Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(361,1014)]
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, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.i (of order \(6\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 823.1 | ||
Root | \(1.56052 - 0.900969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.823 |
Dual form | 1014.2.i.g.361.3 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 4.04892i | − | 1.81073i | −0.424633 | − | 0.905365i | \(-0.639597\pi\) | ||
0.424633 | − | 0.905365i | \(-0.360403\pi\) | |||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | 0.599308 | − | 0.346011i | 0.226517 | − | 0.130780i | −0.382447 | − | 0.923977i | \(-0.624919\pi\) |
0.608964 | + | 0.793198i | \(0.291585\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −2.02446 | + | 3.50647i | −0.640190 | + | 1.10884i | ||||
\(11\) | 4.20096 | + | 2.42543i | 1.26664 | + | 0.731294i | 0.974350 | − | 0.225036i | \(-0.0722501\pi\) |
0.292288 | + | 0.956330i | \(0.405583\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.692021 | −0.184951 | ||||||||
\(15\) | 3.50647 | + | 2.02446i | 0.905365 | + | 0.522713i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.69202 | + | 6.39477i | 0.895447 | + | 1.55096i | 0.833251 | + | 0.552895i | \(0.186477\pi\) |
0.0621960 | + | 0.998064i | \(0.480190\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.54167 | − | 0.890084i | 0.353683 | − | 0.204199i | −0.312623 | − | 0.949877i | \(-0.601208\pi\) |
0.666306 | + | 0.745678i | \(0.267874\pi\) | |||||||
\(20\) | 3.50647 | − | 2.02446i | 0.784069 | − | 0.452683i | ||||
\(21\) | 0.692021i | 0.151011i | ||||||||
\(22\) | −2.42543 | − | 4.20096i | −0.517103 | − | 0.895648i | ||||
\(23\) | 2.55496 | − | 4.42532i | 0.532746 | − | 0.922742i | −0.466523 | − | 0.884509i | \(-0.654494\pi\) |
0.999269 | − | 0.0382335i | \(-0.0121731\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | −11.3937 | −2.27875 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.599308 | + | 0.346011i | 0.113259 | + | 0.0653899i | ||||
\(29\) | 1.67241 | − | 2.89669i | 0.310558 | − | 0.537903i | −0.667925 | − | 0.744228i | \(-0.732817\pi\) |
0.978483 | + | 0.206326i | \(0.0661507\pi\) | |||||||
\(30\) | −2.02446 | − | 3.50647i | −0.369614 | − | 0.640190i | ||||
\(31\) | − | 0.972853i | − | 0.174730i | −0.996176 | − | 0.0873648i | \(-0.972155\pi\) | ||
0.996176 | − | 0.0873648i | \(-0.0278446\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −4.20096 | + | 2.42543i | −0.731294 | + | 0.422213i | ||||
\(34\) | − | 7.38404i | − | 1.26635i | ||||||
\(35\) | −1.40097 | − | 2.42655i | −0.236807 | − | 0.410162i | ||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | −1.11389 | − | 0.643104i | −0.183122 | − | 0.105726i | 0.405637 | − | 0.914034i | \(-0.367050\pi\) |
−0.588759 | + | 0.808309i | \(0.700383\pi\) | |||||||
\(38\) | −1.78017 | −0.288781 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.04892 | −0.640190 | ||||||||
\(41\) | 1.30427 | + | 0.753020i | 0.203693 | + | 0.117602i | 0.598377 | − | 0.801215i | \(-0.295813\pi\) |
−0.394684 | + | 0.918817i | \(0.629146\pi\) | |||||||
\(42\) | 0.346011 | − | 0.599308i | 0.0533906 | − | 0.0924753i | ||||
\(43\) | −4.15883 | − | 7.20331i | −0.634216 | − | 1.09849i | −0.986681 | − | 0.162669i | \(-0.947990\pi\) |
0.352464 | − | 0.935825i | \(-0.385344\pi\) | |||||||
\(44\) | 4.85086i | 0.731294i | ||||||||
\(45\) | −3.50647 | + | 2.02446i | −0.522713 | + | 0.301788i | ||||
\(46\) | −4.42532 | + | 2.55496i | −0.652477 | + | 0.376708i | ||||
\(47\) | − | 7.20775i | − | 1.05136i | −0.850683 | − | 0.525679i | \(-0.823811\pi\) | ||
0.850683 | − | 0.525679i | \(-0.176189\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −3.26055 | + | 5.64744i | −0.465793 | + | 0.806778i | ||||
\(50\) | 9.86726 | + | 5.69687i | 1.39544 | + | 0.805658i | ||||
\(51\) | −7.38404 | −1.03397 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.4765 | 1.85114 | 0.925570 | − | 0.378577i | \(-0.123586\pi\) | ||||
0.925570 | + | 0.378577i | \(0.123586\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 9.82036 | − | 17.0094i | 1.32418 | − | 2.29354i | ||||
\(56\) | −0.346011 | − | 0.599308i | −0.0462376 | − | 0.0800859i | ||||
\(57\) | 1.78017i | 0.235789i | ||||||||
\(58\) | −2.89669 | + | 1.67241i | −0.380355 | + | 0.219598i | ||||
\(59\) | 1.13274 | − | 0.653989i | 0.147471 | − | 0.0851422i | −0.424449 | − | 0.905452i | \(-0.639532\pi\) |
0.571920 | + | 0.820310i | \(0.306199\pi\) | |||||||
\(60\) | 4.04892i | 0.522713i | ||||||||
\(61\) | 0.198062 | + | 0.343054i | 0.0253593 | + | 0.0439236i | 0.878427 | − | 0.477877i | \(-0.158594\pi\) |
−0.853067 | + | 0.521801i | \(0.825260\pi\) | |||||||
\(62\) | −0.486426 | + | 0.842515i | −0.0617762 | + | 0.107000i | ||||
\(63\) | −0.599308 | − | 0.346011i | −0.0755057 | − | 0.0435933i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.85086 | 0.597099 | ||||||||
\(67\) | 5.24317 | + | 3.02715i | 0.640555 | + | 0.369825i | 0.784828 | − | 0.619713i | \(-0.212751\pi\) |
−0.144273 | + | 0.989538i | \(0.546084\pi\) | |||||||
\(68\) | −3.69202 | + | 6.39477i | −0.447723 | + | 0.775480i | ||||
\(69\) | 2.55496 | + | 4.42532i | 0.307581 | + | 0.532746i | ||||
\(70\) | 2.80194i | 0.334896i | ||||||||
\(71\) | 1.15160 | − | 0.664874i | 0.136669 | − | 0.0789061i | −0.430106 | − | 0.902778i | \(-0.641524\pi\) |
0.566776 | + | 0.823872i | \(0.308191\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | − | 7.65279i | − | 0.895692i | −0.894111 | − | 0.447846i | \(-0.852191\pi\) | ||
0.894111 | − | 0.447846i | \(-0.147809\pi\) | |||||||
\(74\) | 0.643104 | + | 1.11389i | 0.0747593 | + | 0.129487i | ||||
\(75\) | 5.69687 | − | 9.86726i | 0.657817 | − | 1.13937i | ||||
\(76\) | 1.54167 | + | 0.890084i | 0.176842 | + | 0.102100i | ||||
\(77\) | 3.35690 | 0.382554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.33944 | −0.938260 | −0.469130 | − | 0.883129i | \(-0.655432\pi\) | ||||
−0.469130 | + | 0.883129i | \(0.655432\pi\) | |||||||
\(80\) | 3.50647 | + | 2.02446i | 0.392035 | + | 0.226341i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.753020 | − | 1.30427i | −0.0831572 | − | 0.144032i | ||||
\(83\) | − | 15.3274i | − | 1.68240i | −0.540727 | − | 0.841198i | \(-0.681851\pi\) | ||
0.540727 | − | 0.841198i | \(-0.318149\pi\) | |||||||
\(84\) | −0.599308 | + | 0.346011i | −0.0653899 | + | 0.0377529i | ||||
\(85\) | 25.8919 | − | 14.9487i | 2.80837 | − | 1.62141i | ||||
\(86\) | 8.31767i | 0.896917i | ||||||||
\(87\) | 1.67241 | + | 2.89669i | 0.179301 | + | 0.310558i | ||||
\(88\) | 2.42543 | − | 4.20096i | 0.258551 | − | 0.447824i | ||||
\(89\) | −2.69327 | − | 1.55496i | −0.285486 | − | 0.164825i | 0.350419 | − | 0.936593i | \(-0.386039\pi\) |
−0.635904 | + | 0.771768i | \(0.719373\pi\) | |||||||
\(90\) | 4.04892 | 0.426793 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.10992 | 0.532746 | ||||||||
\(93\) | 0.842515 | + | 0.486426i | 0.0873648 | + | 0.0504401i | ||||
\(94\) | −3.60388 | + | 6.24210i | −0.371711 | + | 0.643823i | ||||
\(95\) | −3.60388 | − | 6.24210i | −0.369750 | − | 0.640425i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 7.39835 | − | 4.27144i | 0.751188 | − | 0.433699i | −0.0749347 | − | 0.997188i | \(-0.523875\pi\) |
0.826123 | + | 0.563490i | \(0.190542\pi\) | |||||||
\(98\) | 5.64744 | − | 3.26055i | 0.570478 | − | 0.329366i | ||||
\(99\) | − | 4.85086i | − | 0.487529i | ||||||
\(100\) | −5.69687 | − | 9.86726i | −0.569687 | − | 0.986726i | ||||
\(101\) | −5.99880 | + | 10.3902i | −0.596903 | + | 1.03387i | 0.396372 | + | 0.918090i | \(0.370269\pi\) |
−0.993275 | + | 0.115777i | \(0.963064\pi\) | |||||||
\(102\) | 6.39477 | + | 3.69202i | 0.633176 | + | 0.365565i | ||||
\(103\) | 12.3230 | 1.21423 | 0.607113 | − | 0.794616i | \(-0.292328\pi\) | ||||
0.607113 | + | 0.794616i | \(0.292328\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.80194 | 0.273441 | ||||||||
\(106\) | −11.6710 | − | 6.73825i | −1.13359 | − | 0.654477i | ||||
\(107\) | −2.94989 | + | 5.10935i | −0.285176 | + | 0.493940i | −0.972652 | − | 0.232268i | \(-0.925385\pi\) |
0.687476 | + | 0.726207i | \(0.258719\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | − | 0.792249i | − | 0.0758837i | −0.999280 | − | 0.0379418i | \(-0.987920\pi\) | ||
0.999280 | − | 0.0379418i | \(-0.0120802\pi\) | |||||||
\(110\) | −17.0094 | + | 9.82036i | −1.62178 | + | 0.936334i | ||||
\(111\) | 1.11389 | − | 0.643104i | 0.105726 | − | 0.0610407i | ||||
\(112\) | 0.692021i | 0.0653899i | ||||||||
\(113\) | −3.10992 | − | 5.38653i | −0.292556 | − | 0.506722i | 0.681857 | − | 0.731485i | \(-0.261173\pi\) |
−0.974413 | + | 0.224763i | \(0.927839\pi\) | |||||||
\(114\) | 0.890084 | − | 1.54167i | 0.0833640 | − | 0.144391i | ||||
\(115\) | −17.9177 | − | 10.3448i | −1.67084 | − | 0.964659i | ||||
\(116\) | 3.34481 | 0.310558 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.30798 | −0.120409 | ||||||||
\(119\) | 4.42532 | + | 2.55496i | 0.405668 | + | 0.234213i | ||||
\(120\) | 2.02446 | − | 3.50647i | 0.184807 | − | 0.320095i | ||||
\(121\) | 6.26540 | + | 10.8520i | 0.569582 | + | 0.986544i | ||||
\(122\) | − | 0.396125i | − | 0.0358634i | ||||||
\(123\) | −1.30427 | + | 0.753020i | −0.117602 | + | 0.0678976i | ||||
\(124\) | 0.842515 | − | 0.486426i | 0.0756601 | − | 0.0436824i | ||||
\(125\) | 25.8877i | 2.31547i | ||||||||
\(126\) | 0.346011 | + | 0.599308i | 0.0308251 | + | 0.0533906i | ||||
\(127\) | −3.00269 | + | 5.20081i | −0.266446 | + | 0.461497i | −0.967941 | − | 0.251176i | \(-0.919183\pi\) |
0.701496 | + | 0.712674i | \(0.252516\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 8.31767 | 0.732330 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.81700 | 0.770345 | 0.385173 | − | 0.922845i | \(-0.374142\pi\) | ||||
0.385173 | + | 0.922845i | \(0.374142\pi\) | |||||||
\(132\) | −4.20096 | − | 2.42543i | −0.365647 | − | 0.211106i | ||||
\(133\) | 0.615957 | − | 1.06687i | 0.0534103 | − | 0.0925093i | ||||
\(134\) | −3.02715 | − | 5.24317i | −0.261506 | − | 0.452941i | ||||
\(135\) | − | 4.04892i | − | 0.348475i | ||||||
\(136\) | 6.39477 | − | 3.69202i | 0.548347 | − | 0.316588i | ||||
\(137\) | −13.6451 | + | 7.87800i | −1.16578 | + | 0.673063i | −0.952682 | − | 0.303968i | \(-0.901688\pi\) |
−0.213097 | + | 0.977031i | \(0.568355\pi\) | |||||||
\(138\) | − | 5.10992i | − | 0.434985i | ||||||
\(139\) | 3.04892 | + | 5.28088i | 0.258606 | + | 0.447918i | 0.965869 | − | 0.259032i | \(-0.0834036\pi\) |
−0.707263 | + | 0.706951i | \(0.750070\pi\) | |||||||
\(140\) | 1.40097 | − | 2.42655i | 0.118403 | − | 0.205081i | ||||
\(141\) | 6.24210 | + | 3.60388i | 0.525679 | + | 0.303501i | ||||
\(142\) | −1.32975 | −0.111590 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −11.7285 | − | 6.77144i | −0.973997 | − | 0.562337i | ||||
\(146\) | −3.82640 | + | 6.62751i | −0.316675 | + | 0.548497i | ||||
\(147\) | −3.26055 | − | 5.64744i | −0.268926 | − | 0.465793i | ||||
\(148\) | − | 1.28621i | − | 0.105726i | ||||||
\(149\) | 2.21059 | − | 1.27628i | 0.181098 | − | 0.104557i | −0.406710 | − | 0.913557i | \(-0.633324\pi\) |
0.587809 | + | 0.809000i | \(0.299991\pi\) | |||||||
\(150\) | −9.86726 | + | 5.69687i | −0.805658 | + | 0.465147i | ||||
\(151\) | − | 17.7168i | − | 1.44177i | −0.693054 | − | 0.720885i | \(-0.743735\pi\) | ||
0.693054 | − | 0.720885i | \(-0.256265\pi\) | |||||||
\(152\) | −0.890084 | − | 1.54167i | −0.0721953 | − | 0.125046i | ||||
\(153\) | 3.69202 | − | 6.39477i | 0.298482 | − | 0.516986i | ||||
\(154\) | −2.90716 | − | 1.67845i | −0.234265 | − | 0.135253i | ||||
\(155\) | −3.93900 | −0.316388 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.31767 | −0.504205 | −0.252102 | − | 0.967701i | \(-0.581122\pi\) | ||||
−0.252102 | + | 0.967701i | \(0.581122\pi\) | |||||||
\(158\) | 7.22216 | + | 4.16972i | 0.574565 | + | 0.331725i | ||||
\(159\) | −6.73825 | + | 11.6710i | −0.534378 | + | 0.925570i | ||||
\(160\) | −2.02446 | − | 3.50647i | −0.160048 | − | 0.277210i | ||||
\(161\) | − | 3.53617i | − | 0.278689i | ||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | −12.6369 | + | 7.29590i | −0.989796 | + | 0.571459i | −0.905213 | − | 0.424958i | \(-0.860289\pi\) |
−0.0845824 | + | 0.996416i | \(0.526956\pi\) | |||||||
\(164\) | 1.50604i | 0.117602i | ||||||||
\(165\) | 9.82036 | + | 17.0094i | 0.764514 | + | 1.32418i | ||||
\(166\) | −7.66368 | + | 13.2739i | −0.594817 | + | 1.03025i | ||||
\(167\) | −16.8886 | − | 9.75063i | −1.30688 | − | 0.754526i | −0.325304 | − | 0.945610i | \(-0.605467\pi\) |
−0.981574 | + | 0.191083i | \(0.938800\pi\) | |||||||
\(168\) | 0.692021 | 0.0533906 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −29.8974 | −2.29302 | ||||||||
\(171\) | −1.54167 | − | 0.890084i | −0.117894 | − | 0.0680664i | ||||
\(172\) | 4.15883 | − | 7.20331i | 0.317108 | − | 0.549247i | ||||
\(173\) | −4.64526 | − | 8.04583i | −0.353173 | − | 0.611713i | 0.633631 | − | 0.773636i | \(-0.281564\pi\) |
−0.986803 | + | 0.161923i | \(0.948230\pi\) | |||||||
\(174\) | − | 3.34481i | − | 0.253570i | ||||||
\(175\) | −6.82836 | + | 3.94235i | −0.516175 | + | 0.298014i | ||||
\(176\) | −4.20096 | + | 2.42543i | −0.316660 | + | 0.182823i | ||||
\(177\) | 1.30798i | 0.0983137i | ||||||||
\(178\) | 1.55496 | + | 2.69327i | 0.116549 | + | 0.201869i | ||||
\(179\) | 11.3964 | − | 19.7392i | 0.851808 | − | 1.47538i | −0.0277662 | − | 0.999614i | \(-0.508839\pi\) |
0.879575 | − | 0.475761i | \(-0.157827\pi\) | |||||||
\(180\) | −3.50647 | − | 2.02446i | −0.261356 | − | 0.150894i | ||||
\(181\) | −0.537500 | −0.0399520 | −0.0199760 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199760 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.396125 | −0.0292824 | ||||||||
\(184\) | −4.42532 | − | 2.55496i | −0.326239 | − | 0.188354i | ||||
\(185\) | −2.60388 | + | 4.51004i | −0.191441 | + | 0.331585i | ||||
\(186\) | −0.486426 | − | 0.842515i | −0.0356665 | − | 0.0617762i | ||||
\(187\) | 35.8189i | 2.61934i | ||||||||
\(188\) | 6.24210 | − | 3.60388i | 0.455252 | − | 0.262840i | ||||
\(189\) | 0.599308 | − | 0.346011i | 0.0435933 | − | 0.0251686i | ||||
\(190\) | 7.20775i | 0.522905i | ||||||||
\(191\) | 4.89977 | + | 8.48665i | 0.354535 | + | 0.614073i | 0.987038 | − | 0.160485i | \(-0.0513058\pi\) |
−0.632503 | + | 0.774558i | \(0.717972\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −12.2938 | − | 7.09783i | −0.884928 | − | 0.510913i | −0.0126478 | − | 0.999920i | \(-0.504026\pi\) |
−0.872280 | + | 0.489007i | \(0.837359\pi\) | |||||||
\(194\) | −8.54288 | −0.613343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.52111 | −0.465793 | ||||||||
\(197\) | 2.60647 | + | 1.50484i | 0.185703 | + | 0.107216i | 0.589969 | − | 0.807426i | \(-0.299140\pi\) |
−0.404266 | + | 0.914641i | \(0.632473\pi\) | |||||||
\(198\) | −2.42543 | + | 4.20096i | −0.172368 | + | 0.298549i | ||||
\(199\) | 6.44720 | + | 11.1669i | 0.457030 | + | 0.791599i | 0.998802 | − | 0.0489263i | \(-0.0155800\pi\) |
−0.541773 | + | 0.840525i | \(0.682247\pi\) | |||||||
\(200\) | 11.3937i | 0.805658i | ||||||||
\(201\) | −5.24317 | + | 3.02715i | −0.369825 | + | 0.213518i | ||||
\(202\) | 10.3902 | − | 5.99880i | 0.731054 | − | 0.422074i | ||||
\(203\) | − | 2.31468i | − | 0.162459i | ||||||
\(204\) | −3.69202 | − | 6.39477i | −0.258493 | − | 0.447723i | ||||
\(205\) | 3.04892 | − | 5.28088i | 0.212946 | − | 0.368833i | ||||
\(206\) | −10.6721 | − | 6.16152i | −0.743558 | − | 0.429294i | ||||
\(207\) | −5.10992 | −0.355164 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.63533 | 0.597319 | ||||||||
\(210\) | −2.42655 | − | 1.40097i | −0.167448 | − | 0.0966760i | ||||
\(211\) | −3.89977 | + | 6.75460i | −0.268471 | + | 0.465006i | −0.968467 | − | 0.249141i | \(-0.919852\pi\) |
0.699996 | + | 0.714147i | \(0.253185\pi\) | |||||||
\(212\) | 6.73825 | + | 11.6710i | 0.462785 | + | 0.801567i | ||||
\(213\) | 1.32975i | 0.0911129i | ||||||||
\(214\) | 5.10935 | − | 2.94989i | 0.349268 | − | 0.201650i | ||||
\(215\) | −29.1656 | + | 16.8388i | −1.98908 | + | 1.14839i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −0.336618 | − | 0.583039i | −0.0228511 | − | 0.0395792i | ||||
\(218\) | −0.396125 | + | 0.686108i | −0.0268289 | + | 0.0464691i | ||||
\(219\) | 6.62751 | + | 3.82640i | 0.447846 | + | 0.258564i | ||||
\(220\) | 19.6407 | 1.32418 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.28621 | −0.0863246 | ||||||||
\(223\) | 10.5618 | + | 6.09783i | 0.707268 | + | 0.408341i | 0.810049 | − | 0.586363i | \(-0.199441\pi\) |
−0.102781 | + | 0.994704i | \(0.532774\pi\) | |||||||
\(224\) | 0.346011 | − | 0.599308i | 0.0231188 | − | 0.0400430i | ||||
\(225\) | 5.69687 | + | 9.86726i | 0.379791 | + | 0.657817i | ||||
\(226\) | 6.21983i | 0.413737i | ||||||||
\(227\) | 5.83990 | − | 3.37167i | 0.387608 | − | 0.223785i | −0.293515 | − | 0.955954i | \(-0.594825\pi\) |
0.681123 | + | 0.732169i | \(0.261492\pi\) | |||||||
\(228\) | −1.54167 | + | 0.890084i | −0.102100 | + | 0.0589472i | ||||
\(229\) | 19.8237i | 1.30999i | 0.755634 | + | 0.654994i | \(0.227329\pi\) | ||||
−0.755634 | + | 0.654994i | \(0.772671\pi\) | |||||||
\(230\) | 10.3448 | + | 17.9177i | 0.682117 | + | 1.18146i | ||||
\(231\) | −1.67845 | + | 2.90716i | −0.110434 | + | 0.191277i | ||||
\(232\) | −2.89669 | − | 1.67241i | −0.190177 | − | 0.109799i | ||||
\(233\) | 30.0301 | 1.96734 | 0.983670 | − | 0.179983i | \(-0.0576044\pi\) | ||||
0.983670 | + | 0.179983i | \(0.0576044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.1836 | −1.90373 | ||||||||
\(236\) | 1.13274 | + | 0.653989i | 0.0737353 | + | 0.0425711i | ||||
\(237\) | 4.16972 | − | 7.22216i | 0.270852 | − | 0.469130i | ||||
\(238\) | −2.55496 | − | 4.42532i | −0.165613 | − | 0.286851i | ||||
\(239\) | 22.0978i | 1.42939i | 0.699436 | + | 0.714695i | \(0.253435\pi\) | ||||
−0.699436 | + | 0.714695i | \(0.746565\pi\) | |||||||
\(240\) | −3.50647 | + | 2.02446i | −0.226341 | + | 0.130678i | ||||
\(241\) | −8.77056 | + | 5.06369i | −0.564962 | + | 0.326181i | −0.755135 | − | 0.655570i | \(-0.772428\pi\) |
0.190173 | + | 0.981751i | \(0.439095\pi\) | |||||||
\(242\) | − | 12.5308i | − | 0.805510i | ||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −0.198062 | + | 0.343054i | −0.0126796 | + | 0.0219618i | ||||
\(245\) | 22.8660 | + | 13.2017i | 1.46086 | + | 0.843426i | ||||
\(246\) | 1.50604 | 0.0960217 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.972853 | −0.0617762 | ||||||||
\(249\) | 13.2739 | + | 7.66368i | 0.841198 | + | 0.485666i | ||||
\(250\) | 12.9438 | − | 22.4194i | 0.818641 | − | 1.41793i | ||||
\(251\) | 2.77359 | + | 4.80401i | 0.175068 | + | 0.303226i | 0.940185 | − | 0.340665i | \(-0.110652\pi\) |
−0.765117 | + | 0.643891i | \(0.777319\pi\) | |||||||
\(252\) | − | 0.692021i | − | 0.0435933i | ||||||
\(253\) | 21.4666 | − | 12.3937i | 1.34959 | − | 0.779187i | ||||
\(254\) | 5.20081 | − | 3.00269i | 0.326328 | − | 0.188405i | ||||
\(255\) | 29.8974i | 1.87225i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.89977 | + | 11.9508i | −0.430396 | + | 0.745468i | −0.996907 | − | 0.0785862i | \(-0.974959\pi\) |
0.566511 | + | 0.824054i | \(0.308293\pi\) | |||||||
\(258\) | −7.20331 | − | 4.15883i | −0.448459 | − | 0.258918i | ||||
\(259\) | −0.890084 | −0.0553071 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.34481 | −0.207039 | ||||||||
\(262\) | −7.63575 | − | 4.40850i | −0.471738 | − | 0.272358i | ||||
\(263\) | 11.2349 | − | 19.4594i | 0.692773 | − | 1.19992i | −0.278152 | − | 0.960537i | \(-0.589722\pi\) |
0.970926 | − | 0.239382i | \(-0.0769448\pi\) | |||||||
\(264\) | 2.42543 | + | 4.20096i | 0.149275 | + | 0.258551i | ||||
\(265\) | − | 54.5652i | − | 3.35192i | ||||||
\(266\) | −1.06687 | + | 0.615957i | −0.0654139 | + | 0.0377668i | ||||
\(267\) | 2.69327 | − | 1.55496i | 0.164825 | − | 0.0951619i | ||||
\(268\) | 6.05429i | 0.369825i | ||||||||
\(269\) | 13.0070 | + | 22.5288i | 0.793051 | + | 1.37360i | 0.924070 | + | 0.382224i | \(0.124842\pi\) |
−0.131019 | + | 0.991380i | \(0.541825\pi\) | |||||||
\(270\) | −2.02446 | + | 3.50647i | −0.123205 | + | 0.213397i | ||||
\(271\) | 2.49823 | + | 1.44235i | 0.151757 | + | 0.0876167i | 0.573955 | − | 0.818887i | \(-0.305408\pi\) |
−0.422199 | + | 0.906503i | \(0.638742\pi\) | |||||||
\(272\) | −7.38404 | −0.447723 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7560 | 0.951855 | ||||||||
\(275\) | −47.8647 | − | 27.6347i | −2.88635 | − | 1.66643i | ||||
\(276\) | −2.55496 | + | 4.42532i | −0.153790 | + | 0.266373i | ||||
\(277\) | −0.731250 | − | 1.26656i | −0.0439366 | − | 0.0761004i | 0.843221 | − | 0.537567i | \(-0.180657\pi\) |
−0.887157 | + | 0.461467i | \(0.847323\pi\) | |||||||
\(278\) | − | 6.09783i | − | 0.365724i | ||||||
\(279\) | −0.842515 | + | 0.486426i | −0.0504401 | + | 0.0291216i | ||||
\(280\) | −2.42655 | + | 1.40097i | −0.145014 | + | 0.0837239i | ||||
\(281\) | − | 5.68233i | − | 0.338980i | −0.985532 | − | 0.169490i | \(-0.945788\pi\) | ||
0.985532 | − | 0.169490i | \(-0.0542120\pi\) | |||||||
\(282\) | −3.60388 | − | 6.24210i | −0.214608 | − | 0.371711i | ||||
\(283\) | −12.6039 | + | 21.8306i | −0.749223 | + | 1.29769i | 0.198973 | + | 0.980005i | \(0.436239\pi\) |
−0.948196 | + | 0.317687i | \(0.897094\pi\) | |||||||
\(284\) | 1.15160 | + | 0.664874i | 0.0683347 | + | 0.0394530i | ||||
\(285\) | 7.20775 | 0.426950 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.04221 | 0.0615199 | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | −18.7620 | + | 32.4968i | −1.10365 | + | 1.91158i | ||||
\(290\) | 6.77144 | + | 11.7285i | 0.397633 | + | 0.688720i | ||||
\(291\) | 8.54288i | 0.500792i | ||||||||
\(292\) | 6.62751 | − | 3.82640i | 0.387846 | − | 0.223923i | ||||
\(293\) | 6.19134 | − | 3.57457i | 0.361702 | − | 0.208829i | −0.308125 | − | 0.951346i | \(-0.599702\pi\) |
0.669827 | + | 0.742517i | \(0.266368\pi\) | |||||||
\(294\) | 6.52111i | 0.380319i | ||||||||
\(295\) | −2.64795 | − | 4.58638i | −0.154170 | − | 0.267029i | ||||
\(296\) | −0.643104 | + | 1.11389i | −0.0373797 | + | 0.0647435i | ||||
\(297\) | 4.20096 | + | 2.42543i | 0.243765 | + | 0.140738i | ||||
\(298\) | −2.55257 | −0.147866 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 11.3937 | 0.657817 | ||||||||
\(301\) | −4.98485 | − | 2.87800i | −0.287322 | − | 0.165885i | ||||
\(302\) | −8.85839 | + | 15.3432i | −0.509743 | + | 0.882901i | ||||
\(303\) | −5.99880 | − | 10.3902i | −0.344622 | − | 0.596903i | ||||
\(304\) | 1.78017i | 0.102100i | ||||||||
\(305\) | 1.38900 | − | 0.801938i | 0.0795337 | − | 0.0459188i | ||||
\(306\) | −6.39477 | + | 3.69202i | −0.365565 | + | 0.211059i | ||||
\(307\) | 17.9952i | 1.02704i | 0.858077 | + | 0.513521i | \(0.171659\pi\) | ||||
−0.858077 | + | 0.513521i | \(0.828341\pi\) | |||||||
\(308\) | 1.67845 | + | 2.90716i | 0.0956384 | + | 0.165651i | ||||
\(309\) | −6.16152 | + | 10.6721i | −0.350517 | + | 0.607113i | ||||
\(310\) | 3.41127 | + | 1.96950i | 0.193747 | + | 0.111860i | ||||
\(311\) | −3.32975 | −0.188813 | −0.0944064 | − | 0.995534i | \(-0.530095\pi\) | ||||
−0.0944064 | + | 0.995534i | \(0.530095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.8834 | −1.01083 | −0.505414 | − | 0.862877i | \(-0.668660\pi\) | ||||
−0.505414 | + | 0.862877i | \(0.668660\pi\) | |||||||
\(314\) | 5.47126 | + | 3.15883i | 0.308761 | + | 0.178263i | ||||
\(315\) | −1.40097 | + | 2.42655i | −0.0789357 | + | 0.136721i | ||||
\(316\) | −4.16972 | − | 7.22216i | −0.234565 | − | 0.406279i | ||||
\(317\) | 4.39373i | 0.246777i | 0.992358 | + | 0.123388i | \(0.0393761\pi\) | ||||
−0.992358 | + | 0.123388i | \(0.960624\pi\) | |||||||
\(318\) | 11.6710 | − | 6.73825i | 0.654477 | − | 0.377862i | ||||
\(319\) | 14.0514 | − | 8.11260i | 0.786730 | − | 0.454219i | ||||
\(320\) | 4.04892i | 0.226341i | ||||||||
\(321\) | −2.94989 | − | 5.10935i | −0.164647 | − | 0.285176i | ||||
\(322\) | −1.76809 | + | 3.06241i | −0.0985316 | + | 0.170662i | ||||
\(323\) | 11.3838 | + | 6.57242i | 0.633409 | + | 0.365699i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.5918 | 0.808165 | ||||||||
\(327\) | 0.686108 | + | 0.396125i | 0.0379418 | + | 0.0219057i | ||||
\(328\) | 0.753020 | − | 1.30427i | 0.0415786 | − | 0.0720162i | ||||
\(329\) | −2.49396 | − | 4.31966i | −0.137496 | − | 0.238151i | ||||
\(330\) | − | 19.6407i | − | 1.08119i | ||||||
\(331\) | −22.2374 | + | 12.8388i | −1.22228 | + | 0.705683i | −0.965403 | − | 0.260762i | \(-0.916026\pi\) |
−0.256875 | + | 0.966445i | \(0.582693\pi\) | |||||||
\(332\) | 13.2739 | − | 7.66368i | 0.728499 | − | 0.420599i | ||||
\(333\) | 1.28621i | 0.0704838i | ||||||||
\(334\) | 9.75063 | + | 16.8886i | 0.533531 | + | 0.924102i | ||||
\(335\) | 12.2567 | − | 21.2292i | 0.669653 | − | 1.15987i | ||||
\(336\) | −0.599308 | − | 0.346011i | −0.0326949 | − | 0.0188764i | ||||
\(337\) | 24.6504 | 1.34279 | 0.671396 | − | 0.741098i | \(-0.265695\pi\) | ||||
0.671396 | + | 0.741098i | \(0.265695\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.21983 | 0.337815 | ||||||||
\(340\) | 25.8919 | + | 14.9487i | 1.40418 | + | 0.810707i | ||||
\(341\) | 2.35958 | − | 4.08692i | 0.127779 | − | 0.221319i | ||||
\(342\) | 0.890084 | + | 1.54167i | 0.0481302 | + | 0.0833640i | ||||
\(343\) | 9.35690i | 0.505225i | ||||||||
\(344\) | −7.20331 | + | 4.15883i | −0.388377 | + | 0.224229i | ||||
\(345\) | 17.9177 | − | 10.3448i | 0.964659 | − | 0.556946i | ||||
\(346\) | 9.29052i | 0.499461i | ||||||||
\(347\) | −7.14795 | − | 12.3806i | −0.383722 | − | 0.664626i | 0.607869 | − | 0.794037i | \(-0.292025\pi\) |
−0.991591 | + | 0.129411i | \(0.958691\pi\) | |||||||
\(348\) | −1.67241 | + | 2.89669i | −0.0896504 | + | 0.155279i | ||||
\(349\) | 9.57962 | + | 5.53079i | 0.512785 | + | 0.296057i | 0.733978 | − | 0.679173i | \(-0.237662\pi\) |
−0.221193 | + | 0.975230i | \(0.570995\pi\) | |||||||
\(350\) | 7.88471 | 0.421455 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.85086 | 0.258551 | ||||||||
\(353\) | 9.09735 | + | 5.25236i | 0.484203 | + | 0.279555i | 0.722166 | − | 0.691719i | \(-0.243146\pi\) |
−0.237963 | + | 0.971274i | \(0.576480\pi\) | |||||||
\(354\) | 0.653989 | − | 1.13274i | 0.0347591 | − | 0.0602046i | ||||
\(355\) | −2.69202 | − | 4.66272i | −0.142878 | − | 0.247471i | ||||
\(356\) | − | 3.10992i | − | 0.164825i | ||||||
\(357\) | −4.42532 | + | 2.55496i | −0.234213 | + | 0.135223i | ||||
\(358\) | −19.7392 | + | 11.3964i | −1.04325 | + | 0.602320i | ||||
\(359\) | − | 5.10992i | − | 0.269691i | −0.990867 | − | 0.134846i | \(-0.956946\pi\) | ||
0.990867 | − | 0.134846i | \(-0.0430538\pi\) | |||||||
\(360\) | 2.02446 | + | 3.50647i | 0.106698 | + | 0.184807i | ||||
\(361\) | −7.91550 | + | 13.7101i | −0.416605 | + | 0.721582i | ||||
\(362\) | 0.465488 | + | 0.268750i | 0.0244655 | + | 0.0141252i | ||||
\(363\) | −12.5308 | −0.657696 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.9855 | −1.62186 | ||||||||
\(366\) | 0.343054 | + | 0.198062i | 0.0179317 | + | 0.0103529i | ||||
\(367\) | 4.22401 | − | 7.31620i | 0.220492 | − | 0.381903i | −0.734466 | − | 0.678646i | \(-0.762567\pi\) |
0.954957 | + | 0.296743i | \(0.0959005\pi\) | |||||||
\(368\) | 2.55496 | + | 4.42532i | 0.133186 | + | 0.230686i | ||||
\(369\) | − | 1.50604i | − | 0.0784014i | ||||||
\(370\) | 4.51004 | − | 2.60388i | 0.234466 | − | 0.135369i | ||||
\(371\) | 8.07658 | − | 4.66301i | 0.419315 | − | 0.242092i | ||||
\(372\) | 0.972853i | 0.0504401i | ||||||||
\(373\) | −3.84548 | − | 6.66056i | −0.199111 | − | 0.344871i | 0.749129 | − | 0.662424i | \(-0.230472\pi\) |
−0.948241 | + | 0.317553i | \(0.897139\pi\) | |||||||
\(374\) | 17.9095 | − | 31.0201i | 0.926076 | − | 1.60401i | ||||
\(375\) | −22.4194 | − | 12.9438i | −1.15773 | − | 0.668417i | ||||
\(376\) | −7.20775 | −0.371711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.692021 | −0.0355937 | ||||||||
\(379\) | 9.87565 | + | 5.70171i | 0.507278 | + | 0.292877i | 0.731714 | − | 0.681612i | \(-0.238721\pi\) |
−0.224436 | + | 0.974489i | \(0.572054\pi\) | |||||||
\(380\) | 3.60388 | − | 6.24210i | 0.184875 | − | 0.320213i | ||||
\(381\) | −3.00269 | − | 5.20081i | −0.153832 | − | 0.266446i | ||||
\(382\) | − | 9.79954i | − | 0.501388i | ||||||
\(383\) | 17.9010 | − | 10.3351i | 0.914696 | − | 0.528100i | 0.0327572 | − | 0.999463i | \(-0.489571\pi\) |
0.881939 | + | 0.471363i | \(0.156238\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | − | 13.5918i | − | 0.692702i | ||||||
\(386\) | 7.09783 | + | 12.2938i | 0.361270 | + | 0.625738i | ||||
\(387\) | −4.15883 | + | 7.20331i | −0.211405 | + | 0.366165i | ||||
\(388\) | 7.39835 | + | 4.27144i | 0.375594 | + | 0.216849i | ||||
\(389\) | −17.4776 | −0.886148 | −0.443074 | − | 0.896485i | \(-0.646112\pi\) | ||||
−0.443074 | + | 0.896485i | \(0.646112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.7318 | 1.90818 | ||||||||
\(392\) | 5.64744 | + | 3.26055i | 0.285239 | + | 0.164683i | ||||
\(393\) | −4.40850 | + | 7.63575i | −0.222379 | + | 0.385173i | ||||
\(394\) | −1.50484 | − | 2.60647i | −0.0758130 | − | 0.131312i | ||||
\(395\) | 33.7657i | 1.69894i | ||||||||
\(396\) | 4.20096 | − | 2.42543i | 0.211106 | − | 0.121882i | ||||
\(397\) | 16.7661 | − | 9.67994i | 0.841469 | − | 0.485822i | −0.0162944 | − | 0.999867i | \(-0.505187\pi\) |
0.857763 | + | 0.514045i | \(0.171854\pi\) | |||||||
\(398\) | − | 12.8944i | − | 0.646338i | ||||||
\(399\) | 0.615957 | + | 1.06687i | 0.0308364 | + | 0.0534103i | ||||
\(400\) | 5.69687 | − | 9.86726i | 0.284843 | − | 0.493363i | ||||
\(401\) | −12.5428 | − | 7.24160i | −0.626359 | − | 0.361628i | 0.152982 | − | 0.988229i | \(-0.451112\pi\) |
−0.779341 | + | 0.626601i | \(0.784446\pi\) | |||||||
\(402\) | 6.05429 | 0.301961 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −11.9976 | −0.596903 | ||||||||
\(405\) | 3.50647 | + | 2.02446i | 0.174238 | + | 0.100596i | ||||
\(406\) | −1.15734 | + | 2.00457i | −0.0574379 | + | 0.0994854i | ||||
\(407\) | −3.11960 | − | 5.40331i | −0.154633 | − | 0.267832i | ||||
\(408\) | 7.38404i | 0.365565i | ||||||||
\(409\) | −16.3665 | + | 9.44922i | −0.809273 | + | 0.467234i | −0.846703 | − | 0.532065i | \(-0.821416\pi\) |
0.0374304 | + | 0.999299i | \(0.488083\pi\) | |||||||
\(410\) | −5.28088 | + | 3.04892i | −0.260804 | + | 0.150575i | ||||
\(411\) | − | 15.7560i | − | 0.777186i | ||||||
\(412\) | 6.16152 | + | 10.6721i | 0.303556 | + | 0.525775i | ||||
\(413\) | 0.452575 | − | 0.783882i | 0.0222697 | − | 0.0385723i | ||||
\(414\) | 4.42532 | + | 2.55496i | 0.217492 | + | 0.125569i | ||||
\(415\) | −62.0592 | −3.04637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.09783 | −0.298612 | ||||||||
\(418\) | −7.47842 | − | 4.31767i | −0.365781 | − | 0.211184i | ||||
\(419\) | 10.8802 | − | 18.8450i | 0.531531 | − | 0.920638i | −0.467792 | − | 0.883838i | \(-0.654950\pi\) |
0.999323 | − | 0.0367993i | \(-0.0117162\pi\) | |||||||
\(420\) | 1.40097 | + | 2.42655i | 0.0683603 | + | 0.118403i | ||||
\(421\) | 20.5918i | 1.00358i | 0.864989 | + | 0.501791i | \(0.167325\pi\) | ||||
−0.864989 | + | 0.501791i | \(0.832675\pi\) | |||||||
\(422\) | 6.75460 | − | 3.89977i | 0.328809 | − | 0.189838i | ||||
\(423\) | −6.24210 | + | 3.60388i | −0.303501 | + | 0.175226i | ||||
\(424\) | − | 13.4765i | − | 0.654477i | ||||||
\(425\) | −42.0659 | − | 72.8603i | −2.04050 | − | 3.53424i | ||||
\(426\) | 0.664874 | − | 1.15160i | 0.0322133 | − | 0.0557950i | ||||
\(427\) | 0.237401 | + | 0.137063i | 0.0114886 | + | 0.00663296i | ||||
\(428\) | −5.89977 | −0.285176 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.6775 | 1.62408 | ||||||||
\(431\) | −29.8894 | − | 17.2567i | −1.43972 | − | 0.831224i | −0.441893 | − | 0.897068i | \(-0.645693\pi\) |
−0.997830 | + | 0.0658433i | \(0.979026\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −1.06315 | − | 1.84144i | −0.0510920 | − | 0.0884939i | 0.839348 | − | 0.543594i | \(-0.182937\pi\) |
−0.890440 | + | 0.455100i | \(0.849603\pi\) | |||||||
\(434\) | 0.673235i | 0.0323163i | ||||||||
\(435\) | 11.7285 | − | 6.77144i | 0.562337 | − | 0.324666i | ||||
\(436\) | 0.686108 | − | 0.396125i | 0.0328586 | − | 0.0189709i | ||||
\(437\) | − | 9.09651i | − | 0.435145i | ||||||
\(438\) | −3.82640 | − | 6.62751i | −0.182832 | − | 0.316675i | ||||
\(439\) | 10.9160 | − | 18.9071i | 0.520994 | − | 0.902388i | −0.478708 | − | 0.877974i | \(-0.658895\pi\) |
0.999702 | − | 0.0244137i | \(-0.00777191\pi\) | |||||||
\(440\) | −17.0094 | − | 9.82036i | −0.810889 | − | 0.468167i | ||||
\(441\) | 6.52111 | 0.310529 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.54048 | −0.358259 | −0.179130 | − | 0.983825i | \(-0.557328\pi\) | ||||
−0.179130 | + | 0.983825i | \(0.557328\pi\) | |||||||
\(444\) | 1.11389 | + | 0.643104i | 0.0528628 | + | 0.0305204i | ||||
\(445\) | −6.29590 | + | 10.9048i | −0.298454 | + | 0.516938i | ||||
\(446\) | −6.09783 | − | 10.5618i | −0.288741 | − | 0.500114i | ||||
\(447\) | 2.55257i | 0.120732i | ||||||||
\(448\) | −0.599308 | + | 0.346011i | −0.0283146 | + | 0.0163475i | ||||
\(449\) | −17.1092 | + | 9.87800i | −0.807433 | + | 0.466172i | −0.846064 | − | 0.533082i | \(-0.821034\pi\) |
0.0386305 | + | 0.999254i | \(0.487700\pi\) | |||||||
\(450\) | − | 11.3937i | − | 0.537106i | ||||||
\(451\) | 3.65279 | + | 6.32682i | 0.172003 | + | 0.297918i | ||||
\(452\) | 3.10992 | − | 5.38653i | 0.146278 | − | 0.253361i | ||||
\(453\) | 15.3432 | + | 8.85839i | 0.720885 | + | 0.416203i | ||||
\(454\) | −6.74333 | −0.316480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.78017 | 0.0833640 | ||||||||
\(457\) | −20.6618 | − | 11.9291i | −0.966517 | − | 0.558019i | −0.0683441 | − | 0.997662i | \(-0.521772\pi\) |
−0.898173 | + | 0.439643i | \(0.855105\pi\) | |||||||
\(458\) | 9.91185 | − | 17.1678i | 0.463151 | − | 0.802200i | ||||
\(459\) | 3.69202 | + | 6.39477i | 0.172329 | + | 0.298482i | ||||
\(460\) | − | 20.6896i | − | 0.964659i | ||||||
\(461\) | −15.2224 | + | 8.78866i | −0.708978 | + | 0.409329i | −0.810683 | − | 0.585486i | \(-0.800904\pi\) |
0.101704 | + | 0.994815i | \(0.467570\pi\) | |||||||
\(462\) | 2.90716 | − | 1.67845i | 0.135253 | − | 0.0780885i | ||||
\(463\) | − | 23.8431i | − | 1.10808i | −0.832489 | − | 0.554041i | \(-0.813085\pi\) | ||
0.832489 | − | 0.554041i | \(-0.186915\pi\) | |||||||
\(464\) | 1.67241 | + | 2.89669i | 0.0776396 | + | 0.134476i | ||||
\(465\) | 1.96950 | − | 3.41127i | 0.0913334 | − | 0.158194i | ||||
\(466\) | −26.0069 | − | 15.0151i | −1.20474 | − | 0.695559i | ||||
\(467\) | −8.61058 | −0.398450 | −0.199225 | − | 0.979954i | \(-0.563842\pi\) | ||||
−0.199225 | + | 0.979954i | \(0.563842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.18970 | 0.193462 | ||||||||
\(470\) | 25.2737 | + | 14.5918i | 1.16579 | + | 0.673069i | ||||
\(471\) | 3.15883 | − | 5.47126i | 0.145551 | − | 0.252102i | ||||
\(472\) | −0.653989 | − | 1.13274i | −0.0301023 | − | 0.0521387i | ||||
\(473\) | − | 40.3478i | − | 1.85519i | ||||||
\(474\) | −7.22216 | + | 4.16972i | −0.331725 | + | 0.191522i | ||||
\(475\) | −17.5654 | + | 10.1414i | −0.805955 | + | 0.465318i | ||||
\(476\) | 5.10992i | 0.234213i | ||||||||
\(477\) | −6.73825 | − | 11.6710i | −0.308523 | − | 0.534378i | ||||
\(478\) | 11.0489 | − | 19.1373i | 0.505366 | − | 0.875319i | ||||
\(479\) | 5.69935 | + | 3.29052i | 0.260410 | + | 0.150348i | 0.624522 | − | 0.781008i | \(-0.285294\pi\) |
−0.364112 | + | 0.931355i | \(0.618627\pi\) | |||||||
\(480\) | 4.04892 | 0.184807 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.1274 | 0.461289 | ||||||||
\(483\) | 3.06241 | + | 1.76809i | 0.139345 | + | 0.0804507i | ||||
\(484\) | −6.26540 | + | 10.8520i | −0.284791 | + | 0.493272i | ||||
\(485\) | −17.2947 | − | 29.9553i | −0.785312 | − | 1.36020i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −20.1576 | + | 11.6380i | −0.913430 | + | 0.527369i | −0.881533 | − | 0.472122i | \(-0.843488\pi\) |
−0.0318970 | + | 0.999491i | \(0.510155\pi\) | |||||||
\(488\) | 0.343054 | − | 0.198062i | 0.0155293 | − | 0.00896586i | ||||
\(489\) | − | 14.5918i | − | 0.659864i | ||||||
\(490\) | −13.2017 | − | 22.8660i | −0.596392 | − | 1.03298i | ||||
\(491\) | −7.77024 | + | 13.4585i | −0.350666 | + | 0.607372i | −0.986366 | − | 0.164565i | \(-0.947378\pi\) |
0.635700 | + | 0.771936i | \(0.280711\pi\) | |||||||
\(492\) | −1.30427 | − | 0.753020i | −0.0588010 | − | 0.0339488i | ||||
\(493\) | 24.6983 | 1.11235 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.6407 | −0.882784 | ||||||||
\(496\) | 0.842515 | + | 0.486426i | 0.0378301 | + | 0.0218412i | ||||
\(497\) | 0.460107 | − | 0.796929i | 0.0206386 | − | 0.0357472i | ||||
\(498\) | −7.66368 | − | 13.2739i | −0.343418 | − | 0.594817i | ||||
\(499\) | 9.53617i | 0.426898i | 0.976954 | + | 0.213449i | \(0.0684697\pi\) | ||||
−0.976954 | + | 0.213449i | \(0.931530\pi\) | |||||||
\(500\) | −22.4194 | + | 12.9438i | −1.00263 | + | 0.578866i | ||||
\(501\) | 16.8886 | − | 9.75063i | 0.754526 | − | 0.435626i | ||||
\(502\) | − | 5.54719i | − | 0.247583i | ||||||
\(503\) | 6.91723 | + | 11.9810i | 0.308424 | + | 0.534206i | 0.978018 | − | 0.208521i | \(-0.0668651\pi\) |
−0.669594 | + | 0.742728i | \(0.733532\pi\) | |||||||
\(504\) | −0.346011 | + | 0.599308i | −0.0154125 | + | 0.0266953i | ||||
\(505\) | 42.0692 | + | 24.2887i | 1.87205 | + | 1.08083i | ||||
\(506\) | −24.7875 | −1.10194 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.00538 | −0.266446 | ||||||||
\(509\) | 35.4757 | + | 20.4819i | 1.57243 | + | 0.907843i | 0.995870 | + | 0.0907888i | \(0.0289388\pi\) |
0.576560 | + | 0.817054i | \(0.304395\pi\) | |||||||
\(510\) | 14.9487 | − | 25.8919i | 0.661939 | − | 1.14651i | ||||
\(511\) | −2.64795 | − | 4.58638i | −0.117138 | − | 0.202890i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.54167 | − | 0.890084i | 0.0680664 | − | 0.0392982i | ||||
\(514\) | 11.9508 | − | 6.89977i | 0.527125 | − | 0.304336i | ||||
\(515\) | − | 49.8950i | − | 2.19864i | ||||||
\(516\) | 4.15883 | + | 7.20331i | 0.183082 | + | 0.317108i | ||||
\(517\) | 17.4819 | − | 30.2795i | 0.768852 | − | 1.33169i | ||||
\(518\) | 0.770835 | + | 0.445042i | 0.0338686 | + | 0.0195540i | ||||
\(519\) | 9.29052 | 0.407809 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.3672 | 1.59327 | 0.796637 | − | 0.604457i | \(-0.206610\pi\) | ||||
0.796637 | + | 0.604457i | \(0.206610\pi\) | |||||||
\(522\) | 2.89669 | + | 1.67241i | 0.126785 | + | 0.0731993i | ||||
\(523\) | 3.01507 | − | 5.22225i | 0.131840 | − | 0.228353i | −0.792546 | − | 0.609812i | \(-0.791245\pi\) |
0.924386 | + | 0.381459i | \(0.124578\pi\) | |||||||
\(524\) | 4.40850 | + | 7.63575i | 0.192586 | + | 0.333569i | ||||
\(525\) | − | 7.88471i | − | 0.344117i | ||||||
\(526\) | −19.4594 | + | 11.2349i | −0.848471 | + | 0.489865i | ||||
\(527\) | 6.22117 | − | 3.59179i | 0.270998 | − | 0.156461i | ||||
\(528\) | − | 4.85086i | − | 0.211106i | ||||||
\(529\) | −1.55562 | − | 2.69442i | −0.0676357 | − | 0.117149i | ||||
\(530\) | −27.2826 | + | 47.2549i | −1.18508 | + | 2.05262i | ||||
\(531\) | −1.13274 | − | 0.653989i | −0.0491568 | − | 0.0283807i | ||||
\(532\) | 1.23191 | 0.0534103 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.10992 | −0.134579 | ||||||||
\(535\) | 20.6873 | + | 11.9438i | 0.894392 | + | 0.516377i | ||||
\(536\) | 3.02715 | − | 5.24317i | 0.130753 | − | 0.226471i | ||||
\(537\) | 11.3964 | + | 19.7392i | 0.491792 | + | 0.851808i | ||||
\(538\) | − | 26.0140i | − | 1.12154i | ||||||
\(539\) | −27.3949 | + | 15.8165i | −1.17998 | + | 0.681264i | ||||
\(540\) | 3.50647 | − | 2.02446i | 0.150894 | − | 0.0871188i | ||||
\(541\) | 7.92154i | 0.340574i | 0.985395 | + | 0.170287i | \(0.0544694\pi\) | ||||
−0.985395 | + | 0.170287i | \(0.945531\pi\) | |||||||
\(542\) | −1.44235 | − | 2.49823i | −0.0619544 | − | 0.107308i | ||||
\(543\) | 0.268750 | − | 0.465488i | 0.0115332 | − | 0.0199760i | ||||
\(544\) | 6.39477 | + | 3.69202i | 0.274173 | + | 0.158294i | ||||
\(545\) | −3.20775 | −0.137405 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.4155 | 0.787390 | 0.393695 | − | 0.919241i | \(-0.371197\pi\) | ||||
0.393695 | + | 0.919241i | \(0.371197\pi\) | |||||||
\(548\) | −13.6451 | − | 7.87800i | −0.582890 | − | 0.336532i | ||||
\(549\) | 0.198062 | − | 0.343054i | 0.00845309 | − | 0.0146412i | ||||
\(550\) | 27.6347 | + | 47.8647i | 1.17835 | + | 2.04096i | ||||
\(551\) | − | 5.95433i | − | 0.253663i | ||||||
\(552\) | 4.42532 | − | 2.55496i | 0.188354 | − | 0.108746i | ||||
\(553\) | −4.99789 | + | 2.88553i | −0.212532 | + | 0.122705i | ||||
\(554\) | 1.46250i | 0.0621357i | ||||||||
\(555\) | −2.60388 | − | 4.51004i | −0.110528 | − | 0.191441i | ||||
\(556\) | −3.04892 | + | 5.28088i | −0.129303 | + | 0.223959i | ||||
\(557\) | −20.7637 | − | 11.9879i | −0.879786 | − | 0.507944i | −0.00919783 | − | 0.999958i | \(-0.502928\pi\) |
−0.870588 | + | 0.492013i | \(0.836261\pi\) | |||||||
\(558\) | 0.972853 | 0.0411841 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.80194 | 0.118403 | ||||||||
\(561\) | −31.0201 | − | 17.9095i | −1.30967 | − | 0.756138i | ||||
\(562\) | −2.84117 | + | 4.92104i | −0.119847 | + | 0.207582i | ||||
\(563\) | −1.14646 | − | 1.98572i | −0.0483174 | − | 0.0836882i | 0.840855 | − | 0.541260i | \(-0.182053\pi\) |
−0.889173 | + | 0.457572i | \(0.848719\pi\) | |||||||
\(564\) | 7.20775i | 0.303501i | ||||||||
\(565\) | −21.8096 | + | 12.5918i | −0.917538 | + | 0.529741i | ||||
\(566\) | 21.8306 | − | 12.6039i | 0.917607 | − | 0.529780i | ||||
\(567\) | 0.692021i | 0.0290622i | ||||||||
\(568\) | −0.664874 | − | 1.15160i | −0.0278975 | − | 0.0483199i | ||||
\(569\) | −22.1715 | + | 38.4022i | −0.929478 | + | 1.60990i | −0.145281 | + | 0.989390i | \(0.546409\pi\) |
−0.784197 | + | 0.620513i | \(0.786925\pi\) | |||||||
\(570\) | −6.24210 | − | 3.60388i | −0.261453 | − | 0.150950i | ||||
\(571\) | 15.2707 | 0.639058 | 0.319529 | − | 0.947577i | \(-0.396475\pi\) | ||||
0.319529 | + | 0.947577i | \(0.396475\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.79954 | −0.409382 | ||||||||
\(574\) | −0.902583 | − | 0.521106i | −0.0376731 | − | 0.0217506i | ||||
\(575\) | −29.1105 | + | 50.4209i | −1.21399 | + | 2.10270i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 8.77048i | 0.365120i | 0.983195 | + | 0.182560i | \(0.0584383\pi\) | ||||
−0.983195 | + | 0.182560i | \(0.941562\pi\) | |||||||
\(578\) | 32.4968 | − | 18.7620i | 1.35169 | − | 0.780398i | ||||
\(579\) | 12.2938 | − | 7.09783i | 0.510913 | − | 0.294976i | ||||
\(580\) | − | 13.5429i | − | 0.562337i | ||||||
\(581\) | −5.30343 | − | 9.18581i | −0.220023 | − | 0.381092i | ||||
\(582\) | 4.27144 | − | 7.39835i | 0.177057 | − | 0.306671i | ||||
\(583\) | 56.6143 | + | 32.6863i | 2.34472 | + | 1.35373i | ||||
\(584\) | −7.65279 | −0.316675 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.14914 | −0.295328 | ||||||||
\(587\) | 33.0328 | + | 19.0715i | 1.36341 | + | 0.787166i | 0.990076 | − | 0.140531i | \(-0.0448810\pi\) |
0.373335 | + | 0.927697i | \(0.378214\pi\) | |||||||
\(588\) | 3.26055 | − | 5.64744i | 0.134463 | − | 0.232897i | ||||
\(589\) | −0.865921 | − | 1.49982i | −0.0356796 | − | 0.0617989i | ||||
\(590\) | 5.29590i | 0.218029i | ||||||||
\(591\) | −2.60647 | + | 1.50484i | −0.107216 | + | 0.0619010i | ||||
\(592\) | 1.11389 | − | 0.643104i | 0.0457806 | − | 0.0264314i | ||||
\(593\) | 37.9517i | 1.55849i | 0.626720 | + | 0.779244i | \(0.284397\pi\) | ||||
−0.626720 | + | 0.779244i | \(0.715603\pi\) | |||||||
\(594\) | −2.42543 | − | 4.20096i | −0.0995165 | − | 0.172368i | ||||
\(595\) | 10.3448 | − | 17.9177i | 0.424096 | − | 0.734556i | ||||
\(596\) | 2.21059 | + | 1.27628i | 0.0905491 | + | 0.0522786i | ||||
\(597\) | −12.8944 | −0.527732 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.57971 | −0.146263 | −0.0731315 | − | 0.997322i | \(-0.523299\pi\) | ||||
−0.0731315 | + | 0.997322i | \(0.523299\pi\) | |||||||
\(600\) | −9.86726 | − | 5.69687i | −0.402829 | − | 0.232574i | ||||
\(601\) | 2.85839 | − | 4.95087i | 0.116596 | − | 0.201950i | −0.801821 | − | 0.597565i | \(-0.796135\pi\) |
0.918417 | + | 0.395615i | \(0.129468\pi\) | |||||||
\(602\) | 2.87800 | + | 4.98485i | 0.117299 | + | 0.203167i | ||||
\(603\) | − | 6.05429i | − | 0.246550i | ||||||
\(604\) | 15.3432 | − | 8.85839i | 0.624305 | − | 0.360443i | ||||
\(605\) | 43.9388 | − | 25.3681i | 1.78637 | − | 1.03136i | ||||
\(606\) | 11.9976i | 0.487369i | ||||||||
\(607\) | −11.2143 | − | 19.4238i | −0.455175 | − | 0.788387i | 0.543523 | − | 0.839394i | \(-0.317090\pi\) |
−0.998698 | + | 0.0510075i | \(0.983757\pi\) | |||||||
\(608\) | 0.890084 | − | 1.54167i | 0.0360977 | − | 0.0625230i | ||||
\(609\) | 2.00457 | + | 1.15734i | 0.0812295 | + | 0.0468979i | ||||
\(610\) | −1.60388 | −0.0649390 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.38404 | 0.298482 | ||||||||
\(613\) | 34.6066 | + | 19.9801i | 1.39775 | + | 0.806991i | 0.994157 | − | 0.107948i | \(-0.0344281\pi\) |
0.403592 | + | 0.914939i | \(0.367761\pi\) | |||||||
\(614\) | 8.99761 | − | 15.5843i | 0.363114 | − | 0.628932i | ||||
\(615\) | 3.04892 | + | 5.28088i | 0.122944 | + | 0.212946i | ||||
\(616\) | − | 3.35690i | − | 0.135253i | ||||||
\(617\) | 27.2339 | − | 15.7235i | 1.09639 | − | 0.633003i | 0.161123 | − | 0.986934i | \(-0.448489\pi\) |
0.935272 | + | 0.353931i | \(0.115155\pi\) | |||||||
\(618\) | 10.6721 | − | 6.16152i | 0.429294 | − | 0.247853i | ||||
\(619\) | 29.3685i | 1.18042i | 0.807250 | + | 0.590210i | \(0.200955\pi\) | ||||
−0.807250 | + | 0.590210i | \(0.799045\pi\) | |||||||
\(620\) | −1.96950 | − | 3.41127i | −0.0790970 | − | 0.137000i | ||||
\(621\) | 2.55496 | − | 4.42532i | 0.102527 | − | 0.177582i | ||||
\(622\) | 2.88365 | + | 1.66487i | 0.115624 | + | 0.0667554i | ||||
\(623\) | −2.15213 | −0.0862232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47.8485 | 1.91394 | ||||||||
\(626\) | 15.4875 | + | 8.94169i | 0.619003 | + | 0.357382i | ||||
\(627\) | −4.31767 | + | 7.47842i | −0.172431 | + | 0.298659i | ||||
\(628\) | −3.15883 | − | 5.47126i | −0.126051 | − | 0.218327i | ||||
\(629\) | − | 9.49742i | − | 0.378687i | ||||||
\(630\) | 2.42655 | − | 1.40097i | 0.0966760 | − | 0.0558159i | ||||
\(631\) | −18.7754 | + | 10.8400i | −0.747436 | + | 0.431532i | −0.824767 | − | 0.565473i | \(-0.808694\pi\) |
0.0773307 | + | 0.997005i | \(0.475360\pi\) | |||||||
\(632\) | 8.33944i | 0.331725i | ||||||||
\(633\) | −3.89977 | − | 6.75460i | −0.155002 | − | 0.268471i | ||||
\(634\) | 2.19687 | − | 3.80508i | 0.0872487 | − | 0.151119i | ||||
\(635\) | 21.0576 | + | 12.1576i | 0.835647 | + | 0.482461i | ||||
\(636\) | −13.4765 | −0.534378 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.2252 | −0.642362 | ||||||||
\(639\) | −1.15160 | − | 0.664874i | −0.0455564 | − | 0.0263020i | ||||
\(640\) | 2.02446 | − | 3.50647i | 0.0800238 | − | 0.138605i | ||||
\(641\) | 7.00538 | + | 12.1337i | 0.276696 | + | 0.479251i | 0.970562 | − | 0.240853i | \(-0.0774272\pi\) |
−0.693866 | + | 0.720104i | \(0.744094\pi\) | |||||||
\(642\) | 5.89977i | 0.232845i | ||||||||
\(643\) | 26.6627 | − | 15.3937i | 1.05148 | − | 0.607070i | 0.128413 | − | 0.991721i | \(-0.459012\pi\) |
0.923062 | + | 0.384651i | \(0.125678\pi\) | |||||||
\(644\) | 3.06241 | − | 1.76809i | 0.120676 | − | 0.0696723i | ||||
\(645\) | − | 33.6775i | − | 1.32605i | ||||||
\(646\) | −6.57242 | − | 11.3838i | −0.258588 | − | 0.447888i | ||||
\(647\) | −8.30127 | + | 14.3782i | −0.326357 | + | 0.565266i | −0.981786 | − | 0.189990i | \(-0.939154\pi\) |
0.655429 | + | 0.755257i | \(0.272488\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 6.34481 | 0.249056 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.673235 | 0.0263862 | ||||||||
\(652\) | −12.6369 | − | 7.29590i | −0.494898 | − | 0.285729i | ||||
\(653\) | −14.2729 | + | 24.7214i | −0.558543 | + | 0.967425i | 0.439075 | + | 0.898450i | \(0.355306\pi\) |
−0.997618 | + | 0.0689745i | \(0.978027\pi\) | |||||||
\(654\) | −0.396125 | − | 0.686108i | −0.0154897 | − | 0.0268289i | ||||
\(655\) | − | 35.6993i | − | 1.39489i | ||||||
\(656\) | −1.30427 | + | 0.753020i | −0.0509232 | + | 0.0294005i | ||||
\(657\) | −6.62751 | + | 3.82640i | −0.258564 | + | 0.149282i | ||||
\(658\) | 4.98792i | 0.194449i | ||||||||
\(659\) | −13.8593 | − | 24.0051i | −0.539884 | − | 0.935106i | −0.998910 | − | 0.0466830i | \(-0.985135\pi\) |
0.459026 | − | 0.888423i | \(-0.348198\pi\) | |||||||
\(660\) | −9.82036 | + | 17.0094i | −0.382257 | + | 0.662088i | ||||
\(661\) | 9.35383 | + | 5.40044i | 0.363822 | + | 0.210053i | 0.670756 | − | 0.741678i | \(-0.265970\pi\) |
−0.306934 | + | 0.951731i | \(0.599303\pi\) | |||||||
\(662\) | 25.6775 | 0.997986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3274 | −0.594817 | ||||||||
\(665\) | −4.31966 | − | 2.49396i | −0.167509 | − | 0.0967116i | ||||
\(666\) | 0.643104 | − | 1.11389i | 0.0249198 | − | 0.0431623i | ||||
\(667\) | −8.54586 | − | 14.8019i | −0.330897 | − | 0.573130i | ||||
\(668\) | − | 19.5013i | − | 0.754526i | ||||||
\(669\) | −10.5618 | + | 6.09783i | −0.408341 | + | 0.235756i | ||||
\(670\) | −21.2292 | + | 12.2567i | −0.820154 | + | 0.473516i | ||||
\(671\) | 1.92154i | 0.0741803i | ||||||||
\(672\) | 0.346011 | + | 0.599308i | 0.0133477 | + | 0.0231188i | ||||
\(673\) | 8.16301 | − | 14.1388i | 0.314661 | − | 0.545009i | −0.664704 | − | 0.747107i | \(-0.731442\pi\) |
0.979365 | + | 0.202098i | \(0.0647758\pi\) | |||||||
\(674\) | −21.3479 | − | 12.3252i | −0.822289 | − | 0.474749i | ||||
\(675\) | −11.3937 | −0.438545 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.4252 | 1.59210 | 0.796050 | − | 0.605231i | \(-0.206919\pi\) | ||||
0.796050 | + | 0.605231i | \(0.206919\pi\) | |||||||
\(678\) | −5.38653 | − | 3.10992i | −0.206869 | − | 0.119436i | ||||
\(679\) | 2.95593 | − | 5.11982i | 0.113438 | − | 0.196480i | ||||
\(680\) | −14.9487 | − | 25.8919i | −0.573256 | − | 0.992909i | ||||
\(681\) | 6.74333i | 0.258405i | ||||||||
\(682\) | −4.08692 | + | 2.35958i | −0.156496 | + | 0.0903532i | ||||
\(683\) | −27.0481 | + | 15.6163i | −1.03497 | + | 0.597539i | −0.918404 | − | 0.395644i | \(-0.870521\pi\) |
−0.116564 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(684\) | − | 1.78017i | − | 0.0680664i | ||||||
\(685\) | 31.8974 | + | 55.2479i | 1.21874 | + | 2.11091i | ||||
\(686\) | 4.67845 | − | 8.10331i | 0.178624 | − | 0.309386i | ||||
\(687\) | −17.1678 | − | 9.91185i | −0.654994 | − | 0.378161i | ||||
\(688\) | 8.31767 | 0.317108 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −20.6896 | −0.787641 | ||||||||
\(691\) | −21.6192 | − | 12.4819i | −0.822435 | − | 0.474833i | 0.0288205 | − | 0.999585i | \(-0.490825\pi\) |
−0.851255 | + | 0.524752i | \(0.824158\pi\) | |||||||
\(692\) | 4.64526 | − | 8.04583i | 0.176586 | − | 0.305856i | ||||
\(693\) | −1.67845 | − | 2.90716i | −0.0637590 | − | 0.110434i | ||||
\(694\) | 14.2959i | 0.542665i | ||||||||
\(695\) | 21.3818 | − | 12.3448i | 0.811060 | − | 0.468265i | ||||
\(696\) | 2.89669 | − | 1.67241i | 0.109799 | − | 0.0633924i | ||||
\(697\) | 11.1207i | 0.421225i | ||||||||
\(698\) | −5.53079 | − | 9.57962i | −0.209344 | − | 0.362594i | ||||
\(699\) | −15.0151 | + | 26.0069i | −0.567922 | + | 0.983670i | ||||
\(700\) | −6.82836 | − | 3.94235i | −0.258088 | − | 0.149007i | ||||
\(701\) | −8.17151 | −0.308634 | −0.154317 | − | 0.988021i | \(-0.549318\pi\) | ||||
−0.154317 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.28967 | −0.0863564 | ||||||||
\(704\) | −4.20096 | − | 2.42543i | −0.158330 | − | 0.0914117i | ||||
\(705\) | 14.5918 | − | 25.2737i | 0.549559 | − | 0.951864i | ||||
\(706\) | −5.25236 | − | 9.09735i | −0.197675 | − | 0.342383i | ||||
\(707\) | 8.30260i | 0.312251i | ||||||||
\(708\) | −1.13274 | + | 0.653989i | −0.0425711 | + | 0.0245784i | ||||
\(709\) | 31.8682 | − | 18.3991i | 1.19684 | − | 0.690993i | 0.236987 | − | 0.971513i | \(-0.423840\pi\) |
0.959848 | + | 0.280520i | \(0.0905069\pi\) | |||||||
\(710\) | 5.38404i | 0.202060i | ||||||||
\(711\) | 4.16972 | + | 7.22216i | 0.156377 | + | 0.270852i | ||||
\(712\) | −1.55496 | + | 2.69327i | −0.0582745 | + | 0.100934i | ||||
\(713\) | −4.30518 | − | 2.48560i | −0.161230 | − | 0.0930864i | ||||
\(714\) | 5.10992 | 0.191234 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.7928 | 0.851808 | ||||||||
\(717\) | −19.1373 | − | 11.0489i | −0.714695 | − | 0.412629i | ||||
\(718\) | −2.55496 | + | 4.42532i | −0.0953502 | + | 0.165151i | ||||
\(719\) | 17.6112 | + | 30.5034i | 0.656786 | + | 1.13759i | 0.981443 | + | 0.191755i | \(0.0614178\pi\) |
−0.324657 | + | 0.945832i | \(0.605249\pi\) | |||||||
\(720\) | − | 4.04892i | − | 0.150894i | ||||||
\(721\) | 7.38530 | − | 4.26391i | 0.275043 | − | 0.158796i | ||||
\(722\) | 13.7101 | − | 7.91550i | 0.510235 | − | 0.294584i | ||||
\(723\) | − | 10.1274i | − | 0.376641i | ||||||
\(724\) | −0.268750 | − | 0.465488i | −0.00998801 | − | 0.0172997i | ||||
\(725\) | −19.0550 | + | 33.0042i | −0.707683 | + | 1.22574i | ||||
\(726\) | 10.8520 | + | 6.26540i | 0.402755 | + | 0.232531i | ||||
\(727\) | −40.6872 | −1.50901 | −0.754503 | − | 0.656297i | \(-0.772122\pi\) | ||||
−0.754503 | + | 0.656297i | \(0.772122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 26.8343 | + | 15.4928i | 0.993180 | + | 0.573413i | ||||
\(731\) | 30.7090 | − | 53.1896i | 1.13581 | − | 1.96729i | ||||
\(732\) | −0.198062 | − | 0.343054i | −0.00732059 | − | 0.0126796i | ||||
\(733\) | 27.1400i | 1.00244i | 0.865320 | + | 0.501220i | \(0.167115\pi\) | ||||
−0.865320 | + | 0.501220i | \(0.832885\pi\) | |||||||
\(734\) | −7.31620 | + | 4.22401i | −0.270046 | + | 0.155911i | ||||
\(735\) | −22.8660 | + | 13.2017i | −0.843426 | + | 0.486952i | ||||
\(736\) | − | 5.10992i | − | 0.188354i | ||||||
\(737\) | 14.6843 | + | 25.4339i | 0.540901 | + | 0.936869i | ||||
\(738\) | −0.753020 | + | 1.30427i | −0.0277191 | + | 0.0480108i | ||||
\(739\) | 3.22670 | + | 1.86294i | 0.118696 | + | 0.0685292i | 0.558173 | − | 0.829725i | \(-0.311503\pi\) |
−0.439476 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(740\) | −5.20775 | −0.191441 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.32603 | −0.342369 | ||||||||
\(743\) | −18.9301 | − | 10.9293i | −0.694479 | − | 0.400958i | 0.110809 | − | 0.993842i | \(-0.464656\pi\) |
−0.805288 | + | 0.592884i | \(0.797989\pi\) | |||||||
\(744\) | 0.486426 | − | 0.842515i | 0.0178333 | − | 0.0308881i | ||||
\(745\) | −5.16756 | − | 8.95048i | −0.189325 | − | 0.327920i | ||||
\(746\) | 7.69096i | 0.281586i | ||||||||
\(747\) | −13.2739 | + | 7.66368i | −0.485666 | + | 0.280399i | ||||
\(748\) | −31.0201 | + | 17.9095i | −1.13421 | + | 0.654835i | ||||
\(749\) | 4.08277i | 0.149181i | ||||||||
\(750\) | 12.9438 | + | 22.4194i | 0.472642 | + | 0.818641i | ||||
\(751\) | 26.6821 | − | 46.2147i | 0.973644 | − | 1.68640i | 0.289303 | − | 0.957238i | \(-0.406577\pi\) |
0.684341 | − | 0.729162i | \(-0.260090\pi\) | |||||||
\(752\) | 6.24210 | + | 3.60388i | 0.227626 | + | 0.131420i | ||||
\(753\) | −5.54719 | −0.202151 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −71.7338 | −2.61066 | ||||||||
\(756\) | 0.599308 | + | 0.346011i | 0.0217966 | + | 0.0125843i | ||||
\(757\) | 2.31767 | − | 4.01432i | 0.0842370 | − | 0.145903i | −0.820829 | − | 0.571174i | \(-0.806488\pi\) |
0.905066 | + | 0.425271i | \(0.139821\pi\) | |||||||
\(758\) | −5.70171 | − | 9.87565i | −0.207095 | − | 0.358700i | ||||
\(759\) | 24.7875i | 0.899728i | ||||||||
\(760\) | −6.24210 | + | 3.60388i | −0.226425 | + | 0.130726i | ||||
\(761\) | −10.0115 | + | 5.78017i | −0.362918 | + | 0.209531i | −0.670360 | − | 0.742036i | \(-0.733860\pi\) |
0.307442 | + | 0.951567i | \(0.400527\pi\) | |||||||
\(762\) | 6.00538i | 0.217552i | ||||||||
\(763\) | −0.274127 | − | 0.474801i | −0.00992405 | − | 0.0171890i | ||||
\(764\) | −4.89977 | + | 8.48665i | −0.177268 | + | 0.307036i | ||||
\(765\) | −25.8919 | − | 14.9487i | −0.936123 | − | 0.540471i | ||||
\(766\) | −20.6703 | −0.746847 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −12.7686 | − | 7.37196i | −0.460448 | − | 0.265840i | 0.251785 | − | 0.967783i | \(-0.418983\pi\) |
−0.712233 | + | 0.701944i | \(0.752316\pi\) | |||||||
\(770\) | −6.79590 | + | 11.7708i | −0.244907 | + | 0.424192i | ||||
\(771\) | −6.89977 | − | 11.9508i | −0.248489 | − | 0.430396i | ||||
\(772\) | − | 14.1957i | − | 0.510913i | ||||||
\(773\) | −5.56220 | + | 3.21134i | −0.200059 | + | 0.115504i | −0.596683 | − | 0.802477i | \(-0.703515\pi\) |
0.396624 | + | 0.917981i | \(0.370182\pi\) | |||||||
\(774\) | 7.20331 | − | 4.15883i | 0.258918 | − | 0.149486i | ||||
\(775\) | 11.0844i | 0.398164i | ||||||||
\(776\) | −4.27144 | − | 7.39835i | −0.153336 | − | 0.265585i | ||||
\(777\) | 0.445042 | − | 0.770835i | 0.0159658 | − | 0.0276536i | ||||
\(778\) | 15.1360 | + | 8.73878i | 0.542652 | + | 0.313301i | ||||
\(779\) | 2.68100 | 0.0960570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.45042 | 0.230814 | ||||||||
\(782\) | −32.6767 | − | 18.8659i | −1.16852 | − | 0.674644i | ||||
\(783\) | 1.67241 | − | 2.89669i | 0.0597670 | − | 0.103519i | ||||
\(784\) | −3.26055 | − | 5.64744i | −0.116448 | − | 0.201694i | ||||
\(785\) | 25.5797i | 0.912979i | ||||||||
\(786\) | 7.63575 | − | 4.40850i | 0.272358 | − | 0.157246i | ||||
\(787\) | −37.6146 | + | 21.7168i | −1.34081 | + | 0.774119i | −0.986927 | − | 0.161169i | \(-0.948474\pi\) |
−0.353887 | + | 0.935288i | \(0.615140\pi\) | |||||||
\(788\) | 3.00969i | 0.107216i | ||||||||
\(789\) | 11.2349 | + | 19.4594i | 0.399973 | + | 0.692773i | ||||
\(790\) | 16.8828 | − | 29.2419i | 0.600665 | − | 1.04038i | ||||
\(791\) | −3.72760 | − | 2.15213i | −0.132538 | − | 0.0765209i | ||||
\(792\) | −4.85086 | −0.172368 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −19.3599 | −0.687056 | ||||||||
\(795\) | 47.2549 | + | 27.2826i | 1.67596 | + | 0.967615i | ||||
\(796\) | −6.44720 | + | 11.1669i | −0.228515 | + | 0.395799i | ||||
\(797\) | 10.5082 | + | 18.2007i | 0.372219 | + | 0.644703i | 0.989907 | − | 0.141721i | \(-0.0452636\pi\) |
−0.617687 | + | 0.786424i | \(0.711930\pi\) | |||||||
\(798\) | − | 1.23191i | − | 0.0436093i | ||||||
\(799\) | 46.0919 | − | 26.6112i | 1.63061 | − | 0.941436i | ||||
\(800\) | −9.86726 | + | 5.69687i | −0.348860 | + | 0.201415i | ||||
\(801\) | 3.10992i | 0.109883i | ||||||||
\(802\) | 7.24160 | + | 12.5428i | 0.255710 | + | 0.442903i | ||||
\(803\) | 18.5613 | − | 32.1491i | 0.655014 | − | 1.13452i | ||||
\(804\) | −5.24317 | − | 3.02715i | −0.184912 | − | 0.106759i | ||||
\(805\) | −14.3177 | −0.504631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.0140 | −0.915736 | ||||||||
\(808\) | 10.3902 | + | 5.99880i | 0.365527 | + | 0.211037i | ||||
\(809\) | 4.16123 | − | 7.20746i | 0.146301 | − | 0.253401i | −0.783557 | − | 0.621320i | \(-0.786597\pi\) |
0.929858 | + | 0.367920i | \(0.119930\pi\) | |||||||
\(810\) | −2.02446 | − | 3.50647i | −0.0711322 | − | 0.123205i | ||||
\(811\) | 14.4638i | 0.507894i | 0.967218 | + | 0.253947i | \(0.0817288\pi\) | ||||
−0.967218 | + | 0.253947i | \(0.918271\pi\) | |||||||
\(812\) | 2.00457 | − | 1.15734i | 0.0703468 | − | 0.0406147i | ||||
\(813\) | −2.49823 | + | 1.44235i | −0.0876167 | + | 0.0505855i | ||||
\(814\) | 6.23921i | 0.218684i | ||||||||
\(815\) | 29.5405 | + | 51.1656i | 1.03476 | + | 1.79225i | ||||
\(816\) | 3.69202 | − | 6.39477i | 0.129247 | − | 0.223862i | ||||
\(817\) | −12.8231 | − | 7.40342i | −0.448623 | − | 0.259013i | ||||
\(818\) | 18.8984 | 0.660769 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.09783 | 0.212946 | ||||||||
\(821\) | −33.2693 | − | 19.2080i | −1.16111 | − | 0.670365i | −0.209538 | − | 0.977801i | \(-0.567196\pi\) |
−0.951569 | + | 0.307435i | \(0.900529\pi\) | |||||||
\(822\) | −7.87800 | + | 13.6451i | −0.274777 | + | 0.475928i | ||||
\(823\) | −20.4874 | − | 35.4852i | −0.714145 | − | 1.23694i | −0.963288 | − | 0.268469i | \(-0.913482\pi\) |
0.249143 | − | 0.968467i | \(-0.419851\pi\) | |||||||
\(824\) | − | 12.3230i | − | 0.429294i | ||||||
\(825\) | 47.8647 | − | 27.6347i | 1.66643 | − | 0.962116i | ||||
\(826\) | −0.783882 | + | 0.452575i | −0.0272748 | + | 0.0157471i | ||||
\(827\) | 3.51035i | 0.122067i | 0.998136 | + | 0.0610335i | \(0.0194396\pi\) | ||||
−0.998136 | + | 0.0610335i | \(0.980560\pi\) | |||||||
\(828\) | −2.55496 | − | 4.42532i | −0.0887909 | − | 0.153790i | ||||
\(829\) | −6.60925 | + | 11.4476i | −0.229549 | + | 0.397590i | −0.957674 | − | 0.287853i | \(-0.907058\pi\) |
0.728126 | + | 0.685444i | \(0.240392\pi\) | |||||||
\(830\) | 53.7448 | + | 31.0296i | 1.86551 | + | 1.07705i | ||||
\(831\) | 1.46250 | 0.0507336 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −48.1521 | −1.66837 | ||||||||
\(834\) | 5.28088 | + | 3.04892i | 0.182862 | + | 0.105575i | ||||
\(835\) | −39.4795 | + | 68.3805i | −1.36624 | + | 2.36640i | ||||
\(836\) | 4.31767 | + | 7.47842i | 0.149330 | + | 0.258647i | ||||
\(837\) | − | 0.972853i | − | 0.0336267i | ||||||
\(838\) | −18.8450 | + | 10.8802i | −0.650989 | + | 0.375849i | ||||
\(839\) | 48.3667 | − | 27.9245i | 1.66980 | − | 0.964062i | 0.702063 | − | 0.712115i | \(-0.252263\pi\) |
0.967741 | − | 0.251947i | \(-0.0810707\pi\) | |||||||
\(840\) | − | 2.80194i | − | 0.0966760i | ||||||
\(841\) | 8.90611 | + | 15.4258i | 0.307107 | + | 0.531925i | ||||
\(842\) | 10.2959 | − | 17.8330i | 0.354820 | − | 0.614566i | ||||
\(843\) | 4.92104 | + | 2.84117i | 0.169490 | + | 0.0978550i | ||||
\(844\) | −7.79954 | −0.268471 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.20775 | 0.247808 | ||||||||
\(847\) | 7.50981 | + | 4.33579i | 0.258040 | + | 0.148979i | ||||
\(848\) | −6.73825 | + | 11.6710i | −0.231392 | + | 0.400784i | ||||
\(849\) | −12.6039 | − | 21.8306i | −0.432564 | − | 0.749223i | ||||
\(850\) | 84.1318i | 2.88570i | ||||||||
\(851\) | −5.69188 | + | 3.28621i | −0.195115 | + | 0.112650i | ||||
\(852\) | −1.15160 | + | 0.664874i | −0.0394530 | + | 0.0227782i | ||||
\(853\) | 21.8103i | 0.746770i | 0.927676 | + | 0.373385i | \(0.121803\pi\) | ||||
−0.927676 | + | 0.373385i | \(0.878197\pi\) | |||||||
\(854\) | −0.137063 | − | 0.237401i | −0.00469021 | − | 0.00812368i | ||||
\(855\) | −3.60388 | + | 6.24210i | −0.123250 | + | 0.213475i | ||||
\(856\) | 5.10935 | + | 2.94989i | 0.174634 | + | 0.100825i | ||||
\(857\) | −28.8961 | −0.987070 | −0.493535 | − | 0.869726i | \(-0.664296\pi\) | ||||
−0.493535 | + | 0.869726i | \(0.664296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2755 | −0.589431 | −0.294715 | − | 0.955585i | \(-0.595225\pi\) | ||||
−0.294715 | + | 0.955585i | \(0.595225\pi\) | |||||||
\(860\) | −29.1656 | − | 16.8388i | −0.994539 | − | 0.574197i | ||||
\(861\) | −0.521106 | + | 0.902583i | −0.0177593 | + | 0.0307599i | ||||
\(862\) | 17.2567 | + | 29.8894i | 0.587764 | + | 1.01804i | ||||
\(863\) | − | 44.7741i | − | 1.52413i | −0.647503 | − | 0.762063i | \(-0.724187\pi\) | ||
0.647503 | − | 0.762063i | \(-0.275813\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | −32.5769 | + | 18.8083i | −1.10765 | + | 0.639501i | ||||
\(866\) | 2.12631i | 0.0722549i | ||||||||
\(867\) | −18.7620 | − | 32.4968i | −0.637192 | − | 1.10365i | ||||
\(868\) | 0.336618 | − | 0.583039i | 0.0114255 | − | 0.0197896i | ||||
\(869\) | −35.0337 | − | 20.2267i | −1.18844 | − | 0.686144i | ||||
\(870\) | −13.5429 | −0.459147 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.792249 | −0.0268289 | ||||||||
\(873\) | −7.39835 | − | 4.27144i | −0.250396 | − | 0.144566i | ||||
\(874\) | −4.54825 | + | 7.87781i | −0.153847 | + | 0.266471i | ||||
\(875\) | 8.95742 | + | 15.5147i | 0.302816 | + | 0.524493i | ||||
\(876\) | 7.65279i | 0.258564i | ||||||||
\(877\) | −34.8784 | + | 20.1371i | −1.17776 | + | 0.679980i | −0.955495 | − | 0.295006i | \(-0.904678\pi\) |
−0.222265 | + | 0.974986i | \(0.571345\pi\) | |||||||
\(878\) | −18.9071 | + | 10.9160i | −0.638085 | + | 0.368398i | ||||
\(879\) | 7.14914i | 0.241135i | ||||||||
\(880\) | 9.82036 | + | 17.0094i | 0.331044 | + | 0.573385i | ||||
\(881\) | 4.70410 | − | 8.14775i | 0.158485 | − | 0.274505i | −0.775837 | − | 0.630933i | \(-0.782672\pi\) |
0.934323 | + | 0.356428i | \(0.116006\pi\) | |||||||
\(882\) | −5.64744 | − | 3.26055i | −0.190159 | − | 0.109789i | ||||
\(883\) | 51.2271 | 1.72393 | 0.861965 | − | 0.506968i | \(-0.169234\pi\) | ||||
0.861965 | + | 0.506968i | \(0.169234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.29590 | 0.178020 | ||||||||
\(886\) | 6.53025 | + | 3.77024i | 0.219388 | + | 0.126664i | ||||
\(887\) | 19.9608 | − | 34.5731i | 0.670217 | − | 1.16085i | −0.307625 | − | 0.951508i | \(-0.599534\pi\) |
0.977842 | − | 0.209342i | \(-0.0671324\pi\) | |||||||
\(888\) | −0.643104 | − | 1.11389i | −0.0215812 | − | 0.0373797i | ||||
\(889\) | 4.15585i | 0.139383i | ||||||||
\(890\) | 10.9048 | − | 6.29590i | 0.365530 | − | 0.211039i | ||||
\(891\) | −4.20096 | + | 2.42543i | −0.140738 | + | 0.0812549i | ||||
\(892\) | 12.1957i | 0.408341i | ||||||||
\(893\) | −6.41550 | − | 11.1120i | −0.214687 | − | 0.371848i | ||||
\(894\) | 1.27628 | − | 2.21059i | 0.0426853 | − | 0.0739331i | ||||
\(895\) | −79.9223 | − | 46.1432i | −2.67151 | − | 1.54240i | ||||
\(896\) | 0.692021 | 0.0231188 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.7560 | 0.659266 | ||||||||
\(899\) | −2.81806 | − | 1.62701i | −0.0939875 | − | 0.0542637i | ||||
\(900\) | −5.69687 | + | 9.86726i | −0.189896 | + | 0.328909i | ||||
\(901\) | 49.7555 | + | 86.1791i | 1.65760 | + | 2.87104i | ||||
\(902\) | − | 7.30559i | − | 0.243249i | ||||||
\(903\) | 4.98485 | − | 2.87800i | 0.165885 | − | 0.0957739i | ||||
\(904\) | −5.38653 | + | 3.10992i | −0.179153 | + | 0.103434i | ||||
\(905\) | 2.17629i | 0.0723424i | ||||||||
\(906\) | −8.85839 | − | 15.3432i | −0.294300 | − | 0.509743i | ||||
\(907\) | −17.4155 | + | 30.1645i | −0.578272 | + | 1.00160i | 0.417405 | + | 0.908720i | \(0.362940\pi\) |
−0.995678 | + | 0.0928765i | \(0.970394\pi\) | |||||||
\(908\) | 5.83990 | + | 3.37167i | 0.193804 | + | 0.111893i | ||||
\(909\) | 11.9976 | 0.397936 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2125 | 0.437751 | 0.218875 | − | 0.975753i | \(-0.429761\pi\) | ||||
0.218875 | + | 0.975753i | \(0.429761\pi\) | |||||||
\(912\) | −1.54167 | − | 0.890084i | −0.0510498 | − | 0.0294736i | ||||
\(913\) | 37.1754 | − | 64.3897i | 1.23033 | − | 2.13099i | ||||
\(914\) | 11.9291 | + | 20.6618i | 0.394579 | + | 0.683430i | ||||
\(915\) | 1.60388i | 0.0530225i | ||||||||
\(916\) | −17.1678 | + | 9.91185i | −0.567241 | + | 0.327497i | ||||
\(917\) | 5.28410 | − | 3.05078i | 0.174496 | − | 0.100746i | ||||
\(918\) | − | 7.38404i | − | 0.243710i | ||||||
\(919\) | −10.5087 | − | 18.2017i | −0.346651 | − | 0.600417i | 0.639001 | − | 0.769206i | \(-0.279348\pi\) |
−0.985652 | + | 0.168789i | \(0.946015\pi\) | |||||||
\(920\) | −10.3448 | + | 17.9177i | −0.341058 | + | 0.590731i | ||||
\(921\) | −15.5843 | − | 8.99761i | −0.513521 | − | 0.296481i | ||||
\(922\) | 17.5773 | 0.578878 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.35690 | −0.110434 | ||||||||
\(925\) | 12.6914 | + | 7.32736i | 0.417289 | + | 0.240922i | ||||
\(926\) | −11.9215 | + | 20.6487i | −0.391766 | + | 0.678559i | ||||
\(927\) | −6.16152 | − | 10.6721i | −0.202371 | − | 0.350517i | ||||
\(928\) | − | 3.34481i | − | 0.109799i | ||||||
\(929\) | −23.3797 | + | 13.4983i | −0.767063 | + | 0.442864i | −0.831826 | − | 0.555037i | \(-0.812704\pi\) |
0.0647630 | + | 0.997901i | \(0.479371\pi\) | |||||||
\(930\) | −3.41127 | + | 1.96950i | −0.111860 | + | 0.0645825i | ||||
\(931\) | 11.6087i | 0.380459i | ||||||||
\(932\) | 15.0151 | + | 26.0069i | 0.491835 | + | 0.851883i | ||||
\(933\) | 1.66487 | − | 2.88365i | 0.0545055 | − | 0.0944064i | ||||
\(934\) | 7.45698 | + | 4.30529i | 0.244000 | + | 0.140873i | ||||
\(935\) | 145.028 | 4.74292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.1745 | 0.757078 | 0.378539 | − | 0.925585i | \(-0.376427\pi\) | ||||
0.378539 | + | 0.925585i | \(0.376427\pi\) | |||||||
\(938\) | −3.62839 | − | 2.09485i | −0.118471 | − | 0.0683993i | ||||
\(939\) | 8.94169 | − | 15.4875i | 0.291801 | − | 0.505414i | ||||
\(940\) | −14.5918 | − | 25.2737i | −0.475932 | − | 0.824338i | ||||
\(941\) | 7.54048i | 0.245813i | 0.992418 | + | 0.122906i | \(0.0392215\pi\) | ||||
−0.992418 | + | 0.122906i | \(0.960779\pi\) | |||||||
\(942\) | −5.47126 | + | 3.15883i | −0.178263 | + | 0.102920i | ||||
\(943\) | 6.66471 | − | 3.84787i | 0.217033 | − | 0.125304i | ||||
\(944\) | 1.30798i | 0.0425711i | ||||||||
\(945\) | −1.40097 | − | 2.42655i | −0.0455735 | − | 0.0789357i | ||||
\(946\) | −20.1739 | + | 34.9422i | −0.655910 | + | 1.13607i | ||||
\(947\) | 17.8922 | + | 10.3300i | 0.581417 | + | 0.335681i | 0.761696 | − | 0.647934i | \(-0.224367\pi\) |
−0.180279 | + | 0.983615i | \(0.557700\pi\) | |||||||
\(948\) | 8.33944 | 0.270852 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 20.2828 | 0.658059 | ||||||||
\(951\) | −3.80508 | − | 2.19687i | −0.123388 | − | 0.0712383i | ||||
\(952\) | 2.55496 | − | 4.42532i | 0.0828067 | − | 0.143425i | ||||
\(953\) | −15.1468 | − | 26.2349i | −0.490651 | − | 0.849833i | 0.509291 | − | 0.860595i | \(-0.329908\pi\) |
−0.999942 | + | 0.0107614i | \(0.996574\pi\) | |||||||
\(954\) | 13.4765i | 0.436318i | ||||||||
\(955\) | 34.3618 | − | 19.8388i | 1.11192 | − | 0.641968i | ||||
\(956\) | −19.1373 | + | 11.0489i | −0.618944 | + | 0.357348i | ||||
\(957\) | 16.2252i | 0.524487i | ||||||||
\(958\) | −3.29052 | − | 5.69935i | −0.106312 | − | 0.184138i | ||||
\(959\) | −5.45175 | + | 9.44270i | −0.176046 | + | 0.304921i | ||||
\(960\) | −3.50647 | − | 2.02446i | −0.113171 | − | 0.0653391i | ||||
\(961\) | 30.0536 | 0.969470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.89977 | 0.190118 | ||||||||
\(964\) | −8.77056 | − | 5.06369i | −0.282481 | − | 0.163090i | ||||
\(965\) | −28.7385 | + | 49.7766i | −0.925127 | + | 1.60237i | ||||
\(966\) | −1.76809 | − | 3.06241i | −0.0568872 | − | 0.0985316i | ||||
\(967\) | − | 20.7289i | − | 0.666595i | −0.942822 | − | 0.333298i | \(-0.891839\pi\) | ||
0.942822 | − | 0.333298i | \(-0.108161\pi\) | |||||||
\(968\) | 10.8520 | − | 6.26540i | 0.348796 | − | 0.201378i | ||||
\(969\) | −11.3838 | + | 6.57242i | −0.365699 | + | 0.211136i | ||||
\(970\) | 34.5894i | 1.11060i | ||||||||
\(971\) | 19.5547 | + | 33.8698i | 0.627541 | + | 1.08693i | 0.988044 | + | 0.154175i | \(0.0492718\pi\) |
−0.360503 | + | 0.932758i | \(0.617395\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 3.65448 | + | 2.10992i | 0.117157 | + | 0.0676408i | ||||
\(974\) | 23.2760 | 0.745813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.396125 | −0.0126796 | ||||||||
\(977\) | −6.30073 | − | 3.63773i | −0.201578 | − | 0.116381i | 0.395813 | − | 0.918331i | \(-0.370463\pi\) |
−0.597391 | + | 0.801950i | \(0.703796\pi\) | |||||||
\(978\) | −7.29590 | + | 12.6369i | −0.233297 | + | 0.404082i | ||||
\(979\) | −7.54288 | − | 13.0646i | −0.241071 | − | 0.417548i | ||||
\(980\) | 26.4034i | 0.843426i | ||||||||
\(981\) | −0.686108 | + | 0.396125i | −0.0219057 | + | 0.0126473i | ||||
\(982\) | 13.4585 | − | 7.77024i | 0.429477 | − | 0.247958i | ||||
\(983\) | − | 53.4857i | − | 1.70593i | −0.521969 | − | 0.852965i | \(-0.674802\pi\) | ||
0.521969 | − | 0.852965i | \(-0.325198\pi\) | |||||||
\(984\) | 0.753020 | + | 1.30427i | 0.0240054 | + | 0.0415786i | ||||
\(985\) | 6.09299 | − | 10.5534i | 0.194139 | − | 0.336258i | ||||
\(986\) | −21.3893 | − | 12.3491i | −0.681175 | − | 0.393276i | ||||
\(987\) | 4.98792 | 0.158767 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.5026 | −1.35150 | ||||||||
\(990\) | 17.0094 | + | 9.82036i | 0.540593 | + | 0.312111i | ||||
\(991\) | −8.02877 | + | 13.9062i | −0.255042 | + | 0.441746i | −0.964907 | − | 0.262592i | \(-0.915423\pi\) |
0.709865 | + | 0.704338i | \(0.248756\pi\) | |||||||
\(992\) | −0.486426 | − | 0.842515i | −0.0154441 | − | 0.0267499i | ||||
\(993\) | − | 25.6775i | − | 0.814852i | ||||||
\(994\) | −0.796929 | + | 0.460107i | −0.0252771 | + | 0.0145937i | ||||
\(995\) | 45.2138 | − | 26.1042i | 1.43337 | − | 0.827558i | ||||
\(996\) | 15.3274i | 0.485666i | ||||||||
\(997\) | −11.2131 | − | 19.4217i | −0.355123 | − | 0.615092i | 0.632016 | − | 0.774956i | \(-0.282228\pi\) |
−0.987139 | + | 0.159864i | \(0.948894\pi\) | |||||||
\(998\) | 4.76809 | − | 8.25857i | 0.150931 | − | 0.261420i | ||||
\(999\) | −1.11389 | − | 0.643104i | −0.0352419 | − | 0.0203469i |
(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.i.g.823.1 | 12 | ||
13.2 | odd | 12 | 1014.2.e.k.991.1 | 6 | |||
13.3 | even | 3 | inner | 1014.2.i.g.361.4 | 12 | ||
13.4 | even | 6 | 1014.2.b.g.337.3 | 6 | |||
13.5 | odd | 4 | 1014.2.e.k.529.1 | 6 | |||
13.6 | odd | 12 | 1014.2.a.o.1.1 | yes | 3 | ||
13.7 | odd | 12 | 1014.2.a.m.1.3 | ✓ | 3 | ||
13.8 | odd | 4 | 1014.2.e.m.529.3 | 6 | |||
13.9 | even | 3 | 1014.2.b.g.337.4 | 6 | |||
13.10 | even | 6 | inner | 1014.2.i.g.361.3 | 12 | ||
13.11 | odd | 12 | 1014.2.e.m.991.3 | 6 | |||
13.12 | even | 2 | inner | 1014.2.i.g.823.6 | 12 | ||
39.17 | odd | 6 | 3042.2.b.r.1351.4 | 6 | |||
39.20 | even | 12 | 3042.2.a.be.1.1 | 3 | |||
39.32 | even | 12 | 3042.2.a.bd.1.3 | 3 | |||
39.35 | odd | 6 | 3042.2.b.r.1351.3 | 6 | |||
52.7 | even | 12 | 8112.2.a.ce.1.3 | 3 | |||
52.19 | even | 12 | 8112.2.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.3 | ✓ | 3 | 13.7 | odd | 12 | ||
1014.2.a.o.1.1 | yes | 3 | 13.6 | odd | 12 | ||
1014.2.b.g.337.3 | 6 | 13.4 | even | 6 | |||
1014.2.b.g.337.4 | 6 | 13.9 | even | 3 | |||
1014.2.e.k.529.1 | 6 | 13.5 | odd | 4 | |||
1014.2.e.k.991.1 | 6 | 13.2 | odd | 12 | |||
1014.2.e.m.529.3 | 6 | 13.8 | odd | 4 | |||
1014.2.e.m.991.3 | 6 | 13.11 | odd | 12 | |||
1014.2.i.g.361.3 | 12 | 13.10 | even | 6 | inner | ||
1014.2.i.g.361.4 | 12 | 13.3 | even | 3 | inner | ||
1014.2.i.g.823.1 | 12 | 1.1 | even | 1 | trivial | ||
1014.2.i.g.823.6 | 12 | 13.12 | even | 2 | inner | ||
3042.2.a.bd.1.3 | 3 | 39.32 | even | 12 | |||
3042.2.a.be.1.1 | 3 | 39.20 | even | 12 | |||
3042.2.b.r.1351.3 | 6 | 39.35 | odd | 6 | |||
3042.2.b.r.1351.4 | 6 | 39.17 | odd | 6 | |||
8112.2.a.bz.1.1 | 3 | 52.19 | even | 12 | |||
8112.2.a.ce.1.3 | 3 | 52.7 | even | 12 |