Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(529,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.e (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(8.09683076496\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.1 | ||
Root | \(0.900969 + 1.56052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.991 |
Dual form | 1014.2.e.k.529.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −4.04892 | −1.81073 | −0.905365 | − | 0.424633i | \(-0.860403\pi\) | ||||
−0.905365 | + | 0.424633i | \(0.860403\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 0.346011 | − | 0.599308i | 0.130780 | − | 0.226517i | −0.793198 | − | 0.608964i | \(-0.791585\pi\) |
0.923977 | + | 0.382447i | \(0.124919\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.02446 | + | 3.50647i | 0.640190 | + | 1.10884i | ||||
\(11\) | −2.42543 | − | 4.20096i | −0.731294 | − | 1.26664i | −0.956330 | − | 0.292288i | \(-0.905583\pi\) |
0.225036 | − | 0.974350i | \(-0.427750\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.692021 | −0.184951 | ||||||||
\(15\) | 2.02446 | + | 3.50647i | 0.522713 | + | 0.905365i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.69202 | + | 6.39477i | −0.895447 | + | 1.55096i | −0.0621960 | + | 0.998064i | \(0.519810\pi\) |
−0.833251 | + | 0.552895i | \(0.813523\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.890084 | + | 1.54167i | −0.204199 | + | 0.353683i | −0.949877 | − | 0.312623i | \(-0.898792\pi\) |
0.745678 | + | 0.666306i | \(0.232126\pi\) | |||||||
\(20\) | 2.02446 | − | 3.50647i | 0.452683 | − | 0.784069i | ||||
\(21\) | −0.692021 | −0.151011 | ||||||||
\(22\) | −2.42543 | + | 4.20096i | −0.517103 | + | 0.895648i | ||||
\(23\) | −2.55496 | − | 4.42532i | −0.532746 | − | 0.922742i | −0.999269 | − | 0.0382335i | \(-0.987827\pi\) |
0.466523 | − | 0.884509i | \(-0.345506\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 11.3937 | 2.27875 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.346011 | + | 0.599308i | 0.0653899 | + | 0.113259i | ||||
\(29\) | 1.67241 | + | 2.89669i | 0.310558 | + | 0.537903i | 0.978483 | − | 0.206326i | \(-0.0661507\pi\) |
−0.667925 | + | 0.744228i | \(0.732817\pi\) | |||||||
\(30\) | 2.02446 | − | 3.50647i | 0.369614 | − | 0.640190i | ||||
\(31\) | −0.972853 | −0.174730 | −0.0873648 | − | 0.996176i | \(-0.527845\pi\) | ||||
−0.0873648 | + | 0.996176i | \(0.527845\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.42543 | + | 4.20096i | −0.422213 | + | 0.731294i | ||||
\(34\) | 7.38404 | 1.26635 | ||||||||
\(35\) | −1.40097 | + | 2.42655i | −0.236807 | + | 0.410162i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 0.643104 | + | 1.11389i | 0.105726 | + | 0.183122i | 0.914034 | − | 0.405637i | \(-0.132950\pi\) |
−0.808309 | + | 0.588759i | \(0.799617\pi\) | |||||||
\(38\) | 1.78017 | 0.288781 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.04892 | −0.640190 | ||||||||
\(41\) | 0.753020 | + | 1.30427i | 0.117602 | + | 0.203693i | 0.918817 | − | 0.394684i | \(-0.129146\pi\) |
−0.801215 | + | 0.598377i | \(0.795813\pi\) | |||||||
\(42\) | 0.346011 | + | 0.599308i | 0.0533906 | + | 0.0924753i | ||||
\(43\) | 4.15883 | − | 7.20331i | 0.634216 | − | 1.09849i | −0.352464 | − | 0.935825i | \(-0.614656\pi\) |
0.986681 | − | 0.162669i | \(-0.0520104\pi\) | |||||||
\(44\) | 4.85086 | 0.731294 | ||||||||
\(45\) | 2.02446 | − | 3.50647i | 0.301788 | − | 0.522713i | ||||
\(46\) | −2.55496 | + | 4.42532i | −0.376708 | + | 0.652477i | ||||
\(47\) | 7.20775 | 1.05136 | 0.525679 | − | 0.850683i | \(-0.323811\pi\) | ||||
0.525679 | + | 0.850683i | \(0.323811\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 3.26055 | + | 5.64744i | 0.465793 | + | 0.806778i | ||||
\(50\) | −5.69687 | − | 9.86726i | −0.805658 | − | 1.39544i | ||||
\(51\) | 7.38404 | 1.03397 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4765 | 1.85114 | 0.925570 | − | 0.378577i | \(-0.123586\pi\) | ||||
0.925570 | + | 0.378577i | \(0.123586\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 9.82036 | + | 17.0094i | 1.32418 | + | 2.29354i | ||||
\(56\) | 0.346011 | − | 0.599308i | 0.0462376 | − | 0.0800859i | ||||
\(57\) | 1.78017 | 0.235789 | ||||||||
\(58\) | 1.67241 | − | 2.89669i | 0.219598 | − | 0.380355i | ||||
\(59\) | 0.653989 | − | 1.13274i | 0.0851422 | − | 0.147471i | −0.820310 | − | 0.571920i | \(-0.806199\pi\) |
0.905452 | + | 0.424449i | \(0.139532\pi\) | |||||||
\(60\) | −4.04892 | −0.522713 | ||||||||
\(61\) | 0.198062 | − | 0.343054i | 0.0253593 | − | 0.0439236i | −0.853067 | − | 0.521801i | \(-0.825260\pi\) |
0.878427 | + | 0.477877i | \(0.158594\pi\) | |||||||
\(62\) | 0.486426 | + | 0.842515i | 0.0617762 | + | 0.107000i | ||||
\(63\) | 0.346011 | + | 0.599308i | 0.0435933 | + | 0.0755057i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.85086 | 0.597099 | ||||||||
\(67\) | 3.02715 | + | 5.24317i | 0.369825 | + | 0.640555i | 0.989538 | − | 0.144273i | \(-0.0460843\pi\) |
−0.619713 | + | 0.784828i | \(0.712751\pi\) | |||||||
\(68\) | −3.69202 | − | 6.39477i | −0.447723 | − | 0.775480i | ||||
\(69\) | −2.55496 | + | 4.42532i | −0.307581 | + | 0.532746i | ||||
\(70\) | 2.80194 | 0.334896 | ||||||||
\(71\) | −0.664874 | + | 1.15160i | −0.0789061 | + | 0.136669i | −0.902778 | − | 0.430106i | \(-0.858476\pi\) |
0.823872 | + | 0.566776i | \(0.191809\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 7.65279 | 0.895692 | 0.447846 | − | 0.894111i | \(-0.352191\pi\) | ||||
0.447846 | + | 0.894111i | \(0.352191\pi\) | |||||||
\(74\) | 0.643104 | − | 1.11389i | 0.0747593 | − | 0.129487i | ||||
\(75\) | −5.69687 | − | 9.86726i | −0.657817 | − | 1.13937i | ||||
\(76\) | −0.890084 | − | 1.54167i | −0.102100 | − | 0.176842i | ||||
\(77\) | −3.35690 | −0.382554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.33944 | −0.938260 | −0.469130 | − | 0.883129i | \(-0.655432\pi\) | ||||
−0.469130 | + | 0.883129i | \(0.655432\pi\) | |||||||
\(80\) | 2.02446 | + | 3.50647i | 0.226341 | + | 0.392035i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0.753020 | − | 1.30427i | 0.0831572 | − | 0.144032i | ||||
\(83\) | −15.3274 | −1.68240 | −0.841198 | − | 0.540727i | \(-0.818149\pi\) | ||||
−0.841198 | + | 0.540727i | \(0.818149\pi\) | |||||||
\(84\) | 0.346011 | − | 0.599308i | 0.0377529 | − | 0.0653899i | ||||
\(85\) | 14.9487 | − | 25.8919i | 1.62141 | − | 2.80837i | ||||
\(86\) | −8.31767 | −0.896917 | ||||||||
\(87\) | 1.67241 | − | 2.89669i | 0.179301 | − | 0.310558i | ||||
\(88\) | −2.42543 | − | 4.20096i | −0.258551 | − | 0.447824i | ||||
\(89\) | 1.55496 | + | 2.69327i | 0.164825 | + | 0.285486i | 0.936593 | − | 0.350419i | \(-0.113961\pi\) |
−0.771768 | + | 0.635904i | \(0.780627\pi\) | |||||||
\(90\) | −4.04892 | −0.426793 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.10992 | 0.532746 | ||||||||
\(93\) | 0.486426 | + | 0.842515i | 0.0504401 | + | 0.0873648i | ||||
\(94\) | −3.60388 | − | 6.24210i | −0.371711 | − | 0.643823i | ||||
\(95\) | 3.60388 | − | 6.24210i | 0.369750 | − | 0.640425i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −4.27144 | + | 7.39835i | −0.433699 | + | 0.751188i | −0.997188 | − | 0.0749347i | \(-0.976125\pi\) |
0.563490 | + | 0.826123i | \(0.309458\pi\) | |||||||
\(98\) | 3.26055 | − | 5.64744i | 0.329366 | − | 0.570478i | ||||
\(99\) | 4.85086 | 0.487529 | ||||||||
\(100\) | −5.69687 | + | 9.86726i | −0.569687 | + | 0.986726i | ||||
\(101\) | 5.99880 | + | 10.3902i | 0.596903 | + | 1.03387i | 0.993275 | + | 0.115777i | \(0.0369357\pi\) |
−0.396372 | + | 0.918090i | \(0.629731\pi\) | |||||||
\(102\) | −3.69202 | − | 6.39477i | −0.365565 | − | 0.633176i | ||||
\(103\) | −12.3230 | −1.21423 | −0.607113 | − | 0.794616i | \(-0.707672\pi\) | ||||
−0.607113 | + | 0.794616i | \(0.707672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.80194 | 0.273441 | ||||||||
\(106\) | −6.73825 | − | 11.6710i | −0.654477 | − | 1.13359i | ||||
\(107\) | −2.94989 | − | 5.10935i | −0.285176 | − | 0.493940i | 0.687476 | − | 0.726207i | \(-0.258719\pi\) |
−0.972652 | + | 0.232268i | \(0.925385\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −0.792249 | −0.0758837 | −0.0379418 | − | 0.999280i | \(-0.512080\pi\) | ||||
−0.0379418 | + | 0.999280i | \(0.512080\pi\) | |||||||
\(110\) | 9.82036 | − | 17.0094i | 0.936334 | − | 1.62178i | ||||
\(111\) | 0.643104 | − | 1.11389i | 0.0610407 | − | 0.105726i | ||||
\(112\) | −0.692021 | −0.0653899 | ||||||||
\(113\) | −3.10992 | + | 5.38653i | −0.292556 | + | 0.506722i | −0.974413 | − | 0.224763i | \(-0.927839\pi\) |
0.681857 | + | 0.731485i | \(0.261173\pi\) | |||||||
\(114\) | −0.890084 | − | 1.54167i | −0.0833640 | − | 0.144391i | ||||
\(115\) | 10.3448 | + | 17.9177i | 0.964659 | + | 1.67084i | ||||
\(116\) | −3.34481 | −0.310558 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.30798 | −0.120409 | ||||||||
\(119\) | 2.55496 | + | 4.42532i | 0.234213 | + | 0.405668i | ||||
\(120\) | 2.02446 | + | 3.50647i | 0.184807 | + | 0.320095i | ||||
\(121\) | −6.26540 | + | 10.8520i | −0.569582 | + | 0.986544i | ||||
\(122\) | −0.396125 | −0.0358634 | ||||||||
\(123\) | 0.753020 | − | 1.30427i | 0.0678976 | − | 0.117602i | ||||
\(124\) | 0.486426 | − | 0.842515i | 0.0436824 | − | 0.0756601i | ||||
\(125\) | −25.8877 | −2.31547 | ||||||||
\(126\) | 0.346011 | − | 0.599308i | 0.0308251 | − | 0.0533906i | ||||
\(127\) | 3.00269 | + | 5.20081i | 0.266446 | + | 0.461497i | 0.967941 | − | 0.251176i | \(-0.0808174\pi\) |
−0.701496 | + | 0.712674i | \(0.747484\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −8.31767 | −0.732330 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.81700 | 0.770345 | 0.385173 | − | 0.922845i | \(-0.374142\pi\) | ||||
0.385173 | + | 0.922845i | \(0.374142\pi\) | |||||||
\(132\) | −2.42543 | − | 4.20096i | −0.211106 | − | 0.365647i | ||||
\(133\) | 0.615957 | + | 1.06687i | 0.0534103 | + | 0.0925093i | ||||
\(134\) | 3.02715 | − | 5.24317i | 0.261506 | − | 0.452941i | ||||
\(135\) | −4.04892 | −0.348475 | ||||||||
\(136\) | −3.69202 | + | 6.39477i | −0.316588 | + | 0.548347i | ||||
\(137\) | −7.87800 | + | 13.6451i | −0.673063 | + | 1.16578i | 0.303968 | + | 0.952682i | \(0.401688\pi\) |
−0.977031 | + | 0.213097i | \(0.931645\pi\) | |||||||
\(138\) | 5.10992 | 0.434985 | ||||||||
\(139\) | 3.04892 | − | 5.28088i | 0.258606 | − | 0.447918i | −0.707263 | − | 0.706951i | \(-0.750070\pi\) |
0.965869 | + | 0.259032i | \(0.0834036\pi\) | |||||||
\(140\) | −1.40097 | − | 2.42655i | −0.118403 | − | 0.205081i | ||||
\(141\) | −3.60388 | − | 6.24210i | −0.303501 | − | 0.525679i | ||||
\(142\) | 1.32975 | 0.111590 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.77144 | − | 11.7285i | −0.562337 | − | 0.973997i | ||||
\(146\) | −3.82640 | − | 6.62751i | −0.316675 | − | 0.548497i | ||||
\(147\) | 3.26055 | − | 5.64744i | 0.268926 | − | 0.465793i | ||||
\(148\) | −1.28621 | −0.105726 | ||||||||
\(149\) | −1.27628 | + | 2.21059i | −0.104557 | + | 0.181098i | −0.913557 | − | 0.406710i | \(-0.866676\pi\) |
0.809000 | + | 0.587809i | \(0.200009\pi\) | |||||||
\(150\) | −5.69687 | + | 9.86726i | −0.465147 | + | 0.805658i | ||||
\(151\) | 17.7168 | 1.44177 | 0.720885 | − | 0.693054i | \(-0.243735\pi\) | ||||
0.720885 | + | 0.693054i | \(0.243735\pi\) | |||||||
\(152\) | −0.890084 | + | 1.54167i | −0.0721953 | + | 0.125046i | ||||
\(153\) | −3.69202 | − | 6.39477i | −0.298482 | − | 0.516986i | ||||
\(154\) | 1.67845 | + | 2.90716i | 0.135253 | + | 0.234265i | ||||
\(155\) | 3.93900 | 0.316388 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.31767 | −0.504205 | −0.252102 | − | 0.967701i | \(-0.581122\pi\) | ||||
−0.252102 | + | 0.967701i | \(0.581122\pi\) | |||||||
\(158\) | 4.16972 | + | 7.22216i | 0.331725 | + | 0.574565i | ||||
\(159\) | −6.73825 | − | 11.6710i | −0.534378 | − | 0.925570i | ||||
\(160\) | 2.02446 | − | 3.50647i | 0.160048 | − | 0.277210i | ||||
\(161\) | −3.53617 | −0.278689 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −7.29590 | + | 12.6369i | −0.571459 | + | 0.989796i | 0.424958 | + | 0.905213i | \(0.360289\pi\) |
−0.996416 | + | 0.0845824i | \(0.973044\pi\) | |||||||
\(164\) | −1.50604 | −0.117602 | ||||||||
\(165\) | 9.82036 | − | 17.0094i | 0.764514 | − | 1.32418i | ||||
\(166\) | 7.66368 | + | 13.2739i | 0.594817 | + | 1.03025i | ||||
\(167\) | 9.75063 | + | 16.8886i | 0.754526 | + | 1.30688i | 0.945610 | + | 0.325304i | \(0.105467\pi\) |
−0.191083 | + | 0.981574i | \(0.561200\pi\) | |||||||
\(168\) | −0.692021 | −0.0533906 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −29.8974 | −2.29302 | ||||||||
\(171\) | −0.890084 | − | 1.54167i | −0.0680664 | − | 0.117894i | ||||
\(172\) | 4.15883 | + | 7.20331i | 0.317108 | + | 0.549247i | ||||
\(173\) | 4.64526 | − | 8.04583i | 0.353173 | − | 0.611713i | −0.633631 | − | 0.773636i | \(-0.718436\pi\) |
0.986803 | + | 0.161923i | \(0.0517695\pi\) | |||||||
\(174\) | −3.34481 | −0.253570 | ||||||||
\(175\) | 3.94235 | − | 6.82836i | 0.298014 | − | 0.516175i | ||||
\(176\) | −2.42543 | + | 4.20096i | −0.182823 | + | 0.316660i | ||||
\(177\) | −1.30798 | −0.0983137 | ||||||||
\(178\) | 1.55496 | − | 2.69327i | 0.116549 | − | 0.201869i | ||||
\(179\) | −11.3964 | − | 19.7392i | −0.851808 | − | 1.47538i | −0.879575 | − | 0.475761i | \(-0.842173\pi\) |
0.0277662 | − | 0.999614i | \(-0.491161\pi\) | |||||||
\(180\) | 2.02446 | + | 3.50647i | 0.150894 | + | 0.261356i | ||||
\(181\) | 0.537500 | 0.0399520 | 0.0199760 | − | 0.999800i | \(-0.493641\pi\) | ||||
0.0199760 | + | 0.999800i | \(0.493641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.396125 | −0.0292824 | ||||||||
\(184\) | −2.55496 | − | 4.42532i | −0.188354 | − | 0.326239i | ||||
\(185\) | −2.60388 | − | 4.51004i | −0.191441 | − | 0.331585i | ||||
\(186\) | 0.486426 | − | 0.842515i | 0.0356665 | − | 0.0617762i | ||||
\(187\) | 35.8189 | 2.61934 | ||||||||
\(188\) | −3.60388 | + | 6.24210i | −0.262840 | + | 0.455252i | ||||
\(189\) | 0.346011 | − | 0.599308i | 0.0251686 | − | 0.0435933i | ||||
\(190\) | −7.20775 | −0.522905 | ||||||||
\(191\) | 4.89977 | − | 8.48665i | 0.354535 | − | 0.614073i | −0.632503 | − | 0.774558i | \(-0.717972\pi\) |
0.987038 | + | 0.160485i | \(0.0513058\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 7.09783 | + | 12.2938i | 0.510913 | + | 0.884928i | 0.999920 | + | 0.0126478i | \(0.00402603\pi\) |
−0.489007 | + | 0.872280i | \(0.662641\pi\) | |||||||
\(194\) | 8.54288 | 0.613343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.52111 | −0.465793 | ||||||||
\(197\) | 1.50484 | + | 2.60647i | 0.107216 | + | 0.185703i | 0.914641 | − | 0.404266i | \(-0.132473\pi\) |
−0.807426 | + | 0.589969i | \(0.799140\pi\) | |||||||
\(198\) | −2.42543 | − | 4.20096i | −0.172368 | − | 0.298549i | ||||
\(199\) | −6.44720 | + | 11.1669i | −0.457030 | + | 0.791599i | −0.998802 | − | 0.0489263i | \(-0.984420\pi\) |
0.541773 | + | 0.840525i | \(0.317753\pi\) | |||||||
\(200\) | 11.3937 | 0.805658 | ||||||||
\(201\) | 3.02715 | − | 5.24317i | 0.213518 | − | 0.369825i | ||||
\(202\) | 5.99880 | − | 10.3902i | 0.422074 | − | 0.731054i | ||||
\(203\) | 2.31468 | 0.162459 | ||||||||
\(204\) | −3.69202 | + | 6.39477i | −0.258493 | + | 0.447723i | ||||
\(205\) | −3.04892 | − | 5.28088i | −0.212946 | − | 0.368833i | ||||
\(206\) | 6.16152 | + | 10.6721i | 0.429294 | + | 0.743558i | ||||
\(207\) | 5.10992 | 0.355164 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.63533 | 0.597319 | ||||||||
\(210\) | −1.40097 | − | 2.42655i | −0.0966760 | − | 0.167448i | ||||
\(211\) | −3.89977 | − | 6.75460i | −0.268471 | − | 0.465006i | 0.699996 | − | 0.714147i | \(-0.253185\pi\) |
−0.968467 | + | 0.249141i | \(0.919852\pi\) | |||||||
\(212\) | −6.73825 | + | 11.6710i | −0.462785 | + | 0.801567i | ||||
\(213\) | 1.32975 | 0.0911129 | ||||||||
\(214\) | −2.94989 | + | 5.10935i | −0.201650 | + | 0.349268i | ||||
\(215\) | −16.8388 | + | 29.1656i | −1.14839 | + | 1.98908i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.336618 | + | 0.583039i | −0.0228511 | + | 0.0395792i | ||||
\(218\) | 0.396125 | + | 0.686108i | 0.0268289 | + | 0.0464691i | ||||
\(219\) | −3.82640 | − | 6.62751i | −0.258564 | − | 0.447846i | ||||
\(220\) | −19.6407 | −1.32418 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.28621 | −0.0863246 | ||||||||
\(223\) | 6.09783 | + | 10.5618i | 0.408341 | + | 0.707268i | 0.994704 | − | 0.102781i | \(-0.0327740\pi\) |
−0.586363 | + | 0.810049i | \(0.699441\pi\) | |||||||
\(224\) | 0.346011 | + | 0.599308i | 0.0231188 | + | 0.0400430i | ||||
\(225\) | −5.69687 | + | 9.86726i | −0.379791 | + | 0.657817i | ||||
\(226\) | 6.21983 | 0.413737 | ||||||||
\(227\) | −3.37167 | + | 5.83990i | −0.223785 | + | 0.387608i | −0.955954 | − | 0.293515i | \(-0.905175\pi\) |
0.732169 | + | 0.681123i | \(0.238508\pi\) | |||||||
\(228\) | −0.890084 | + | 1.54167i | −0.0589472 | + | 0.102100i | ||||
\(229\) | −19.8237 | −1.30999 | −0.654994 | − | 0.755634i | \(-0.727329\pi\) | ||||
−0.654994 | + | 0.755634i | \(0.727329\pi\) | |||||||
\(230\) | 10.3448 | − | 17.9177i | 0.682117 | − | 1.18146i | ||||
\(231\) | 1.67845 | + | 2.90716i | 0.110434 | + | 0.191277i | ||||
\(232\) | 1.67241 | + | 2.89669i | 0.109799 | + | 0.190177i | ||||
\(233\) | −30.0301 | −1.96734 | −0.983670 | − | 0.179983i | \(-0.942396\pi\) | ||||
−0.983670 | + | 0.179983i | \(0.942396\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.1836 | −1.90373 | ||||||||
\(236\) | 0.653989 | + | 1.13274i | 0.0425711 | + | 0.0737353i | ||||
\(237\) | 4.16972 | + | 7.22216i | 0.270852 | + | 0.469130i | ||||
\(238\) | 2.55496 | − | 4.42532i | 0.165613 | − | 0.286851i | ||||
\(239\) | 22.0978 | 1.42939 | 0.714695 | − | 0.699436i | \(-0.246565\pi\) | ||||
0.714695 | + | 0.699436i | \(0.246565\pi\) | |||||||
\(240\) | 2.02446 | − | 3.50647i | 0.130678 | − | 0.226341i | ||||
\(241\) | −5.06369 | + | 8.77056i | −0.326181 | + | 0.564962i | −0.981751 | − | 0.190173i | \(-0.939095\pi\) |
0.655570 | + | 0.755135i | \(0.272428\pi\) | |||||||
\(242\) | 12.5308 | 0.805510 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0.198062 | + | 0.343054i | 0.0126796 | + | 0.0219618i | ||||
\(245\) | −13.2017 | − | 22.8660i | −0.843426 | − | 1.46086i | ||||
\(246\) | −1.50604 | −0.0960217 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.972853 | −0.0617762 | ||||||||
\(249\) | 7.66368 | + | 13.2739i | 0.485666 | + | 0.841198i | ||||
\(250\) | 12.9438 | + | 22.4194i | 0.818641 | + | 1.41793i | ||||
\(251\) | −2.77359 | + | 4.80401i | −0.175068 | + | 0.303226i | −0.940185 | − | 0.340665i | \(-0.889348\pi\) |
0.765117 | + | 0.643891i | \(0.222681\pi\) | |||||||
\(252\) | −0.692021 | −0.0435933 | ||||||||
\(253\) | −12.3937 | + | 21.4666i | −0.779187 | + | 1.34959i | ||||
\(254\) | 3.00269 | − | 5.20081i | 0.188405 | − | 0.326328i | ||||
\(255\) | −29.8974 | −1.87225 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.89977 | + | 11.9508i | 0.430396 | + | 0.745468i | 0.996907 | − | 0.0785862i | \(-0.0250406\pi\) |
−0.566511 | + | 0.824054i | \(0.691707\pi\) | |||||||
\(258\) | 4.15883 | + | 7.20331i | 0.258918 | + | 0.448459i | ||||
\(259\) | 0.890084 | 0.0553071 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.34481 | −0.207039 | ||||||||
\(262\) | −4.40850 | − | 7.63575i | −0.272358 | − | 0.471738i | ||||
\(263\) | 11.2349 | + | 19.4594i | 0.692773 | + | 1.19992i | 0.970926 | + | 0.239382i | \(0.0769448\pi\) |
−0.278152 | + | 0.960537i | \(0.589722\pi\) | |||||||
\(264\) | −2.42543 | + | 4.20096i | −0.149275 | + | 0.258551i | ||||
\(265\) | −54.5652 | −3.35192 | ||||||||
\(266\) | 0.615957 | − | 1.06687i | 0.0377668 | − | 0.0654139i | ||||
\(267\) | 1.55496 | − | 2.69327i | 0.0951619 | − | 0.164825i | ||||
\(268\) | −6.05429 | −0.369825 | ||||||||
\(269\) | 13.0070 | − | 22.5288i | 0.793051 | − | 1.37360i | −0.131019 | − | 0.991380i | \(-0.541825\pi\) |
0.924070 | − | 0.382224i | \(-0.124842\pi\) | |||||||
\(270\) | 2.02446 | + | 3.50647i | 0.123205 | + | 0.213397i | ||||
\(271\) | −1.44235 | − | 2.49823i | −0.0876167 | − | 0.151757i | 0.818887 | − | 0.573955i | \(-0.194592\pi\) |
−0.906503 | + | 0.422199i | \(0.861258\pi\) | |||||||
\(272\) | 7.38404 | 0.447723 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7560 | 0.951855 | ||||||||
\(275\) | −27.6347 | − | 47.8647i | −1.66643 | − | 2.88635i | ||||
\(276\) | −2.55496 | − | 4.42532i | −0.153790 | − | 0.266373i | ||||
\(277\) | 0.731250 | − | 1.26656i | 0.0439366 | − | 0.0761004i | −0.843221 | − | 0.537567i | \(-0.819343\pi\) |
0.887157 | + | 0.461467i | \(0.152677\pi\) | |||||||
\(278\) | −6.09783 | −0.365724 | ||||||||
\(279\) | 0.486426 | − | 0.842515i | 0.0291216 | − | 0.0504401i | ||||
\(280\) | −1.40097 | + | 2.42655i | −0.0837239 | + | 0.145014i | ||||
\(281\) | 5.68233 | 0.338980 | 0.169490 | − | 0.985532i | \(-0.445788\pi\) | ||||
0.169490 | + | 0.985532i | \(0.445788\pi\) | |||||||
\(282\) | −3.60388 | + | 6.24210i | −0.214608 | + | 0.371711i | ||||
\(283\) | 12.6039 | + | 21.8306i | 0.749223 | + | 1.29769i | 0.948196 | + | 0.317687i | \(0.102906\pi\) |
−0.198973 | + | 0.980005i | \(0.563761\pi\) | |||||||
\(284\) | −0.664874 | − | 1.15160i | −0.0394530 | − | 0.0683347i | ||||
\(285\) | −7.20775 | −0.426950 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.04221 | 0.0615199 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −18.7620 | − | 32.4968i | −1.10365 | − | 1.91158i | ||||
\(290\) | −6.77144 | + | 11.7285i | −0.397633 | + | 0.688720i | ||||
\(291\) | 8.54288 | 0.500792 | ||||||||
\(292\) | −3.82640 | + | 6.62751i | −0.223923 | + | 0.387846i | ||||
\(293\) | 3.57457 | − | 6.19134i | 0.208829 | − | 0.361702i | −0.742517 | − | 0.669827i | \(-0.766368\pi\) |
0.951346 | + | 0.308125i | \(0.0997015\pi\) | |||||||
\(294\) | −6.52111 | −0.380319 | ||||||||
\(295\) | −2.64795 | + | 4.58638i | −0.154170 | + | 0.267029i | ||||
\(296\) | 0.643104 | + | 1.11389i | 0.0373797 | + | 0.0647435i | ||||
\(297\) | −2.42543 | − | 4.20096i | −0.140738 | − | 0.243765i | ||||
\(298\) | 2.55257 | 0.147866 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 11.3937 | 0.657817 | ||||||||
\(301\) | −2.87800 | − | 4.98485i | −0.165885 | − | 0.287322i | ||||
\(302\) | −8.85839 | − | 15.3432i | −0.509743 | − | 0.882901i | ||||
\(303\) | 5.99880 | − | 10.3902i | 0.344622 | − | 0.596903i | ||||
\(304\) | 1.78017 | 0.102100 | ||||||||
\(305\) | −0.801938 | + | 1.38900i | −0.0459188 | + | 0.0795337i | ||||
\(306\) | −3.69202 | + | 6.39477i | −0.211059 | + | 0.365565i | ||||
\(307\) | −17.9952 | −1.02704 | −0.513521 | − | 0.858077i | \(-0.671659\pi\) | ||||
−0.513521 | + | 0.858077i | \(0.671659\pi\) | |||||||
\(308\) | 1.67845 | − | 2.90716i | 0.0956384 | − | 0.165651i | ||||
\(309\) | 6.16152 | + | 10.6721i | 0.350517 | + | 0.607113i | ||||
\(310\) | −1.96950 | − | 3.41127i | −0.111860 | − | 0.193747i | ||||
\(311\) | 3.32975 | 0.188813 | 0.0944064 | − | 0.995534i | \(-0.469905\pi\) | ||||
0.0944064 | + | 0.995534i | \(0.469905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.8834 | −1.01083 | −0.505414 | − | 0.862877i | \(-0.668660\pi\) | ||||
−0.505414 | + | 0.862877i | \(0.668660\pi\) | |||||||
\(314\) | 3.15883 | + | 5.47126i | 0.178263 | + | 0.308761i | ||||
\(315\) | −1.40097 | − | 2.42655i | −0.0789357 | − | 0.136721i | ||||
\(316\) | 4.16972 | − | 7.22216i | 0.234565 | − | 0.406279i | ||||
\(317\) | 4.39373 | 0.246777 | 0.123388 | − | 0.992358i | \(-0.460624\pi\) | ||||
0.123388 | + | 0.992358i | \(0.460624\pi\) | |||||||
\(318\) | −6.73825 | + | 11.6710i | −0.377862 | + | 0.654477i | ||||
\(319\) | 8.11260 | − | 14.0514i | 0.454219 | − | 0.786730i | ||||
\(320\) | −4.04892 | −0.226341 | ||||||||
\(321\) | −2.94989 | + | 5.10935i | −0.164647 | + | 0.285176i | ||||
\(322\) | 1.76809 | + | 3.06241i | 0.0985316 | + | 0.170662i | ||||
\(323\) | −6.57242 | − | 11.3838i | −0.365699 | − | 0.633409i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.5918 | 0.808165 | ||||||||
\(327\) | 0.396125 | + | 0.686108i | 0.0219057 | + | 0.0379418i | ||||
\(328\) | 0.753020 | + | 1.30427i | 0.0415786 | + | 0.0720162i | ||||
\(329\) | 2.49396 | − | 4.31966i | 0.137496 | − | 0.238151i | ||||
\(330\) | −19.6407 | −1.08119 | ||||||||
\(331\) | 12.8388 | − | 22.2374i | 0.705683 | − | 1.22228i | −0.260762 | − | 0.965403i | \(-0.583974\pi\) |
0.966445 | − | 0.256875i | \(-0.0826930\pi\) | |||||||
\(332\) | 7.66368 | − | 13.2739i | 0.420599 | − | 0.728499i | ||||
\(333\) | −1.28621 | −0.0704838 | ||||||||
\(334\) | 9.75063 | − | 16.8886i | 0.533531 | − | 0.924102i | ||||
\(335\) | −12.2567 | − | 21.2292i | −0.669653 | − | 1.15987i | ||||
\(336\) | 0.346011 | + | 0.599308i | 0.0188764 | + | 0.0326949i | ||||
\(337\) | −24.6504 | −1.34279 | −0.671396 | − | 0.741098i | \(-0.734305\pi\) | ||||
−0.671396 | + | 0.741098i | \(0.734305\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.21983 | 0.337815 | ||||||||
\(340\) | 14.9487 | + | 25.8919i | 0.810707 | + | 1.40418i | ||||
\(341\) | 2.35958 | + | 4.08692i | 0.127779 | + | 0.221319i | ||||
\(342\) | −0.890084 | + | 1.54167i | −0.0481302 | + | 0.0833640i | ||||
\(343\) | 9.35690 | 0.505225 | ||||||||
\(344\) | 4.15883 | − | 7.20331i | 0.224229 | − | 0.388377i | ||||
\(345\) | 10.3448 | − | 17.9177i | 0.556946 | − | 0.964659i | ||||
\(346\) | −9.29052 | −0.499461 | ||||||||
\(347\) | −7.14795 | + | 12.3806i | −0.383722 | + | 0.664626i | −0.991591 | − | 0.129411i | \(-0.958691\pi\) |
0.607869 | + | 0.794037i | \(0.292025\pi\) | |||||||
\(348\) | 1.67241 | + | 2.89669i | 0.0896504 | + | 0.155279i | ||||
\(349\) | −5.53079 | − | 9.57962i | −0.296057 | − | 0.512785i | 0.679173 | − | 0.733978i | \(-0.262338\pi\) |
−0.975230 | + | 0.221193i | \(0.929005\pi\) | |||||||
\(350\) | −7.88471 | −0.421455 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.85086 | 0.258551 | ||||||||
\(353\) | 5.25236 | + | 9.09735i | 0.279555 | + | 0.484203i | 0.971274 | − | 0.237963i | \(-0.0764798\pi\) |
−0.691719 | + | 0.722166i | \(0.743146\pi\) | |||||||
\(354\) | 0.653989 | + | 1.13274i | 0.0347591 | + | 0.0602046i | ||||
\(355\) | 2.69202 | − | 4.66272i | 0.142878 | − | 0.247471i | ||||
\(356\) | −3.10992 | −0.164825 | ||||||||
\(357\) | 2.55496 | − | 4.42532i | 0.135223 | − | 0.234213i | ||||
\(358\) | −11.3964 | + | 19.7392i | −0.602320 | + | 1.04325i | ||||
\(359\) | 5.10992 | 0.269691 | 0.134846 | − | 0.990867i | \(-0.456946\pi\) | ||||
0.134846 | + | 0.990867i | \(0.456946\pi\) | |||||||
\(360\) | 2.02446 | − | 3.50647i | 0.106698 | − | 0.184807i | ||||
\(361\) | 7.91550 | + | 13.7101i | 0.416605 | + | 0.721582i | ||||
\(362\) | −0.268750 | − | 0.465488i | −0.0141252 | − | 0.0244655i | ||||
\(363\) | 12.5308 | 0.657696 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.9855 | −1.62186 | ||||||||
\(366\) | 0.198062 | + | 0.343054i | 0.0103529 | + | 0.0179317i | ||||
\(367\) | 4.22401 | + | 7.31620i | 0.220492 | + | 0.381903i | 0.954957 | − | 0.296743i | \(-0.0959005\pi\) |
−0.734466 | + | 0.678646i | \(0.762567\pi\) | |||||||
\(368\) | −2.55496 | + | 4.42532i | −0.133186 | + | 0.230686i | ||||
\(369\) | −1.50604 | −0.0784014 | ||||||||
\(370\) | −2.60388 | + | 4.51004i | −0.135369 | + | 0.234466i | ||||
\(371\) | 4.66301 | − | 8.07658i | 0.242092 | − | 0.419315i | ||||
\(372\) | −0.972853 | −0.0504401 | ||||||||
\(373\) | −3.84548 | + | 6.66056i | −0.199111 | + | 0.344871i | −0.948241 | − | 0.317553i | \(-0.897139\pi\) |
0.749129 | + | 0.662424i | \(0.230472\pi\) | |||||||
\(374\) | −17.9095 | − | 31.0201i | −0.926076 | − | 1.60401i | ||||
\(375\) | 12.9438 | + | 22.4194i | 0.668417 | + | 1.15773i | ||||
\(376\) | 7.20775 | 0.371711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.692021 | −0.0355937 | ||||||||
\(379\) | 5.70171 | + | 9.87565i | 0.292877 | + | 0.507278i | 0.974489 | − | 0.224436i | \(-0.0720540\pi\) |
−0.681612 | + | 0.731714i | \(0.738721\pi\) | |||||||
\(380\) | 3.60388 | + | 6.24210i | 0.184875 | + | 0.320213i | ||||
\(381\) | 3.00269 | − | 5.20081i | 0.153832 | − | 0.266446i | ||||
\(382\) | −9.79954 | −0.501388 | ||||||||
\(383\) | −10.3351 | + | 17.9010i | −0.528100 | + | 0.914696i | 0.471363 | + | 0.881939i | \(0.343762\pi\) |
−0.999463 | + | 0.0327572i | \(0.989571\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 13.5918 | 0.692702 | ||||||||
\(386\) | 7.09783 | − | 12.2938i | 0.361270 | − | 0.625738i | ||||
\(387\) | 4.15883 | + | 7.20331i | 0.211405 | + | 0.366165i | ||||
\(388\) | −4.27144 | − | 7.39835i | −0.216849 | − | 0.375594i | ||||
\(389\) | 17.4776 | 0.886148 | 0.443074 | − | 0.896485i | \(-0.353888\pi\) | ||||
0.443074 | + | 0.896485i | \(0.353888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.7318 | 1.90818 | ||||||||
\(392\) | 3.26055 | + | 5.64744i | 0.164683 | + | 0.285239i | ||||
\(393\) | −4.40850 | − | 7.63575i | −0.222379 | − | 0.385173i | ||||
\(394\) | 1.50484 | − | 2.60647i | 0.0758130 | − | 0.131312i | ||||
\(395\) | 33.7657 | 1.69894 | ||||||||
\(396\) | −2.42543 | + | 4.20096i | −0.121882 | + | 0.211106i | ||||
\(397\) | 9.67994 | − | 16.7661i | 0.485822 | − | 0.841469i | −0.514045 | − | 0.857763i | \(-0.671854\pi\) |
0.999867 | + | 0.0162944i | \(0.00518690\pi\) | |||||||
\(398\) | 12.8944 | 0.646338 | ||||||||
\(399\) | 0.615957 | − | 1.06687i | 0.0308364 | − | 0.0534103i | ||||
\(400\) | −5.69687 | − | 9.86726i | −0.284843 | − | 0.493363i | ||||
\(401\) | 7.24160 | + | 12.5428i | 0.361628 | + | 0.626359i | 0.988229 | − | 0.152982i | \(-0.0488876\pi\) |
−0.626601 | + | 0.779341i | \(0.715554\pi\) | |||||||
\(402\) | −6.05429 | −0.301961 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −11.9976 | −0.596903 | ||||||||
\(405\) | 2.02446 | + | 3.50647i | 0.100596 | + | 0.174238i | ||||
\(406\) | −1.15734 | − | 2.00457i | −0.0574379 | − | 0.0994854i | ||||
\(407\) | 3.11960 | − | 5.40331i | 0.154633 | − | 0.267832i | ||||
\(408\) | 7.38404 | 0.365565 | ||||||||
\(409\) | 9.44922 | − | 16.3665i | 0.467234 | − | 0.809273i | −0.532065 | − | 0.846703i | \(-0.678584\pi\) |
0.999299 | + | 0.0374304i | \(0.0119172\pi\) | |||||||
\(410\) | −3.04892 | + | 5.28088i | −0.150575 | + | 0.260804i | ||||
\(411\) | 15.7560 | 0.777186 | ||||||||
\(412\) | 6.16152 | − | 10.6721i | 0.303556 | − | 0.525775i | ||||
\(413\) | −0.452575 | − | 0.783882i | −0.0222697 | − | 0.0385723i | ||||
\(414\) | −2.55496 | − | 4.42532i | −0.125569 | − | 0.217492i | ||||
\(415\) | 62.0592 | 3.04637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.09783 | −0.298612 | ||||||||
\(418\) | −4.31767 | − | 7.47842i | −0.211184 | − | 0.365781i | ||||
\(419\) | 10.8802 | + | 18.8450i | 0.531531 | + | 0.920638i | 0.999323 | + | 0.0367993i | \(0.0117162\pi\) |
−0.467792 | + | 0.883838i | \(0.654950\pi\) | |||||||
\(420\) | −1.40097 | + | 2.42655i | −0.0683603 | + | 0.118403i | ||||
\(421\) | 20.5918 | 1.00358 | 0.501791 | − | 0.864989i | \(-0.332675\pi\) | ||||
0.501791 | + | 0.864989i | \(0.332675\pi\) | |||||||
\(422\) | −3.89977 | + | 6.75460i | −0.189838 | + | 0.328809i | ||||
\(423\) | −3.60388 | + | 6.24210i | −0.175226 | + | 0.303501i | ||||
\(424\) | 13.4765 | 0.654477 | ||||||||
\(425\) | −42.0659 | + | 72.8603i | −2.04050 | + | 3.53424i | ||||
\(426\) | −0.664874 | − | 1.15160i | −0.0322133 | − | 0.0557950i | ||||
\(427\) | −0.137063 | − | 0.237401i | −0.00663296 | − | 0.0114886i | ||||
\(428\) | 5.89977 | 0.285176 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.6775 | 1.62408 | ||||||||
\(431\) | −17.2567 | − | 29.8894i | −0.831224 | − | 1.43972i | −0.897068 | − | 0.441893i | \(-0.854307\pi\) |
0.0658433 | − | 0.997830i | \(-0.479026\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 1.06315 | − | 1.84144i | 0.0510920 | − | 0.0884939i | −0.839348 | − | 0.543594i | \(-0.817063\pi\) |
0.890440 | + | 0.455100i | \(0.150397\pi\) | |||||||
\(434\) | 0.673235 | 0.0323163 | ||||||||
\(435\) | −6.77144 | + | 11.7285i | −0.324666 | + | 0.562337i | ||||
\(436\) | 0.396125 | − | 0.686108i | 0.0189709 | − | 0.0328586i | ||||
\(437\) | 9.09651 | 0.435145 | ||||||||
\(438\) | −3.82640 | + | 6.62751i | −0.182832 | + | 0.316675i | ||||
\(439\) | −10.9160 | − | 18.9071i | −0.520994 | − | 0.902388i | −0.999702 | − | 0.0244137i | \(-0.992228\pi\) |
0.478708 | − | 0.877974i | \(-0.341105\pi\) | |||||||
\(440\) | 9.82036 | + | 17.0094i | 0.468167 | + | 0.810889i | ||||
\(441\) | −6.52111 | −0.310529 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.54048 | −0.358259 | −0.179130 | − | 0.983825i | \(-0.557328\pi\) | ||||
−0.179130 | + | 0.983825i | \(0.557328\pi\) | |||||||
\(444\) | 0.643104 | + | 1.11389i | 0.0305204 | + | 0.0528628i | ||||
\(445\) | −6.29590 | − | 10.9048i | −0.298454 | − | 0.516938i | ||||
\(446\) | 6.09783 | − | 10.5618i | 0.288741 | − | 0.500114i | ||||
\(447\) | 2.55257 | 0.120732 | ||||||||
\(448\) | 0.346011 | − | 0.599308i | 0.0163475 | − | 0.0283146i | ||||
\(449\) | −9.87800 | + | 17.1092i | −0.466172 | + | 0.807433i | −0.999254 | − | 0.0386305i | \(-0.987700\pi\) |
0.533082 | + | 0.846064i | \(0.321034\pi\) | |||||||
\(450\) | 11.3937 | 0.537106 | ||||||||
\(451\) | 3.65279 | − | 6.32682i | 0.172003 | − | 0.297918i | ||||
\(452\) | −3.10992 | − | 5.38653i | −0.146278 | − | 0.253361i | ||||
\(453\) | −8.85839 | − | 15.3432i | −0.416203 | − | 0.720885i | ||||
\(454\) | 6.74333 | 0.316480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.78017 | 0.0833640 | ||||||||
\(457\) | −11.9291 | − | 20.6618i | −0.558019 | − | 0.966517i | −0.997662 | − | 0.0683441i | \(-0.978228\pi\) |
0.439643 | − | 0.898173i | \(-0.355105\pi\) | |||||||
\(458\) | 9.91185 | + | 17.1678i | 0.463151 | + | 0.802200i | ||||
\(459\) | −3.69202 | + | 6.39477i | −0.172329 | + | 0.298482i | ||||
\(460\) | −20.6896 | −0.964659 | ||||||||
\(461\) | 8.78866 | − | 15.2224i | 0.409329 | − | 0.708978i | −0.585486 | − | 0.810683i | \(-0.699096\pi\) |
0.994815 | + | 0.101704i | \(0.0324296\pi\) | |||||||
\(462\) | 1.67845 | − | 2.90716i | 0.0780885 | − | 0.135253i | ||||
\(463\) | 23.8431 | 1.10808 | 0.554041 | − | 0.832489i | \(-0.313085\pi\) | ||||
0.554041 | + | 0.832489i | \(0.313085\pi\) | |||||||
\(464\) | 1.67241 | − | 2.89669i | 0.0776396 | − | 0.134476i | ||||
\(465\) | −1.96950 | − | 3.41127i | −0.0913334 | − | 0.158194i | ||||
\(466\) | 15.0151 | + | 26.0069i | 0.695559 | + | 1.20474i | ||||
\(467\) | 8.61058 | 0.398450 | 0.199225 | − | 0.979954i | \(-0.436158\pi\) | ||||
0.199225 | + | 0.979954i | \(0.436158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.18970 | 0.193462 | ||||||||
\(470\) | 14.5918 | + | 25.2737i | 0.673069 | + | 1.16579i | ||||
\(471\) | 3.15883 | + | 5.47126i | 0.145551 | + | 0.252102i | ||||
\(472\) | 0.653989 | − | 1.13274i | 0.0301023 | − | 0.0521387i | ||||
\(473\) | −40.3478 | −1.85519 | ||||||||
\(474\) | 4.16972 | − | 7.22216i | 0.191522 | − | 0.331725i | ||||
\(475\) | −10.1414 | + | 17.5654i | −0.465318 | + | 0.805955i | ||||
\(476\) | −5.10992 | −0.234213 | ||||||||
\(477\) | −6.73825 | + | 11.6710i | −0.308523 | + | 0.534378i | ||||
\(478\) | −11.0489 | − | 19.1373i | −0.505366 | − | 0.875319i | ||||
\(479\) | −3.29052 | − | 5.69935i | −0.150348 | − | 0.260410i | 0.781008 | − | 0.624522i | \(-0.214706\pi\) |
−0.931355 | + | 0.364112i | \(0.881373\pi\) | |||||||
\(480\) | −4.04892 | −0.184807 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.1274 | 0.461289 | ||||||||
\(483\) | 1.76809 | + | 3.06241i | 0.0804507 | + | 0.139345i | ||||
\(484\) | −6.26540 | − | 10.8520i | −0.284791 | − | 0.493272i | ||||
\(485\) | 17.2947 | − | 29.9553i | 0.785312 | − | 1.36020i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 11.6380 | − | 20.1576i | 0.527369 | − | 0.913430i | −0.472122 | − | 0.881533i | \(-0.656512\pi\) |
0.999491 | − | 0.0318970i | \(-0.0101548\pi\) | |||||||
\(488\) | 0.198062 | − | 0.343054i | 0.00896586 | − | 0.0155293i | ||||
\(489\) | 14.5918 | 0.659864 | ||||||||
\(490\) | −13.2017 | + | 22.8660i | −0.596392 | + | 1.03298i | ||||
\(491\) | 7.77024 | + | 13.4585i | 0.350666 | + | 0.607372i | 0.986366 | − | 0.164565i | \(-0.0526219\pi\) |
−0.635700 | + | 0.771936i | \(0.719289\pi\) | |||||||
\(492\) | 0.753020 | + | 1.30427i | 0.0339488 | + | 0.0588010i | ||||
\(493\) | −24.6983 | −1.11235 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.6407 | −0.882784 | ||||||||
\(496\) | 0.486426 | + | 0.842515i | 0.0218412 | + | 0.0378301i | ||||
\(497\) | 0.460107 | + | 0.796929i | 0.0206386 | + | 0.0357472i | ||||
\(498\) | 7.66368 | − | 13.2739i | 0.343418 | − | 0.594817i | ||||
\(499\) | 9.53617 | 0.426898 | 0.213449 | − | 0.976954i | \(-0.431530\pi\) | ||||
0.213449 | + | 0.976954i | \(0.431530\pi\) | |||||||
\(500\) | 12.9438 | − | 22.4194i | 0.578866 | − | 1.00263i | ||||
\(501\) | 9.75063 | − | 16.8886i | 0.435626 | − | 0.754526i | ||||
\(502\) | 5.54719 | 0.247583 | ||||||||
\(503\) | 6.91723 | − | 11.9810i | 0.308424 | − | 0.534206i | −0.669594 | − | 0.742728i | \(-0.733532\pi\) |
0.978018 | + | 0.208521i | \(0.0668651\pi\) | |||||||
\(504\) | 0.346011 | + | 0.599308i | 0.0154125 | + | 0.0266953i | ||||
\(505\) | −24.2887 | − | 42.0692i | −1.08083 | − | 1.87205i | ||||
\(506\) | 24.7875 | 1.10194 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.00538 | −0.266446 | ||||||||
\(509\) | 20.4819 | + | 35.4757i | 0.907843 | + | 1.57243i | 0.817054 | + | 0.576560i | \(0.195605\pi\) |
0.0907888 | + | 0.995870i | \(0.471061\pi\) | |||||||
\(510\) | 14.9487 | + | 25.8919i | 0.661939 | + | 1.14651i | ||||
\(511\) | 2.64795 | − | 4.58638i | 0.117138 | − | 0.202890i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.890084 | + | 1.54167i | −0.0392982 | + | 0.0680664i | ||||
\(514\) | 6.89977 | − | 11.9508i | 0.304336 | − | 0.527125i | ||||
\(515\) | 49.8950 | 2.19864 | ||||||||
\(516\) | 4.15883 | − | 7.20331i | 0.183082 | − | 0.317108i | ||||
\(517\) | −17.4819 | − | 30.2795i | −0.768852 | − | 1.33169i | ||||
\(518\) | −0.445042 | − | 0.770835i | −0.0195540 | − | 0.0338686i | ||||
\(519\) | −9.29052 | −0.407809 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.3672 | 1.59327 | 0.796637 | − | 0.604457i | \(-0.206610\pi\) | ||||
0.796637 | + | 0.604457i | \(0.206610\pi\) | |||||||
\(522\) | 1.67241 | + | 2.89669i | 0.0731993 | + | 0.126785i | ||||
\(523\) | 3.01507 | + | 5.22225i | 0.131840 | + | 0.228353i | 0.924386 | − | 0.381459i | \(-0.124578\pi\) |
−0.792546 | + | 0.609812i | \(0.791245\pi\) | |||||||
\(524\) | −4.40850 | + | 7.63575i | −0.192586 | + | 0.333569i | ||||
\(525\) | −7.88471 | −0.344117 | ||||||||
\(526\) | 11.2349 | − | 19.4594i | 0.489865 | − | 0.848471i | ||||
\(527\) | 3.59179 | − | 6.22117i | 0.156461 | − | 0.270998i | ||||
\(528\) | 4.85086 | 0.211106 | ||||||||
\(529\) | −1.55562 | + | 2.69442i | −0.0676357 | + | 0.117149i | ||||
\(530\) | 27.2826 | + | 47.2549i | 1.18508 | + | 2.05262i | ||||
\(531\) | 0.653989 | + | 1.13274i | 0.0283807 | + | 0.0491568i | ||||
\(532\) | −1.23191 | −0.0534103 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.10992 | −0.134579 | ||||||||
\(535\) | 11.9438 | + | 20.6873i | 0.516377 | + | 0.894392i | ||||
\(536\) | 3.02715 | + | 5.24317i | 0.130753 | + | 0.226471i | ||||
\(537\) | −11.3964 | + | 19.7392i | −0.491792 | + | 0.851808i | ||||
\(538\) | −26.0140 | −1.12154 | ||||||||
\(539\) | 15.8165 | − | 27.3949i | 0.681264 | − | 1.17998i | ||||
\(540\) | 2.02446 | − | 3.50647i | 0.0871188 | − | 0.150894i | ||||
\(541\) | −7.92154 | −0.340574 | −0.170287 | − | 0.985395i | \(-0.554469\pi\) | ||||
−0.170287 | + | 0.985395i | \(0.554469\pi\) | |||||||
\(542\) | −1.44235 | + | 2.49823i | −0.0619544 | + | 0.107308i | ||||
\(543\) | −0.268750 | − | 0.465488i | −0.0115332 | − | 0.0199760i | ||||
\(544\) | −3.69202 | − | 6.39477i | −0.158294 | − | 0.274173i | ||||
\(545\) | 3.20775 | 0.137405 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.4155 | 0.787390 | 0.393695 | − | 0.919241i | \(-0.371197\pi\) | ||||
0.393695 | + | 0.919241i | \(0.371197\pi\) | |||||||
\(548\) | −7.87800 | − | 13.6451i | −0.336532 | − | 0.582890i | ||||
\(549\) | 0.198062 | + | 0.343054i | 0.00845309 | + | 0.0146412i | ||||
\(550\) | −27.6347 | + | 47.8647i | −1.17835 | + | 2.04096i | ||||
\(551\) | −5.95433 | −0.253663 | ||||||||
\(552\) | −2.55496 | + | 4.42532i | −0.108746 | + | 0.188354i | ||||
\(553\) | −2.88553 | + | 4.99789i | −0.122705 | + | 0.212532i | ||||
\(554\) | −1.46250 | −0.0621357 | ||||||||
\(555\) | −2.60388 | + | 4.51004i | −0.110528 | + | 0.191441i | ||||
\(556\) | 3.04892 | + | 5.28088i | 0.129303 | + | 0.223959i | ||||
\(557\) | 11.9879 | + | 20.7637i | 0.507944 | + | 0.879786i | 0.999958 | + | 0.00919783i | \(0.00292780\pi\) |
−0.492013 | + | 0.870588i | \(0.663739\pi\) | |||||||
\(558\) | −0.972853 | −0.0411841 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.80194 | 0.118403 | ||||||||
\(561\) | −17.9095 | − | 31.0201i | −0.756138 | − | 1.30967i | ||||
\(562\) | −2.84117 | − | 4.92104i | −0.119847 | − | 0.207582i | ||||
\(563\) | 1.14646 | − | 1.98572i | 0.0483174 | − | 0.0836882i | −0.840855 | − | 0.541260i | \(-0.817947\pi\) |
0.889173 | + | 0.457572i | \(0.151281\pi\) | |||||||
\(564\) | 7.20775 | 0.303501 | ||||||||
\(565\) | 12.5918 | − | 21.8096i | 0.529741 | − | 0.917538i | ||||
\(566\) | 12.6039 | − | 21.8306i | 0.529780 | − | 0.917607i | ||||
\(567\) | −0.692021 | −0.0290622 | ||||||||
\(568\) | −0.664874 | + | 1.15160i | −0.0278975 | + | 0.0483199i | ||||
\(569\) | 22.1715 | + | 38.4022i | 0.929478 | + | 1.60990i | 0.784197 | + | 0.620513i | \(0.213075\pi\) |
0.145281 | + | 0.989390i | \(0.453591\pi\) | |||||||
\(570\) | 3.60388 | + | 6.24210i | 0.150950 | + | 0.261453i | ||||
\(571\) | −15.2707 | −0.639058 | −0.319529 | − | 0.947577i | \(-0.603525\pi\) | ||||
−0.319529 | + | 0.947577i | \(0.603525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.79954 | −0.409382 | ||||||||
\(574\) | −0.521106 | − | 0.902583i | −0.0217506 | − | 0.0376731i | ||||
\(575\) | −29.1105 | − | 50.4209i | −1.21399 | − | 2.10270i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 8.77048 | 0.365120 | 0.182560 | − | 0.983195i | \(-0.441562\pi\) | ||||
0.182560 | + | 0.983195i | \(0.441562\pi\) | |||||||
\(578\) | −18.7620 | + | 32.4968i | −0.780398 | + | 1.35169i | ||||
\(579\) | 7.09783 | − | 12.2938i | 0.294976 | − | 0.510913i | ||||
\(580\) | 13.5429 | 0.562337 | ||||||||
\(581\) | −5.30343 | + | 9.18581i | −0.220023 | + | 0.381092i | ||||
\(582\) | −4.27144 | − | 7.39835i | −0.177057 | − | 0.306671i | ||||
\(583\) | −32.6863 | − | 56.6143i | −1.35373 | − | 2.34472i | ||||
\(584\) | 7.65279 | 0.316675 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.14914 | −0.295328 | ||||||||
\(587\) | 19.0715 | + | 33.0328i | 0.787166 | + | 1.36341i | 0.927697 | + | 0.373335i | \(0.121786\pi\) |
−0.140531 | + | 0.990076i | \(0.544881\pi\) | |||||||
\(588\) | 3.26055 | + | 5.64744i | 0.134463 | + | 0.232897i | ||||
\(589\) | 0.865921 | − | 1.49982i | 0.0356796 | − | 0.0617989i | ||||
\(590\) | 5.29590 | 0.218029 | ||||||||
\(591\) | 1.50484 | − | 2.60647i | 0.0619010 | − | 0.107216i | ||||
\(592\) | 0.643104 | − | 1.11389i | 0.0264314 | − | 0.0457806i | ||||
\(593\) | −37.9517 | −1.55849 | −0.779244 | − | 0.626720i | \(-0.784397\pi\) | ||||
−0.779244 | + | 0.626720i | \(0.784397\pi\) | |||||||
\(594\) | −2.42543 | + | 4.20096i | −0.0995165 | + | 0.172368i | ||||
\(595\) | −10.3448 | − | 17.9177i | −0.424096 | − | 0.734556i | ||||
\(596\) | −1.27628 | − | 2.21059i | −0.0522786 | − | 0.0905491i | ||||
\(597\) | 12.8944 | 0.527732 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.57971 | −0.146263 | −0.0731315 | − | 0.997322i | \(-0.523299\pi\) | ||||
−0.0731315 | + | 0.997322i | \(0.523299\pi\) | |||||||
\(600\) | −5.69687 | − | 9.86726i | −0.232574 | − | 0.402829i | ||||
\(601\) | 2.85839 | + | 4.95087i | 0.116596 | + | 0.201950i | 0.918417 | − | 0.395615i | \(-0.129468\pi\) |
−0.801821 | + | 0.597565i | \(0.796135\pi\) | |||||||
\(602\) | −2.87800 | + | 4.98485i | −0.117299 | + | 0.203167i | ||||
\(603\) | −6.05429 | −0.246550 | ||||||||
\(604\) | −8.85839 | + | 15.3432i | −0.360443 | + | 0.624305i | ||||
\(605\) | 25.3681 | − | 43.9388i | 1.03136 | − | 1.78637i | ||||
\(606\) | −11.9976 | −0.487369 | ||||||||
\(607\) | −11.2143 | + | 19.4238i | −0.455175 | + | 0.788387i | −0.998698 | − | 0.0510075i | \(-0.983757\pi\) |
0.543523 | + | 0.839394i | \(0.317090\pi\) | |||||||
\(608\) | −0.890084 | − | 1.54167i | −0.0360977 | − | 0.0625230i | ||||
\(609\) | −1.15734 | − | 2.00457i | −0.0468979 | − | 0.0812295i | ||||
\(610\) | 1.60388 | 0.0649390 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.38404 | 0.298482 | ||||||||
\(613\) | 19.9801 | + | 34.6066i | 0.806991 | + | 1.39775i | 0.914939 | + | 0.403592i | \(0.132239\pi\) |
−0.107948 | + | 0.994157i | \(0.534428\pi\) | |||||||
\(614\) | 8.99761 | + | 15.5843i | 0.363114 | + | 0.628932i | ||||
\(615\) | −3.04892 | + | 5.28088i | −0.122944 | + | 0.212946i | ||||
\(616\) | −3.35690 | −0.135253 | ||||||||
\(617\) | −15.7235 | + | 27.2339i | −0.633003 | + | 1.09639i | 0.353931 | + | 0.935272i | \(0.384845\pi\) |
−0.986934 | + | 0.161123i | \(0.948489\pi\) | |||||||
\(618\) | 6.16152 | − | 10.6721i | 0.247853 | − | 0.429294i | ||||
\(619\) | −29.3685 | −1.18042 | −0.590210 | − | 0.807250i | \(-0.700955\pi\) | ||||
−0.590210 | + | 0.807250i | \(0.700955\pi\) | |||||||
\(620\) | −1.96950 | + | 3.41127i | −0.0790970 | + | 0.137000i | ||||
\(621\) | −2.55496 | − | 4.42532i | −0.102527 | − | 0.177582i | ||||
\(622\) | −1.66487 | − | 2.88365i | −0.0667554 | − | 0.115624i | ||||
\(623\) | 2.15213 | 0.0862232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47.8485 | 1.91394 | ||||||||
\(626\) | 8.94169 | + | 15.4875i | 0.357382 | + | 0.619003i | ||||
\(627\) | −4.31767 | − | 7.47842i | −0.172431 | − | 0.298659i | ||||
\(628\) | 3.15883 | − | 5.47126i | 0.126051 | − | 0.218327i | ||||
\(629\) | −9.49742 | −0.378687 | ||||||||
\(630\) | −1.40097 | + | 2.42655i | −0.0558159 | + | 0.0966760i | ||||
\(631\) | −10.8400 | + | 18.7754i | −0.431532 | + | 0.747436i | −0.997005 | − | 0.0773307i | \(-0.975360\pi\) |
0.565473 | + | 0.824767i | \(0.308694\pi\) | |||||||
\(632\) | −8.33944 | −0.331725 | ||||||||
\(633\) | −3.89977 | + | 6.75460i | −0.155002 | + | 0.268471i | ||||
\(634\) | −2.19687 | − | 3.80508i | −0.0872487 | − | 0.151119i | ||||
\(635\) | −12.1576 | − | 21.0576i | −0.482461 | − | 0.835647i | ||||
\(636\) | 13.4765 | 0.534378 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.2252 | −0.642362 | ||||||||
\(639\) | −0.664874 | − | 1.15160i | −0.0263020 | − | 0.0455564i | ||||
\(640\) | 2.02446 | + | 3.50647i | 0.0800238 | + | 0.138605i | ||||
\(641\) | −7.00538 | + | 12.1337i | −0.276696 | + | 0.479251i | −0.970562 | − | 0.240853i | \(-0.922573\pi\) |
0.693866 | + | 0.720104i | \(0.255906\pi\) | |||||||
\(642\) | 5.89977 | 0.232845 | ||||||||
\(643\) | −15.3937 | + | 26.6627i | −0.607070 | + | 1.05148i | 0.384651 | + | 0.923062i | \(0.374322\pi\) |
−0.991721 | + | 0.128413i | \(0.959012\pi\) | |||||||
\(644\) | 1.76809 | − | 3.06241i | 0.0696723 | − | 0.120676i | ||||
\(645\) | 33.6775 | 1.32605 | ||||||||
\(646\) | −6.57242 | + | 11.3838i | −0.258588 | + | 0.447888i | ||||
\(647\) | 8.30127 | + | 14.3782i | 0.326357 | + | 0.565266i | 0.981786 | − | 0.189990i | \(-0.0608456\pi\) |
−0.655429 | + | 0.755257i | \(0.727512\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −6.34481 | −0.249056 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.673235 | 0.0263862 | ||||||||
\(652\) | −7.29590 | − | 12.6369i | −0.285729 | − | 0.494898i | ||||
\(653\) | −14.2729 | − | 24.7214i | −0.558543 | − | 0.967425i | −0.997618 | − | 0.0689745i | \(-0.978027\pi\) |
0.439075 | − | 0.898450i | \(-0.355306\pi\) | |||||||
\(654\) | 0.396125 | − | 0.686108i | 0.0154897 | − | 0.0268289i | ||||
\(655\) | −35.6993 | −1.39489 | ||||||||
\(656\) | 0.753020 | − | 1.30427i | 0.0294005 | − | 0.0509232i | ||||
\(657\) | −3.82640 | + | 6.62751i | −0.149282 | + | 0.258564i | ||||
\(658\) | −4.98792 | −0.194449 | ||||||||
\(659\) | −13.8593 | + | 24.0051i | −0.539884 | + | 0.935106i | 0.459026 | + | 0.888423i | \(0.348198\pi\) |
−0.998910 | + | 0.0466830i | \(0.985135\pi\) | |||||||
\(660\) | 9.82036 | + | 17.0094i | 0.382257 | + | 0.662088i | ||||
\(661\) | −5.40044 | − | 9.35383i | −0.210053 | − | 0.363822i | 0.741678 | − | 0.670756i | \(-0.234030\pi\) |
−0.951731 | + | 0.306934i | \(0.900697\pi\) | |||||||
\(662\) | −25.6775 | −0.997986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3274 | −0.594817 | ||||||||
\(665\) | −2.49396 | − | 4.31966i | −0.0967116 | − | 0.167509i | ||||
\(666\) | 0.643104 | + | 1.11389i | 0.0249198 | + | 0.0431623i | ||||
\(667\) | 8.54586 | − | 14.8019i | 0.330897 | − | 0.573130i | ||||
\(668\) | −19.5013 | −0.754526 | ||||||||
\(669\) | 6.09783 | − | 10.5618i | 0.235756 | − | 0.408341i | ||||
\(670\) | −12.2567 | + | 21.2292i | −0.473516 | + | 0.820154i | ||||
\(671\) | −1.92154 | −0.0741803 | ||||||||
\(672\) | 0.346011 | − | 0.599308i | 0.0133477 | − | 0.0231188i | ||||
\(673\) | −8.16301 | − | 14.1388i | −0.314661 | − | 0.545009i | 0.664704 | − | 0.747107i | \(-0.268558\pi\) |
−0.979365 | + | 0.202098i | \(0.935224\pi\) | |||||||
\(674\) | 12.3252 | + | 21.3479i | 0.474749 | + | 0.822289i | ||||
\(675\) | 11.3937 | 0.438545 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.4252 | 1.59210 | 0.796050 | − | 0.605231i | \(-0.206919\pi\) | ||||
0.796050 | + | 0.605231i | \(0.206919\pi\) | |||||||
\(678\) | −3.10992 | − | 5.38653i | −0.119436 | − | 0.206869i | ||||
\(679\) | 2.95593 | + | 5.11982i | 0.113438 | + | 0.196480i | ||||
\(680\) | 14.9487 | − | 25.8919i | 0.573256 | − | 0.992909i | ||||
\(681\) | 6.74333 | 0.258405 | ||||||||
\(682\) | 2.35958 | − | 4.08692i | 0.0903532 | − | 0.156496i | ||||
\(683\) | −15.6163 | + | 27.0481i | −0.597539 | + | 1.03497i | 0.395644 | + | 0.918404i | \(0.370521\pi\) |
−0.993183 | + | 0.116564i | \(0.962812\pi\) | |||||||
\(684\) | 1.78017 | 0.0680664 | ||||||||
\(685\) | 31.8974 | − | 55.2479i | 1.21874 | − | 2.11091i | ||||
\(686\) | −4.67845 | − | 8.10331i | −0.178624 | − | 0.309386i | ||||
\(687\) | 9.91185 | + | 17.1678i | 0.378161 | + | 0.654994i | ||||
\(688\) | −8.31767 | −0.317108 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −20.6896 | −0.787641 | ||||||||
\(691\) | −12.4819 | − | 21.6192i | −0.474833 | − | 0.822435i | 0.524752 | − | 0.851255i | \(-0.324158\pi\) |
−0.999585 | + | 0.0288205i | \(0.990825\pi\) | |||||||
\(692\) | 4.64526 | + | 8.04583i | 0.176586 | + | 0.305856i | ||||
\(693\) | 1.67845 | − | 2.90716i | 0.0637590 | − | 0.110434i | ||||
\(694\) | 14.2959 | 0.542665 | ||||||||
\(695\) | −12.3448 | + | 21.3818i | −0.468265 | + | 0.811060i | ||||
\(696\) | 1.67241 | − | 2.89669i | 0.0633924 | − | 0.109799i | ||||
\(697\) | −11.1207 | −0.421225 | ||||||||
\(698\) | −5.53079 | + | 9.57962i | −0.209344 | + | 0.362594i | ||||
\(699\) | 15.0151 | + | 26.0069i | 0.567922 | + | 0.983670i | ||||
\(700\) | 3.94235 | + | 6.82836i | 0.149007 | + | 0.258088i | ||||
\(701\) | 8.17151 | 0.308634 | 0.154317 | − | 0.988021i | \(-0.450682\pi\) | ||||
0.154317 | + | 0.988021i | \(0.450682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.28967 | −0.0863564 | ||||||||
\(704\) | −2.42543 | − | 4.20096i | −0.0914117 | − | 0.158330i | ||||
\(705\) | 14.5918 | + | 25.2737i | 0.549559 | + | 0.951864i | ||||
\(706\) | 5.25236 | − | 9.09735i | 0.197675 | − | 0.342383i | ||||
\(707\) | 8.30260 | 0.312251 | ||||||||
\(708\) | 0.653989 | − | 1.13274i | 0.0245784 | − | 0.0425711i | ||||
\(709\) | 18.3991 | − | 31.8682i | 0.690993 | − | 1.19684i | −0.280520 | − | 0.959848i | \(-0.590507\pi\) |
0.971513 | − | 0.236987i | \(-0.0761598\pi\) | |||||||
\(710\) | −5.38404 | −0.202060 | ||||||||
\(711\) | 4.16972 | − | 7.22216i | 0.156377 | − | 0.270852i | ||||
\(712\) | 1.55496 | + | 2.69327i | 0.0582745 | + | 0.100934i | ||||
\(713\) | 2.48560 | + | 4.30518i | 0.0930864 | + | 0.161230i | ||||
\(714\) | −5.10992 | −0.191234 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.7928 | 0.851808 | ||||||||
\(717\) | −11.0489 | − | 19.1373i | −0.412629 | − | 0.714695i | ||||
\(718\) | −2.55496 | − | 4.42532i | −0.0953502 | − | 0.165151i | ||||
\(719\) | −17.6112 | + | 30.5034i | −0.656786 | + | 1.13759i | 0.324657 | + | 0.945832i | \(0.394751\pi\) |
−0.981443 | + | 0.191755i | \(0.938582\pi\) | |||||||
\(720\) | −4.04892 | −0.150894 | ||||||||
\(721\) | −4.26391 | + | 7.38530i | −0.158796 | + | 0.275043i | ||||
\(722\) | 7.91550 | − | 13.7101i | 0.294584 | − | 0.510235i | ||||
\(723\) | 10.1274 | 0.376641 | ||||||||
\(724\) | −0.268750 | + | 0.465488i | −0.00998801 | + | 0.0172997i | ||||
\(725\) | 19.0550 | + | 33.0042i | 0.707683 | + | 1.22574i | ||||
\(726\) | −6.26540 | − | 10.8520i | −0.232531 | − | 0.402755i | ||||
\(727\) | 40.6872 | 1.50901 | 0.754503 | − | 0.656297i | \(-0.227878\pi\) | ||||
0.754503 | + | 0.656297i | \(0.227878\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 15.4928 | + | 26.8343i | 0.573413 | + | 0.993180i | ||||
\(731\) | 30.7090 | + | 53.1896i | 1.13581 | + | 1.96729i | ||||
\(732\) | 0.198062 | − | 0.343054i | 0.00732059 | − | 0.0126796i | ||||
\(733\) | 27.1400 | 1.00244 | 0.501220 | − | 0.865320i | \(-0.332885\pi\) | ||||
0.501220 | + | 0.865320i | \(0.332885\pi\) | |||||||
\(734\) | 4.22401 | − | 7.31620i | 0.155911 | − | 0.270046i | ||||
\(735\) | −13.2017 | + | 22.8660i | −0.486952 | + | 0.843426i | ||||
\(736\) | 5.10992 | 0.188354 | ||||||||
\(737\) | 14.6843 | − | 25.4339i | 0.540901 | − | 0.936869i | ||||
\(738\) | 0.753020 | + | 1.30427i | 0.0277191 | + | 0.0480108i | ||||
\(739\) | −1.86294 | − | 3.22670i | −0.0685292 | − | 0.118696i | 0.829725 | − | 0.558173i | \(-0.188497\pi\) |
−0.898254 | + | 0.439476i | \(0.855164\pi\) | |||||||
\(740\) | 5.20775 | 0.191441 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.32603 | −0.342369 | ||||||||
\(743\) | −10.9293 | − | 18.9301i | −0.400958 | − | 0.694479i | 0.592884 | − | 0.805288i | \(-0.297989\pi\) |
−0.993842 | + | 0.110809i | \(0.964656\pi\) | |||||||
\(744\) | 0.486426 | + | 0.842515i | 0.0178333 | + | 0.0308881i | ||||
\(745\) | 5.16756 | − | 8.95048i | 0.189325 | − | 0.327920i | ||||
\(746\) | 7.69096 | 0.281586 | ||||||||
\(747\) | 7.66368 | − | 13.2739i | 0.280399 | − | 0.485666i | ||||
\(748\) | −17.9095 | + | 31.0201i | −0.654835 | + | 1.13421i | ||||
\(749\) | −4.08277 | −0.149181 | ||||||||
\(750\) | 12.9438 | − | 22.4194i | 0.472642 | − | 0.818641i | ||||
\(751\) | −26.6821 | − | 46.2147i | −0.973644 | − | 1.68640i | −0.684341 | − | 0.729162i | \(-0.739910\pi\) |
−0.289303 | − | 0.957238i | \(-0.593423\pi\) | |||||||
\(752\) | −3.60388 | − | 6.24210i | −0.131420 | − | 0.227626i | ||||
\(753\) | 5.54719 | 0.202151 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −71.7338 | −2.61066 | ||||||||
\(756\) | 0.346011 | + | 0.599308i | 0.0125843 | + | 0.0217966i | ||||
\(757\) | 2.31767 | + | 4.01432i | 0.0842370 | + | 0.145903i | 0.905066 | − | 0.425271i | \(-0.139821\pi\) |
−0.820829 | + | 0.571174i | \(0.806488\pi\) | |||||||
\(758\) | 5.70171 | − | 9.87565i | 0.207095 | − | 0.358700i | ||||
\(759\) | 24.7875 | 0.899728 | ||||||||
\(760\) | 3.60388 | − | 6.24210i | 0.130726 | − | 0.226425i | ||||
\(761\) | −5.78017 | + | 10.0115i | −0.209531 | + | 0.362918i | −0.951567 | − | 0.307442i | \(-0.900527\pi\) |
0.742036 | + | 0.670360i | \(0.233860\pi\) | |||||||
\(762\) | −6.00538 | −0.217552 | ||||||||
\(763\) | −0.274127 | + | 0.474801i | −0.00992405 | + | 0.0171890i | ||||
\(764\) | 4.89977 | + | 8.48665i | 0.177268 | + | 0.307036i | ||||
\(765\) | 14.9487 | + | 25.8919i | 0.540471 | + | 0.936123i | ||||
\(766\) | 20.6703 | 0.746847 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −7.37196 | − | 12.7686i | −0.265840 | − | 0.460448i | 0.701944 | − | 0.712233i | \(-0.252316\pi\) |
−0.967783 | + | 0.251785i | \(0.918983\pi\) | |||||||
\(770\) | −6.79590 | − | 11.7708i | −0.244907 | − | 0.424192i | ||||
\(771\) | 6.89977 | − | 11.9508i | 0.248489 | − | 0.430396i | ||||
\(772\) | −14.1957 | −0.510913 | ||||||||
\(773\) | 3.21134 | − | 5.56220i | 0.115504 | − | 0.200059i | −0.802477 | − | 0.596683i | \(-0.796485\pi\) |
0.917981 | + | 0.396624i | \(0.129818\pi\) | |||||||
\(774\) | 4.15883 | − | 7.20331i | 0.149486 | − | 0.258918i | ||||
\(775\) | −11.0844 | −0.398164 | ||||||||
\(776\) | −4.27144 | + | 7.39835i | −0.153336 | + | 0.265585i | ||||
\(777\) | −0.445042 | − | 0.770835i | −0.0159658 | − | 0.0276536i | ||||
\(778\) | −8.73878 | − | 15.1360i | −0.313301 | − | 0.542652i | ||||
\(779\) | −2.68100 | −0.0960570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.45042 | 0.230814 | ||||||||
\(782\) | −18.8659 | − | 32.6767i | −0.674644 | − | 1.16852i | ||||
\(783\) | 1.67241 | + | 2.89669i | 0.0597670 | + | 0.103519i | ||||
\(784\) | 3.26055 | − | 5.64744i | 0.116448 | − | 0.201694i | ||||
\(785\) | 25.5797 | 0.912979 | ||||||||
\(786\) | −4.40850 | + | 7.63575i | −0.157246 | + | 0.272358i | ||||
\(787\) | −21.7168 | + | 37.6146i | −0.774119 | + | 1.34081i | 0.161169 | + | 0.986927i | \(0.448474\pi\) |
−0.935288 | + | 0.353887i | \(0.884860\pi\) | |||||||
\(788\) | −3.00969 | −0.107216 | ||||||||
\(789\) | 11.2349 | − | 19.4594i | 0.399973 | − | 0.692773i | ||||
\(790\) | −16.8828 | − | 29.2419i | −0.600665 | − | 1.04038i | ||||
\(791\) | 2.15213 | + | 3.72760i | 0.0765209 | + | 0.132538i | ||||
\(792\) | 4.85086 | 0.172368 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −19.3599 | −0.687056 | ||||||||
\(795\) | 27.2826 | + | 47.2549i | 0.967615 | + | 1.67596i | ||||
\(796\) | −6.44720 | − | 11.1669i | −0.228515 | − | 0.395799i | ||||
\(797\) | −10.5082 | + | 18.2007i | −0.372219 | + | 0.644703i | −0.989907 | − | 0.141721i | \(-0.954736\pi\) |
0.617687 | + | 0.786424i | \(0.288070\pi\) | |||||||
\(798\) | −1.23191 | −0.0436093 | ||||||||
\(799\) | −26.6112 | + | 46.0919i | −0.941436 | + | 1.63061i | ||||
\(800\) | −5.69687 | + | 9.86726i | −0.201415 | + | 0.348860i | ||||
\(801\) | −3.10992 | −0.109883 | ||||||||
\(802\) | 7.24160 | − | 12.5428i | 0.255710 | − | 0.442903i | ||||
\(803\) | −18.5613 | − | 32.1491i | −0.655014 | − | 1.13452i | ||||
\(804\) | 3.02715 | + | 5.24317i | 0.106759 | + | 0.184912i | ||||
\(805\) | 14.3177 | 0.504631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.0140 | −0.915736 | ||||||||
\(808\) | 5.99880 | + | 10.3902i | 0.211037 | + | 0.365527i | ||||
\(809\) | 4.16123 | + | 7.20746i | 0.146301 | + | 0.253401i | 0.929858 | − | 0.367920i | \(-0.119930\pi\) |
−0.783557 | + | 0.621320i | \(0.786597\pi\) | |||||||
\(810\) | 2.02446 | − | 3.50647i | 0.0711322 | − | 0.123205i | ||||
\(811\) | 14.4638 | 0.507894 | 0.253947 | − | 0.967218i | \(-0.418271\pi\) | ||||
0.253947 | + | 0.967218i | \(0.418271\pi\) | |||||||
\(812\) | −1.15734 | + | 2.00457i | −0.0406147 | + | 0.0703468i | ||||
\(813\) | −1.44235 | + | 2.49823i | −0.0505855 | + | 0.0876167i | ||||
\(814\) | −6.23921 | −0.218684 | ||||||||
\(815\) | 29.5405 | − | 51.1656i | 1.03476 | − | 1.79225i | ||||
\(816\) | −3.69202 | − | 6.39477i | −0.129247 | − | 0.223862i | ||||
\(817\) | 7.40342 | + | 12.8231i | 0.259013 | + | 0.448623i | ||||
\(818\) | −18.8984 | −0.660769 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.09783 | 0.212946 | ||||||||
\(821\) | −19.2080 | − | 33.2693i | −0.670365 | − | 1.16111i | −0.977801 | − | 0.209538i | \(-0.932804\pi\) |
0.307435 | − | 0.951569i | \(-0.400529\pi\) | |||||||
\(822\) | −7.87800 | − | 13.6451i | −0.274777 | − | 0.475928i | ||||
\(823\) | 20.4874 | − | 35.4852i | 0.714145 | − | 1.23694i | −0.249143 | − | 0.968467i | \(-0.580149\pi\) |
0.963288 | − | 0.268469i | \(-0.0865178\pi\) | |||||||
\(824\) | −12.3230 | −0.429294 | ||||||||
\(825\) | −27.6347 | + | 47.8647i | −0.962116 | + | 1.66643i | ||||
\(826\) | −0.452575 | + | 0.783882i | −0.0157471 | + | 0.0272748i | ||||
\(827\) | −3.51035 | −0.122067 | −0.0610335 | − | 0.998136i | \(-0.519440\pi\) | ||||
−0.0610335 | + | 0.998136i | \(0.519440\pi\) | |||||||
\(828\) | −2.55496 | + | 4.42532i | −0.0887909 | + | 0.153790i | ||||
\(829\) | 6.60925 | + | 11.4476i | 0.229549 | + | 0.397590i | 0.957674 | − | 0.287853i | \(-0.0929416\pi\) |
−0.728126 | + | 0.685444i | \(0.759608\pi\) | |||||||
\(830\) | −31.0296 | − | 53.7448i | −1.07705 | − | 1.86551i | ||||
\(831\) | −1.46250 | −0.0507336 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −48.1521 | −1.66837 | ||||||||
\(834\) | 3.04892 | + | 5.28088i | 0.105575 | + | 0.182862i | ||||
\(835\) | −39.4795 | − | 68.3805i | −1.36624 | − | 2.36640i | ||||
\(836\) | −4.31767 | + | 7.47842i | −0.149330 | + | 0.258647i | ||||
\(837\) | −0.972853 | −0.0336267 | ||||||||
\(838\) | 10.8802 | − | 18.8450i | 0.375849 | − | 0.650989i | ||||
\(839\) | 27.9245 | − | 48.3667i | 0.964062 | − | 1.66980i | 0.251947 | − | 0.967741i | \(-0.418929\pi\) |
0.712115 | − | 0.702063i | \(-0.247737\pi\) | |||||||
\(840\) | 2.80194 | 0.0966760 | ||||||||
\(841\) | 8.90611 | − | 15.4258i | 0.307107 | − | 0.531925i | ||||
\(842\) | −10.2959 | − | 17.8330i | −0.354820 | − | 0.614566i | ||||
\(843\) | −2.84117 | − | 4.92104i | −0.0978550 | − | 0.169490i | ||||
\(844\) | 7.79954 | 0.268471 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.20775 | 0.247808 | ||||||||
\(847\) | 4.33579 | + | 7.50981i | 0.148979 | + | 0.258040i | ||||
\(848\) | −6.73825 | − | 11.6710i | −0.231392 | − | 0.400784i | ||||
\(849\) | 12.6039 | − | 21.8306i | 0.432564 | − | 0.749223i | ||||
\(850\) | 84.1318 | 2.88570 | ||||||||
\(851\) | 3.28621 | − | 5.69188i | 0.112650 | − | 0.195115i | ||||
\(852\) | −0.664874 | + | 1.15160i | −0.0227782 | + | 0.0394530i | ||||
\(853\) | −21.8103 | −0.746770 | −0.373385 | − | 0.927676i | \(-0.621803\pi\) | ||||
−0.373385 | + | 0.927676i | \(0.621803\pi\) | |||||||
\(854\) | −0.137063 | + | 0.237401i | −0.00469021 | + | 0.00812368i | ||||
\(855\) | 3.60388 | + | 6.24210i | 0.123250 | + | 0.213475i | ||||
\(856\) | −2.94989 | − | 5.10935i | −0.100825 | − | 0.174634i | ||||
\(857\) | 28.8961 | 0.987070 | 0.493535 | − | 0.869726i | \(-0.335704\pi\) | ||||
0.493535 | + | 0.869726i | \(0.335704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2755 | −0.589431 | −0.294715 | − | 0.955585i | \(-0.595225\pi\) | ||||
−0.294715 | + | 0.955585i | \(0.595225\pi\) | |||||||
\(860\) | −16.8388 | − | 29.1656i | −0.574197 | − | 0.994539i | ||||
\(861\) | −0.521106 | − | 0.902583i | −0.0177593 | − | 0.0307599i | ||||
\(862\) | −17.2567 | + | 29.8894i | −0.587764 | + | 1.01804i | ||||
\(863\) | −44.7741 | −1.52413 | −0.762063 | − | 0.647503i | \(-0.775813\pi\) | ||||
−0.762063 | + | 0.647503i | \(0.775813\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −18.8083 | + | 32.5769i | −0.639501 | + | 1.10765i | ||||
\(866\) | −2.12631 | −0.0722549 | ||||||||
\(867\) | −18.7620 | + | 32.4968i | −0.637192 | + | 1.10365i | ||||
\(868\) | −0.336618 | − | 0.583039i | −0.0114255 | − | 0.0197896i | ||||
\(869\) | 20.2267 | + | 35.0337i | 0.686144 | + | 1.18844i | ||||
\(870\) | 13.5429 | 0.459147 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.792249 | −0.0268289 | ||||||||
\(873\) | −4.27144 | − | 7.39835i | −0.144566 | − | 0.250396i | ||||
\(874\) | −4.54825 | − | 7.87781i | −0.153847 | − | 0.266471i | ||||
\(875\) | −8.95742 | + | 15.5147i | −0.302816 | + | 0.524493i | ||||
\(876\) | 7.65279 | 0.258564 | ||||||||
\(877\) | 20.1371 | − | 34.8784i | 0.679980 | − | 1.17776i | −0.295006 | − | 0.955495i | \(-0.595322\pi\) |
0.974986 | − | 0.222265i | \(-0.0713450\pi\) | |||||||
\(878\) | −10.9160 | + | 18.9071i | −0.368398 | + | 0.638085i | ||||
\(879\) | −7.14914 | −0.241135 | ||||||||
\(880\) | 9.82036 | − | 17.0094i | 0.331044 | − | 0.573385i | ||||
\(881\) | −4.70410 | − | 8.14775i | −0.158485 | − | 0.274505i | 0.775837 | − | 0.630933i | \(-0.217328\pi\) |
−0.934323 | + | 0.356428i | \(0.883994\pi\) | |||||||
\(882\) | 3.26055 | + | 5.64744i | 0.109789 | + | 0.190159i | ||||
\(883\) | −51.2271 | −1.72393 | −0.861965 | − | 0.506968i | \(-0.830766\pi\) | ||||
−0.861965 | + | 0.506968i | \(0.830766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.29590 | 0.178020 | ||||||||
\(886\) | 3.77024 | + | 6.53025i | 0.126664 | + | 0.219388i | ||||
\(887\) | 19.9608 | + | 34.5731i | 0.670217 | + | 1.16085i | 0.977842 | + | 0.209342i | \(0.0671324\pi\) |
−0.307625 | + | 0.951508i | \(0.599534\pi\) | |||||||
\(888\) | 0.643104 | − | 1.11389i | 0.0215812 | − | 0.0373797i | ||||
\(889\) | 4.15585 | 0.139383 | ||||||||
\(890\) | −6.29590 | + | 10.9048i | −0.211039 | + | 0.365530i | ||||
\(891\) | −2.42543 | + | 4.20096i | −0.0812549 | + | 0.140738i | ||||
\(892\) | −12.1957 | −0.408341 | ||||||||
\(893\) | −6.41550 | + | 11.1120i | −0.214687 | + | 0.371848i | ||||
\(894\) | −1.27628 | − | 2.21059i | −0.0426853 | − | 0.0739331i | ||||
\(895\) | 46.1432 | + | 79.9223i | 1.54240 | + | 2.67151i | ||||
\(896\) | −0.692021 | −0.0231188 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.7560 | 0.659266 | ||||||||
\(899\) | −1.62701 | − | 2.81806i | −0.0542637 | − | 0.0939875i | ||||
\(900\) | −5.69687 | − | 9.86726i | −0.189896 | − | 0.328909i | ||||
\(901\) | −49.7555 | + | 86.1791i | −1.65760 | + | 2.87104i | ||||
\(902\) | −7.30559 | −0.243249 | ||||||||
\(903\) | −2.87800 | + | 4.98485i | −0.0957739 | + | 0.165885i | ||||
\(904\) | −3.10992 | + | 5.38653i | −0.103434 | + | 0.179153i | ||||
\(905\) | −2.17629 | −0.0723424 | ||||||||
\(906\) | −8.85839 | + | 15.3432i | −0.294300 | + | 0.509743i | ||||
\(907\) | 17.4155 | + | 30.1645i | 0.578272 | + | 1.00160i | 0.995678 | + | 0.0928765i | \(0.0296062\pi\) |
−0.417405 | + | 0.908720i | \(0.637060\pi\) | |||||||
\(908\) | −3.37167 | − | 5.83990i | −0.111893 | − | 0.193804i | ||||
\(909\) | −11.9976 | −0.397936 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2125 | 0.437751 | 0.218875 | − | 0.975753i | \(-0.429761\pi\) | ||||
0.218875 | + | 0.975753i | \(0.429761\pi\) | |||||||
\(912\) | −0.890084 | − | 1.54167i | −0.0294736 | − | 0.0510498i | ||||
\(913\) | 37.1754 | + | 64.3897i | 1.23033 | + | 2.13099i | ||||
\(914\) | −11.9291 | + | 20.6618i | −0.394579 | + | 0.683430i | ||||
\(915\) | 1.60388 | 0.0530225 | ||||||||
\(916\) | 9.91185 | − | 17.1678i | 0.327497 | − | 0.567241i | ||||
\(917\) | 3.05078 | − | 5.28410i | 0.100746 | − | 0.174496i | ||||
\(918\) | 7.38404 | 0.243710 | ||||||||
\(919\) | −10.5087 | + | 18.2017i | −0.346651 | + | 0.600417i | −0.985652 | − | 0.168789i | \(-0.946015\pi\) |
0.639001 | + | 0.769206i | \(0.279348\pi\) | |||||||
\(920\) | 10.3448 | + | 17.9177i | 0.341058 | + | 0.590731i | ||||
\(921\) | 8.99761 | + | 15.5843i | 0.296481 | + | 0.513521i | ||||
\(922\) | −17.5773 | −0.578878 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.35690 | −0.110434 | ||||||||
\(925\) | 7.32736 | + | 12.6914i | 0.240922 | + | 0.417289i | ||||
\(926\) | −11.9215 | − | 20.6487i | −0.391766 | − | 0.678559i | ||||
\(927\) | 6.16152 | − | 10.6721i | 0.202371 | − | 0.350517i | ||||
\(928\) | −3.34481 | −0.109799 | ||||||||
\(929\) | 13.4983 | − | 23.3797i | 0.442864 | − | 0.767063i | −0.555037 | − | 0.831826i | \(-0.687296\pi\) |
0.997901 | + | 0.0647630i | \(0.0206291\pi\) | |||||||
\(930\) | −1.96950 | + | 3.41127i | −0.0645825 | + | 0.111860i | ||||
\(931\) | −11.6087 | −0.380459 | ||||||||
\(932\) | 15.0151 | − | 26.0069i | 0.491835 | − | 0.851883i | ||||
\(933\) | −1.66487 | − | 2.88365i | −0.0545055 | − | 0.0944064i | ||||
\(934\) | −4.30529 | − | 7.45698i | −0.140873 | − | 0.244000i | ||||
\(935\) | −145.028 | −4.74292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.1745 | 0.757078 | 0.378539 | − | 0.925585i | \(-0.376427\pi\) | ||||
0.378539 | + | 0.925585i | \(0.376427\pi\) | |||||||
\(938\) | −2.09485 | − | 3.62839i | −0.0683993 | − | 0.118471i | ||||
\(939\) | 8.94169 | + | 15.4875i | 0.291801 | + | 0.505414i | ||||
\(940\) | 14.5918 | − | 25.2737i | 0.475932 | − | 0.824338i | ||||
\(941\) | 7.54048 | 0.245813 | 0.122906 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122906 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(942\) | 3.15883 | − | 5.47126i | 0.102920 | − | 0.178263i | ||||
\(943\) | 3.84787 | − | 6.66471i | 0.125304 | − | 0.217033i | ||||
\(944\) | −1.30798 | −0.0425711 | ||||||||
\(945\) | −1.40097 | + | 2.42655i | −0.0455735 | + | 0.0789357i | ||||
\(946\) | 20.1739 | + | 34.9422i | 0.655910 | + | 1.13607i | ||||
\(947\) | −10.3300 | − | 17.8922i | −0.335681 | − | 0.581417i | 0.647934 | − | 0.761696i | \(-0.275633\pi\) |
−0.983615 | + | 0.180279i | \(0.942300\pi\) | |||||||
\(948\) | −8.33944 | −0.270852 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 20.2828 | 0.658059 | ||||||||
\(951\) | −2.19687 | − | 3.80508i | −0.0712383 | − | 0.123388i | ||||
\(952\) | 2.55496 | + | 4.42532i | 0.0828067 | + | 0.143425i | ||||
\(953\) | 15.1468 | − | 26.2349i | 0.490651 | − | 0.849833i | −0.509291 | − | 0.860595i | \(-0.670092\pi\) |
0.999942 | + | 0.0107614i | \(0.00342552\pi\) | |||||||
\(954\) | 13.4765 | 0.436318 | ||||||||
\(955\) | −19.8388 | + | 34.3618i | −0.641968 | + | 1.11192i | ||||
\(956\) | −11.0489 | + | 19.1373i | −0.357348 | + | 0.618944i | ||||
\(957\) | −16.2252 | −0.524487 | ||||||||
\(958\) | −3.29052 | + | 5.69935i | −0.106312 | + | 0.184138i | ||||
\(959\) | 5.45175 | + | 9.44270i | 0.176046 | + | 0.304921i | ||||
\(960\) | 2.02446 | + | 3.50647i | 0.0653391 | + | 0.113171i | ||||
\(961\) | −30.0536 | −0.969470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.89977 | 0.190118 | ||||||||
\(964\) | −5.06369 | − | 8.77056i | −0.163090 | − | 0.282481i | ||||
\(965\) | −28.7385 | − | 49.7766i | −0.925127 | − | 1.60237i | ||||
\(966\) | 1.76809 | − | 3.06241i | 0.0568872 | − | 0.0985316i | ||||
\(967\) | −20.7289 | −0.666595 | −0.333298 | − | 0.942822i | \(-0.608161\pi\) | ||||
−0.333298 | + | 0.942822i | \(0.608161\pi\) | |||||||
\(968\) | −6.26540 | + | 10.8520i | −0.201378 | + | 0.348796i | ||||
\(969\) | −6.57242 | + | 11.3838i | −0.211136 | + | 0.365699i | ||||
\(970\) | −34.5894 | −1.11060 | ||||||||
\(971\) | 19.5547 | − | 33.8698i | 0.627541 | − | 1.08693i | −0.360503 | − | 0.932758i | \(-0.617395\pi\) |
0.988044 | − | 0.154175i | \(-0.0492718\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −2.10992 | − | 3.65448i | −0.0676408 | − | 0.117157i | ||||
\(974\) | −23.2760 | −0.745813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.396125 | −0.0126796 | ||||||||
\(977\) | −3.63773 | − | 6.30073i | −0.116381 | − | 0.201578i | 0.801950 | − | 0.597391i | \(-0.203796\pi\) |
−0.918331 | + | 0.395813i | \(0.870463\pi\) | |||||||
\(978\) | −7.29590 | − | 12.6369i | −0.233297 | − | 0.404082i | ||||
\(979\) | 7.54288 | − | 13.0646i | 0.241071 | − | 0.417548i | ||||
\(980\) | 26.4034 | 0.843426 | ||||||||
\(981\) | 0.396125 | − | 0.686108i | 0.0126473 | − | 0.0219057i | ||||
\(982\) | 7.77024 | − | 13.4585i | 0.247958 | − | 0.429477i | ||||
\(983\) | 53.4857 | 1.70593 | 0.852965 | − | 0.521969i | \(-0.174802\pi\) | ||||
0.852965 | + | 0.521969i | \(0.174802\pi\) | |||||||
\(984\) | 0.753020 | − | 1.30427i | 0.0240054 | − | 0.0415786i | ||||
\(985\) | −6.09299 | − | 10.5534i | −0.194139 | − | 0.336258i | ||||
\(986\) | 12.3491 | + | 21.3893i | 0.393276 | + | 0.681175i | ||||
\(987\) | −4.98792 | −0.158767 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.5026 | −1.35150 | ||||||||
\(990\) | 9.82036 | + | 17.0094i | 0.312111 | + | 0.540593i | ||||
\(991\) | −8.02877 | − | 13.9062i | −0.255042 | − | 0.441746i | 0.709865 | − | 0.704338i | \(-0.248756\pi\) |
−0.964907 | + | 0.262592i | \(0.915423\pi\) | |||||||
\(992\) | 0.486426 | − | 0.842515i | 0.0154441 | − | 0.0267499i | ||||
\(993\) | −25.6775 | −0.814852 | ||||||||
\(994\) | 0.460107 | − | 0.796929i | 0.0145937 | − | 0.0252771i | ||||
\(995\) | 26.1042 | − | 45.2138i | 0.827558 | − | 1.43337i | ||||
\(996\) | −15.3274 | −0.485666 | ||||||||
\(997\) | −11.2131 | + | 19.4217i | −0.355123 | + | 0.615092i | −0.987139 | − | 0.159864i | \(-0.948894\pi\) |
0.632016 | + | 0.774956i | \(0.282228\pi\) | |||||||
\(998\) | −4.76809 | − | 8.25857i | −0.150931 | − | 0.261420i | ||||
\(999\) | 0.643104 | + | 1.11389i | 0.0203469 | + | 0.0352419i |
(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 | 1014.2.e.k.991.1 | 6 | ||
13.2 | odd | 12 | 1014.2.b.g.337.3 | 6 | |||
13.3 | even | 3 | 1014.2.a.o.1.1 | yes | 3 | ||
13.4 | even | 6 | 1014.2.e.m.529.3 | 6 | |||
13.5 | odd | 4 | 1014.2.i.g.361.3 | 12 | |||
13.6 | odd | 12 | 1014.2.i.g.823.6 | 12 | |||
13.7 | odd | 12 | 1014.2.i.g.823.1 | 12 | |||
13.8 | odd | 4 | 1014.2.i.g.361.4 | 12 | |||
13.9 | even | 3 | inner | 1014.2.e.k.529.1 | 6 | ||
13.10 | even | 6 | 1014.2.a.m.1.3 | ✓ | 3 | ||
13.11 | odd | 12 | 1014.2.b.g.337.4 | 6 | |||
13.12 | even | 2 | 1014.2.e.m.991.3 | 6 | |||
39.2 | even | 12 | 3042.2.b.r.1351.4 | 6 | |||
39.11 | even | 12 | 3042.2.b.r.1351.3 | 6 | |||
39.23 | odd | 6 | 3042.2.a.be.1.1 | 3 | |||
39.29 | odd | 6 | 3042.2.a.bd.1.3 | 3 | |||
52.3 | odd | 6 | 8112.2.a.bz.1.1 | 3 | |||
52.23 | odd | 6 | 8112.2.a.ce.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.3 | ✓ | 3 | 13.10 | even | 6 | ||
1014.2.a.o.1.1 | yes | 3 | 13.3 | even | 3 | ||
1014.2.b.g.337.3 | 6 | 13.2 | odd | 12 | |||
1014.2.b.g.337.4 | 6 | 13.11 | odd | 12 | |||
1014.2.e.k.529.1 | 6 | 13.9 | even | 3 | inner | ||
1014.2.e.k.991.1 | 6 | 1.1 | even | 1 | trivial | ||
1014.2.e.m.529.3 | 6 | 13.4 | even | 6 | |||
1014.2.e.m.991.3 | 6 | 13.12 | even | 2 | |||
1014.2.i.g.361.3 | 12 | 13.5 | odd | 4 | |||
1014.2.i.g.361.4 | 12 | 13.8 | odd | 4 | |||
1014.2.i.g.823.1 | 12 | 13.7 | odd | 12 | |||
1014.2.i.g.823.6 | 12 | 13.6 | odd | 12 | |||
3042.2.a.bd.1.3 | 3 | 39.29 | odd | 6 | |||
3042.2.a.be.1.1 | 3 | 39.23 | odd | 6 | |||
3042.2.b.r.1351.3 | 6 | 39.11 | even | 12 | |||
3042.2.b.r.1351.4 | 6 | 39.2 | even | 12 | |||
8112.2.a.bz.1.1 | 3 | 52.3 | odd | 6 | |||
8112.2.a.ce.1.3 | 3 | 52.23 | odd | 6 |