20440 | −0.175032 | −0.0875158 | − | 0.996163i | \(-0.527893\pi\) | ||||
−0.0875158 | + | 0.996163i | \(0.527893\pi\) | |||||||
\(578\) | −13.3215 | −0.554102 | ||||||||
\(579\) | 40.2708 | 1.67360 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −76.2731 | −3.16434 | ||||||||
\(582\) | −41.5076 | −1.72055 | ||||||||
\(583\) | −55.7262 | −2.30795 | ||||||||
\(584\) | −12.6132 | −0.521938 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.644516 | 0.0266247 | ||||||||
\(587\) | 24.7915 | 1.02326 | 0.511628 | − | 0.859207i | \(-0.329043\pi\) | ||||
0.511628 | + | 0.859207i | \(0.329043\pi\) | |||||||
\(588\) | 41.7863 | 1.72324 | ||||||||
\(589\) | 5.55465 | 0.228875 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.2917 | −0.587882 | ||||||||
\(592\) | −11.4088 | −0.468899 | ||||||||
\(593\) | 4.67176 | 0.191846 | 0.0959231 | − | 0.995389i | \(-0.469420\pi\) | ||||
0.0959231 | + | 0.995389i | \(0.469420\pi\) | |||||||
\(594\) | 30.4998 | 1.25142 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.9452 | 0.530255 | ||||||||
\(597\) | 10.7695 | 0.440767 | ||||||||
\(598\) | 1.91014 | 0.0781113 | ||||||||
\(599\) | 39.2369 | 1.60318 | 0.801588 | − | 0.597877i | \(-0.203989\pi\) | ||||
0.801588 | + | 0.597877i | \(0.203989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.4267 | −1.73062 | −0.865311 | − | 0.501235i | \(-0.832879\pi\) | ||||
−0.865311 | + | 0.501235i | \(0.832879\pi\) | |||||||
\(602\) | 16.6900 | 0.680235 | ||||||||
\(603\) | −41.5868 | −1.69355 | ||||||||
\(604\) | 5.70830 | 0.232268 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 29.2630 | 1.18873 | ||||||||
\(607\) | −2.98173 | −0.121025 | −0.0605123 | − | 0.998167i | \(-0.519273\pi\) | ||||
−0.0605123 | + | 0.998167i | \(0.519273\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −38.2890 | −1.55155 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.5271 | 0.466336 | ||||||||
\(612\) | 9.04028 | 0.365432 | ||||||||
\(613\) | −28.9452 | −1.16908 | −0.584542 | − | 0.811363i | \(-0.698726\pi\) | ||||
−0.584542 | + | 0.811363i | \(0.698726\pi\) | |||||||
\(614\) | 26.6457 | 1.07533 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.0910 | −1.21240 | ||||||||
\(617\) | −15.0365 | −0.605349 | −0.302674 | − | 0.953094i | \(-0.597879\pi\) | ||||
−0.302674 | + | 0.953094i | \(0.597879\pi\) | |||||||
\(618\) | −47.1638 | −1.89721 | ||||||||
\(619\) | 8.25515 | 0.331803 | 0.165901 | − | 0.986142i | \(-0.446947\pi\) | ||||
0.165901 | + | 0.986142i | \(0.446947\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.54535 | 0.342913 | ||||||||
\(622\) | 11.5494 | 0.463089 | ||||||||
\(623\) | 46.9527 | 1.88112 | ||||||||
\(624\) | 2.95449 | 0.118274 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −23.0638 | −0.921814 | ||||||||
\(627\) | −17.7993 | −0.710837 | ||||||||
\(628\) | 9.26295 | 0.369632 | ||||||||
\(629\) | −21.8814 | −0.872468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.09103 | −0.361908 | −0.180954 | − | 0.983492i | \(-0.557919\pi\) | ||||
−0.180954 | + | 0.983492i | \(0.557919\pi\) | |||||||
\(632\) | −1.96345 | −0.0781020 | ||||||||
\(633\) | 47.6300 | 1.89312 | ||||||||
\(634\) | −13.9232 | −0.552960 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −24.1496 | −0.957593 | ||||||||
\(637\) | 16.0052 | 0.634150 | ||||||||
\(638\) | 18.8176 | 0.744996 | ||||||||
\(639\) | −6.72658 | −0.266099 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.1171 | 1.18955 | 0.594777 | − | 0.803891i | \(-0.297240\pi\) | ||||
0.594777 | + | 0.803891i | \(0.297240\pi\) | |||||||
\(642\) | −4.97242 | −0.196246 | ||||||||
\(643\) | −35.3174 | −1.39278 | −0.696392 | − | 0.717662i | \(-0.745212\pi\) | ||||
−0.696392 | + | 0.717662i | \(0.745212\pi\) | |||||||
\(644\) | −8.43081 | −0.332220 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.91794 | −0.0754603 | ||||||||
\(647\) | 4.12234 | 0.162066 | 0.0810330 | − | 0.996711i | \(-0.474178\pi\) | ||||
0.0810330 | + | 0.996711i | \(0.474178\pi\) | |||||||
\(648\) | −0.923174 | −0.0362657 | ||||||||
\(649\) | −36.0910 | −1.41670 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 72.4342 | 2.83892 | ||||||||
\(652\) | 4.28123 | 0.167666 | ||||||||
\(653\) | 8.62741 | 0.337617 | 0.168808 | − | 0.985649i | \(-0.446008\pi\) | ||||
0.168808 | + | 0.985649i | \(0.446008\pi\) | |||||||
\(654\) | 6.70457 | 0.262169 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.14585 | −0.0447379 | ||||||||
\(657\) | −59.4528 | −2.31948 | ||||||||
\(658\) | −50.8773 | −1.98340 | ||||||||
\(659\) | −37.3853 | −1.45632 | −0.728162 | − | 0.685405i | \(-0.759625\pi\) | ||||
−0.728162 | + | 0.685405i | \(0.759625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8997 | −0.501739 | −0.250869 | − | 0.968021i | \(-0.580716\pi\) | ||||
−0.250869 | + | 0.968021i | \(0.580716\pi\) | |||||||
\(662\) | −0.735546 | −0.0285878 | ||||||||
\(663\) | 5.66652 | 0.220070 | ||||||||
\(664\) | 16.2447 | 0.630416 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −53.7758 | −2.08377 | ||||||||
\(667\) | 5.27226 | 0.204143 | ||||||||
\(668\) | −15.2264 | −0.589127 | ||||||||
\(669\) | 21.7919 | 0.842522 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.7292 | −0.838848 | ||||||||
\(672\) | −13.0403 | −0.503040 | ||||||||
\(673\) | 10.4349 | 0.402235 | 0.201118 | − | 0.979567i | \(-0.435543\pi\) | ||||
0.201118 | + | 0.979567i | \(0.435543\pi\) | |||||||
\(674\) | −2.28123 | −0.0878696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.8684 | −0.456475 | ||||||||
\(677\) | 12.4401 | 0.478112 | 0.239056 | − | 0.971006i | \(-0.423162\pi\) | ||||
0.239056 | + | 0.971006i | \(0.423162\pi\) | |||||||
\(678\) | 19.8463 | 0.762194 | ||||||||
\(679\) | 70.1716 | 2.69294 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4596 | 0.669052 | ||||||||
\(682\) | −35.5987 | −1.36314 | ||||||||
\(683\) | 17.5364 | 0.671011 | 0.335505 | − | 0.942038i | \(-0.391093\pi\) | ||||
0.335505 | + | 0.942038i | \(0.391093\pi\) | |||||||
\(684\) | −4.71354 | −0.180227 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −37.7758 | −1.44229 | ||||||||
\(687\) | −8.73705 | −0.333339 | ||||||||
\(688\) | −3.55465 | −0.135520 | ||||||||
\(689\) | −9.24992 | −0.352394 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.2734 | −0.961446 | −0.480723 | − | 0.876872i | \(-0.659626\pi\) | ||||
−0.480723 | + | 0.876872i | \(0.659626\pi\) | |||||||
\(692\) | −12.2630 | −0.466168 | ||||||||
\(693\) | −141.835 | −5.38787 | ||||||||
\(694\) | −2.56246 | −0.0972695 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.15482 | 0.309108 | ||||||||
\(697\) | −2.19767 | −0.0832426 | ||||||||
\(698\) | −5.67176 | −0.214679 | ||||||||
\(699\) | 0.506567 | 0.0191601 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.0545 | −0.606370 | −0.303185 | − | 0.952932i | \(-0.598050\pi\) | ||||
−0.303185 | + | 0.952932i | \(0.598050\pi\) | |||||||
\(702\) | 5.06262 | 0.191076 | ||||||||
\(703\) | 11.4088 | 0.430291 | ||||||||
\(704\) | 6.40880 | 0.241541 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.6665 | −0.890701 | ||||||||
\(707\) | −49.4711 | −1.86055 | ||||||||
\(708\) | −15.6404 | −0.587804 | ||||||||
\(709\) | 13.5076 | 0.507290 | 0.253645 | − | 0.967297i | \(-0.418371\pi\) | ||||
0.253645 | + | 0.967297i | \(0.418371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.25482 | −0.347083 | ||||||||
\(712\) | −10.0000 | −0.374766 | ||||||||
\(713\) | −9.97392 | −0.373526 | ||||||||
\(714\) | −25.0105 | −0.935993 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.57292 | −0.0587829 | ||||||||
\(717\) | −31.9501 | −1.19320 | ||||||||
\(718\) | 31.9724 | 1.19320 | ||||||||
\(719\) | 0.803402 | 0.0299619 | 0.0149809 | − | 0.999888i | \(-0.495231\pi\) | ||||
0.0149809 | + | 0.999888i | \(0.495231\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 79.7337 | 2.96944 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −1.23688 | −0.0460000 | ||||||||
\(724\) | 11.4088 | 0.424005 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 83.5218 | 3.09979 | ||||||||
\(727\) | 51.6860 | 1.91693 | 0.958463 | − | 0.285217i | \(-0.0920655\pi\) | ||||
0.958463 | + | 0.285217i | \(0.0920655\pi\) | |||||||
\(728\) | −4.99477 | −0.185118 | ||||||||
\(729\) | −44.0037 | −1.62977 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.81761 | −0.252158 | ||||||||
\(732\) | −9.41661 | −0.348048 | ||||||||
\(733\) | −22.3723 | −0.826338 | −0.413169 | − | 0.910654i | \(-0.635578\pi\) | ||||
−0.413169 | + | 0.910654i | \(0.635578\pi\) | |||||||
\(734\) | 1.14585 | 0.0422940 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.79560 | 0.0661866 | ||||||||
\(737\) | −56.5438 | −2.08282 | ||||||||
\(738\) | −5.40100 | −0.198814 | ||||||||
\(739\) | 33.4271 | 1.22963 | 0.614817 | − | 0.788669i | \(-0.289230\pi\) | ||||
0.614817 | + | 0.788669i | \(0.289230\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.95449 | −0.108536 | ||||||||
\(742\) | 40.8266 | 1.49879 | ||||||||
\(743\) | 14.4998 | 0.531947 | 0.265974 | − | 0.963980i | \(-0.414307\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414307\pi\) | |||||||
\(744\) | −15.4271 | −0.565584 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 32.8579 | 1.20301 | ||||||||
\(747\) | 76.5699 | 2.80155 | ||||||||
\(748\) | 12.2917 | 0.449429 | ||||||||
\(749\) | 8.40623 | 0.307157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.6169 | −0.971266 | −0.485633 | − | 0.874163i | \(-0.661411\pi\) | ||||
−0.485633 | + | 0.874163i | \(0.661411\pi\) | |||||||
\(752\) | 10.8359 | 0.395144 | ||||||||
\(753\) | 36.8355 | 1.34236 | ||||||||
\(754\) | 3.12351 | 0.113751 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −22.3450 | −0.812680 | ||||||||
\(757\) | −31.0362 | −1.12803 | −0.564015 | − | 0.825764i | \(-0.690744\pi\) | ||||
−0.564015 | + | 0.825764i | \(0.690744\pi\) | |||||||
\(758\) | −18.2865 | −0.664194 | ||||||||
\(759\) | 31.9605 | 1.16009 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.8083 | −1.00805 | −0.504025 | − | 0.863689i | \(-0.668148\pi\) | ||||
−0.504025 | + | 0.863689i | \(0.668148\pi\) | |||||||
\(762\) | 25.7262 | 0.931963 | ||||||||
\(763\) | −11.3345 | −0.410338 | ||||||||
\(764\) | −6.35805 | −0.230026 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.8542 | 0.753491 | ||||||||
\(767\) | −5.99070 | −0.216312 | ||||||||
\(768\) | 2.77733 | 0.100218 | ||||||||
\(769\) | −19.2279 | −0.693376 | −0.346688 | − | 0.937980i | \(-0.612694\pi\) | ||||
−0.346688 | + | 0.937980i | \(0.612694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.2159 | −2.34869 | ||||||||
\(772\) | 14.4998 | 0.521860 | ||||||||
\(773\) | 6.00373 | 0.215939 | 0.107970 | − | 0.994154i | \(-0.465565\pi\) | ||||
0.107970 | + | 0.994154i | \(0.465565\pi\) | |||||||
\(774\) | −16.7550 | −0.602245 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.9452 | −0.536501 | ||||||||
\(777\) | 148.774 | 5.33724 | ||||||||
\(778\) | −24.9086 | −0.893018 | ||||||||
\(779\) | 1.14585 | 0.0410543 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.14585 | −0.327264 | ||||||||
\(782\) | 3.44385 | 0.123152 | ||||||||
\(783\) | 13.9736 | 0.499375 | ||||||||
\(784\) | 15.0455 | 0.537340 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 31.9895 | 1.14103 | ||||||||
\(787\) | 22.2797 | 0.794187 | 0.397093 | − | 0.917778i | \(-0.370019\pi\) | ||||
0.397093 | + | 0.917778i | \(0.370019\pi\) | |||||||
\(788\) | −5.14585 | −0.183313 | ||||||||
\(789\) | 77.5621 | 2.76128 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.5517 | −1.19296 | ||||||||
\(792\) | 30.2081 | 1.07340 | ||||||||
\(793\) | −3.60680 | −0.128081 | ||||||||
\(794\) | −24.7445 | −0.878150 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.87766 | 0.137440 | ||||||||
\(797\) | 26.6259 | 0.943138 | 0.471569 | − | 0.881829i | \(-0.343688\pi\) | ||||
0.471569 | + | 0.881829i | \(0.343688\pi\) | |||||||
\(798\) | 13.0403 | 0.461621 | ||||||||
\(799\) | 20.7826 | 0.735234 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.1354 | −1.66545 | ||||||||
\(802\) | 15.6457 | 0.552468 | ||||||||
\(803\) | −80.8355 | −2.85262 | ||||||||
\(804\) | −24.5039 | −0.864186 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.90897 | −0.208135 | ||||||||
\(807\) | 45.7747 | 1.61134 | ||||||||
\(808\) | 10.5364 | 0.370669 | ||||||||
\(809\) | 0.651250 | 0.0228967 | 0.0114484 | − | 0.999934i | \(-0.496356\pi\) | ||||
0.0114484 | + | 0.999934i | \(0.496356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0780 | −0.459230 | −0.229615 | − | 0.973281i | \(-0.573747\pi\) | ||||
−0.229615 | + | 0.973281i | \(0.573747\pi\) | |||||||
\(812\) | −13.7863 | −0.483804 | ||||||||
\(813\) | −4.07533 | −0.142928 | ||||||||
\(814\) | −73.1168 | −2.56274 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.32674 | 0.186473 | ||||||||
\(817\) | 3.55465 | 0.124362 | ||||||||
\(818\) | 30.5804 | 1.06922 | ||||||||
\(819\) | −23.5430 | −0.822660 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.6640 | 0.511776 | 0.255888 | − | 0.966706i | \(-0.417632\pi\) | ||||
0.255888 | + | 0.966706i | \(0.417632\pi\) | |||||||
\(822\) | 41.9489 | 1.46314 | ||||||||
\(823\) | −18.2850 | −0.637374 | −0.318687 | − | 0.947860i | \(-0.603242\pi\) | ||||
−0.318687 | + | 0.947860i | \(0.603242\pi\) | |||||||
\(824\) | −16.9817 | −0.591587 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.4413 | 0.920010 | ||||||||
\(827\) | 40.1910 | 1.39758 | 0.698790 | − | 0.715327i | \(-0.253722\pi\) | ||||
0.698790 | + | 0.715327i | \(0.253722\pi\) | |||||||
\(828\) | 8.46362 | 0.294131 | ||||||||
\(829\) | 28.3760 | 0.985539 | 0.492769 | − | 0.870160i | \(-0.335985\pi\) | ||||
0.492769 | + | 0.870160i | \(0.335985\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.9814 | 1.52570 | ||||||||
\(832\) | 1.06379 | 0.0368802 | ||||||||
\(833\) | 28.8564 | 0.999815 | ||||||||
\(834\) | −1.94552 | −0.0673677 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.40880 | −0.221653 | ||||||||
\(837\) | −26.4349 | −0.913723 | ||||||||
\(838\) | 1.96345 | 0.0678264 | ||||||||
\(839\) | 6.93471 | 0.239413 | 0.119706 | − | 0.992809i | \(-0.461805\pi\) | ||||
0.119706 | + | 0.992809i | \(0.461805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.3787 | −0.702712 | ||||||||
\(842\) | −25.5949 | −0.882060 | ||||||||
\(843\) | −17.3726 | −0.598344 | ||||||||
\(844\) | 17.1496 | 0.590313 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 51.0753 | 1.75601 | ||||||||
\(847\) | −141.200 | −4.85167 | ||||||||
\(848\) | −8.69527 | −0.298597 | ||||||||
\(849\) | −46.3827 | −1.59185 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4856 | −0.702238 | ||||||||
\(852\) | −3.96345 | −0.135786 | ||||||||
\(853\) | 21.9739 | 0.752373 | 0.376186 | − | 0.926544i | \(-0.377235\pi\) | ||||
0.376186 | + | 0.926544i | \(0.377235\pi\) | |||||||
\(854\) | 15.9194 | 0.544752 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.79036 | −0.0611934 | ||||||||
\(857\) | 13.6091 | 0.464879 | 0.232440 | − | 0.972611i | \(-0.425329\pi\) | ||||
0.232440 | + | 0.972611i | \(0.425329\pi\) | |||||||
\(858\) | 18.9347 | 0.646420 | ||||||||
\(859\) | 5.17192 | 0.176464 | 0.0882319 | − | 0.996100i | \(-0.471878\pi\) | ||||
0.0882319 | + | 0.996100i | \(0.471878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.9422 | 0.509228 | ||||||||
\(862\) | −15.3540 | −0.522959 | ||||||||
\(863\) | 15.9635 | 0.543402 | 0.271701 | − | 0.962382i | \(-0.412414\pi\) | ||||
0.271701 | + | 0.962382i | \(0.412414\pi\) | |||||||
\(864\) | 4.75905 | 0.161906 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.6640 | 0.566264 | ||||||||
\(867\) | −36.9982 | −1.25652 | ||||||||
\(868\) | 26.0806 | 0.885232 | ||||||||
\(869\) | −12.5834 | −0.426862 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.38563 | −0.318020 | ||||||||
\(872\) | 2.41404 | 0.0817496 | ||||||||
\(873\) | −70.4447 | −2.38419 | ||||||||
\(874\) | −1.79560 | −0.0607370 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −35.0310 | −1.18359 | ||||||||
\(877\) | −15.8866 | −0.536453 | −0.268227 | − | 0.963356i | \(-0.586438\pi\) | ||||
−0.268227 | + | 0.963356i | \(0.586438\pi\) | |||||||
\(878\) | −19.5987 | −0.661423 | ||||||||
\(879\) | 1.79003 | 0.0603762 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.1458 | −0.543967 | −0.271984 | − | 0.962302i | \(-0.587680\pi\) | ||||
−0.271984 | + | 0.962302i | \(0.587680\pi\) | |||||||
\(882\) | 70.9176 | 2.38792 | ||||||||
\(883\) | 38.2887 | 1.28852 | 0.644259 | − | 0.764808i | \(-0.277166\pi\) | ||||
0.644259 | + | 0.764808i | \(0.277166\pi\) | |||||||
\(884\) | 2.04028 | 0.0686221 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.0183 | 0.437357 | ||||||||
\(887\) | 19.2809 | 0.647389 | 0.323695 | − | 0.946162i | \(-0.395075\pi\) | ||||
0.323695 | + | 0.946162i | \(0.395075\pi\) | |||||||
\(888\) | −31.6860 | −1.06331 | ||||||||
\(889\) | −43.4920 | −1.45868 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.91644 | −0.198208 | ||||||||
\(892\) | 7.84635 | 0.262715 | ||||||||
\(893\) | −10.8359 | −0.362609 | ||||||||
\(894\) | 35.9530 | 1.20245 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.69527 | −0.156858 | ||||||||
\(897\) | 5.30507 | 0.177131 | ||||||||
\(898\) | 6.77359 | 0.226038 | ||||||||
\(899\) | −16.3096 | −0.543957 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.6770 | −0.555591 | ||||||||
\(902\) | −7.34352 | −0.244512 | ||||||||
\(903\) | 46.3537 | 1.54255 | ||||||||
\(904\) | 7.14585 | 0.237667 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15.8538 | 0.526708 | ||||||||
\(907\) | 43.0205 | 1.42847 | 0.714236 | − | 0.699905i | \(-0.246774\pi\) | ||||
0.714236 | + | 0.699905i | \(0.246774\pi\) | |||||||
\(908\) | 6.28646 | 0.208624 | ||||||||
\(909\) | 49.6636 | 1.64724 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.7733 | −0.853906 | −0.426953 | − | 0.904274i | \(-0.640413\pi\) | ||||
−0.426953 | + | 0.904274i | \(0.640413\pi\) | |||||||
\(912\) | −2.77733 | −0.0919664 | ||||||||
\(913\) | 104.109 | 3.44550 | ||||||||
\(914\) | −27.3189 | −0.903630 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.14585 | −0.103942 | ||||||||
\(917\) | −54.0806 | −1.78590 | ||||||||
\(918\) | 9.12758 | 0.301255 | ||||||||
\(919\) | −29.5897 | −0.976074 | −0.488037 | − | 0.872823i | \(-0.662287\pi\) | ||||
−0.488037 | + | 0.872823i | \(0.662287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 74.0037 | 2.43851 | ||||||||
\(922\) | −27.7993 | −0.915522 | ||||||||
\(923\) | −1.51811 | −0.0499691 | ||||||||
\(924\) | −83.5726 | −2.74934 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 38.2369 | 1.25654 | ||||||||
\(927\) | −80.0440 | −2.62899 | ||||||||
\(928\) | 2.93621 | 0.0963859 | ||||||||
\(929\) | −1.42334 | −0.0466983 | −0.0233491 | − | 0.999727i | \(-0.507433\pi\) | ||||
−0.0233491 | + | 0.999727i | \(0.507433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0455 | −0.493097 | ||||||||
\(932\) | 0.182394 | 0.00597451 | ||||||||
\(933\) | 32.0765 | 1.05014 | ||||||||
\(934\) | 23.4711 | 0.767998 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.01420 | 0.163894 | ||||||||
\(937\) | 28.2276 | 0.922155 | 0.461077 | − | 0.887360i | \(-0.347463\pi\) | ||||
0.461077 | + | 0.887360i | \(0.347463\pi\) | |||||||
\(938\) | 41.4256 | 1.35259 | ||||||||
\(939\) | −64.0556 | −2.09038 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.8672 | −0.517256 | −0.258628 | − | 0.965977i | \(-0.583270\pi\) | ||||
−0.258628 | + | 0.965977i | \(0.583270\pi\) | |||||||
\(942\) | 25.7262 | 0.838206 | ||||||||
\(943\) | −2.05748 | −0.0670009 | ||||||||
\(944\) | −5.63148 | −0.183289 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.7811 | −0.740676 | ||||||||
\(947\) | 43.6718 | 1.41914 | 0.709571 | − | 0.704634i | \(-0.248889\pi\) | ||||
0.709571 | + | 0.704634i | \(0.248889\pi\) | |||||||
\(948\) | −5.45315 | −0.177110 | ||||||||
\(949\) | −13.4178 | −0.435559 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.6692 | −1.25393 | ||||||||
\(952\) | −9.00523 | −0.291861 | ||||||||
\(953\) | 16.0261 | 0.519136 | 0.259568 | − | 0.965725i | \(-0.416420\pi\) | ||||
0.259568 | + | 0.965725i | \(0.416420\pi\) | |||||||
\(954\) | −40.9855 | −1.32695 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.5039 | −0.372063 | ||||||||
\(957\) | 52.2626 | 1.68941 | ||||||||
\(958\) | −19.6900 | −0.636156 | ||||||||
\(959\) | −70.9176 | −2.29005 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.145848 | −0.00470478 | ||||||||
\(962\) | −12.1365 | −0.391298 | ||||||||
\(963\) | −8.43895 | −0.271941 | ||||||||
\(964\) | −0.445349 | −0.0143437 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −23.4151 | −0.753369 | ||||||||
\(967\) | −11.5987 | −0.372988 | −0.186494 | − | 0.982456i | \(-0.559712\pi\) | ||||
−0.186494 | + | 0.982456i | \(0.559712\pi\) | |||||||
\(968\) | 30.0728 | 0.966575 | ||||||||
\(969\) | −5.32674 | −0.171120 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.0362 | −0.867633 | −0.433817 | − | 0.901001i | \(-0.642833\pi\) | ||||
−0.433817 | + | 0.901001i | \(0.642833\pi\) | |||||||
\(972\) | −16.8411 | −0.540179 | ||||||||
\(973\) | 3.28903 | 0.105442 | ||||||||
\(974\) | 16.3357 | 0.523430 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.39053 | −0.108528 | ||||||||
\(977\) | 14.1537 | 0.452815 | 0.226408 | − | 0.974033i | \(-0.427302\pi\) | ||||
0.226408 | + | 0.974033i | \(0.427302\pi\) | |||||||
\(978\) | 11.8904 | 0.380212 | ||||||||
\(979\) | −64.0880 | −2.04826 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3787 | 0.363293 | ||||||||
\(982\) | 27.1093 | 0.865093 | ||||||||
\(983\) | −32.8542 | −1.04788 | −0.523942 | − | 0.851754i | \(-0.675539\pi\) | ||||
−0.523942 | + | 0.851754i | \(0.675539\pi\) | |||||||
\(984\) | −3.18239 | −0.101451 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.63148 | 0.179343 | ||||||||
\(987\) | −141.303 | −4.49772 | ||||||||
\(988\) | −1.06379 | −0.0338436 | ||||||||
\(989\) | −6.38273 | −0.202959 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.9709 | 1.52385 | 0.761923 | − | 0.647667i | \(-0.224255\pi\) | ||||
0.761923 | + | 0.647667i | \(0.224255\pi\) | |||||||
\(992\) | −5.55465 | −0.176360 | ||||||||
\(993\) | −2.04285 | −0.0648279 | ||||||||
\(994\) | 6.70050 | 0.212527 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 45.1168 | 1.42958 | ||||||||
\(997\) | 44.1716 | 1.39893 | 0.699464 | − | 0.714668i | \(-0.253422\pi\) | ||||
0.699464 | + | 0.714668i | \(0.253422\pi\) | |||||||
\(998\) | −4.69003 | −0.148460 | ||||||||
\(999\) | −54.2951 | −1.71782 |
(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 | 950.2.a.m.1.3 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.cj.1.1 | 3 | |||
4.3 | odd | 2 | 7600.2.a.bm.1.1 | 3 | |||
5.2 | odd | 4 | 950.2.b.g.799.4 | 6 | |||
5.3 | odd | 4 | 950.2.b.g.799.3 | 6 | |||
5.4 | even | 2 | 950.2.a.k.1.1 | ✓ | 3 | ||
15.14 | odd | 2 | 8550.2.a.co.1.3 | 3 | |||
20.19 | odd | 2 | 7600.2.a.cb.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.a.k.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
950.2.a.m.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
950.2.b.g.799.3 | 6 | 5.3 | odd | 4 | |||
950.2.b.g.799.4 | 6 | 5.2 | odd | 4 | |||
7600.2.a.bm.1.1 | 3 | 4.3 | odd | 2 | |||
7600.2.a.cb.1.3 | 3 | 20.19 | odd | 2 | |||
8550.2.a.cj.1.1 | 3 | 3.2 | odd | 2 | |||
8550.2.a.co.1.3 | 3 | 15.14 | odd | 2 |