Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9262112932\) |
Analytic rank: | \(1\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-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 | ||||||||
\(3\) | −1.60528 | −0.926809 | −0.463404 | − | 0.886147i | \(-0.653372\pi\) | ||||
−0.463404 | + | 0.886147i | \(0.653372\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.61064 | 0.720301 | 0.360151 | − | 0.932894i | \(-0.382725\pi\) | ||||
0.360151 | + | 0.932894i | \(0.382725\pi\) | |||||||
\(6\) | −1.60528 | −0.655353 | ||||||||
\(7\) | −2.90280 | −1.09716 | −0.548578 | − | 0.836099i | \(-0.684831\pi\) | ||||
−0.548578 | + | 0.836099i | \(0.684831\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.423077 | −0.141026 | ||||||||
\(10\) | 1.61064 | 0.509330 | ||||||||
\(11\) | 0.613143 | 0.184869 | 0.0924347 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924347 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(12\) | −1.60528 | −0.463404 | ||||||||
\(13\) | 5.17210 | 1.43448 | 0.717241 | − | 0.696825i | \(-0.245405\pi\) | ||||
0.717241 | + | 0.696825i | \(0.245405\pi\) | |||||||
\(14\) | −2.90280 | −0.775807 | ||||||||
\(15\) | −2.58553 | −0.667581 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.85314 | −0.691987 | −0.345993 | − | 0.938237i | \(-0.612458\pi\) | ||||
−0.345993 | + | 0.938237i | \(0.612458\pi\) | |||||||
\(18\) | −0.423077 | −0.0997201 | ||||||||
\(19\) | −2.15783 | −0.495040 | −0.247520 | − | 0.968883i | \(-0.579616\pi\) | ||||
−0.247520 | + | 0.968883i | \(0.579616\pi\) | |||||||
\(20\) | 1.61064 | 0.360151 | ||||||||
\(21\) | 4.65981 | 1.01685 | ||||||||
\(22\) | 0.613143 | 0.130722 | ||||||||
\(23\) | 6.80112 | 1.41813 | 0.709066 | − | 0.705142i | \(-0.249117\pi\) | ||||
0.709066 | + | 0.705142i | \(0.249117\pi\) | |||||||
\(24\) | −1.60528 | −0.327676 | ||||||||
\(25\) | −2.40583 | −0.481166 | ||||||||
\(26\) | 5.17210 | 1.01433 | ||||||||
\(27\) | 5.49500 | 1.05751 | ||||||||
\(28\) | −2.90280 | −0.548578 | ||||||||
\(29\) | −8.18878 | −1.52062 | −0.760309 | − | 0.649561i | \(-0.774953\pi\) | ||||
−0.760309 | + | 0.649561i | \(0.774953\pi\) | |||||||
\(30\) | −2.58553 | −0.472051 | ||||||||
\(31\) | −5.91754 | −1.06282 | −0.531411 | − | 0.847114i | \(-0.678338\pi\) | ||||
−0.531411 | + | 0.847114i | \(0.678338\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.984265 | −0.171339 | ||||||||
\(34\) | −2.85314 | −0.489309 | ||||||||
\(35\) | −4.67538 | −0.790283 | ||||||||
\(36\) | −0.423077 | −0.0705128 | ||||||||
\(37\) | −4.25115 | −0.698885 | −0.349443 | − | 0.936958i | \(-0.613629\pi\) | ||||
−0.349443 | + | 0.936958i | \(0.613629\pi\) | |||||||
\(38\) | −2.15783 | −0.350046 | ||||||||
\(39\) | −8.30266 | −1.32949 | ||||||||
\(40\) | 1.61064 | 0.254665 | ||||||||
\(41\) | −4.79864 | −0.749422 | −0.374711 | − | 0.927142i | \(-0.622258\pi\) | ||||
−0.374711 | + | 0.927142i | \(0.622258\pi\) | |||||||
\(42\) | 4.65981 | 0.719025 | ||||||||
\(43\) | 2.35920 | 0.359774 | 0.179887 | − | 0.983687i | \(-0.442427\pi\) | ||||
0.179887 | + | 0.983687i | \(0.442427\pi\) | |||||||
\(44\) | 0.613143 | 0.0924347 | ||||||||
\(45\) | −0.681425 | −0.101581 | ||||||||
\(46\) | 6.80112 | 1.00277 | ||||||||
\(47\) | 5.37760 | 0.784404 | 0.392202 | − | 0.919879i | \(-0.371713\pi\) | ||||
0.392202 | + | 0.919879i | \(0.371713\pi\) | |||||||
\(48\) | −1.60528 | −0.231702 | ||||||||
\(49\) | 1.42627 | 0.203753 | ||||||||
\(50\) | −2.40583 | −0.340236 | ||||||||
\(51\) | 4.58008 | 0.641340 | ||||||||
\(52\) | 5.17210 | 0.717241 | ||||||||
\(53\) | −2.42943 | −0.333707 | −0.166854 | − | 0.985982i | \(-0.553361\pi\) | ||||
−0.166854 | + | 0.985982i | \(0.553361\pi\) | |||||||
\(54\) | 5.49500 | 0.747774 | ||||||||
\(55\) | 0.987553 | 0.133162 | ||||||||
\(56\) | −2.90280 | −0.387903 | ||||||||
\(57\) | 3.46392 | 0.458807 | ||||||||
\(58\) | −8.18878 | −1.07524 | ||||||||
\(59\) | 1.10964 | 0.144463 | 0.0722314 | − | 0.997388i | \(-0.476988\pi\) | ||||
0.0722314 | + | 0.997388i | \(0.476988\pi\) | |||||||
\(60\) | −2.58553 | −0.333791 | ||||||||
\(61\) | 6.36668 | 0.815170 | 0.407585 | − | 0.913167i | \(-0.366371\pi\) | ||||
0.407585 | + | 0.913167i | \(0.366371\pi\) | |||||||
\(62\) | −5.91754 | −0.751528 | ||||||||
\(63\) | 1.22811 | 0.154727 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.33040 | 1.03326 | ||||||||
\(66\) | −0.984265 | −0.121155 | ||||||||
\(67\) | 9.58442 | 1.17092 | 0.585461 | − | 0.810700i | \(-0.300913\pi\) | ||||
0.585461 | + | 0.810700i | \(0.300913\pi\) | |||||||
\(68\) | −2.85314 | −0.345993 | ||||||||
\(69\) | −10.9177 | −1.31434 | ||||||||
\(70\) | −4.67538 | −0.558815 | ||||||||
\(71\) | −4.11233 | −0.488044 | −0.244022 | − | 0.969770i | \(-0.578467\pi\) | ||||
−0.244022 | + | 0.969770i | \(0.578467\pi\) | |||||||
\(72\) | −0.423077 | −0.0498601 | ||||||||
\(73\) | −1.09065 | −0.127651 | −0.0638257 | − | 0.997961i | \(-0.520330\pi\) | ||||
−0.0638257 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(74\) | −4.25115 | −0.494186 | ||||||||
\(75\) | 3.86203 | 0.445949 | ||||||||
\(76\) | −2.15783 | −0.247520 | ||||||||
\(77\) | −1.77983 | −0.202831 | ||||||||
\(78\) | −8.30266 | −0.940092 | ||||||||
\(79\) | −6.18755 | −0.696154 | −0.348077 | − | 0.937466i | \(-0.613165\pi\) | ||||
−0.348077 | + | 0.937466i | \(0.613165\pi\) | |||||||
\(80\) | 1.61064 | 0.180075 | ||||||||
\(81\) | −7.55178 | −0.839086 | ||||||||
\(82\) | −4.79864 | −0.529921 | ||||||||
\(83\) | −3.24919 | −0.356645 | −0.178322 | − | 0.983972i | \(-0.557067\pi\) | ||||
−0.178322 | + | 0.983972i | \(0.557067\pi\) | |||||||
\(84\) | 4.65981 | 0.508427 | ||||||||
\(85\) | −4.59538 | −0.498439 | ||||||||
\(86\) | 2.35920 | 0.254399 | ||||||||
\(87\) | 13.1453 | 1.40932 | ||||||||
\(88\) | 0.613143 | 0.0653612 | ||||||||
\(89\) | −6.20320 | −0.657538 | −0.328769 | − | 0.944410i | \(-0.606634\pi\) | ||||
−0.328769 | + | 0.944410i | \(0.606634\pi\) | |||||||
\(90\) | −0.681425 | −0.0718285 | ||||||||
\(91\) | −15.0136 | −1.57385 | ||||||||
\(92\) | 6.80112 | 0.709066 | ||||||||
\(93\) | 9.49931 | 0.985032 | ||||||||
\(94\) | 5.37760 | 0.554657 | ||||||||
\(95\) | −3.47549 | −0.356578 | ||||||||
\(96\) | −1.60528 | −0.163838 | ||||||||
\(97\) | 3.83804 | 0.389694 | 0.194847 | − | 0.980834i | \(-0.437579\pi\) | ||||
0.194847 | + | 0.980834i | \(0.437579\pi\) | |||||||
\(98\) | 1.42627 | 0.144075 | ||||||||
\(99\) | −0.259406 | −0.0260713 | ||||||||
\(100\) | −2.40583 | −0.240583 | ||||||||
\(101\) | −1.06912 | −0.106381 | −0.0531907 | − | 0.998584i | \(-0.516939\pi\) | ||||
−0.0531907 | + | 0.998584i | \(0.516939\pi\) | |||||||
\(102\) | 4.58008 | 0.453496 | ||||||||
\(103\) | −14.8502 | −1.46324 | −0.731618 | − | 0.681715i | \(-0.761235\pi\) | ||||
−0.731618 | + | 0.681715i | \(0.761235\pi\) | |||||||
\(104\) | 5.17210 | 0.507166 | ||||||||
\(105\) | 7.50529 | 0.732441 | ||||||||
\(106\) | −2.42943 | −0.235967 | ||||||||
\(107\) | 16.1974 | 1.56586 | 0.782929 | − | 0.622111i | \(-0.213725\pi\) | ||||
0.782929 | + | 0.622111i | \(0.213725\pi\) | |||||||
\(108\) | 5.49500 | 0.528756 | ||||||||
\(109\) | 10.4020 | 0.996331 | 0.498166 | − | 0.867082i | \(-0.334007\pi\) | ||||
0.498166 | + | 0.867082i | \(0.334007\pi\) | |||||||
\(110\) | 0.987553 | 0.0941595 | ||||||||
\(111\) | 6.82429 | 0.647733 | ||||||||
\(112\) | −2.90280 | −0.274289 | ||||||||
\(113\) | −4.47004 | −0.420506 | −0.210253 | − | 0.977647i | \(-0.567429\pi\) | ||||
−0.210253 | + | 0.977647i | \(0.567429\pi\) | |||||||
\(114\) | 3.46392 | 0.324426 | ||||||||
\(115\) | 10.9542 | 1.02148 | ||||||||
\(116\) | −8.18878 | −0.760309 | ||||||||
\(117\) | −2.18819 | −0.202299 | ||||||||
\(118\) | 1.10964 | 0.102151 | ||||||||
\(119\) | 8.28209 | 0.759218 | ||||||||
\(120\) | −2.58553 | −0.236026 | ||||||||
\(121\) | −10.6241 | −0.965823 | ||||||||
\(122\) | 6.36668 | 0.576413 | ||||||||
\(123\) | 7.70316 | 0.694571 | ||||||||
\(124\) | −5.91754 | −0.531411 | ||||||||
\(125\) | −11.9281 | −1.06689 | ||||||||
\(126\) | 1.22811 | 0.109409 | ||||||||
\(127\) | 4.96090 | 0.440209 | 0.220104 | − | 0.975476i | \(-0.429360\pi\) | ||||
0.220104 | + | 0.975476i | \(0.429360\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.78717 | −0.333442 | ||||||||
\(130\) | 8.33040 | 0.730624 | ||||||||
\(131\) | −11.7767 | −1.02894 | −0.514468 | − | 0.857510i | \(-0.672010\pi\) | ||||
−0.514468 | + | 0.857510i | \(0.672010\pi\) | |||||||
\(132\) | −0.984265 | −0.0856693 | ||||||||
\(133\) | 6.26375 | 0.543136 | ||||||||
\(134\) | 9.58442 | 0.827967 | ||||||||
\(135\) | 8.85047 | 0.761727 | ||||||||
\(136\) | −2.85314 | −0.244654 | ||||||||
\(137\) | −4.65592 | −0.397783 | −0.198891 | − | 0.980022i | \(-0.563734\pi\) | ||||
−0.198891 | + | 0.980022i | \(0.563734\pi\) | |||||||
\(138\) | −10.9177 | −0.929376 | ||||||||
\(139\) | −20.3902 | −1.72947 | −0.864737 | − | 0.502225i | \(-0.832515\pi\) | ||||
−0.864737 | + | 0.502225i | \(0.832515\pi\) | |||||||
\(140\) | −4.67538 | −0.395142 | ||||||||
\(141\) | −8.63256 | −0.726993 | ||||||||
\(142\) | −4.11233 | −0.345099 | ||||||||
\(143\) | 3.17123 | 0.265192 | ||||||||
\(144\) | −0.423077 | −0.0352564 | ||||||||
\(145\) | −13.1892 | −1.09530 | ||||||||
\(146\) | −1.09065 | −0.0902632 | ||||||||
\(147\) | −2.28956 | −0.188840 | ||||||||
\(148\) | −4.25115 | −0.349443 | ||||||||
\(149\) | −12.6933 | −1.03988 | −0.519938 | − | 0.854204i | \(-0.674045\pi\) | ||||
−0.519938 | + | 0.854204i | \(0.674045\pi\) | |||||||
\(150\) | 3.86203 | 0.315334 | ||||||||
\(151\) | −21.3037 | −1.73367 | −0.866834 | − | 0.498598i | \(-0.833849\pi\) | ||||
−0.866834 | + | 0.498598i | \(0.833849\pi\) | |||||||
\(152\) | −2.15783 | −0.175023 | ||||||||
\(153\) | 1.20709 | 0.0975878 | ||||||||
\(154\) | −1.77983 | −0.143423 | ||||||||
\(155\) | −9.53104 | −0.765552 | ||||||||
\(156\) | −8.30266 | −0.664745 | ||||||||
\(157\) | −4.94059 | −0.394302 | −0.197151 | − | 0.980373i | \(-0.563169\pi\) | ||||
−0.197151 | + | 0.980373i | \(0.563169\pi\) | |||||||
\(158\) | −6.18755 | −0.492255 | ||||||||
\(159\) | 3.89991 | 0.309283 | ||||||||
\(160\) | 1.61064 | 0.127332 | ||||||||
\(161\) | −19.7423 | −1.55591 | ||||||||
\(162\) | −7.55178 | −0.593324 | ||||||||
\(163\) | −14.0732 | −1.10230 | −0.551149 | − | 0.834407i | \(-0.685810\pi\) | ||||
−0.551149 | + | 0.834407i | \(0.685810\pi\) | |||||||
\(164\) | −4.79864 | −0.374711 | ||||||||
\(165\) | −1.58530 | −0.123415 | ||||||||
\(166\) | −3.24919 | −0.252186 | ||||||||
\(167\) | 14.1468 | 1.09471 | 0.547356 | − | 0.836900i | \(-0.315635\pi\) | ||||
0.547356 | + | 0.836900i | \(0.315635\pi\) | |||||||
\(168\) | 4.65981 | 0.359512 | ||||||||
\(169\) | 13.7506 | 1.05774 | ||||||||
\(170\) | −4.59538 | −0.352450 | ||||||||
\(171\) | 0.912927 | 0.0698132 | ||||||||
\(172\) | 2.35920 | 0.179887 | ||||||||
\(173\) | −10.9244 | −0.830564 | −0.415282 | − | 0.909693i | \(-0.636317\pi\) | ||||
−0.415282 | + | 0.909693i | \(0.636317\pi\) | |||||||
\(174\) | 13.1453 | 0.996542 | ||||||||
\(175\) | 6.98366 | 0.527915 | ||||||||
\(176\) | 0.613143 | 0.0462174 | ||||||||
\(177\) | −1.78128 | −0.133889 | ||||||||
\(178\) | −6.20320 | −0.464950 | ||||||||
\(179\) | −13.6406 | −1.01955 | −0.509773 | − | 0.860309i | \(-0.670271\pi\) | ||||
−0.509773 | + | 0.860309i | \(0.670271\pi\) | |||||||
\(180\) | −0.681425 | −0.0507904 | ||||||||
\(181\) | −11.1492 | −0.828716 | −0.414358 | − | 0.910114i | \(-0.635994\pi\) | ||||
−0.414358 | + | 0.910114i | \(0.635994\pi\) | |||||||
\(182\) | −15.0136 | −1.11288 | ||||||||
\(183\) | −10.2203 | −0.755507 | ||||||||
\(184\) | 6.80112 | 0.501385 | ||||||||
\(185\) | −6.84708 | −0.503408 | ||||||||
\(186\) | 9.49931 | 0.696523 | ||||||||
\(187\) | −1.74938 | −0.127927 | ||||||||
\(188\) | 5.37760 | 0.392202 | ||||||||
\(189\) | −15.9509 | −1.16026 | ||||||||
\(190\) | −3.47549 | −0.252138 | ||||||||
\(191\) | −1.19781 | −0.0866707 | −0.0433353 | − | 0.999061i | \(-0.513798\pi\) | ||||
−0.0433353 | + | 0.999061i | \(0.513798\pi\) | |||||||
\(192\) | −1.60528 | −0.115851 | ||||||||
\(193\) | −15.3062 | −1.10177 | −0.550884 | − | 0.834582i | \(-0.685709\pi\) | ||||
−0.550884 | + | 0.834582i | \(0.685709\pi\) | |||||||
\(194\) | 3.83804 | 0.275555 | ||||||||
\(195\) | −13.3726 | −0.957633 | ||||||||
\(196\) | 1.42627 | 0.101876 | ||||||||
\(197\) | 11.8758 | 0.846112 | 0.423056 | − | 0.906103i | \(-0.360957\pi\) | ||||
0.423056 | + | 0.906103i | \(0.360957\pi\) | |||||||
\(198\) | −0.259406 | −0.0184352 | ||||||||
\(199\) | 11.3550 | 0.804933 | 0.402467 | − | 0.915435i | \(-0.368153\pi\) | ||||
0.402467 | + | 0.915435i | \(0.368153\pi\) | |||||||
\(200\) | −2.40583 | −0.170118 | ||||||||
\(201\) | −15.3857 | −1.08522 | ||||||||
\(202\) | −1.06912 | −0.0752230 | ||||||||
\(203\) | 23.7704 | 1.66836 | ||||||||
\(204\) | 4.58008 | 0.320670 | ||||||||
\(205\) | −7.72890 | −0.539809 | ||||||||
\(206\) | −14.8502 | −1.03466 | ||||||||
\(207\) | −2.87739 | −0.199993 | ||||||||
\(208\) | 5.17210 | 0.358620 | ||||||||
\(209\) | −1.32306 | −0.0915177 | ||||||||
\(210\) | 7.50529 | 0.517914 | ||||||||
\(211\) | 25.4028 | 1.74880 | 0.874401 | − | 0.485203i | \(-0.161254\pi\) | ||||
0.874401 | + | 0.485203i | \(0.161254\pi\) | |||||||
\(212\) | −2.42943 | −0.166854 | ||||||||
\(213\) | 6.60144 | 0.452323 | ||||||||
\(214\) | 16.1974 | 1.10723 | ||||||||
\(215\) | 3.79982 | 0.259146 | ||||||||
\(216\) | 5.49500 | 0.373887 | ||||||||
\(217\) | 17.1775 | 1.16608 | ||||||||
\(218\) | 10.4020 | 0.704513 | ||||||||
\(219\) | 1.75081 | 0.118308 | ||||||||
\(220\) | 0.987553 | 0.0665808 | ||||||||
\(221\) | −14.7567 | −0.992643 | ||||||||
\(222\) | 6.82429 | 0.458016 | ||||||||
\(223\) | −0.685057 | −0.0458748 | −0.0229374 | − | 0.999737i | \(-0.507302\pi\) | ||||
−0.0229374 | + | 0.999737i | \(0.507302\pi\) | |||||||
\(224\) | −2.90280 | −0.193952 | ||||||||
\(225\) | 1.01785 | 0.0678567 | ||||||||
\(226\) | −4.47004 | −0.297342 | ||||||||
\(227\) | −15.0151 | −0.996585 | −0.498293 | − | 0.867009i | \(-0.666039\pi\) | ||||
−0.498293 | + | 0.867009i | \(0.666039\pi\) | |||||||
\(228\) | 3.46392 | 0.229404 | ||||||||
\(229\) | 8.40883 | 0.555671 | 0.277836 | − | 0.960629i | \(-0.410383\pi\) | ||||
0.277836 | + | 0.960629i | \(0.410383\pi\) | |||||||
\(230\) | 10.9542 | 0.722297 | ||||||||
\(231\) | 2.85713 | 0.187985 | ||||||||
\(232\) | −8.18878 | −0.537620 | ||||||||
\(233\) | −25.6289 | −1.67900 | −0.839501 | − | 0.543358i | \(-0.817153\pi\) | ||||
−0.839501 | + | 0.543358i | \(0.817153\pi\) | |||||||
\(234\) | −2.18819 | −0.143047 | ||||||||
\(235\) | 8.66139 | 0.565007 | ||||||||
\(236\) | 1.10964 | 0.0722314 | ||||||||
\(237\) | 9.93275 | 0.645201 | ||||||||
\(238\) | 8.28209 | 0.536848 | ||||||||
\(239\) | 8.44585 | 0.546317 | 0.273158 | − | 0.961969i | \(-0.411932\pi\) | ||||
0.273158 | + | 0.961969i | \(0.411932\pi\) | |||||||
\(240\) | −2.58553 | −0.166895 | ||||||||
\(241\) | −3.39704 | −0.218823 | −0.109411 | − | 0.993997i | \(-0.534897\pi\) | ||||
−0.109411 | + | 0.993997i | \(0.534897\pi\) | |||||||
\(242\) | −10.6241 | −0.682940 | ||||||||
\(243\) | −4.36227 | −0.279840 | ||||||||
\(244\) | 6.36668 | 0.407585 | ||||||||
\(245\) | 2.29721 | 0.146763 | ||||||||
\(246\) | 7.70316 | 0.491136 | ||||||||
\(247\) | −11.1605 | −0.710126 | ||||||||
\(248\) | −5.91754 | −0.375764 | ||||||||
\(249\) | 5.21586 | 0.330542 | ||||||||
\(250\) | −11.9281 | −0.754402 | ||||||||
\(251\) | 24.4826 | 1.54533 | 0.772664 | − | 0.634815i | \(-0.218924\pi\) | ||||
0.772664 | + | 0.634815i | \(0.218924\pi\) | |||||||
\(252\) | 1.22811 | 0.0773636 | ||||||||
\(253\) | 4.17006 | 0.262169 | ||||||||
\(254\) | 4.96090 | 0.311275 | ||||||||
\(255\) | 7.37687 | 0.461958 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.4841 | −1.77679 | −0.888393 | − | 0.459083i | \(-0.848178\pi\) | ||||
−0.888393 | + | 0.459083i | \(0.848178\pi\) | |||||||
\(258\) | −3.78717 | −0.235779 | ||||||||
\(259\) | 12.3403 | 0.766787 | ||||||||
\(260\) | 8.33040 | 0.516629 | ||||||||
\(261\) | 3.46448 | 0.214446 | ||||||||
\(262\) | −11.7767 | −0.727567 | ||||||||
\(263\) | −7.29287 | −0.449697 | −0.224849 | − | 0.974394i | \(-0.572189\pi\) | ||||
−0.224849 | + | 0.974394i | \(0.572189\pi\) | |||||||
\(264\) | −0.984265 | −0.0605773 | ||||||||
\(265\) | −3.91294 | −0.240370 | ||||||||
\(266\) | 6.26375 | 0.384055 | ||||||||
\(267\) | 9.95788 | 0.609412 | ||||||||
\(268\) | 9.58442 | 0.585461 | ||||||||
\(269\) | 13.1350 | 0.800858 | 0.400429 | − | 0.916328i | \(-0.368861\pi\) | ||||
0.400429 | + | 0.916328i | \(0.368861\pi\) | |||||||
\(270\) | 8.85047 | 0.538623 | ||||||||
\(271\) | −6.14537 | −0.373304 | −0.186652 | − | 0.982426i | \(-0.559764\pi\) | ||||
−0.186652 | + | 0.982426i | \(0.559764\pi\) | |||||||
\(272\) | −2.85314 | −0.172997 | ||||||||
\(273\) | 24.1010 | 1.45866 | ||||||||
\(274\) | −4.65592 | −0.281275 | ||||||||
\(275\) | −1.47512 | −0.0889530 | ||||||||
\(276\) | −10.9177 | −0.657168 | ||||||||
\(277\) | 10.7915 | 0.648400 | 0.324200 | − | 0.945989i | \(-0.394905\pi\) | ||||
0.324200 | + | 0.945989i | \(0.394905\pi\) | |||||||
\(278\) | −20.3902 | −1.22292 | ||||||||
\(279\) | 2.50357 | 0.149885 | ||||||||
\(280\) | −4.67538 | −0.279407 | ||||||||
\(281\) | −21.2837 | −1.26968 | −0.634839 | − | 0.772645i | \(-0.718933\pi\) | ||||
−0.634839 | + | 0.772645i | \(0.718933\pi\) | |||||||
\(282\) | −8.63256 | −0.514061 | ||||||||
\(283\) | 9.37486 | 0.557278 | 0.278639 | − | 0.960396i | \(-0.410117\pi\) | ||||
0.278639 | + | 0.960396i | \(0.410117\pi\) | |||||||
\(284\) | −4.11233 | −0.244022 | ||||||||
\(285\) | 5.57913 | 0.330479 | ||||||||
\(286\) | 3.17123 | 0.187519 | ||||||||
\(287\) | 13.9295 | 0.822233 | ||||||||
\(288\) | −0.423077 | −0.0249300 | ||||||||
\(289\) | −8.85962 | −0.521154 | ||||||||
\(290\) | −13.1892 | −0.774496 | ||||||||
\(291\) | −6.16113 | −0.361172 | ||||||||
\(292\) | −1.09065 | −0.0638257 | ||||||||
\(293\) | −9.99871 | −0.584131 | −0.292065 | − | 0.956398i | \(-0.594342\pi\) | ||||
−0.292065 | + | 0.956398i | \(0.594342\pi\) | |||||||
\(294\) | −2.28956 | −0.133530 | ||||||||
\(295\) | 1.78723 | 0.104057 | ||||||||
\(296\) | −4.25115 | −0.247093 | ||||||||
\(297\) | 3.36922 | 0.195502 | ||||||||
\(298\) | −12.6933 | −0.735303 | ||||||||
\(299\) | 35.1761 | 2.03428 | ||||||||
\(300\) | 3.86203 | 0.222975 | ||||||||
\(301\) | −6.84829 | −0.394729 | ||||||||
\(302\) | −21.3037 | −1.22589 | ||||||||
\(303\) | 1.71624 | 0.0985951 | ||||||||
\(304\) | −2.15783 | −0.123760 | ||||||||
\(305\) | 10.2545 | 0.587168 | ||||||||
\(306\) | 1.20709 | 0.0690050 | ||||||||
\(307\) | 20.1444 | 1.14970 | 0.574851 | − | 0.818258i | \(-0.305060\pi\) | ||||
0.574851 | + | 0.818258i | \(0.305060\pi\) | |||||||
\(308\) | −1.77983 | −0.101415 | ||||||||
\(309\) | 23.8388 | 1.35614 | ||||||||
\(310\) | −9.53104 | −0.541327 | ||||||||
\(311\) | −4.42643 | −0.251000 | −0.125500 | − | 0.992094i | \(-0.540053\pi\) | ||||
−0.125500 | + | 0.992094i | \(0.540053\pi\) | |||||||
\(312\) | −8.30266 | −0.470046 | ||||||||
\(313\) | −14.6136 | −0.826010 | −0.413005 | − | 0.910729i | \(-0.635521\pi\) | ||||
−0.413005 | + | 0.910729i | \(0.635521\pi\) | |||||||
\(314\) | −4.94059 | −0.278813 | ||||||||
\(315\) | 1.97804 | 0.111450 | ||||||||
\(316\) | −6.18755 | −0.348077 | ||||||||
\(317\) | 7.70700 | 0.432868 | 0.216434 | − | 0.976297i | \(-0.430557\pi\) | ||||
0.216434 | + | 0.976297i | \(0.430557\pi\) | |||||||
\(318\) | 3.89991 | 0.218696 | ||||||||
\(319\) | −5.02089 | −0.281116 | ||||||||
\(320\) | 1.61064 | 0.0900376 | ||||||||
\(321\) | −26.0013 | −1.45125 | ||||||||
\(322\) | −19.7423 | −1.10020 | ||||||||
\(323\) | 6.15658 | 0.342561 | ||||||||
\(324\) | −7.55178 | −0.419543 | ||||||||
\(325\) | −12.4432 | −0.690224 | ||||||||
\(326\) | −14.0732 | −0.779442 | ||||||||
\(327\) | −16.6981 | −0.923409 | ||||||||
\(328\) | −4.79864 | −0.264961 | ||||||||
\(329\) | −15.6101 | −0.860614 | ||||||||
\(330\) | −1.58530 | −0.0872679 | ||||||||
\(331\) | −13.5935 | −0.747169 | −0.373584 | − | 0.927596i | \(-0.621871\pi\) | ||||
−0.373584 | + | 0.927596i | \(0.621871\pi\) | |||||||
\(332\) | −3.24919 | −0.178322 | ||||||||
\(333\) | 1.79856 | 0.0985607 | ||||||||
\(334\) | 14.1468 | 0.774078 | ||||||||
\(335\) | 15.4371 | 0.843417 | ||||||||
\(336\) | 4.65981 | 0.254214 | ||||||||
\(337\) | 7.20994 | 0.392751 | 0.196375 | − | 0.980529i | \(-0.437083\pi\) | ||||
0.196375 | + | 0.980529i | \(0.437083\pi\) | |||||||
\(338\) | 13.7506 | 0.747934 | ||||||||
\(339\) | 7.17566 | 0.389728 | ||||||||
\(340\) | −4.59538 | −0.249219 | ||||||||
\(341\) | −3.62830 | −0.196483 | ||||||||
\(342\) | 0.912927 | 0.0493654 | ||||||||
\(343\) | 16.1794 | 0.873608 | ||||||||
\(344\) | 2.35920 | 0.127199 | ||||||||
\(345\) | −17.5845 | −0.946718 | ||||||||
\(346\) | −10.9244 | −0.587298 | ||||||||
\(347\) | 9.99912 | 0.536781 | 0.268390 | − | 0.963310i | \(-0.413508\pi\) | ||||
0.268390 | + | 0.963310i | \(0.413508\pi\) | |||||||
\(348\) | 13.1453 | 0.704661 | ||||||||
\(349\) | 20.8433 | 1.11572 | 0.557859 | − | 0.829936i | \(-0.311623\pi\) | ||||
0.557859 | + | 0.829936i | \(0.311623\pi\) | |||||||
\(350\) | 6.98366 | 0.373292 | ||||||||
\(351\) | 28.4207 | 1.51698 | ||||||||
\(352\) | 0.613143 | 0.0326806 | ||||||||
\(353\) | −7.01615 | −0.373432 | −0.186716 | − | 0.982414i | \(-0.559784\pi\) | ||||
−0.186716 | + | 0.982414i | \(0.559784\pi\) | |||||||
\(354\) | −1.78128 | −0.0946740 | ||||||||
\(355\) | −6.62350 | −0.351539 | ||||||||
\(356\) | −6.20320 | −0.328769 | ||||||||
\(357\) | −13.2951 | −0.703650 | ||||||||
\(358\) | −13.6406 | −0.720928 | ||||||||
\(359\) | −27.0092 | −1.42549 | −0.712746 | − | 0.701422i | \(-0.752549\pi\) | ||||
−0.712746 | + | 0.701422i | \(0.752549\pi\) | |||||||
\(360\) | −0.681425 | −0.0359143 | ||||||||
\(361\) | −14.3438 | −0.754936 | ||||||||
\(362\) | −11.1492 | −0.585991 | ||||||||
\(363\) | 17.0546 | 0.895133 | ||||||||
\(364\) | −15.0136 | −0.786926 | ||||||||
\(365\) | −1.75665 | −0.0919475 | ||||||||
\(366\) | −10.2203 | −0.534224 | ||||||||
\(367\) | −24.2512 | −1.26590 | −0.632951 | − | 0.774192i | \(-0.718157\pi\) | ||||
−0.632951 | + | 0.774192i | \(0.718157\pi\) | |||||||
\(368\) | 6.80112 | 0.354533 | ||||||||
\(369\) | 2.03019 | 0.105688 | ||||||||
\(370\) | −6.84708 | −0.355963 | ||||||||
\(371\) | 7.05215 | 0.366129 | ||||||||
\(372\) | 9.49931 | 0.492516 | ||||||||
\(373\) | −36.4166 | −1.88558 | −0.942789 | − | 0.333390i | \(-0.891807\pi\) | ||||
−0.942789 | + | 0.333390i | \(0.891807\pi\) | |||||||
\(374\) | −1.74938 | −0.0904582 | ||||||||
\(375\) | 19.1480 | 0.988799 | ||||||||
\(376\) | 5.37760 | 0.277329 | ||||||||
\(377\) | −42.3532 | −2.18130 | ||||||||
\(378\) | −15.9509 | −0.820426 | ||||||||
\(379\) | 27.9204 | 1.43417 | 0.717087 | − | 0.696984i | \(-0.245475\pi\) | ||||
0.717087 | + | 0.696984i | \(0.245475\pi\) | |||||||
\(380\) | −3.47549 | −0.178289 | ||||||||
\(381\) | −7.96364 | −0.407989 | ||||||||
\(382\) | −1.19781 | −0.0612854 | ||||||||
\(383\) | −32.6657 | −1.66914 | −0.834570 | − | 0.550902i | \(-0.814284\pi\) | ||||
−0.834570 | + | 0.550902i | \(0.814284\pi\) | |||||||
\(384\) | −1.60528 | −0.0819191 | ||||||||
\(385\) | −2.86667 | −0.146099 | ||||||||
\(386\) | −15.3062 | −0.779068 | ||||||||
\(387\) | −0.998122 | −0.0507374 | ||||||||
\(388\) | 3.83804 | 0.194847 | ||||||||
\(389\) | 26.0544 | 1.32101 | 0.660505 | − | 0.750822i | \(-0.270342\pi\) | ||||
0.660505 | + | 0.750822i | \(0.270342\pi\) | |||||||
\(390\) | −13.3726 | −0.677149 | ||||||||
\(391\) | −19.4045 | −0.981328 | ||||||||
\(392\) | 1.42627 | 0.0720375 | ||||||||
\(393\) | 18.9049 | 0.953626 | ||||||||
\(394\) | 11.8758 | 0.598292 | ||||||||
\(395\) | −9.96593 | −0.501440 | ||||||||
\(396\) | −0.259406 | −0.0130357 | ||||||||
\(397\) | −9.13473 | −0.458459 | −0.229230 | − | 0.973372i | \(-0.573621\pi\) | ||||
−0.229230 | + | 0.973372i | \(0.573621\pi\) | |||||||
\(398\) | 11.3550 | 0.569174 | ||||||||
\(399\) | −10.0551 | −0.503383 | ||||||||
\(400\) | −2.40583 | −0.120292 | ||||||||
\(401\) | −12.5481 | −0.626623 | −0.313312 | − | 0.949650i | \(-0.601438\pi\) | ||||
−0.313312 | + | 0.949650i | \(0.601438\pi\) | |||||||
\(402\) | −15.3857 | −0.767367 | ||||||||
\(403\) | −30.6061 | −1.52460 | ||||||||
\(404\) | −1.06912 | −0.0531907 | ||||||||
\(405\) | −12.1632 | −0.604395 | ||||||||
\(406\) | 23.7704 | 1.17971 | ||||||||
\(407\) | −2.60656 | −0.129202 | ||||||||
\(408\) | 4.58008 | 0.226748 | ||||||||
\(409\) | 19.3480 | 0.956696 | 0.478348 | − | 0.878170i | \(-0.341236\pi\) | ||||
0.478348 | + | 0.878170i | \(0.341236\pi\) | |||||||
\(410\) | −7.72890 | −0.381703 | ||||||||
\(411\) | 7.47406 | 0.368668 | ||||||||
\(412\) | −14.8502 | −0.731618 | ||||||||
\(413\) | −3.22107 | −0.158498 | ||||||||
\(414\) | −2.87739 | −0.141416 | ||||||||
\(415\) | −5.23328 | −0.256892 | ||||||||
\(416\) | 5.17210 | 0.253583 | ||||||||
\(417\) | 32.7320 | 1.60289 | ||||||||
\(418\) | −1.32306 | −0.0647128 | ||||||||
\(419\) | −1.07450 | −0.0524927 | −0.0262464 | − | 0.999656i | \(-0.508355\pi\) | ||||
−0.0262464 | + | 0.999656i | \(0.508355\pi\) | |||||||
\(420\) | 7.50529 | 0.366221 | ||||||||
\(421\) | −5.64351 | −0.275048 | −0.137524 | − | 0.990498i | \(-0.543914\pi\) | ||||
−0.137524 | + | 0.990498i | \(0.543914\pi\) | |||||||
\(422\) | 25.4028 | 1.23659 | ||||||||
\(423\) | −2.27514 | −0.110621 | ||||||||
\(424\) | −2.42943 | −0.117983 | ||||||||
\(425\) | 6.86416 | 0.332961 | ||||||||
\(426\) | 6.60144 | 0.319841 | ||||||||
\(427\) | −18.4812 | −0.894370 | ||||||||
\(428\) | 16.1974 | 0.782929 | ||||||||
\(429\) | −5.09072 | −0.245782 | ||||||||
\(430\) | 3.79982 | 0.183244 | ||||||||
\(431\) | 22.9508 | 1.10550 | 0.552750 | − | 0.833347i | \(-0.313579\pi\) | ||||
0.552750 | + | 0.833347i | \(0.313579\pi\) | |||||||
\(432\) | 5.49500 | 0.264378 | ||||||||
\(433\) | 0.363609 | 0.0174739 | 0.00873696 | − | 0.999962i | \(-0.497219\pi\) | ||||
0.00873696 | + | 0.999962i | \(0.497219\pi\) | |||||||
\(434\) | 17.1775 | 0.824545 | ||||||||
\(435\) | 21.1724 | 1.01514 | ||||||||
\(436\) | 10.4020 | 0.498166 | ||||||||
\(437\) | −14.6756 | −0.702031 | ||||||||
\(438\) | 1.75081 | 0.0836567 | ||||||||
\(439\) | −1.56165 | −0.0745333 | −0.0372666 | − | 0.999305i | \(-0.511865\pi\) | ||||
−0.0372666 | + | 0.999305i | \(0.511865\pi\) | |||||||
\(440\) | 0.987553 | 0.0470798 | ||||||||
\(441\) | −0.603422 | −0.0287344 | ||||||||
\(442\) | −14.7567 | −0.701904 | ||||||||
\(443\) | 17.7606 | 0.843831 | 0.421915 | − | 0.906635i | \(-0.361358\pi\) | ||||
0.421915 | + | 0.906635i | \(0.361358\pi\) | |||||||
\(444\) | 6.82429 | 0.323866 | ||||||||
\(445\) | −9.99114 | −0.473626 | ||||||||
\(446\) | −0.685057 | −0.0324384 | ||||||||
\(447\) | 20.3763 | 0.963766 | ||||||||
\(448\) | −2.90280 | −0.137145 | ||||||||
\(449\) | −23.4349 | −1.10596 | −0.552982 | − | 0.833193i | \(-0.686510\pi\) | ||||
−0.552982 | + | 0.833193i | \(0.686510\pi\) | |||||||
\(450\) | 1.01785 | 0.0479820 | ||||||||
\(451\) | −2.94225 | −0.138545 | ||||||||
\(452\) | −4.47004 | −0.210253 | ||||||||
\(453\) | 34.1983 | 1.60678 | ||||||||
\(454\) | −15.0151 | −0.704692 | ||||||||
\(455\) | −24.1815 | −1.13365 | ||||||||
\(456\) | 3.46392 | 0.162213 | ||||||||
\(457\) | −21.6662 | −1.01350 | −0.506750 | − | 0.862093i | \(-0.669153\pi\) | ||||
−0.506750 | + | 0.862093i | \(0.669153\pi\) | |||||||
\(458\) | 8.40883 | 0.392919 | ||||||||
\(459\) | −15.6780 | −0.731785 | ||||||||
\(460\) | 10.9542 | 0.510741 | ||||||||
\(461\) | −13.0752 | −0.608974 | −0.304487 | − | 0.952516i | \(-0.598485\pi\) | ||||
−0.304487 | + | 0.952516i | \(0.598485\pi\) | |||||||
\(462\) | 2.85713 | 0.132926 | ||||||||
\(463\) | 20.6552 | 0.959927 | 0.479963 | − | 0.877288i | \(-0.340650\pi\) | ||||
0.479963 | + | 0.877288i | \(0.340650\pi\) | |||||||
\(464\) | −8.18878 | −0.380155 | ||||||||
\(465\) | 15.3000 | 0.709520 | ||||||||
\(466\) | −25.6289 | −1.18723 | ||||||||
\(467\) | 28.3332 | 1.31111 | 0.655553 | − | 0.755149i | \(-0.272436\pi\) | ||||
0.655553 | + | 0.755149i | \(0.272436\pi\) | |||||||
\(468\) | −2.18819 | −0.101149 | ||||||||
\(469\) | −27.8217 | −1.28469 | ||||||||
\(470\) | 8.66139 | 0.399520 | ||||||||
\(471\) | 7.93102 | 0.365442 | ||||||||
\(472\) | 1.10964 | 0.0510753 | ||||||||
\(473\) | 1.44652 | 0.0665113 | ||||||||
\(474\) | 9.93275 | 0.456226 | ||||||||
\(475\) | 5.19137 | 0.238196 | ||||||||
\(476\) | 8.28209 | 0.379609 | ||||||||
\(477\) | 1.02783 | 0.0470613 | ||||||||
\(478\) | 8.44585 | 0.386304 | ||||||||
\(479\) | −18.8996 | −0.863546 | −0.431773 | − | 0.901982i | \(-0.642112\pi\) | ||||
−0.431773 | + | 0.901982i | \(0.642112\pi\) | |||||||
\(480\) | −2.58553 | −0.118013 | ||||||||
\(481\) | −21.9874 | −1.00254 | ||||||||
\(482\) | −3.39704 | −0.154731 | ||||||||
\(483\) | 31.6919 | 1.44203 | ||||||||
\(484\) | −10.6241 | −0.482912 | ||||||||
\(485\) | 6.18171 | 0.280697 | ||||||||
\(486\) | −4.36227 | −0.197877 | ||||||||
\(487\) | −12.7492 | −0.577721 | −0.288861 | − | 0.957371i | \(-0.593276\pi\) | ||||
−0.288861 | + | 0.957371i | \(0.593276\pi\) | |||||||
\(488\) | 6.36668 | 0.288206 | ||||||||
\(489\) | 22.5914 | 1.02162 | ||||||||
\(490\) | 2.29721 | 0.103777 | ||||||||
\(491\) | −10.8195 | −0.488276 | −0.244138 | − | 0.969741i | \(-0.578505\pi\) | ||||
−0.244138 | + | 0.969741i | \(0.578505\pi\) | |||||||
\(492\) | 7.70316 | 0.347285 | ||||||||
\(493\) | 23.3637 | 1.05225 | ||||||||
\(494\) | −11.1605 | −0.502135 | ||||||||
\(495\) | −0.417811 | −0.0187792 | ||||||||
\(496\) | −5.91754 | −0.265705 | ||||||||
\(497\) | 11.9373 | 0.535461 | ||||||||
\(498\) | 5.21586 | 0.233728 | ||||||||
\(499\) | 35.9161 | 1.60782 | 0.803912 | − | 0.594748i | \(-0.202748\pi\) | ||||
0.803912 | + | 0.594748i | \(0.202748\pi\) | |||||||
\(500\) | −11.9281 | −0.533443 | ||||||||
\(501\) | −22.7096 | −1.01459 | ||||||||
\(502\) | 24.4826 | 1.09271 | ||||||||
\(503\) | −4.54899 | −0.202830 | −0.101415 | − | 0.994844i | \(-0.532337\pi\) | ||||
−0.101415 | + | 0.994844i | \(0.532337\pi\) | |||||||
\(504\) | 1.22811 | 0.0547043 | ||||||||
\(505\) | −1.72197 | −0.0766266 | ||||||||
\(506\) | 4.17006 | 0.185382 | ||||||||
\(507\) | −22.0736 | −0.980321 | ||||||||
\(508\) | 4.96090 | 0.220104 | ||||||||
\(509\) | 22.9769 | 1.01843 | 0.509217 | − | 0.860638i | \(-0.329935\pi\) | ||||
0.509217 | + | 0.860638i | \(0.329935\pi\) | |||||||
\(510\) | 7.37687 | 0.326653 | ||||||||
\(511\) | 3.16596 | 0.140054 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.8573 | −0.523511 | ||||||||
\(514\) | −28.4841 | −1.25638 | ||||||||
\(515\) | −23.9184 | −1.05397 | ||||||||
\(516\) | −3.78717 | −0.166721 | ||||||||
\(517\) | 3.29724 | 0.145012 | ||||||||
\(518\) | 12.3403 | 0.542200 | ||||||||
\(519\) | 17.5367 | 0.769774 | ||||||||
\(520\) | 8.33040 | 0.365312 | ||||||||
\(521\) | 29.6392 | 1.29852 | 0.649259 | − | 0.760567i | \(-0.275079\pi\) | ||||
0.649259 | + | 0.760567i | \(0.275079\pi\) | |||||||
\(522\) | 3.46448 | 0.151636 | ||||||||
\(523\) | 2.26804 | 0.0991743 | 0.0495871 | − | 0.998770i | \(-0.484209\pi\) | ||||
0.0495871 | + | 0.998770i | \(0.484209\pi\) | |||||||
\(524\) | −11.7767 | −0.514468 | ||||||||
\(525\) | −11.2107 | −0.489276 | ||||||||
\(526\) | −7.29287 | −0.317984 | ||||||||
\(527\) | 16.8835 | 0.735459 | ||||||||
\(528\) | −0.984265 | −0.0428347 | ||||||||
\(529\) | 23.2552 | 1.01110 | ||||||||
\(530\) | −3.91294 | −0.169967 | ||||||||
\(531\) | −0.469462 | −0.0203729 | ||||||||
\(532\) | 6.26375 | 0.271568 | ||||||||
\(533\) | −24.8190 | −1.07503 | ||||||||
\(534\) | 9.95788 | 0.430920 | ||||||||
\(535\) | 26.0882 | 1.12789 | ||||||||
\(536\) | 9.58442 | 0.413984 | ||||||||
\(537\) | 21.8970 | 0.944924 | ||||||||
\(538\) | 13.1350 | 0.566292 | ||||||||
\(539\) | 0.874507 | 0.0376677 | ||||||||
\(540\) | 8.85047 | 0.380864 | ||||||||
\(541\) | −34.9925 | −1.50445 | −0.752223 | − | 0.658909i | \(-0.771018\pi\) | ||||
−0.752223 | + | 0.658909i | \(0.771018\pi\) | |||||||
\(542\) | −6.14537 | −0.263966 | ||||||||
\(543\) | 17.8976 | 0.768061 | ||||||||
\(544\) | −2.85314 | −0.122327 | ||||||||
\(545\) | 16.7539 | 0.717659 | ||||||||
\(546\) | 24.1010 | 1.03143 | ||||||||
\(547\) | 28.0256 | 1.19829 | 0.599144 | − | 0.800641i | \(-0.295508\pi\) | ||||
0.599144 | + | 0.800641i | \(0.295508\pi\) | |||||||
\(548\) | −4.65592 | −0.198891 | ||||||||
\(549\) | −2.69360 | −0.114960 | ||||||||
\(550\) | −1.47512 | −0.0628992 | ||||||||
\(551\) | 17.6700 | 0.752767 | ||||||||
\(552\) | −10.9177 | −0.464688 | ||||||||
\(553\) | 17.9612 | 0.763790 | ||||||||
\(554\) | 10.7915 | 0.458488 | ||||||||
\(555\) | 10.9915 | 0.466563 | ||||||||
\(556\) | −20.3902 | −0.864737 | ||||||||
\(557\) | 27.9829 | 1.18567 | 0.592836 | − | 0.805323i | \(-0.298008\pi\) | ||||
0.592836 | + | 0.805323i | \(0.298008\pi\) | |||||||
\(558\) | 2.50357 | 0.105985 | ||||||||
\(559\) | 12.2020 | 0.516090 | ||||||||
\(560\) | −4.67538 | −0.197571 | ||||||||
\(561\) | 2.80824 | 0.118564 | ||||||||
\(562\) | −21.2837 | −0.897798 | ||||||||
\(563\) | 16.8376 | 0.709619 | 0.354810 | − | 0.934939i | \(-0.384546\pi\) | ||||
0.354810 | + | 0.934939i | \(0.384546\pi\) | |||||||
\(564\) | −8.63256 | −0.363496 | ||||||||
\(565\) | −7.19963 | −0.302891 | ||||||||
\(566\) | 9.37486 | 0.394055 | ||||||||
\(567\) | 21.9213 | 0.920609 | ||||||||
\(568\) | −4.11233 | −0.172550 | ||||||||
\(569\) | −13.5294 | −0.567181 | −0.283591 | − | 0.958945i | \(-0.591526\pi\) | ||||
−0.283591 | + | 0.958945i | \(0.591526\pi\) | |||||||
\(570\) | 5.57913 | 0.233684 | ||||||||
\(571\) | −1.44675 | −0.0605446 | −0.0302723 | − | 0.999542i | \(-0.509637\pi\) | ||||
−0.0302723 | + | 0.999542i | \(0.509637\pi\) | |||||||
\(572\) | 3.17123 | 0.132596 | ||||||||
\(573\) | 1.92282 | 0.0803271 | ||||||||
\(574\) | 13.9295 | 0.581407 | ||||||||
\(575\) | −16.3623 | −0.682357 | ||||||||
\(576\) | −0.423077 | −0.0176282 | ||||||||
\(577\) | 11.4814 | 0.477975 | 0.238988 | − | 0.971023i | \(-0.423184\pi\) | ||||
0.238988 | + | 0.971023i | \(0.423184\pi\) | |||||||
\(578\) | −8.85962 | −0.368512 | ||||||||
\(579\) | 24.5708 | 1.02113 | ||||||||
\(580\) | −13.1892 | −0.547652 | ||||||||
\(581\) | 9.43176 | 0.391295 | ||||||||
\(582\) | −6.16113 | −0.255387 | ||||||||
\(583\) | −1.48958 | −0.0616923 | ||||||||
\(584\) | −1.09065 | −0.0451316 | ||||||||
\(585\) | −3.52440 | −0.145716 | ||||||||
\(586\) | −9.99871 | −0.413043 | ||||||||
\(587\) | −2.72740 | −0.112572 | −0.0562860 | − | 0.998415i | \(-0.517926\pi\) | ||||
−0.0562860 | + | 0.998415i | \(0.517926\pi\) | |||||||
\(588\) | −2.28956 | −0.0944200 | ||||||||
\(589\) | 12.7690 | 0.526139 | ||||||||
\(590\) | 1.78723 | 0.0735792 | ||||||||
\(591\) | −19.0639 | −0.784184 | ||||||||
\(592\) | −4.25115 | −0.174721 | ||||||||
\(593\) | 10.0423 | 0.412387 | 0.206194 | − | 0.978511i | \(-0.433892\pi\) | ||||
0.206194 | + | 0.978511i | \(0.433892\pi\) | |||||||
\(594\) | 3.36922 | 0.138241 | ||||||||
\(595\) | 13.3395 | 0.546866 | ||||||||
\(596\) | −12.6933 | −0.519938 | ||||||||
\(597\) | −18.2279 | −0.746019 | ||||||||
\(598\) | 35.1761 | 1.43846 | ||||||||
\(599\) | 7.34230 | 0.299998 | 0.149999 | − | 0.988686i | \(-0.452073\pi\) | ||||
0.149999 | + | 0.988686i | \(0.452073\pi\) | |||||||
\(600\) | 3.86203 | 0.157667 | ||||||||
\(601\) | 40.5772 | 1.65518 | 0.827589 | − | 0.561334i | \(-0.189712\pi\) | ||||
0.827589 | + | 0.561334i | \(0.189712\pi\) | |||||||
\(602\) | −6.84829 | −0.279115 | ||||||||
\(603\) | −4.05494 | −0.165130 | ||||||||
\(604\) | −21.3037 | −0.866834 | ||||||||
\(605\) | −17.1116 | −0.695684 | ||||||||
\(606\) | 1.71624 | 0.0697173 | ||||||||
\(607\) | −35.6343 | −1.44635 | −0.723175 | − | 0.690664i | \(-0.757318\pi\) | ||||
−0.723175 | + | 0.690664i | \(0.757318\pi\) | |||||||
\(608\) | −2.15783 | −0.0875115 | ||||||||
\(609\) | −38.1582 | −1.54625 | ||||||||
\(610\) | 10.2545 | 0.415191 | ||||||||
\(611\) | 27.8135 | 1.12521 | ||||||||
\(612\) | 1.20709 | 0.0487939 | ||||||||
\(613\) | −11.7896 | −0.476179 | −0.238089 | − | 0.971243i | \(-0.576521\pi\) | ||||
−0.238089 | + | 0.971243i | \(0.576521\pi\) | |||||||
\(614\) | 20.1444 | 0.812963 | ||||||||
\(615\) | 12.4070 | 0.500300 | ||||||||
\(616\) | −1.77983 | −0.0717115 | ||||||||
\(617\) | 6.84209 | 0.275452 | 0.137726 | − | 0.990470i | \(-0.456021\pi\) | ||||
0.137726 | + | 0.990470i | \(0.456021\pi\) | |||||||
\(618\) | 23.8388 | 0.958936 | ||||||||
\(619\) | −13.6702 | −0.549452 | −0.274726 | − | 0.961523i | \(-0.588587\pi\) | ||||
−0.274726 | + | 0.961523i | \(0.588587\pi\) | |||||||
\(620\) | −9.53104 | −0.382776 | ||||||||
\(621\) | 37.3721 | 1.49969 | ||||||||
\(622\) | −4.42643 | −0.177484 | ||||||||
\(623\) | 18.0067 | 0.721423 | ||||||||
\(624\) | −8.30266 | −0.332373 | ||||||||
\(625\) | −7.18281 | −0.287313 | ||||||||
\(626\) | −14.6136 | −0.584077 | ||||||||
\(627\) | 2.12388 | 0.0848194 | ||||||||
\(628\) | −4.94059 | −0.197151 | ||||||||
\(629\) | 12.1291 | 0.483619 | ||||||||
\(630\) | 1.97804 | 0.0788071 | ||||||||
\(631\) | 18.6938 | 0.744187 | 0.372094 | − | 0.928195i | \(-0.378640\pi\) | ||||
0.372094 | + | 0.928195i | \(0.378640\pi\) | |||||||
\(632\) | −6.18755 | −0.246127 | ||||||||
\(633\) | −40.7786 | −1.62081 | ||||||||
\(634\) | 7.70700 | 0.306084 | ||||||||
\(635\) | 7.99024 | 0.317083 | ||||||||
\(636\) | 3.89991 | 0.154641 | ||||||||
\(637\) | 7.37681 | 0.292280 | ||||||||
\(638\) | −5.02089 | −0.198779 | ||||||||
\(639\) | 1.73983 | 0.0688267 | ||||||||
\(640\) | 1.61064 | 0.0636662 | ||||||||
\(641\) | −23.1132 | −0.912915 | −0.456457 | − | 0.889745i | \(-0.650882\pi\) | ||||
−0.456457 | + | 0.889745i | \(0.650882\pi\) | |||||||
\(642\) | −26.0013 | −1.02619 | ||||||||
\(643\) | −27.2569 | −1.07491 | −0.537454 | − | 0.843293i | \(-0.680614\pi\) | ||||
−0.537454 | + | 0.843293i | \(0.680614\pi\) | |||||||
\(644\) | −19.7423 | −0.777956 | ||||||||
\(645\) | −6.09978 | −0.240179 | ||||||||
\(646\) | 6.15658 | 0.242227 | ||||||||
\(647\) | −38.4786 | −1.51275 | −0.756374 | − | 0.654139i | \(-0.773031\pi\) | ||||
−0.756374 | + | 0.654139i | \(0.773031\pi\) | |||||||
\(648\) | −7.55178 | −0.296662 | ||||||||
\(649\) | 0.680367 | 0.0267067 | ||||||||
\(650\) | −12.4432 | −0.488062 | ||||||||
\(651\) | −27.5746 | −1.08074 | ||||||||
\(652\) | −14.0732 | −0.551149 | ||||||||
\(653\) | −3.54866 | −0.138870 | −0.0694349 | − | 0.997586i | \(-0.522120\pi\) | ||||
−0.0694349 | + | 0.997586i | \(0.522120\pi\) | |||||||
\(654\) | −16.6981 | −0.652949 | ||||||||
\(655\) | −18.9681 | −0.741143 | ||||||||
\(656\) | −4.79864 | −0.187356 | ||||||||
\(657\) | 0.461430 | 0.0180021 | ||||||||
\(658\) | −15.6101 | −0.608546 | ||||||||
\(659\) | 5.33248 | 0.207724 | 0.103862 | − | 0.994592i | \(-0.466880\pi\) | ||||
0.103862 | + | 0.994592i | \(0.466880\pi\) | |||||||
\(660\) | −1.58530 | −0.0617077 | ||||||||
\(661\) | −36.9767 | −1.43823 | −0.719113 | − | 0.694893i | \(-0.755452\pi\) | ||||
−0.719113 | + | 0.694893i | \(0.755452\pi\) | |||||||
\(662\) | −13.5935 | −0.528328 | ||||||||
\(663\) | 23.6886 | 0.919990 | ||||||||
\(664\) | −3.24919 | −0.126093 | ||||||||
\(665\) | 10.0887 | 0.391222 | ||||||||
\(666\) | 1.79856 | 0.0696929 | ||||||||
\(667\) | −55.6929 | −2.15644 | ||||||||
\(668\) | 14.1468 | 0.547356 | ||||||||
\(669\) | 1.09971 | 0.0425172 | ||||||||
\(670\) | 15.4371 | 0.596386 | ||||||||
\(671\) | 3.90369 | 0.150700 | ||||||||
\(672\) | 4.65981 | 0.179756 | ||||||||
\(673\) | 33.6190 | 1.29592 | 0.647960 | − | 0.761675i | \(-0.275623\pi\) | ||||
0.647960 | + | 0.761675i | \(0.275623\pi\) | |||||||
\(674\) | 7.20994 | 0.277717 | ||||||||
\(675\) | −13.2200 | −0.508839 | ||||||||
\(676\) | 13.7506 | 0.528869 | ||||||||
\(677\) | 17.2853 | 0.664329 | 0.332164 | − | 0.943222i | \(-0.392221\pi\) | ||||
0.332164 | + | 0.943222i | \(0.392221\pi\) | |||||||
\(678\) | 7.17566 | 0.275580 | ||||||||
\(679\) | −11.1411 | −0.427555 | ||||||||
\(680\) | −4.59538 | −0.176225 | ||||||||
\(681\) | 24.1034 | 0.923644 | ||||||||
\(682\) | −3.62830 | −0.138935 | ||||||||
\(683\) | 15.8935 | 0.608149 | 0.304075 | − | 0.952648i | \(-0.401653\pi\) | ||||
0.304075 | + | 0.952648i | \(0.401653\pi\) | |||||||
\(684\) | 0.912927 | 0.0349066 | ||||||||
\(685\) | −7.49903 | −0.286523 | ||||||||
\(686\) | 16.1794 | 0.617734 | ||||||||
\(687\) | −13.4985 | −0.515001 | ||||||||
\(688\) | 2.35920 | 0.0899436 | ||||||||
\(689\) | −12.5652 | −0.478697 | ||||||||
\(690\) | −17.5845 | −0.669431 | ||||||||
\(691\) | 52.1085 | 1.98230 | 0.991150 | − | 0.132743i | \(-0.0423786\pi\) | ||||
0.991150 | + | 0.132743i | \(0.0423786\pi\) | |||||||
\(692\) | −10.9244 | −0.415282 | ||||||||
\(693\) | 0.753006 | 0.0286043 | ||||||||
\(694\) | 9.99912 | 0.379561 | ||||||||
\(695\) | −32.8413 | −1.24574 | ||||||||
\(696\) | 13.1453 | 0.498271 | ||||||||
\(697\) | 13.6912 | 0.518590 | ||||||||
\(698\) | 20.8433 | 0.788932 | ||||||||
\(699\) | 41.1415 | 1.55611 | ||||||||
\(700\) | 6.98366 | 0.263957 | ||||||||
\(701\) | −31.7666 | −1.19981 | −0.599903 | − | 0.800073i | \(-0.704794\pi\) | ||||
−0.599903 | + | 0.800073i | \(0.704794\pi\) | |||||||
\(702\) | 28.4207 | 1.07267 | ||||||||
\(703\) | 9.17326 | 0.345976 | ||||||||
\(704\) | 0.613143 | 0.0231087 | ||||||||
\(705\) | −13.9040 | −0.523654 | ||||||||
\(706\) | −7.01615 | −0.264056 | ||||||||
\(707\) | 3.10344 | 0.116717 | ||||||||
\(708\) | −1.78128 | −0.0669447 | ||||||||
\(709\) | 13.1374 | 0.493385 | 0.246693 | − | 0.969094i | \(-0.420656\pi\) | ||||
0.246693 | + | 0.969094i | \(0.420656\pi\) | |||||||
\(710\) | −6.62350 | −0.248575 | ||||||||
\(711\) | 2.61781 | 0.0981754 | ||||||||
\(712\) | −6.20320 | −0.232475 | ||||||||
\(713\) | −40.2459 | −1.50722 | ||||||||
\(714\) | −13.2951 | −0.497556 | ||||||||
\(715\) | 5.10772 | 0.191018 | ||||||||
\(716\) | −13.6406 | −0.509773 | ||||||||
\(717\) | −13.5580 | −0.506331 | ||||||||
\(718\) | −27.0092 | −1.00797 | ||||||||
\(719\) | 47.4367 | 1.76909 | 0.884546 | − | 0.466454i | \(-0.154469\pi\) | ||||
0.884546 | + | 0.466454i | \(0.154469\pi\) | |||||||
\(720\) | −0.681425 | −0.0253952 | ||||||||
\(721\) | 43.1073 | 1.60540 | ||||||||
\(722\) | −14.3438 | −0.533820 | ||||||||
\(723\) | 5.45320 | 0.202807 | ||||||||
\(724\) | −11.1492 | −0.414358 | ||||||||
\(725\) | 19.7008 | 0.731671 | ||||||||
\(726\) | 17.0546 | 0.632955 | ||||||||
\(727\) | −30.8221 | −1.14313 | −0.571564 | − | 0.820558i | \(-0.693663\pi\) | ||||
−0.571564 | + | 0.820558i | \(0.693663\pi\) | |||||||
\(728\) | −15.0136 | −0.556441 | ||||||||
\(729\) | 29.6580 | 1.09844 | ||||||||
\(730\) | −1.75665 | −0.0650167 | ||||||||
\(731\) | −6.73111 | −0.248959 | ||||||||
\(732\) | −10.2203 | −0.377754 | ||||||||
\(733\) | −3.36484 | −0.124283 | −0.0621416 | − | 0.998067i | \(-0.519793\pi\) | ||||
−0.0621416 | + | 0.998067i | \(0.519793\pi\) | |||||||
\(734\) | −24.2512 | −0.895128 | ||||||||
\(735\) | −3.68767 | −0.136022 | ||||||||
\(736\) | 6.80112 | 0.250693 | ||||||||
\(737\) | 5.87661 | 0.216468 | ||||||||
\(738\) | 2.03019 | 0.0747325 | ||||||||
\(739\) | −32.1841 | −1.18391 | −0.591955 | − | 0.805971i | \(-0.701644\pi\) | ||||
−0.591955 | + | 0.805971i | \(0.701644\pi\) | |||||||
\(740\) | −6.84708 | −0.251704 | ||||||||
\(741\) | 17.9157 | 0.658151 | ||||||||
\(742\) | 7.05215 | 0.258893 | ||||||||
\(743\) | 33.2602 | 1.22020 | 0.610099 | − | 0.792325i | \(-0.291130\pi\) | ||||
0.610099 | + | 0.792325i | \(0.291130\pi\) | |||||||
\(744\) | 9.49931 | 0.348262 | ||||||||
\(745\) | −20.4444 | −0.749023 | ||||||||
\(746\) | −36.4166 | −1.33331 | ||||||||
\(747\) | 1.37466 | 0.0502960 | ||||||||
\(748\) | −1.74938 | −0.0639636 | ||||||||
\(749\) | −47.0178 | −1.71799 | ||||||||
\(750\) | 19.1480 | 0.699186 | ||||||||
\(751\) | 0.749297 | 0.0273422 | 0.0136711 | − | 0.999907i | \(-0.495648\pi\) | ||||
0.0136711 | + | 0.999907i | \(0.495648\pi\) | |||||||
\(752\) | 5.37760 | 0.196101 | ||||||||
\(753\) | −39.3014 | −1.43222 | ||||||||
\(754\) | −42.3532 | −1.54241 | ||||||||
\(755\) | −34.3126 | −1.24876 | ||||||||
\(756\) | −15.9509 | −0.580128 | ||||||||
\(757\) | 34.8482 | 1.26658 | 0.633290 | − | 0.773915i | \(-0.281704\pi\) | ||||
0.633290 | + | 0.773915i | \(0.281704\pi\) | |||||||
\(758\) | 27.9204 | 1.01411 | ||||||||
\(759\) | −6.69411 | −0.242981 | ||||||||
\(760\) | −3.47549 | −0.126069 | ||||||||
\(761\) | 11.8636 | 0.430053 | 0.215027 | − | 0.976608i | \(-0.431016\pi\) | ||||
0.215027 | + | 0.976608i | \(0.431016\pi\) | |||||||
\(762\) | −7.96364 | −0.288492 | ||||||||
\(763\) | −30.1950 | −1.09313 | ||||||||
\(764\) | −1.19781 | −0.0433353 | ||||||||
\(765\) | 1.94420 | 0.0702926 | ||||||||
\(766\) | −32.6657 | −1.18026 | ||||||||
\(767\) | 5.73916 | 0.207229 | ||||||||
\(768\) | −1.60528 | −0.0579255 | ||||||||
\(769\) | 15.6706 | 0.565097 | 0.282549 | − | 0.959253i | \(-0.408820\pi\) | ||||
0.282549 | + | 0.959253i | \(0.408820\pi\) | |||||||
\(770\) | −2.86667 | −0.103308 | ||||||||
\(771\) | 45.7249 | 1.64674 | ||||||||
\(772\) | −15.3062 | −0.550884 | ||||||||
\(773\) | −23.8886 | −0.859212 | −0.429606 | − | 0.903016i | \(-0.641348\pi\) | ||||
−0.429606 | + | 0.903016i | \(0.641348\pi\) | |||||||
\(774\) | −0.998122 | −0.0358767 | ||||||||
\(775\) | 14.2366 | 0.511394 | ||||||||
\(776\) | 3.83804 | 0.137778 | ||||||||
\(777\) | −19.8096 | −0.710664 | ||||||||
\(778\) | 26.0544 | 0.934095 | ||||||||
\(779\) | 10.3546 | 0.370994 | ||||||||
\(780\) | −13.3726 | −0.478817 | ||||||||
\(781\) | −2.52145 | −0.0902244 | ||||||||
\(782\) | −19.4045 | −0.693904 | ||||||||
\(783\) | −44.9973 | −1.60807 | ||||||||
\(784\) | 1.42627 | 0.0509382 | ||||||||
\(785\) | −7.95752 | −0.284016 | ||||||||
\(786\) | 18.9049 | 0.674316 | ||||||||
\(787\) | 15.8142 | 0.563714 | 0.281857 | − | 0.959456i | \(-0.409050\pi\) | ||||
0.281857 | + | 0.959456i | \(0.409050\pi\) | |||||||
\(788\) | 11.8758 | 0.423056 | ||||||||
\(789\) | 11.7071 | 0.416784 | ||||||||
\(790\) | −9.96593 | −0.354572 | ||||||||
\(791\) | 12.9756 | 0.461361 | ||||||||
\(792\) | −0.259406 | −0.00921760 | ||||||||
\(793\) | 32.9291 | 1.16935 | ||||||||
\(794\) | −9.13473 | −0.324180 | ||||||||
\(795\) | 6.28136 | 0.222777 | ||||||||
\(796\) | 11.3550 | 0.402467 | ||||||||
\(797\) | 17.8895 | 0.633679 | 0.316840 | − | 0.948479i | \(-0.397378\pi\) | ||||
0.316840 | + | 0.948479i | \(0.397378\pi\) | |||||||
\(798\) | −10.0551 | −0.355946 | ||||||||
\(799\) | −15.3430 | −0.542797 | ||||||||
\(800\) | −2.40583 | −0.0850590 | ||||||||
\(801\) | 2.62443 | 0.0927297 | ||||||||
\(802\) | −12.5481 | −0.443090 | ||||||||
\(803\) | −0.668727 | −0.0235989 | ||||||||
\(804\) | −15.3857 | −0.542611 | ||||||||
\(805\) | −31.7978 | −1.12073 | ||||||||
\(806\) | −30.6061 | −1.07805 | ||||||||
\(807\) | −21.0854 | −0.742242 | ||||||||
\(808\) | −1.06912 | −0.0376115 | ||||||||
\(809\) | 35.8976 | 1.26209 | 0.631047 | − | 0.775745i | \(-0.282626\pi\) | ||||
0.631047 | + | 0.775745i | \(0.282626\pi\) | |||||||
\(810\) | −12.1632 | −0.427372 | ||||||||
\(811\) | −6.17127 | −0.216703 | −0.108351 | − | 0.994113i | \(-0.534557\pi\) | ||||
−0.108351 | + | 0.994113i | \(0.534557\pi\) | |||||||
\(812\) | 23.7704 | 0.834179 | ||||||||
\(813\) | 9.86503 | 0.345982 | ||||||||
\(814\) | −2.60656 | −0.0913600 | ||||||||
\(815\) | −22.6669 | −0.793986 | ||||||||
\(816\) | 4.58008 | 0.160335 | ||||||||
\(817\) | −5.09074 | −0.178103 | ||||||||
\(818\) | 19.3480 | 0.676486 | ||||||||
\(819\) | 6.35190 | 0.221953 | ||||||||
\(820\) | −7.72890 | −0.269905 | ||||||||
\(821\) | −19.8132 | −0.691484 | −0.345742 | − | 0.938330i | \(-0.612373\pi\) | ||||
−0.345742 | + | 0.938330i | \(0.612373\pi\) | |||||||
\(822\) | 7.47406 | 0.260688 | ||||||||
\(823\) | 42.6614 | 1.48708 | 0.743542 | − | 0.668689i | \(-0.233144\pi\) | ||||
0.743542 | + | 0.668689i | \(0.233144\pi\) | |||||||
\(824\) | −14.8502 | −0.517332 | ||||||||
\(825\) | 2.36798 | 0.0824424 | ||||||||
\(826\) | −3.22107 | −0.112075 | ||||||||
\(827\) | 45.7757 | 1.59178 | 0.795889 | − | 0.605443i | \(-0.207004\pi\) | ||||
0.795889 | + | 0.605443i | \(0.207004\pi\) | |||||||
\(828\) | −2.87739 | −0.0999964 | ||||||||
\(829\) | −34.1301 | −1.18539 | −0.592693 | − | 0.805428i | \(-0.701935\pi\) | ||||
−0.592693 | + | 0.805428i | \(0.701935\pi\) | |||||||
\(830\) | −5.23328 | −0.181650 | ||||||||
\(831\) | −17.3234 | −0.600943 | ||||||||
\(832\) | 5.17210 | 0.179310 | ||||||||
\(833\) | −4.06934 | −0.140994 | ||||||||
\(834\) | 32.7320 | 1.13342 | ||||||||
\(835\) | 22.7854 | 0.788522 | ||||||||
\(836\) | −1.32306 | −0.0457589 | ||||||||
\(837\) | −32.5169 | −1.12395 | ||||||||
\(838\) | −1.07450 | −0.0371180 | ||||||||
\(839\) | −55.3500 | −1.91089 | −0.955447 | − | 0.295162i | \(-0.904626\pi\) | ||||
−0.955447 | + | 0.295162i | \(0.904626\pi\) | |||||||
\(840\) | 7.50529 | 0.258957 | ||||||||
\(841\) | 38.0562 | 1.31228 | ||||||||
\(842\) | −5.64351 | −0.194488 | ||||||||
\(843\) | 34.1663 | 1.17675 | ||||||||
\(844\) | 25.4028 | 0.874401 | ||||||||
\(845\) | 22.1473 | 0.761890 | ||||||||
\(846\) | −2.27514 | −0.0782209 | ||||||||
\(847\) | 30.8396 | 1.05966 | ||||||||
\(848\) | −2.42943 | −0.0834269 | ||||||||
\(849\) | −15.0493 | −0.516490 | ||||||||
\(850\) | 6.86416 | 0.235439 | ||||||||
\(851\) | −28.9126 | −0.991111 | ||||||||
\(852\) | 6.60144 | 0.226162 | ||||||||
\(853\) | 20.2567 | 0.693576 | 0.346788 | − | 0.937944i | \(-0.387272\pi\) | ||||
0.346788 | + | 0.937944i | \(0.387272\pi\) | |||||||
\(854\) | −18.4812 | −0.632415 | ||||||||
\(855\) | 1.47040 | 0.0502866 | ||||||||
\(856\) | 16.1974 | 0.553615 | ||||||||
\(857\) | 32.3309 | 1.10440 | 0.552202 | − | 0.833711i | \(-0.313788\pi\) | ||||
0.552202 | + | 0.833711i | \(0.313788\pi\) | |||||||
\(858\) | −5.09072 | −0.173794 | ||||||||
\(859\) | 4.78636 | 0.163309 | 0.0816543 | − | 0.996661i | \(-0.473980\pi\) | ||||
0.0816543 | + | 0.996661i | \(0.473980\pi\) | |||||||
\(860\) | 3.79982 | 0.129573 | ||||||||
\(861\) | −22.3608 | −0.762053 | ||||||||
\(862\) | 22.9508 | 0.781706 | ||||||||
\(863\) | −3.49398 | −0.118936 | −0.0594682 | − | 0.998230i | \(-0.518941\pi\) | ||||
−0.0594682 | + | 0.998230i | \(0.518941\pi\) | |||||||
\(864\) | 5.49500 | 0.186944 | ||||||||
\(865\) | −17.5952 | −0.598256 | ||||||||
\(866\) | 0.363609 | 0.0123559 | ||||||||
\(867\) | 14.2222 | 0.483010 | ||||||||
\(868\) | 17.1775 | 0.583041 | ||||||||
\(869\) | −3.79385 | −0.128698 | ||||||||
\(870\) | 21.1724 | 0.717810 | ||||||||
\(871\) | 49.5715 | 1.67967 | ||||||||
\(872\) | 10.4020 | 0.352256 | ||||||||
\(873\) | −1.62378 | −0.0549568 | ||||||||
\(874\) | −14.6756 | −0.496411 | ||||||||
\(875\) | 34.6251 | 1.17054 | ||||||||
\(876\) | 1.75081 | 0.0591542 | ||||||||
\(877\) | 18.7186 | 0.632083 | 0.316041 | − | 0.948745i | \(-0.397646\pi\) | ||||
0.316041 | + | 0.948745i | \(0.397646\pi\) | |||||||
\(878\) | −1.56165 | −0.0527030 | ||||||||
\(879\) | 16.0507 | 0.541378 | ||||||||
\(880\) | 0.987553 | 0.0332904 | ||||||||
\(881\) | −14.0115 | −0.472059 | −0.236030 | − | 0.971746i | \(-0.575846\pi\) | ||||
−0.236030 | + | 0.971746i | \(0.575846\pi\) | |||||||
\(882\) | −0.603422 | −0.0203183 | ||||||||
\(883\) | 40.6697 | 1.36864 | 0.684321 | − | 0.729181i | \(-0.260099\pi\) | ||||
0.684321 | + | 0.729181i | \(0.260099\pi\) | |||||||
\(884\) | −14.7567 | −0.496321 | ||||||||
\(885\) | −2.86901 | −0.0964406 | ||||||||
\(886\) | 17.7606 | 0.596678 | ||||||||
\(887\) | −34.9929 | −1.17495 | −0.587473 | − | 0.809244i | \(-0.699877\pi\) | ||||
−0.587473 | + | 0.809244i | \(0.699877\pi\) | |||||||
\(888\) | 6.82429 | 0.229008 | ||||||||
\(889\) | −14.4005 | −0.482978 | ||||||||
\(890\) | −9.99114 | −0.334904 | ||||||||
\(891\) | −4.63032 | −0.155121 | ||||||||
\(892\) | −0.685057 | −0.0229374 | ||||||||
\(893\) | −11.6039 | −0.388311 | ||||||||
\(894\) | 20.3763 | 0.681485 | ||||||||
\(895\) | −21.9701 | −0.734380 | ||||||||
\(896\) | −2.90280 | −0.0969759 | ||||||||
\(897\) | −56.4674 | −1.88539 | ||||||||
\(898\) | −23.4349 | −0.782034 | ||||||||
\(899\) | 48.4575 | 1.61615 | ||||||||
\(900\) | 1.01785 | 0.0339284 | ||||||||
\(901\) | 6.93148 | 0.230921 | ||||||||
\(902\) | −2.94225 | −0.0979663 | ||||||||
\(903\) | 10.9934 | 0.365838 | ||||||||
\(904\) | −4.47004 | −0.148671 | ||||||||
\(905\) | −17.9574 | −0.596925 | ||||||||
\(906\) | 34.1983 | 1.13616 | ||||||||
\(907\) | −35.5327 | −1.17984 | −0.589922 | − | 0.807460i | \(-0.700841\pi\) | ||||
−0.589922 | + | 0.807460i | \(0.700841\pi\) | |||||||
\(908\) | −15.0151 | −0.498293 | ||||||||
\(909\) | 0.452319 | 0.0150025 | ||||||||
\(910\) | −24.1815 | −0.801609 | ||||||||
\(911\) | −49.1174 | −1.62733 | −0.813666 | − | 0.581333i | \(-0.802531\pi\) | ||||
−0.813666 | + | 0.581333i | \(0.802531\pi\) | |||||||
\(912\) | 3.46392 | 0.114702 | ||||||||
\(913\) | −1.99222 | −0.0659327 | ||||||||
\(914\) | −21.6662 | −0.716653 | ||||||||
\(915\) | −16.4613 | −0.544193 | ||||||||
\(916\) | 8.40883 | 0.277836 | ||||||||
\(917\) | 34.1855 | 1.12890 | ||||||||
\(918\) | −15.6780 | −0.517450 | ||||||||
\(919\) | 23.4462 | 0.773420 | 0.386710 | − | 0.922201i | \(-0.373611\pi\) | ||||
0.386710 | + | 0.922201i | \(0.373611\pi\) | |||||||
\(920\) | 10.9542 | 0.361148 | ||||||||
\(921\) | −32.3374 | −1.06555 | ||||||||
\(922\) | −13.0752 | −0.430610 | ||||||||
\(923\) | −21.2694 | −0.700090 | ||||||||
\(924\) | 2.85713 | 0.0939927 | ||||||||
\(925\) | 10.2276 | 0.336280 | ||||||||
\(926\) | 20.6552 | 0.678771 | ||||||||
\(927\) | 6.28278 | 0.206354 | ||||||||
\(928\) | −8.18878 | −0.268810 | ||||||||
\(929\) | −2.97924 | −0.0977456 | −0.0488728 | − | 0.998805i | \(-0.515563\pi\) | ||||
−0.0488728 | + | 0.998805i | \(0.515563\pi\) | |||||||
\(930\) | 15.3000 | 0.501706 | ||||||||
\(931\) | −3.07765 | −0.100866 | ||||||||
\(932\) | −25.6289 | −0.839501 | ||||||||
\(933\) | 7.10566 | 0.232629 | ||||||||
\(934\) | 28.3332 | 0.927092 | ||||||||
\(935\) | −2.81762 | −0.0921461 | ||||||||
\(936\) | −2.18819 | −0.0715234 | ||||||||
\(937\) | 59.1944 | 1.93380 | 0.966898 | − | 0.255163i | \(-0.0821291\pi\) | ||||
0.966898 | + | 0.255163i | \(0.0821291\pi\) | |||||||
\(938\) | −27.8217 | −0.908410 | ||||||||
\(939\) | 23.4589 | 0.765554 | ||||||||
\(940\) | 8.66139 | 0.282504 | ||||||||
\(941\) | 7.58648 | 0.247312 | 0.123656 | − | 0.992325i | \(-0.460538\pi\) | ||||
0.123656 | + | 0.992325i | \(0.460538\pi\) | |||||||
\(942\) | 7.93102 | 0.258407 | ||||||||
\(943\) | −32.6361 | −1.06278 | ||||||||
\(944\) | 1.10964 | 0.0361157 | ||||||||
\(945\) | −25.6912 | −0.835734 | ||||||||
\(946\) | 1.44652 | 0.0470306 | ||||||||
\(947\) | −3.45331 | −0.112218 | −0.0561088 | − | 0.998425i | \(-0.517869\pi\) | ||||
−0.0561088 | + | 0.998425i | \(0.517869\pi\) | |||||||
\(948\) | 9.93275 | 0.322601 | ||||||||
\(949\) | −5.64097 | −0.183114 | ||||||||
\(950\) | 5.19137 | 0.168430 | ||||||||
\(951\) | −12.3719 | −0.401186 | ||||||||
\(952\) | 8.28209 | 0.268424 | ||||||||
\(953\) | −30.3400 | −0.982808 | −0.491404 | − | 0.870932i | \(-0.663516\pi\) | ||||
−0.491404 | + | 0.870932i | \(0.663516\pi\) | |||||||
\(954\) | 1.02783 | 0.0332773 | ||||||||
\(955\) | −1.92925 | −0.0624290 | ||||||||
\(956\) | 8.44585 | 0.273158 | ||||||||
\(957\) | 8.05994 | 0.260541 | ||||||||
\(958\) | −18.8996 | −0.610619 | ||||||||
\(959\) | 13.5152 | 0.436430 | ||||||||
\(960\) | −2.58553 | −0.0834477 | ||||||||
\(961\) | 4.01729 | 0.129590 | ||||||||
\(962\) | −21.9874 | −0.708901 | ||||||||
\(963\) | −6.85273 | −0.220826 | ||||||||
\(964\) | −3.39704 | −0.109411 | ||||||||
\(965\) | −24.6529 | −0.793605 | ||||||||
\(966\) | 31.6919 | 1.01967 | ||||||||
\(967\) | −43.9810 | −1.41433 | −0.707166 | − | 0.707048i | \(-0.750027\pi\) | ||||
−0.707166 | + | 0.707048i | \(0.750027\pi\) | |||||||
\(968\) | −10.6241 | −0.341470 | ||||||||
\(969\) | −9.88303 | −0.317489 | ||||||||
\(970\) | 6.18171 | 0.198483 | ||||||||
\(971\) | 48.1984 | 1.54676 | 0.773380 | − | 0.633943i | \(-0.218565\pi\) | ||||
0.773380 | + | 0.633943i | \(0.218565\pi\) | |||||||
\(972\) | −4.36227 | −0.139920 | ||||||||
\(973\) | 59.1887 | 1.89750 | ||||||||
\(974\) | −12.7492 | −0.408511 | ||||||||
\(975\) | 19.9748 | 0.639706 | ||||||||
\(976\) | 6.36668 | 0.203793 | ||||||||
\(977\) | 0.822113 | 0.0263017 | 0.0131509 | − | 0.999914i | \(-0.495814\pi\) | ||||
0.0131509 | + | 0.999914i | \(0.495814\pi\) | |||||||
\(978\) | 22.5914 | 0.722394 | ||||||||
\(979\) | −3.80345 | −0.121559 | ||||||||
\(980\) | 2.29721 | 0.0733817 | ||||||||
\(981\) | −4.40085 | −0.140508 | ||||||||
\(982\) | −10.8195 | −0.345263 | ||||||||
\(983\) | −21.3221 | −0.680070 | −0.340035 | − | 0.940413i | \(-0.610439\pi\) | ||||
−0.340035 | + | 0.940413i | \(0.610439\pi\) | |||||||
\(984\) | 7.70316 | 0.245568 | ||||||||
\(985\) | 19.1276 | 0.609456 | ||||||||
\(986\) | 23.3637 | 0.744052 | ||||||||
\(987\) | 25.0586 | 0.797625 | ||||||||
\(988\) | −11.1605 | −0.355063 | ||||||||
\(989\) | 16.0452 | 0.510207 | ||||||||
\(990\) | −0.417811 | −0.0132789 | ||||||||
\(991\) | 9.59233 | 0.304710 | 0.152355 | − | 0.988326i | \(-0.451314\pi\) | ||||
0.152355 | + | 0.988326i | \(0.451314\pi\) | |||||||
\(992\) | −5.91754 | −0.187882 | ||||||||
\(993\) | 21.8214 | 0.692482 | ||||||||
\(994\) | 11.9373 | 0.378628 | ||||||||
\(995\) | 18.2888 | 0.579794 | ||||||||
\(996\) | 5.21586 | 0.165271 | ||||||||
\(997\) | 42.4252 | 1.34362 | 0.671809 | − | 0.740724i | \(-0.265517\pi\) | ||||
0.671809 | + | 0.740724i | \(0.265517\pi\) | |||||||
\(998\) | 35.9161 | 1.13690 | ||||||||
\(999\) | −23.3601 | −0.739080 |
(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 | 6002.2.a.a.1.14 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.a.1.14 | ✓ | 47 | 1.1 | even | 1 | trivial |